Compendium of Meteorology

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COMPENDIUM OF METEOROLOGY

h

COMPENDIUM OF

METEOROLOGY Prepared under the Direction of the

B.

Committee on the Compendium of Meteorology H. R, BYERS H. E. LANDSBERG H. WEXLER HAURWITZ A. F. SPILHAUS H. C. WILLETT H. G. HOUGHTON, Chairman

Edited by

THOMAS

F.

MALONE

AMERICAN METEOROLOGICAL SOCIETY BOSTON, MASSACHUSETTS 1951

COPYRIGHT

BY THE AMERICAN METEOROLOGICAL SOCIETY 1951

All rights reserved. parts thereof,

may

This book, or

not be reproduced

without the permission of the publisher

and

the

sponsoring agency.

COMPOSED AND PRINTED AT THE

WAVERLY

PRESS, INC.

BALTIMORE, MD..

U.S.A.

PREFACE The purpose

of the

Compendium

of Meteorology

is

to take stock of the present position of meteorology, to

sum-

marize and appraise the knowledge which untiring research has been able to wrest from nature during past years, and to indicate the avenues of further study and research which need to be explored in order to extend the frontiers

Perhaps it is appropriate that this stocktaking should be made as we enter the second half of for surely no one can read the pages which follow without experiencmg the feeling that century, twentieth the the threshold of an exciting era of meteorological history in which significant advancements are possible on we are understanduig of the physical laws which govern the workings of the atmosphere. That this progress better toward a of our knowledge.

will not be made without some difficulty is quite apparent from the number of unsolved problems which still remain as a challenge to the research worker in spite of the centuries of study which have been devoted to the nature and behavior of the atmosphere. If this book will have clarified and defined these problems, it will have fulfilled the purpose of those who planned it. The desirability of a survey of the current state of meteorology became apparent during the years following World War II, when research effort was being greatly intensified not only in meteorology but also in other fields of pure and applied science in which the importance of meteorological factors was coming into recognition. The idea that meteorologists and atmospheric physicists from all over the world might combine their efforts to prepare a work of this nature took definite shape in 1948 when the Geophysics Research Division of the Air Force Cambridge Research Center invited the American Meteorological Society to draw up plans for a book in which specialists in

the several fields of meteorology would appraise the state of knowledge in their respective specialties. The work was decided upon by representatives of the Society and the Geophysics Research Divi-

general scope of the sion,

W

28-099 ac-399 with the Soand support and sponsorship was provided by the latter under Contract No. understood, however, that the recommendations and conclusions presented in the articles which follow

ciety. It is

do not necessarily represent those of the sponsoring agency. Capt. H. T. Orville, U.S.N. (Ret.), president of the Society from 1948 to 1950, appointed the Committee on the Compendium of Meteorology, under the chairmanship of Professor H. G. Houghton, to organize and supervise this undertaking. This committee sought and obtained suggestions from many eminent meteorologists and, in a series of meetings in the latter part of 1948, formulated the specific nature of the present work. One hundred and two authors were commissioned in 1949 to prepare the one hundred and eight articles which comprise this book. In most cases, more than one author was invited to contribute on a single broad topic. This was done intentionally, despite some slight duphcation, to uisure the presentation of specialized aspects of certain general subjects and to provide ample opportunity for the exposition of different viewpoints.

A logical

grouping of papers on related topics has resulted in a division of the book into twenty-five sections. and physics of the atmosphere are fundamental to a consideration of meteorological problems, the first part of the book is concerned with the field generally referred to as physical meteorology. Then comes a discussion of the upper atmosphere a topic in which the interests of meteorologists and physicists are now converging followed by a section which deals with extraterrestrial effects on the atmosphere and with the meteorology of other planets. The section in which is presented a general discussion of the dynamics of the atmosphere is folSince the composition

—

—

lowed by three sections which treat various aspects of the primary, secondary, and tertiary circulations, respectively. These papers provide a logical introduction to the treatment of synoptic meteorology and weather forecasting and to the discussions of the meteorology of the tropical and polar regions and the section on climatology.

Hydrometeorology, marine meteorology, biological and chemical meteorology, and atmospheric pollution are fields in which the interests of meteorologists meet those of hydrologists, oceanographers, biologists and chemists, and engineers, and these topics are treated in that order. The topics of clouds, fog, and aircraft icmg have been included in a single section because of their obvious relationship to one another. The discussions of meteorological instruments and laboratory investigations and the theory of radiometeorology and microseisms and their applica-

problems constitute the final sections. References to the literature are indicated by bracketed nimabers in the text. A fist of references is given at the end of each article. Some care has been exercised to insure complete and accurate bibhographic information. Abbreviations for the titles of periodicals have, with a few minor modifications, followed the convenient system used

tions to meteorological

A

World List of Scientific Periodicals, pubUshed by the Oxford University Press in 1934. successive entries have one or more authors in common, dashes have been used to replace the name, or

in the second edition of

When

names, given in the preceding entry. It is a pleasure to acknowledge the interest and cooperation, quite apart from the financial support, of the Geo-

vi

PREFACE

physics Research Division in this undertaking. The Division's Ubrary was kindly made available for use in the editorial work and the friendly counsel and suggestions of Division personnel have been most helpful. Sincere apis due to Professor Hans Neuberger for carefully checking and editing the papers translated from the German. Miss Eleanor Richmond and Mr. W. Lawrence Gates have labored long and faithfully in systematizing and checking the Usts of references and in assisting with the editing and proofreading. The assistance of Mr. Jean Le Corbeiller in the editorial work and proofreading is also gratefully acknowledged, as is the careful proofreading by Mrs. William Greene and Mrs. Israel Kopp. Mr. Kenneth C. Spengler, executive secretary of the American Meteorological Society, his assistant, Mrs. Holt Ashley, and their staff have capably handled all of the administrative

preciation

matters connected with this work. Preparation of the illustrations for publication has been efficiently accomplished by Mr. Chester Jancewicz. BOSTON, MASSACHUSETTS

August 1951

-

T. F.

M.

TABLE OF CONTENTS COMPOSITION OF THE ATMOSPHERE The Composition

of

3

Atmospheric Au- by E. Glueckauf

RADIATION Solar Radiant

Energy and

Long-Wave Radiation by

Its Modification

by the Earth and

Its

Atmosphere hj Sigmund

13

Fritz

34 50

~

Fritz Moller

Actinometric Measurements by Anders Angstrom

METEOROLOGICAL OPTICS General Meteorological Optics by Hans Neuberger Polarization of Skylight by Zdenek Sekera Visibility in Meteorology by W. E. Knowles Middleton

61

79 91

ATMOSPHERIC ELECTRICITY Universal Aspeette of Atmospheric Electricity by 0. H. Gish Ions in the Atmosphere by G. R. Wait and Precipitation Electricity by Ross

101

120

W. D. Parkinson

Gunn

128

The Lightning Discharge by J. H. Hagenguth Instruments and Methods for the Measurement

136 of

144

Atmospheric Electricity by H. Israel

155

Radioactivity of the Atmosphere by H. Israel

CLOUD PHYSICS 165

the Physics of Clouds and Precipitation by Henry G. Houghton Nuclei of Atmospheric Condensation by Christian Junge

On

The Physics of Ice Clouds and MLxed Clouds by F. H. Ludlam Thermodynamics of Clouds by Fritz Moller The Formation of Ice Crystals by Ukichiro Nakaya Snow and Its Relationship to Experimental Meteorology by Vincent

182 192

199

207 221

J. Schaefer

Relation of Artificial Cloud-Modification to the Production of Precipitation by Richard D. Coons and Ross

Gunn

235

THE UPPER ATMOSPHERE 245 262

General Aspects of Upper Atmospheric Physics by S. K. Milra

Photochemical Processes in the Upper Atmosphere and Resultant Composition by Sidney

Ozone

in the

Chapman

275 292

Atmosphere by F. W. Paul Gqtz

Radiative Temperature Changes in the Ozone Layer by Richard A. Craig

Temperatures and Pressures

303

Water Vapour

311

Diffusion in

in the Upper Atmosphere by Homer E. Newell, Jr Upper Air by G. M. B. Dobson and A W. Brewer the Upper Atmosphere by Heinz Lettau

in the

The Ionosphere by

320 334 341

S. L. Seaton

Night-Sky Radiations from the Upper Atmosphere by E.O. Hulburt Aurorae and Magnetic Storms by L. Harang Meteors as Probes of the Upper Atmosphere by Fred L. Whipple Sound Propagation in the Atmosphere by B. Gutenberg

•

•

•

•

347 356 366

COSMICAL METEOROLOGY Solar Energy Variations

The Atmospheres

of the

Possible Cause of Anomalous Weather Changes by Richard A. Craig and H. C. Other Planets by S. L. Hess and H. A. Panofsky

As a

Willett. ...

379 391

DYNAMICS OF THE ATMOSPHERE The Perturbation Equations in Meteorology by B. Haurwitz The Solution of NonUnear Meteorological Problems by the Method Hydrodynamic Instability by Jacques M. Van Mieghem Stability Properties of Large-Scale

Atmospheric Disturbances by R. vii

401 of Characteristics by

John C. Freeman

421

434 Fj^rtoft

454

.

TABLE OF CONTENTS

viii

The Quantitative Tlieory of Cyclone Development by E. T. Eady Dynamic Forecasting by Numerical Process by J. G. Charney

464 470 483 492 510

Energy Equations by James E. Miller Atmospheric Turbulence and Diffusion by 0. 0. Sutton Atmospheric Tides and Oscillations by Sydney Chapman Application of the Thermodynamics of Open Systems to Meteorology by Jacques M. Van Mieghem

531

THE GENERAL CIRCULATION The

Physical Basis for the General Circulation by Victor P. Starr

Observational Studies of General Circulation Patterns by Jerome

541

Namias and Philip F. Clapp

551

Apphcations of Energy Principles to the General Circulation by Victor P. Starr

568

MECHANICS OF PRESSURE SYSTEMS Extratropical Cyclones by J. Bjerknes

The Aerology

of Extratropical Disturbances by E.

Palmen

577 599 621 630

;

Anticyclones by H. Wexler

Mechanism

of Pressure

Change by James M. Austin

Large-Scale Vertical Velocity and Divergence by H. A. Panofsky

The Instabihty Line by

;

J. R. Fulks

.

.

.

639 647

LOCAL CIRCULATIONS Local Winds by Friedrich Defant

655 673 681 694

Tornadoes and Related Phenomena by Edward M. Brooks Thunderstorms by Horace R. Byers Cumulus Convection and Entrainment by James M. Austin

OBSERVATIONS AND ANALYSIS World Weather Network by Athelstan F. Spilhaus Models and Techniques of Synoptic Representation by John C. Bellamy Meteorological Analysis in the Middle Latitudes by V. J. Oliver and M. B.

705 711 Oliver

715

WEATHER FORECASTING The Forecast Problem

by

H. C.

731

Willett

Short-Range Weather Forecasting by Gordon E. Dunn A Procedure of Short-Range Weather Forecasting by Robert C. Bundgaard Objective Weather Forecasting by R. A. Allen and E. M. Vernon

747

General Aspects of Extended-Range Forecasting by Jerome Namias

Extended-Range Weather Forecasting by Franz Baur Extended-Range Forecasting by Weather Types by Robert D. Elliott Verification of Weather Forecasts by Glenn W. Brier and Roger A. Allen Application of Statistical Methods to Weather Forecasting by George P. Wadsworth

766 796 802 814

834 841

849

TROPICAL METEOROLOGY Tropical Meteorology by C. E. Palmer

859

Equatorial Meteorology by A. Grimes

881

Dunn

887 902

Tropical Cyclones by Gordon E.

Aerology of Tropical Storms by Herbert Riehl

POLAR METEOROLOGY 917 942

Antarctic Atmospheric Circulation by Arnold Court Arctic Meteorology by Herbert G. Dorsey, Jr

Some

Climatological Problems of the Arctic

952

and Sub-Arctic by F. Kenneth Hare

CLIMATOLOGY Climate—The Synthesis

Weather by C. S. Durst Applied Climatology by Helmut E. Landsberg and Woodrow C. Jacobs

967

of

Microclimatology by Rudolf Geiger

-.

976 993

TABLE OF CONTENTS Geological and Historical Aspects of Climatic

ix

Change by C. E. P. Brooks

1004

Climatic Implications of Glacier Research by Richard Foster Flint

Tree-Ring Indices of Rainfall, Temperature, and River Flow by

1019

Edmund Schulman

1024

HYDROMETEOROLOGY Hydrometeorology

in the

United States by Robert D. Fletcher River Forecasting by Ray K. Linsley Its Relation to Meteorology

—

The Hydrologic Cycle and

1033

1048

MARINE METEOROLOGY Large-Scale Aspects of Energy Transformation over the Oceans by Woodrow C. Jacobs Evaporation from the Oceans by H. U. Sverdrup Forecasting Ocean Waves by W. H. Munk and R. S. Arthur

Munk

Ocean Waves as a Meteorological Tool by W. H.

BIOLOGICAL

Some Problems

of

Human

1071

1082

1090

AND CHEMICAL METEOROLOGY

Aerobiology by Woodrow C. Jacobs Physical Aspects of

1057

1103

Bioclimatology by Konrad J. K. Buettner

1112

Atmospheric Chemistry by H. Cauer

1 1

26

ATMOSPHERIC POLLUTION Atmospheric Pollution by E. Wendell Hewson

1139

CLOUDS, FOG,

AND AIRCRAFT ICING

The Classification of Cloud Forms by Wallace E. Howell The Use of Clouds in Forecasting by Charles F. Brooks Fog by Joseph J. George

:

1161

1167 1179

Physical and Operational Aspects of Aircraft Icing by Lewis A. Rodert

1190

Meteorological Aspects of Aircraft Icing by William Lewis

1197

METEOROLOGICAL INSTRUMENTS Instruments and Techniques for Meteorological Measurements by Michael Ference, Jr Aircraft Meteorological Instruments by Alan C. Bemis

1207 1223

LABORATORY INVESTIGATIONS Experimental Analogies to Atmospheric Motions by Dave Fultz Model Techniques in Meteorological Research by Hunter Rouse

1249

Experimental Cloud Formation by Sir David Brunt

1255

1235

RADIOMETEOROLOGY Radar Storm Observation by Myron G. H. Ligda Theory and Observation of Radar Storm Detection by Raymond Wexler Meteorological Aspects of Propagation Problems by H. G. Booker Sferics by R. C.

1265 1283

1290

Wanta

1297

MICROSEISMS Observations and Theory of Microseisms by B. Gutenberg Practical Application of Microseisms to Forecasting by

Index

James B. Macelwane,

1303 S.

J

1312

1317

COMPOSITION OF THE ATMOSPHERE The Composition of Atmospheric Air

by E. Glueckauf

3

THE COMPOSITION OF ATMOSPHERIC AIR By

E.

GLUECKAUF

Atomic Energy Research Establishment, Harwell, England

For many reasons it is desirable to have a complete knowledge of the composition of the atmosphere as regards both the molecular species present and their absolute quantities. This applies not only to the main components, but also to rare species of polyatomic molecules whose importance in the radiation balance is

often quite out of proportion to their actual quantity.

Any observed

variation in the composition of air

—with

time, with geographical location, with height, with the seasons, or with meteorological conditions

—seriously

our conception of the processes in the atmosphere. It follows from this that the present article must lay its emphasis on facts in order to see where our knowledge is still inadequate. affects

SURVEYS OF VARIATIONS IN THE COMPOSITION OF THE

ATMOSPHERE Oxygen

(O2).

The

first

"international" investigation

with adequate equipment was carried out as early as 1852 by Regnault [18] (see Table I). He concluded that atmospheric air presents only small of the O2 content

variations.

Table

I.

Sukvet of Oxtgbn Content (After Regnault [18])

Location

COMPOSITION OF THE ATMOSPHERE

An oxygen deficiency in antarctic air, claimed by Lockhart and Court [c. 12], cannot yet be regarded as well established, since no check analyses with normal air were carried out. In spite of Paneth's conservative estimate [16] that the second decimal is still not exactly known, the author feels inclined, in view of the agreement of the two best surveys with a recent redetermination by M. Shepherd [c. 16] which gave 20.945 per cent, to recommend an absolute value of 20.946

±

0.002 per cent as the most

uncontaminated air, in combination with an average CO2 value of 0.033 per likely figure for the O2 content of

cent.

Apart from possible minor changes resulting from the greater solubility of O2 than of A''2 in ocean water, all major variations of the O2 content must result from the combustion of fuel, from the respiratory exchange of organisms, or from the assimilation of CO2 in plants. The first process does not result in more than local changes of the O2 content, while the latter two processes, though locally altering the CO2/O2 ratio, leave their sum unchanged. Carbon Dioxide (CO2). Though the extensive investigations of Benedict and of Krogh suggest that the CO2 content of atmospheric air over land does not vary except within very narrow limits, significant variations of the CO2 content have been observed by workers both before and after them. In particular, Callendar [5] has dra\vn attention to an increase in the CO2 content during the last fifty years which is best demonstrated in Fig. 1. This in330

carbonate ions, the quantities being roughly of the order 1:8:150. The result of this is that one litre of sea water contains about 150 times as much CO2 as the

same volume of air. For a given content

of total CO2, the equilibrium pressure varies considerably with the water temperature. To give an example: For water with a chloride content of 1.95 per cent and a total CO2 of 2.07 X 10~' mol 1~\ the CO2 pressures^ in air at equilibrium at

OC, IOC, 20c, and 30C are 1.6, 2.5, 3.6, and 5.1 X 10~* atm, respectively. Thus, far from having an equalizing effect on the CO2 content of the air, as was believed during the last century and the earlier part of this century, changes in the surface temperature of the sea upset the otherwise comparatively constant CO2 content of air. This explains the low values of the CO2 content found near the polar regions. The lowest value (1.52 X 10^* atm) was observed near Spitsbergen by Buch [c. 5]. This value corresponds roughly to the equilibrium value at OC. In the most northerly regions, particularly over polar ice, the CO2 content is again normal, a feature which was explained by Buch on the basis of Bjerknes' scheme of the air circulation over the Atlantic. According to the latter, air in the Arctic is more or less constantly descending, and since it has by-passed at great height the .cold-water regions on its way from the south, its CO2 content would be expected to be near that of the temperate zones. Buch found 2.57 and 2.91 X' 10"* atm. Equally complicated is the situation in regions where masses of water rise to the surface from greater depths. The CO2 content of sea water, after falling slightly in below the surface (due to CO2 assimilathe first 50 tion) rises to a maximum at about 500-m depth where the CO2 pressure may be as much as 11 X 10~* atm (obviously due to decay of organic matter). If these C02-rich water masses rise to the surface (as observed near the west coast of Africa), the CO2 content of air may locally rise to 7 X 10"* atm. Similarly high values have been observed by Krogh [14] in the vicinity of West Greenland, and by Moss [c. 14] at latitude 82°27'N, though in these two cases the origin of the CO2 was not traced, and the effect may possibly, but not necessarily, be spurious. These phenomena apparently do not affect the air masses to a very great depth. Near Petsamo, Finland, arctic air (range 297 to 313 ppm) differs unmistakably from continental and tropical air (range 319 to 335 ppm), so that in this region the CO2 content can serve as an indicator for the origin of the air masses. However, these differences become smaller as we go farther

m

,

o o 290 I860 Fig.

1.

—Increase

1900 of

COt

in

1925 air.

(After

Callendar

1950 [5].)

crease in the total atmosphere of about 30 ppm (parts per miUion) represents a quantity of CO2 (2 X 10 '' tons) which is approximately equal to the amount resulting from the combustion of fuels produced during this period. This implies that not much of this excess CO2 has been lost to the ocean water, an assumption which is justified in view of the fact that, apart from a thin agitated surface layer, the transport of CO2 inside the water proceeds by diffusion and is very slow. Variations of the CO2 Content over the Sea. The variations of CO2 over the sea are now well understood (Buch, Wattenberg [c. 5]). Because of an excess of strongly basic cations over strongly acid anions in sea water, CO2 is soluble in sea water not only as dissolved CO2, but also in the form of carbonate and bi-

south.

Thus the

difference

is still

appreciable at

Kew,

England, where, on the average, subtropical air contains 19 ppm more CO2 than polar and maritime air; but the mean difference is only 8 ppm near Dieppe, France, and Gembloux, Belgium

2.

The CO2 pressure

quite, identical

atm

!~ 100

[c.

5].

in atmospheres is very nearly, but not with the "parts per volume" unit, i.e., 10~^

ppm.

THE COMPOSITION OF ATMOSPHERIC AIR The contaminations

of

CO2 caused by

large

towns

are also fairly localised. At Kew, about 6 miles west of the centre of London, on the average only 27 ppm more CO2 are found in easterly than in westerly winds. Argon {A). The constancy of the composition of air

with respect to its minor constituents has been investigated in the cases of A and He. The former was investigated by Moissan [c. 16], who, after chemical removal of O2, A'^2, and CO2 by calcium metal, measured the remaining rare gases and obtained for the A content the figures shown in Table IV. The standard deviation of these analyses (excepting the value of 0.949 over the Atlantic Ocean which must be considered erroneous) is ±0.002 per cent, or 0.2 per cent of the A content, and within these limits there are no significant variations.

Table IV. Survet op Argon Contents of Air {After Location

Moissan

[c.

16])

COMPOSITION OF THE ATMOSPHERE atmospheric methane and found it to coincide with that of biological methane. The analysis also places an upper limit of about 200 years on the mean hfetime of the methane in the atmosphere and suggests an annual production of upwards of 10' tons of methane from biological sources.

Hydrogen {H^). The H^ content of air is known only approximately. Paneth [16] concludes that it is a constant constituent of atmospheric air and that its amount can be assumed to be about 5 X 10"'' by volume. Recent analyses by the author and G. P. Kitt gave varying amounts of Hi upwards of 0.4 ppm, and investigations are in progress to see whether these variations occur in the free air or are due to local contamination.

Summary. The

figures believed to

be most reliable Table V.

for the constituents of dry air are listed in

Table V. Nonvariable Components of Atmospheric Air Constituent

THE COMPOSITION OF ATMOSPHERIC AIR oceans), but no experimental data are available to check this argument. Ozone during Thunderstorms. Dobson [c. 10] has observed many cases where the total O3 increases during thunderstorms and during the passage of thunderclouds. There can be little doubt that these changes occur in the tropospheric air and are caused by electric phenomena. A continuous measurement [10] during a thunderstorm gave no indication of any abnormal increase of O3 near the ground and on this occasion, at least, the Oj-bearing air masses did not reach ground level. Other observers [13], however, found abnormally high O3 values in ground air on some thundery days. Vertical Distribution of Ozone in the Troposphere. An increase of the O3 content with height in the troposphere is shown by the data of Chalonge, Gotz, and Vassy [7], who found an average of 1.7 X 10~* at Lauterbrunnen, Switzerland (800 m), and 3.0 X 10"^ at Jungfraujoch, Switzerland (3450 m). ID

AUG

21,

1942

AUG 24,1942

7-

would be expected if the mixing ratio is kept constant by turbulence. Much less obvious is the fact that the O3 content is high in cloudy regions and reaches a maximum just below cloud level. Regener [17] explains these maxima as produced by advection, which may sometimes be the case. However, the repeated occurrence of stratified clouds near such an O3 maximum seems to indicate that under these conditions O3 may be produced by phenomena of an electrical height. This

nature.

Sulphur Dioxide (SO2). The quantities of SO2 found vary greatly according to the nearness of towns and the turbulence of the air. To give a few examples: An average of 0.033 ppm was found at the Boyce Thompson Institute (about 15 miles from New York City) at Chicago an average of from 0.06 to 0.27 ppm was found in residential districts and from 0.4 to 0.5 ppm in manufacturing districts. In the presence of O3, air may be expected to be free of Sd. Nitrogen Dioxide {NO2). No systematic determinations of this constituent seem to have been made. This is largely because of the small quantity present in air and the difficulty of analysis. A very reliable method of NO2 analysis in air, based on the use of 2:4 xylenl-ol was used by Edgar and Paneth [c. 12]. From the fact that on a large number of days the NO2 content found in this way was below the threshold of sensitivity (5 X 10~"), one is tempted to conclude that NO2 is not a normal constituent of air. This may be due essentially to its high solubility in water. In large to^^ms, however, where NO2 occurs as a by-product from the combustion of nitrogenous matter, varying quantities up to 2 X 10~* were found by a number of authors. Ammonia {NH{). The presence of minute amounts of NH3 in atmospheric air over Michigan has been claimed by Mohler, Goldberg, and McMath [c. 15, Chap. 10] from absorption bands in the 2-;u region. But, as Migeotte and Chapman [c. 15, Chap. 10] have pointed out, the 10.5-/X fundamental band of NH3 is much more suitable for testing the presence of atmospheric NHi, and no evidence could be found in this region of absorption either above Flagstaff, Arizona, or above Columbus, Ohio. Moreover, NH3 is very soluble in water and thus is not likely to be retained in the air for any lengthy period. Carbon Monoxide (CO). This gas was observed spectroscopically by Migeotte [c. 1] over Columbus, Ohio, altitude) but, as well as on the Jungfraujoch (3580 as none could be found by Adel over Flagstaff, Arizona [1], it is not yet certain whether it is a permanent constituent of the atmosphere. in air

;

m

12

OZONE

Fig- 2.

—Vertical

3 IN I0"8

4

PER VOL.

distribution of ozone in the troposphere. (After Ehmert [c. 17].)

Ozone determinations made in aircraft by Ehmert 17] show a variety of features (see Fig. 2). In one case the air above cloud level has O3 contents which, if measured in volume per volume, are independent of [c.

THE UPPER ATMOSPHERE The composition of air in the upper atmosphere is of considerable interest as an indicator of whether or not large-scale mixing of air masses takes place in the stratosphere. It is often assumed that the absence of a systematic temperature gradient in the stratosphere is incompatible with large-scale mixing. In the absence of turbulent mixing, however, diffusive separation of the gases should take place and the lighter gases should

COMPOSITION OF THE ATMOSPHERE

8

become

relatively

more abundant with increasing

height.

The most

direct

method

of finding the level

where

the chemical analysis of air samples taken at great heights, since the gravitational equilibrium should cause the O2 content to decrease by 2 per cent per kilometre and the He content to increase by 14 per cent per kilometre. Air samples from the stratosphere have been obtained by manned and unmanned balloon flights. The results of these analyses are shown in Table VII. diffusive separation begins

is

Table VII. Composition of Air in the Stratosphere Height (km)

THE COMPOSITION OF ATMOSPHERIC AIR ments. The connection of We in minerals with Li is borne out by the abnormally high ^He/*He ratio in spodumene, a lithium aluminium silicate. Carbon. Another isotope which owes its existence to the neutrons from cosmic radiation is the radioactive i^C, which is produced by ^W n '^C. As cosmic ray neutrons are produced mainly in the

+

upper atmosphere, the enters into

all

"C

^W+

starts its career as

organic matter

by the

CO2 and

process of plant

assimilation. After the death of the plant the radioactive carbon decays with a half-life of 5720 years, so

that old coal and oil deposits are no longer radioactive. The proportion of radiocarbon was found to be 0.95 X 10-1- g of "C per g i^C in living matter [3].

FUTURE DEVELOPMENTS Oxygen and Carbon Dioxide. Our best values of the O2 content or, for that matter, of the O2 and CO2 content of air date from 1912. Since then a number of improvements in the control of thermostats and in all manner

of

detailed investigation, including a study of

mode

There are, moreover, the unexplained O2 values of Lockhart and Court in the Antarctic which should be either confirmed or refuted. This applies also to the high CO2 values observed by Krogh in certain arctic regions, where the observed variations were very large, and further investigations are likely to bring to light some interesting phenomena responsible for such changes. Callendar's suggestion of a CO2 increase during this century due to industrial CO2 production requires that the CO2 content of the Northern Hemisphere should be slightly larger than that of the Southern Hemisphere, a feature which should be subject to experimen-

by modern techniques. The results of Buch and of Wattenberg make it fairly certain that there is a CO1 circulation in the oceans involving uptake of CO2 at high latitudes and its retal verification

low latitudes. Some light on the time scale of might be thrown by a '^C analysis of the CO2 released from the sea at low latitudes, which, if lease at

An explanation for this turbulence has been suggested by Brewer [4] who assumes an air circulation involving a movement of air into the stratosphere at the equator followed by slow poleward movement in the stratosphere, accompanied by a slow sinking movement in the temperate and polar regions. As this hypothesis requires the abandonment of the idea of a stratosphere which

new and

many

in radiative equilibrium,

REFERENCES 1.

Adel, a., "Concerning the Abundance of Atmospheric Carbon Monoxide." Phys. Rev., 75:1766-1767 (1949). Aldbich, L. T., and Nier, A. C, "The Occurrence of 3He in Natural Sources of Helium." Phys. Rev., 74:15901594 (1948).

3.

4.

5.

Andeeson, E. C, and others, "Natural Radiocarbon from Cosmic Radiation." Phys. Rev., 72:931-936 (1947). Brewer, A. W., "Evidence for a World Circulation Provided by the Measurements of Helium and Water Vapour Distribution in the Stratosphere." Quart. J. R. meteor. Soc, 75:351-363 (1949). Callendar, G. S., "Variations of the Amount of Carbon Dioxide in Different Air Currents." Quart. J. R. meteor.

6.

Soc, 66:395-400 (1940). Chackett, K. F., Paneth, F. A., and Wilson, E. J., "Chemical Analysis of Stratosphere Samples from 50

7.

Chalonge, D., Gotz,

Km.

to 70

8.

Height." J. atmos.

W.

ierr.

Phys., 1:49-55 (1950).

Vassy, E., "Mesures simultan^es de la teneur en ozone des basses couches de I'atmosphere a Jungfraujoch et k Lauterbrunnen." C. R. Acad. Set., Paris, 198:1442 (1934). Coon, J. H., "Isotopic Abundance of 'He." Phys. Rev., F.

P., et

75:1355-1357 (1949). 9.

the cycle exceeds 10' years, would result in a noticeable decrease of ^*C activity. 10

atmosphere, discovered only recently, still offers a few problems. Its percentage in air requires more accurate determination, and the question of its production requires further study. Hydrogen. Our knowledge of the H2 content of the air is so far inadequate. Ozone. Large gaps still exist in our knowledge of the atmospheric O3 near the ground. Its geographical distribution at ground level is quite unexplored; its dependence on weather conditions has only been touched on, and requires much more systematic investigation, particularly with reference to its vertical distribution. The increased occurrence of O3 near cloud levels and its connection with thunder clouds also require more

is

interesting problems arise which require ex-

perimental confirmation.

this cycle

Methane. The CHi

possible

formerly expected.

2.

of air.

its

under such conditions. Upper Atmosphere. It now seems certain that the upper atmosphere has essentially the same composition as that found at the ground, at least up to heights of 70 km, though further confirmation of the rocket data is desirable and will no doubt be obtained in the near future. This uniformity means that turbulent mixing in the stratosphere is considerably greater than was of generation

measuring devices have been made, which

should render possible an increased accuracy. A redetermination is particularly desirable in order to get an idea of any long-term variations of the O2 content

9

in the

Dole, M., and Slobod, R. L., "Isotopic Composition of O.xygen in Carbonate Rocks and Iron Oxide Ores." J. Amer. chem. Soc., 62:471-479 (1940). B., "The Ozone Content of Surface Air

Glueckauf,

and

Relation to Some Meteorological Conditions." Quart. J. R. meteor. Soc, 70:13-19 (1944). "A Micro-analysis of the Helium and Neon Contents of Air." Proc roy. Soc, (A) 185:98-119 (1946). Its

11.

12

— — and Paneth, F. A.,

"The Helium Content

of

Atmos-

pheric Air." Proc. roy. Soc, (A) 185:89-98 (1946). 13.

Gotz, F. W.

P.,

Schein, M., und Stoll, B., "Messungen in Zurich." Beitr. Geophys.,

des bodennahen Ozons 45:237-242 (1935). 14

Krogh, Air

A.,

in

"Abnormal Carbon Dioxide Percentage

Greenland.

.

.

."

Medd.

Grt^nland,

in the

26:407-435

(1904).

15

P., ed.. Atmospheres of the Earth and Planets. Chicago, University of Chicago Press, 1949. (See Chaps.

Kuiper, G. 8, 9, 10,

and

12.)

COMPOSITION OF THE ATMOSPHERE

10

"The Chemical Composition

Atmos-

16.

Paneth, F.

17.

phere." Quart. J. R. meteor. Soc, 63:433-438 (1937). Regenbr, E., "Ozonschieht und atmospharisohe Turbu-

18.

Regnault, M.

a.,

of the

lenz." Meteor. Z., 60:235-269 (1943). v., "Recherches sur la composition de Pair atmosph^rique." Ann. Chim. (Phys.), 3* s^r., 36:385-

405 (1852). 19.

20.

RiBSENFELD, E. H., und Chang, T. L., "Die Verteilung der schweren Wasser Isotope auf der Erde." Naturwissenschaflen, 24:616-618 (1936). J., and Kbogh, M. E., "Nitrous Oxide as a

Slobod, R.

Constituent of the Atmosphere." /. Amer. chem. Soc, 72: 1175-1177 (1950).

SuEss, H., "Isotopen Austauch Gleichgewichte" in FIAT Rev. of German Sci., 1939-1946, Vol. 30, Physical Chemistry, pp. 19-24. Off. Milit. Govt. Germany, Field Inform. Agencies, Tech. Wiesbaden, 1948. 22. Usher, F. L., and Rao, B. S., "The Determination of Ozone and Oxides of Nitrogen in the Atmosphere." /. chem. Soc, 111:799-809 (1917). 23. Vinogradow, A. P., and Teis, R. V., "Isotopic Composition of Oxygen of Different Origins." C. R. (Doklady) Acad. Sci. URSS, 33:490-493 (1941). 24. WiLDT, R., "The Geochemistry of the Atmosphere and the Constitution of the Terrestrial Planets." Rev. mod. Phys., 14:151-159 (1942).

21.

RADIATION Solar Radiant Energy

Atmosphere

and

Its

Modification by the Earth and

Sigmund

Fritz

13

Long- Wave Radiation by Fritz Moller

34

Its

by

o

Actinometric Measurements by Anders Angstrom

50

SOLAR RADIANT ENERGY AND ITS MODIFICATION BY THE EARTH

AND

ITS

By

ATMOSPHERE

SIGMUND FRITZ

U. S. Weather Bureau, Washington, D. C.

The sun is the principal source of the energy which, by devious means, becomes the internal, potential, and kinetic energy of the atmosphere. The solar irradiation

tively thin reversing layer, so called because the spectral lines ordinarily seen as dark absorption lines in the photospheric spectrum appear as bright emission lines when examined in the reversing layer; still farther from the photosphere is the chromosphere; and beyond that is the corona [4]. The sun's "surface" and its surroimding atmosphere are by no means static. The presence of short-lived photospheric grains, dark sunspots, bright areas (faculae and flocculi), and erupting prominences indicate that the entire observable sim is in a state of considerable turmoil. This turmoil is associated with variations in the quantity and spectral intensity distribution of the solar energy which subsequently irradiates the outer limits of the earth's atmosphere. Average Spectral Distribution of Sunlight. To calculate the solar energy available for meteorological processes, it is desirable to measure the amount of solar energy Jo (the so-called solar constant) which reaches the outer atmosphere of the earth. To determine the interaction between our atmosphere and the sxm's energy, the distribution of spectral intensity lox of the extraterrestrial solar energy is also required. For both of these quantities we are largely indebted to the Astrophysical Observatory of the Smithsonian Institution, whose determinations of Jo and /ox are monuments to the work of the Observatory. Until recently, the sun's energy had not been directly observed below wave lengths of about 2900 A because of the absorption of energy of shorter wave lengths by the envelope of ozone which surrounds the earth up to about 50 km. For wave lengths greater than 2900 A, selective scattering and absorption, mainly by air, dust, and water vapor, modify the solar spectrum; these troublesome modifications must be eliminated from measurements made at the ground under cloudless skies to obtain the extraterrestrial spectrum. In the region

of a unit horizontal surface at the outer limits of the

atmosphere can be evaluated, at least in relative from astronomical and trigonometrical considerations [61]; thus on a relative scale, the diurnal and seasonal variations of this solar irradiation above the atmosphere are known. On the average, variations similar to these occur also at the earth's surface, and the associated diurnal and seasonal changes in atmospheric temperature are commonplace knowledge [52]. There are, however, additional changes in effective solar irradiation of the planet Earth which are superposed on the trigonometrical variations. These are of two kinds. The first is due to the change in the quality and quantity of energy which leaves the sun. The second is caused by changes in the reflectivity of the atmosphere (including clouds) and of the earth's surface; the solar energy which is immediately reflected to space earth's

units,

cannot be meteorologically effective. In contrast to the regular, astronomically induced changes in meteorological parameters (notably diurnal and seasonal atmospheric temperature changes), the large-scale meteorological consequences of these irregular changes in solar irradiation are far from obvious, if, indeed, any such meteorological effects can be shown to be induced at all by them. For example, changes of the first kind {i.e., in solar output) have been invoked as possible causes of abnormal heating in the ozone layer with subsequent pressure changes at the earth's surface [44]; changes of the second kind {i.e., in reflection by the earth or clouds) are important, for instance, in local turbulence of the air near the ground, but are rarely used to explain widespread meteorological phenomena. These as well as other solar-induced meteor-

phenomena Compendium. In this ological

are

discussed elsewhere

article

examine the solar energy

we

itself

shall, for

and

in

this

from about 0.29

the most part,

shall

mention

its

to 2.5 m

numerous measurements and

the region above 3400 A, but its latest smnmary of data in 1923 [2]. Recently, V-2 rocket observations have ex-tended the measured spectrum down to

meteorological effects only incidentally.

was compiled

SOLAR RADIATION OUTSIDE THE EARTH'S

ATMOSPHERE The Sun. The

ix

extrapolations have been made. The Smithsonian Institution [3] is the main source of spectral information for

2200

A

[47].

and Near Infrared Radiation. Both the total amount and the spectral distribution of the radiant energy emitted by a black body are detennined by its

sun, located about 93,000,000 miles

Visible

from the earth, is a large, hot, gaseous mass. When viewed through a smoked glass it appears as a smooth circular disk which is called the -photosphere, but when examined with the aid of more refined techniques, the photospheric surface appears highly granulated and is surrounded by a gaseous envelope which is commonly divided into three layers for descriptive purposes. Of these the one just outside the photosphere is the rela-

temperature. It

is

therefore convenient to describe the

radiant energy from a source in terms of the black-body temperature which would most nearly produce the observed energy. The sun does not radiate as a black

body. Despite this fact, the average observed energy curve from about 0.45 m to about 2.0 ju closely approxi13

RADIATION

14

mates the spectral-energy distribution (Fig.

It

1).

of a black

body

therefore not unusual to speak of the

is

black-body temperatiu-e of the sun as 6000K, although this numerical value may vary by several hundred degrees depending upon the method used to calculate it [4]. For example, the total energy emitted by a black body per unit area per imit time is given by aT^, where T is its temperature in degrees absolute and o- is the Stefan-Boltzmann constant. The solar constant is commonly taken as 1.94 ly min"' (where ly = langley =

g cal cm^^), and considering the distance from the earth to the sun, we can calculate the total energy emitted by the sun. Then, by introducing the sun's

km

which no ozone could be detected and was one up to 88 km. Other measurements from rockets up to 155 km [20] show results similar to those at 55 km and indicate that the energy is less than that of a black body at 6000K. A recent curve by Gotz and Schoimiann [35], based on five observations in the region from 3300 A to 5000 A, lies far below (by a factor of 2 or more at 3400 A) Moon's curve of Fig. 1 this is also true of Hess's data [55, p. 324]. Perhaps these lower values are due to the fact that the Smithsonian observations were troubled by scattered hght at short wave lengths. If the rocket data (Fig. 2) had been joined to the data of Gotz and Schonmann, the resultant spectral curve would obin

of a series of spectra observed at levels

;

200

700 500

100

300 50 >-

>:2oo

I-

ID

z

UJ

I-

^ 20

- 100

>

(Ij

>

70

10

I-


2.5 m) then the area under the curve, e S/xAX, will be proportional to the corresponding pyrheliometric measurement I. The area loa under the curve of 7o\ versus X (for 0.34 /i < X < 2.5 ix) can now be converted to energy

and 2.5 n, but and X > 2.5 /u

energy ordinarily added for X

(since

We

jit

+

I_

S/xAX

+

t

(5)

S/oxAX loa

the pyrheliometrically measured radiation, is known in absolute units (langleys per minute). In practice the 7,

corrections

for

all

unmeasured

6000K this should amount to about 3.1 per cent. Hence if the energy beyond 2.5 n is that of a black body at 6000K or more [5, 63], it would appear that a somewhat greater amount than 3.1 per cent is the necessary at

correction.

of adjustment, errors in the estimated correction are

somewhat by the adjustment mechanism itself. This adjustment process, however, does not account for errors in eo in the spectral regions which cannot be observed at the ground. It is difficult therefore to say offset

the energy eo for X < 0.34 n and X > 2.5 /i in order to obtain 7o, the solar constant. This "long" method implies that ox is constant during the period of measurements (2-3 hr), and also that

add to

tion represents 7ox for X < 0.34 ix. In the infrared, 2 per cent is added for radiation beyond 2.5 IX during Ig determinations. For a black body

The area S7xAX is adjusted to agree with 7 by estimating the unmeasured spectral energy. In this process

units, since

It remains to

< 0.34 n is about right. have assumed here that the 55-km rocket observa-

also the energy for 0.29

spectral

regions

are

applied together.

Equation (4) requires that the atmospheric transmission ax be constant during a series of spectral measurements which are performed during a period of a few hours (from air mass 5.0 to 1.5). To the extent that ax is not constant, errors will be introduced in 7ox and hence in the solar constant. Partly for that reason, the Smithsonian Institution devised a "short" method for measuring the solar constant. In this method, a\ is determined by a measurement of the brightness of the sky in the vicinity of the sun and from an empirical relation between the brightness and the transmission coefficient a\.

The Numerical Value of the Solar Constant. Let us consider 7. The standard of pyrheliometry adopted by the Smithsonian Institution in 1913, when applied to solar-constant measurements, leads to 1.94 ly min~^ as the average value for 7o. This is the value most often used at present. The Smithsonian standard was known to be about 3.5 per cent higher than the Angstrom standard, but in 1932 and on subsequent occasions Abbot and Aldrich redetermined their standard and

found that their 1913 standard was too high by 2.3 per cent [12], thus decreasing the disagreement with the Angstrom scale. The new Smithsonian standard scale reduces the value of the average solar constant from 1.94 to 1.90 ly min-i.

Before accepting this new value we should examine the corrections applied to the solar constant for the unmeasured spectral radiation [3, Vol. 5, p. 103]. In practice a correction is made for the umneasured radiation in the interval 0.34 ;u > X > 0.27 ju, and for this spectral region about 3.4 per cent of the total measured radiation is added. Apparently no energy is added for radiation below 0.27 ix. composite curve of the 55km rocket measurement and Smithsonian surface meas-

A

urements indicates that the region from 0.34 n to 0.27 /x comprises 2.9 per cent of the area between 0.34 /i and 2.5 IX and that about 0.5 per cent of the total radiation is included between 0.22 ^ and 0.27 ^ [56]; hence the

exactly what effect the substitution of new corrections would have on 7o. As a first approximation we might assume that the ultraviolet correction is about right and that the infrared correction is too low by 1 or 2 per cent, so that the computed solar constant can tentatively be given by 1.90 < 7o < 1.94, the range making some allowance for the uncertainty of the corrections. On the basis of the Smithsonian measurements there does not seem to be much justification for a solar constant of more than 2.0 ly min~'.^

We

turn Variation of the Solar Constant. consideration of the following questions: (1) "solar

to a

Does the

Do

the

of 7o indicate the actual variation?

The

constant" vary with time? and

measurements

now

(2)

controversy regarding these questions has been raging for a long time, and a definite answer to the second question cannot yet be given. The state of the controversy is shown in a criticism by Paranjpe [67] and a reply by Abbot [1]; Waldmeir [77] has summarized some of the earlier arguments. Two main points have been at issue: (1) Do the measured values at two or more widely separated stations vary in the same way with time? and (2) Do the 7o measurements or the transmission coefficients a\ vary seasonally? If so, one would expect that the earth's atmosphere is introducing the variations and that they are not true solar changes. Abbot has pointed out on several occasions that the data from the various stations do agree for monthly means, but that daily values show appreciable departures. Paranjpe [67] states, however, that the data from the stations undergo statistical adjustment in such a way as to make the data between stations comparable. From this view, of course, interstation correspondence

would have no

significance.

Abbot

[1]

states definitely

3. Karandikar [50] assumed a value of more than 2.0 ly min~^ At the Ionospheric Physics Conference held at State College, Pennsylvania, in July, 1950, Dr. M. O'Day announced that a measurement from a rocket indicated a value of more than 2.0 ly min~i. This measurement has apparently not yet

been completely checked. See Discussion

of the

paper "Physical

Upper Atmosphere" by T. R. Burnight in "Proceedings of the Conference on Ionospheric Physics (July 1950)." Geophys. Res. Pap. Air Force Cambridge Research Characteristics of the

,

Laboratories, Cambridge, Mass. (1951) (in press).

SOLAR RADIANT ENERGY that this is not the case, but that the data are independent. It should be pointed out, however, that questions regarding the accuracy of data from all solarconstant stations except Monteziuna have been raised

from time to time by Abbot and

his colleagues, es-

pecially regarding the data prior to 1920

[8].

With regard to the seasonal variation of solar constants. Abbot has made comparisons of differences between solar-constant measurements at Southern Hemisphere and Northern Hemisphere stations on a monthly basis and finds no seasonal variation in the differences. The season being opposite in the two hemispheres, this would indicate lack of seasonal variation in 7o. Although he foimd no twelve-month period in /o variations. Abbot has found fourteen other different periods in the solar-constant variations. Paranjpe questioned the existence of these periods, but Sterne [73], while supporting Abbot's claim as to the statistical significance of some of his periods, found a strongly significant period of twelve months, suggesting a possible terres-

19

absorbed energy. This is to be compared with a poschange of ±1 per cent in the solar constant. Extraterrestrial Solar Energy on a Horizontal Surface. Of fundamental importance for meteorology is the energy Q which reaches a horizontal area at the earth's surface. For purposes of comparison and to permit certain computations of Q, Milanl'covitch [61J computed Qe, the extraterrestrial value of Q, from the sible

relation

cos

Z

dt.

(6)

is the time of sunrise, h the time of sunset, Z the sun's zenith distance, and p the radius vector of the earth. If we take 7o = 1.94 ly min~\ Qb, in langleys per day, is given in Fig. 3.

where h

MAR

APRIL

MAY

JUNE

JULY

MAR.

APRIL

MAY

JUNE

JULY

AUG

SEPT

OCT

trial effect.

We see therefore that there has been considerable controversy regarding the reality of the variations shown by the solar-constant measurements, and numerous additional arguments, pro and con, could be unearthed. But the present state of affairs can be summed up as follows: The energy emitted by the sun does change from time to time. This is indicated by the changes which can be seen in the sun's surface and by the changes revealed by the ionospheric and radio measurements. However, the percentage change in the total energy output is small, amounting at most to 1 [3], and whether the solar-constant measurements as observed from the earth's surface are sufficiently accurate to reveal the time and/or magnitude of such variations is still a debatable question. This controversy may be resolved in several ways. The surest way would be to make the measurements from a satellite stationed outside the earth's atmosphere. If rockets could be adequately equipped, frequent measurements from them would also be satisfactory. Perhaps balloons may serve for this pur-

or 2 per cent

pose. But if these methods are economically or experimentally remote, the establishment of a few additional surface stations might help. In science, important results ordinarily are not finally accepted until they have been corroborated by independent observers. Here too, if the questions raised as to the amount and time variations of the solar constant are to be answered, any additional stations should be operated by independent observers, as was long ago suggested by Marvin [58]. However, there is a more important parameter to measure than the variation of Jo; that parameter is the earth's albedo. From the meteorological viewpoint, the predominant interest is not in Jo variations as such, but in the amount of energy absorbed by the earth and its atmosphere, and in the variations of this amount. As will be shown later, the solar energy reflected by the planet Earth varies so much that the energy absorbed may vary by ±15 per cent or more from the mean

JAN,

Fig.

FEB.

3.

AUG

SEPT.

,OCT.

NOV.

DEC.

— Solar radiation on a horizontal surface outside the

earth's atmosphere (ly daj'~'). {After List

[56].)

TERRESTRIAL EFFECTS ON SOLAR RADIATION Having considered the amount and the tensity of extraterrestrial solar energy,

spectral in-

we turn now

to

the effect which the earth and its atmosphere have upon the incident radiation. In general the atmospheric elements absorb and scatter part of the incident solar energy. Absorption. At the outset it should be noted that X < 2900 A (approx-imately) is not observed at the ground; nearly all energy of X < 2900 A is absorbed and a small part is scattered back to space by the gases of the atmosphere.

The Ionosphere and Ozmiosphere. Energy

of

X


7' over the whole range, although this often occurs over strongly heated surfaces; it is sufficient that the isopycnic surfaces be inclined upwards toward the observer, so that the air density is greater there than at the distant point on the horizon [42]. The great increases in, or the reversals of, the normal vertical density gradients are generally confined to the air layers near the ground. When the light rays from the upper portion of a distant object LU in Fig. 6 (A) have a different curvature than those from the lower portion, the geometric

Fig.

6.

—Effect

of abnormal density gradients on the curvature of light rays.

Because of the increase in density with height, the rays are convex toward the ground, and the objects appear depressed. The mathematical theory for these phenomena, as well as for the corresponding ones involving

horizontal objects, was developed

by Exner

[42].

In case the density distribution in the lower layers is such that the rays from an object reach the observer along two or more different paths, so that he sees one or more images of the object, we speak of superior, inferior, or lateral mirages, depending on whether the image appears above, below, or to the side of the object. The latter case can occur only when the isopycnic surfaces are vertical or nearly so, for example, in proximity to strongly heated walls. This phenomenon was theoretically treated by Hillers [17]. In case of a complicated density distribution in the lower layers, complex distorted images of distant objects, the Fata Morgana, may appear. General theories of mirages were

developed by Nolke, A. Wegener, and others

[c.

42],

and

GENERAL METEOROLOGICAL OPTICS recently by Fujiwhara and others [c. 21]. There however, still a thermodynamic problem connected with inferior mirages such as can be observed over heated highway surfaces. There, the vigorous stirring of the air by passing vehicles apparently has little effect on the existing density distribution. It would be interesting to study the "tenacity" of the mirageproducing air layer. Ives [24] has investigated largerscale mirages of this nature and found that phenomena caused by steep lapse rates re-form, after disturbance, within a few minutes, while mirages produced by low inversions are more readily disturbed and "heal" much more slowly. Laboratory experiments, which permit control of the variables, and theoretical study of the heat transfer rate seem desirable to expand our knowledge of mirages. Scintillation. Scintillation is due to temporal and spatial variations of density in the atmosphere. It consists of one or more of the following characteristics, depending on the nature of the object viewed. If the object is a point source, scintillation causes (1) apparent

more is,

directional vibrations (unsteadiness in position of fixed

apparent intensity fluctuations (light even appear to flash on and off), or (3) color changes (white light shows alternately its individual chromatic components). For extended objects, inhomogeneities in air density will cause (1) varying objects),

source

(2)

may

distortions of the contours or of internal line-structure of distant objects,

thereby producing apparent expaneven disruption of the visible area;

67

has frequency characteristics similar to those of directional vibrations, was given by Montigny [c. 42] and is

briefly outlined (Fig. 7).

The

difference in refractive

index for the extreme visible wave lengths causes a white light ray Li, entering the atmosphere at ^4, to send its red component toward at the ground, its violet component toward an observer at 0. Another light ray L2, which is lower than Li by a distance and enters

d

D

Fig.

7.

—Dispersion

of light rays

by the atmosphere.

red beam toward 0, while Other rays between Li and L2 send the intermediate colors toward 0, so that the observer there sees the entire color mixture as white, because the angular subtense of the spectrum is generally too small to be resolved by the eye. The distance D between rays of the extreme colors varies with the angular elevation of the light source and the height above the earth's surface. Table VI represents an abstract of the corresponding table by Exner [42]. The

the atmosphere at B, sends its violet

beam

its

falls at O2.

sion, contraction, or

or (2) inhomogeneous brightness distribution, so-called shadow hands, over the surface of an object that is illuminated by a coUimated light beam.

Astronomical

scintillation

involves

extraterrestrial

light sources. Its effect, in general, decreases

crease in angular elevation of the source.

with in-

The amplitude

motion of stars (or of the edge of the amounts to a few seconds of arc at the most, with a frequency of roughly 2 to 30 sec~^, although the vibrations are seldom of truly periodic nature [7, 42, 55]. The relationship between the quality of star images in telescopes and weather elements has long been recognized [42] the image quality deteriorates as wind speed, turbulence, or temperature lapse rate in the lower atmosphere increase [2, 55]. Respighi [c. 42] ascribed a greater effectiveness to the rotation of the earth than to wind, because he observed spectroscopically that stars on the western horizon pass through the spectral color sequence from red to violet, while those on the eastern horizon show the reverse. PozdSna [43] shares this opinion, stating that of the vibratory

sun's or moon's disk)

;

the linear speed of the earth's rotation is much greater than the relative speed of the Avinds. Exner [42], however, pointed out that the observed phenomenon was due to the prevailing westerlies at higher altitudes and

suggested that the argument could be decided by means of observations in regions with prevailing easterly circulation. There, the phenomenon observed by Respighi should appear reversed if wind is the dominant factor. Such a test has apparently not yet been made. The explanation of chromatic scintillation, which

Table VT. Variation op the Distance betweei^ Violet AND Red Rats (in cm) with Zenith Distance (O) AND Height (After Exner)

— METEOROLOGICAL OPTICS

68

the ground such a parcel must have an extremely small diameter to cause scintillation.

The mechanism of intensity fluctuations was exby K. Exner [c. 42] as follows: In Fig. 8, density schlieren around S are embedded at certain intervals plained

an otherwise more or less homogeneous field and cause concavities (or convexities) in an

in

of density

originally

plane wave-front of light and, thus, divergence of the rays at A and A' and convergence at B and B'. If the system of schlieren moves horizontally, an observer say at B will perceive alternate increases in flux density where the rays converge, and decreases where they diverge. He wifl also see the light come from slightly varying directions, that is, apparent vibratory motions of the star. It is easily envisioned that the same variations occur if the schlieren system moves vertically. K. Exner measured the radius of curvature r of the wave-front deformation to be roughly between 2 and 20 km. In addition to discrete schlieren, we may also consider the wavy structure of surfaces of temperature or wind discontinuity as a cause of variations in flux

—

density discontinuities near the receiver are optically the most effective. Brocks [2] similarly found that the atmospheric conditions in the first tenth of a horizontal ray path (counting from the observer) are nineteen times as effectual in producing scintillation as the same conditions in the last tenth of the path. This seems to be the reason why various meteorological elements, observed near the receiver, correlate so well with the degree of terrestrial (and to a certain extent, astronomical) scintillation that predictions of atmospheric optical conditions are possible [4, 24, 42, 55]. Such predictions not hold where, for example, thermal turbulence is present near the light source but not near the receiver. In this case, scintillation presumably could still occur,

may

if,

at the receiver, the angular subtense of the responsible were large as compared to that of the light

air parcels

which the central portion of very surface, this portion is earth's the grazes long rays particularly exposed to density discontinuities that may not exist at the elevated end points of the rays. source. Also, in cases in

The

optical distortions

by the atmosphere

of

non-

luminescent, diffusely reflecting sources are generally

density.

hoil. Riggs and measured photographically the apparent lateral displacement of vertical linear targets and the distortion of rectangular grids at several hundred meters distance. They found angular deviations from the mean position of line elements of the order of 1" to 5". For targets separated by more than 3' to 5', there was no

referred to as shimmer, or atmospheric LIGHT

Fig.

8.

— Scintillation

resulting

{after

The short-term

RAYS

others

from density schlieren

K. Exner).

fluctuations of images received

from

terrestrial light sources or objects, or terrestrial scintillation, is of great practical importance; in particular, strong scintillation may interfere with blinker signaling. Scintillation also limits the precision of telescope pointing and the useful magnification of telescopic devices [46]. Siedentopf and Wisshak'' recently investigated the case of collimated light sources over a range 1 km long and 1 above the ground, employing an objective receiver. With strong scintillation, the frequency of apparent intensity fluctuations was most often observed

m

between 5 and 9 sec~^ with lesser scintillation between 1 and 3 sec^^ The whole range covered the frequencies between 1 and 50 sec~^ The relative variability of the and 100 per cent apparent intensity ranged between and did not materially increase with lengthening of the ray path* beyond 1 km. The mean frequency of intensity fluctuation was found to be independent of the path length. Shadow bands of from 5 to 10 cm width and several seconds duration were also observed moving horizontally with the wind across a screen several hundred meters from the searchlight. The fact that an air column of 1 km length produces almost the entire effect of scintillation shows that the 4.

R. Meyer

a concise

[36] cites

summary

their paper as unpublished

and gives

of their results.

5. According to K. Exner's results, the minimum source distance that chromatic terrestrial scintillation is observable is

about 10

km

[c.

42].

[46]

appreciable coherence of the observed deviations, that is, the horizontal dimensions of the schlieren subtended, at the camera, angles of less than 3' to 5'. Unfortunately, no exact linear dimensions of the experimental arrangement are given, so that only the minimum size of the

can be estimated (roughly 10 cm). In general, the characteristics of terrestrial scintillation appear to be very similar to those of astronomical scintillation; this fact indicates that the cause of the latter must lie predominantly in the lower layers of the atmosphere. air parcels

Nevertheless, the extent to which the upper atmosphere contributes to astronomical scintillation must still be

considered an open question, whose answer must come direct exploration of the properties of the upper

from air.

The theories of scintillation by Montigny, K. Exner, and others [c. 42] explain qualitatively the observed phenomena. However, an exact mathematical expression of the relationship between the frequency and apparent object motion, apparent intensity and chromatic effects on the one hand, and periodic time-space variations of meteorological factors on the other, remains undeveloped. There are also experimental problems as follows: The scintillatory behavior of uncollimated and difi^use light sources needs further investigation, although it is to be expected that

amplitude

of

fluctuations,

show a much

lesser degree of scintil-

J

do collimated sources. Of particular interest would be an investigation into the size, shape, spacing, and transport velocity of schlieren in relation to the size, distance, and optical characteristics of the light source for various degrees of scintillation. Such studies

'

diffuse sources will

lation than

GENERAL METEOROLOGICAL OPTICS could be made, for example, with the aid of a spatial arrangement of a field of light sources and receivers in connection with a dense micrometeorological network. For recording the apparent vibration of objects, motion picture cameras could be employed, whereas photoelectric devices seem to be preferable for measuring the apparent intensity fluctuations. The variation of scintillation with the altitude of the ray path above the ground, as well as with oblique upward and downward direction of the rays, is another problem which seems of practical interest for flight operations.

PHENOMENA DUE TO ATMOSPHERIC SUSPENSIONS In this section, the sun is considered as the source of although the moon or artificial luminants may also produce the phenomena. Hales. The term "halo," although implying ring

light,

shape, is generally applied to all optical phenomena that are produced by ice crystals suspended in the atmosphere and, occasionally, by those deposited on the ground [34, 36]. In Fig. 9, the sun is roughly 25° above the horizon HH; ring A represents the 2^ -halo (radius 22°), ring B the 46°-halo. The two parhelia CC lie to the right and left of the sun at the same elevation, but at angular distances from the sun that vary between 22° and 32°

69

On

the sky opposite the sun, the anthelion, a bright spot on the parhelic circle, is sometimes obliquely crossed by anihelic arcs. Also rings of unusual radii, 8-9°, 17-19°, 23-24°, etc., have been observed on rare occasions, as well as skewed forms such as inclined pillars and parhelic circles, and secondary phenomena caused by reflection or refraction of light emitted from primary halos.

The geometrical optics of the various halo phenomena was theoretically treated by various authors [21, 34, 42, 44, 58]. In general, most phenomena can be explained by refraction with minimum deflection and/or by reflection involving simple hexagonal ice crystals of columnar or platelet shape, with various attitudes and, in some cases, oscillating motion while falling. The principal genetic features of the major halo phenomena are summarized in Table VII, in which the optical relationship, for example, between the circumzenithal arc and the infralateral arcs of the 46°-halo, becomes evident. There are, however, many phenomena that have been explained by different patterns of ray paths, or by more complicated crystals or crystal aggregates. Thus, for example, the optical origin of the anthelion, its oblique arcs [53], Hevelius' parhelia at about 90°

between 0° and 50°, respectively. through the sun and parallel to the horizon is rarely seen as a complete ring; often only short segments of it extend outward from the parhelia. Tangent to the 22°-halo are the upper and lower tangent arcs EE and E'E', respectively, which are only one of the metamorphic forms of the circumscribed halo. This for sun's elevations

The

parhelic circle

halo

>

is

30°.

DD

truly circumscribed only for sun's elevation of

For the various forms

literature [21, 34, 42].

The

of this halo see pertinent

FF, curve concavely toward the sun from the parhelia and touch the 22°-halo below its equator. The vertex (in the sun's meridian) of the Parry-arc G has an angular distance from the sun that decreases from 43° at 0° sun's elevation to tangency with the 22°-halo for sun's elevations between 40° and 60°, and then increases again for higher sun's elevations. The circumzenithal arc J is centered around the zenith 22°-halo, or Lowitz-arcs,

and very near,

or even tangent to, the 46°-halo.

The

infralateral tangent arcs of the 46°-halo are repi'esented these arcs also are metamorphosed as their by

KK;

points of tangency

move downward and meet

at a sun's

same time their curvature (convex toward the sun) decreases and reverses itself for sun's elevations > 58°. The single arc separates from the 46°-halo when the sun is higher than 68°. The sun pillar LL lies in the sun's meridian and is, like the

elevation of 68°, while at the

parhelic circle, generally white because of

by

reflection,

its

origin

whereas the other halos are produced by

and thus more or less colored. There are also other halos, such as the circiimhori-

refraction

zontal arc that corresponds to the circumzenithal are, lies about 46° below the sun. Supralateral tangent arcs of the 46° -halo correspond to the infi'alateral arcs.

but

Fig.

9.

— Schematic

view

of

major halo phenomena.

lateral tangent arcs of the

from the sun, and other phenomena, is still uncertain; Bouguer's halo, a white ring of about 38° radius around the anthelic point, may even be a fogbow produced by very small supercooled water droplets [34, 47]. Decisive explanations will not come from additional theories, but from an accumulation of better observations. In particular, sampling of the ice crystals producing rare halos or those of lurcertain origin would be most desirable. Many halos, theoretically established, have never been observed [58] on the other hand, some phenomena, such as those observed by Arctowski [c. 42], are still ;

unexplained. Meyer [34] discusses the various geometric problems of halo phenomena, and outlines as prerequisites for a complete theory the various physical aspects, such as the concentration of ice crystals in the clouds, and the brightness and polarization of the halos relative to those of the clouds in the environment. The physical optics of halos is almost entirely unexplored in addition ;

to refraction and/or reflection by ice crystals, diffraction plays a role in the formation of halos [34, 42].

Photometric observations, that have been introduced into halo investigations by E. and D. Briiche [5], would advance our pertinent knowledge of halos and the constitution of ice clouds

[34].

METEOROLOGICAL OPTICS

70

The frequency of different halos, their diurnal and annual or seasonal variations, and their relation to weather situations, have been investigated [1, c. 34, 52]. The similarities or differences in the results can generally be ascribed to climatic characteristics. The relationship between halo occurrence and solar activity is, however, still quite problematic. Visser [52] found a decrease in halo frequency with increasing relative number of sunspots* up to 90 and then an increase for higher sunspot numbers. Archenhold [1] arrived at a direct linear relationship, and a halo periodicity of 27-28 days, which he associates with the rotation of the sun. This periodic-

Table VII.

Principal Genetic

rainbow, whose radius to the red inner border is about 51°. Inside the primary and outside the secondary bow,

suTpernumerary bows showing fewer and fainter colors When the sun's rays are reflected by a smooth water surface before striking the suspended droplets, primary and secondary reflection rainbows may appear whose center lies as much above the horizon as that of the regular bows lies below it. Thus, the reflection bows intersect the respective regular ones at the horizon. When the reflecting water surface is undulated by a smooth swell, the reflection bow may deform into vertical shafts [57]. Droplets of radii < 30 m may proare often visible.

'

GENERAL METEOROLOGICAL OPTICS the light after refraction and reflection by the droplets was computed, notably by Pernter and Mobius [c. 42]. Bucerius [6] developed an asj'mptotic method (in analogy to Debye's treatment of cylindric functions) by means of which Mie's theory of scattering of electromagnetic waves by dielectric spheres [c. 29] can be extended to large waterdrops. Applying this general theory to the rainbow phenomenon, he showed that it contains the older rainbow theories as approximations, and that the rainbow is an areal phenomenon that actually covers the entire region between the antisolar point and the first ring.

Meyer

considers the classical diffraction

[36]

adequate, particularly for the intense rainfrom comparatively large droplets. He developed this theory further to permit the determination of the luminous density of rainbows. He takes into consideration the total optical effect of all droplets contained in a surface element of the cloud deck, the thickness of the cloud, and the attenuation of the rays to and from the cloud. He finds the luminous density of the primary rainbow to be twelve times that of the secondary bow. The theoretical advancement of our knowledge of rainbows appears to have surpassed our fund of observational data. Aside from older visual measurements, there are, to my knowledge, no results of up-to-date colorimetric photometry of rainbows available for application to the theoretical findings. In this connection an almost forgotten problem may be recalled, the fluctuations of colors during lightning and thunder [42], an observation

theory

still

bows that

originate

where

the order of the minimum counting from the 0.22 for spherical, a = for nonspherical

A'' is

center, a

71

=

particles. Ramachandran [45] based his new corona theory on wave optics and included the wave-front portion that is transmitted through the droplets. In Fig. 10 the results of his calculation of intensities (X = 0.5 ju) at various diffraction angles (6) for small droplets (radii in m ascribed to the curves) are reproduced. These curves indicate that the ring systems oscillate as the small droplets increase in size. Only

relatively large droplets diffract like

opaque disks

of

the same size, which explains some of the discrepancies formerly noted between the classical theory and observations. The position of the ring systems appears

40

and explanation. Corona and Related Phenomena. The sun shining through relatively thin clouds often produces one or more sets of colored rings, the corona, having diameters of a few degrees. When poorly developed, only an aureole, a bluish -white disk with brownish rim, may be visible. After violent volcanic eruptions, a broad reddish-brown ring of large radius (20° and more), Bishop's ring, has been observed in dust clouds [11]. We speak of iridescent requiring objective verification

clouds,

when the

colors are not arranged concentrically

around the sun, but are irregularly distributed over, or follow the contours of, the cloud. This group of coronal phenomena around the sun is paralleled around the antisolar point

by a

similar group:

An

observer, seeing

shadow, the Bracken-specter, on a fog bank or cloud, often finds the shadow of his head surrounded by one or more sets of colored rings, the anticorona or glory, well-known to pilots. If the shadow falls on a bedewed surface on the ground at some distance from the observer, the shadow of his head may be rinmied by a narrow white sheen, the heiligenschein, which also can be observed around one's head-shadow on a beaded projection screen. The classical diffraction theory applied to the corona, under the assumption that the droplets are opaque, has been found to be in fair agreement \vith observations [42]. The well-known approximation formula by K. Exner [c. 42] for the angular radius d of the circulai' intensity minima produced by particles of the diameter d in light of wave length X, is

his slightly enlarged

sin e

= {N +

a)X/d,

—

Fig. 10. Intensity of diffracted light as funetion of angular distance from light source. {After Ramachandran. Ordinate scale presumably in relative units; numbers on curves are drop radii in microns.)

(6)

unaffected by the thickness and density of the clouds. Bucerius' work [6], mentioned above, also includes the application of the rigorous diffraction theory by Mie [c. 29] to both corona and anticorona. The anticorona was similarly treated by van de Hulst [20]. This theory

and polarization of the diffracted and the position of intensity maxima and minima. Table VIII gives a comparison of the values for the argument of the Bessel function at which corona maxima occur according to the old and the newer theories. It is noteworthy that in Ramachandran'3 theory the location and intensity of the maximum for small drops also depends on the value of (sin ^)/?, where 5 is a function of rf/X. For this reason the maxima oscillate as shown in Fig. 10. According to Bucerius the sine [6, equation (47)], the argument contains tmce of half the angle between primary and diffracted rays,

yields the intensity light

METEOROLOGICAL OPTICS

72

instead of the sine of the whole angle d. This is also true [6, equation (48)], the theory of which shows that it is produced by rearward diffraction, not

for the anticorona

by reflection of the primary ray with subsequent forward diffraction [Richarz, c. 42]. Bucerius' results may be summarized as follows: The intensity of the corona

= (ird/X)- times as great as that of the anticorona; the intensity at the center of the anticorona is a minimum, that of the corona a maximum. Values for the angle 6 of the successive intensity maxima of the antiis a;2

corona^ are determined by 2x sin (6/2) = 3.05, 6.7, the minima are located at relatively 10.0, 13.2, the same position as are the corona maxima (Table VIII). This explains why the application of the classical •

•

•

;

corona formula

(6)

to the

minima

of the anticorona

yielded values of the drop diameter d, that varied with

the order of the

minimum

[c.

42, 47]. Also the decrease

is much greater for the corona than for the anticorona; therefoi'e, multiple glories are more frequently observable than multiple

in intensity of successive

maxima

coronas.

The old controversy regarding the possibility of coronas and glories in ice-crystal clouds [21] now stands as Table

VIII.

Unfortunately, none of the new theories considers difby nonspherical particles, so that no final decision can be made. Iridescence of clouds is explained as diffraction patterns produced by groups of uniform droplets that vary in size in different portions of the cloud. In view of the great sensitivity of the diffraction patterns to slight differences in size of small droplets [45] (Fig. 10), it is no longer difficult to explain the occurrence of iridescence at relatively large angular distances from the sun [c. 42]. The heiligenschein is considered the result of external reflection by the dew droplets [21, 42]; to what extent diffraction plays a role in this phenomenon is not known. Experimental data or intensity measurements are completely lacking. The corona and anticorona have been widely employed in the study of cloud and fog elements. Measurements were largely confined to the angular radius of prominent rings and subsequent evaluation in terms of droplet radius. In view of recent theoretical developments [6, 20, 45] this geometric method seems unreliable; also the difficulty in visually locating diffuse rings, produced by inhomogeneous fogs or clouds, causes fraction

Comparison of Position of Corona Maxima of Various Orders According to Different Theories

GENERAL METEOROLOGICAL OPTICS For the measurements

Description. At, or shortly after, sunset, the anti-

purphsh band of some 3° or more in seen to rise above the solar counterpoint width, can be on the eastern horizon. At about 1° sun's depression, the gray-blue dark segment or earth's shadow begins to rise beneath the antitwilight arch. At approximately 2° sun's depression, the purple light appears as a purplish area above the solar point in the western sky. This area has a vertical angular extent of 10° to 50°, a lateral extent of 40° to 80°. Its upper boundary, which has an elevation of about 50° at the beginning, descends steadily to the horizon. The purple light reaches its maximum intensity at about 4° sun's depression and usually disappears at about 6° sun's depression. The rising antitwilight arch usually fades from view when the purple light is at its height, and shortly afterwards, the dark segment becomes indistinguishable from the rest of the darkening sky. Its transit through the zenith generally cannot be observed, but it reappears as the bright segment^ or twilight arch above the solar point, when the sun's depression is about 7°. The bright segment disappears below the western horizon at about 16° sun's twilight arch, a

of twilight

phenomena the

following spatial and temporal aspects are generally considered: The elevation angle of the upper boundary

dark and bright segments, and the sun's depression at the time of beginning, end, and maximum intensity of the purple light. In addition, photometric measurements of of the antitwilight arch, of

and

of purple light;

the light intensity in various spectral ranges along significant portions of the sun's meridian are of major interest.

Results of Observations. The development pattern has been found to be practically the same everywhere except at altitudes above 2000 where the pui'ple light ends at somewhat greater sun's depressions and where its upper boundary reaches of the purple light

m

greater elevations.

A

observations, such as

greatly detailed analysis of visual

made by Gruner

[14]

and Dorno

view of the fact that the sun's depressions are computed without regard to the variable refraction, that the intensity is estimated [11],

seems hardly warranted

according to a

in

memory scale, and

that the measurement boundary of the delicately affected by subjective factors

of elevation of the diffuse

tinted

depression.

73

phenomenon

is

In Europe, a maximum frequency of bright purple hghts occurs in autumn, a minimum in spring; this fact has been attributed to the corresponding frequency of anticyclones with clear skies in that area [51]. Otherwise no significant relationship between weather and purple hghts has been found. Secular variations of intense purple lights have been observed associated with dust produced by volcanic eruptions [c. 42, 50]. There exists, however, a time lag; for example, after the Katmai eruption in summer 1912, purple lights did not reach their maximum intensity until summer 1913 [11]; this delay was obviously due to the time involved in the sedimentation of dust particles necessary to produce the optimum concentration and size distribution for the formation of the purple light. For this reason, an absence of dust layers cannot be deduced from an absence of intense purple lights [50].

ZENITH

PURPLE LIGHT

SOLAR POINT

HORIZON

SLIM

—

Fig. 11. Schematic diagram of major twilight phenomena (elevation angles are a = antitwilight arch, /3 = maximum purple light intensity, 7 and 7' = upper and lower boundary of purple light, b = antisolar point, and e = dark segment).

When the sun's rays are partially obstructed by clouds or mountain peaks, the purple light may assume a ray-structure because of the interruption by the shadow bands (crepuscular rays) which seem to converge towards the sun. Similarly, the continuation of these shadow bands (anticrepuscular

may

rays) on the eastern sky

give the antitwilight arch a fanlike appearance.

Colored illustrations of the various twilight phenomena can be found in [16]. During brilliant twilight phenomena, a secondaiy purple light may become visible after the main piu'ple light has disappeared. Also a secondary antitwilight arch and dark segment may develop within the primary dark segment. These secondary phenomena are much

more

diffuse in outline

and show

fainter colors.

[50].

Although visual observations have long been recognized as inadequate, objective methods have been employed only in relatively recent times [13, 14, 32]. The techniques involved still need improvement and standardization. The results obtained at different stations from photoelectric [13] and photographic [32] intensitymeasurements with color filters show a maximum red content of the sky light between 4° and 5° sun's deprescorresponding to the visually observed maximum relative intensity of the purple light. The absolute

sion,

luminous density of the sky light decreases steadily in all spectral ranges with increasing sun's depression in contrast to the visual impression

[14].

^Vhereas the re-

from visual observations were essentially confirmed by objective methods [13], the latter have shown

sults S. The descriptive term "bright segment" is preferable because of its fundamental identity with the dark segment and the basic difference from the "antitwilight arch." The term "earth's shadow" is physicallj' incorrect [40] and does not

readily

permit differentiation between the phenomena on

either side of the zenith.

the presence of the purple light when the spectral differences in intensity were below the threshold of visual

perception

Gruner

[32].

[14]

has indicated a method for determining

METEOROLOGICAL OPTICS

74

the height of the layer responsible for the purple light. graphical approximation he arrived at values between 25 and 31 Ian for the upper boundary of the layer, and 18 km for the thickness of the generating ray beam, that is, a thickness of the layer of roughly the same magnitude. Smosarski [c. 14, 50] estimated the lower boundary at 8 km and the upper boundary at 17 km. The relationship between purple lights and high dust layers of volcanic origin seems to confirm at least the order of magnitude of these values. The possibility of a connection with the ozone layer is an un-

By

explored question. Incidentally, Gruner [14], assuming the purple light to be a corona, also determined the order of magnitude of the particle diameter as between 1 and 1.5 m- For these small particles, however, the classical diffraction theory fails [45] as was shown in the preceding section.

POINT 4

5

6

7

8

9

10

SUN'S DEPRESSION

Fig.

12.-

II

12

-

13

14 15

(")

-Average course of dark and bright segments at two Swiss stations.

Several series of geometric measurements of the elevation of the upper boundary and the width of the antitwilight arch have been made. The course of its angular elevation is similar to that of the dark segment (Fig. 12). Mendelssohn and Dember [33] made a few spectral measurements by photographic photometry, but their results confuse, rather than elucidate, the visual observation. The armual and secular variations of antitwilightarch occurrence were determined by Smosarski [SO] who found, in Poland, a maximum frequency in autumn and winter, a minimum in summer, and a good correlation with volcanic activities. A direct connection with the occurrence of purple lights does not seem to exist. According to computations by Smosarski [c. 14], as the sun's depression increases, the antitwilight arch is produced by the rearward scattering of sunlight by smaller particles at higher altitudes. However, according to Mendelssohn and Dember [33], the antitmlight arch is supposedly fixed in a layer between 4 and 9 km. This problem will be discussed below.

Of the many observations on the movement of the dark and bright segments, only the averages of two series

obtained at Piz Languard (3280

m) and

Steck-

born (430 m) in Switzerland, as reported by Gruner [14], are sho'WTi as examples in Fig. 12. As the sun sinks below the horizon, the dark segment rises more rapidly than does the antisolar point; the ascent rate increases with the sun's depression, until the segment fades from view between 5° and 6° depression. Between 7° and 8° depression the bright segment appears at an elevation of roughly 25° above the solar point and descends, first rapidly then more slowly, to the western horizon. According to the interpolated (dashed) portions of the curves, the invisible transit through the zenith occurs at a sun's depression between 6° and 7°. This agrees well with observations of the zenith brightness by Brunner [c. 14] and Hulburt [18], and of global illumi-

nation by Siedentopf and Holl [48]; these authors present curves of brightness and illumination, respectively, versus sun's depression, that show a definite inflection point between 6° and 7° sun's depressions. This fact is involved in the problem of the height at which this phenomenon occurs. In this connection the change in relative variability of the dark segment's elevation at various sun's depressions deserves attention. It has been shown [26, 40] that the variability decreases rapidly until the sun's depression is about 2.5°, then more slowly, although the opposite trend was to be expected in view of the decreased accuracy of measurement at greater sun's depressions. This fact was interpreted as being caused by a transition of the dark segment at about 2.5° sun's depression into the stratosphere, where marked changes in turbidity from day to day are less frequent [40]. The sun's depressions at which the last traces of the bright segment disappear below the' horizon have been variously used to compute the height at which the density of the atmosphere is sufficiently great to produce visible scattering of the direct sunlight. However, the resulting values of 50-65 km [14] are still quite problematic because of subjective factors involved in the perception of faint light and of the effects of attenuation of the direct light rays at various altitudes. Except for a slight increase in elevation of the dark segment in summer and with diminished transparency of the lower layers of the atmosphere, no clear-cut relationships between the turbidity of the air and the bright segment, nor a definite seasonal variation of either

segment have been established

[14,

16, 18, 26,

40].

Theories and Problems. Although many theoretical approaches to the problems of twilight phenomena have been made, no complete theory exists as yet. The theories of the dark and bright segments and of the antitwilight arch [15, 16] agree qualitatively with, but differ quantitatively from, the observations. For example, the elevations of the dark segment, computed from the spectral intensities of light scattered by a Rayleigh atmosphere (disregarding multiple scattering), were considerably smaller than the observed ones [14, 15]. The principal ideas underlying the explanations of

GENERAL METEOROLOGICAL OPTICS the segments and antitwilight arch are schematically demonstrated with the aid of Fig. 13 as follows: Ro to Rs are sun's rays passing through the atmosphere whose optically effective height may be E3D3. The lowest ray

Ro touches the earth's surface at Og. Owing to scatterand absorption on their way through the air, any rays between Ro and Ri lose part of their short-wave components and their intensity is depleted, so that Ro may not reach much beyond Oo, the next higher ray a little farther, and so on. The envelope of the end points of all these rays is represented by the curve OoDiD^Ds. ing

Consequently, the atmosphere to the right of this curve lies in the shadow of the earth. An observer Oi, for whom the sun's depression is 5i, sights the vertex of the dark segment at Di, the point of tangency of his line of sight OySi to the ray envelope. If he raises his line of sight slightly, he perceives light scattered from the still illuminated portion of the atmosphere near the envelope. This prevalently reddish hght constitutes the antitwilight arch. Its upper boundary is seen when the line of sight at Oi is further raised so that the diminishing light from the zone of red rays is compensated by the increasing light of shorter wave lengths from the higher

Fig.

13.

— Schematic diagram for the dark and bright segments.

When the sun sinks further, the relative position of the observer shifts to O2, where the line of sight 02'•''*»•V•''*''''V

"'-^v'-V-.'

'v'.v.V

*.>'>>*>'«

.

VERTICAL SCALE IN VOLTS PER METER

Fig.

3.— Electrograms, Watheroo Magnetic Observatory, "quiet" day.

time) is about five times the value registered two hours earlier. In the formei', there is a relatively small and gradual increase of gradient, beginning at about S'' local time and continuing throughout the daylight hours. The universal diurnal variation, which

8''30"' (local

will be discussed later, is, of course, present in both these cases, but allowance for that would not change the order of contrast seen here. Analyses of such records

from these two stations indicate to the author that the local aspect of the diurnal variation of potential gradi-

ent at Watheroo is largely of type (c) while that for Huancayo is chiefly of type (6). At the Kew Observatory, where the influence of local

prominent, a semidiurnal variation of gradient of local origin appears with maxima at about 8'' and 21'' local time. These apparently are a combination of types (6) and (c) with type (6) dominant in the morning and type (c) coming into evidence later in the day [22]. The latter is an interesting example of a local influence which may be explained as follows.

air pollution

is

The

introduction into the air in the general vicinity which serve as nuclei for the formation of large ions proceeds at an enhanced rate during the period 4'' to 20''. Near the surface the of the observatory of substances

cayo Magnetic Observatory, respectively. Figures 3-6 inclusive are samples selected from the thousands of such registrations made during the years 1922-46 at Watheroo and 1925-46 at Huancayo. Points for zero gradient are recorded each hour. Ordinates above this line of "zeros" correspond to positive values of gradient. During the 24-hr period of record shown in Fig. 4, three periods of rainfall were indicated by the station rain gauge. These are indicated at the top of the figure. The corresponding storm effects in potential gradient are exliibited in the lowest electrogram. Most of these were of moderate intensity on that day, and varied from positive to negative values of gradient.

During the ten-minute period beginning at 18''10'" the gradient was entirely negative and at its greatest intensity exceeded 400 v m~', the limit of registration. During the period 0'' to 0''50'", several changes from negative to positive gradient occurred. The trace of the changes these may not appear in the reproduction were rapid and the extreme values exceeded the limits

—

of registration, namely,

—400 and 700 v

m"'. But for-

tunately, in cases where the trace for potential gradient is not clearl}' shown, the sign of the gradient can usually be ascertained by an examination of the traces for con-

a

ATMOSPHERIC ELECTRICITY

no

charge -cloud does not necessarily coincide with a visible cloud. Ten such charge-clouds are indicated by the record for the latter storm. So many alternations of potential gradient in one series (barring changes which accompany lightning discharges and which are of too short duration to register with the apparatus used here) is somewhat unusual. They appear more frequently in records for the Huancayo station than in any other records available to the author. The suggestion that such a series of changes in gradient may be attributed to a number of charge-clouds drifting by in tandem array may be an oversimplification. The only model of this sort which could account for the abrupt change of sign within about one minute

ductivity, because of the electrode effect previously dis-

A

that a low value of negative conductivity and a normal value of positive conductivity should accompany a large positive potential gradient, while for a large negative gradient the roles of positive and negative conductivity cussed.

characteristic of that effect

should be interchanged. There

is

is

abundant evidence as

well as a rational basis for this rule, but such evidence is not clearly shown in Figs. 4 and 6 during periods of

greater activity because the original gradient trace was very dim when rapid changes of gradient occurred and "off scale" for considerable periods. However, the reader doubtless can see evidence of trends of this character in these figures.

was

—n^ooj

RAINFALL IN INCH

AUGUST

e,

—

19je

ISO'

0.025^

(-

\~-O.II—

0.02

—

1>-

AUGUST

-AVCO OjOS

EAST MERIDIAN HOURS

7,

1936

a

kosmVE CONDUCTIVITY

VERTICAL SCALE IN UNITS OF IQ-^ESU

ifS^pivi^'

9., .?.

.i :. .^

.

.

.9

.

.

.V

'"•^ '

VERTICAL SCALE IN UNITS

OF KT^ ESU

9,

if

i

,

i

,f

,

i

,f

,

I'r"

A**^

«^/*

L.f.i.?

POTENTIAL GftAOIENT:

>tJ*l)J\

.

-yrrrc-f]

t/ERT/CAL

Fig.

4.

SCALE IN VOLTS PER METER

—Electrograms,

2

34 DAYS

140

N0V.-DEC^-_JAN^_^,-°'^,,-i'+q+v+

+

n^q-v-).

(5)

.

PRECIPITATION ELECTRICITY Before integration of this expression is possible, the and the velocities of fall must be expressed as a function of the gravitational forces and electric field. Under most conditions, the velocity of fall may be determined from the terminal velocity of fall of a spherical body in the earth's gravitational field together with known values for the electric field and the mobility of the particle. The terminal velocity of fall, V, for droplets of various sizes has been accurately determined and may be read from tables [6]. The mobility u is defined as the velocity of the particle in unit electric field, whence one may write approxidistributions

mately

= V

y

+

UE.

relation,

n+q+V.

1

+

E a

—

ri-q-U.

[1

-e

1

n+q+V+_

+

n+q+u+

is

(7)

-47r[(T— n_Q_«_(H-(n+ff^u.|.)/(n_Q_u_))]

whence, approximating, the

maximum

t-i

equilibrium field

given nearly enough by

E

n+q+(V+ a

where

all

+

-

V-) (8)

Ti-q-U-

now expressed as positive numdra^vn to the fact that the selection

quantities are

bers. Attention

is

above is arbitrary, and that in nature a negative instead of a positive charge frequently comes of signs given

down on

enough to produce a discharge in air and thus initiate lightning. Equation (8) is therefore consistent with observation.

Using balloons, Simpson and Robinson [26] made measurements purporting to show that the electric fields inside active electrical storm clouds are "of the order of 100 volts/cm." This conclusion

rain.

In interpreting equation (7), it is noted that when the positive carriers are small and have very low terminal velocities of fall, their actual velocities closely approximate the velocities of the carriers of negative charges. Thus the difference in terminal velocities becomes small, and the electric field approaches zero. In nonprecipitating clouds, therefore, one would expect that the measured electric fields would be very small; this is in accordance with direct observation [16]. When the rain droplets become reasonably large, the electric fields increase to large values. In fact, according to equation (7), the electric field is proportional to the rainfall intensity and to the free electric charge carried by the larger droplets. Since the negative carriers are very small compared to a raindrop, one may ignore their velocity and calculate Table II from equations (1) and (8), using the best available data [13, p. 94] to show how the eciuilibrium electric field increases with the size of the raindrop. It is interesting to note in Table II that, while cloud droplets produce a negligible field, the equilibrium field for large droplets is great

is

seriously in

measurements in aircraft show that 1000 V cm"' commonly occur in such clouds

error, for actual fields of

without producing a lightning stroke [16]. The electric field on the belly of a B-25 aircraft at the beginning of an energetic lightning stroke has been measured as 3400 V cm-i [14].

Table

(6)

Thus, droplets carrying charges of one sign move faster than their normal terminal velocity, while those of opposite sign move slower. Substituting this approximation in (5), assuming that the droplets are all the same, and integrating, one finds that the electric field increases with the time t in accordance with the following

133

II.

Electric Field and Dkoplet Size Droplet radius (cm)

Fog Drizzle

Medium

rain.

.

Excessive rain

,

ATMOSPHERIC ELECTRICITY

134

all kinds of precipitation and under varying meteorological conditions, established the basic mechanisms responsible for precipitation static. By using a specially instrumented aircraft, it was found that the two most important sources of electrification of the

through

were (1) closely adjacent, highly electrified cloud centers, and (2) friction of snow and ice crystals as they slid over the wings at low temperatures. Ordinary rain or shower clouds showing little vertical convection were relatively inactive. The Research Team was able to demonstrate that the interference with communications on the aircraft resulted from St. Elmo's fire or corona discharges from the aircraft antenna or closely adjacent structures. Because of the intermittent pulselike nature of the corona discharge, adjacent radio circuits were strongly shock-excited and rendered insensitive to the ordinary aircraft

mph, generated an average current of This current transferred a negative charge to the airplane and raised its potential to more than 450, 000 V. The electrical energy dissipated, therefore, was 330 w. It was not surprising that corona discharge from the antenna was initiated causing such severe radio interference as to override urgently required communications. Precipitation static is still a serious operational hazard because the present high operating speed of aircraft has greatly increased the charging rates that were already troublesome at low speed. The modern trend toward still higher speeds will ultimately demand housed antennas for communication purposes. Such construction will greatly assist in meeting future requirements. cruising at 165

750

;ua.

^

REFERENCES

radio signals.

Normal thunderstorm

activity produces large electric fields in the atmosphere; when the plane is in the vicinity of these fields, corona currents frequently are pro-

1.

duced on the aircraft. Because an airplane traverses a typical electrically active cloud center in a relatively short interval of time, this type of disturbance (while

2.

and there-

3.

especially severe) does not persist for long

not a serious handicap to navigational radio communication. The main difficulty arises from the fact that lightning sometimes strikes the aircraft or that very intense electric fields break down the insulating wire used on antennas. The second type of electrification is self-produced by the aircraft as a result of frictional effects of snow or ice crystals as they slide over metallic parts of the aircraft. In frontal conditions this type of electrification may last for hours and, because radio navigational facilities must be constantly employed on aircraft, it is evident that such continuous electrification constitutes a dangerous operational hazard. The frictional charge produced on the airplane proper when flying in dry snow or ice crystals is always negative, while flakes leaving the plane after sliding along its surface carry a positive charge. Experimental investigations have established the fact that the rate of charge production depends on the character of the

fore

the precipitation. The charging increases with snow or ice-crystal density and with the cube of the air speed. As one might expect, the Research Team found that the charging rate was dependent upon the temperature, being relatively small surface

intercepting

near the freezing temperature and increasing as the temperature dropped to about — 15C. It is impractical to review the detailed effects that result from flying through precipitation. Interested readers are urged to read the extensive technical reports of the Precipitation-Static Project [7, 18]. As an illustration of the severity of precipitation static, it seems worth while to give some numerical results obtained off Yakutat, Alaska, in a typical upslope storm. Cloud and charging conditions were singularly uniform and serious electrification was observed

more than three hours.

A four-engine

B-17

aircraft.

Phys., 12:409-436 (1938). and Lble, S. R., "Electric Charges on Raindrops."

Nature, 130:998-999 (1932).

is

metallic

for

Baneeji, S. K., "Does Thunderstorm Rain Play Any Part in the Replenishment of the Earth's Negative Charge?" Qiiart. J. R. meteor. Soc, 64:293-299 (1938). "On the Interchange of Electricity between Solids, Liquids and Gases in Mechanical Actions." Indian J.

J. A., and Pasquill, F., "The Electric Charges on Single Raindrops and Snowflakes." Proc. phys. Soc.

4.

Chalmers,

5.

Chapman,

6.

Dinger,

Land., 50:1-15 (1938).

7.

S., "Mechanisms of Charge Production in Thunderclouds." Abstract. Phys. Rev., 68:103 (1945). J. E.,

and Gdnn, R., "Electrical Effects Associ-

ated with a Change of State of Water." Terr. Magn. atmos. Elect., 51:477-494 (1946). Edwards, R. C, and Brock, G. W., "Meteorological Aspects of Precipitation Static." /. Meteor., 2:205-213 (1945).

8.

FiNDEisEN, W., "tJber die Entstehung der Gewitterelektrizitat." Meteor. Z., 57:201-215 (1940).

9.

Gilbert, H. W., and Shaw, P. E., "Electrical Charges Arising at a Liquid-Gas Interface." Proc. phys. Soc. Land., 37:195-213 (1925).

10.

GoTT, J. P., "On the Electric Charge Collected by WaterDrops Falling through a Cloud of Electrically Charged Particles in a Vertical Electric Field." Proc. roy. Soc, (A) 151:665-684 (1935).

11.

12.

GscHWEND, Ladungen

"Beobachtungen

iiber

einzelner Regentropfen

Its Relation to

elektrischen

die

und Schneeflocken."

Jb. Radioakl., 17:62-79 (1920). R., "The Free Electrical Charge on

GuNN,

Rain and 13.

P.,

Thunderstorm

Droplet Size." J. geophys. Res.,

54:57-63 (1949). "The Electricity of Rain and Thunderstorms." Terr. Magn. atmos. Elect., 40:79-106 (1935).

"The

14.

Electrical

Charge on Precipitation at Various '

Phys. Rev., Altitudes and Its Relation to Thunderstorms 71:181-186(1947). "Free Electrical Charge on Precipitation Inside an Active Thunderstorm." J. geophys. Res., 55:171-178 .

'

15.

(1950). 16.

17.

"Electric Field Intensity Inside of Natural Clouds." J. appl. Phys., 19:481-484 (1948). and Kinzer, G. D., "The Terminal Velocity of Fall for

Water Droplets

248 (1949).

in

Stagnant Air." J. Meteor., 6:243-

.

PRECIPITATION ELECTRICITY 18.

and others, "Technical Reports on Precipitation N. Y., 34:1S6P-177P;

23.

Static." Proc. Inst. Radio Engrs.,

234-254 (1046). 19. Len.'Vrd,

P.,

9,

24.

der

Flussiglceiten."

Ann.

25.

Phijs., Lpz., 47:463-524 (1915).

20.

Nakata, U., and Tehada, T., "On the Electrical Nature of Snow Particles." /. Fac. Sci. Hokkaido Univ., 1:181 Pauthenier, M., et Moheau-Hanot, M., "Controle experimental du mouvement de petites spheres m^talliques dans un champ ^lectrique ionise." C. R. Acad. Sci., Paris, 194:544-546 (1932).

22.

Pearce, D. C, and Cxjrrie, B. W., "Some Qualitative Results on the Electrification of Snow." Canad. J. Res., 27(A) :l-8 (1949).

"Electricity on Rain." Geophys. Mem., Vol.

(1938).

"The Air-Earth Current at Kew Observatory." GeoMem., Vol. 7, No. 58 (1933).

Simpson, G. C, "Atmospheric Electricity during Disturbed Weather." Terr. Magn. atmos. Elect., 53:27-33 (1948).

26.

(1934) 21.

J.,

No. 75

phys.

"tjber Wasserfallelektrizitat und iiber die

Oberflachenbeschaffenheit

ScRASE, F.

135

and Robinson, G. D., "The Distribution of Electricity in Thunderclouds, II." Proc. roy. Soc, (A) 177: 281-329 (1941).

WiGAND,

A., "Ladungsmessungen an natiirliehen Nebel." Phys. Z., 27:803-808 (1926). 28. Wilson, C. T. R., "Some Thundercloud Problems." /. Franklin Inst., 208:1-12 (1929). 29. Workman, E. J., and Reynolds, S. E., "Electrical Phenomena Resulting from the Freezing of Dilute Aqueous Solutions." Abstract. Phys. Rev., 75:347 (1949). 27.

THE LIGHTNING DISCHARGE By

J.

H.

HAGENGUTH

General Electric Company,

The thunderstorm process and the theories relating to the formation of charges in the clouds are explained in another article.' This

paper will contain information on the lightning discharge only. The mechanism of the lightning discharge can be

divided into three regions of interest: (1) cloud-to-cloud discharges, (2) cloud-to-ground discharges, and (3) phenomena on the ground end of cloud-to-ground discharges. From the practical point of view, the greatest effort has been devoted to understanding and interpreting the phenomena associated with the lightning stroke when it contacts man-made installations [1, 2]. Qualitative data have been obtained to give confidence in the principles of protection used to guard buildings and electrical transmission systems against the effects of lightning. It becomes progressively more difficult to determine the mechanism and physics of the lightning stroke as it occurs away from the earth.

Leaders

The study of the mechanism of strokes to ground has been accomplished primarily by means of photography The

lightning stroke starts at the cloud in the stepped leader, as illustrated in the upper part of Fig. 1. The steps have an average length of 50 m. The time interval between successive steps is of the [15, 16].

form

of a

Table

I.

Characteristic Data for Leaders AND Return Strokes

Pittsfield,

Massachusetts

THE LIGHTNING DISCHARGE and due to the presence of water droplets, it is estimated that a gradient of 10,000 v cm~' may be sufficient. Tlie process is started by the acceleration of one or more free electrons in the air.

By

collision

with

air molecules,

more and more electrons as they advance in the field, the number increasing very rapidly in the form of an avalanche. Large numbers of positive ions are left behind in the field. The resulting positive these electrons liberate

space charge increases the field gradient sufficiently the attraction of photoelectrons. These in turn produce greater ionization and rapidly complete the

for

breakdown

process.

137

ten to several hundred feet. However, the evidence is insufficient to determine whether ground streamers occur on every lightning discharge. If light intensity is considered a measure of the current amplitude in the return stroke, then in the majority of the cases photographed the first in a series of multiple strokes appears to carry current of the highest amplitude. This is not always the case. Oscillographic evidence also indicates that the first current peak does not always have the highest amphtude. In many photographs taken in South Africa [9], the light intensity of the channel decreases as the

RETURN STROKE STILL CAMERA

PHOTOGRAPH OF STROKE

DOWNWARD

INITIAL

STEPPED HIGH

LEADER

SUBSEQUENT DISCHARGES WITH DOWNWARD CONTINUOUS LEADERS

SPEED BOYS CAMERA PHOTOGRAPH OF THE

SAME STROKE

CLOUD TO EARTH

BRIGHT TIPS OF

LEADER STROKE

'RETURN STROKE

SUBSEQUENT DISCHARGES WITH DOWNWARD CONTINUOUS LEADERS HIGH SPEED SOYS CAMERA PHOTOGRAPH OF THE SAME STROKE

INITIAL

UPWARD

STEPPED LEADER

CAMERA PHOTOGRAPH OF STROKE STILL

Fig

1.

CLOUD TO TALL CONDUCTING STRUCTURE

—Schematic diagram showing the mechanism of the lightning discharge from cloud to ground.

Laboratory experiments on long sparks have confirmed the stepped-leader process from negative point to plane, but not from positive point to plane. More sensitive measuring methods are needed to record the complete development of the streamers or leaders. There is considerable doubt as to the existence of the pilot streamer. The theory of the long discharge is not yet sufficiently developed, however, to provide a better answer to the formation of the lightning stroke by means of the stepped leader.

I'cturn stroke progresses toward the cloud. Points of discontinuity are observed, particularly at the junctions of the main channel and the branches. There is a question of whether current surges proceed from the branch

The Return Stroke

In those cases where charges are readily available, the current in the return stroke can be maintained up to higher altitudes at higher amphtudes than in ground

As

the leader approaches the ground, the charges

ground begin to move in the direction of the approaching leader. As the leader touches the ground, the charges in the channel and the ground charges can neutralize each other, resulting in the return stroke. Since the channel is partly ionized, further ionization can result at a more rapid rate. The current in the chanin the

nel increases rapidly

and the velocitj' of propagation upward becomes of the order of ten times that of the continuous downward leader. There is some evidence that streamers from the ground start up toward the approaching leader, thus producing contact between leader and charges in the air [11]. The length of such streamers may vary from

to ground or from the ground to the branch.

The

veloc-

most cases exceeds 10'" cm sec~', and therefore cannot be accurately measured from the photographs. Measurements in other parts of the world do not seem itj^

in

to indicate such drastic changes in intensity in the channel as the return stroke progresses toward the cloud. This difference may be due to ground conditions.

with high

Data

resistivity.

are not available on current amplitudes in the

leader strokes, the relation between ciu'rents and charges in the leader stroke, the charges available in the ground, and the wave shape and amplitude of the return stroke. The mechanism in^^olved in the wave shape of the

current in the return stroke is not too clear. It is thought by some that the front is formed shortly before the leader touches the ground and completed on contact [12]. Other theories indicate that maximum peak current is reached at the ground end after the current wave has traveled a short distance upwards in the channel.

ATMOSPHERIC ELECTRICITY

138 Stroke

Mechanism

for

High Buildings

Observations at the Empire State Building in New York [11] have shown that the starting mechanism of the stepped leader is quite different (bottom part of Fig. 1). In most cases the stroke starts as a stepped leader at the building rather than at the cloud. The length of the steps, the time interval between steps, and the velocity of propagation of the steps fall within the range of leaders from cloud to ground. Another significant difference is the absence of a return stroke after the leader has reached the cloud. Instead, a continuous flow of current of the order of magnitude of a few hundred amperes is observed. Frequently the stroke current stops without any further manifestation. In many cases, however, the initial discharge is followed by subsequent continuous downward leaders from the cloud to the building, followed by a return stroke upward from the building, as in the case of strokes reaching the ground in open country. This sequence leads to the conclusion that charges in the cloud are not sufficiently concentrated to provide a return stroke. In spite of the large drainage of charges (as much as 80 coulombs) in the preliminary continuous-current period and a rather well-ionized channel, the cloud can precipitate a continuous leader to the building. This may be due to a more rapid increase of potential gradients within the cloud or to rapid interchange of charges from other charge centers within the cloud. The reason for establishing a continuous leader in a channel, quite well ionized by the preceding continuing current, is not clear. Photographs and oscillograms show that the return stroke, coupled with a hea^ry current discharge or peak current, is governed principally by conditions in the ground.

Continuous Current Oscillographic and photographic evidence from the Empire State Building investigation seems to indicate that successive discharges are always connected by continuing current flow. Other investigators have made measurements which indicate that the current between successive discharges may drop to zero. The fact that successive lightning discharges in a stroke have the same shape is an indication that sufficient ionization

remains in the channel for subsequent leaders to choose the same path. In some cases the time interval between such successive discharges is 0.5 sec. In the laboratory it was found that on establishing a long, sixty-cycle arc, a series of multiple discharges take place within a few hundreds of microseconds. The shape of these discharges differs greatly, indicating that ionization

has ceased. The currents available in this case are of the order of a few amperes. To solve this question it is necessary to greatly enlarge our knowledge on deionization time of the air and to determine more accurately whether current flow exists during deionization.

The Chaimel

of the Lightning Stroke

The channel of the lightning stroke almost invariably follows an irregular path. This path and its branches

by the conditions in the atmosphere surrounding the tips of the stepped leaders as they progress downward. Space charges produced by the leader mechanism, and perhaps charge distributions involved in the thunderstorm process itself, may be are probably determined

largely responsible for the field distortion resulting in

the irregular pattern of the lightning channel. The diameter of the channel is apparently a function of the rate of rise of current flowing in the channel

and the

amplitude of current flow. Experiments have shown that the channel diameter experiences equilibrium when the density of the current flowing reaches 1000 amp cm~^. Much greater current densities, as high as 30,000 amp cm~-, are reached when current flowing in the channel has a rate of rise of a few thousand amperes per /isec. As the result of such measurements, the probable maximum diameter of the channel was deduced as of the order of 5 cm. Other computations and experiments indicate diameters as high as 23 em. The change in current density and consequent enlargement of the channel as a result of ionization, heating, and disassociation along the path of the lightning discharge, results in pressure effects. For continuous discharges involving only low currents, the pressure effects are so negligible that thunder cannot be heard. Such observations permit the deduction that pressure effects will be greater the higher the rate of rise of current flowing in the channel and the greater the amplitude of the current. This is confirmed by laboratory experiments where the pressure effects are associated with high surge currents, while low-current discharges produce negligible pressure. At times the path of the lightning channel is affected by wind. In such cases a stationary camera film and lens will record the multiplicity of the discharge. In some such cases the stroke path changes its shape considerably, indicating perhaps the disruption of current flow. However, it is quite possible that differences in

wind velocity

at various heights are responsible for

distortion of the pre-established channel. In other cases

the channel retains

its

precise

form to the end

of the

stroke.

The Multiple Stroke The formation of multiple strokes [6, 11] has been explained as the extension of the stroke channel to new charge centers in other portions of the cloud. Alternatively, it has been suggested that new charge centers develop toward the original channel by means of the leader process. In some strokes the regularity of the time interval between successive discharges has been suggested to be due to repeated charging of the original stroke center. Statistical data on the number of multiple discharges in a stroke are given in Table II. Potential Involved in the Stroke Formation

Based on potential gradients measured at the earth and within clouds, it now appears that a lightning discharge can be initiated and completed with average gradients of the order of 100 v cm-^ On this basis the total voltage required to initiate a stroke of 10,000-ft

— THE LIGHTNING DISCHARGE length has been estimated at twenty to thirty miUion volts. Considering the formation of the channel by means of the stepped-leader process, it is reasonable to assume that the average gradient for the lightning stroke may be considerably less than that required to break down a gap in the laboratory (30,000 v cm"',

uniform

field;

5000 v cm"', nonuniform

field

—large

gaps). It

is

known what

not

where the leader

is

139

stroke or current peak of approximately 15,000 amp in which the time to half value of the crest current

was roughly 40 ^sec. A short period of continuing current was followed by a second current peak of 4000 amp. A total of four current peaks were measured in this the third one having the highest amplitude, 23,000 amp. The total duration of the stroke was approximately 0.46 sec.

stroke,

gradients exist at the point

initiated in the cloud.

TIME IN SECONDS (INSERT SCALE - MICROSECONDS)

The lower

density of the air, and the presence of waterdrops with their associated charges, may greatly alter the gradient requirements initiating a discharge.

-2

J

0.08

Cloud-to-Cloud Discharges

While the occurrence is

relatively

discharges

of

cloud-to-cloud discharges

tr uj

-I

fe

-2

much

greater than that of cloud-to-ground estimates range between 50:1 and 0.7:1

—

the mechanism involved is not as well known because these strokes are frequently obscured by the cloud masses. However, the available photographs seem to indicate that cloud-to-cloud discharges are initiated by stepped leaders in the same manner as that of the first discharge in a cloud-to-ground stroke. Return strokes are not known to occur. Measurements of field changes associated with cloudto-cloud strokes also indicate the absence of return of the wave form of atmoshas disclosed that some types of cloud-to-cloud strokes result in wave forms similar to cloud-to-ground strokes, but of smaller 'amplitude and separated by short, quiet intervals. These probably arise from multiple discharges within the clouds. Photographic evidence indicates that discharges within clouds can take place from the tip to the bottom of the cloud, as well as in a horizontal direction within clouds. The importance of cloud strokes lies in their effects

strokes.

Vo

of

Cloud-to-Groimd Dis-

charges

;p

To

safeguard electrical installations against

damage

—

of the current in the stroke, the charges involved in the stroke, the wave shapes of currents, and other data

needed to provide reliable protective systems. Figure 2 shows a composite oscillogram of a lightning stroke current to the Empire State Building. In this case an upward leader, followed by a long period of continuing current flow, initiated the stroke and terminated at 0.25 sec. At this moment a continuous downward leader to the building resulted in a return

/

(

60

/J

20

0.26rO

«

.

sec.

40

40

X

/-0.320 +

^3„.

20

(

60

TOTAL DURATION: 0.47 SECONDS TOTAL CHARGE: - 84 COULOMBS

—

Fig 2. Replot of low-speed cathode-ray oscillogram with inserts of high-speed cathode-ray oscillograms showing current peaks, Empire State Building, New York City, 1940.

In strokes to open country, the stroke starts at the cloud rather than at the ground, and consequently a current peak would be the first measurement made. The value of continuing current between current peaks is expected to vary greatly and may even be zero. Nevertheless, this oscillogram shows all the principal components of a cloud-to-ground stroke and the relative relations between amplitudes and wave shapes of the two principal components current peaks and continuing currents as well as the multiple character of the

—

—

stroke.

From

from lightning strokes, a large number of measurements have been made to determine the characteristics of lightning strokes at the ground end. Such measurements have involved the determination of voltages on transmission lines (maximum measured 5,000,000 v), but have dealt principally with the statistical evaluation

40

">0

The measurement

Phenomena on Ground End

20

0.320^ -B-

pherics, however,

on radio reception and on the safety of airplanes. It has been suggested that airplanes may trigger off cloudto-cloud discharges, and evidence is accumulating that the susceptibility of planes to lightning strokes increases as the size and speed of the planes become greater.

u sec.

I

the available measurements,

it

has been pos-

to derive statistical data which are

sible

Table

II.

These

statistics in all cases give the

shown

in

minimum

and maximum curves obtained from published data for 90, 50, and 10 per cent of the strokes, as well as the

maximum

some

available values.

of the data

is

The

great spread in

due to the various methods

of

observations used.

Stroke Current

Item 1 of Table II shows the amplitudes of current peaks measured in the path of the lightning stroke, with an average peak current of 7000 amp. A much greater number of records, which show a surprising agreement, have been obtained on transmission line towers (Item 2). Fifty per cent of the lower currents are in excess of 10,000 amp, while the maximum meas-

ATMOSPHERIC ELECTRICITY

140

ured was 130,000 amp. By making various assumptions, the lightning stroke currents responsible for tower cur-

shown in Item 3. some of these assumptions is quesand the values shown in the table are probably

rents measured were deduced as

The

correctness of

tionable,

Table

II.

Characteristics of

THE LIGHTNING DISCHARGE not kno^vn, it cannot be determined whether were conducted to ground or to what extent they occvu-red within the cloud only.

nism all

is

of the charges

Forms

of Lightning

Names

The

polarity of lightning strokes, in the great

ma-

is negative; that is, negative charges are lowered from the cloud. The relation for grounded structures is approximately 15:1 in favor of negative charges. Since most measurements have been made on transmission line towers and other rather well-grounded structures, it has been pointed out that this would be conducive to a higher number of negative strokes on account of the possibility of guiding a negative leader to the structure by means of streamers produced at the positive grounded object. In the case

jority of cases measured,

streamer would not be as it is expected that strokes to open ground may include a lower percentage with negative polarity. Measurements of field changes seem to favor this view because in many of these cases the ratio of negative to positive polarity cloud-toground strokes is of the order of 6: 1 or less. In cases where direct strokes to grovmd have been measured by means of oscillographs or other devices which permit detailed examination of the stroke current throughout its duration, it was found that the majority of the strokes were entirely of negative polarity. In some cases, however, the polarity of the continuing current flow changed, usually toward the end of the stroke. In other cases one of the current peaks was of positive polarity, while the remaining current peaks resulted from a negative cloud charge. The polarity relations throughout the length of the stroke are probably governed by the mechanism of of a positive stroke, a negative

likely to occur.

From

this reasoning

multiple discharges which was discussed previously. The process must be governed by the means of charge exchange within the cloud during and following the leader stroke to ground, as well as by the rate of production of charges within the original stroke center in the cloud. The fact that charges of negative polarity are lowered to the ground in the majority of the cases seems to indicate that negative charges predominate in the bot-

first

tom

of the cloud.

The

fact that

some

and have been used to describe various ob-

like streak, bead, ribbon, fork, heat, sheet,

ball lightning

Polarity

141

served forms of lightning discharges. Streak lightning is the normally observed type as described in the foregoing discussion. Bead, ribbon, fork, and heat lightning probably have the same characteristics as streak lightning. Bead lightning is assumed to be a form of streak lightning. The appearance of the beads may be caused by variations in the luminosity along the channel,

perhaps caused by brush discharges. Ribbon lightning is probably a streak lightning stroke with multiple discharges where the channel is blown along by the wind. Fork lightning is the term used for strokes with several apparently simultaneous paths to ground. As explained, these ground termini may be formed simultaneously or during successive discharges of multiple strokes. Heat lightning is a form of streak lightning at a distance sufficiently far away so that thunder is not heard. Sheet lightning usually occurs in clouds between the lower and upper atmosphere over a considerable area. This areal distribution of sheet lightning,

and

its long persistence, constitute the principal difference between it and streak lightning. Ball lightning is described as a luminous ball of reddish color, with an average diameter of 20 cm. When seen emerging from the cloud, its velocity has been sec"'; while on the ground estimated as high as 100 Usually the ball explodes sec~'. at 1 to 2 it travels

m

m

an average life of 3 to 5 sec. There is much controversy regarding this form of lightning. It has been described as an optical illusion caused by retention of vision of a heavy lightning discharge in the retina of the eye. However, the testimony of a few apparently well-qualified observers seems to indicate that such phenomena may exist. No reliable explanation for the after

existence of ball lightning has been offered. However, several theories exist explaining the phenomenon on the

and physical reactions. Some photographic evidence submitted as possibly caused by ball lightning has been proved to have had an erroneous

basis of chemical

interpretation.

Measurements

of Lightning Characteristics

of the highest

current peaks measured were of positive polarity might be accepted as proof that centers of positive polarity can exist in the lower portions of some storm clouds.

Stroke Density It is extremely difficult to obtain information on stroke density. Analysis has shown that the density per square mile is approximately one-half of the number of storm days from the isokeraunic map. This was

by a two-year count in a region with 27 storm days per year where the average stroke density was approximately 15 strokes per square mile

partially confirmed

per year. Observed figures depend on the size of the area under observation and rapidly decrease with increased area. Accurate data would be of value to determine lightning risks.

The most exact measurements can be made at the ground end of a stroke. For this purpose a variety of instruments have been developed. The Lichtenberg figure on photographic film [7, 13] placed between two electrodes is a corona discharge. The size of the figure is a measure of the voltage applied and the polarity of the discharge. By suitable shunts, currents can be measured. The accuracy of such de\nces has been estimated at 25 to 50 per cent. A very simple method of measuring the peak value and polarity of surge or lightning currents is the mag[4]. It consists of a number of steel strips of high retentivity. The magnetic flux associated with a lightning stroke magnetizes the link. The magnetization measured after exposure gives a very accurate indication of current crest. Two links at different spacing from

netic link

ATMOSPHERIC ELECTRICITY

142

the conductor carrying the lightning surge are used to increase the accuracy, particularly where currents of

may flow. These links will measure maximum peak in a multiple stroke.

opposite polarity

only the

Fulchronographs

[17],

devices where a niunber of

mounted on a

rotating wheel, permit determination of the variation of current with time. The resolution for continuing currents is good. The highlinks are

speed wheels used permit separation of amplitudes of successive high current peaks, but the speed is insufficient to determine the wave shapes of current peaks.

Magnetic links applied in circuits in which inductances or capacitances are used in combination with resistance permit determination of the maximum rate of current change of a current peak. The photographic surge-current recorder [10] measures the intensity of light produced by a surge current across a short spark gap. A range of 0.1 amp to 150,000 amp is claimed for this device. The cathode-ray oscillograph [3] is the most versatile, but also the most elaborate device for measuring surges. Several types of oscillograph must be used to record the high-speed (current peaks) and slow-speed (continuing currents) components of a complete lightning stroke. The development of the sealed-in cathode-ray tube has made this instrument simpler and subject to automatic operation. Of considerable value for determining the mechanism of the discharge are the so-called Boys cameras [5, 15].

With high-speed lenses,

the amplitude of current peaks and the charge conducted in the stroke. Damage produced on metal parts of airplanes is in many respects the only means by which lightning currents occurring in the clouds can be determined.

rotating film, or high-speed rotating

the speed of propagation of the leaders and

return strokes can be analyzed. The low-speed cameras give valuable information on the time sequence of current peaks and the continuing-current flow between multiple discharges. It has been possible to obtain fairly good correlation between density of the film exposed to a stroke and the current flow causing the illumination, principalljr for the continuing components. microphotometer has been used to correlate these quantities. For accuracy it is necessary to avoid overexposure of the film, as well as to have highest sensitivity for the weaker illumination. For this purpose multiple-lens cameras are used with apertures varied to cover the complete range of exposure expected in a straight-line

A

relation.

measurements permit investigation of phenomena from the point of view of the charges involved. Some of the measurements made differentiate the leader, the return stroke, and the Electric field

lightning-stroke

continuing-discharge portions of strokes. The wave shapes of atmospherics and correlation with various

forms of lightning discharges have been investigated. Such measurements have been extended to cover distances of hundreds of miles. By using two or more instruments, the distance of the source of atmospherics can be determined with good accuracy. A rather useful means of determining lightning characteristics is the examination of damage produced by lightning. By reproducing similar effects in the laboratory it is possible to determine approximately the type of stroke responsible for the damage, as well as

Lightning Protection

The

statistical

knowledge gained over the past

fifteen

to twenty years has largely confirmed the effectiveness of a properly installed lightning-rod

system (advocated

by Benjamin Franklin more than 150 years ago) to protect ordinary buildings and houses against direct strokes. Such systems consist of interconnected air terminals mounted on the highest points of the structure, and connected to the ground at several points. The "Code for Protection Against Lightning" issued by the National Bureau of Standards and designated as Handbook Hlfl, and the British Code of Practice C. P. 1:1943 published by the British Standard Institution, contain the essential rules to follow for installation, and other factors essential for an effective durable installation. For continuity of electrical service to homes, farms, and factories, many practices have evolved, based directly on the many lightning studies and their results. For protection of electrical apparatus, the lightning arrester is a commonly accepted device. Such arresters have the property of conducting surge currents to ground at a reduced voltage. Any system power current (follow current) which may flow through the arrester immediately following the lightning discharge is interrupted, and the line is restored to its original condition. Many different types of arresters are in use. In some cases plain gaps are used for protection. These cannot limit the voltage applied to the apparatus to voltages as low as arresters. After sparkover of the gap occurs, circuit power current usually follows and must be interrupted by opening a breaker. Transmission lines of higher voltage ratings can be effectively protected by the use of ground wires properly suspended above the transmission wires to intercept the direct strokes. The lightning currents contacting the ground wire and the towers to which they are connected will raise the tower potential by virtue of the resistance of the tower to ground and the current in the stroke. To this is added the inductive voltage drop caused by the inductance of wire and tower and the rate of rise of current on the current front. By reducing the ground resistance to less than one ohm materials, size,

per 12 kv of circuit voltage, it has been possible to reduce outages on circuits of 66 kv and above to an extremely low value. Ground resistance can be reduced by the use of buried wires counterpoise or deeply driven ground rods. Lower voltage circuits have been made lightningresistant in many cases by the use of wood as insulation in addition to the normal porcelain or glass insulators. Reclosing circuit breakers are another tool for preventing circuit outages. These breakers are able to open a circuit and reclose it in as little as one-fifth of a second

—

by means

of suitable relaying.

—

Proper balance between

J

\

THE LIGHTNING DISCHARGE circuit

the

breaker duty and protective means for reducing of flashovers must be considered.

1.

number

2.

Conclusions 3.

The

physical

phenomena

of the lightning discharge

are not entirely understood. Photographic evidence in-

4.

dicates a stepped-leader initiation of the stroke fol-

lowed by a return stroke from its ground terminal. Tlieoretical stipulation of a pilot streamer has not been proven. To complete the understanding of the physical phenomena involved in lightning discharges, more information is required on these principal questions: 1. The gradient at the point of origin of the stroke. 2. Gradient distribution within clouds, as well as

beneath clouds. 3. Gradients at the ground end of a stroke. 4. Existence and character of ground streamers prior to stroke contact with the ground. 5. Ionization processes within the stepped leader, continuous leader, and the return stroke. 6. Ionization and deionization of the stroke channel with special reference to continuing current discharges. 7. Influence of ground conditions on the return-stroke

5.

6.

7.

8.

evidence

is

statis-

10.

The wave shape

of lightning stroke currents of

The

12.

13.

14.

15.

16.

17.

incidence of lightning to various structures as

determined by height and physical location with regard to other structures and natural terrain.

From the numerous taken during the

investigations of lightning under-

it has been systems and practices which reduce damage due to lightning to a negligible factor on electrical installations as well as on buildings.

possible

459^74 (1940). and Collens, H., "Progressive Lightning, III." Proc. ray. Soc, (A) 162: 175-203 (1937). McCann, G. D., "The Measurement of Lightning Currents in Direct Strokes." Trans. Amer. Inst, elect. Engrs., 63:

Malan, D.

J.,

McEacheon, K.

B., "Lightning to the

Empire State Build-

and McMorris, W. A., "The Lightning Stroke: Mechanism of Discharge." Gen. elect. Rev., 39: 487-496

last twenty-five years,

to devise protective

J. F.,

"The Klydonograph."

Elect. World,

N.

Y

.,

ScHONLAND, B. F. J., "Progressive Lightning, IV." Proc. roy. Soc, (A) 164: 132-150 (1938). and Collens, H., "Progressive Lightning." Proc. roy. Soc, (A) 143: 654-674 (1934). ScHONLAND, B. F. J., Malan, D. J., and Collens, H., "Progressive Lightning, II." Proc. roy. Soc, (A) 162: 595-625 (1935). C. F., and

McCann, G. D., "New Instruments Recording Lightning Currents." Trans. Amer. Inst,

Wagner, for

elect.

Engrs., 59: 1061-1068 (1940).

Further articles containing comprehensive references are: 18. Bruce, C. E. R., and Golde, R. H., "The Lightning Discharge." /. Instn. elect. Engrs., 88: 487-505 (1941). 19. McEachron, K. B., "Lightning and Lightning Protection" in Encyclopaedia Britannica, Vol. 14. Chicago, 1948. (See pp. 114-116) 20.

and Hagenguth, J. H., "Lightning and the Protection and Structures from Lightning" in Standard Handbook for Electrical Engineers, A. E. Knowlton, ed. New York, McGraw, 8th ed., 1949. (See pp. 2230-2254) Meek, J. M., and Perry, F. R., "The Lightning Disof Lines

REFERENCES The sources of information are extensive. References to 750 papers are found in [1] and [2] below. To keep the number of references at a reasonable figure, only a few additional references are listed.

Peters,

83: 769-773 (1924).

lightning stroke density in various regions of

the earth.

The

J. W., "The Direct Measurement of Lightning Current." /. Franklin Inst., 232: 425-450 (1941). FousT, C. M., and Kubhni, H. P., "The Surge-Crest Ammeter." Gen. elect. Rev., 35: 644-648 (1932). Hagenguth, J. H., "Lightning Recording Instruments." Gen. elect. Rev., 43: 195-201, 248-255 (1940). Larsen, a., "Photographing Lightning with a Moving Camera." Rep. Smithson. Insin., pp. 119-127 (1905). Lee, E. S., and Foust, C. M., "The Measurement of Surge Voltages on Transmission Lines Due to Lightning." Trans. Amer. Inst, elect. Engrs., 46: .339-356 (1927). LoEB, L. B., and Meek, J. M., "The Mechanism of Spark Discharge in Air at Atmospheric Pressure." /. appl.

'ing." /. Franklin Inst., 227: 149-217 (1939).

earth.

4.

Flowers,

1157-1164 (1944). 11.

desirable on:

both current peaks and continuing currents. 2. The distribution of such currents in the ground network of protective installations, as well as in the 3.

,

(1936).

For further progress on the protection problem, 1.

A.I.E.E. Lightning Reference Book, 1918-1935. New York, American Institute of Electrical Engineers, 1937. A.I.E.E. Lightning Reference Bihliographij 1936-1949. New York, American Institute of Electi-ical Engineers, 1950.

Phys., 11: 438^47,

9.

process.

tical

143

21.

charge" in Reports on Progress in Physics, 10: 314-357. Phys. Soc, London, 1944-45.

INSTRUMENTS AND METHODS FOR THE MEASUREMENT OF ATMOSPHERIC ELECTRICITY* By H. ISRAEL Institute for

System

Atmospheric Electric Research of Buchau

of Units

Various systems of units are used in

electricity.

Each

an entity in itself and is built up on a definite fundamental physical relationship: 1. The "electrostatic cgs system" is based on Coulomb's law of the force effects of interacting electrical charges and arbitrarily takes the proportionality factor to be nondiniensional and equal to unity. 2. The "electromagnetic cgs system" is based on the Biot-Savart law of the forces between an electric current and a magnetic pole, and again the proportionality of these is

factor

is

set equal to unity.

"natural m-sec-v-amp system" assumes voltage and amperage as fundamental quantities, with the second (sec) as the time unit and the meter (m) as the length unit. In the first two systems the electrical quantities are reduced to the mechanical units, cm, g, and sec (cgs), which appear in complicated, nonvisualizable com3. Giorgi's

binations. The third system of units is more suitable to the scope of physics in general; therefore, its adoption for consistent use in the field of atmospheric electricity is

recommended. In

this system, the interna-

tional standards for volt, ampere, etc., are employed.

Auxiliary Equipment and Practical Suggestions

The atmospheric

electrical

consist predominantly of the

of potential

medium magnitude and of minute eleccharges. They belong, therefore, to the do-

differences of trostatic

main

of electrometry proper. Although increasing use being made of "vacuum tube electrometers" (d-c current amplifiers or d-c voltage amplifiers), thorough familiarity with the electrometer is a prerequisite for work in atmospheric electricity. All electrometers are based on the principle of electrostatic attraction or repulsion. An exception is the capillary electrometer which utilizes the change in the sui'face tension of mercury when traversed by an electric current. Therefore, strictly speaking, the capillary electrometer represents a type of galvanometer [103]. Quadrant electrometers have long oscillation periods and are therefore suited chiefly for the measurement of constant potential differences, whereas filament electrometers adjust themselves aperiodically and almost instantaneously at sensitivities that are not excessively high. The highest sensitivities are attained with the modern modifications of the quadrant electrometer. Figure 1 shows schematically the well-known principle of the quadrant electrometer. Special electrometer types are: the model developed by Elster and Geitel is

*

F.

[37], particularly suited to photographic recording; the Dolezalek electrometer [30, 31] for high sensitivities; a special design by Schultze [119]; the "Binanten" electrometer [49] and the "Duanten" electrometer of Hoffmann [48, 50, 51]; the Benndorf electrometer [11, 12], the familiar, low sensitivity quadrant electrometer for mechanical recording of potential gradients. Figures 2 and 3 are sectional drawings of the bifilar electrometer without auxiliary potential and of the unifilar electrometer with auxiliary potential according to Wulf's design [152]. More modern designs for attaining the highest sensitivites include those of Lindemann and Keeley [85], Compton [26, 27], Shimizu [127], Swann [139] and Perucca [104, 105]. The development of the so-called electrometer tubes with their characteristically high insulation of the control grid and very low grid current (10~^^ amp and less) has resulted in the substitution of vacuum-tube electrometers for the ordinary electrometers. Many types of electrometer tubes are now commercially available. During continuous operation, maintenance of a constant zero point is sometimes difficult; some amelioration can be provided by using oversized filament batteries and by the use of selected pairs of tubes in a bridge circuit (for further details see, for example, [22, 28, 36,

46, 47, 69, 77, 82, 106, 109, 114]).

problems of measurement

measurement

a.

Translated from the original German. 144

There are several types of circuits available for use with quadrant and filament electrometers provided with auxiliary potentials: In the idiostatic circuit the needle (lemniscate or electrometer filament) and one pair of quadrants (knife edge) are grounded; the unknown voltage is applied to the other pair of quadrants (knife edge). The deflection is proportional to the square of the unkno^^'n voltage, thus making possible a-c measurement. In the quadrant circuit the needle is at a fixed high voltage; one pair of quadrants is grounded, and the is

unknown

voltage applied to the other. Deflection

proportional to the

unknown

voltage.

The

hetero-

has both pairs of quadrants connected to a fixed auxiliary voltage of opposite sign and the unknown voltage applied to the needle. This is the static or needle circuit

most frequently used and most

sensitive circuit,

has the lowest capacitance. In the current

circuit

and the

voltage measurement is made at the terminals of a resistor which is usually of the high-ohmic type. Measurements of atmospheric electricity are almost exclusively electrostatic

measurements and therefore

high quality of the dielectric materials. The best insulating materials are the natural products, amber and sulfur. Good substitutes include high quality plastic dielectric materials such as hard rubber (ebonite), plexiglass, and Trolitul. Meticulous surface treatcall for

MEASUREMENT OF ATMOSPHERIC ELECTRICITY ment

is

particularly important.

Such treatment includes

high polish, drying, dust removal, paraffin coating in some cases, and protection against direct sunlight.

working in the open air, careful maintenance of the dryness of the dielectric surfaces by drying with hot air or by electrical heating is essential. The relative humidity on the insulator must not exceed approxi-

When

Fig.

1.

—Schematic

diagram

of a

145

maintain good grounding of all parts to be maintained at zero potential. In general, grounding to a water pipe is satisfactory. It is particularly important that all parts to be grounded are connected to the same ground

quadrant electrometer.

Fig.

3.

— Wulf's unifilar electrometer.

ff

M

,>y< P2o

P2c

V^

P5o

CPIo

CP3

3900) there are very many lines and bands, and there are others, very distinct, in the ultraviolet (X < 3900). Of the latter, the strongest have at X 3900;

been ascribed to the Herzberg bands of O2 (excitation energy 4.7 ev), and others, weaker, as the SchumannRunge bands of O2 (6.2 ev). In the visible region many bands are ascribed to the Vegard- Kaplan bands of A''2 (>7.0 ev). Barbier has ascribed some of the visible bands to CO. Not all these ascriptions are certain. The OH emission may be due to the reaction

H+

O^-^OH'

+

O2

(+76

kilocalories),

the

,

.

At twilight (dawn and sunset), part of thei emission spectrum is enhanced: chiefly the red oxygen line and the sodium yellow line. At these times there also appears emission of light in the band spectrum of ionized nitrogen (Nt), in the region 3914 A, correlated with the enhanced emission of the red oxygen line. This betokens higher energy absorption from sunlight in the high atmosphere then irradiated, and consequent emission, some of which is visible from places on the ground where the sun has already set or not yet risen. The auroral spectrum shows chiefly the green and red lines of atomic oxygen, bands of A'^2 and Nt; it seems also to indicate the presence of atomic nitrogen, hydrogen, helium, and perhaps He+ The energy of excitation is much greater than for the night-sky spectrum, and can reasonably be attributed to impacts caused by fast-moving particles coming from the sun and entering the atmosphere from above; they will "knock on" many atmospheric particles, which will thus be secondarily responsible for the impacts causing most of the observed excitation effects. Auroral emission caused by weak corpuscular streams impinging on the upper atmosphere may at times be mingled with the true night-sky recombination spectrum, even when there iy no obvious visual sign of the presence of an aurora. Recently it has been found that the atomic hydrogen .

lines in the auroral

spectrum,

when their light

at a small inclination to the auroral rays,

is

received

may show

much broadening and

large Doppler displacements towards the ultraviolet. This indicates that the emitting atoms are travelling do^^^lwards through the atmosphere with speeds up to some thousands of kilo-

H

metres per second. 20. The Heights of the Absorbing and Emitting Layers. By observing the intensity of absorption or emission of any particular kind along paths of different inclination to the vertical, or (by day) of different zenith distances of the sun, it is possible to estimate the level of absorption or emission,

and

also the height-distrilnition

in

some

cases to infer con-

of the atmospheric

stituent concerned. In this way it has been possible to determine the height-distribution of atmospheric ozone,^

5.

Consult "Ozone in the Atmosphere" by F. W. P. Gotz,

pp. 275-291 in this

Compendium.

,

THE UPPER ATMOSPHERE

272

and the results have been substantially confirmed by more direct measurements, namely, by obtaining the solar spectrum at different altitudes, in and above the

maximum

ozone

level,

nitrogen (neutral and ionized) between heights of 100 and 1000 km, the greater heights being associated with

The

deteiTnination of the levels of emis-

sion of the various spectral light is

much more

difficult,

components

of night-sky because of the faintness

of the light. The level of the sodium emission is estimated as mainly between 70 and 100 km, though part

of the emission has been acribed to greater heights.

The red oxygen light is ascribed to a level extending upwards from 100 km. A. and E. Vassy conclude that there is a second layer of emission at 800 to 1000 km. The green oxygen light is estimated to proceed partly from 75 to 100 km, and partly from a much higher level. These results must be considered as still provi-

a three-body

green

is

light.

Ozone and Atomic Oxygen [26]. The ozone layer produced by photolysis of O2 into atomic oxygen.

22. is

The O2 absorption of the dissociating radiation occurs at different wave lengths and extends from more than 100 km down to 20 km or so. Let Q2 and Q3 denote the respective numbers of O2 and O3 molecules dissociated per cubic centimetre per second. Let n, Wi, n2, rig denote the number per cubic centimetre of air molecules in general,

and

cubic centimetre.

of 0, O2,

The ozone

and O3 respectively, per formed by attachment -|- X—>- O3 + X), and

is

+

three-body collisions O2 destroyed by the reactions 2O3 —> 3O2 (probably negligible in the atmosphere) and -f O3 —> 2O2, as well as by photodissociation. The atomic oxygen is removed by attachment and also by combination (20 -|-^ Oi X). These various processes lead to the equations (in

is

X

+

= 2Q2 + Q3 — knnin^n — kisUina = knmni — Q3 — kutiina = —Qi — kuniiHn -j- knn\n -]- 2ki3nin3

drii/dl

,

dris/dt

sional.

21. The Amounts of the Absorbing and Emitting Constituents. The amount of a gas which contributes to the terrestrial part of the absorption spectrum of

which the third body is the thereby excited so as to emit the

collision, in

oxygen atom which,

using instruments carried in

balloons or rockets. The height of the auroral emission has been much studied, chiefiy by Stormer; and the spectrum has shown the presence of atomic oxygen and molecular

sunlit aurorae.

is

,

dui/dt

where the reaction.

k's

One

denote coefficients of combination or

difficulty in using these equations to de-

sunhght can be estimated therefrom in cases in which the absorption coefficient is known through laboratory

Qs

or other studies. It is in this way that the number of atmo-millimetres of ozone in the atmosphere is deter-

latitudinal distribution of ozone

mined daily

formulas, using the

at several places.

In the case of emission it is possible to infer from the intensity the number of quanta received per second from within a vertical column of atmosphere of, say, an area of one square centimetre at the ground. This was first done by Rayleigh for the light of the green oxygen line in the night sky. He found that 2 X 10* photons of this light are radiated per square centimetre per second, and later studies have confirmed this. The 'corresponding number for the D fine of Na is 8 X 10'. There is a very strong infrared emission band of OH at about 10,400 A, for which the number of photons may be 10'" or even more. Studies of this kind are still in their infancy: they do not indicate the total amount of the emitting gas, but they give very valuable information to be fitted into our total conception of the state and phenomena of the upper atmosphere [24]. As an example of the type of argument that can be based on such data, consider the green oxygen emission; as it continues all night long with no very great change of intensity, the number of quanta emitted from a column one centimetre square per night (about 40,000 sec) is of order 10'^ It is not difficult to show that this exceeds the number that might be derived from ionelectron recombination in the ionized layers of the ionosphere, but that the number of the -^ O2 recombinations is more than adequate. Hence this green hght may draw its energy from the daily dissociation of oxygen by sunlight during the daytime, a reservoir of energy steadily drawn upon without apparent serious depletion throughout the night. The process suggested .

+

termine is

and

Til

na as functions of height

known only when

na

is

It is possible to explain

known

and time

is

that

known.

the seasonal variation and on the basis of these type of seasonal variation

and latitude distribution of Q2 and Q3, depending merely on the changing zenith distance of the sun. The constants k are not directly known, but may be chosen (with values reasonable from a photochemical standpoint) consistent with the attempted explanation. The primary process in ozone formation is O2 dissociation, with the formation of atomic oxygen. With increasing height above the region of maxinmm ozone, the rate of attachment of atoms to Oo molecules, which will be mainly by three-body collisions, will decrease upwards as e~^''/^ (see § 11). As the rate of ozone formation thus decreases rapidly upwards, the life of the free oxygen atoms will increase upwards. By simple quantitative arguments it may be inferred that at about 100 or 120 km the value of ^3 will have decreased to less than 10^ (from over 10'- at the maximum level, about 25 km), whereas Ui will be of the order 10'^ comparable with ^2; and that not far above this level rii will exceed rii, the ratio ni/n-2 increasing upwards. Thus from the observed presence of the ozone layer, and from the theory of the associated reactions, the increasingly complete dissociation of oxygen as we ascend to high levels can be inferred independently of, though in accordance with, the spectral evidence for the presence of atomic oxygen as a permanent constituent of the upper atmosphere. 23. Atmospheric Sodium. Our knowledge of the presence of atomic sodium in the high atmosphere comes solely from the emission spectra, night-sky, twilight,

PHOTOCHEMICAL PROCESSES IN THE UPPER ATMOSPHERE sk}% and auroral. Intensity measurements at different have led to widelj' different estimates of the

altitudes

heights of emission of the sodium light. Bricard and Kastler have shown that for the twihght emission the spectral line

is

very narrow, whereas

much wider

it is

in the night-sky emission.

The problems connected with

the sodium light con-

cern not only the levels and processes of emission; they concern also the amount of invisible sodium that may be present in the upper atmosphere, that is, the amount of

sodium not

in a state to

observable) light. Sodium in the Hartley band, and

is

emit the yellow (or other

by sunlight some of this

easily ionized

must

intercept

hght, though most of it is absorbed lower down, in the ozone layer. The presence of some ionized sodium in the high atmosphere, though not likely to make an important contribution to any of the ionized layers except possibly to the D-laj^er. Further, sodium forms oxides, NaO and NaOi, and these also would not be lilvely to give direct

atoms must be expected

their presence

is

spectral indication of their presence.

The proportions of Na, Na+, NaO, NaO^ and any other forms in which sodium maj' exist in the upper atmosphere will difier with differing height, and the distribution and reaction processes of the sodium present a fascinating problem of atmospheric photochemistry, on which some speculation has been exercised, though any clear and definite conclusions being established. The oxides of nitrogen (as well as oxygen as yet without

may

play a significant part in the reactions The discussion of these oxides, as well as of the sodium itself, demands much knowledge that is still lacking, concerning, for example, energy data and reaction coefficients. As an illustration, one process suggested for the excitation of sodium atoms to the state ^Po from which they can emit the light is itself)

associated with sodium.

D

Na+0 + X-^NaO + X, NaO + 0-^Na' +

Or, for

the excited sodium atom Na' in the latter equation to be in the ^Po state, the energy 2.1 ev must be derivable from the oxygen dissociation energy gained (5.1 ev) less the energy needed to dissociate NaO; this is about 3 ev, but it is not yet certain that it is not slightly too great for this process to provide the excitation energy, unless the colliding particles

NaO

and

ha^e kinetic

energies substantially greater than their average ther-

mal energy (see § 14). This suggested process is based on the dissociation energy of oxygen stored up in the daj^time from absorbed sunlight. Another possible process, involving only two-body collisions, is Na -f- O3 NaO + O2 NaO -f —> Na'-{- O-,; it involves the same

^

,

doubt as to the latter reaction. The photochemical problems briefly discussed here have an intrinsic interest and also some practical im-

SUGGESTIONS FOR FUTURE

of the various ionized layers, themselves so vital to radio communication, is far from being properly understood, and every additional clue or sidelight concerning the electrical and chemical processes in those regions is likely to prove valuable.

WORK

On

the observational side the study of the photochemical processes in the upper atmosphere has vast scope. A basic necessity is the determination of the

composition of the upper atmosphere as well as the height-distribution of temperature and density. Rocket investigations may aid greatly in this field, particularly

with regartl to the composition, which indicates the extent to which diffusive separation occurs. Such investigations will also provide basic knowledge as to the solar radiation received at high levels in the atmosphere. Spectroscopic studies, from the ground and in situ

(by means of balloons and rockets), have much to add concerning the nature and distribution of the constituents of the upper atmosphere, including water vapor, carbon dioxide, ozone, atomic oxygen and nitrogen, the oxides of nitrogen, hydroxyl (OH), and sodium. The study of the absorption and emission by these and other gases in the high atmosphere, by night, at twilight, and during the day will enhance our understanding of the nature and processes of chemical, electrical, and energetic change there. For this

work it is necessary to develop instruments of enhanced light-gathering power, and dispersion, in particular for the auroral and night-sky luminosity. Radio investigations will greatly extend our knowledge of the energy absorption, photoelectric processes, spectral range,

and motions in the ionosphere, both at normal times and during magnetic disturbances, when corpuscular energy as well as wave energy is operative. Such observations need to be made not only at one or two places on the earth, but at a network of stations, so that the world distribution of the phenomena may be kno-wn for its own interest, and also to aid in understanding the processes occurring in any one place.

—

Continued observations to determine seasonal changes and changes throughout the sunspot cycle are desirable in

many cases. On the theoretical

side the subject is still young. additional purely chemical and physical data are required as a basis for atmospheric theories, namely

Many

data on the rates of various types of atomic and molecular processes, and in some cases on the temperature dependence of these rates. These data must be obtained partly by laboratory measurements, and partly by theoretical calculations in atomic and molecular physics. Such data are needed to elucidate the main processes of photochemical and photoelectrical change in the upper atmosphere, and to determine their height-distribution,

among the vast number of possible reand processes, those whose rate and number give them real significance. distinguishing,

actions

portance in that their solution is lilvely to aid in a full understanding of the phenomena of the ionosphere.

At present the formation

273

REFERENCES I.

Books on chemistry, particularly photochemistry. 1. BoNiiOEFFER, K. F., und Harteck, p., Grundlagen der Photochemie. Dresden & Leipzig, T. Steinkopff, 1944. 2. PIiNSHELWooD, C. N., The Kinetics of Chemical Change in Gaseoits Systems, 4th ed. Oxford, Clarendon Press, 1938.

.

THE UPPER ATMOSPHERE

274 3.

JosT, W., Explosion and Combustion Processes in Gases.

New

4.

5.

6.

York, McGraw, 1946. Kassbl, L. S., Kinetics of Homogeneous Gas Reactions. New York, Reinhold, 1932. NoYES, W. A., Jr., and Leighton, P. A., The Photochemistry of Gases. New York, Reinhold, 1941. RoLLBFSON, G. K., and Burton, M., Photochemistry and the Mechanism of Chemical Reactions. New York, Prentice-Hall, Inc., 1939.

Sbmenoff, N. N., Chemical Kinetics and Chain Reactions. Oxford, Clarendon Press, 1935. Books on atomic and molecular physics and spectra. 8. Arnot, F. L., Collision Processes in Gases. London, Methuen, 1933. 9. Backer, R. F., and Goudsmit, S. A., Atomic Energy States as Derived from the Analysis of Optical Spectra. 7.

II.

New 10.

York, McGraw, 1932.

Erode, W. R., Chemical Spectroscopy.

12.

13.

FooTB, P. D., andMoHLER, F. L., The Origin of Spectra. New York, Chemical Catalog Co., 1922. Gatdon, A. G., Dissociation Energies and Spectra of Diatomic Molecules. London, Chapman, 1947. Jeans, J. H., Dynamical Theory of Gases, 4th ed. Cam-

15.

16.

Moore, C.

17.

Bureau of Standards, 1949. MoTT, N. F., and Massey, H.

sity Press, 1938.

18.

E.,

Atomic Energy

Levels.

Washington, U.S.

S. W., The Theory of Atomic Collisions. O.xford, Clarendon Press, 1949. Pearse, R. W. B., and Gaydon, A. G., The Identification of Molecular Spectra. London, Chapman,

1941. 19.

M

olekiilspektren und ihre Anwendung Sponer, H., auf chemische Probleme, 2 Bde. Berlin, Springer,

1935-36.

Barbier, D.,

et

Chalongb, D., De

la stratosphere a

I'ionosphhre. Paris, Presses Universitaires de France,

1942.

Fleming,

Terrestrial Magnetism and ElecYork, McGraw, 1939. 22. Ktjiper, G. p., ed.. The Atmospheres of the Earth and Planets. Chicago, Chicago University Press, 1949. 23. MiTRA, S. K., The Upper Atmosphere. Calcutta, Royal 21.

tricity.

J. A., ed..

New

Asiatic Society of Bengal, 1948. IV. Summarizing reports and discussions, containing extensive detailed bibliographies. 24. 'Bates, D. R., "The Earth's Upper Atmosphere." Mon. Not. R. astr. Soc, 109: 215-245 (1949).

Dejardin, G., "The Light

of the Night Sky." Rev. mod. Phys., 8: 1-21 (1936). 26. Gassiot Committee, Reports on Progress in Physics, 25.

27.

bridge, University Press, 1925. Jevons, W. S., Report on Band-Specira of Diatomic Molecules. Phys. Soc, London, 1932. Massey, pi. S. W., Negative Ions. Cambridge, Univer-

14.

General references.

20.

New York, Wiley,

1943. 11.

III.

28.

9; 1-100. Phys. Soc, London, 1943. Gassiot Committee, The Emission Spectra of the Night Sky and Aurora. Phys. Soc, London, 1948. Panbth, F. a., "The Chemical Composition of the Atmosphere." Quart. J. R. meteor. Soc, 63: 433-438

(1937).

V. Articles cited in text. 29. Bates, D. R., and Massey, H. S. W., "The Basic Reactions in the Upper Atmosphere. II The Theory of Recombination in the Ionized Layers." Proc. roy. Soc, (A) 192: 1-16 (1947). 30. Bates, D. R., and Seaton, M. J., "The Quantal Theory of Continuous Absorption of Radiation by Various Atoms in Their Ground States, II." Mon. Not. R. astr. Soc, 109:698-704 (1950). 31. Hirschfelder, J. O., "Semi-empirical Calculations of Activation Energies." J. Chem. Phys., 9 645-653 (1941) 32. Livingston, M. S., and Bethe, H. A., "Nuclear Physics. C. Nuclear Dynamics, Experimental." Rev. mod. Phys., 9: 245-390 (1937). (See p. 370, Table LXX) 33. Meinel, a. B., "OH Emission Bands in the Spectrum of the Night Sky." Astrophys. J., Ill: 555-566 (1950).

—

:

OZONE

IN

By

F.

THE ATMOSPHERE* W. PAUL GOTZ

Lichtklimatisches Observatorium Arosa and University of Zurich

METHODS OF OBSERVATION

INTRODUCTION As

early as 1845 the chemist Schonbein, discoverer

attempted to prove that traces of this gas are a constant constituent of the atmosphere. However the ozone problem in its entii-e scope was revealed only when Fabry and Buisson [32] recognized by spectrographic methods that the principal quantities of ozone are present in the upper strata of the atmosphere. Although the ozone amount, that is, the total quantity of ozone present when reduced to standard conditions, amounts to but a few millimeters of the 8-km height to which the homogeneous ocean of air rises, this small of ozone,

is nevertheless sufficient (because of the enormous absorption in the ultraviolet) for intercepting the entire extraterrestrial radiation below 2900 A, for heating the "warm layer" at a height of 50 km, and for protecting the biosphere against an excess of short-wave radiation. Only during recent years has it been possible to pass through the high ozone layer with the aid of V-2 rockets, a feat which opened an entirely new spectral range of solar radiation to agtrophysical investigations. But how is it possible for such a relatively heavy component of air to maintain itself high in the atmosphere? Only if it is constantly being regenerated, if short-wave radiation from the sun is capable of transforming oxygen to ozone. The opposing effect of long-wave ultraviolet which is again absorbed by ozone thereby destroying it (E. Regener), produces a spontaneous chemical ozone equilibrium in the upper layers of the atmosphere; below 35 km, however, this latter process is so slow that ozone which, by some meteorological processes, has been transported to these altitudes is largely "protected." In lower layers ozone becomes an important conservative property of the air until the stream from the high altitude ozone source is finally destroyed near ground level due to photochemical, chemical, and catalytic decomposition. In view of its intimate connection with weather processes (Dobson), the study of ozone provides methods of indirect aerology; there is an everincreasing tendency to supplement a mere observation of total ozone amount with a detailed measurement of its vertical distribution and changes thereof. Only by

trace

investigation of this latter type will

it be possible to ozone on the flux of radiation. An intriguing aspect of the ozone problem is that the most diverse scientific fields converge at it. Two

understand the

special

*

Union

duces the intensity of radiation to one tenth. On the short-wave side, in the region of the ozone-oxygen gap which is so important for the theory, Mme. A. Vassy [96] satisfactorily verified the older measurements of Edgar Meyer. The long-wave side of the Hartley band connects with the Huggins bands which extend up to 3690 A, and these bands are temperature dependent. However, new determinations [4] yielded the opposite

maxima too are influenced by temperature. The Chappuis bands, although relatively weak, coincide with the region of maximal solar finding that the absorption

energy because of the superposition of the vapor bands in the solar spectrum, they are not suitable for ozone determination, according to Mme. Vassy. Absorption in the long-wave region is important for the problem of heat balance; the absorption band between 9.0 and 9.7 M seems particularly significant because it lies in the otherwise very transparent atmospheric window between 9 and 13.5 m- According to Strong [92], and Adel and Lampland [1], absorption in the 9.6-;u band exceeds all previous assumptions by a factor of about ten and is very dependent on pressure, approximately proportional to the fourth root of pressure, a fact which Strong uses for determining the average height of the ozone layer by simultaneous determination of the ozone absorption in the ultraviolet and the infrared. Oxygen has absorption properties which form the basis for the theory of the ozone layer. In this connection, the region of maximal absorption between 1300 and 1750 A [56] is of less interest than the wave lengths around 2000 A [96] which overlap the ozone absorption. Deviations from Beer's law are significant. I am indebted to W. Heilpern and E. Meyer [51] for information regarding the current state of this question. If the absorption of light is given by J = Jo X 10~'', where € denotes the extinction coefficient for a pressure P in kilograms per square centimeter, and if the thickness of the layer I = 1 cm, then e for pure oxygen is given by ;

effect of

international conferences [16, 31] and several national conferences [71] have so far been devoted to this problem. The Meteorological Association of the Inter-

Geodesy and Geophysics has a commission on ozone.

national

Absorption Coefficients. Ozone has its principal absorption in the Hartley band [68] extending from 3200 to 2000 A. At X = 2553 A the decadic absorption coefficient is 145, that is, a layer as thin as 3d!45 cm re-

for

Translated from the original German. 275

e{02)

=

e,P

+

e,P\

(1)

For an arbitrary mixture of O2 and A^2, where Ci denotes the volume concentration of O2 and C2 that of A^2, e is given by €(G)

=

«iPci

+ i^PW +

hP-Cic,

,

(2)

where P denotes the total pressure. The third term represents the effect of the "extraneous gas." In the region investigated, the constants ei, €2, and 63 have

THE UPPER ATMOSPHERE

276 the following values: X(A)

:

OZONE IN THE ATMOSPHERE as z continues to increase, however, the function iji' reaches a minimum at about z = 85°, and shows an inversion (Umkehr) [36] at £ > 85°, that is, i/i' increases again at A'ery low elevations of the sun. This experimental result (Fig. 2) is explained on the basis of

Thus the

277

characterization of the vertical distribution

involves only

two unknowns,

56.3

(

DEGREES) 79.5

74.0

66.9

84.5

88.0 90.0

and

xi,

which

,

may not be too difficult. The unkno^vns enter into the expression for the thickness I tions

ozone layer which Z

x^

is

de-

sirable in order that the numerical solution of the equa-

instrument ozone shell to tabulate

Fig.

3.

of

xi

an

traversed by a sun ray incident The ray is scattered at point A barometric pressure is h and reaches the at the point B. The path length in each is determined trigonometrically; it sufifices the distance s of Fig. 3 as a function of the z.

— Subdivision

quantity h

and

is

at a zenith distance

where the

rri

cm

—

of the

atmosphere into layers.

independently of r). Of significance is the air mass L traversed by the ray, which is easily found to be r {i.e.,

for the Rayleigh scattering Fig.

2.

— Umkehr curves.

L = l-f the distribution of ozone in the scattering atmosphere. Zenith light is the sum of the components scattered at various altitudes corresponding to the prevailing air density. Because of

its smaller density, the atmosphere above the ozone layer scatters to a lesser extent than the atmosphere below this layer. However, the shortwave radiation scattered vertically do^wnward traverses the attenuating ozone layer by the shortest path and,

as the zenith distance increases,

it

attains ever

more

sig-

nificance in comparison with the radiation scattered

below the ozone would indeed be

power which is to be scattered has been considerably weakened by tralayer; in this case scattering

greater, but the sunlight

versing the ozone layer by the long, oblique path. The stronger the absorption, the greater the tendency for the sky radiation of the shortest wave length to find

the shortest path directly from above through the ozone layer. The variation of the Umkehr function iji' with z depends on the type of stratification, that is, the vertical distribution of ozone. It thus provides a

means

measuring the vertical distribution. We divide the atmosphere into a number of shells within each of which we assume the ozone content (expressed in centimeters of ozone per kilometer) to be constant. We might assume the following shells [39, 45] for

Ozone amount

Altitude

65-50 50-35 35-20 20- 5 5-

km km km km km

but scattering not zero

0,

(xi -h

",

a-2 -|-

where u

is

u) since x is known. assumed to be known.

(&/760)

(m

-

1).

(7)

We sum

the light scattered by each kilometer A from the ground to an altitude of 65 km and find the intensity of zenith radiation i to be ^lO'^'-felO"" const

(8)

i/i' or i' /i. The corresponding the same as the result of observations (Fig. 2). It is to be noted that the undetermined constant in the observed curve may be determined by calculating i' /i for z = Q, since the vertical distribution

and similarly

expression for

of

for

i'

and

i' /i is

ozone has no effect for

and

2

=

0.

The two unkno\vns

as an equation 90° and one for z = 80°. The solution is obtained graphically by plotting x^ as a function of Xi for both cases and determining the intersection of the two curves. Choice of a third value of z, such as 2 = 86.5°, provides Xi

for 2

X2 require

two equations, such

=

a convenient check. The values of Xi and Xi then characterize the vertical distribution stepwise. In adchtion to this analytical method A use has also been made of a more synthetic method B, which consists of starting with an assumed vertical ozone distribution and varying it until calculated and measured Umkehr curves are in agreement. In both methods secondary scattering should be further considered. In order to obtain a more detailed ozone distribution curve it is, of course, desirable to choose our shells as thin as possible. It has been verified that essentially no ozone is present above 50 km. Between 50 and 35 km the ozone may be assumed constant as will be seen ,

THE UPPER ATMOSPHERE

278

From the ground upwards, the region of known ozone concentration could today easily be extended from 5 to 10 km above ground by modern aerological methods later.

(chemical measurements by airplane). A subdivision of the region between 10 and 35 km into three shells would then remain for the Umkehr measurement. Day-to-day measurement of these three layers would be of the most important meteorological interest. 2. Techniques Using Recording Balloons, Stratospheric Balloons, and V-2 Rockets. In addition to the rather indirect method involving the Umkehr effect, there is of course the challenge of sending spectrographs to ever higher altitudes until finally the ozone layer is penetrated.

The

first

great success in this

respect

was

achieved by E. and V. H. Regener on July 31, 1934 when they sent a recording spectrograph to an altitude of 31 km by means of a balloon [85]. The lightweight spectrograph was pointed downward against a horizontal magnesium oxide disk exposed to sunlight; magnesium oxide effectively reflects ultraviolet. The apparatus is installed in a light wooden frame, the lower half of which is covered with aluminum foil, the upper half

with cellophane, an arrangement which affords excellent protection against cold. The photographic plate Fig. 4) is rotated through a small angle every ten

and the smaller the quantity

—Regener-photographs

of

the

ultraviolet

mer-

shortest wave length of the solar spectrum at an altitude hn and zenith distance z„, and if Xn represents the total quantity of ozone located above the instrument, then, approximately. a;2a2

sec

22

=

a^iai

sec

Zi

(9)

Further improvements are obtained with an accurate intensity measurement at the end of the spectrum and elimination of diffuse sky light, for instance with the aid of a magnetically oriented hemispherical stop [86]. Coblentz and Stair [15] and Stranz [91] attempted to simplify the methods by replacing the spectrograph by a cadmium cell and filter as was done in the first ozone in 1921 at Arosa. The intensity values are transmitted radiotelegraphically as in the radiosondes. With the aid of a fi-ee balloon, A. Wigand as early as 1913 measured the ultraviolet end of the solar spectrum up to a height of 9 km. Shortly after the Regener experiments, the stratosphere balloon, which is capable of carrying aloft high quality instruments, was employed for this purpose. Under the leadership of Stevens and Anderson, Explorer II reached an altitude of 22 km in November 1935; ozone at even higher altitudes was determined indirectly from the sky radiation [39, 69]. Ozone determination by means of captured V-2 rockets [95] represents the climax of this brilliant development. It was the fulfillment of a dream when on October 10, 1946 in White Sands the ozone layer was penetrated and a large unknown range of the solar spectnmi be-

measurements

Fig. 4.

ozone traversed by the

cury calibration spectrum. The entire device, including a protective frame, weighs 2.7 kg. If X„ represents the

came

Fig.

of

solar radiation. In addition, the plate also bears a

accessible (Fig. 5).

5.

— Short-wave

end of the solar spectrum taken from V-2 rocket.

spectrum

taken in the stratosphere.

RESULTS OF OBSERVATIONS

minutes, being continuously exposed in the meantime. At the instant the plate is advanced, a small light bulb is turned on by which the readings of two aneroid gauges (standard barograph and low-pressure barograph) as well ai of a bimetallic strip to indicate the temperature of the instrument are recorded. On the plate which has a diameter of 10 cm the step-shaped interruptions of the long rays are the shadows of the two indicators connected to the aneroids they represent lower pressures the closer thej' approach the center. The clear ultraviolet spectra are located diametrically opposite the pressure indications and they are seen to extend to shorter wave lengths the greater the altitude

The Ozone Amount. The first ozone determinations made in Marseille [32], as well as the measurements made at Arosa with filtered cadmium cells since 1921,

;

revealed irregular ozone fluctuations from day to day. Dobson [24] discovered their connection with the general distribution of air pressure so that they may be

designated as meteorological fluctuations. The interdiurnal variability of the ozone amount at Arosa was found to be: January

OZONE IN THE ATMOSPHERE During the summer season there are no great meridional and August, in India it is 0.005 cm, at Tromso 0.010 cm, at Spitsbergen 0.007 cm; in December it rises to 0.056 cm at Troms5. The fluctuations frequently become manifest even during a single measui'ing day, in the form of an "ozone cloud" [55]. In one case in which ozone was determined by sighting on stars in various directions of the sky, it was possible to delineate such differences in the interdiurnal variabiUty. In July

n

o

279

of ozone amount is revealed by an increase from 0.17 cm at the equator to an "ozone belt" (Gotz) of 0.26 cm at latitude 60°N; the ozone amount again decreases

toward higher

latitudes. In the Southern Hemisphere, the gradient is more pronounced, and here again it is the maxima rather than the minima that are significant. The variation is best described by an isoplethic representation (Fig. 7), in which the ozone belt is shown by means of a dot-dash line.

THE UPPER ATMOSPHERE

280 average

is

ozone and solar activity, then the double fluctuations of the Eurasian large-scale weather within the sunspot cycle according to Baur [7] would be of interest. In the lower yearly average curve of Fig. 8, the vertical solid lines represent sunspot maxima, the vertical broken lines represent sunspot minima. For the yearly averages the following correlation corelation between

given below: cm

January ±0.014 February ±0.014 ±0.012 March ±0.012 April

cm

May

September ±0.007 ±0.007 October

±0.008 ±0.006 ±0.005 July August ±0.006 June

November ±0.005 December ±0.00,S

apparent that the fluctuation is twice as great in winter as it is in summer and fall in winter, as well as in spring, it is considerably greater at Tromso than it It is

;

efficients are obtained. Correlation coefficient

Ozone and Ozone and Ozone and

relative sunspot

number

+0.01 —0.43 +0.48

air pressure

solar constant

As regards the

analysis of other long series of observa-

only the attempt [11, 93] to determine ozone by means of the Chappuis band from the Smithsonian measurements. Even though wide scattering of tions, there exists

these values

makes them seem rather

unreliable,

it is

nevertheless interesting to note the very slight ozone 0.250 0.240 0.230 0.220

amount during the year 1912

mm —

Such a

tor-cocno — c\Jr''.>-t') (27)

dm

-(»

dx

This derivation is based on the simplifying assumptions that the air density varies only with altitude and that the vertical temperature gradient is zero, an assumption that is justified only as applied to the lower stratosphere. Reed [80] therefore took the vertical temperature gradient into account and obtained the expression

m-'M

28. 9g

RT +

d\nT\ dz

)

+ dm dz

(28)

He uses this equation primarily in treating the diurnal meteorological ozone fluctuations and in establishing a theory concerning seasonal and zonal ozone fluctuations. Diitsch, moreover, finds the effect of turbulent exchange (austausch) to be

(dm\ \

dt

[Od

A

p

5_

1^

dz\

a_ [O3]

(29)

dz

[O-i

where the subscript a denotes the effect of the austausch and A represents the austausch coefficient. Diffusion may be neglected. Because of the long time required for establishment of photochemical equilibrium at lower altitudes, changes in the concentration owing to flow and turbulence play an essential role. If B is the change in ozone concentration per second caused only by air motion (flow and austausch) then equation (23) becomes

;

[O3]

=

and the equation

(30)

[Od for disequilibrium

becomes

/.

mu) =

m

it,)

^/

K[M]

+^v^ +

'^*{''-^m}''' K[M]

/

+ iS^tanh KmiMi

rection of the disturbed equilibrium takes place almost

immediately; between 30 and 25

[O2]

2io;

km

from several days to several months are required; at low altitudes ("protected regions") equilibrium is practically never regained. At high elevation of the sun, equilibrium is established more rapidly than in the ca,se of low sun.

tanh

W

it

K[M]

-

to) ,

(31)

K[M]

(/

-

to)

Thus, equilibrium can be established only

if

f^

>

B/i2[Oo]); equation (31) is always valid. Dutsch used this expression to recompute the seasonal variation of ozone at various latitudes. For the layers

above 16 km, the austausch on the basis of experimental

coefficient

results

of

is

calculated

Paneth and

THE UPPER ATMOSPHERE

284

E. Regener concerning separation in the atmosphere; it is assumed that the turbulence extends to higher altitudes corresponding to the greater altitude of the tropopause. The result of this calculation indicates a constant do\\'nward stream of ozone caused by turbulence. It follows that ozone must constantly be destroyed in the layers near ground level. The mean ozone distribution in the lowermost 15 to 20 km is determined essentially by the austausch. The small amount of total ozone in the tropical zone (O3 = 0.185 cm) is due to high-reaching turbulence combined with a rapid destruction of the downward transported ozone in the layers near the ground level, which seems plausible for tropical conditions. Disregarding the possibility of achieving a better agreement between theory (as indicated in Table III) and observation by making for the equatorial zone

Table *

III.

Amount of Ozone According to Equation (mm O3)

(31)

the surface weather map and fronts have supported this observation [23, 94] and have shown that the center of high ozone amount on the rear side of a cyclone is particularly the property of a newly developing depression (Fig. 12). Since its axis is inclined back-

ISOBARS

OZONE

OZONE IN THE ATMOSPHERE hand, and continuous measurements of the vertical ozone distribution on the other hand. As a first possibihty, one considers the meteorological ozone distribution as a result of horizontal advection. Every veteran observer of ozone has long been familiar with the fact that invasions of arctic air extending to high altitudes are accompanied by an increase in ozone amount, whereas the ozone amount is slight in the case of European anticyclones composed of air of southern origin. The increased ozone amount accompanying invasions of cold air has been particularly noted by various expeditions [5, 97]. Lejay [58] points out that in the Siberian anticyclone in which the ozone amount is high, cold northern air masses advance so that the "transportation theory" removes the apparent contradiction with European findings. Penndorf [76] finds the 96-mb surface as suitable for indicating the flow conditions. Moser [65], in examining drawings of the trajectories at 5, 11, and 16 km, finds the best correlation between the trajectories at 11 -km height and the ozone amount; he therefore assumes the main location of ozone fluctuations to be in the stratosphere near the tropopause where the maximum in wind velocity is located. This ozone maximum coincides with the lower secondary ozone layer which was first suggested, at least intermittently,

by the

investigations at Arosa

[39]. This lower secondary layer is generally separated from the very constant high-altitude layer of ozone by a minimum in wind velocity between 15 and 22 km.

The

trajectories of

Moser

(Fig. 13) illustrate well the

TRAJECTORIES ENDING OVER: =TR0MS6 (0.315 CM O3) 3 = POTSDAM (0.339 CM O3) 2 = AARHUS(0.258 CM O3) 4 = AR0SA (0.357 CM O3) 1

Fig. 13.

— Air trajectories at

11

km.

temporal constancy of ozone amount at various points situated in the same air current, indicating that ozone is a conservative property of the air and may thus serve as an important indicator for air-mass determinations. On the other hand, in Fig. 14, Moser shows that at Arosa the ozone amount is higher the more northerly the latitudes from which the air current comes. The source of ozone, in this case, is the ozone belt located

by us

(Fig. 7).

285

But how

is this

secondary source of low-

Moser and Schroer suggest that the great temperature gradient at the shadow boundary between polar night and the sun-illuminated altitude ozone supplied?

0.36

-

POLAR TERRITORY

< in

o < 0.32 LABRADOR GREENLAND

0.28

NORTH AMERICAN BASINAZORES 12

Fig. 14.

—

13

14

16

15

APRIL 1942 Ozone amount and origin of

17

air at 11

km.

atmosphere leads to increased shear-turbulence between the layer of photochemical equilibrium and the lower ozone layer at an altitude of 23 km. They also suggest that a further connection with the lower stratosphere is provided by high-reaching cold-core lows within which the barrier by the minimum in wind velocity is lacking. This theory needs corroboration by additional measurements. Flohn [33] sees a possible source of the winter singularities in the 30.5-day oscillations of the winter circumpolar vortex of the warm layer [43]. Craig also suggests continuous subsidence of ozone in the polar cap during the cold months. This leads us to the second possibility for ozone distribution, that of transport bj^ vertical flow. A sinking column of air, such as exists in low-pressure regions at least at the height of the tropopause, is lengthened (stretched) in its upper ozone-containing portion and this is accompanied by a horizontal convergence or contraction. This is equivalent to an increase in ozone amount. An ascending current has the opposite effect. Thus, the explanation of the day-to-day changes does not even require the assumption that sinking air comes directly from the layer of photochemical equilibrium and is there replenished with ozone. Dobson [25] pointed out long ago "that the air immediately in the rear of a cyclone often has a higher ozone value than in the same general air stream further to the north or northwest." Haurwitz [50] emphasizes that horizontal advection cannot explain closed lines of equal ozone deviation such as those in Fig. 12. Moreover, the ozone content at the rear of a cyclone is sometimes higher than it is during the same season in the northern ozone source. Reed [81] emphasizes: Particularly noteworthy is the fact that closed isopleths of positive and negative ozone deviations liear the same I'elationship to surface cyclone centers as the closed isotherms which are invariably observed on the 200

mb

chart (approximately

— THE UPPER ATMOSPHERE

286

warm

pocket at this level coinciding with the poswith the negative. Since these warm and cold areas are unquestionably due to subsidence and lifting respectively, it seems reasonable to suspect that the vertical displacements also in some fashion affect the ozone con12 km), the

itive deviations, the cold

centration.

Reed, moreover, recently calculated the change in ozone content during vertical displacements on the basis of the fact, already emphasized by Regener, that in strong vertical mixing the ozone mixing ratio (grams of ozone per gram of air) is independent of altitude. To begin with, the curve of ozone content versus altitude is transformed into a curve of ozone mixing ratio versus altitude. The curve is thereupon raised or lowered and finally reconverted back to an ozone content curve. In Fig. 15 it is assumed, at first, that the vertical dis-

," AFTER SUBSIDENCE (COMPUTED) .004

.002

,006

.008

.010

.012

.014

CM O3 PER KM Fig. 15.

— The

subsidence on the ozone distribution.

effect of

placement extends through the entire column of air [80]. More recently [81] the assumption was made that, in the closed region of high ozone amount to the west and southwest of an intense surface cyclone, the air subsides most markedly near the tropopause and that the sinking motion becomes unnoticeable above the tropopause between 16 and 18 km and below it at 7 to 8 km. Thus, the vertical displacements take place only within the secondary advection layer. Figure 16 is 1

1

1

1

..•••"l^

20

2

5

15

H X S2

10

llJ

.002 .004 .006 .008 .010 .012 CM O3 PER KM Fig.

16.

—The

effect of

.014

,016

subsidence on the ozone distribution.

based on an Arosa curve for an ozone amount of 0.131 cm between altitudes of 5 and 20 km and an assumed

;

OZONE IN THE ATMOSPHERE hardly be denied. Moller [64] explains the stratospheric temperature differences between tropics and temperate latitudes on the basis of the variable protective action of the ozone located above the emitting carbon dioxide Dobson [23] arrives at an identical result even more directly. For the lower stratosphere he estimates the temperature of radiative equilibrium of HiO to be 200C, that of C0^_ to be 200C, and that of O3 to be 260C, which, for equal portions of these three absorbers, would lead to the plausible mean value of 220C. In comparison with higher latitudes, the lower secondary advection layer is absent in the vicinity of the equator, and ozone has correspondingly less effect on temperature. But even considering only the indirect action due to advection of air masses of different temperature, ozone has a significant effect on our weather.

ADDITIONAL REMARKS CONCERNING THE SIGNIFICANCE OF ATMOSPHERIC

OZONE Ozone and the Constitution The

Warm

of the

Upper Atmosphere.

Layer. Absorption of the short-wave radi-

ation from the sun at the upper boundary of the ozone layer results in a temperature of -|-50 to -|-80C at an

km. This region is known as the warm warm layer was first encountered in 1922 by Lindemann and Dobson in connection with

altitude of 55

layer [34]. This

the determination of the altitude at which meteors become incandescent. The anomalous propagation of

sound, which results when sound encounters the warm layer and is refracted back to the earth [101], leads to good temperature data for this high layer; taking an average of the values given by Duckert [26], Gutenberg [48], and Whipple [26], the temperature in summer

— 50C

an altitude of 30 km, -|-28C at 40 km, and -F70C at 50 km. If a gas, such as ozone at its upper boundary, absorbs mainly in the ultraviolet part of the spectrum but emits according to the laws of temperis

at

temperature must rise to a and emitted radiation will attain equilibrium. This is even more applicable, incidentally, to the case of oxygen absorption in the ionosphere [38]. On the other hand, water vapor with its absorption in the infrared tends to lower the equilibrium temperature. Considering the fact that the sun's temperature is lower in the short-wave continuum, ature radiation, then

its

rather high value before incident

Gowan

[46] finds

that his calculations show satisfactory

agreement between ozonosphere temperature and the data on record. According to his calculations [47], the warm layer persists even during the night. Barbier and Chalonge, E. Vassy and D^jardin (for references see [19]) attempted to calculate the mean temperature of the ozone layer on the basis of the temperature dependence of absorption in the Huggins bands by methods of indirect aerology; they also attempted to calculate the mean temperature of ozone above 30 km on the basis of the temperature distribution up to 30 km. In order to analyze the warm layer proper, Gotz suggests that, instead of measuring the ozone bands in sunlight as customary, the Umkehr effect should be used in zenith light at low elevation of the sun. In-

287

direct conclusions concerning the vertical temperature

distribution have recently been verified [66] quite satisfactorily by means of V-2 rockets.'

Pekeris layer

it is

[74]

has shown that on the basis of the

warm

possible to calculate a free oscillation of the

atmosphere with a period of very nearly 12 hours, such as is necessary for the resonance theory of the migratory pressure wave of a half day's duration. As a heat source at high altitudes, the warm layer is capable of damping the circulation currents in the troposphere and is thus of climatic significance [8]. Many years ago, Wegener [100] deduced the existence of a high altitude troposphere (Hochtroposphdre) above 60 km from the existence of noctilucent clouds at an altitude of 82 km; we now know that the heat source for this phenomenon is the warm layer caused by ozone. The Screening Effect of the Ozone Layer. The atmosphere of the earth forms an opaque screen for shortwave ultraviolet, so that the shadow cone for this radiation is not tangent to the earth's surface but rather to a sphere of enlarged radius. Gotz [37] has therefore suggested that the upper boundary of the ozone layer be determined from ultraviolet observations during lunar eclipses. Barbier, Chalonge, and Vigroux [6] have accomplished this up to an altitude of 16 km [71a]. According to Gotz this screening effect is of particular significance if the altitude of atmospheric dissociation, excitation, and ionization processes is to be calculated from the time of onset of these processes at dawn or the time at which they cease in the evening. When the altitude of sodium luminescence was given as 60 km on the basis of the dawn effect, it was pointed out [39] that the altitude of the ozone layer would have to be

photoluminescence were assumed. [99], by simultaneous measurement of the intensity drop of the sodium line at the zenith and at the horizon, found the upper sodium boundary to be at 116 km and the altitude of the screening layer at 56 km. Penndorf [75], rigorously defining the ozone shadow boundary, has carefully calculated the conditions in an effort to determine accurately the upper boundary of the ozone layer from such observations. The ozone shadow boundary seems also to be significant in connection with certain delay processes observed in the E-layer by Lugeon and Mitra [39]. Stormer [90] found that noctilucent clouds always appear only when the sunlight striking them is no closer to the earth's surface than 30 to 45 km. It does not follow, of course, that it is the ozone shadow which is significant in all .similar cases. In the case of the photoluminescent effect of the red twilight line at 6300 A, it is the shadow of the oxygen sphere which is opaque up to an altitude of about 100 km [41].

added to

this figure

if

And indeed, Vegard and T0nsberg

Ozone and Bioclimatology. The

biological significance

ozone layer can be touched upon but briefly within the scope of the present article. The ozone layer is of the greatest importance in controlling the ultraof the

2.

Consult Fig. S

in

"Temperatui-es and Pressures

Upper Atmosphere" by H. E. Newell, this Compendium.

Jr.,

in

the

pp. 303 to 310 in

THE UPPER ATMOSPHERE

288

violet radiation climate [10, 37, 57, 84] in a spectral

range distinguished by a number of biological effects such as the formation of erythema, the formation of vitamin D, and bactericidal effects. Radiation intensities in the ultraviolet range of the solar spectrum are highly variable from wave length to wave length; however, the ozone measurements can entirely account for these variations in intensity. Our present-day knowledge concerning ozone amount is sufficient to allow us to estimate the incidence of ultraviqjet over the entire earth. Without the ozone layer, sunburn would easily be fifty times as effective as it is during the highest sun's elevation during summer in high mountains. On the other hand, an increase in the ozone screen would completely eliminate the stimulating radiation, that, in proper dosage, is essential to life, and would leave us in biological darkness. Therefore it is probably significant if, as Fig. 8 would indicate, the ozone amount increases over a period of years while the ultraviolet radiation decreases. The zoologist Rowan [88] has recently raised the question as to whether such fiuctuations may not provide an explanation for the tenyear cycle in the abundance of certain species among the Canadian fauna. Equally stimulating from the bioclimatological viewpoint are speculations as to whether the protective effect of the ozone layer has undergone changes during the development of the earth. For a mature oxygen planet such as Mars, the photochemical equilibrium layer must rest on the ground, a fact which would substantiate the explanation of the red discoloration of extended portions of the surface of Mars [102]. This oxidizing effect leads us, finally, to the groundlevel ozone of the earth's biosphere. Gotz and Ladenburg [44] have emphasized the desirability of investigating anj' possible direct influences of ozone on the human body. As E. Regener has pointed out, ozone bioclimatoJogically plays the important role of an air purifier [82]. It may even be said that it is ozone which characterizes "living air." The physician Curry [18] draws very extensive conclusions concerning the effect of ozone, and in general, of active forms of atmospheric oxygen on the human body. Even though these assertions have aroused much interest in this problem, they have not yet been substantiated by the use of rigorous statistical methods.

CONCLUSION If we consider the results obtained thus far, the data concerning ozone amount appear the most reliable. Of course, the observation network is still not sufficiently dense, particularly in the region of large vortices. It has justly been pointed out that the present state of synoptic meteorology would leave much to be desired if it were dependent on a dozen barometers distributed over the entire earth! The continuous series of observations which were started at several locations must be carried on for prolonged periods of time because secular fluctuations reflect long-term changes in atmospheric circulation. The most interesting armual curve of ozone amount was observed in Tromso, a fact which urgently suggests

that the observation network be extended to the polar regions proper, such as Spitsbergen, for example.' Since the ozone problem is fundamentally a flow

problem, ozone amount must also be observed continuously in the third dimension. Information now available concerning the vertical distribution of ozone is far from adequate and, above all, much too disconnected. Vertical ozone distribution, together with information concerning water vapor, could be exploited directly in connection with forecasting and would provide the material necessary for approaching the problem of radiation flow. Perhaps it is a desire for more simple and less expensive apparatus which is discouraging meteorologists from attempting large-scale experiments? Stratosphere flights and V-2 rockets are rare opportunities. The Umkehr-effect method could be refined considerably if it were supplemented by ozone determinations in the lower ten kilometers by flight measurements if one does not expect to measure the LTmkehr effect continuously from meteorological aircraft at cloud-free altitudes. Perfection of the radiosonde should meet with no further fundamental difficulties. It is fascinating to observe how ozone pulsates through the atmosphere like blood circulating in an organism. Ozone is created by radiation in high-altitude layers. Primarily at the shadow boundary of the polar night, and at the altitude of the warm layer, it produces the temperature contrasts and resulting polar vortices which enable it to sink as a secondary layer

—

down

to the theater of meteorological activity. diffusing to the vicinity of

ground

And

the ozone re-enters the oxygen metabolism. Much work remains to be done before this sketchy picture is comfinally,

level,

pleted and verified by obsei'vation. This task requires ever-increasing international cooperation. It would be appropriate to pool all available tools (apparatus as well as observers, including other aerological methods) during international ozone

and

to distribute

them over

weeks

suitable regions. Inter-

national cooperation has indeed alwaj^s been exemplary in the ozone field. Typical single cases could then be treated in a united effort which would help us in a decisive manner to push forward to the last meteorological

consequences.

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in

"The Theoretical CalcuPhotoohemically-Formed

the Atmosphere." Terr. Magn. atmos. Elect.,

41: 299-310 (1936). 104.

(1940).

Wegener,

Veroff.

(1934).

L.,

100.

WiLDT, R., "Ozon und Sauerstoff pharen."

and T0nsberg, E., "Investigations on the Auroral and Twilight Luminescence Including Temperatures in the Ionosphere." Geofys. Publ., Vol. 13, No. 1

Vbgard,

of Zones of Audibility."

Nature, 111:187 (1923).

"Role de la temperature dans la distribution de I'ozone atmosph^rique." /. Phys. Radium, (8) 2: 8191 (1941).

99.

291

"The Distribution of Atmospheric Ozone in Equilibrium with Solar Radiation and the Rate of Maintenance of the Distribution." Terr. Magn. atmos. Elect., 42: 195-202 (1937).

RADIATIVE TEMPERATURE CHANGES IN THE OZONE LAYER By RICHARD

.

A.

CRAIG

Harvard College Observatory

THE OZONE LAYER The term "ozone layer" as used here refers to that part of the atmosphere that hes above the tropopause and below about 60 km. The bulk of the atmospheric ozone lies in this region. The physical characteristics of the ozone layer have been studied, principally from the surface of the earth, by various indirect methods. Some of the conclusions reached by these methods, however, have been verified by a few direct measurements obtained by means of manned and unmanned sounding balloons and rockets. The present state of knowledge with regard to the ozone layer is outlined elsewhere in this volume by Gotz.^ Gotz has also presented a very complete summary of ozone work as of the year 1938 [20] and in a more recent paper has brought this summary up to the year 1944 [21]. Even more recently Craig [10] has given a somewhat less comprehensive summary. Nevertheless, in order that this contribution may be more or less self-contained, certain basic facts about the ozone layer, particularly those that are necessary to an understanding of the remainder of this paper, are outlined briefly in this section.

Ozone Distribution. The total amount column above the earth's surface

vertical

of is

ozone in a small com-

pared to that of other atmospheric constituents, namely, about 0.3 cm at NTP.^ Nevertheless, because of its absorbing qualities, ozone is an extremely important constituent of the atmosphere.

A

large

number

of

measurements at the earth's

sur-

face have determined the variations with season and geographical position of this total amount of ozone.'

At a given

maximum fall.

The

amount and a minimum in the

place on the earth, the ozone

in the early spring

total ozone

amount

is

a

minimum

is

a

late

at the equa-

and increases toward higher latitudes. At least in the Northern Hemisphere, it apparently reaches a maximum near 60°N and decreases poleward from there. tor

A

further interesting feature of ozone distribution in middle and high latitudes is that the total amount of ozone above a given place may vary markedly from day to day. The amplitude of this variation of daily values in any given month may be as large as the amplitude of the annual variation of the monthly means. Moreover, the day-to-day ozone variations reveal marked correspondence to weather conditions at the surface,

1.

See

"Ozone

in

the Atmosphere" pp.

275-291

of

this

Compendium. 2. Ozone amounts

are generally expressed in terms of the height of the resulting volume of ozone if all the ozone in the

column were brought to normal temperature and pressure

at

the earth's surface. 3.

see

For references to published

series of

ozone observations,

[10].

292

as shown by Dobson and Olsen [55].

The

[12],

Lejay

[37],

and T^nsberg

been most genby means of the Umkehr effect. This effect, first noted by Gotz at Arosa and applied by Gotz, Meetham, and Dobson [22], refers to the observations vertical distribution of ozone has

erally studied

of scattered zenith light

zon.

The

when

the sun

ratio of the intensities of

is

near the hori-

two wave

lengths,

both absorbed by ozone but to different degrees, decreases as the sun nears the horizon, reaches a minimum, and then increases. This phenomenon results from the fact that the effective height of scattering increases as the sun nears the horizon and finally lies above the ozone layer. The shape of the Umltehr curve may be used to deduce the vertical distribution of ozone, as has been shown by Gotz, Meetham, and Dobson [22] for Arosa observations. Meetham and Dobson at Tromso [40], T0nsberg and Olsen at Tromso [55], and Karandikar and Ramanathan at Delhi and Poona [33] have also applied the method. The Umkehr method is only approximate, but its results have been verified

by various direct measurements [8, 9, 43, 47, 51]. The measurements show that the maximum density of ozone occurs between 20 and 30 km and that it decreases rapidly above the level of maximum. The density of ozone below the maximum level is quite variable. In fact, the observations show that most of the variability in the total amount of ozone (latitudinal, seasonal, and day-to-day) reflects variability between the tropopause and the level of maximum ozone. Temperature Distribution. The temperature distribution in the ozone layer, at least above 30 km, is less well known. In the vertical, the temperature between the tropopause and about 30 km is nearly isothermal. This region has been studied directly by radiosonde. Above 30 km, mainly indirect evidence points to a rapid increase of temperature with height, reaching a maximum at 50-60 km. This evidence is based on observations of the anomalous propagation of sound [58] and of the characteristics of meteor trails [38, 59, 60]. Recently, measurements from a V-2 rocket have verified this quahtative picture [31]. In the lower, isothermal region, where direct measurements are available, seasonal and latitudinal variations of temperature are known. In the summer, the temperature is lowest over the equator and increases toward the poles. In the winter, the poleward increase of temperature also occurs in lower latitudes, but a maximum of temperature occurs in middle latitudes and the temperature is again lower at higher latitudes [29]. At a given point in middle latitudes the maximum temperature in the lower part of the ozone layer occurs just before the summer solstice, the minimum just before the winter solstice. This contrasts with the behavior of the upper troposphere, where the maximum and

M "

RADIATIVE TEMPERATURE CHANGES IN THE OZONE LAYER

minimum

follow the solstices. Dobson, Brewer, and Cwilong [11] and Goody [19] explain this behavior as a balance between two conflicting factors. They point out that the temperature of the lower stratosphere is

by radiative processes, and is heated at least in part by ozone absorption of infrared radiation from the troposphere. The flux of this radiation reaches a maximum (or minimum) after the solstices. On the other hand, the amount of ozone reaches a maximum (or minimum) much earlier, just after the primarily

where

v is the frequency of the incident light and h is Planck's constant. Ozone is then formed by the collision of an oxygen atom, an oxygen molecule, and any third

body:

controlled

0.^-0 Ozone

seasonal variations, at least, Jacchia,

and Kopal

[60]

have shown from

their

O3

ing qualities of ozone. Laboratory measurements of ozone absorption reveal intense absorption bands in

the ultraviolet and less intense bands in the visible. The Hartley bands of ozone, the most intense of all, lie between 2000 and 3200 A, with a strong maximum near 2500 A. The Huggins bands occur in the 3200-

3600 A region. In the visible are the Chappuis bands at 4800-7800 A. The most detailed and homogeneous set of laborator5'-derived absorption coefficients stem from the work of Ny Tsi-z6 and Choong Shin-piaw [45, 46]

and

(2)

by absorption

of solar

From

+ +

hv (X


0 11. The Time Required for Establishing Equilibrium. By definition, n^ = dxpjdz; therefore, 2* is the level The "transition period" is the time needed to transform where (w^),- = (n.^),-; or {vs)i = {vs)ii that is, where the state (76) into (77). The special transformation, where initial j^s-curve intersects the final j's-curve (compare (maximum mixture) and Qu = 1 (Dalton equations (76) and (77) and, as an illustration. Fig. 3). Qi = atmosphere), was studied by Epstein [9] in terms of 100 Bessel functions, and by Maris [24] and Mitra and Raksit [26] with the aid of numerical and graphical integrations. Lettau [21] derived (68) and (73) in the 80 forms given above, which allow us to discuss more general cases where ;

^

< Qu ^

Q,

1.

(78)

s i 60 N

Since the gas is permanent, the total amount of smolecules in vertical columns of infinite height must be

t-

!£ UJ

40

I

constant,

=

^s

Us dz == const.

/

(79)

20

Jo

We

number

define the

=

iZ-s

lim

Hs dz,

I

=

v^n, it ris

\p,

=

-^s

(80)

z->x

•'0

Since Us

H-»

integral of s-molecules as

follows from (65)

=

Uso

and

+

exp[-(l

(72) that

fi,Q)z/H],

(81)

and ^.

(wso

=

1

Equation

—

n,)H

+ m4

^s

'

nsoH

= 1

relates

(82)

liso

to

+

= ^a/H =

=

const.

(82)

Q. Therefore, a general

value of the ground concentration WsOO

=.

M.Q

is

defined: (83)

Vsoono

Then, nso

=

+

nsoo(l

ns

fj-sQ);

= 1

Mi

=

VsOO

1

+

MsQ,

+

exp

exp[-(l M»Q i

— ixsQiz/H),

+

n.Q)z/H],

(84)

(85)

^

DIFFUSION IN THE UPPER ATMOSPHERE where

when (cs)?,- is the by the final diffusion

(n.Oi refers to, the initial state

vertical diffusion velocity as fixed

conditions

(Q,-,)

and the

concentration-distribu-

initial

tion {vs)i The changes of both v^ and c« with the progress of the transition are not considered; therefore, Ats in equation (91) represents a minimum value of the .

transition period.

Expressions more accurate than equation (91) could be obtained; however, the gain in accuracy does not justify the added complexity of computation in view of the crude assumptions that Q is independent of height and changes its value suddenly and simultaneously throughout the entire atmosphere.

With the

Ms =

aid of (87)

and

(91),

H (C»)^i[l+M.QJ

Let us investigate the three special transformations: (a)

(6)

^

complete mixture (Q; = 0) Dalton atmosphere {Qa

Dalton atmosphere {Qi

=

1)

1)

=

ei)

-^

partial separation (c)

=

{Qu

(93)

—

partial separation (Q, = ei) partial separation

when




i]

lOyT-^'

[sin i

-

(W/C)

cos^

(21)

i].

Equation (21) shows that for our problem the lapse rate y and the change a of wind velocity with elevation are more important than the ratio of the wind velocity to the sound velocity (W/C). For very flat rays (i near 90°) equation (21) leads to

>

a

from which

it

lOyT-^\

(22)

follows that under average conditions

in the lower troposphere (7 about 6C km~', T — 290K) the wind must increase with elevation by more than

about 33^ m sec~' kmr~^ in the direction of the sound propagation to bring the sound rays, which leave the source nearly horizontally, back to the surface. In the opposite direction the sound rays are curved upward more strongly than in still air (r is smaller). The following are a few critical values of a for straight rays under the same assumptions for y and T and sup-

W/C

posing that

is

0.1:

i

a

= dW/dz {m

sec-^ km-^)

80°

45°

3.1

2.5

5.7°

0°

-0.4

the ray curves downis smaller, the rays turn upward. It is noteworthy that in general the wave front is no longer perpendicular to the rays if sound is propagated in air in which the wind velocity changes If

a exceeds these

ward

in the

critical values,

wind

direction;

if

a

with elevation. If the paths of the rays are close to a part of a circle, use of trigonometry shows that the maximum height H* which is reached by a ray at the distance A is given approximately by

H* = If,

r{l

for example, a

T =

300K,

sec~^, r

=

A

TFo

=

= 5

-

[1

5

m

(^/2ryf^]

m

=

sec~' km~i, 7 sec-i (which gives

AVSr.

(23)

= 6C km~\ C = 348 m

235 km), the following values result: 1

km

i

89.9°

H*

lim

10 km 88.8° 54

m

100 km 77.6°

All preceding results are based on the assumption that the change in pressure during the process is small compared with the pressure itself. For larger changes in pressure, the sound velocity is greater than given by the preceding equations. Since the theory is very complicated and has rarely been needed in problems of sound propagation in the atmosphei'e, it is not considered here. Another assumption is that the wave length is small as compared with the height A of the homogeneous atmosphere, since otherwise dispersion results as an effect of gravity. Assuming that the gravitational constant g does not change with altitude (which does not hold for the higher parts of the stratosphere), Schrodinger [26] found that the velocity v of sound waves moving vertically upward is given approximately by

v/C

=

1

+

(1/32^2)

(L/AY =

1

-I-

0.003166 (L/A^, (24)

where L = wave length, C = sound velocity in quiet air and for waves moving horizontally; C is given by equation (7). For waves with periods of less than 1 sec, the last term in equation (24) is smaller than 10~ *, and the effect of the dispersion (long waves travel faster) is negligible. In addition, in most practical cases the sound waves travel much closer to the horizontal than the vertical direction, which decreases the effect of dispersion. The group velocity for waves travelling upward is given by an equation similar to (24) except that the last term is negative. For long waves, equation (24) cannot be used. In addition to the effect of decrease in gravity with elevaatmosphere affect the wave propagation. The theory for various models representing the atmosphere has been developed by Pekeris [23]. In addition to the body waves discussed above, tion, free vibrations of the

waves corresponding to

free oscillations

may

be ex-

cited within certain ranges of frequencies, depending

on

the assumed model.

Energy of Sound Waves in the Atmosphere. The energy and amplitudes of sound waves in the atmosphere with periods not exceeding a few seconds depend on two major effects: (1) absorption, and (2) changes

5M km

due to the increase (or occasionally decrease) in the distance between rays (which controls the energy flux).

values in the last column would normally be usethe assumption of circular rays is not fulfilled between the ground and an elevation of 5j^ km.

The absorption of the energy is iisually introduced by a factor e~*°, where k is the coefficient of absorption,

The

less, since

On

the other hand, the results show that conditions favorable to good audibility of sound waves to distances of many kilometers at the ground need not

extend to great heights. The preceding equations can also be used to answer the question, How close must a sound source at an elevation h be in order that the sound can be heard at the ground? If, for example, the lapse rate is 7 and the

wind is negligible, the maximum horizontal distance A* at which direct rays arrive at the ground is given approximately (assuming circular rays) by

supposed to be constant over the distance D along the kD has to be replaced by J/c dD. The propagation of sound is a molecular process. The velocity C of sound and the molecular velocity c are connected by the equation (see, for example, Schroray. If k changes along the ray,

dinger

[26]):

for air

As long A*

=

a (Th/y)^,

K

=

Cp/cv

{C/cy = K/3; = 1.403, and C = 0.6840c.

(25)

as the molecules are relatively close together, absorption of sound remains small. It increases rapidly

i

'

j '

SOUND PROPAGATION if

the

wave length L approaches the mean

of the molecules.

Schrodinger k

=

7rV3[(A'

-

[26]

free

path

I

writes

Fl/U,

(26)

where

F =\2

1)

AK-''-

+

4

BK-'%

K

= Cp/ci,; A and B are constants depending on the heat conduction q of the gas, its coefficient of internal friction u, the molecular velocity c, and the mean free path Z of the molecules: q

=

u/c

Ac,

=

Bd.

(27)

Schrodinger calculated from laboratory experiments F = 30.1 Kolzer [18] later used F = 33.0. Consequently, loss of energy E from absorption between two points close enough to each other so that the absorption can be assumed to be constant is given by ;

In (Ei/Ei)

= -

0.4343 Fl

D/U = - 0.0013 e'^'yU.

(28)

The

factor e'''* is based on the assumption of constant temperature throughout the atmosphere, but the resulting mean free paths are within the limits given by the N.A.C.A. tables for the stratosphere (see Table I).

Table

I.

Mean Free Path

{I

X

lO'"'*

cm) of Molecules at

Different Levels

IN

THE ATMOSPHERE

369

THE UPPER ATMOSPHERE

370

where A and B depend on the energy at the source. Neglecting the absorption along the path D (Fig. 5) the energy arrives on a zone of area Z perpendicular to the rays,

Z = The energy

7r[A2

E

flux

(A

C

5y\ cos

i

at the distance

=^= Z

= A

/d cos i\

^

E

-

Eoz

^) 5

A

27r6A cos

is

(31)

then given by

C(tan

'"-y = cos

i.

,

di i)

^

.

(32)

i

a constant depending on the energy at the source. factor tan i is partly a consequence of the fact that near the source less energy passes through the zone a (Fig. 4) than through the larger zone b (see also Fig. 6a). The greatest changes are produced by di/dA. If i changes slowly with distance (Fig. 6c), the energy flux is

The

near

B

is

relatively small.

simplify the picture, we assume that rays are parts of circles (r = radius). Then cos i = A/2r, and equation (32) becomes in this special case [8]

To

E* =

(C/A^)

[1

-

(A/r) (dr/dA)],

(33)

in energy with the square of the distance. It is evident that in general the energy at a given point is especially large if the (mean) radius of curvature r decreases rapidly with distance A (or with the maximum height reached by the ray). According to equation (20), this requires that either the wind or the temperature or both increase rapidly with increasing height in the region of the highest point reached by the sound wave. Focal points (caustics) will result if di/dA becomes infinite; this would correspond to Fig. 6b, if two rays with small differences in i arrive at the same point B. On the other hand, the energy decreases considerably with distance if the highest parts of the rays enter a region where the radius of curvature increases rapidly, until the limit for straight rays is reached (equation (21)) and no energy arrives at the ground. For rays through the stratosphere, the absorption must be considered, and

which shows the expected decrease

E =

(tan Ce-^f"^"

~A

i)

di (34)

dA'

INSTRUMENTS FOR THE RECORDING OF SOUND WAVES Most instruments used in recording sound waves through the atmosphere react to the change in pressure produced by the sound. In addition, records of distant explosions are sometimes obtained through seismographs; in such instances the vibrations of the atmosphere are transmitted by buildings or otherwise to the ground near the instrument. For sound-recording instruments, membranes or pistons which form a part of an airtight container of a given volume of air are frequently used; their movements are magnified either by levers which operate a recording pen, by the mirror of an optical recording system, or through electro-

magnetic systems which record by means of galvanometers. Even rather simple devices, such as a wire attached to the center of a windowpane and wound under tension around a thin needle carrying a mirror, have been used successfully for the recording of sound

waves from distant

explosions.

The magnification

of

these types of instruments for long-period movements equals their magnification for a constant continuous pressure; it decreases in the case of high damping to

about 25 per cent for waves with half the free period of the vibrating system and exponentially toward zero for waves with still higher frequencies. If the damping ratio is less than 23:1, resonance increases the magnification near the free period of the instrument [9] and produces a maximum there of about twice the static magnification for a damping ratio of about 23^:1. Many types of microbarographs with galvanometric recording have been developed in recent years. In Benioff's microbarograph [13] a permanent-magnet moving-conductor type loud-speaker mounted in one of the sides of a sealed container is used as the responding element. Output currents are recorded on standard seismograph galvanometric recorders. With a 1.2 sec galvanometer the maximum sensitivity is approximately 1 nun deflection for 0.001 mb. In the microbarograph of Baird and Banwell [2] a diaphragm thick, separates the body of of "dulalivim," 0.005

mm

the microphone into two compartments, one of which is closed to short-period pressure changes. Parallel to is a the diaphragm at a distance of about 0.015 brass disk which together with the diaphragm acts as a condenser whose capacity changes are magnified by electronic means and recorded by a galvanometer. The

mm

sensitivity is about 1-mm deflection for less than 0.0001 mb. In the instruments designed and built at the Naval Ordnance Laboratory, Washington, D. C. [1] to record the subsonic waves from the Helgoland explosion in 1947, the flexing of a diaphragm in a microphone alters one of two matched inductive circuits; the unbalance produces a signal voltage. This signal, the low-frequency modulation of an audiofrequency carrier, is amplified and used to drive a modified Est erline- Angus graphic recorder for which a response curve has been given by Cox [4]. The maximum sensitivity is about 0.8-mm deflection for 0.001 mb. Other microbarographs, such as Macelwane's, have their maxi-

maximum

mum

response for longer waves. Unfortunately, all these instruments respond not only to pressure waves, but also to pressure changes caused by air currents. If three instruments, forming a triangle with sides of somewhat less than one half the wave length of the sound waves, are used, the time differences between the instruments indicate whether the disturbance has travelled with the velocity of sound or with the much smaller velocity of air currents [3]. Simultaneously, the time differences between the passing of a given point of the same wave at two pairs of stations makes it possible to calculate the direction from which the waves arrive and their angle of inci-

dence

[19]

;

the sound velocity must be calculated from

the temperature.

SOUND PROPAGATION IN THE ATMOSPHERE

OBSERVATIONS AND THEIR INTERPRETATION Natural Sound. Microbarographs of sufRcient sensibackground which consists of the effect

tivity record a

of air currents and of natural pressure waves which are sometimes especially clear on calm winter days. There are several types of natural sound waves. At Pasadena, California, the most frequent are sinusoidal waves with variable amplitudes and periods of about 3^ to 5 sec [3, 13] (Fig. 7), corresponding to wave lengths of about

a

371

dence with high ocean waves at the coast, and the lack of other unusual phenomena make it likely that they are "sound" from surf. The causes of longer pressure waves which were recorded occasionally (Fig. 7c) could not be found due to the scarcity of the observations. Sound Waves through the Troposphere. When unusually strong sound waves from distant explosions were first heard, attempts were made to explain the observed zones of audibility and of silence by combinations of temperature, lapse rates, and change of wind with elevation [20]. This possibility was disproved by the occasional occurrence of instances in which the abnormal zone formed a full ring around the source of sound, separated from the normal zone of sound by a zone of silence. However, there are instances, not infrequent, of strong sound in relatively small areas, which are due to meteorological conditions in the troposphere. It follows from equations (20) to (22)

that either a temperature inversion, or a certain increase of wind with elevation (depending on the lapse or both jointly, may produce zones of strong sound. It is of interest to note that in the attempted explanations mentioned above an increase of wind with rate),

—

Fig. 7. Pressure waves recorded by Benioff microbarographs at Pasadena, (a) January 6, 1939; these coincided with the largest surf waves in several years near Scripps Institute of Oceanography at La Jolla; no meteorological element had unusuallj' great values within several hundred miles; the two apart, (b) records correspond to two instruments about 30 Pressure waves recorded on December 27, 1940, with three microbarographs forming a triangle with sides of 290, 320, and 264 m, respectively; these waves are frequent during the winter and arrive usually from the SW. (c) Pressure waves with longer periods, recorded on January 8, 1939, by two instruments 120 ni apart. (After Benioff and Gutenberg [3].)

m

m

by 4 or 5 sec~^ km"' was usually assumed together with the typical temperature lapse rate, after considering a variety of conditions; such requirements follow now from equation (22). Figiu-e Ua shows records with clear dispersion. Schulze [27] explained this dispersion as a consequence of the fact that the velocity changes with elevation, and because the energy of longer waves is propagated in a thicker layer than that of shorter waves. elevation

Strong audibility of certain sounds occasionally used

by laymen

the coast of southern California; as soon as the lowpressure area passed the coast, the amplitudes decreased rather rapidly. The waves arrived almost horizontally, but this is to be expected (even if the source is rather high in the atmosphere) due to the curvature of the rays. No connection with microseisms could be found. Similar air-pressure oscillations have been recorded in Christchurch, New Zealand [2]. Their periods were between 4 and 10 sec, and they showed similarity to microseisms, but a time lag of pressure oscillations, up to 200 sec, was suspected. Baird and Banwell beheved that the two types of waves are independent phenomena but possibly have the same cause. Polli (1949) found similar results in Trieste. Observations of these pressure waves at other locations are very desirable. Occasionally, short groups of pressure oscillations were recorded at Pasadena with periods of about J^ to 1 sec and occurring at intervals of about 20 sec (Fig. 7a). Their direction (from SW), their regular coinci-

of trains) is

weather based on the fact that the repeated occurrence of a certain unusually strong sound from the same source will frequently be a consequence of similar meteorological conditions at a given

forecasting. This possibility

100 m to 1500 m. In general, they are largest in winter. During the three winter months of 1940/41, three microbarographs were operating (Fig. 75) which permitted the calculation of the direction from which the waves arrived; all came from southwest to west (azimuths between west and 40° south of west). In all instances of large amplitudes a low-pressure area was situated off

{e.g.,

for short-range

is

place.

Sound Waves Through the Stratosphere and Abnormal Audibility Zones. In 1903 an accidental explosion of dynamite in Westphalia resulted in sound waves which were heard far away, beyond a zone of silence. The observations were investigated by von dem Borne who believed that an increase in the percentage of light gases with elevation in the atmosphere causes an increase in sound velocity. (For historical data and bibliographies see [28, 10].) The details of these abnormal zones were studied in instances of artificial explosions, especially in

Germany

[16], of

gun

fire,

and

of

accidental explosions, using ear observations (Fig. 8) as well as instrumental records. There are instances

where the abnormal zone forms a complete ring around the source, and others in which only parts of a ring with audible sound were developed. Frequently, parts of a second or third ring of abnormal audibility were found (Figs. 8 and 9). In Europe and in Japan, the radius of the ring as well as the distance of the largest sound intensity shows a yearly period (Fig. 10) with a minimum distance of about 100 km late in winter or early in spring,

THE UPPER ATMOSPHERE

372

and a maximum (about 200 km)

late in

summer

[28;

Europe, the ring is much better developed to the east of the source during winter, 29, pp. 184-187]. In central

usually larger than 0.98. If the temperature at the point of observation is more than about IOC higher than at the source (continent in summer, ocean in winter), it becomes increasingly probable that this difference makes

the return of the ray to the ground impossible; the rays turn upward again at a level with a temperature given by equation (10). Similar effects can be produced by prevailing winds (equation (19)).

Records show relatively small differences in travel time of rays to the abnormal zone between day and night [19], although details of the records change grad(Fig. lib). Wide variations in the amount of explosive do not result in different travel times. This proves that the return of the rays to the ground is not

ually

affected

—

Fig. 8. Observations ot sound waves through the stratosphere after explosion of 5000 kg of ammunition, December 18, 1925. {After Hergesell and Duckert [16].)

to the west during summer. This is due to the fact that the rays have rather large angles of incidence (normally between 75° and 90°) so that at the source sin i is

Fig.

9.

— Sound

by an

increase in the ratio of the pressure

change to the pressure itself and that, even at the highest levels reached by the rays, equation (7) holds. This conclusion has been confirmed by the agreement between the temperatures calculated from equation (7) and those found from records made with V-2 experiments (Fig. 12). Finally, records taken at equidistant points in opposite directions from the source did not give appreciably different travel times. Therefore, the

conclusion can be

drawn that

relatively high tempera-

tures in the stratosphere account for the sound in the

outer zones, as suggested

by Whipple

[30].

intensities observed after an explosion near Vergiate, Italy. [After Oddone.)

— SOUND PROPAGATION Annual changes in the travel-time curves (Fig. 12), and the annual period of the radius of the zone of abnormal audibility, are caused by (1) annual changes

IN

THE ATMOSPHERE

373

the angles of incidence corresponding to the travel-time curve [b in Fig. 12); usually they change little with distance. Equation (14) gives the horizontal distance (b)

250 ^MAXIMUM

I

INTENSITY

I

-k'

(•)

|^5~-^l

—^tv-*-

•^yV*—;A(V'

4t%

or


or

^zz

— fgde

(S-^>

Ar^-^£?;^10-'to

lO-^ec-l

e

(33)

as well as from (2),

/

du

dQ an

ae an

dz

dy dz

dz dy (34)

edy

2kco

or

Ve-curl

U
/), Vd is a pure imaginary, the corresponding displacement increases exponentially with time, and the oscillation is unstable. We also observe that the period td is greater or less than the Foucault pendulum halfor < 0. In the day depending on whether 8u/5y > first case, which is the one usually encountered in the atmosphere, the period td is of the same order of magnitude as the period of cyclonic waves. When, through an increase in the baroclinity, 8u/5y finally exceeds the threshold value / (0 < / < Su/Sy) the quasi-isentropic inertial oscillations of period greater than the Foucault pendulum half -day and the hydrodynamic equilibrium for corresponding transverse displacements become unstable simultaneously. It is worth noting that the inertial oscillation which may become unstable in the atmosphere is a quasi-isentropic oscillation whose period is precisely of the order of the period of atmospheric disturbances [31], and that this instability can appear only where these disturbances would normally occur [34, 37]. In summary, there exists a unique and reciprocal correspondence between the stability and instabihty of inertial oscillations in the atmosphere on one hand, and the stability and instability of hydrostatic and hydrodynamic equilibrium on the other [34, 37].

Hydrodynamic

Instability

and Cyclogenesis

in Extra-

tropical Latitudes

ponents of the acceleration of the air are practically zero. We can then reasonably assume that the state of geostrophic motion in these regions is that which precedes the initial stage of cyclogenesis. If we suppose

=

that the geostrophic current u is zonal (a = 0, coi 0), any particle displaced in the interior of this current r^) r^ ry z from point {x, y, z) to point {x y acquires an orbital motion according to equations (47)

+

+

,

+

,

(48)

du

du

dy

dz

Ty

=

^^..(51)

iv

i^a and ^p^ are the meridional and vertical comwhich acts on the displaced parponents of the force ticle because of the nonuniformity of the field of flow u and of the field of potential temperature 9 associated with it [20]. These components are given by

Here

i^r

where

=

;

=

period (approximately 10 min) and of an amplitude which is smaller the greater the stability, the particle returns to its equilibrium position in the geostrophic current [39, 40]. Therefore, in an atmosphere possessing vertical hydrostatic equilibrium in which the air undergoes adiabatic transformations only, we can assume as a first approximation that on a synoptic scale the air particles are displaced along isentropic surfaces. The existence of these isentropic displacements, favored by vertical stability, led Rossby [29] to the concept of lateral mixing and Raethjen [27] to the similar idea of Gleitaustausch of the air. To the approximation adopted above, the inertial oscillations of long period take place in the isentropic surfaces, and we are led to consider isentropic displacements. In this case we have {dQ/dy)ry -f- {dQ/dz)r^ = 0, and consequently the transverse force ^ which the surroundings apply to the displaced particle is horizontal to a iZ-j

=

approximation; this gives

first

The

0.

particle

and the

=

vo

=

—vlry and

then defined by the differential system

is

r-x

j-y

\py

horizontal orbital motion of the displaced

-

{vl/f)ry

initial

,ioT

t

=

0,

conditions r^

=

=

to

Two

0.

=

-|-

Viry

r^

=

=

(53)

0,

and

r^

=

0,

cases can be distinguished

depending on whether the meridional force is a restoring {ipyry < 0, stability) or a force which carries the displaced particle always farther from its point of de-

force

parture

(ipyry

>

0, instability) [39, 40].

=

—

>

0. In this case the parametric equations

8u/8y) {f integral of (53) is an ellipse with r^

=

Vo, '^ {I

f

—

cos

ry

Vdt),

= Vo

/

sin Vdt.

(54)

" 0) or descends {vo < 0) along the isentropic surface. The major axis of the ellipse is longitudinal or transverse depending on whether the vorticity, proinitial position in

r.= [f-

^y

=

First case: vl

Far from any perturbation, the vertical component of the velocity and the horizontal and vertical com-

and

r^ 9^ 0). In this case the earth's rotation can be and i^z neglected (/ —vlrz. 0) therefore lAj/ Since the vertical distribution of mass is assumed to be stable, the vertical force 4'^ is a restoring force which tends to bring the displaced particle back to its point of departure, so that after several oscillations of short

0,

^

vl

,v]

-v\ry ,

and

+ A''

Nr^,

^,

^ Nry

have been defined

-

v]r„

(52)

first

face, is cyclonic {Su/&y

anticyclonic

(0


0) or descends {vo < 0) along the isentropic surface. The longitudinal axis is the transverse^ axis of the hyperbola and is the major or minor axis depending on whether Su/Sy > or < 2/. The hyperbola is equilateral when 8ii/5y = 2f. We observe that the curvature of the branch of the hyperbola increases with the hydrodyas namic instability. However, here Tx is > or < rj, < or > and consequently the unstable isentropic inertial oscillation generates cyclonic circulation. Once set in motion, this circulation is maintained by the energy of instability released in the course of the isentropic displacement of the air particles. As before, it could be shown that the transverse isentropic exchange of air involves in this case a weakening of anticyclonic

face which passes through

its

\

vorticity (0

> —/ >

—Su/5y), that

is,

a diminution

hydrodynamic instability. The cyclonic circulation which results from transverse isentropic displacement of the air in an nnstahle geostrophic flow tends to reestablish a state of stable dynamic equilibrium in the of the

isentropic surfaces.

The

result of this stabilizing action

that isentropic hydrodynamic instability is only a transitory state of short duration, which, according to what we have seen earlier, can develop only in regions is

of

follows directly from the

of a westerly geostrophic current

terion for

hydrodynamic

pronounced baroclinity.

l.As used here, the term "transverse" refers to the which passes through the vertices of the hj'perbola.

axis

u and from the

cri-

instability that this instability

= const and u = can appear only when the surfaces const are closely packed and intersect one another at a large angle. By referring to the vertical meridional cross sections of Palmen [22-24], we can verify that these conditions are established in only two regions [40]: (1) in the upper troposphere between 200 and 500 mb south of the belt of maximum westerlies, where du/8y — / is positive and of the order 10~^ sec~\ and (2) in the lower troposphere between 600 and 900 mb in the zone of the polar front and immediately north of it. We observe that in the latter region the isopleths of should be replaced by isopleths of the wet-bulb potential temperature, whose slopes are necessarily larger; actually therefore, the

hydrodynamic

in this portion of the lower troposphere

regions,

=

it

definition of the isentropic meridional gradient 5u/Sy

Palm^n's cross sections make

equations ri

443

hydrodynamic

it

instability

is

instability

greater than

appear. In these two

may

occur.

On

the other hand, (1) in the higher troposphere north of the belt of maximum westerlies the isopleths = const are practically parallel, and u = const and (2) in the lower troposphere south of the belt of maxi= const are nearly mum westerlies the isopleths horizontal. Hence these two regions are normally characterized

by pronounced hydrodynamic

stability [40].

In the higher troposphere, consequently, meridional isentropic displacements of air particles bring about the formation of cyclonic circulation at low latitudes in the temperate zone and anticyclonic circulation at higher latitudes [40].

The

existence of these

two

circulations

has been demonstrated by Rossby, Palmen, and their collaborators [32]. On the other hand, in the lower troposphere, meridional isentropic displacements of air particles bring about the formation of cyclonic circulation at high latitudes in the temperate zone and anticyclonic circulation at low latitudes in this zone. The existence of this latter circulation was shown by Wexler and Namias [45]. The cyclonic circulations at middle latitudes in the lower troposphere are simply those characterizing the normal activity of the polar front. In summary, when the geostrophic motion becomes

unstable for isentropic and quasi-isentropic transverse displacements in a baroclinic region of the atmosphere, the surrounding medium favors these displacements; the displaced particles set free energy of instability which augments the kinetic energy of the initial impulse [35-37]. Moreover, they acquire cyclonic circulation relative to the geostrophic current along branches of hyperbolas whose conjugate axes are perpendicular

to the geostrophic flow

Thus we

perceive that

[39].

an isentropic

inertial oscillation

of period greater than the Foucault pendidum half-day (27r//), which becomes unstable in a region of large baro-

may give rise to a cyclonic circulation. A nascent cyclonic circulation hence seems to be no more than an unstable inertial oscillation of the atmosphere [31, 37]. But such a circulation inevitably involves major displacements of air and consequently a perturbation clinity,

DYNAMICS OF THE ATMOSPHERE

444 of the pressure field.

dWdU

inertial character.

dx' dx'

The motion then set up loses its In short a theory of cyclogenesis cannot be established without consideration of a pi'essure perturbation [31, 42]. Hydrodynamic

and the Theory

Instability

of

Atmos-

pheric Perturbations

In order to simplify the equations, we will designate x^ the horizontal meridional coordinate y and by x^ the vertical coordinate z hence the Eulerian variables and t. In this X, y, z, and t will here be written x, x^, x system of notation we have: cnx = 0, 2o3y = 2a) cos

by

;

,

the current u, whether cyclonic |

When

dy

an

particles acquire

cyclonic circulation with respect to the current u (see

u Ry

W + u being the absolute velocity of the

the current u is stable, this exchange can only at the expense of the surrounding

itself

medium, and the displaced

2co„ -f

.

When

maintain

|

fits

|

|

{Ris

).

>

it

when

it is

In this case, 0) or

weakly

with \Ris\ > \R%\) will be transformed progressively into an anticyclonic current whose radius of curvature will approach the limit lO" m. On the other hand, if the current u R*s were unstable {Ris < and Ris < R% ), the transanticyclonic

{Ris


Rt approaches the limit Rt would thus appear to be a current of some persistence [46]. Inasmuch as hydrodynamic instability is a transi\

|

I

\

I

tory state of ephemeral duration, it will not manifest itself unless its cause is of even less duration {i.e., produced instantaneously); according to Kleinschmidt

DYNAMICS OF THE ATMOSPHERE

448

[18], large-scale condensation is such a cause. The gradient bu/5y in a cloud layer should be determined in surfaces of equal wet-bulb potential temperature rather than in surfaces of equal dry-bulb potential temperature. Inasmuch as the slope of the former is much more marked than that of the latter, it follows

that bu/by undergoes, at the moment of condensation, a sudden increase which is capable of bringing about hydrodynamic instability {Su/Sy > /). We then have Ru > and, as a result, the current u will spontaneously become a cyclonic current of the stable domain (0 < Ris ^ R*s) (cyclogenesis according to Wipper-

mann

it is evident from (78) that the zonal circulation in tropical regions can reach the threshold of instability more easily than that of

eter increases with latitude,

temperate regions. However, inasmuch as the isentropic nearly horizontal, is favored there. Finally it is easy to show, using criteria (81), that the permanent circular vortex is stable or unstable depending on whether its absolute angular momentum 911 = R{u -f- Rw) increases {d'dR/dR > 0) or decreases (59R/6i? < 0) toward the exterior of the vortex in the surfaces in tropical latitudes

isentropic surfaces

The

[46]).

state

ical

Circular Vortex. Application to Trop-

Cyclones

The problem of the stability of this state of motion has been treated in several different ways [2, 5, 6, 8, 9, 13-18, 21, 31]; we will consider it here as a special case of permanent, horizontal, isobaric motion. To this end we compare the atmosphere to a circular vortex around we adopt Kleinthe polar axis and at some point schmidt's coordinate system OXYZ, having axis OX and directed easttangent to the parallel through ward, and axis OY perpendicular to the vortex axis and directed toward the earth's interior. Under these conditions, dY = —dR, Ry = R, Rz = oo where R is the radius of rotation from 0; there follows from (76), ;

+

a-YY

2C0

-

^ oY^ R, -K

'-i

anae dfdY'

anae

-2(a,-t-^y-"---, ^ RjdZ dYdZ'

(Iyz

\

'

anae OzY

anae azz

~dZdY'

where arz

=

azY

=

arz

dZdZ'

and u

,

zonal velocity of the here to

a

(79)

CIyy

air.

=

u{R, Z) represents the The discriminant a reduces

dzz (80)

=

2

dZ 8Y

R

where gz

is the absolute value of the component of gravity parallel to the earth's axis. Since the inequality dQ/dZ > generally holds in the atmosphere, the permanent circular vortex is stable or unstable depending on whether

^-j,2co+-.

[2],

neutral

equilibrium

by the invariance

of

(S9R/5jffi

=

0),

absolute

on page 436. Moreover, the method we followed in studying the inertial oscillations of a geostrophic current (pp. 032040) will naturally extend itself to cover the case of a stationary circular vortex [31]. We thus obtain the results which we had established earlier for the case or a of zonal geostrophic motion (coi 0, ir).

=

=

Similarly, the equations of adiabatic perturbations of

gzdQ du

+ R/e

of

angular momentum 911 in the isentropic surfaces, would be the state of exchange equilibrium {Austauschgleichgewicht) according to Raethjen [27] and Kleinschmidt [18]. In other words it is that equilibrium condition toward which atmospheric air would tend if subjected to isentropic lateral mixing, Raethjen's Gleitaustausch, or Rossby's lateral mixing. If this condition prevailed, the lateral Reynolds stress Tl due to isentropic turbulence would be proportional to 8u/Sy — / (neglecting the curvature term in (78)), where x represents the eastward tangent to the parallel and y the northward tangent to the meridian. However, this is true only if the isentropic turbulence is purely transverse. In reality the turbulent particles move in the isentropic surfaces parallel to the mean flow as well as perpendicular to it. Priebsch [25] has been able to show that the stress Tl is actually proportional to 8u/5y and not to 8u/8y — /. As a result, the absolute angular momentum relative to the earth's axis of rotation is not an invariant property of isentropic exchange of air [44]. We observe that the permanent circular vortex satisfies an extremum principle [38] identical to that stated characterized

The Permanent

are

stabilization of the zonal circulation

(81)

The cii'culation along the parallels being cyclonic or anticy clonic as u > or < 0, we observe that anticyclonic circulation favors the instability of the vortex. Consequently an easterly zonal circulation will become unstable more easily than a westerly one. Since the zonal circulation is easterly in tropical latitudes and westerly in temperate latitudes, and the Coriolis param-

a permanent circular vortex can be derived in the same way as those for a zonal geostrophic current (pp. 444-446) provided cylindrical or spherical coordinates are used. This problem has recently been treated in terms of cylindrical coordinates, in a slightly different fashion, by Queney [26], who has in addition proposed a method for the simplification of the equations

which differs from Charney's [4]. Let us further note that Fj0rtoft [10] has recently taken up the study of the stability of stationary circular vortices with the aid of a new method based on the primary integral of the equations of motion (integral of the equation of mechanical energy) and utilizing the calculus of variations. Finally, we consider a permanent circular vortex whose vertical axis z is located at latitude 0. If we designate by u the linear velocity of the vortex, w >

HYDRODYNAMIC INSTABILITY


0), decreases or increases depending on whether the vortex is stable

or unstable. It follows that

when

vertically oriented, unstable,

circular vortex undergo

a an

the air 'particles in

outward radial, isentropic displacement, they release instability energy which reinforces their cyclonic circulation around the vertical axis of the vortex. According to Sawyer [30], this mechanism plays an important role in the formation of tropical cyclones. The probable truth of this opinion is enhanced by the fact that at low latitudes the Coriolis parameter / is relatively small (10~^ sec~^) so that condition (82) there than in middle latitudes.

is

more

easily

fulfilled

Inertial Oscillations of

an Arbitrary Flow

has given the equation of circular frequencies an air parcel in arbitrary motion. This more general problem has recently been taken up by W. L. Godson [11]. If the atmosphere is referred to a right-handed Cartesian system, x x x chosen at random but at rest with respect to the earth, the equation of motion and the equation of continuity are, respectively, Ertel

[7]

of the inertial oscillations of

,

dx

df

an dx'

_

a$ dx'

|49

DYNAMICS OF THE ATMOSPHERE

450

summation with respect to the index the normal differential system

= -L

LiAx")

The

we then have

i;

pression,

(86)

'(«t?)^

general integral of the nonhomogeneous linear is composed additively of a particular

system (86)

integral of this

homogeneous

system and the general integral system

in

the

of

differential

LiAx")

=

=

(fc

0,

(87)

3)

1, 2,

which

^-

S+ + P=

^^'•^^-

+

(7.7

I'd

0,

I'd




0,

\

„

^J

dQ

edy'

< C


w

GS)'

are unstable unless a layer of smaller is underlying one of greater sta-

vertical stability

coi)]

bility.

and Vt '^ exp

[ii/xx

+

wt)]

3.

Compare with the

result obtained

on

p. 457.

:

:

:

DYNAMICS OF THE ATMOSPHERE

460

Fj0rtoft Assumptions Incompressibility. Vertical stability zero.

1.

2. 3.

Constant Coriolis parameter: df/dy

4.

Finite atmosphere bounded at distance h apart.

=

0.

by horizontal

walls

Conclusion All

;

waves are unstable

if

and only

W

\h)

if

\d~z)

/

may

be remarked that Eady's second conclusion will no longer hold if the simplification mentioned in his fourth assumption is not made, in other words, even the infinite atmosphere with unifortn vertical stability will be unstable if account is taken of the fact that density diminishes to zero for increasing heights. The appearance of a stabilizing influence from the vertical shear for short wave lengths in Fj0rtoft's conclusion is due to effects to be discussed at the end of the following section. This stabilizing effect could not possibly appear in the other studies because there (o) 2Tni/LY was neglected compared with f [14, pp. It

the linearized equations, particularly when there is a variable zonal current [18]. It is, however, possible and also useful to obtain an understanding of several of the most important barotropic phenomena by direct physical considerations [14, pp. 15-35]. In the following discussion this kind of argument will be used. We will make the purely formal simplification of assuming that the horizontal motion takes place as if on a circular disk however, / will be kept a variable parameter. One of the physical principles which may be used for a general discussion of some barotropic phenomena is the conservation of total angular momentum

+

R is

Here

uR dF =

const.

(31)

the distance from the pole, and dF a surface By introducing the

element in the plane of motion. velocity circulation

c

=

uR

I

d^p

along zonal

circles,

Jo

(31)

becomes equivalent t6

rcdF =

const.

Another equivalent expression can be

(32)

easily be

shown

to

[14, p. 21]

41-42].

G = Barotropic Disturbances

In the case of barotropy there can be no vertical in the state of quasi-balance which characterizes the motions with which this article is concerned. Equations (18) and (21) therefore reduce to

wind shear

Di abs

=

0;

dt

Vv

=

0,

(30)

J UsiRo

,

h)R^ dF =

const.

(33)

represented as a function of Lagrangian is therefore independent of time because the absolute vorticity is conserved, and R represents the generally time-variable radial positions of the fluid particles. Equation (33) is now a condition which restricts all future radial positions. In Fig. 3

Here,

fabs is

coordinates,

and

with the asterisks now dropped as superfluous. These equations represent the classical equations for conservation of vorticity in a two-dimensional nondivergent flow of a nonviscous fluid. The fundamental investigation of wave motions in such flows was carried out by Rayleigh [22]. Although in the studies of polar front waves the destabilizing effects of a gliding discontinuity were considered to be important, it has not been until

phenomena in their full and complex generality have been taken up for systematic investigations, primarily by the Chicago school of meteorology. Starting with Rossby's work on planetary waves [24], in which the specific importance of the variability of the Coriolis parameter was discovered, a series of papers have followed in which different barotropic phenomena have been discussed. Briefly, one may say that while some of them, apart from the modifications following from the spherical shape of the earth, are analogous to the classical works by Rayleigh, others represent original investigations as exemrecently that barotropic

by those treating stationary solutions of the nonlinear vorticity equation [9, 13, 17, 20]. The mathematical solution of (30) involves, of course, all the difficulties connected with the solution of nonlinear equations. The difficulties may even be very great for

Fig. 3.- Isolines for the vertical

component

of absolute

vorticity.

plified

the irregular lines are curves of equal absolute vorticity for the case that fabs varies monotonically from one isoline to the other. Clearly, a necessary and sufficient condition for having a pure zonal flow is that the lines

STABILITY PROPERTIES OF LARGE-SCALE ATMOSPHERIC DISTURBANCES of equal vorticity have a zonal distribution. The motion corresponding to the vorticity distribution in Fig. 3 is therefore certainly not zonal. It may now be inferred from (33) that neither can it be so at any later time. The reason for this is that by varying the positions of the fluid particles, G assumes an extreme value if and only if the lines of equal vorticity are zonal. In the present case this extremum would be either an absolute minimum or maximum. Therefore, the isolines of faba could not possibly become zonal unless at the same time G varied in contradiction to (33). Thus, at all

simply the reversal of the one stating that it was not possible to come arbitrarily near to a zonal distribution. The corresponding zonal flow is, therefore, stable in this case. Let f o + / and f o be the initial vorticities

mean zonal flow and in the disturbances. expression and criterion for the present stability is in the

M ^h" dF ^ M ~^0 when

times one must have f ^'^dF

^

(m

m,

>

(34)

0),

f

where a prime again has been used to indicate deviations from zonal means. With possible exceptions for some singular cases, it can be shown that (34) must be true for a quite general distribution of vorticities. A problem of considerable interest is involved in the question as to what will happen in a barotropic

atmosphere left with a certain distribution of vorticities that do not correspond to a motion which is stationary, either absolutely or with respect to a coordinate system rotating at a constant speed. Will the structure of the subsequent motion tend to approach a more or less definite limit, or will different structures be repeated more or less periodically? Synoptic experience is probably most in favor of the first point of view, though there have been attempts to interpret some cycles in the general circulation on a strictly barotropic basis. In favor of the first point of view one can at least say with certainty that theoretically no oscillations in the strict sense are possible. This is because in a purely oscillatory motion the fluid particles would simultaneously have to reassume earlier positions,

but with different velocities. However, this

is

impossible because, according to the conservation of vorticity, the positions of the fluid particles determine uniquely the vorticity distribution which in turn determines the velocities.

From there

is

the condition also

/

f

'^

dF

an upper limit to

+ /

fi,

dF =

const,

t^dF, so that (34)

may be extended to

M a/r- dF > Returning now to the kind which are illustrated in Fig.

(m

>

0).

(35)

of vorticity distributions 3, it will

be assumed as a

particular case that the vorticity distribution deviates only slightly from a zonal one. The corresponding flow

a zonal flow upon which there are superimposed small disturbances. The time-invariant value of G will now be but slightly different from a maximum or minimum value, which implies that no change in the vorticity pattern from the nearly zonal one to one charactei'ized as in Fig. 3 can take place without necessarily changing the value of G. The proof for this is

is

461

+

/

(m

m,

/

fo'

>

dF -^

An

0),

(36a)

0,

(366)

varies monotonically with latitude. (36c)

It should be mentioned that the result which has been found that polar anticyclones are always unstable in a barotropic atmosphere [23] cannot be true if (36) is true. That is because anticyclones may exist for which condition (36c) still may be true. Suppose now again that the absolute vorticity for the mean zonal flow varies monotonically with latitude and consider the possible changes in the mean zonal flow which will result from the meridional exchange of air. It may be assumed, in accordance with the

most frequent conditions, that

d(fo

+

f)/dy

>

0.

One

has

u

= 2tR

2irfl

Jf

F is the area north of the latitude circle which is being considered. Since equal areas of fluid are going in and out of a latitude circle, u will have to decrease or increase according as the vorticities leaving the circle are replaced by vorticities of lower or higher magnitudes, respectively. Now, each fluid particle is assigned

where

+ +

a certain absolute vorticity fo / f o which is moving with the particle. The effect of this transport may be considered as a separate effect from those of the transport of f / and of f o As to the first effect it is easily understood that because fo / is increasing northwards, air streaming out of a zonal circle will have to be replaced by air with lower value of the absolute vorticity. This effect, when considered alone, will therefore amount to a decrease in c at all latitudes. This is in conflict with the principle of the conservation of total angular momentum, equation (32). It can, therefore, immediately be inferred that the effect from

+

.

+

the transport of the initial irregular vorticities must be to compensate exactly this loss in angular momentum, that is, to create in the mean a compensating [14, p. 28]. In consequence of this it be concluded that, in the mean at least, the air with positive fo has to be transported to the north, and that with negative fi to the south. In the special case of a stationary flow pattern, as for instance for the Rossby waves, the two effects compensate each other exactly at each latitude. In other cases, however, one can only expect that the compensation is accomplished after integration over all latitudes. It has been

westerly flow

may

assumed by Kuo

[19]

that the effect of the transport

DYNAMICS OF THE ATMOSPHERE

462

of the irregular vorticities will be the dominating one at middle latitudes, resulting there in an increase of the westerlies. However, the arguments used are not convincing, and without carrying out numerical calculations nothing certain can be said with respect to the resulting changes in the mean zonal flow. Preliminary calculations [15] seem to indicate that rather than increasing the westerlies at middle latitudes, the tendency under certain conditions may as well be to decrease the westerlies at middle latitudes and increase them in belts to the north and south, particularly to the north. In a barotropic atmosphere the energy equation re-

duces to

lw^dF=-j Jw

dF

-\-

const.

Consequently, there is an upper bound to the kinetic energy of the disturbances. In the case where f abs varied monotonically from one isoline of vorticity to the next it was found that there must be a lower bound to /

f '^

dF which

is

from

different

zero.

The same must,

-j-ifo+f)>0

where -^

is

large,

(40) -;- (fo

dy

The •un/R

and

trivial case

—

+ /)
0. By similar arguments one will find that u on the other hand has to increase where d(fo f)/dy < 0. So, the necessary conditions for real instability will be that

+

+

+

which furthermore must tend to be the dominating effect for the shortest wave lengths. An understanding of the stabilizing influence arising from vorticities, fo

(38)

= —

+

increase as a result of a transport of fo f- Therefore, when the shortest waves become stable this can only be a result of the transport of the initial irregular

Writing

,

the transport of irregular vorticities may be obtained in the following way: Suppose a wavelike disturbance with untilted troughs and ridges to exist initially in a nonuniform zonal current. The instantaneous transport of the irregular vorticities is accomplished by a component Moi of the mean flow and a component Vo of the irregular flow. When small disturbances are considered, or disturbances in which Vo is essentially parallel to the lines f o = const, only the transport by the first component has to be considered. It is now obvious that if the angular velocity uq/R varies with latitude, the lengths of the lines f' = const have to increase as a result of this transport. On the other hand, the areas enclosed by these lines are conserved as are also the values of f because the effects of the transverse displacements of the vorticities fo / are disregarded in this connection. Consequently, it follows from Stokes' theorem that the velocity circulation for the disturbances taken along the closed curves yf = const, which approximately are also streamlines for v', must remain '

+

'

STABILITY PROPERTIES OF LARGE-SCALE ATMOSPHERIC DISTURBANCES constant.

But

v' increase,

since the lengths of the streamhnes for

the average intensity of

|

v'

|

3.

must decrease

correspondingly. When this stabilizing influence dominates the destabilizing influence from the transverse transport of vorticities of the basic flow, which can be shown to be the case for the shortest waves [14, p. 31], kinetic energy must flow from the disturbances to the

deei-ease

where u/R

is

4.

5.

6.

Baroclinic

and Holmboe,

J,,

"On

the Theory of Cy-

Bjerknes, V., "Application of Line Integral Theorems to the Hydrodynamics of Terrestrial and Cosmic Vortices." Astrophys. norveg., 2:263-339 (1937). and others, Hydrodynamiqiie physique. Paris, Presses Universitaires de France, 1934.

Charney,

J. G., "The Dynamics of Long Waves in a BaroWesterly Current." /. Meteor., 4:135-162 (1947). "On the Scale of Atmospheric Motions." Geofys. Publ., Vol. 17, No. 2, 17 pp. (1948). FJ0RTOFT, R., and Neumann, J. v., "Numerical Integration of the Barotropic Vorticity Equation."

clinic

7.

small. 8.

Combined

J.,

clones." J. Meteor., 1:1-22 (1944).

mean

flow so that in accordance with what was said above, u will have to increase where u/R is large and

Bjerknes,

463

and Barotropic Disturbances

Tellus, 2:237-254 (1950).

While there is enough evidence for the importance both of baroclinic and barotropic effects, there must be a limit to the extent to which phenomena can be explained purely barotropically or baroclinically. In general, one must expect that barotropic and baroclinic effects either add together in a more or less simple fashion, or they may be coupled to such a degree that the consideration of both effects simultaneously may give rise to entirely new types of phenomena. The only studies until now on waves for which both potential and kinetic energy are possible sources for the growth of the disturbance are those on polar front waves. Because of the complexity in the solutions for these waves one does not know whether the one or the other of these two possible sources is the more important, although the shearing instability has been interpreted as the decisive one, seemingly, however, without anyconvincing justification. The unstable baro-

waves treated in this article have accordingly been looked upon as physically entirely different waves.

9.

178 (1945). 10.

not true. Further investigations on this subject can be carried out with relative ease when the quasi-geostrophic approximation is made. Relatively simple equations appropriate for the most simple polar front model have been worked out by Phillips [21]. It is not unlikely that the study of an atmosphere where typical barotropic and baroclinic effects are operating in full generality may contribute considerably to a further understanding of the behavior of the atmosphere. For this purpose equations (23) and (25), or essentially similar equations, may prove useful, at least for theoretical investigations, because of their is

the writer's opinion that this probably

lished manuscript (1951). of Motion with Pressure Independent Variable." Geofys. Publ., Vol. 17, No. 3,

"The Quasi-static Equations

12.

as

44 pp. (1949). 13.

Ertel, H., "Die Westwindgebiete der Troposphare

als

Instabilitatszonen." Meteor. Z., 60:397-400 (1943). 14.

15. 16.

FJ0RTOFT, R., "Application of Integral Theorems in Deriving Criteria of Stability for Laminar Flows and for the Baroclinic Circular Vortex." Geofys. Publ., Vol. 17, No. 6 (1950). Unpublished manuscript, 1950. H0ILAND, E., "On the Interpretation and Application of the

17.

is

great simplicity and generality.

Eady, E. T., "Long Waves and Cyclone Waves." Tellus, Vol. 1 No. 3, pp. 33-52 (1949). Eliassen, a., "Slow Thermally or Frictioually Controlled Meridional Circulation in a Circular Vortex." Unpub,

11.

clinic

It

Craig, R. A., "A Solution of the Nonlinear Vorticity Equation for Atmospheric Motion." /. Meteor., 2:175-

18.

Circulation

Theorems

of

V.

Bjerknes."

Arch.

Math. Naturv., Vol. 42, No. 5, pp. 25-57 (1939). "On Horizontal Motion in a Rotating Fluid." Geofys. Publ., Vol. 17, No. 10 (1950).

Kuo,

H.-L.,

"Dynamic

Nondivergent Flow

in

Instability of

Two-Dimensional

a Barotropic Atmosphere." J.

Me(eor., 6:105-122 (1949). 19.

"The Motion

of

Atmospheric Vortices and the Gen-

eral Circulation." J. Meteor., 7:247-258 (1950). 20.

21. 22.

S. M., "The Motion of Harmonic Waves in the Atmosphere." J. Meteor., 3:53-56 (1946). Phillips, N. A., Unpublished manuscript, 1950. Rayleigh, Lord, Scientific Papers, 6 Vols. Cambridge,

Neamtan,

University Press, 1899-1920. (See Vol. I, pp. 474-490; Vol. Ill, pp. 17-23, 575-584; Vol. VI, pp. 197-204.) 23. RossBY, C.-G., "On a Mechanism for the Release of Potential Energy in the Atmosphere." /. Meteor., 6:163180 (1949). 24.

and Collaborators, "Relation between Variations Atmosphere and the Displacements of the Semi-permanent in the Intensity of the Zonal Circulation of the

REFERENCES 1.

Beeson, F.

a.,

"Summary

of a Theoretical Investigation

into the Factors Controlling the Instability of

Waves

in Zonal Currents." Tellus, Vol. 1,

No.

25.

Long pp.

26.

Bjerknes, J., and Godske, C. L., "On the Theory of Cyclone Formation at Extra-tropical Fronts." Astrophys. noTveg., Vol. 1, No. 6 (1936).

27.

4,

44-52 (1949). 2.

Centers of Action." J. mar. Res., 2:38-55 (1939). SoLBERG, H., "Das Zyklonenproblem." Verh. Ill intern. Kongress fiir techn. Mechanik (1930). SuTCLiFFE, R. C, "A Contribution to the Problem of Development." Quart. J. R. meteor. Soc., 73:370-383 (1947). and Forsdyke, A. G., "The Theory and Use of Upper Air Thickness Patterns in Forecasting." Quart. J. R. meteor. Soc, 76:189-217 (1950).

THE QUANTITATIVE THEORY OF CYCLONE DEVELOPMENT By

EADY

E. T.

Imperial College of Science and Technology

analysis that instability (to a greater or less degree)

Introduction

a normal feature of atmospheric motion. important to be quite clear as, to the meaning of the term "unstable" when applied to a system of fluid motion. If we suppose the initial field of motion to be given, the final field of motion, after a given interval of time, is determined precisely by the equations of motion, continuity, radiation, etc., together with the appropriate boundary conditions. If we consider a slightly different (perturbed) initial state, the is

indicates its principal theme but not its full scope, for although we shall explain the method of formulating and solving certain theoreti-

The

title of this article

problems and shall interpret the answers in terms development of extratropical cyclones and anticyclones, our analysis has also a wider significance. Not only does a fundamentally similar theoretical analysis apply to a wide variety of development problems (including, for example, the development of "long" waves as well as the shorter "frontal" waves and even phenomena due primarily to ordinary convective instability) so that a comprehensive analysis is desirable, but this analysis gives results of primary importance in the theory of development in general, that is, from the point of view of the general forecasting problem. We shall infer from our results that there cal

of the initial stages of

exist,

in general,

certain ultimate limitations to the

weather forecasting. Certain apparently sensible questions, such as the question of weather conditions at a given time in the comparatively distant future, say several days ahead, are in principle unanswerable and the most we can hope to do is to determine the relative probabilities of different outcomes. The full significance of our theoretical problems becomes apparent only when it is clear what kind of question we should attempt to answer. The science of meteorology is a branch of mathematical physics it can be fully understood only in a quantitative manner. Moreover, all the practical questions we should like to answer are of a quantitative characpossibilities of

;

Having discovered the relevant equations of motion, we ought to aim at obtaining significant integrals ter.

(more precisely, solutions of significant boundary-value problems) which may be applied directly to practical problems. In order to obtain tractable problems, and at the same time to see clearly what we are doing {i.e., "to see the wood for the trees"), we may, for a first analysis, simplify the equations by omitting all factors not vitally affecting the nature of the answer. Later we may refine our solutions by taking into account factors previously omitted (e.g., by the method of successive approximations), thereby testing whether we have in fact included all the vital factors. This is a procedure with which we are familiar and, however laborious it may be in practice, it introduces no new difficulty in principle.

The

really serious difficulty

is

to discover what kind of problem ought to be solved, for this difficulty arises as soon as we consider the question of the stability of atmospheric motion. Observation suggests that the motion times, be unstable,

and we

may, at least somefrom subsequent

shall infer

It is

final state, after the same interval of time, will be determined in a similar manner. The stability or instability of the motion depends on the behaviour of the resulting change (perturbation) in the final state as the time interval is increased. If the final perturbation remains small for all time for all possible initial perturbations, the motion is stable. If, on the other hand, the perturbation in some or all regions grows (initially) at an exponential rate for any possible initial perturbation, the motion is unstable. There is an inter-

new

mediate case, conveniently described as neutral

stability,

the perturbations grow linearly or according to a low-degree power law, but this need not concern us here. The practical significance of a demonstration that

when

the motion is unstable is clear, for in practice, however good our network of observations may be, the initial state of motion is never given precisely and we never know what small perturbations may exist below a certain margin of error. Since the perturbation may grow at an exponential rate, the margin of error in the forecast (final) state will grow exponentially as the period of the forecast

is

increased,

and

this possible

unavoidable whatever our method of forecasting. After a limited time interval, which, as we shall see, can be roughly estimated, the possible error will become so large as to make the forecast valueless. In other words, the set of all possible future developments consistent with our initial data is a divergent set and any direct computation will simply pick out, arbitrarily, one member of the set. Clearly, if we are to glean any information at all about developments beyond the limited time interval, we must extend our analysis and consider the properties of the set or "ensemble" (corresponding to the Gibbs-ensemble of statistical mechanics) of all possible developments. Thus long-range forecasting is necessarily a branch of statistical physics in its widest sense: both our questions and answers must be expressed in terms of probabilities. There are two important connections between these general considerations and subsequent analysis. Firstly, this analysis will show the existence of at least one type of large-scale unstable disturbance in a simplified but typical system, and we shall infer that instability is a error

464

is

THE QUANTITATIVE THEORY OF CYCLONE DEVELOPMENT normal feature of atmospheric motion. Although the unstable disturbances are continually tending to establish a new stable state, radiative processes are continuously tending to restore the initial system, which therefore remains permanently unstable. Secondly, for such a system the study of the ensemble of all possible perturbations is relatively simple. In each system there exists a disturbance of maximum growth-rate (so that we can determine the growth of the margin of error and estimate the limited time interval referred to above) which eventually becomes dominant in subsequent developments by a process analogous to Darwinian natural selection. Almost any initial disturbance tends eventually to resemble the dominant, which is therefore the most probable development. The "ensemble" possesses at least some strongly marked statistical properties which may be utilised to extend the range of forecasts. In spite of inaccuracies due to oversimplification this result is practically significant. The disturbances referred to are approximations to nascent cyclones, long waves, etc.; were it not that "natural selection"

be

is

a very real process, weather systems would variable in size, structure, and beha-

much more

viour.

The Basic Equations

We shall

regard as basic equations the three dynamical equations, the thermal equation, and the equation of continuity; others, such as the gas laws and the laws of radiation, will be regarded as subsidiary. The number of dependent variables we need, or that we find it convenient to use, depends on the nature of the problem and the degree of accuracy aimed at. In the problems with which we shall be concerned it is possible to express the basic equations in terms of the three components of velocity, pressure, and entropy (or density) alone so that the five basic equations, together with appropriate boundary conditions, form a complete set. Clearly these equations can be appropriate only for a limited range of problems when certain approximations are justified; we shall in fact make fui'ther approximations, our aim being to retain only those terms which are of prime importance in the range in which we are interested.

A completely realistic theory of the stability of atmospheric motion should deal with nonsteady initial conditions, but for simplicity we shall confine our attention to the case in which the initial motion is steady, and in fact we shall be concerned mainly with rectilinear horizontal motion. Our analysis will be approximately true even when the very-large-scale distribution is slowly changing. The relative importance of the terms in our equations depends partly on the scale of the phenomena with which we are concerned. Here we are interested in disturbances of the order of magnitude of nascent cyclones, say 1000 km in horizontal extent and occupying a large part (or the whole depth) of the troposphere. From our point of view ordinary or gravitational convection, originating from static instability (i.e., superadiabatic lapse rate), and ordinary turbulence of fric-

465

tional or convective origin are small-scale

The

phenomena.

appropriate in each case because the disturbances whose nascent form we are studying may be regarded as elements of a large-scale convective process and this process, regarded statistically, is a kind of large-scale turbulence. From our point of view the significance of small-scale turbulence, including ordinary convection, lies in its statistical properties, such as ability to transport heat, momentum, etc. Now frictionally induced turbulence is most effective near the earth's surface, and rough calculations (which we have not space to describe) using empirical estimates of skin friction indicate that frictional dissipation of energy usually has a relatively small effect on the development of large-scale disturbances (especially over a sea surface) in their nascent stage, provided the unstabilising factors are not too weak. Since we are most interested in those regions where the unstabilising factors are relatively strong, we may obtain a useful first approximation during the nascent stage if we neglect the frictional terms in the equations of motion. It is not possible to neglect frictional terms throughout the whole life-history of a disturbance because in the long run the kinetic energy destroyed by friction must equal that generated as a epithet "ordinary"

is

result of instability.

Surface friction transports heat vertically through a shallow layer, but since we are interested in the behaviour of deep layers this effect will be neglected. Moreover, surface turbulence is partly convective in origin, and we may I'egard shallow convection as included in this argument. But sometimes {e.g., in strong polar outbreaks) deep and widespread convection transports heat to great heights at a great rate. We shall ignore this possible complication and concentrate our attention on systems in middle and high latitudes

which are

statically stable in their initial stages.

we cannot we cannot

ignore skin fricignore radiative processes. Large-scale turbulence (the statistical aspect of our disturbances) appears to be a major factor in transporting heat poleward to compensate the unbal-

Just

as, in

the long run,

tion so, in the long run,

anced radiation flux. But during the nascent stage, development (measured by the time for growth of the disturbance

and

it is

by a given

factor)

is

precisely for this reason that

Hence

relatively rapid

we

are able to

reasonable to suppose that in the nascent stage we may, for a first approximation, neglect the change in the radiation balance caused by the disturbance and use for our thermal

neglect frictional terms.

it is

equation the adiabatic equation. Consider first the case of unsaturated air. To a close enough approximation the entropy of dry air is measured, in suitable units,

p

=

*

is

pressure, p

=

^

by $ (1/t) In p— In p, where 7 = specific heat ratio, and

density,

conserved during the motion. In this case

we

shall

define the static stability, which measures the restoring force due to gravity on a particle displaced verti-

Now

conas d^/dz (2 = vertical coordinate). sider the case of saturated air in contact with a cloud. The static stability is now measured by the difference cally,

:

:

DYNAMICS OF THE ATMOSPHERE

466

between the actual entropy lapse and that of the appropriate wet-adiabatic. Thus there is a sharp, and usually a large, reduction in static stability when air becomes saturated. The effective horizontal entropy gradients are also modified as a result of saturation, but to a much smaller extent. Normally a cloud mass behaves, to a sufficiently close approximation, as if the air were unsaturated except for the appropriate modification in static stability. Our equations are complicated by the fact that air is a compressible fluid, but it is clear that this feature is not, for our purposes, a significant one. We are concerned essentially with a particular type of "vibration" problem though our disturbances have mathematically complex wave velocities. The moduli of these wave velocities are in all cases, as our calculations verify, small compared with the velocity of sound. It is not surprising therefore that the forces associated with compressibility are negligible, that is, that the air behaves dynamically as if it were incompressible. The static effect of compressibility, involving a large change of density with height, is a complication which prevents atmospheric motion from being quite the same as that of an incompressible fluid. Nevertheless, even for deep disturbances, the behaviour differs little from that of an incompressible fluid of similar mean density the modifications are essentially of the nature of distortions of wave structure without much change in more

We

growth rate. shall therefore confine our attention to "equivalent" incompressible fluid systems. Our results are, of course, more directly significant features like

applicable to analogous oceanographic problems.

Lack in [3]

of space prevents a discussion of these points

mathematical terms. It has been shown elsewhere that the basic equations may be further simplified

by the elimination

of the pressure field, so that

we

have finally four equations connecting the four dependent variables Vx Vy V^ (velocity components), and $ (entropy) But our present concern is the physical interpretation and practical significance of certain calcu,

,

.

lations rather than the calculations themselves.

The General Theory The various types

of the Instability of Fluid of instability occurring in

Motion

dynami-

meteorology merge into one another so that most systems encountered in practice are, to a greater or less degree, hybrid. Nevertheless it is not only simpler but theoretically more instructive to consider certain ideal limiting cases where one or another unstabilising factor acts alone. Four simple types of instability will interest us cal

la. Gravitational instability (ordinary

convection or

static instability). 16.

Centrifugal instability (dynamic instability).

2a. Baroclinic instability (with thermal wind). 26.

Helmholtz instability

(at a velocity discontinu-

ity).

Instability of type la is, in middle and high latitudes, nearly always a small-scale phenomenon, but in low

latitudes a modified form,

taking into account the

rotation of the earth,

development

is

intimately concerned with the

of tropical cyclones.

Instability of type 16 has been the subject of much recent investigation, usually under the heading "dy-

namic

but despite its theoretical imporprobably rare for large-scale motion. The name "centrifugal" has been preferred to "dynamic" because it is more descriptive and less confusing other types of instability may reasonably be called "dynamic." Instability of type 2a is probably the most important, on a large scale, in middle and high latitudes. It is to this type that our earlier remarks regarding the normality of instability and the existence of "natural selectance

instability,"

it

is

—

tion" directly apply. Instability of type 26 was investigated by Helmholtz and Rayleigh for nonrotating barotropic fluids. The Norwegian wave theory of cyclones was a partially

successful attempt to extend the theory to rotating

barotropic fluids.

Although we shall choose our initial systems so that only one type of instability is in question, the same general method of analysis applies in every case. Using the method of small perturbations, we obtain a set of simultaneous, linear, partial differential equations involving the perturbations as dependent variables. By elimination we obtain a partial differential equation with only one dependent variable and look for simple solutions satisfying appropriate boundary conditions. Usually these solutions involve only circular or exponential functions in the horizontal (x and y directions) and all contain the factor e'^' where t represents time and di is a constant called the growth rate. For di to be real we usually have to use a moving coordinate system. Fortunately these solutions for unstable waves are, practically, the most important ones and the disturbance of maximum growth rate, when it exists, is probably dominant relative to one of arbitrary initial structure. In any case a study of these particular solutions enables us to understand the process of breakdown of the initial system and to estimate the relative importance of various factors. The method of analysis outlined above is necessary if we require precise results and is the only one which is completely unequivocal. But it is mathematical in form and usually rather involved so that significant physical principles, which give us insight into our problems and immediately suggest generalisations, tend to be obscured. Now, except that our interest is centred in the unstable region, we are concerned with what are essentially vibration problems and we may expect to find that energy considerations are of paramount importance. For, by the law of conservation of energy, the kinetic energy associated with any perturbation must be equal to the decrease in "potential" energy of the system, and a necessary condition for instability is that it should be possible to find displacements which will decrease "potential" energy; the condition will be sufficient only if these displacements are consistent with all the equations of motion and boundary conditions. More precisely, using Rayleigh's method, we

THE QUANTITATIVE THEORY OF CYCLONE DEVELOPMENT express separately the changes in kinetic and "potential" energy in terms of arbitrary displacements

may

form 8x = e'^'dznix, y, z), etc. The kinetic energy change contains the factor dl while the "potential" energy change does not, so that the law of conservation of energy gives an expression for dl in terms of the displacements. The possible simultaneous values of the of the

,

467

slowly interchanged. Then since potential density would depend only on entropy, we should obtain, if B were negative, a net release of energy for any two parcels at different levels, while if B were positive no interchange could release potential energy. Clearly the constraints associated with the continuity equation cannot alter this result

—the overturning process

is

equivalent

displacements are restricted (or constrained) by the equations of motion and we can to some extent delimit possible values of Ol by considering only some of the constraints, as in somewhat analogous problems in dynamics. In the present instance we consider only the equation of continuity and one momentum equation (and suitable boundary conditions) and then apply algebraic ineciuality theory to our undetermined displacements. We thereby obtain an upper bound to the possible value of dl (corresponding to negative square of frequency) just as in dynamics we obtain a lower bound to frequency (squared) by considering a less

to a set of such interchanges of different amplitudes. Since horizontal motion does not affect potential en-

constrained system. The value of the foregoing, described in more detail elsewhere [3], derives partly from the fact that we can treat a wider variety of problems than we can by complete solution, while the value of dl (maximum) thereby obtained is usually not much greater than the true value of dl But its greatest usefulness is that it

la and lb. lb. Centrifugal Instability. We shall suppose the motion to be barotropic and horizontal with the initial velocity V:, a function of y only. For simplicity we take dVx/dy constant and, to begin with, we put B = (isentropic conditions). Then "potential" energy exists only in the "kinetic" form. Let us consider the change

of breakdown of unstable systems immediately intelligible. If we take into account only our limited set of constraints, it is immediately evident what kind of displacement field is necessary for a re-

due to overturning in the (vertical) y, z plane. Filaments of air in the x--direction move as a whole and we easily derive from the equations of motion that, during displacement, hV^ = J&y, where/ is the Coriolis parameter. If the X-axis is directed toward the east, this cor-

.

makes the process

lease of "potential" energy. It

is

of course essential

that the term "potential" energy be correctly interpreted. For our purpose it comprises all forms of energy other than the kinetic energy of the perturbation and therefore includes, besides gravitational potential energy, the organised kinetic energy of the mean flow (smoothed of harmonic variation). This distinction be-

tween two kinds

of kinetic

energy change

is

justified

their different roles in the turbulent motion which the ultimate state in practice turbulent energy may arise either from a decrease in gravitational potential energy or from a decrease in kinetic energy of the mean motion. We may classify our systems according to

by is

:

whether the "potential" energy source is (o) static (gravitational) or (b) dynamic (kinetic). Now the displacement field is merely the nascent form of a process of overturning and we shall need to consider only two possibilities:

(1)

overturning in a

vertical

overturning in a quasi-horizontal plane.

plane;

(2)

Thus we may

also classify our systems according to the kind of overturning associated with instability. In our list of four

simple types of instability we anticipated their classification from both points of view. Let us consider the characteristics of these systems. la. Gravitational Instability. We consider barotropic conditions, so that initially there is no wind change with height, and for simplicity we suppose that di/dz = B, where B is constant. If, to begin with, we neglect the rotation of the earth, then "potential" energy exists only in gravitational potential form. Suppose that two small parcels of air of equal potential volume were

ergy

we need consider only vertical overturning; calcuby the energy method give dl < -gB, where

lations

=

gravitational acceleration. Of course in this simple case it is easy to obtain complete solutions, representing the nascent stage of Benard cells, and calculations

g

dl (maximum) is nearly attained for narrow deep cells, where little energy is wasted in horizontal motion. We shall postpone the extension to large-scale convection, where the rotation of the earth is considered, since this is really a combination of types

show that

responds to constancy of absolute angular momentum. for our purposes, where a mean value of / is used, the orientation of the x-axis is arbitrary. A simple calculation shows that potential energy is released only if dVJdy > f, corresponding to negative absolute vor-

But

ticity, and the energy method gives dl < f(dVJdy — /). Although values of dVJdy near the critical value are sometimes observed in narrow bands, it is doubtful whether centrifugal instability ever occurs on a large scale except perhaps in low latitudes. The rotation of the earth, normally at least, has a stabilising effect so

far as vertical overturning

is

concerned.

Similar results are obtained if, instead of rectilinear motion, we consider a barotropic circular vortex (with no motion relative to the earth as a special case). The condition for instability is again negative absolute vorticity.

We may note that in both mum instability occurs for

the foregoing cases maxishallow,

flat,

cells

since

"potential" energy changes depend only on horizontal motion (no energy is wasted in vertical motion). lab. Gravitational-Centrijugal Instability. It is easy to combine the results of the previous sections for a system in which neither B nor dVJdy vanishes. There

B or (/ - dV,/dy) is negative, be either so deep that centrifugal stability is negligible or so shallow that static stability of no is negligible. The important practical case is that motion (special case of circular vortex) with B < 0. is

instability

for the cells

if

either

may

Instability occurs for disturbances

which are

sufficiently

:

DYNAMICS OF THE ATMOSPHERE

468

deep relative to their breadth, the condition being that there should be a net release of "potential" energy. In low latitudes not only is — S sometimes (temporarily)

relatively large but the stabilising effect of the

earth's rotation relatively

is

small, so that convection cells of

enormous diameter (nascent hurricanes) can

develop.

In general, maximum growth rate corresponds either to very deep or to very shallow cells but this result is not of great significance because practical systems are

very inhomogeneous.

We suppose the initial moand take the initial velocity Vx only. For equilibrium this implies

2a. Baroclinic Instability

.

tion to be rectilinear

to be a function of z a horizontal gradient of entropy A d^/dy, where, approximately (A not too small), dV^/dz = —gA/f.

^

For simplicity we suppose

A

to be

constant. Pure

B = 0, but be convenient to consider directly the more general case B ^ 0. In practice we usually have (at least in the mean) B > 0, and this is the only case we need examine, for when B < the system is obviously unstable. The isentropic surfaces have an angle of slope a( the latitude; p is the pressure; a, (3, and 7 are functions of p and its space derivatives; 6 is the potential temperature, and fj, is Coriolis

parameter

2fi sin

with

(^,

fi

a>\

/a_p

used with a degree of success in present-day synoptic practice. Hence, in accordance with the plan of utilizing the results of synoptic experience in the construction of models, we shall investigate the form taken by the equations of motion under this hypothesis. First, by way of further justification, we shall show by means of scale considerations that the term

the geostrophic vorticity: 1.

1

2

(2)

where V;, is the horizontal operator, p the density, and the symbol "~" denotes approximate equality. For

u d In 6/dx + y 3 In 6/dy is usually larger in order of magnitude than wd \n d/dz in the adiabatic equation,

d\nd

a In e

dt

dt

here ignored.

/)5 In d/dz, we may infer that the elliptic or hyperbolic character of (1) is preserved at a material point. Thus we are assured that if (1) is everywhere elliptic initially it will remain so. On the other hand, if (1) is elliptic at some points and hyperbolic at others it will retain this property. In the latter case the integration problem becomes exceedingly complicated. Moreover, it is not known if, or to what extent, the geostrophic approximation applies when the potential is

and we may

and then only

locally,

therefore be justified in assuming at the

everywhere and for all time. (In the more general case, where the isentropic surfaces are not assumed quasi-horizontal, it can also be proved that the pressure-tendency equation is and remains a second order elliptic differential equation if start that equation (1)

We

time t, we evaluate its coefficients and nonhomogeneous terms at time t and solve for dp/dt by a relaxation

method (Southwell

The boundary

[14]).

5 In

6>

dij

,

V

0, (3)

du

a In

,

dx

g\

dy

dz

'dz

and from the vertical vorticity and continuity equations

r

+ / \3« +

d

M

—d\

(f

+ /)

d2l

dv

1

d{pw)

dw

dx

dy

p

dz

dz'

.

\-

V

]

dx

dy/

(4)

+

p{t

The sequence

+

At)

of steps

is

The symbol "'~" denotes equahty

=

'x

,

J

,

+ y/ly + z/Q] = V exp [2Tri{x/h + y/ly + z/lz)] = IF exp [2TTi{x/h + y/ly + z/U)],

u = V

w

U exp

[2n(x/lx

^

where U V and Ix '^ ly on the left-hand side of magnitude, we obtain

wa wa where

Vj

=

/

In e/dx is

and

osciflation

,

and noting that each term has the same order of

(4)

In d/dz

+

-{-

2 At),

SAt), etc.

IzVb

\

vd\n d/dy

\

the frequency of a horizontal inertial = gd\n O/dz is the frequency of a

vl

For the large-scale motions in = 2 X to_6 X lO' m; h = 10"^ 10"* sec '; and Vb 10' m to 2 X 10'* m; vt sec~\ Hence the above ratio varies between 0.03 and 1. For a typical large-scale system (l^ ly = -i X 10 m; = 1.5 X 10* m) its value is about 0.14. We note, Zz however, that the advective hypothesis is less valid in the stratosphere where the buoyancy frequency vt is several times greater than 10~ sec"

buoyancy

osciflation. l^

,

W

ly

^

then iterated to give p{t

magnitude

sinusoidal dependency, with wave lengths

Assuming a and iz ty

middle latitudes

p(t).+ At dp/dt.

in order of

only.

conditions are

that there shall be no influx or efflux of mass through the bottom or top of the atmosphei-e, translated into equivalent conditions on the pressure tendency. Having obtained dp/dt we calculate the pressure at time At from t

^

,

As computing machinery for calculations of such great complexity have not yet been available, more simplified atmospheric models have been devised to test the validity of some of the basic assumptions. These

In 9

-

we have

is elliptic

the potential vorticity is initially positive everywhere.) may envisage a solution of equation (1) by the following procedure. Assuming that p is kno^vn at

+

V

\-

negative. Fortunately, however, negative

potential vorticities occur rarely,

pit

a w— —= dz

d\ne

,

dx

which u, v, and w are the x, y, and z velocity components, respectively. From the geostrophic and thermal wind equations

+

vorticity

a In e

u

in

Equation (1) is elliptic or hyperbolic in the pressure tendency according as the factor multiplying the z-derivative terms is positive or negative. Since this factor has the same sign as the approximate potential vorticity, P~\f(7

,

-\-

simplicity of presentation, the curvature of the earth is

471

will

now

be described.

Advective Models

it is

A

obtained by ignoring the effect of vertical motion on the change in potential temperature. Although this assumption is more questionable than those already made, one cannot ignore the fact that the advective hypothesis has been

The General Case.

.

foflowing derivation of the geostrophic-advective equations is due substantially to Fj0rtoft [5], although

The

first

simplification

much

If the

is

in the spirit of Sutcliffe's

dVg ;

dz in

which

work

[15].

thermal wind ecjuation

v^

is

^

k

X

V, In

(5)

d,

the ^eeostrophic wind and

k

is

the vertical

'

DYNAMICS OF THE ATMOSPHERE

472 unit vector, z,

integrated from the ground to the level

is

we obtain

fixed with respect to time,

+

X

k

V;.

In e

rfz

We now

with po the surface pressure. advective hypothesis.

aine

(6)

-v„-V,

introduce the

ln6l.

(16)

dt

and,

by

differentiating with respect to

t

and taking the

so that

curl,

~P0

A dz.

dt

/

dt

' Jo

(7)

^ ga- Jp Ji

Vj-V„ In

dp e

P

dt 1

since the variability of / may be ignored in the differentiation. To eliminate d^go/dt we proceed as follows: If

we

f equation

(7)

fg Jp

dz (8)

.dz

becomes, by integration Avith respect to

dt

"

that of the general quasi-geostrophic equation. solves the two-dimensional Poisson's equation

VpS =

z,

and determines the dt

-|^4,

field of

Jp

a In 9 dz.

Utilizing the relationship

dF^

[2,

eq. 68]

-v,-V*(f,

dt

which

may

+/),

also be derived directly

we

tion of (4),

(10)

dt

Jo Jo

(11)

by

vertical integra-

eliminate d^go/dt between (7)

and

(9) to

obtain af,

ft

=

-v«-v.(f.

now becomes

+ f)+j (vU -

vU).

+

convenient to replace

The

baric surface.

For the

The

latter are

denoted by the subscript

large-scale systems in

p.

which we are primarily

interested (since only for these

is the geostrophic approximation valid), / is usually several times greater than f„ and the mean defined by (8) may be replaced by the simple average with respect to pressure. Then, ,

since

A.

(19)

There are a number of methods, both analjd}ic and numerical, by which (18) can be solved. The best for hand calculation is probably the relaxation method of Southwell [14] as it is rapid and can be used with any type of boundary. However this method is not always suitable for automatic machine computation as it makes large memory demands. It has been found best for a machine with a small internal and large external memory to use the analytic solution expressed in terms of a Green's function G:

S =

(12)

z by p as the geopotential ^ = gz may then be introduced as a dependent variable in place of p, and, with slight approximation, the local and horizontal derivatives may be replaced by derivatives in an iso-

It

vertical coordinate.

(18)

d$/dt from

= S - A

-f

One

(9)

where

A =

/a# 9) dp, \dp

with the result that all quantities in (13) are expressed in terms of $ and its derivatives. The numerical integration of (13) is simpler than

define

/ Jo f«+/

(17)

r"

Jf

G{x,

y, x',

v')J dx'dy',

(20)

where the integral extends over the forecast area and J is regarded as a fxmction of x' and y'. The function G is a solution of the homogeneous equation V^G = 0, satisfying the same condition as S on the boundary. Finally we mention that one may also use an "analogy" device, consisting of a physical system whose equilibrium state is governed by an equation having the same form as (18). The physical magnitude J appearing in (18) is varied at will and the magnitude S determined by measurement from the resulting equilibrium configuration.

A Simplified Version. While (13) is already a considerable simplification of the quasi-geostrophic equation, •

equation (12) becomes

it

still

presents appreciable difficulties for numerical

therefoi'e be based on the observation that the isolines of temperature and potential temperature in large-scale systems are approximately parallel at

integration. Further simplifications will

di

where Jp

is

+A -A

d

7)

^ V^$

+

/,

*

(13)

the Jacobian operator defined by

considered.

all levels,

dad^

Jpia, P)

The

that

first is

is.

_dad^

dx dy

dy dx'

(14)

1

Vp ine

rip) Vr,

\nd

(21)

and

A =

1

r° dine dp

g Jp

where the bar (15)

dt

p

I Vg

,

p,

T,

and

refers to a fixed isobaric surface p. If

6 are

the velocity, density, temperature,

DYNAMIC FORECASTING and potential temperature respectively at

=

Vs

av,

+ /:

v„

dp =

+

V„

this level

(22)

-

At

Let us, therefore, consider a Fourier component of

—

'

At ^ Aa;

the entire solution. the form exp [i(kx

—

sm

c

must be presumed

Once the physical problem of determining the equations of motion and the boundary conditions has been solved, there arises the purely mathematical problem

kAx —

.

> -

+

ij,

t)

As,

t)

As,

-

finite-differ-

t)

(59) ii^ix, y,

t).

Fourier component of the form exp /ly)]. Substitution in rf]= CO exp [i{kx

+

(58) gives co'

+

2aico

—1

=

0,

DYNAMICS OF THE ATMOSPHERE

478

where

=

a

^(As)V4

U+

be a

sin kAs.

-

sin^

The

— ,Ms

,/cAs

'^ +

As

sin'

condition for stabihty, < 1, and we obtain

|

w

|


C7sinfcAs+M?M!^^5:(^). At

.

„

IcAs

sin'' -TT-

+

.

,

,

is

m=

2a"' (1

-|-

sin )v2

=

a

J—,

aXk

dt

dv2 ~di

d^i dVj

Sum .

+

(2co

—

(2a)

sm

4>)Vi

= a

-!-~,

dXk COS

(j))vi

It

\

(6)

= a-^ — dXk

where w which is the three-dimensional velocity divergence. Any component of pki is a force per unit area, acting in the plane perpendicular to the -Ts-axis. If it is regarded as acting on the fluid lying to the negative side of that plane, then the force is positive in the Xi-direction. If the velocity gradients are vanishingly small, or if the fluid is

nonviscous (m

=

0), pki

is the angular velocity of the earth's rotation; the latitude; and g, gravity. The Xi-axis is directed toward east; the a;9-axis toward north; and the a;3-axis toward the zenith. When the first equation is multiplied by Vi the second by V2 the third by Vs and the resulting equations are added, the Coriolis terms disappear, 2.5. The analysis above appears to be adequate if the layer concerned is very shallow, but since it implies .

that the effect of the irregularities is equally felt at all distances above the surface it cannot be applied, without care, to the deeper layers met with in most meteorological applications. An alternative treatment of the rough-surface

problem, due to Rossby and

Mont-

DYNAMICS OF THE ATMOSPHERE-

496

gomery [55], appears to be more appropriate for such Rossby and Montgomery assume that

cases.

I

=

+

k{z

zq),

which expresses the intuitive conception that the effects of the irregularities are most strongly felt in the immediate vicinity of the surface and hardly at all at the greater heights. Equation (3), with this form for I, yields

=

T^ln f \

+

z

Zo

zo

\ J'

(7)

on z = 0. Thus using the boundary condition w = theoretically, the profile of mean velocity over a rough surface is fully determined provided both m* and zo are known (fc being regarded as a universal constant). These may be combined to form the quantity termed by Sutton [63, 65] the macroviscosity, defined by iV" = The introduction of this quantity enables a single tt*2o profile, applicable to both smooth and rough surfaces, to be obtained, thus overcoming the difficulty felt in the free use of equations (6) and (7), that neither of these tends to the smooth-surface form (5) as zo —> 0. The generalized profile is

and

for this reason

the Prandtl treatment

is

often

"momentum-transport theory." From the aspect of exact hydrodynamical theory this hypothesis is questionable, since it involves the assumption that the pressure fluctuations do not affect the transfer of momentum. An alternative hypothesis, in many ways more attractive, is that vorticity is conserved and this forms the basis of Taylor's treatment of the problem [72]. Space does not allow an adequate discussion of referred to as the

the matter here, nor, in the present state of development of the theory of atmospheric turbulence, are the differences between the two theories of major importance for meteorology, except perhaps in one respect. According to the momentum transport theory, the rate at which momentum is communicated to unit volume of the fluid by turbulence is dr

K{z)^-^

dz

dz

dz

•

M _

/

1

\

u^z

whereas on the vorticity transport theory, Ot

—

=

rrl

\

pK{z)

dz

d ii -—

.

dz^

These two forms are equivalent if, and only if, K{z) = constant. For further details the reader is referred to Taylor's original papers, or to the accounts given by Brunt [4] and Goldstein [22] the latter gives considerable detail as regards tests on the laboratory scale. An illuminating discussion, chiefly from the standpoint ;

corresponding to

I

=

kz, or

+N — = ^In /u^z \N + v/Q

)

=

2o)- As2o (and hence N) tends to zero these equations tend to the smooth-surface form, but in most meteorological applications A'^ is of the order of 10 to 10' cm- sec^^ and is thus much greater than v. Schlichting's criteria may be written

if I

k{z

-\-

smooth flow: rough flow:

Power-Law

N< N>

Profiles.

Q.Viv 2.5v ?

A

0.02 cm2 sec-i,

rf

cm^ sec~^

0.4

somewhat

less satisfactory

representation of the flow near a boundary is obtained by the use of power laws, but this tj^pe of profile is often much easier to handle mathematically than the logarithmic profile. The usual form of the profile near a

smooth surface

is

Ui{z/ZiY,

(8)

where Wi is the mean wind speed at height zi and p is a positive number whose value for moderate Reynolds numbers is about }^^. If r/p = dii/dz is invariable with height, it follows that

K

K

=

K^{z/z^y~^,

K

where Ki is the value oi at z and (9) constitute the so-called laws" of Schmidt.

=

(9) zi

.

Equations

(8)

conjugate power-

The

Vorticity-Transport Hypothesis. The preceding analysis is based essentially upon the hypothesis that is

clusion is reached that all such theories fail at some point or other. Considerable doubt is now thrown on the validity of the mixing-length idea and even on the fundamental hypothesis that the eddy velocities and the turbulent shear-stresses are directly related to the mean velocity and its derivatives at a point (equations (3) above). These considerations may perhaps indicate that one fruitful period of development in the theory of turbulence is drawing to its close, and that the time

now

advances along quite different lines. Theories of Turbulence. One such fundamentally different approach to the general problem is that of the so-called "statistical" theory of turbulence, initiated by Taylor [73] in 1920 and later expanded by him in a remarkable series of papers in 1935 [74]. Subsequent developments were made by Karman and Howarth [32] and an account of the position reached by 1943 has been given by Dryden [15]. All theories of turbulence are necessarily statistical in some sense or other, but whereas the theories described in the first part of this article start with a is

ripe for

Statistical

u =

momentima

of the experimental worker, of the validity of the various hypotheses which have been advanced in the last two or three decades in order to develop further the Reynolds theory of stresses has been given by Dryden [14]. When the predictions of the various theories are compared with the results of accurate measurements made in turbulent boundary layers, the disquieting con-

conserved during the motion of an eddy,

measured distribution of mean velocity and mean pressure and relate these to the virtual stresses, the methods about to be described originate in the statistical properties of the fluctuations and seek to establish exact

.

ATMOSPHERIC TURBULENCE AND DIFFUSION relations

between these properties and the mean motion.

The two approaches have

their counterparts in molecu-

one being analogous to the kinetic theory of the elastic sphere models while the other has certain affinities to the statistical mechanics of an assembly of molecules. In his initial (1920) contribution Taylor considered what statistical properties of a fluctuating field of flow lar theory,

are required to determine the diffusion of a group of

medium. _If the turbulence

particles suspended in the

uniform and steady («'- independent of locality and time), the spread of a cluster of particles is

statistically

over a plane

given by

is

dt, Jo

Ja

X

is the distance travelled by a particle in time where T and R{i) is the correlation coefficient between the fluctuating velocities which affect a particle at times t and t + ^. Taylor's theorem means, in effect, that a knowledge of the mean eddying energy and of the

completely the diffusion in

correlation i?(|) specifies

The

application of this result to meteorological problems is considered later. The analysis also analogous to the mixing length indicates a length li but independent of any model, defined by

such a

field.

,

=

k

Vu'-'

[

R(^) d^,

Jo

which as ^

is finite if

—

^

R{^) tends to zero in a suitable

manner

00

Another way

of representing

such a

field utilises

the

correlation R{y) between velocities at points separated

by a

variable distance

L =

y.

I

The length L

defined

by

Riy)dy

Jo

called the "scale of the turbulence" and may be regarded as a measure of the average size of the eddies which constitute the pattern of flow. Evidence presented later suggests that in meteorological problems L has no efi'ective upper bound or, in other words, that in atmospheric diffusion, account must be taken of eddies ranging from the minute convectional whorl to full-size disturbances which affect the general circulation of the atmosphere. In later development of this theory attention has been particularly concentrated upon the problem of the decay of disturbances {e.g., downstream of a grid in a

is

especially in isotropic turbulence, for which Taylor has introduced another important length X called the "microscale of turbulence" and defined by

pipe),

lA^^iim/L^-?^n. y /

related to the curvature of the R(y)

497 curve at the

origin.

Later Developments; Kolmogoroff's Theory. The striking advances in the statistical theory of turbulence since 1941 are due to Kolmogoroff [34], Onsager [37], Weizsacker [79], and Heisenberg [25]. These theories have many points of resemblance, and the most promising appears to be that advanced by Kolmogoroff', whose work has been well summarized in English by Batchelor [1]. Kolmogoroff's basic conception is that, at very high Reynolds numbers, all turbulent motion has the same sort of small-scale structure, although the mean flow may differ widely from situation to situation, and that the motion caused by the small eddies is isotropic and statistically uniform. A turbulent flow may be thought of as giving rise to a spectrum of oscillations whose wave lengths vary in scale from those characteristic of the mean flow to a lower limit below which the motion is entirely laminar. Within this spectrum, energy is continually being transferred from one length scale to another by the generation, from any given band of oscillations, of a set of smaller oscillations, and so on, until it is no longer possible to form smaller eddies. Thus the process may be thought of as one in which energy from the mean motion is fed into the long-wave end of the spectrum by the largest eddies and passed down the spectrum in the direction of decreasing wave length, until ultimately it is absorbed into the random heat motion of the molecules by viscosity. Kolmogoroff then puts forward two similarity hypotheses: (1) that the statistical characteristics can depend only on the mean energy dissipation per unit mass of fluid (e) and on viscosity; (2) that the statistical characteristics of the motion due to the larger eddies are independent of viscosity and depend only upon the energy dissipation e. From these plausible hypotheses it is possible, by arguments chiefly of a dimensional

most

make certain definite predictions about the properties of the mean flow, and in particular, to show that as the Reynolds number increases without limit, the coefficient of correlation between fluctuations at points distance y apart tends to the form 1 — Ay''^ {A = constant), provided that y is small compared character, to

with the scale of the turbulence. Wind-tumiel measurements so far have provided excellent confirmation of deductions made from Kolmogoroff's hypotheses and there is little doubt that the theory constitutes a powerful tool for the resolution of many complex problems, and one which should especially appeal to meteorologists because of the emphasis laid upon the passage of energy from disturbances of one size to another. An account of this and other theories, together with some promising new developments, has recently been given by Karman [31], who considers that the principal aim of the present period is to find the laws

The

which govern the shapes of either the correlation or the spectrum functions. We now pass from these theoretical and laboratory

size of

studies to detailed consideration of the meteorological

!/->0

microscale of turbulence indicates the average the small eddies which are responsible for the greater part of the dissipation of energy, and is also

problem.

DYNAMICS OF THE ATMOSPHERE

498

PHYSICAL FEATURES OF ATMOSPHERIC

TURBULENCE Experimental investigations into atmospheric turbumay be conveniently divided into: (1) those deahng with localized effects, usually in shallow layers near the ground, in which the consequences of the earth's rotation may be disregarded (2) those relating lence

;

to larger-scale processes, usually in the so-called "friction layer" or "planetary boundary-layer" (Lettau),

extending from the surface to the level at which the geostrophic velocity is attained (c. 500 m); and (3) those concerned with the atmosphere as a whole.

The Temperature Field. The most direct manifestation of atmospheric turbulence is the presence of fluctuations in the wind, but in view of the controlling influence temperature gradient, it is convenient to begin by discussing the temperature field near the ground. Accurate continuous observations of temperature differof

ences between various heights extending from 2.5 cm have been tabulated and analysed for southern

to 87.7

m

England by Johnson [28], Best [2], Johnson and Heywood [30], and by Flower [19] for Ismailia, Egypt, while Ramdas [48] has given mean values of air temperature at various levels from 2.5 cm to 10.6 at

m

maximum- and minimum-temperature epochs at Poona, India. From these investigations there emerges the now familiar picture of the temperature field in the lowest 100 m. In clear weather there is a well-marked diurnal variation of temperature gradient, with superadiabatic lapse rates during the hours of daylight and pronounced inversions at night. With overcast skies, and especially with strong winds, the gradient remains close to the adiabatic lapse rate both day and night. The gradient of temperature near the ground is subject to such large variations with locality and season,

time of day and height above the surface that it would be misleading to attempt to give representative values here. Very large gradients, as high as thousands of times the adiabatic lapse rate, are a persistent feature of the temperature field in the first few centimetres above the ground, especially in summer, but the sharp curvature in the temperature-height curve is confined to the first few metres. Sheppard [60] states that on the average the daytime fall of temperature is roughly proportional to the logarithm of the height, but more detailed investigations by Deacon [12] indicate that, in general, the gradient of temperature is inversely

proportional to a power of the height over the first 17 m, the index being greater than unity during lapse conditions and less than unity in inversions.

In warm weather the temperature of the air near the ground shows rapid fluctuations of considerable amplitude, as much as several degrees centigrade. Schmidt [58] gives observations by Robitzsch which show that these oscillations have a well-marked diurnal variation in phase with the temperature gradient, the fluctuations tending to die away as the lapse rate approaches the adiabatic value. Sutton [64], from an examination of records obtained in clear warm weather, has found

that in these conditions the oscillations decrease as z-^-^ over the range 7 ^ 2 ^ 45 m, but this is an

m

and a complete picture of the variation with height does not exist at present. During the inverisolated result

sion period the gradient shows large long-period fluctuations unlike those met with in dajrtime.

There

is

much

less

information concerning tempera-

ture gradients over the ocean, but data have been

given by Wust [80], Johnson [29], Montgomery [35], Craig [10], Emmons [16], and Sverdrup [71]. Because of the relatively small effects of insolation and long-wave radiation on the sea, the gradients are much less than those found over land and diurnal effects are hardly noticeable, except in shallow landlocked waters. The exploration of the mean temperature field near the ground is thus virtually complete except in one important respect. It has now become clear that radiation, especially in the longer wave lengths, is quite as important as convection in the problem of heat transfer, and systematic simultaneous records of both temperature gradient and radiative flux are needed to complete the picture of the thermal structure of the lower atmosphere. The Velocity Field. Following the lead given by the theory of the turbulent boundary layer in aerodynamics, it has now been shown conclusively by many workers that the profile of mean velocity near the ground in conditions of small temperature gradient is adequately represented by a logarithmic law (e.g., of the type proposed by Rossby and Montgomery, equation (7)), provided that the vegetation cover is not too high. For profiles measured above long grass it is necessary to use an empirical modification of the equation, namely

u

^H-i")

{z

^

Zf,

+

d),

where d is a zero-plane displacement, of the order of the depth of the layer of air trapped among the plants. Model has used the same equation for the wind profile over the sea.

The most above

is

significant feature of the work referred to that which emerges from the detailed investi-

gations of Sheppard

and

[61],

Paeschke

[38],

Deacon

[12]

others. In conditions of small temperature gradi-

ground is identical with that observed in the turbulent boundary layer of a fully rough surface in the laboratory, despite the great differences in scale. Sheppard has shown that the Karman constant k has much the same value as in wind-tunnel work, while Deacon has provided good evidence that the aerodynamical theory of the roughness length is equally appropriate for natural surfaces. The real difficulties and complexities of the meteorological problem begin to appear when the temperature gradient differs from the adiabatic lapse rate. The general high level of turbulence during the superadiabatic lapse-rate period promotes a free exchange of momentum between higher and lower levels, while the reverse holds during inversions. Thus, in general, the velocity gradient exhibits a diurnal variation, being small in daytime and large at night, but this is not all. Thornthwaite and Kaser [78] and, more recently. Deacon [12] have shown that for nonadiabatic gradients ent, air flow near the

g

\

1

ATMOSPHERIC TURBULENCE AND DIFFUSION the u, In - plots are no longer linear, but are convex to the w-axis in the lapse period and concave to the same axis in the inversion period. Deacon concludes that, in all

conditions.

du/dz (a

independent of

gradients,

/3

=

for inversions.

1

—

2),

az

with

{z

j8

>

1

for adiabatic gradients,

and

13

m)

for superadiabatic

for the adiabatic lapse rate

Thus the logarithmic

^

and

/3


0, where 3

»S'

time

since the specific state functions x

J

= >

corresponds to reversible transformations and corresponds to irreversible transformations. The physical meaning of the uncompensated heat of Clausius dQ' appears in the simplest fashion when a closed isothermal cycle is considered. During such a change of state, the uncompensated heat of Clausius received by the system is equal to the excess of the heat effectively given up over that effectively received by the system. In the case of an open system, however, dQ' is composed of two terms: the first depends on arbitrary addition or removal of mass and consequently may sometimes be positive and sometimes negative; the second depends on the internal physico-chemical

dQ' dQ'

transformation and

is always positive. It is this latter term which actually generalizes, in the more reahstic case of an open system, the classical concept of the uncompensated heat of Clausius.

In order to make clearly evident the differences in the significances of dQ and dQ', first for a closed and then for an open system, it is enough to set down the two laws for the case of a closed system consisting of two phases (a liquid and its vapor, for example) which undergoes only isobaric and isothermal transformations (vaporization and condensation at constant p and T), then to regard this system as being composed of two open systems (the gaseous phase and the liquid phase) and to see how the relations (2), (3), (5), and (6) reduce in this case

[7].

Pseudoadiabatic Transformations. When the heat received by an open system does not alter the internal transformation of which the open system is the site, the system is said to undergo a pseudoadiabatic transformation [14]. In this case diQ = 0, and as a result of (3)

and

(7),

diH = dH

—

Yl hjdemj = Vdp, i

(8)

diS

= dS — "^Sidemj = — X^s^d.-my ^ 3

i

THERMODYNAMICS OF OPEN SYSTEMS Let us now consider a system containing mass nia of dry air, mass m„ of water vapor, and mass m„ of water (aqueous cloud), and further let us suppose that the system receives water or gives it up (rain). In this case dnia

^ dinia ^ dema ^ ^ deftiv

+

di77iy

=

diVit^

The equation this

0,

d7n

0,

^ dim^, dm.^ ^ + rf^m^, dm„

0,

dein

=

^

de^riu,

0.

(9)

for pseudoadiabatic transformations of

system can be deduced at once from

(8)

;

it

phases, and by the masses of the constituents of the The thermodynamics of polythermic systems,

all

phase.

therefore,

follows

that

where A„

^

—

—

=

SyideVito

-p^dmv

>

(10)

0,

the affinity of vaporization [2]. its value S = maSa{T, pa) niy, Sy, (T), where pa and pv represent viv s„ {T, pv) the partial pressures of dry air and water vapor, we If

S

Mu.

Mf

+

by

+

T

obtain, after using the relation

(s„

—

s„)

=

L„

+

[7,

14].

4„

[14], the differential equation of pseudoadiabatic transformations of moist air,

from

=

^

+

0, deViv

=

deMw

=

0, dnia

0, drUy

^

derriy,

Application of the first law (2) to each of the two phases [7, 14] leads to the relation

dniw

deiriv,.

[(dW +

is

in (10) is replaced

only a special case of the thermodynamics

In order to establish our ideas, let us treat a closed polythermic system consisting of two phases a gaseous phase (first phase) and a liquid phase (second phase). The gaseous phase comprises a mass nia of dry air and a mass m„ of water vapor at temperature T"; the liquid phase, a mass rriy, of water at temperature T"; the two phases are assumed to be at atmospheric pressure p. In this case we have d{ma = d^m-o = d{mw = 0, deTtia

diS = dS

is

open systems

of

:

rfi?n,„

=

533

h'dmA

+

{(d"Q)'

+

h"dm„]

=

0,

(14)

which shows that the heat (d'Q)" received by the first phase (gas) from the second phase (liquid) is not equal and opposite in sign to the heat (d"Q) given up by the first phase to the second phase. Furthermore, by a similar application [7, 14] of the second law (5) we '

obtain

d inia

Sa

-^

+

)

+

(^"

+

I^Cw

,„

-jT

(d'Q)*

(11)

+ Here L^ stands

m^d

» (t) =

for the heat of vaporization

water

d[

-\-

Sa

[14].

+ r„c,

r

and

dT = T

0,

r*cJhiT - Ralnp.

+

''-^

=

const,

,Xy(T', p.)

ml

(15)

-

y>j/i,„(r")Jrfm„,

Cw

(12)

^

+

,

\ n.(T") rpll

We

where r„ m^/nia represents the mixing ratio of the water vapor. This equation is immediately integrable; employing the theorem of the mean, we find [9, 14] {c^a

(d"Q)*

I

suppose that the water vapor is at saturation value {A^ = 0), and we assume that the water that is brought in evaporates as soon as it is introduced or that the water formed in the interior of the system leaves as soon as it is formed (m,„ ^0, rfj-m,,, = —denim = —dim^). Under these conditions the pseudoadiabatic transformation of the air is said to be reversible and dry [9, 14]; following (11) for the specific heat of

,

r

(13)

-

[jTi

where (d'Q)* and (d"Q)* represent the heats added to the first and second phases by the surroundings of the (d'Q)* + (d'Q)" and system. It is clear that d'Q (d"Q)* -\- (d"Q)', where d'Q and d"Q are the d"Q quantities of heat received by each of the two phases. Equation (15) shows that the increase dS in the entropy S of the system consisting of two phases includes: 1. The change of entropy due to influx of heats (d'Q)* and (d"Q)* from the surroundings, and 2. The production of entropy resulting from exchanges of heat (d"Q)' and matter dniy between the phases. The second law states that there definitely is production and never destruction of entropy in the

=

=

interior of the system.

Finally, the first law applied to the closed

where r„ is a mean value of r^, c-pa is the specific heat of dry air at constant pressure, and Ra is the specific perfect gas constant for dry air.

The

finite

equation (13) of reversible, pseudoadia-

batic transformations of air saturated with water vapor

one of the fundamental equations of atmospheric thermod3Tiamics we have just derived it rigorously. Polythermic Systems. A polythermic system is one in which all the phases do not have the same temperature. Since, by hypothesis, the temperature is a quantity which is constant throughout the interior of each phase, we can treat each one of them as an open system whose state is defined by the temperature of the is

;

phase, by the pressure p which

is

assumed the same

for

consisting of the

two phases provides the

dQ = dH

-

Vdp,

system

relation (16)

=

where dQ (d'Q)* + (d"Q)*, and where the enthalpy depends among other things on the temperatures T' and T" of the first (gas) phase and the second

H

(liquid) phase, respectively.

The fundamental equations (14), (15), and (16) allow made of the "horizontal mixing" of two

studies to be air

masses of diiTerent temperature and of the evapora-

tion of rain in the free atmosphere [14]. The Temperature of the Wet-Bulb

Thermometer and the Equivalent Temperature. Let us consider a closed system consisting of a mass m„ of dry air, a mass

DYNAMICS OF THE ATMOSPHERE

534

m^

of water vapor at temperature T", and a mass ?n„ of water at temperature T" Both phases are presumed to be at atmospheric pressure p. We will assume that the system undergoes only adiabatic {dQ — 0) and isobaric .

=

{dp

we have,

0) transformations; in this case

ma =

m^

m*,

= mt

-\- rriw

+

(16),

m*,

the equation of continuity in p and w*; its is governed by gravity, the Coriolis force, and the pressure gradient force. The equations of balance of momentum pv defined by the components satisfies

movement

and H{T', T", ma, m.,

mj = H{K,

T'i,

m*, m?, m*),

where (T", T" ma, m„, mj) and (T'*, T"'^, m*, mt, m*) represent two states of the system at the same pressure ,

turns out

p. It

(maCpa

+

m„

that

[14]

Cpv){T'

—

X

X and

T*)

m.) [L„(T;)

+

+

/!„(r;)

-

m: [KiTl) -

K{T")]

(17)

+

=

mula T^

= T

[r,(r.)

-

rAT)]U{T^) (18)

where ?'„(T) stands for the mixing ratio of water vapor at temperature T. Now let us consider a mass ma m„ of moist air at temperature T = T's^,. We will assume that at constant pressure p one can condense the mass mt of water vapor contained in the mixture. The temperature T' which the system then reaches is the equivalent temperature Te of the moist air under consideration, provided it is assumed that the vapor can be condensed at temperature T'if of the gaseous phase. Thus we are led to put r; T" T,T'^ Te, and mS m„ in (17), from which results von Bezold's formula

=

=

T+

=

by

A'

=

pA'/p the corresponding weighted mean.

should be recalled that

where X'

Z' =

and pX" = pX" =

= X- X and X" = X - X.

The m,ean state of mean motion by

/i.(r")],

where Ly{T^) = /i.„(r*) — ^^(r*) is the heat of vaporization of water and Cpa and Cj,„ are the specific heats at constant pressure of dry air and water vapor. Let us first consider a mass {ma win) of moist air at temperature T = T'. At pressure p, assumed constant, we evaporate into this system a mass of water mu, such that the vapor becomes saturated at temperature T*. This temperature, which is represented by T',„, is by definition the temperature of the wet-bulb thermometer if the evaporating water assumes the temperature Tw of the saturated gaseous phase. Thus we are led to put T'^T,T'^=T"^ T^, and ml Q in (17) from which is obtained the psychrometric for-

s

^

pw*, and of kinetic energy fc \v'v', can easily be deduced from the Eulerian equations of motion [11]. We designate by the Reynolds mean of the function

It

= (m? -

the fluid

its

is

=

(fc

i>*,

defined

1, 2, 3).

by p and Since pv

p,

0,

and

=

there is no difi'usion at the scale of the mean state and of the mean motion, and as a result the mass element phxyhx^hx^, moving at the mean velocity y'% does not exchange matter with its environment. Therefore the mean system satisfies the equation of continuity in p

and

v''.

We know

that the

movement

is

governed by

w'O, the force due pressure p, and the re sultant

gravity, the Coriolis force (velocity to the gradient of

force

mean

due to the Reynolds

stresses

R)^Rl^ —

pv"H"'

= 1, 2, 3). The equations of balance of the momentum components pv'' and of the corresponding ki{j,

k

^

^v'v' of the mean motion can easily be deduced from the equations of motion [11]. We observe that the absence of diffusion of mass (pv"* = 0) at the scale of the mean state does not imply the

netic energy km

absence, at this scale, of diffusion of the properties of the fluid. In fact, if / represents the specific magnitude of any property whatever, we have in general pfv" ' 7^ 0.

^

we would obtain appears that the Reynolds stresses R) result from turbulent diffusion of momentum pv*. By contrast, a mass element pbx^bx-hx^ For example, by substituting /

pvV' =

pv"^v"'

= —R). Thus

y*

it

moving with mean velocity w* diffuses mass and for this reason constitutes an open system, which does not admit an equation of continuity. Finally, by subtracting the equations of kinetic energies k

and

/;;„,,

we

find the equation of balance of tur-

bulent kinetic energy

kt

^

\v"'v"'

[1, 11],

r,{T)U{T) (19)

We note that this isobaric condensation is a fictitious transformation, since it can never be realized physically.

^

(pAO

+

^.

{pktv'

+

p/w v"i)

General Remarks. The open nonhomogeneous sysof greatest interest to meteorologists consists of a

turbulent fluid. The 'physical state of the fluid is defined by the specific mass p and the pressure p, its state of motion by the components (y^, v-, v^) of velocity v in a

=p(A,

-t-

A,)

=

pK, (20)

where

R)dv^

NONHOMOGENEOUS SYSTEMS tem

system of rectangular Cartesian coordinates {x'^, x^, x^), fixed with respect to the earth. ^ Scalars p and p and vector V are functions of re', x^, x^ and of time t. By hypothesis, a mass element^ phx^hx^hx^, moving at velocity w*, exchanges no mass with the surroundings (absence of molecular diffusion). Therefore the system

^'^yii^

"^^

Ilk

^'^Tt'

(21) (i,

k

=

1, 2, 3).

1. In order to simplify the discussion we have neglected molecular viscosity. E.xtension of the results of this section to the case of a viscous fluid does not present any difficulty [11]. 2. By hypothesis, U = 0.

THERMODYNAMICS OF OPEN SYSTEMS Here, A( represents the fraction of kinetic energy of dissipated by turbulence per unit mass and time, and A,- the work per unit mass and time done in the course of edd3dng motion v"' by the resultant of all the effective forces (excluding Reynolds' apparent force dRi/dx') applied to the unit of mass considered. Work Aj can be regarded as being energy released by instability, per unit mass and time, in the course of the eddying motion v'"' [11]. When A, < 0, the turbulent motion is stable; when Ai> 0, it is unstable [11]. In the first case A; represents the fraction of turbulent kinetic energy transformed into heat per unit mass and per unit time; in the second, it represents the quantity of heat transformed into turbulent kinetic energy [13]. Finally we observe that turbulence can maintain itself only if k > (generalization of the criterion of L. F. Richardson). The First Law. The unit mass of the fluid (p, p, v'') being a closed system, we can apply to it the principle of conservation of energy, from which we obtain [10]

mean motion

.

d

,

dq

.

,

J

,

1

dpv (fc

=

(22)

This equation states that, per unit mass and time, the increase in the sum, of internal energy e, kinetic energy fc, and potential energy (p, is equal to the quantity of heat received dq/dt, plus the surface work done by the surroundings on the unit of mass under consideration during

same time interval. Because of the equation

the

of kinetic energy fc and the equation of continuity in p and v'', equation (22) takes the form (1), the enthalpy h being defined by ph =

pe

+ By

p.

setting

dq ^^ pa

(23)

'Tt

where a represents the rate of production of heat per unit mass and W' the components of heat flux (conductivity and radiation), equation (22) assumes (taking account of the equation of continuity) the form of an equation of balance

+

- p(e

fc

+

11]:

[1,

^) (24)

+ dx" The

pie

+

existence of

k

+

p

(32)

represents the rate of production of entropy. The second law states that the entropy production is real (o- > 0) k = -A,- from (20). recall that A, Equation (31) shows that the flux of mean entropy

-

We

includes a convective flux and a thermal flux due to radiation, conduction, and turbulence. The production

from

of entropy results

the

nonuniformity of

the

tempera-

production of heat, from the dissipation of mean motion by turbulence, and from destruction the of turbulent kinetic energy [11]. Finally, it should be noted that in the case of a

ture,

from

the

force per unit mass equal to gT'^/T. According to whether T* < or > 0, that is to say according to whether the particle is more or less dense than its and consequently surroundings, we have v" < or >

>

T'iv"

0.

This inequality brings out the manner of

organization of thermal convection. It turns out that

kinetic energy of

the energy of instability due to the excess T'i of the parcel's temperature above the mean temperature of

viscous fluid the expression A.- which appears in (25), (27), and (32) must be replaced by Aj — A„ where

its starting level is always positive and therefore corresponds to a positive production of turbulent kinetic energy. This production can result only from a transformation of heat into kinetic energy, and consequently

A„(>0) represents Rayleigh's dissipation function, that is, the fraction of kinetic energy of mean motion which is

dissipated

by viscosity

on the molec-

(internal friction

and per unit time. The Heat Flux Due to Atmospheric Turbulence in tihie Vertical Direction. If it is assumed that the mean motion of the air is horizontal, the adiabatic eddying motion in the vertical direction is governed by the

pa

>

re.

II

rr

pT

>

Vz

(36)

0.

ular scale) into heat per unit mass

Moreover we observe that the thermal-convective of heat

by returning to equation (32), it can be that the intensity of the entropy source as-

sociated with heat flux (35) dv^ [(r

Hi

-

y)r.

flux

always upward.

Finally,

shown

differential equation [11]

is

(33)

ACpaiT

—

T

Cj,ay

7)

is

given by »

rp"

(y)2

where v"

=

(37)

the eddying

velocity in the vertical z direc-

+

tion,

= T = 7 = T = rz

the mixing length,

the

mean temperature

of the

dry

air,

provided that T^

the vertical lapse rate —ST/dz, the adiabatic lapse rate {g/cpa where g represents gravity),

T'i

=

the excess of the temperature of the parcel above the mean temperature of the level

from which

it

originated.

After multiplying (33) by pv" for the energy of

eddying motion,

//

dvz

^

we obtain the

instability A, released

expression

during the

[A(r

-

t)

ptU:]

(34)

pr,v" > is the exchange coefficient A (Schmidt's austausch) in the vertical direction.

where

>

0,

>

0,

^ T- From

the inequality of (37)

(36) is

and the inequality

always

verified.

The

flux Wt is therefore compatible with the second law of thermodynamics without the necessity of assuming a priori that it is upward (as Ertel claims). It should be

noted' that the heat flux of Schmidt involves an effective production of entropy represented by the perfect

square in the

first

term

of the expression for

cr.

Application to the General Circulation of the Atmosphere. The equations which we have considered above

(21),

re.

7

pT^Vz

pa

T L

can be of use in the study of the general atmospheric circulation. The "mean motion" is then a zonal current (westerly or easterly), and the "eddying motion" cor3.

Bibliographical information and further details can be

found in

[11].

THERMODYNAMICS OF responds to perturbations embedded in this current. In this case it is clearly a question of turbulence on a very large scale (synoptic scale), essentially different from the small-scale turbulence which is usually studied. At the scale of the general circulation it becomes difficult indeed, if not impossible, to admit the conservation of potential temperature and of momentum or angular momentum of the large eddies along their trajectories.

On

the other hand nothing allows us to state a energy of the zonal

priori that a fraction of the kinetic

current

is

really transformed into kinetic energy of

large-scale turbulence (macroturbulence)

;

in this case,

the opposite might very well occur and probably does occur. In short, a thermomechanical theory of macroturbulence {Grossturbulenz of A. Defant) remains to be

worked

out.

of balance of momentum and kinetic energy can be used to obtain qualitative indications of the production and transport of these quantities in the atmosphere [8, 12]. Unfortunately, in the case of largescale turbulence we do not have the exact values of the Reynolds stresses R), the fraction A( (> or < 0) of the kinetic energy of mean motion dissipated by turbulence, and the energy of instability A^ released in the course of the eddying motion. It is therefore impossible to make a quantitative theoretical study of

The equations

the distribution of sources of zonal momentum, of kinetic energy, of internal energy, and of entropy, as well as of their manner of redistribution in the atmosphere.

Knowledge of the tensor of large-scale turbulence would permit us to achieve a better comprehension of the processes and the evolution of the general circulation of the atmosphere.

New investigations,

both theoretical

and synoptic, into the sources and the mentum, of energy in its various forms

flux of [13],

mo-

and

of

entropy appear desirable. Final Remarks.

When

the system under considera-

is homogeneous, the fundamental equations of thermodynamics can be written for the case of arbitrary addition of mass (dm ^ 0) to the system. These equations have manifold applications not only in

tion

meteorology (clouds with precipitation, evaporation of precipitation, mixing of air masses of different temperatures, psychrometry), but also in chemistry, in biology,

and

in industry.

The

situation

is

not quite the same

when

the system

nonhomogeneous (gradients of T and p), for in this case the material points of the system are necessarily in motion. Now the notion of movement can be defined

SYSTEMS

0PP:N

537

scale of the individual elementary

eddy

(the scale of

the molecule, if one envisions diffusion and molecular viscosity), then the macroscopic scale, that is, the scale of the mean motion. It must be observed that the latter scale cannot be adopted arbitrarily, for there

must be no

diffusion of

mass

at this scale

(pv'"'

^

0).

were not true, there would be no equation of continuity on the macroscopic scale, and it would be impossible to define and study the mean motion. Therefore the extension of the laws of thermodynamics for nonhomogeneous systems, to which mass can be added or removed arbitrarily, encounters difficulty in the very beginning unless it is possible to satisfy the condition pv'"' 0. We shall assume this condition to be met; then for an observer who is carried along with the mean motion and follows the evolution of the system on a microscopic scale, the flux of the diffusion If this

^

mass

of

expressed by means of

is

by means

intensity of diffusion 1, 2,

3).

-^-^^

^

—

dpv"'' .,

^

7^

(fc

=

However, as we have said before, the absence

of diffusion at the scale of

dpv"^

of

and the

9^

pv'"'

0) does not

diffusion of

mean

conditions

imply the absence at

any arbitrary property /

tity) of the fluid,

(pv'"'

^

this scale of

(intensive quan-

within the flow of which the

mean

/ is given by pfv'"' 7^ 0. Thus it is possible to carry out a study of the turbulent diffusion (eddy the diffusion) in the atmosphere of water vapor (/ specific humidity e) or of any other substance in susc^a'F), of pension in the air, of sensible heat (/ e), of eL), of internal energy (/ latent heat (/ k), of mos), of kinetic energy (/ entropy (/ flux of

^

^

mentum (/^

^ ^ ^

^

v), etc.

^

remark: The necessary condition pv'"' shows that y"* is the fluctuation relative to a weighted mean, and consequently the components of the mean

One

final

flow are necessarily the weighted means v' of the components v* of the velocity of the elementary eddies. The weighted mean has the unique property of decomposing, in an additive fashion, the average of the kinetic energy k into kinetic energy of mean motion and mean kinetic energy of turbulence (fc = k,n + 'ki) No other mean possesses this same property. total

.

Therefore, it is impossible to avoid the necessity of introducing the weighted mean into the study of tur-

bulence of

fluids.

REFERENCES

is

"The

Stability of Gaseous Stars."

Mon.

1.

Cowling, T.

retains its

2.

displacement; in other words, a system of dynamical equations can give a true representation of motion only if it includes the equation of continuity of mass, expressing the invariance of the mass of an element along its trajectory. Furthermore, in the case of a nonhomogeneous system, it is necessary to adopt in succession two scales of observation: first the microscopic scale, that is, the

3.

Not. R. astr. Soc, 96: 42-60 (1935). DE DoNDER,T.,"Z/'a^fU((5." Paris, Gauthier-Villars, 1927. and Van Rys.sblberghe, P., Thermodynamic Theory

and studied only

if

the

moving element

identity in the process of

its

G.,

of Affinity. Palo Alto, Calif., Stanford University Press, 1936.

R., "Introduction k la thermodynanuque des systemes ouverts." Bull. Acad. Belg. CI. Sci., 5" s6r.,

4.

Defay,

5.

GiBBs,

15: 678-688 (1929). J.

W., "Equilibrium of Heterogeneous Substances" Works, Vol. I: Thermodynamics. New York,

in Collected

Longmans,

1928.

DYNAMICS OF THE ATMOSPHERE

538

Eddy Flux

Heat

in the

6.

Montgomery, R.

7.

Atmosphere." /. Meteor., 5: 265-274 (1948). Prigogine, I., Etude thermodynamique des phinombnes

B., "Vertical

irriversihles. Li^ge, 8.

9.

Starr, V. P., "On the Production of Kinetic Energy in the Atmosphere." J. Meteor., 5: 193-196 (1948). VAN Lebberghe, G., et Glansdorff, P., "Contribution Acad. Belg.

11.

systemes ouverts." Bull.

484^97 (1936). "Thermodynamique des systemes non

12.

J.,

uniformes en vue des applications k la m6t6orologie." Geofys. Publ., Vol. 10,

No.

14, 18 pp. (1935).

"Production et redistribution de la quantity de et de l'4nergie cin^tique dans I'atmosphere. Application a la circulation atmosphSrique g^n^rale."

mouvement

Mmor., 1: 53-67 (1949). "Comment on the Global Energy Balance

J. sci. 13.

CI. Set., 5" s6r., 22:

Van Mieghem,

"Les Equations g^n^rales de la m^canique et de I'&ergStique des milieux turbulents en vue des applications k la m6t6orologie." Inst. B. inUior. Belg., Mim., 34: 1-60 (1949).

Desoer, 1947.

k la thermodynamique des

10.

of

14.

of the

At-

mosphere." Cent. Proc. R. meteor. Soc, pp. 173-175 (1950). et DuFOUR, L., Thermodynamique de I'atmosphhre. Bruxelles, Office International de Librairie, 1949. (See

pp. 107-133)

THE GENERAL CIRCULATION The

541

Physical Basis for the General Circulation by Victor P. Starr

Observational Studies of General Circulation Patterns by Jerome Namias and Philip

Applications of Energy Principles to the General Circulation by Victor P. Starr

F.

Clapp

551 568

THE PHYSICAL BASIS FOR THE GENERAL CIRCULATION By VICTOR

P.

STARR

Massachusetts Institute of Technology

Since time immemorial man has inescapably observed the atmosphere in which he Hves and has his being. It would therefore seem reasonable to expect that at the present date the science of meteorology should be one of the most advanced fields of human endeavor. Yet, if a distinction is made between the mere collection of descriptive facts of observation on the one hand

the avenue to sound progress is wide open and, at least as far as the writer is concerned, quite inviting.

and interpretative work which aims to give a rational phenomena on the other, it must be confessed that our knowledge concerning

It is therefore in the spirit of appraising our knowledge from the larger point of view that this commentary is written. Admittedly and intentionally the treatment reflects the writer's viewpoint gained through a number of years of concentration on the subject under consideration. As a candid personal sidelight it should be mentioned, however, that much of the material is in a sense a relatively recent culmination of the writer's striving toward a more unified and coherent conception

intellectual understanding of

the large-scale motions of the atmosphere is restricted mostly to the former category of information. Thus, for example, no one has as yet given a satisfactory rational explanation for one of the most outstanding

of the global circulation.

Nor

is

there currently

tallization.

This paper

is

therefore in the nature of an

and and approach

features of the general circulation, namely the large belts of westerly winds in the temperate latitudes of each hemisphere. However, it must be recognized that

individualistic progress report designed to portray

only in the last few decades that anything approaching sufficiently complete global observations for the checking of hypotheses regarding the general circulation has become available, so that progress at a more accelerated pace should now be forthcoming. The physiognomy of present-day meteorology bears much of the imprint imparted to it by the (so to speak) accidental way in which synoptic reporting networks developed and grew. In fairly recent times it was quite an achievement for a meteorologist to have at his command a network of reports large enough to depict an entire cyclone. The immediate temptation was then to treat this feature as an independent entity and to separate it artificially from its meteorological environment in seeking a rational explanation for it. The cyclone thus became a phenomenon that existed independently. More extensive observations now available point to the inadequacy of this tacit assumption. The cyclone constitutes a cogwheel in a larger mechanism and probably can be understood only in relation to and not independent of its atmospheric context. A criticism which is the same in principle can be leveled against many other efforts to explain synoptic structures. Indeed meteorology is replete with attempts to formulate ad hoc explanations for individual details of the general circulation without due cognizance of their role as functioning parts of a global scheme. In the more recent literature there are signs that we are outgrowing this restricted point of view; there are indications which emphasize the essential oneness of the atmosphere which must be studied as an internally integrated and coordinated unit. The general circulation presents a puzzle to be solved. We must learn how the various parts fit together into a whole if we are to understand it. With the hemispherical data now becoming available and the clues already at our disposal

ress

it

is

'

any

sign that this process has reached a state of final crys-

to share with others a certain outlook

hope that really substantial and enduring progeventually be attained thereby. Within the space of these pages we cannot hope to give anything approaching an exhaustive exposition of various topics. For this reason only certain basically important highfights will be elaborated, and we shall rely upon the reader's competence to interpolate various items of information which are generally available in the literature. Furthermore, the selection of the subjects touched upon is not one dictated by an aim at logical completeness, but rather is limited to those aspects which in the writer's mind are most likely to be conducive to further results at the present stage of development of in the

may

the science. As an outstanding problem of paramount importance for human activities, it is rather astonishing that the global circulation of the atmosphere has not up to the present time received more consideration from physical scientists generally. This situation is probably due in part to the lack of proper observational information so necessary for the successful prosecution of research concerning the subject. The gaps in at least our gross factual information are currently being removed rather rapidly, with the consequence that questions regarding the proper interpretation of the data begin to be the major issues. We might, with benefit in this connection,

moment and compare the development of meteorology with that of another physical science, namely astronomy. No one can dispute the claims that Galileo and Newton created a new and orderly conception of the solar system. This achievement was necessarily preceded not only by the laborious accumulation of observational knowledge by Tycho Brahe and others but also by the proper interpretation of these data by Kepler who, it might be said, defined in precise terms the dynamic puzzle to be resolved. In meteorology we find ourselves in what might be called digress for a

541

THE GENERAL CIRCULATION

542

the Keplerian era. It behooves us to marshal and correlate our observations into as precise

and consistent

a scheme as possible in order that we may Imow in what is to be explained. From what has been said it might seem to the reader that meteorology must still undergo a rather protracted period of development before results can be expected at the final fruition of this process. Although there is sufficient detail

reason to expect this pattern of events in the philosophical aspects of the subject, it should not be forgotten that the main practical use of meteorological knowledge, the preparation of weather forecasts, is at present largely an empirical procedure. As such, every improvement in our empirical information about the atmosphere enhances in some degree the possibility of improved forecasts, even though satisfactory understanding still remains to be achieved. Here only the intellectual aspects of problems are touched upon, leaving any possible practical applications for treatment elsewhere.

Following the general plan implied in what has been us begin by examining how the general circulation, as we observe it, achieves internal dynamic consistency in several important respects. As will be seen, this is merely the extraction from data and interpretation of certain information, and does not in any sense constitute an explanation of why the facts are as they are found. In oi'der to concentrate attention on the most basic processes, let us first consider the mean state, leaving the temporal fluctuations in the general circulation as a problem of much greater difficulty to be touched upon later. If an observer equipped with suitable instruments were to measure the motions of the atmosphere from some extraterrestrial vantage point, in the same manner as we measure the motions in the sun, he would probably be impressed by the irregularities of the details, but at the same time he would discern that there is a pronounced general drift of the air from west to east relative to the earth in middle latitudes, extending from the surface to the stratosphere and even beyond. On the other hand, in the more equatorial regions (and at times near the poles, at least the North Pole) he would discern a drift from east to west from the surface to great heights. This situation immediately poses perhaps the most important problem concerning the general circulation. The specific question involved here is how the belts of westerlies can maintain their high said, let

rate of rotation in the face of the retarding effect of

surface friction, flanked as they are

by oppositely

rected winds on at least their equatorial sides. really

satisfactory rational theory for this state

di-

No of

has yet been given, although some deductions can easily be made concerning the nature of certain aspects of the mechanism which is necessary to maintain these existing motions. affairs

The

retarding effect of the surface frictional forces

may

be looked upon as a continuous abstraction of absolute angular momentum from the atmosphere in these regions. According to simple principles of Newtonian mechanics, this

on the middle-latitude

westerlies

drain can be compensated only by an equivalent flow of angular momentum into the westerly belts. Likewise the surface frictional effect in the regions of the easterhes may be interpreted as a flow of angular momentum from the earth into the atmosphere. In order that the angular momentum so transferred into the easterly regions should not progressively accumulate and destroy these wind systems, it is necessary that an equivalent flow out of these regions should exist. The inescapable conclusion is that the accounts are balanced by a flow of angular momentum from the easterlies in the more tropical regions poleward to the westerly belts (the polar easterlies are of relatively small importance in this connection). Such a flow of angular momentum, let us say northward at the northern border of the tropical easterlies, can be measured in terms of an equivalent tangential stress acting across a vertical surface parallel to the latitude circle. A crude estimate of the value of this stress may be made from existing information concerning the surface frictional forces on the easterlies to the south.' The result is of the order of 50 to 100 dynes cm~'. Molecular and small-scale eddy viscosity cannot transmit stresses of this magnitude under the existing conditions, so that

very large-scale nonzonal components of motion must furnish the necessary eddy-transfer of angular momentum. We thus come to the very pertinent observation due to Jeffreys [5], namely that the large nonzonal components of motion in the atmosphere are necessary for the maintenance of the average zonal components. Most classical models for the general circulation as well as some more recent ones (see for example Rossby [9]) have followed along hnes originally proposed by Hadley [4] in that they assume the existence of large, slow, convectively driven closed circulations in meridi-

The development of the mean zonal mothen ascribed to the effect of the earth's rotation on these primary circulations. According to this view the necessary transport of angular momentum could be achieved if, for example, the poleward branches of the meridional circulations carry more angular momentum than the returning ones at other levels. onal planes. tions

is

For several reasons many modern meteorologists have to view models of the Hadley type with skepticism. In the first place, the warmest regions of the atmosphere are not usually found in the tropics as most schemes of this kind visualize, but rather some distance away from the equator. Also, at best it is difficult to account for the great extent of the westerUes in the atmosphere on any such basis. Finally, there is

come

a suggestion in the climatological distribution of precipitation and in the poleward flow of air in the friction layer for the existence of a slow meridional circulation with an upward branch in middle latitudes and a downward branch toward the subtropics, as originally suggested by Bergeron [2]. Such a "reverse" cell with aloft would, due to the action of tend to establish east winds in the

equatorward flow Coriolis forces,

L It is here assumed that the main transfer of takes place in the troposphere.

momentum

THE PHYSICAL BASIS FOR THE GENERAL CIRCULATION region where the strongest westerlies are actually encountered. The writer rather inclines to the view that although very small mean meridional circulations do perhaps exist, their role in the horizontal transport of angular momentum, at least in the middle latitudes, is

overshadowed by the characteristics

zontal motions. This

is

expressed by Jeffreys

[5]

of data to be

of other hori-

not in conflict with the views

and

is

reinforced

by

analysis

quoted presently.

placed upon the horizontal circulations momentum poleward, by and large the zonal and meridional components of velocity should be correlated at each level where such transport occurs. Evidences of this correlation are then to be expected in the detailed structure of the instantaneous horizontal streamline patterns observed, as pointed out by the writer elsewhere [10]. Qualitatively these expectations are amply borne out even by casual inspection of weather maps. Except at high latitudes, closed horizontal circulations usually exhibit a northeastsouthwest elongation (Northern Hemisphere) and the troughs, ridges, and shear hnes show a tendency to tilt in this same sense. All these characteristics ai-e recognized almost instinctively by the meteorologist as typical of atmospheric flow patterns. From our viewpoint they are telltale indications of a poleward flow of angular momentum. One may nevertheless ask whether an objective quantitative evaluation of the transport by this mechanism can be made from actual hemispheric data. For it is not sufficient to advance merely a qualitative substitute for the classical hypothesis without investigating the potency of the new alternative to produce the needed effect. A question involved here is whether the observations we possess are extensive enough and of sufficient accuracy. It is a simple matter to set up an integral expression for this (say) northward flow of absolute angular momentum across the vertical surface at a given latitude after If

emphasis

is

in transporting angular

the manner of Jeffreys, or to derive it from the atmospheric equations of motion as has been done by Widger

543

years (Widger [17], Miatz,^ Starr and White [12]) both from isobaric charts making use of the geostrophic approximation, and directly from a circumpolar network of actual wind observations. The survey of the angular momentum balance made by Widger covers the month of January 1946 and the results give the total geostrophic transfer by latitudes for various layers during this period up to the 7.5 km level. In this study estimates were made of the surface frictional torques. The investigation by Mintz covers the month of January 1949 and

momentum at various levels up to 100 mb. Starr and White made use of a circumpolar network of actual wind observations at a mean latitude of 31°N for a period of his results give the geostrophic flux of angular

months from February 1949 to August 1949 up to an elevation of 50,000 ft. For various details of these investigations reference must be made to the original six

papers.

The computations give results which are entirely reasonable, being quite in accord with what would be expected on the basis of the foregoing discussion. Thus the total northward transport increases in magnitude from low latitudes to about 30°N as the surface easterlies are passed, then decreases progressively northward as angular momentum is removed by surface frictional

torques acting in the westerly belt. Nearer to the pole the transport is reversed, indicating a flow southward from the polar easterly zone, although the magnitudes involved here are small as is to be expected from the fact that the torque arm associated with the surface frictional forces is small in the polar regions.

The main

transfer across

30°N

increases in intensity

with elevation, reaching a pronounced maximum at about the level of the jet stream. On the basis of estimates of the surface torques during these periods it appears that sufficient angular momentum is transported into the belt of westerlies to maintain them against friction. Let it be noted, however, that the general results appear to be in harmony with the thesis

author proceeded to evaluate this flow of angular momentum by finite difference methods, as

that 'practically all the necessary horizontal transfer of angular momentum could he accomplished without recourse to the agency of mean meridional circulations. On the

follows.

basis of

[17].

The

latter

During the last several years sufficient observations of the free atmosphere have been made to allow the construction of daily isobaric charts through most of the troposphere. In addition it is becoming possible to obtain fairly complete direct radiowind observations

extending to great heights on a circumpolar basis within restricted latitude belts.

The

global

wind distributions

may

be approximated from isobaric charts according to the geostrophic wind formula or may be taken directly from actual wind observations. The use of the geostrophic estimates may introduce certain errors for the present purpose. On the other hand this use of the geostrophic winds automatically excludes the contributions to the angular momentum transport due to mean meridional circulations of the Hadley type, so that an advantage

gained if it is desired to study other modes of such transport. Several surveys of the angular momentum balance have been made in the past few is

what has been said, however, we cannot make any statement concerning other possible functions of meridional circulations such as, for example, the vertical transport of angular momentum. At this point let us pause in order to take stock of what has been described and to see more clearly how it fits into the plan for research advanced in the introductory paragraphs. Have we by this study of angularmomentum considerations provided a theory for or achieved a rational solution for the problem of the distribution of zonal westerlies and easterlies in the atmosphere? Not by a long way. We did not solve the equations of motion^ nor did we deal with radiative 2.

tum

Flu.x of Angular MomenJanuary 1949." Presented at the 109th the American Meteorological Society,

"The Geostrophic Meridional for the

Month

of

national meeting of Jan. 29-Feb. 1, 1951, New York. 3. Actually only one equation of motion, namely the one for

the zonal direction,

is

needed to treat the balance

of absolute

THE GENERAL CIRCULATION

544

which must ultimately be responsible for all motions and are a determining factor for the form of the general circulation. What we have done is simply make a systematic analysis of data to portray as clearly as possible one important, but not patently apparent, attribute of the general circulation namely, the angular-momentum balance. This study attempts to show how the actual atmosphere attains an internal consistency in one important respect. What purpose can such information as this serve in the future of meteorological theory? The answer to processes,

air

—

query is obvious. Once the announcement was made by Kepler that planets move in ellipses, any proposed dynamic theory of mechanics which would require them to move in significantly different paths was immediately this

pushed into the limbo. Likewise for the atmosphere any proposed rational theory for the general circulation which significantly contradicts the general outlines of the needed angular-momentum balance at once finds itself afflicted with a serious and perhaps even crucial drawback. On the other hand, the uses of such information need not be purely negative. The facts might well serve am one guide (among many others) for the formulation of satisfactory rational schemes. What has been described is not a very profound concept, but merely a rather simple consequence of Newton's laws of motion applied to the atmosphere. The

this spirit that the writer would recommend the further exploration of the essential properties of the global circulation as we know it from observations with regard to such dynamic quantities as angular momentum,

vorticity, kinetic energy, heat energy, geopotential en-

and latent heat, so that we may find ourselves more advantageous position in formulating rational

ergy, in a

hypotheses. For the purpose of exemplifying further the suggestions previously made, let us consider in a general way their application to questions concerning energy in the atmosphere. Much of what has been written concerning this subject has been deficient in two respects. In the place investigators have been prone to lump together various diverse forms of energy indiscriminately, thereby losing the advantages to be gained from the fact that each form of energy is produced from and converted to other forms in its own characteristic fashion, permitting individual study. Likewise for each first

form there

exist specific

modes

of transfer

and

redis-

tribution. Unless these specific characteristics are sub-

shalt not enter here," seeking thereby to channel

very broad generalizations can be reached, which lack a keen enough resolving power to yield much that is new concerning the mechanism of the atmosphere. In the second place, as will be discussed presently, the modes of energy transfer within the atmosphere are so effective that no feature such as a cyclone can be treated independently without due allowance for exchanges of energy between it and the remaining atmosphere. It is therefore inappropriate to treat such a feature as in any sense a closed system. Modern trends in the literature are beginning to give proper cognizance to this circumstance, although much of the toorestricted point of view is still prevalent. Probably the only system which can be treated as a closed one (mechanically) is the atmosphere as a whole and even then it caimot be treated as closed from a thermodynamic viewpoint because of radiative exchanges of energy with the cosmic environment and otherwise. Proceeding now to a discussion of the kinetic energy balance of the atmosphere, it is worthy of note in the first place to observe that whereas angular momentum is a quantity which is conserved in the sense that no real sources of it can exist, kinetic energy on the other hand may appear or disappear because of transformation processes involving other forms of energy. In other

True science no prohibitions, and in principle no servile adherence to tradition. Rather we must open up and exploit all possible new channels that appear reasonable in order that we do not miss important facts. * It is in

words, the flow and redistribution processes for kinetic energy are not source-free as is the case with absolute angular momentum. We may therefore say a priori that there is no reason to suppose that there may not exist in the atmosphere preferred source-regions for

angular momentum about the earth's polar axis. In effect this equation takes on the form of a continuity equation for absolute angular momentum. 4. When one compares the general nature of the results of research in meteorology as reported in our journals with the nature of research communications in let us say chemistry, there is a fundamental contrast to be noted. In our field there is a great diversity of views expressed on individual topics. Often these views are in direct conflict. Also one gains the im-

pression that there

was presented many years ago, by is it then that it was permitted so long a time? Aside from the lack of

gist of the idea

Jeffreys in 1926.

to

lie

fallow for

How

proper data, a contributing factor has doubtless been the preoccupation of research meteorologists with phenomena on a relatively local scale, this in turn being due to the limitation of our mental horizons to a scale commensurate with the daily weather map. One might well venture the guess that at present we have not attained even a measure of the tasks which confront us. And this statement is in no way intended as a repetition of a common platitude. We have not fathomed the profundity of our subject, let alone solved the fundamental problems. In the years to come, when our knowledge will have increased, we may in retrospect wonder why we were so inappreciative of various

and essential attributes of the general circulation. would therefore be wrong and dangerous to post a sign along any plausible path of research which states

gross It

"Thou

activity along certain predetermined lines. tolerates

ject to scrutiny in detail, only

is less

tion of knowledge. This fact that meteorology

is

of the orderly progressive

phenomenon

is

in a far different stage of

as a science. In the better sense of the

accumula-

doubtless due to the

word we

development

are alchemists

in the process of groping for a common denominator of unifying principles. We must not relax but rather continue to stumble and grope with more determination. The writer has the immutable belief that a proper foundation does exist and still

will

be found.

THE PHYSICAL

BASIS FOR

atmospheric Idnetic energy as well as preferred regions for its disappearance by conversion into other forms of energy through friction or otherwise. With the aid of the examination and interpretation of the fundamental dynamical principles relating to Idnetic energy given elsewhere in this volume^ we shall now attempt to discuss this phase of the energy problem. In the reference mentioned there is presented a discussion of the process whereby Idnetic energy is produced in the atmosphere. According to the views expressed there, kinetic energy of large-scale motions can be generated only through the work of expansion by pressure forces. Furthermore, Idnetic energy associated with horizontal motions can be generated only through work done by horizontal pressure forces. It is thus pointed out that the rate at which horizontal kinetic energy is generated at a given point in the atmosphere is equal to the product of the pressure into the horizontal divergence of velocity. This carries the implication that regions of horizontal convergence are hydrodynamic sinks for kinetic energy which act independently of friction. Speaking next of the transport of horizontal kinetic energy, it has been shown that this process is accomplished either through the work done by the pressure forces in virtue of the horizontal velocities across the boundary or by the advection of sensible kinetic energy. Since the latter (meridional) transport is small, it follows that the significant (meridional) transport of kinetic energy is accomplished through the work done by the pressure forces, which in turn is proportionil to the advection of internal heat energy

and occurs

in ad-

Applying these ideas to the transfer of Idnetic energy across the vertical boundaries of an equatorial strip between two fixed middle latitudes -\-(t> and —(f>, our general information would lead us to suppose that there exists a net transport of internal heat energy and therefore of kinetic energy poleward across these boundaries. Estimates from data tend to dition to

it.

confirm this supposition, and indeed it also appears reasonable from common synoptic experience. We are therefore confronted by the very important conclusion that regardless of the nature of other details of the atmospheric circulations the more tropical regions appear to be preferred regions for kinetic-energy generation in that they not only produce sufficient kinetic energy to overcome frictional losses within these regions, but also provide an excess which is transferred to the polar caps.

Apparently we may also conclude that in the long run the moi'e polar regions must serve as preferred regions for the disappearance of kinetic energy, since here the losses must be sufficiently great not only to offset whatever amounts of Idnetic energy are generated locally

but also to absorb the Idnetic energy which

supplied from the

more

tropical regions. It

is

is

therefore

THE GENERAL CIRCULATION fairs

in

545

the atmosphere there are vast

kinetic energy generated in the

and vast amounts consumed existing kinetic energy

is

more

amounts

of

tropical regions

in the polar caps.

The

merely a small difference due

to the fact that the positive generation process in the more tropical regions is slightly larger than the losses in regions of negative generation in the polar caps. It is a matter of interest to examine the import of the views expressed above for the nature of the secondary circulations of the middle latitudes. It would thus be suggested that the kinetic energy supply for the main cyclone belt of each hemisphere is perhaps provided by the poleward flow of such energy from more tropical regions. Furthermore this flow is measured by (but exists in addition to) the poleward flow of internal heat energy. Although this flux of energy has some average mean value, there can be no doubt that in its details the process is a sporadic one with irregularities both in time and in longitude. Each cyclone may thus be considered as producing a spurt or poleward surge in this transport locally during its period of develop-

ment. According to the classical view, the kinetic energy for a developing cyclone is obtained from the sinl^ing of dense masses of cold air in the immediate vicinity, so that

by and

large the decrease in potential

and internal

energy represents a corresponding increase in kinetic energy. From the present viewpoint the kinetic energy increase could equally well be derived from a pronounced local poleward flow from the more tropical regions, since a developing cyclone is accompanied by a marked increase in the net local poleward transfer of internal heat energy. As a matter of fact it is not too difficult to visualize the general outlines of a certain type of instability associated with a developing cyclone when viewed in this way. For if it is granted that there exists a supply of warm and cold air in the vicinity, it may be that the pronounced local surge of kinetic energy once started serves to increase the intensity of the cyclone which in turn further increases the flow of kinetic energy and the intensity of the cyclone. The intensification finally ceases when complete occlusion takes place and the net heat transport disappears. In a recent discussion the writer [11] has made an endeavor to elaborate further this picture of the kinetic energy balance of the atmosphere, making use of the

assumption that mean meridional circulations do not play a significant role in these processes.

The

plausi-

supported by the study of the angular momentum balance outlined earlier. Under such circumstances, since data show that near the surface poleward-moving individual air masses possess a higher specific volume than the equatorward-moving ones, it follows that there should exist a mean horizontal velocity divergence in the more tropical regions and a bility of this supposition is

reasonable to suppose that in the normal state of af-

7nean horizontal velocity convergence in the polar caps. This situation should thus contribute to a net pro-

Consult "Applications of Energy Principles to the Gen-

duction of Idnetic energy, in view of the normal mean meridional distribution of pressure along horizontal

5.

eral Circulation"

by Victor P.

Starr, pp. 568-574.

THE GENERAL CIRCULATION

546 surfaces.*

Such estimates as can be made indicate that

this gross average action

may

be of very great

effec-

tiveness.

In view of the fact that the correlation of density with meridional motion is most marked near the surface, it follows that the mean meridional distribution of this divergence and convergence shows greatest contrasts at low levels. This at once suggests that the mean meridional distribution of net external heating and cooling of the atmosphere is linked with the process, since the heating of the atmosphere is most intense near the surface and much of the cooling is accomplished through surface effects also. Thus it would be logical to suppose that the net external heating in the more equatorial latitudes causes a net horizontal expansion, while the net cooling in the polar caps brings about a net horizontal contraction, accounts then being balanced, as far as mass continuity is concerned, by differential advection across middle latitudes. If one agrees to argue on this basis, a far-reaching observation may be made, subject of course to the correctness of the premises involved. Earlier in the discourse it was pointed out that one of the most fundamental questions in meteorology relates to the presence of broad belts of westerlies in the middle latitudes of each hemisphere. Speaking now only of the lower levels we see that the presence of the westerlies coincides with the requirement that the regions of net external heating and divergence should coincide with regions of higher pressure along horizontal surfaces. Unless this situation exists a net production of kinetic energy to overcome friction would be impossible. Thus, if for a moment we were to visualize a hypothetical situation with mean easterlies in middle latitudes, the net heating and consequent divergence would take place at a relatively low pressure in the more tropical regions, while the convergence and coohng in the polar caps would take place at a relatively high pressure. Such a hypothetical situation would then be rapidly destroyed, since more kinetic energy would necessarily disappear in the polar caps through convergence than could be generated in the more tropical regions by heating and divergence. Although the net heating and cooling of the earth is ultimately caused by radiational exchanges with space, when one isolates the atmosphere and considers the circumstances in the winter season especially, due regard has to be given to the strong heating of the atmosphere by the oceans when cold air masses flow out over relatively warm water surfaces. As has been pointed out by Sverdrup and others [13], the oceans serve in a manner of spealdng as a hot-water heating system. It should thus be expected that during winter the regions of net heating for the atmosphere extend much farther into middle latitudes than might otherwise be supposed. 6.

Since variations of pressure along horizontal surfaces are

amount of kinetic energy indeed reasonable on general grounds to suppose that the atmosphere behaves in such a way as to take advantage of the large systematic pressure differences between the polar and tropical regions.

necessarj' for the generation of a net

to overcome friction,

it is

Since

we have been speaking

of the meridional transheat energy, it is desirable to mention also the effects of the meridional transfer of latent heat. Crude estimates made by the writer using such data as are available indicate that very considerable amounts of energy are transferred poleward by this means. However, whereas the transport of internal heat energy cannot take place without a proportional transport of kinetic energy, the meridional transfer of latent heat energy is not related to the kinetic energy in the same way. It is thus possible to transfer large amounts of energy in the form of latent heat without a proportional kinetic energy flow being present. Whereas the flow of kinetic energy and therefore of internal heat energy may be regulated by the distribution of pressure and of divergence and convergence, this particular limitation does not enter as far as latent heat is concerned. One could therefore find arguments to support the view that the transport of latent heat furnishes a means for balancing the radiation requirements of the general circulation which bypasses the Idnetic energy balance. For if the portion of the total meridional energy flow represented by the transfer of latent heat energy had instead to be transported as additional internal heat energy, a far more intense flow of kinetic energy would also be necessary. Whether this would imply a more "vigorous" general circulation is, however, a question which cannot be readily dealt with. The meridional transport of geopotential energy is of course immediately ruled out in the avei-age condition discussed here, because of the assumption that mean meridional circulations are not significant. In the discussion mentioned above [11], an endeavor was made to study the fluctuations in the kinetic energy balance of the Northern Hemisphere with the aid of 5-day mean data such as are used by the U. S. Weather Bureau in extended-period forecasting. Only data for the colder half of each of seven successive years were used, so that essentially winter conditions were studied. By approximate methods a measure was secured of the intensity of differential advection of air with varying density across 45°N. This quantity r is therefore a measure of the net volume transport northward across 45°N and hence also a measure of the mean convergence in the polar cap and to some degree probably a measure of the mean divergence in the more tropical zones of the Northern Hemisphere. A mean for the layer be-

fer of internal

level and 10,000 ft was used. became immediately apparent that the quantity

tween sea It

T undergoes large fluctuations, being high during those periods which are commonly designated as "low-index" periods and low during "high-index" conditions. The practical question involved here concerns itself with the cause of these vagaries in the behavior of the general circulation, for if this were known a better insight into

the long-range forecasting problem might result. In view of the fact that t is also a rough measure of the rate of kinetic energy transport into the polar cap, it is interesting to note its relationship to the general pressure distribution there. If these pressures are low

compared

to the pressures farther south, a relatively

THE PHYSICAL

BASIS

FOR THE GENERAL CIRCULATION

large fraction of the kinetic energy so transferred should remain without being destroyed by the mean conver-

gence, while if these pressures are high practically all the kinetic energy fed into the cap should disappear because of the mean convergence. For this purpose it was decided to examine r with reference to the areamean pressure deficit north of 45°N as compared to the pressure at 45°N. This pressure deficit was denoted by

X and was computed from sea-level pressures. came apparent that abnormally large values of

It bet are,

generally speaking, encountered only when the pressure deficit is small or negative, in other words when the

capacity of the polar cap to destroy kinetic energy

is

abnormally great.

From

these general observations

it

would appear that and

large meridional transports of internal heat energy

energy take place during those periods when meridional pressure distribution at lower levels is relatively flat north of the subtropics with no marked polar low present. How can a situation such as this maintain itself over appreciable intervals of time, as is known to be the case? Is it a quasi -steady state or is it a dislocation which becomes progressively more difficult to maintain? We can only speculate about the answers, but it is rather interesting to do so. First let us consider the fact that it is during these low-index conditions that very cold air masses are injected into southerly latitudes. This in turn means a very strong heating of the atmosphere in middle latitudes and the subtropics, especially over ocean areas, so that a rapid replenishment of heat and also a rapid generation of kinetic energy would be a normal accompaniment of this state of affairs. This consideration would argue for the possibility of quasi-steady state. On the other hand in order to maintain a quasi-steady condition, means would have to be present to dispose of large quantities of heat in the polar cap. It is unlikely that the net heat loss through radiation could be stepped up enough to meet this requirement. Progressive melting of ice in the polar regions could absorb large quantities of heat, but probably exactly the opposite is actually the case, since very low temperatures are apt to prevail at low levels in the arctic and subarctic regions under these circumstances. Observationally there is some qualitative evidence that during prolonged low-index conditions there is apt to be present in polar regions an accumulation of abnormally warm air a little distance above the surface in the troposphere and in the stratosphere. Also there is some evidence that there is actually a progressive depletion of heat energy from middle latitudes (in spite of the strong surface heating) with a consequent progressive southward shift of the latitude of the maximum westerlies at higher levels. What ultimately puts a stop to the trend of developments is not obvious. Contrasted with the low-index regime, during periods of a strong polar vortex at low levels the heat and kinetic energy transport is weak. Relatively warm air streams across the continents and oceans in a more zonal manner so that no very vigorous heating takes place. So far no difficulties seem to be present as far of kinetic

the

mean

547

more southerly regions are concerned. It would appear, however, that progressive cooling should now take place in the arctic regions since the abnormally low heat input would appear to be insufficient to maintain the status quo. On the whole there may be good and sufficient physical reasons, such as those mentioned above, why the as the

general circulation does not persist indefinitely in one or the other abnormal conditions but rather tends to shift about a general average state. There is neverthe-

the important question why the average state does not persist without such pronounced departures as those just described. The writer's conjecture on the matter is that the average state can too easily be disrupted by the effects of the nonzonal continentaUty found especially in the Northern Hemisphere. Such effects may be partly due to the fact that the continents provide avenues for the southward penetration of intensely cold air masses which can thus arrive at relatively low latitudes without undue modification. The occasional outpourings of such cold masses over adjacent water areas at fairly low latitudes could easily result in abnormal heating of the atmosphere sufficient to disrupt the average regime. Also it should not be forgotten that large mountain ranges extending over an appreciable spread of latitude can exert powerful mechanical effects upon the atmosphere, as pointed out by White [16]. By way of example large pressure differences across the Rockies in North America could perhaps disrupt the angular momentum balance in the belt of the prevailing westerlies. Finally the suggestion made by Willett [18] that the seat of the variation could perhaps be found in the variations in solar output, and hence the heating of the atmosphere, deserves study. For it ma}' be that the final answer is bound up in a combination of effects, especially if long-term aberrations of the general circulation during historic and geological periods are also less

considered.

From what has been said in the several preceding paragraphs it might appear that too little emphasis has been placed upon the influence of the conditions in the upper troposphere and in the stratosphere. In the final analysis it is obvious that the entire atmosphere must form an integrated system. It would seem, however, that the lower layers furnish the seat of thermodynamic activity and provide the motive force for the general cii'culation. The writer's colleague. Dr. H. L. Kuo, is currently engaged in a theoretical study of the effects which might result at the level of the jet stream from forced disturbances originating in the lower levels. From his preliminary work it would appear that the generation and maintenance of the jet stream itself are a necessary consequence of such impulses received from below. Likewise the characteristics of the angular momentum balance as outlined previously, including such features as the tilted (and properly curved) trough and ridge lines, as well as the development of regions of sharp shear to the north and to the south of the jet follow as consequences of the analysis. Having made an excursion into some of the ramifi-

548

THE GENERAL CIRCULATION

cations involved in the study of the balance of angular

own

momentum and of kinetic energy in the atmosphere, let us now consider the general circulation from the

diverse problems which are worth while.

standpoint of a rational theory for atmospheric motions. this term we mean essentially a solution of the equations of motion which purports to give a picture of the circulation or some portion of it. This is sharply contrasted with the study of the balance of various quantities, because the latter involves hydrodynamical principles only to the extent of formulating several integral requirements for the atmosphere. The investigation of how the atmosphere actually fulfills these requirements is then necessarily an empirical and observational problem. Logically, then, the empirical picture obtained from the study of the balance of various quantities and from other observational studies should give us the fundamental physical characterization of the atmosphere which is then to be explained in terms of some rational theory. But, in a larger sense, the proper physical characterization of the general circulation is a subject which up to the present has hardly been entered upon. We need quantitative estimates of the flow of heat, of kinetic energy, of momentum, etc., for the mean state and also when consideration is given to synoptic and seasonal variations. The labor involved in order to supply this information is bound to be tremendous, involving the cooperation of meteorological services over the entire globe. Nevertheless progress is being made and there is reason for optimism. In view of this state of affairs it is not surprising that the development of a rational theory for the general circulation has not made very much headway up to the present time. Thus the scope of the more successful efforts toward the solution of the hydrodynamic equations has necessarily been severely limited to certain portions of the atmospheric circulation where the introduction of drastic simplifications still leads to results of interest. As an example we might cite the several solutions of the two-dimensional barotropic vorticity equation given by Rossby [8] and recently elaborated by Chai'ney and Eliassen [3] and others. For short-period extrapolation it appears that these results may prove to be of more and more value in forecasting,

By

even though these solutions leave unanswered some of the fundamental questions concerning the energy balance when long-term effects are contemplated. As a general comment it can be said that really adequate solutions which link the mechanics of the atmospheric circulation to the source of energy from solar radiation are a desideratum for future research, although the situation does not warrant undue pessimism. In this connection reference may be made to a recent publication by Lorenz [6] which is concerned with the solution of the two-dimensional equations of motion for the region near the pole, taking into account friction and external heating and cooling. Leaving now the discussion of illustrative topics, what are the avenues for future progress which are indicated as of today? This is necessarily a subjective matter in which various investigators must follow their

inclinations

and

tastes, for there is

no shortage of

The

inclina-

tions of the writer, as one of these investigators, are

probably quite apparent from what has already been said. The underlying and oft-recurring motif of this essay is the need for a more complete and systematic empirical description of the basic physical processes involved in the general circulation. We are now beginning to have sufficient observational material at least

Northern Hemisphere. Before making concrete proposals, let us take a glance at what is being done which may serve as a beginning toward this aim. In the enumeration of activities which follows, any omission of important work is inadvertent and is due simply to the writer's lack of information. At the Massachusetts Institute of Technology Willett [18] has for a period of years gathered statistical information concerning the general circulation in the Northern Hemisphere in the form of 5-day averages. More recently he has begun gathering similar data for the Southern Hemisphere. The writer has found this material invaluable for the study of the general circulation. The Department of Meteorology of the University of California at Los Angeles has undertaken a study of the angular momentum balance of the atmosphere in the

by means

of finite difference integration procedures.

This project will probably also include a similar study of the energy balance later. Priestley [7] of Australia has proposed a program for the observational study of the momentum and energy balance of the atmosphere, utilizing radiosonde and radio-wind observations directly. Samples of his analyses already prepared by him have proven to be of great interest, but require elaboration. Van Mieghem [15] of Belgium has proposed the study of the balance of various forms of energy, entropy, and momentum, emphasizing the importance of such studies for the progress of research concerning the general circulation.

The Extended Forecast Division of the U. S. Weather Bureau has for some years been amassing observational material in the form of 5-day averages for the Northern Hemisphere. The Weather Bureau [14] has recently also been preparing in published form very complete daily Northern Hemisphere maps for the surface and 500 millibars. These charts are most excellent and should prove to be invaluable for research purposes. Finally mention may again be made of the studies of the angular momentum and energy balance initiated by the writer at the Massachusetts Institute of Technology.

The items listed above do not purport to cover all important research on the general circulation conducted currently, but rather only such activities as are apt to furnish statistical information concerning the gross character of the general circulation. Thus various other synoptic and theoretical activities are not included even though they may in the end furnish indispensable insight as to the interpretation of the empirical picture

given by the

The

statistics.

general trend to be discerned

is

that the em-

THE PHYSICAL

BASIS FOR

THE GENERAL CIRCULATION

pirical study of the general circulation is becoming a matter involving vast amounts of data properly and

purposefully organized in order to be useful for the systematic evaluation of various specific and well-defined processes over long periods of time. It is being undertaken piecemeal by various institutions to an extent determined by their financial resources and facilities. In the initial stages of such exploratory activities it is

probably most desirable that there should

exist diversified direction of individual small-scale proj-

However, once the best general patterns for such research have become apparent, a number of considerations point to the desirability of ects of this nature.

more consohdated

effort.

Thus some

central organiza-

tion could perhaps offer the advantages of a long-term

program, more economical operation, better facilities such as high-speed computing equipment and better availability of

computed

results.

Such an

institute could

even be of an international character under the auspices of the United Nations, since the purpose would indeed be of global importance in a very literal sense. Beyond the broad recommendations just set forth, the writer wishes to state his belief that periodic reviews of progress such as the ones contained in this volume should be planned by appropriate organizations in an effort to stimulate comparison of differing opinions and to bring forth suggestions. Another matter of somewhat similar nature is the periodic publication of selected reprinted papers, adjudged to be of fundamental importance, in the form of collections similar to those edited by Cleveland Abbe [1] several decades ago. A practical problem here would be the selection of a capable (and so to speak disinterested) editor. Finally a word about certain philosophical and theoretical aspects. In a science such as meteorology in which the rational explanation of the most gross features is still to be found, much attention must be given to questions regarding the general techniques for in-

thing of the spirit of daring which prompted Newton to propose the theory of universal gravitation and Einstein to suggest anew the quantum character of radiation.

Much of what has been said in the last two paragraphs has a direct beai'ing upon the use of mathematics in meteorological research. To regard the fundamental problems of meteorology as purely mathematical ones is hardly warranted. It is true that many of the hydrodynamical and physical principles involved are capable of mathematical statement, but it is only through the leaven of some purely physical hypothesis that we are guided to the appropriate mathematical use of these principles.

As stated previously, present-day meteorology may be thought of as being in the Keplerian era. It finds itself, however, side by side with very much more advanced physical sciences in which research is carried on ^vith the aid of very sophisticated mathematical and theoretical tools designed for the purpose through the laborious efi^orts of past generations. Although much may be gained by borrowing certain of these techniques where proper analogies have been established, still there are certain philosophical pitfalls which arise when this is done merely in slavish effort at imitation without proper caution. Such superficial efforts are sometimes entered upon in order to gloss over the prerequisite of

stemmed from

the deliberate introduction of new physical Such hypotheses are usually the direct product of creative minds who through sufficient insight are able to recast a given problem into a new form. Although such formulation of novel hypotheses is perhaps the most difficult task confronting a scientist, we cannot afford to dispense with it in any attempt at understanding the motions of the atmosphere at the

lution of a

new

science

by omitting

mechanics.

REFERENCES 1.

Abb£, C, "The Mechanics

A

of the Earth's

Collection of Translations

Bergeron,

Atmosphere.

by Cleveland Abb^." Third

Collection. Smithson. misc. Coll., Vol. 51, 2.

No. 4

(1910).

T., "tjber die dreidimensional verkniipfende

5, No. 6 (1928). Numerical Method for Predicting the Perturbations of the Middle Latitude Westerlies." Tellus, Vol. 1, No. 2, pp. 38-54 (1949). Hadlby, G., "Concerning the Cause of the General Trade Winds." Phil. Trans, roy. Soc. London, 39: 58 (1735-36).

Wetteranalyse. I." Geofys. Publ., Vol.

3.

4.

hypotheses.

5.

6.

7.

Charney,

J.,

and Eliassen, A.,

"A

(Reprinted in [1, pp. 5-7].) Jeffreys, H., "On the Dynamics of Geostrophic Winds." Quart. J. R. meteor. Soc, 52: 85-104 (1926). Lorenz, E. N., "Dynamic Models Illustrating the Energy Balance of the Atmosphere." J. Meteor., 7 -.30-38 (1950). Priestley, C. H. B., "Heat Transport and Zonal Stress

between Latitudes." Quart.

present time.

Without the use

We

cannot telescope the evoessential phases of its natural development. We cannot hope for a magic carpet which would carry us directly from Kepler to Einstein, eliminating the growing pains of Newtonian clear physical thinking.

terpretive research in order to ascertain

if possible the ones which are suitable. In any well-developed science, as for instance physics, it is often possible to arrive at new results by purely deductive means. However, it must be granted that the more fundamental scientific achievements of an interpretative nature have usually

549

J. R. meteor. Soc., 75: 28-40

(1949).

of creative imagination to give it

form, our science could easily become a repetitious accumulation of bits of petty dogma, a jargon of catchwords and sophistries, a species of scholasticism lacking a firm basis or unifying principles. We need men with vision and courage who would not be content in occupying themselves with odd bits of research, but would tackle the fundamental problems. Men who have some-

8.

RossBY, C.-G., and Collaborators, "Relation between Variations in the Intensity of the Zonal Circulation of the .Atmosphere and the Displacements of the Semipermanent Centers of Action." /. mar. Res., 2: 38-55 (1939).

9.

Ro-ssby, C.-G., "The Scientific Basis of Modern Meteorology" in Climate and Man: Yearbook of Agriculture. Washington, D. C, U. S. Govt. Printing Office, 1941. (See pp. 599-655.)

THE GENERAL CIRCULATION

550 10.

11.

P., "An Essay on the General Circulation of the Earth's Atmosphere." /. Meteor., 5: 39-43 (1948). A Physical Characterization of the General Circulation. Dept. of Meteorology, Mass. Inst. Tech., Rep. No. 1, General Circulation Project No. AF 19-122-153, Geo-

D. C, U.

15.

and White, R. M., "A Hemispherical Study Atmosplierie

of the

Angular-Momentum Balance." Quari.

16.

meteor. Soc, 77: 215-225 (1951). SvERDRUP, H. U., Johnson, M. W., and Fleming, R. H., The Oceans. New York, Prentice-Hall, Inc. 1942.

14.

U.

S. Weather Bureau, Daily Synoptic Series Weather Maps, Northern Hemisphere, Sea Level and 500 Millibar

White, R. M., "The Role

Momentum

/. B.

13.

S.

quantity de mouvement et de I'energie cin^tique dans I'atmosphere. Application k la circulation atmosph^rique g^n^rale." /. sci. Meteor., 1: 53-67 (1949).

phys. Res. Lab., Cambridge, Mass., 1949. 12.

Data Tabulations. Washington, Department of Commerce. Van Mibqhbm, J., "Production et redistribution de la Charts with Synoptic

Starr, V.

of Mountains in the Angular Balance of the Atmosphere." J. Meteor.,

6:353-355 (1949). 17.

18.

Widger, W. K., "A Study of the Flow of Angular Momentum in the Atmosphere." /. Meteor., 6: 291-299 (1949). WiLLETT, H. C, "Patterns of World Weather Changes.'' Trans. Amer. geophys. Un., 29: 803-809 (1948).

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS By JEROME NAMIAS and PHILIP

F.

CLAPP

U. S. Weather Bureau, Washington, D. C.

Any

reasonably brief treatment of a subject so vast

as "Observational Studies of General Circulation Pat-

bound to be biased in its selection of material. any and all real information derived from the atmosphere constitutes an integral part of the material upon which students of the general circulation must draw. Inasmuch as our knowledge of the general circulation is very far from complete, it is difficult at this time to decide what statistically or observationally terns"

is

To be

sure,

determined facts are especially pertinent. In selecting these data the authors confess to a bias in the direction of hemispheric or world-wide phenomena and also to those facts which have emerged from a fifteen-year-old experiment in the anatomy and physiology of the general circulation with which the authors have had the pleasure to be affiliated [33].

NORMAL STATE OF THE GENERAL

decades.

At the present writing

from being

this ideal state of affairs

For the Northern Hemisphere the longest series of analyzed charts at sea level embrace a period of about fifty years and at upper levels about fifteen years. Such a short period is woefully inadequate for studies of large-scale weather phenomena, particularly when one considers time intervals of a month or more. Furthermore, many of these charts are incomplete or inaccurate, and the upper-air charts are mainly for one level only (either 700 or 500 mb). In the Southern Hemisphere the situation is materially worse, although it will be partly remedied in a few years is

far

realized.

after several units, including the

Department

of

Me-

teorology at the Massachusetts Institute of Technology,

have completed files of Southern Hemisphere sea-level charts. The M.I.T. series began with January 1949. Figures 1 and 2 give some idea of the amount and extent of data currently available for the construction

CIRCULATION OVER THE EARTH

—

Sources of Data ^Historical and Current. Ideally, the data upon which studies of general circulation pat-

—

—

FiG. 1 Typical data coverage at sea level for the Northern Hemisphere. Solid circles represent data actually received at 1200Z June 25, 1949. Some data have been omitted over the United States and parts of Europe because of space limita.

tions.

terns are based should consist of a series of complete and well-analyzed sea-level and upper-level charts covering the globe or at least a hemisphere for a period of

Fig. 2. Tj'pical data coverage at 500 mb. Small solid circles represent radiosonde data; large open circles, wind data; and large solid circles, both radiosonde and wind data actually received at 0300Z June 24, 1949. Winds are by pilot balloon, radar, or direction finder. The three observations near the pole and the five in the southwest Pacific centered at 20°N,

147°E are aircraft reconnaissance data.

Northern Hemisphere charts at the Central Office of the U. S. Weather Bureau. This represents a vast improvement over conditions existing ten years ago, largely as a result of the increasing need for data during of

World War 551

II.

THE GENERAL CIRCULATION

552

While the coverage shown in these figures is reasonably adequate in heavily populated land areas and in the much-traveled North Atlantic, there are still many important gaps, notably in the southern portions of the

North Atlantic and North

Pacific

Oceans and in

many

parts of Asia. This situation is due in part to communication difficulties and to the fact that it is more expensive and difficult (or even dangerous) to establish

and less habitable areas. Nevand economic forces are also partly

stations in unfrequented ertheless, political

responsible for the tendency of the density of observanumber of inhabitants.

tions to be proportional to the

Since there is mounting evidence (some of which will be presented in this paper) that weather in any given area of the globe may be importantly influenced by conditions in other areas, no matter how remote, it would appear preferable to reduce the amount of data in populated areas and use the money thus saved to increase the number of reports, particularly upper-air reports, from remote areas. Certainly it is a mistake to reduce the amount of hemispheric data on the grounds it is no longer necessary for military purposes. For the past two or three years there has been a strong tendency in this direction. The International Meteoro-

that

logical Organization, the International Civil Aviation

Organization, the Pacific Science Association, and simibe commended for and en-

lar organizations should

have been constructed partly by extrapolation from sea level for the period 1932 to 1939.^

Reasons

for the

Use

of

Mean

Charts.

Mean

charts,

showing the average state of the general circulation for specified periods of time, have been used extensively by many investigators, including the authors, for studying the observed behavior of the general circulation. Here are some of the advantages of mean charts over daily synoptic charts: Because of the unreliable nature of portions of hemisphere-wide analysis, the use of means leads to a smoothing which tends to eliminate experimental errors. Furthermore, such smoothing also eliminates irregularities in the flow pattern, such as small eddies or minor atmospheric waves. These irregularities, while real enough, tend to confuse the large-scale features of the circulation, which are of most importance in long-range forecasting. To a lesser degree this second type of smoothing may be attained by the use of synoptic charts from higher tropospheric layers or by mathematical devices, such as Charney's geostrophic wind approxi-

mation [10]. Perhaps the most important justification for the use of means is that they reveal large-scale features having a long period. Indeed the speed with which a given pattern changes appears to vary inversely as the number of days over which the averaging is done. The

couraged in their present efforts to improve the data coverage of the world. A brief list of published hemisphere charts is given

authors feel that slow evolution of this character holds out the hope for successful long-range weather fore-

The

Granting the correctness of the arguments given above, the question has often been raised as to how mean charts are to be interpreted from a physical point of view. In particular, it has been argued that the equations of motion cannot be applied to a mean flow pattern, for, since these equations are nonlinear, the average value of acceleration will not equal the sum of the corresponding average values of the other terms. The answer to this question cannot yet be given. However, this problem seems to be closely connected with the statistical theory of turbulence [3]. Briefly, this theory states that if a given fluid consists of an average flow upon which are superimposed random eddies, then the equations of motion for laminar flow can be applied, provided certain frictional stress terms are added which express the cross-flow eddy transfer of momentum. There seems to be no obvious reason why it should be necessary to place any arbitrary time limit to the average flow, so that the equations of motion ought to be just as applicable to mean charts of a month's duration as they are to mean charts of a few minutes (synoptic charts) ^provided the proper frictional terms are added [20]. This type of reasoning has been used by Defant [16], Lettau [32], and more recently by Elliott and Smith [21] to measure the frictional stress exerted by traveling cyclones and anticyclones. The omission of frictional terms in applying the equations of motion to

in the references

[1, 9,

17, 28, 29, 30, 46, 50, 51].

Air Weather Service and U. S. Weather Bureau North-

ern Hemisphere sea-level and 500-mb analyses contain, in addition to analyzed charts, a valuable listing of all

data received. To date the Air Weather Service charts have been published only from October 1945 to Sep-

tember 1946. The U. S. Weather Bureau commenced analysis and publication of this series beginning with January 1949. Charts for January through November 1949 are currentlj' available. Efforts should be made to gap in the historical map series from 1939 to 1945. This includes the years 1944 and 1945 when hemispheric data, particularly in the South Pacific, were more complete than at any other time. close the

Many

of the investigations to be discussed in this were made using unpublished operational analyses. These include twice-daily sea-level and 10,000-ft (or 700-mb) charts over the Northern Hemisphere from 1940 to date as analyzed at the Extended Forecast Section of the U. S. Weather Bureau. Not until mid1943 do these charts cover half a hemisphere or more. From them, twice-weekly five-day mean maps and twice-monthly thirty-day charts have been constructed. Five-day mean twice-weekly sea-level and 3-km charts for the cold season October through March 1933 to 1940 have been prepared by the Department of Meteorology at M.I.T. The 40-yr daily historical map series [28] has led to the construction of monthly mean sea-level article

charts. Corresponding 10,000-ft

monthly mean charts

casting.

—

1. All of these charts have been microfilmed and copies may be purchased by writing to the Librarian, U. S. Weather Bureau, Washington, D. C.

.

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS

may

be no more serious than on daily it will be seen that mean circulations behave as though they were true physical

mean

charts

charts. In the following pages

553

taken with some reservation, and one cannot scale from them numerical values upon which to draw

off

re-

fined conclusions. Besides, they represent only the zonal

entities.

Normal

Circulation of the Troposphere and Lower The prevailing motion of the greatest

Stratosphere.

mass

of the earth's

atmosphere

is

in general eastward.

The most recent normal maps prepared by the U. S. Weather Bureau [30, 50] and by the British Meteor[9] effectively bring to light the existence circumpolar whirl which, while somewhat obscured at the earth's surface, becomes stronger with elevation until near the base of the stratosphere it assumes the characteristics of a sharp maximum in speed. This narrow band of high speed, called the jet

ological Office of a vast

stream, and illustrated by Willett [56] and Hess [24] in north-south mean wintertime sections (not reproduced), seems to be found at most meridians around the Northern Hemisphere. What meager data are available

Southern Hemisphere (worked up by Flohn [22]) stream there. A series of unpublished vertical cross sections for each 20° of longitude around the Northern Hemisphere have been prepared at the U. S. Weather Bureau as part of the work in constructing normal monthly maps at various levels up to 19 km [30]. From these cross sections, showing the geostrophic in the

also suggest a jet

zonal wind component as a function of elevation, the latitude, strength, and horizontal shear across the jet stream have been entered and analyzed around the Northern Hemisphere as sho^vn in Figs. 3 and 4 [38]

Fig.

4.

—Average

position and strength of the jet stream for July. (See Fig. 3 for legend.)

component of flow; but this is by far the ponent, and an analysis of the total flow

largest

com-

(not shown)

gives a quite similar picture of the normal character of

the jet stream.

The

characteristic features of the

normal

jet

stream

seem to be: 1.

Its nature

mer and 2.

It

is

essentially circumpolar in

both sum-

winter. is

considerably farther north and weaker in from a surprisingly low latiin winter

summer than

—

tude of about 20°N to 35°N in winter, to perhaps 35°N to 45°N in summer, and with roughly double the speed in winter. 3. The location of the jet stream appears to coincide with the strongest meridional temperature gradient just below it in the mid-troposphere. 4. The jet stream is found where the tropopause has its greatest change in elevation. 5. The ideal circumpolar appearance of the jet stream

marred by appreciable longitudinal differences in Thus in winter (Fig. 3) the jet stream reaches its maximum strength along and just off the east coasts of Asia and North America and decays in the eastern parts of the oceans. Another maximum appears over is

strength.

—

Fig. 3. Average position and strength of the jet stream for January, prepared from eighteen hemispheric meridional cross sections. Heavy solid lines indicate geostrophic wind speed in miles per hour at the level of maximum speed. Heavy arrows rejiresent axis of the jet. {After Namias and Clapp

Africa. 6. The distribution of wind speed across the jet stream shows very strong lateral shear both to the north

and to the south; the

vertical

component

of the total ab-

solute vorticity north of the jet stream (not illustrated

[38].)

is

here) suggests approximate constancy with latitude. To a considerable extent charts constructed in mid-

in the range between 11 and 14 km. The material presented in these figures must, of course, be

troposphere (Figs. 5 and 6) bear a striking resemblance to those at the level of the jet stream. This might be

The

elevation of the

everywhere

jet,

not shown on these figures,

THE GENERAL CIRCULATION

554

inferred from the classical work of Dines [18] in which was pointed out the good correlations between temperature and pressure in mid-troposphere and at the tropopause. The strength of the circumpolar whirl is diminished with decreasing elevation. Below the level of 700 mb the circumpolar vortex begins to be somewhat obscured by the appearance of a more cellular character of the general circulation, and by the time we reach maps at sea level (Figs. 5 and 6) the "centers of action" take on considerable cellular character. Noteworthy is

1

90°

the emergence of easterly winds north of the subpolar lows and in the subtropics. The easterlies of the polar regions are for the most part shallow

phenomena gen-

below 3 km, but in low latitudes, particularly in summer, easterly winds are very deep and extend well erally

into the stratosphere.

The circumpolar vortex in the upper troposphere and lower stratosphere, while primarily zonal in character, undergoes gentle north-south undulations so that the isobars have a roughly sinusoidal character. The ridges and troughs aloft have their reflections at the surface

:

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS in the centers of action.

and Aleutian lows

at 300 mb the Icelandic have not lost their iden-

Even

of winter

tity although they are displaced considerably northwestward. The Siberian wintertime anticyclone appar-

ently gives

way

to westerlies aloft.

contrast between -winter and summer shows up chiefly in diminished gradients and northward migration. With the approach of summer the sea-level subpolar lows lose much of their strength, the subtropical

The

much stronger, and over Eurasia the well-known monsoonal reversal of pressure sets in. The comparison of circulations between the Northern oceanic highs become

and Southern Hemispheres is much more difficult in view of the relatively scant supply of data in the Southern Hemisphere particularly at upper levels.^ Certain attempts have recently been made to improve on Shaw's Southern Hemisphere charts [47] notably by the British Meteorological Office [9] for upper levels and by Willett [60] for sea level using Serra's world charts [46]. From these data a few seemingly reliable statements appear to be possible 1. The zonal circulation at sea level appears to be stronger in the Southern Hemisphere than in the Northern Hemisphere. This is strongly indicated in a table of average circumpolar zonal wind speeds computed by

—

Willett [60]

maps

use of Serra's monthly mean the months of January, April, July, and

who made

[46] for

October from 1879 through 1934. (See Table

Table

I.

I.)

Selected Normal Circulation Indices AT Sea Level*

555

THE GENERAL CIRCULATION

556 in

February and March, the zonal index reaching a

minimum around the beginning of March. Clearly such a minimum could not show up in monthly mean values such as are represented in Fig.

7.

But averages com-

NORMAL INDICES M SEC 4r 2

>

6

'^

4

UJ

5

o o 10

8

-

'

(COMPLETE NORTHERN HEMISPHERE)

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS ented solenoidal

fields at coast lines.

similar role has been ascribed to

More

mountain

recently a

barriers.

By the use of Rossby's now classical formula,^ plus the normal strength of the westerly flow, theoretical stationary wave lengths may be computed for each season for North America and Asia. The smallest of these has a length of 2500 mi, considerably larger than the dimensions of the average cyclone. Also, the seasonal variation of theoretical and observed stationary wave lengths is similar over North America. However, the observed waves are considerably longer than the theoretical waves. In view of the fact that average zonal wind speeds over the Eastern Hemisphere are somewhat lower than those over the Western, it becomes difficult to explain the larger observed wave Among the many factors responsible for these dis-

lengths over Asia.

crepancies perhaps the most obvious is that the continents, in contrast to the oceans, interpose not merely one narrow obstacle in the path of the westerly flow but a whole series of more or less continuous obstacles of

Fig.

8.— Normal

field of

557

a system of free stationary waves of constant wave length in such a current is to have a distribution of divergence such that in the lower layers there is mass convergence east of the trough lines and mass divergence to the west. At high levels they postulate the reverse distribution of divergence. Now the average level of nondivergence has been estimated to be at roughly 16,000 ft. Thus, the assumption of nondivergence at the 10,000-ft level, made in deriving the classical wave formula, is not valid. The distribution of divergence postulated above has the effect of increasing the stationary wave length. Charney and Eliassen [11, 12] have shown that the

topography, surface friction, and baroclinity be expressed in terms of divergence at upper

effects of

can

all

obtain an estimate normal fields of divergence. An attempt along this line has been made for the 10,000-ft level by the authors [37] and a sample of the results for February is

levels. It is therefore desirable to

of the

sho\vn in Fig.

8.

divergence at 10,000 ft for February. Thin curved lines are isobars for 5-mb intervals; heavy curves, divergence for intervals of 5 X lO"' sec""i. (From Namias and Clapp [37].)

varying importance all the way around the globe. Thus, at best, we must regard the observed flow pattern as a heterogeneous combination of waves set up by each of the numerous obstructions. Precisely this line of attack has been taken by Charney and Eliassen [12]. Perhaps the most important reason for the discrepancies is that the atmosphere is baroclinic so that the westerly ^vinds increase with height. As shown by Bjerknes and Holmboe [4], the only way to maintain 3. L, = 2iry/u /0, where U is the zonal wind speed (index), Ls the stationary wave length, and /3 the northward rate of change of the Coriolis parameter.

large-scale features \\'ithin the belt of strongest westerlies indicated in Fig. 8 show regions of maximum

The

divergence to the west and convergence to the east of the trough lines, in partial confirmation of theBjerknesHolmboe theory [4] mentioned above. Another noteworthy finding (not illustrated here) is the increasing strength of the divergence fields from winter to summer accompanying subtropical highs while the fields associated with the circumpolar westerlies are weakening. is also apparent from Fig. 8. over the Rocky Mountain chain from vUaska to Mexico, it is subjected to vertical shrinking (horizontal divergence), and as it sinks down the eastern

The As air

effect of is

lifted

topography

THE GENERAL CIRCULATION

558

subjected to vertical stretching (horizontal convergence). A similar phenomenon is observed in August but is interrupted at lower latitudes by the upper-level anticyclone over the United States. Similar charts, prepared for other levels, might throw considerable light on many problems of the dynamics of the slopes

it is

general circulation. If the normal fields of divergence at 10,000 ft are fairly representative of the average divergence in lower atmospheric levels where there are no mountains, it is

some idea of the normal fields of Thus there is probably a region of gradual subsidence over the eastern United States and a region of gradual ascent over most of the Atlantic. Similar regions are indicated over the Pacific. The charts possible to obtain

vertical motion.

also indicate subsidence in eastern portions of the sub-

tropical highs

and ascent

in western portions, conclu-

sions which are in good agreement with the Bjerknes

subtropical models

[5]

and with observed precipitation

regimes. It is recognized that in order to obtain a

explanation of the normal tion

tude

it is

complete

state of the general circula-

necessary to locate and determine the magni-

of the sources of heat

world's atmosphere, for

it is

and moisture

in the entire

these sources which supply

the necessary energy to drive the atmospheric heat Some of the most recent work on this topic has

engine.

been done by Wexler

[54]

and by Jacobs

-V

-500--,

^N

\

[25, 26].

^-^^^

\

study, Winston and Aubert,* estimating the effects of vertical motion, find that Wexler's method appears to give good estimates of total heating in regions where this

heating or cooling is large. Thus, while part of the heat gain shown over eastern North America in Fig. 9 may be attributed to adiabatic warming through subsidence, it is not possible to explain in this manner the centers of strong heating appearing off the coasts of the continents. Apparently these represent heat sources instrumental in driving the circulation of the Northern Hemisphere. Similar reasoning applied to other areas suggests that the regions of cooling over the northeastern parts of oceans are heat sinks, while subsidence accounts for the apparent heat sources over the southeastern Atlantic and Pacific. The studies discussed above do not consider individual heating processes affecting the circulation, for example, radiation, condensation, sensible heat exchange with the earth's surface, and mixing. Contributions to these aspects of the problem have been made by Jacobs [25, 26] who calculated for the air overlying oceanic regions the normal seasonal heating due to condensation and to sensible heat exchange with the surface. Jacobs found that the air was being heated from below in both the western and the northeastern portions of the oceans. The amounts of heating he found are in general agreement with the total heating as given by Wexler only in the western portions, but in the northeastern portions Wexler's values (showing net

Vr/

'^

IN

IN

Fig.

9.— Regions

of

normal heat gain and

loss for the layer

Using data for the Northern Hemisphere, Wexler estimated the normal regions of heating and cooling of the air in the layer between sea level and 10,000 ft for the months of February (Fig. 9) and August. As Wexler points out, more exact values of the total heat gain or loss would be possible

if the effects of vertical motion were considered. But the quantitative evaluation of this term is difficult. In an attempt to extend Wexler's

from sea

RATE CAL CM"2 RATE CAL CM"2

OF HEAT GAIN OAY OF HEAT LOSS DAY"'

level to 10,000 ft for February. {Ajler Wexler [54].)

cooling) must be accounted for in some other manner, perhaps by radiation or mixing. Indeed the importance of horizontal mixing in cooling northward-moving air 4. Part of the work of this continuing project at the Extended Forecast Section of the U. S. Weather Bureau will be published shortly. A further study is being made of normal and anomalous sources and sinks for other months and other

levels.

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS masses in the northeastern oceans

is

the normal map computed from a long series of data achieves a certain character. The variations of the circulation about its normal, considering weekly or monthly mean charts, is far greater than that which one would obtain if the circulation types followed each other in purely random sequence. This fact is reflected in the amazingly large

strongly suggested

and Smith [21]. In studying the sources and transformations of atmospheric moisture Jacobs showed that the greatest evapo-

by the work

of Elliott

ration in winter takes place over western oceans. According to him this latent heat appears to be released to the atmosphere largely in the eastern portions of the

oceans where condensation reaches

Another method

its

559

maximum.

means

for a month, year, or decade and longer periods up to the ice ages, as stressed by Willett [58] and Tannehill [49]. The observed sequence of types in any particular

variability of

probably for

of investigating the availability of

moisture for atmospheric processes resulted from the technique of isentropic analysis. By this means Namias and Wexler [55] were able to construct monthly mean isentropic charts for summer over the United States and thereby indicate the normal upper-level sources of moisture. Unfortunately, due more to the discontinuance of the isentropic technique than to the lack of upper-air data, such charts for other areas and seasons have not been constructed. The transport of various meteorological quantities by methods other than isentropic analysis has received considerable attention in recent years. Thus, Priestley [41] has suggested a systematic study of the transport of heat, moisture, and momentum through the use of radiosonde and radiowind measurements at a large

still

month

or season more often than not takes the form of an alternation between two or more mid-tropospheric flow patterns, one of which persistently recurs and dominates the mean over longer periods. It is presumably this persistent recurrence which led the Multanovsky School of long-range forecasting [39] to draw conclusions with regard to "natural synoptic periods," to the opposition of types between natural periods, and to the relative constancy of length of the natural period during one "synoptic season."^ Some idea of the weekly variations of the strength of the zonal circulation at sea level may be obtained from Fig. 10. The absolute variations at higher eleva-

15

10

PRESSURE DIFFERENCE

5

IN

MILLIBARS

_

29

13

27 1024 7

21

7

21

4

18 2

16

30

13

27

II

25 8 22 5

19

3

17 31

14

28

12

26 9 23 6 20 6 20 3

17

I

15

NOV DEC JAN FEB MAR -APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY BEGINNING 1936 1938 1937 1936 1938. May Fig. 10. Weekly averages of zonal westerlies index, November

WEEK

—

—

of individual stations. The importance of the transport and convergence of momentum and heat in producing local wind accelerations has been stressed by

network

Namias and Clapp [38] and by can profitably be made of the

Starr

[48].

More study

significance of thermal

convergence in producing local transformations of energy.

NONSEASONAL (IRREGULAR) VARIATIONS IN THE GENERAL CIRCULATION Qualitative Synoptic Studies. The "normal" state of the general circulation, as shown by normal hemisphere in any any weekly mean or monthly mean. Indeed, the nonnal map is composed of the averages of circulations which appear remarkably different from week to week and even between corresponding months of different years. In any

maps,

is

one which

given daily

map

is

never strictly encountered

nor, for that matter, in

given region, however, there appears to be a preferi'ed circulation type for a given month or season, so that

tions appear to increase

up

to the level of the jet stream,

but the percentage variation of normal strength is probably ciuite similar at all levels. If the average zonal wind speed for the hemisphere is considered as a whole and for weekly periods, this variation is of the order of 50-150 per cent of the normal speed. Regional and shorter-period variations may, of course, exceed these values, and localized jet streams reaching three times their normal value have been recorded. There is some suggestion in the distribution of zonal indices of midtroposphere that the frequency curve of index values is skewed in a direction such that high values (relative to normal) are less frequent than low. Perhaps this is suggestive of an atmospheric braking mechanism whereby some form of stability permits veiy low zonal wind speeds to persist but kills off unusually fast currents.

5.

Consult

casting" by

J.

"General

Aspects

Namias, pp. S02-S13

of

E.xtended-Range Fore-

in this

Compendium.

THE GENERAL CIRCULATION

560

The

variation in speed of the zonal circulation

may

from the standpoint of the maximum index, or the values of zonal wind speed taken at whatever latitude the maximum speed is reached. While the also be treated

changes go on somewhat as follows: In the

initial

stage

(illustrated schematically in Fig. 11) there are extensive

zones of confluence where deep cold polar and

warm

nature of the speed variations thus treated is similar to those taken between fixed latitudes, this form of treatment brings out some important additional information indicating that some of the highest speeds are reached when the jet is found at low latitudes. It also brings to light latitudinal variations in the position of the jet stream about the normal which are amazinglylarge. Even if averaged over the hemisphere for periods as long as a month, this variation can be as large as 20°

For shorter periods, and

of latitude during one season.

particularly for selected regions, the latitudinal varia-

much greater. Regional streams have been apparently observed in areas ranging from the pole almost to the equator. To the extent that we may speak of the maximum high-level zonal current averaged over the hemisphere as a jet stream, we may summarize the foregoing remarks by saying that there are large day-to-day, weekto-week, and month-to-month variations in the strength tion of the jet stream can be jet

and latitude

of the jet stream.

The latitudinal

—

Fig. 11. Schematic representation of successive circulation patterns of the index cycle. The time interval from Stage 1 to Stage 4 is about two weeks.

variations

may

by

be looked upon fundamentally as an expansion and contraction of the circumpolar vortex toward or

tropical air masses are forced to flow side

away from the The regional

of the zones of confluence. In Stage 2 the waves, perhaps through some form of relative motion associated with a nonstationary wave length, have combined into deep full latitude troughs and ridges. This combination permits vast meridional transports of deep polar and tropical air. Stage 3 results from a refracture of the troughs at high and low latitudes, again perhaps in an attempt to readjust wave lengths to equilibrium values. The cold polar air masses brought equatorward and the warm currents which were delivered to polar regions by the in-phase troughs and ridges now have no return

pole.

variations in the latitude

and perhaps

in the strength of the jet stream are associated with the wave patterns in the circumpolar vortex which were,

to some extent, treated in a foregoing section. Ideally these long waves are generally looked upon as a simple wave pattern in the upper troposphere and lower stratosphere with from four to six meridionally extensive ridges and troughs around the hemisphere. The observed wave patterns are rarely if ever so ideal, and a more accurate description would be that there are generally

waves

in

two (sometimes more)

different families of

different latitude bands.

These two wave

may, and usually do, possess different wave lengths (in degrees of longitude) and hence around the hemisphere there may be a different number of waves jn higher latitude bands than in lower latitude bands. For this reason, too, the waves in the two bands are trains

frequently out of phase. These remarks pertain equally well to daily, weekly, or monthly mean maps. When the jet stream of the circumpolar vortex is well to the north of its normal position, the ridges and troughs are generally strongly tilted in a northeastsouthwest direction or even fractured as indicated in

When

the waves get into phase {i.e., ridges are more or less meridionally extensive) the latitude of the jet stream usually lowers but does not reach its lowest value. This position is reached only after the entire character of the Fig. 11, Stage

1.

when the troughs and

hemispheric upper-tropospheric circulation is radically altered to a cellular rather than a wavelike structure. The explanation of this fundamental change in character, in spite of its enormous importance to meteorology, is not yet kno^^n. However, in following the development of such transitions it often appears that the

side, asso-

ciated ^vith filaments of regional jet streams to the east

—

passage to their source regions that is, the evolution of the flow patterns is now in the direction of trapping both the equatorial air in the north and polar air in the south. Finally, in Stage 4 the cold pools {Kaltlufttropfen) in the subtropics and the warm pools in the subpolar regions take on characteristic cyclonic and anticyclonic cellular circulations. In these schematic models it will be noted that certain asynmietry and tilt of the troughs and ridges are introduced where necessary to bring about the advection of momentum required to maintain the westerlies in the manner postulated. Jeffreys [27] and lately Starr [48] have emphasized the importance of such asymmetry as related to the transfer of mo-

mentum. This idealized sequence of events generally does not take place simultaneously in all parts of the hemisphere. However, when such a development on a large scale takes place in one region, it is often followed by similar reactions in other regions. This transition of the circulation wherein deep cold cyclones are ultimately formed at low latitudes and deep warm anticyclones are formed at high latitudes is referred to as blocking. The most commonly observed behavior of blocking action

is

a progressively westward development of re-

:

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS gionally low-index circulation patterns at a variable speed which synoptic experience suggests may be of the order of 60° of longitude per week. At the surface in the area of blocking, (or cyclolysis)

is

pronounced anticyclogenesis

observed in higher latitudes, while

wave cyclones are forced to skirt the perimeter of the developing high-latitude anticyclone, either northward west of the developing upper-level ridge at high

lati-

tudes, or southeastward into the cold developing vortex of southern latitudes. good description of the evolu-

A

tion of the day-to-day westerly

sphere westerlies

[2]

waves

during blocking

is

in the mid-tropo-

that they appear in ampli-

become progressively shorter and increase

to

tude as the scene of the blocking action is approached. In this respect they may be likened to waves advancing on to a beach, or to the pleats in an accordion.

Westward progression of by no means

characteristic

circulation

not appear to be as common as eastward progression. Thus a sudden increase in amplitude of a wave system in North America may be shortly followed by a similar increase over the Atlantic and Europe. The speed at which this readjustment occurs often exceeds that of the zonal speed of the air particles a fact which of late has refeatures, while

rare, does

—

ceived considerable attention from theoreticians [43, 61] following its discovery in synoptic practice [36]. The transition in temperate latitudes from strong

weak zonal

to

circulation

and back again has been

referred to as the index cycle.

On

the basis of a careful synoptic and statistical study of seven years of Northern Hemisphere data, Willett [45] has given a description of the index cycle which can hardly be improved upon. His statements follow: .

.

.four principal states of the index cycle are recognized,

each of which can be briefly characterized essentially as follows

high index (strong sea-level zonal westerlies), characterized by (a) sea-level westerlies strong and north of their normal position, long wavelength pattern aloft; (6) pressure systems oriented east-west, with strong cyclonic activity only in higher latitudes; (c) maximum latitudinal temperature gradient in the higher middle latitudes, little au' mass exchange; and (d) the circumpolar vortex and jet stream expanding and increasing in strength, but still north of the normal seasonal latitude. (2) Initial lowering of sea-level high-index pattern, characterized by (a) diminishing sea-level westerlies moving to lower latitudes, shortening wave-length pattern aloft; (fe) appearance of cold continental polar anticj'clones in high latitudes, strong and frequent cyclonic activity in middle latitudes; (c) maximum latitudinal temperature gradient becoming concentrated in the lower middle latitudes, strong air mass exchange in the lower troposphere in middle latitudes; and (d) maximum strength of the circumpolar vortex and jet stream reached near or south of the normal seasonal latitude. (3) Lowest sea-level index pattern, characterized by (a) complete breakup of the sea-level zonal westerlies in the low latitudes into closed cellular centers, with corresponding breakdown of the wave pattern aloft; (6) maximum dynamic anticyclogenesis of polar anticyclones and deep occlusion of stationary cyclones in middle latitudes, and north-south orientation of pressure cells and frontal systems; (c) maximum east-west rather than north-south air mass and tempera(1)

Initial

561

ture contrasts; and (d) development of strong troughs and ridges in the circumpolar vortex and jet stream, with cutting off of warm highs in the higher latitudes and cold cyclones in

the lower latitudes. (4) Initial

increase of sea-level index pattern, character-

by (a) a gradual inci'ease of the sea-level zonal westerlies with an open wave pattern aloft in the higher latitudes; (6) a gradual dissipation of the low-latitude cyclones, and a merging of the higher-latitude anticyclones into the subized

tropical high-pressure belt;

(c)

a gradual cooling in the polar

and heating of the cold air masses at low latitudes to re-establish a normal poleward temperature gradient in the higher latitudes and (d) dissipation of the high-level cyclonic and anticyclonic cells, with a gradual re-establishment of the regions

;

circumpolar vortex jet stream in the higher latitudes.

While the index cycle described above appears to be recognized in its essential character during most winters, its precise form of operation, time of onset, and even its length and intensity are subject to appreciable variations. Extensive studies directed along these specific lines appear to be long overdue. A beginning on this problem [35] was made with the help of hemisphere-wide upper-air coverage obtained during the six-year period 1944-49. These data suggested the following conclusions: 1. There is a strong preference for the winter's primary index cycle to occur in February and March, the minimum index occurring around the beginning of

March, and the beginning and end points being moved by about three weeks from the minimum. 2.

The

total

re-

momentum of the mid-troposphere west-

around the hemisphere tends to reach a certain value characteristic of the season, and it is only the distribution of this momentum with latitude that varies. Hence the low index of temperate latitudes really conerlies

sists

of

a displacement of the "high-index" strong

westerlies (farther southward).

Each primary index cycle is usually associated at onset with a strong wave of Atlantic blocking, with a tendency to form warm anticyclones in high latitudes and cold cyclones in low latitudes. However, the blocking appears to be only a necessary and not a 3.

its

sufficient condition for 4.

The

a primary index cycle.

intensity of long index cycles appears to be

largely determined

by the

reservoir of cold air in polar

regions preceding their onset.

These four statements appear to be sufficiently backed by empirical evidence to be considered in any theoretical treatment of the problem of the evolution of the radically different states of the general circula-

A qualitative treatment along these lines has been given [35]. The reader is referred to this paper since the presentation of theories lies outside the scope of this article. Other earlier attempts to explain the index

tion.

by Rossby and Willett [45]. consuming about six weeks, is naturally not the only important period of evolution of radically dilferent circulation patterns. Indeed for many years the problem of monthly mean, seasonal, and even secular large-scale circulation anomalies has been of paramount concern to meteorologists. While such evolutions undoxibtedly lie in the province of "Observed cycle have been given

The index

cycle,

THE GENERAL CIRCULATION

562

Studies of General Circulation Patterns," it would appear that the principal treatment of this vast subject belongs elsewhere in this Compendium.^ Before we leave the subject, however, a few pertinent remarks are in order. First, it appears from actual studies that the choice of the length of period does not essentially change the character of the problem of oscillations of circulations from high- to low-index states. In fact, there is evidence to suggest (Willett [57], Tannehill [49]) that the longer the period, the correspondingly greater the interperiod variability compared with what might be expected if the variations were random in character. Secondly, experience with monthly mean charts over the past eight years suggests an evolution which is not entirely chaotic and which indeed appears capable of kinematic and possibly physical rationalization [31, 34]. The kinematic aspects were

fundamental

pointed out as early as 1926 by Brooks [8]. In short, the problem of the index cycle and its evolution would appear to be an integral part of any theory of secular, climatic,

and

geological

{i.e.,

ice-age) varia-

—a fact repeatedly stressed by

tions of world weather

Willett

[58].

Quantitative Empirical Studies. The qualitative behavior of large-scale circulation patterns described above is obviously of sufficient interest to justify more objective quantitative studies. Such studies have two basic purposes: to provide empirical formulas for pre-

and development of large-scale cirand to furnish the theoretical meteor-

dicting the motion

culation features,

with quantitative evidence for supporting or extending his theories. Since the forecasting aspects of ologist

these studies are treated elsewhere,' we shall treat here only the theoretical implications. One investigation of this sort, involving the motion of long waves at different latitudes, was made by the

authors with the aid of two-and-a-half years of five-day mean 700-mb charts [36]. This study was an attempt to verify and make use of the simple theory of planetary wave motion based on the principle of conservation of absolute vorticity [44].

From

it was found that while there is from perfect) correlation between observed and theoretically computed displacements of selected trough systems, observed waves usually travel much faster than the speed given by the vorticity the-

this material

positive (but far

making necessary large empirical correcThe reason for this discrepancy seems to lie in

ory, thereby tions.

part in the fields of divergence accompanying observed waves, whereas the theoretical formula is based on the assumption of no divergence. This problem, as it affects the stationary wave length, was discussed in the section of this article dealing with physical climatology.

Of considerable importance is the empirical finding when wave length and zonal wind speed are considered separately there appears no significant relationship between wind speed and displacement. This was that

6.

Energy VariAnomalous Weather Changes"

See, for example, the discussion in "Solar

ations as a Possible Cause of

by R. A. Craig and H. C.

Willett, pp. 379-390.

certainly not expected from theory. While no satisfactory explanation for this discrepancy has yet been found, it may be due in part to a possible interdependence of wave length and zonal index [13] or, as Cressman [14] indicates,

to the small variability of the zonal index

which cannot produce changes in displacement larger than the errors of measurement. Because of this finding, empirical formulas were derived by considering that displacement is a simple linear function of wave length. This is equivalent to substituting the average or normal value for zonal wind speed in the theoretical displacement formula and then assuming that the range in wave length is small in com-

average magnitude. unpublished studies of this kind show that the stationary wave lengths (the wave lengths observed when trough displacement is zero) for North America are roughly the same as the normal wave lengths obtained from normal upper-level charts. This means that when the wave lengths found on individual five-day mean charts exceed the normal value, the waves will tend to retrograde (move westward) while they will be progressive (move eastward) if the observed wave

parison to

The

its

latest

lengths are smaller. It was previously suggested that seasonal variations of the normal wave lengths could be accounted for by seasonal changes in the zonal index. But there are also pronounced geographical variations. Thus the stationary wave lengths for the Atlantic are found to be shorter

than those for North America, suggesting that for the same wave length, displacements in an easterly direction are slower over the Atlantic. This better agreement with the theoretical wave formula indicates that waves over flat ocean areas more closely approximate free perturbations. of

The empirical studies also show a systematic decrease wave speed with time. This may be a purely statis-

tical result,

but a possible physical explanation

may

lie

Rossby wave formula in which a decrease in wave speed may result from a systematically increasing wave length. It has been suggested [36] that such an increase in wave length as troughs move eastward may be due to the tendency for certain troughs and ridges to be in the

fixed because

of topographical

or solenoidal effects.

For example, the length between a trough moving eastward over the Mississippi Valley and a ridge fixed to the Rocky Mountain area must continually increase, resulting in a deceleration. Perhaps a more universal explanation for systematic

changes in wave length has been offered by Cressman [15], who has adapted the theory of group velocity to changes in wave length of individual systems. Synoptic evidence, on both daily and five-day mean charts, appears to support his conclusion that if the wave length increases in an upstream direction the easternmost wave will slow down, while the opposite distribution of wave length will lead to acceleration. In investigating other parameters besides wave length which might be related to displacement, it was found that the shape of the wave was often quite important [13]. Thus, if the wave amplitude to the west of a given

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS trough is greater than that to the east, the trough will tend to moA'e faster than expected from the empirical wave formula. The opposite result is often obtained if the amplitude to the east is greater. Studies of trough motion similar to those above have been made with the aid of constan*: absolute vorticity trajectories [42]. The theory, which gives an estimate of the paths of individual air parcels, is based on the conservation of absolute vorticity just as in the wave theory, but avoids many of the latter's assumptions. For example, local wind speeds are used in place of a fictitious uniform zonal wind, and the assumption of small perturbations is avoided, so that estimates of wave amplitude may be obtained. However, a new assumption that the speeds of individual air parcels remain constant is introduced. Using this theory, Bortman [6] obtained empirical corrections (for each season and several geographical areas) to the "first characteristic points." These are the first trough or ridge points following the inflection point of the vorticity path at which the computation is made. The results were quite similar to those using the wave formula in that large eastward empirical corrections were found for the theoretical trough points over eastern North America, indicating that the theoretical trough speeds are too low. Also, there is a positive correlation

563

be made for other levels and North America, to which the above study

of a similar nature should

areas besides applies.

-lO

O

10

1/2

20

30 40 50 60 70 80 90 100

WAVE

LENGTH

110

120130

110

120 130

("LONGITUDE)

(C)

between theoretical and observed wave speeds.

Corrections are generally less over ocean than over land areas. Of special interest are the corrections in the

western Rocky Mountain area, where both trough and ridge points give evidence of strong divergence as a result of lifting. The study thereby emphasizes the importance of geographical and climatological features on the behavior of long waves. Another impublished empirical study of wave motion on five-day mean 700-mb charts [7] over North America attempts to make use both of the theory of planetary waves and that of constant vorticity trajectories. Thus, following a suggestion by Cressman [14], the wave length and wind speed of observed waves were measured along the streamlines (or isobars) rather than along fixed latitude circles. Amplitudes were measured in the same manner. These three parameters were then related by graphical correlation methods to the observed trough displacements at 45°N. Such a procedure is an empirical attempt to take cognizance of the jet stream, which tends to follow the streamline flow. The results show not only the expected relationship between wave length and displacement, but indicate that amplitude and to a certain extent wind speed are also significant parameters. The most interesting result was the significant positive correlations found among all three independent parameters. The relationships among wave length, amplitude, and wind speed for small and intermediate values of wave length were found to be qualitatively the same as those to be expected from the theory of constant vorticity trajectories, while for larger wave lengths the agreement was poor (Fig. 12). The explanation for this discrepancy has not yet been found but when found it should aid in seeking an understanding of the observed behavior of planetary waves. Studies

-10

o

10

20 30 40 50 60 70 80 90 100 WAVE LENGTH ("LONGITUDE)

1/2 (b)

—

Fig. 12. (a) Observed relationship between wave length, amplitude, and wind speed for waves whose minimum latitude is 45°N, from five-day mean 700-mb charts for the j'ears 1941-47. (6) Theoretical relationship between wave length, amplitude, and wind speed for waves whose minimum latitude is 45°N, using the Bellamy vorticity slide rule. {From Bortman [7].)

One

of the basic difficulties of all studies treated so that they require the identification from map to map of various characteristic points or lines (highs, lows, troughs, or ridges). Because of the complexity of atmospheric behavior this is not always easy. This suggests that a more profitable empirical (or theoretical) approach is to study local changes in various meteorological quantities, since this does not involve

far

is

the troublesome problem of continuity. To a certain extent the vorticity paths are designed to do this, and such u.se has been made of them by Dorsey and Brier [19] and by Fultz [23]. Dorsey and Brier, using selected trajectories made on daily synoptic 10,000-ft charts, compared the theoretically computed wind speeds and directions with those observed at the same points at intervals of 24 hr up to seven days in advance. Among their interesting results is the finding that trajectories are likely to be more successful also

in a well-defined fast flow. It was the trajectory verified well for the

when made

found that

if

THE GENERAL CIRCULATION

564

24 hr it was more likely to be good for subsequent time intervals. In spite of the obvious advantage of avoiding the necessity for determining continuity, it is felt that this method, unlike that used by Bortman [6] places too heavy requirements on the theory, and makes the determination of empirical corrections difficult. A similar study has been made by Fultz [23] who also used trajectories computed on daily 10,000-ft charts, and in addition estimated the true trajectory of the air parcels. Such a method could obviously lead to quantitative empirical corrections to the vorticity paths first

in

many

number

However, the by Fultz was small (largely time necessary to compute true

different geographical areas.

of cases studied

because of the length of

paths) and the corrections were apparently so complex that the author confined his practical results to a number of valuable qualitative rules. T^ong recent studies designed to avoid the problems of determining continuity perhaps the

most important

the work of Charney and Eliassen [11, 12] mentioned previously. This represents a considerable refinement of the simple planetary wave formula particularly as it applies to the determination of local pressure (or height) changes. Several empirical studies are currently underway to test and expand this theory. Before concluding this brief review of quantitative studies of circulation patterns it is necessary to say a few words about the accuracy that has been attained. It must be confessed that in spite of the fact that they seem to fit into a logical pattern which can be explained on physical grounds, these empirical results represent only the average behavior of circulation features. For example, the largest correlation coefficient found beis

-

tween theoretical and observed wave displacement represents a degree of success accounting for perhaps only

50 per cent of the variability of observed motions. These meager results are probably due in part to the great complexity of the atmosphere which makes it impossible for any single factor, such as a wave length, a vorticity path, or a region of confluence to be responsible for more than a small part of the subsequent circulation changes. Only by integrating in some way all the many processes taking place throughout the whole atmosphere

can one hope to approximate a complete solution. Such a desirable goal can be obtained only through continued close collaboration between theoretical and synoptic meteorologists.

Another contributing factor lies in the limits of observational accuracy. Because of instrumental errors, sparseness of upper-air reports, and analytical diffinot generally possible to define a trough or ridge at 45°N any closer than about four degrees of longitude. Because of this one source of error (even supposing that a perfect linear relationship exists between wave length and trough speed), the highest correlation that could be attained is —0.85. This result suggests that in meteorology, as in other sciences, it is highly desirable to include in any quantitative comparison of theoretical and empirical findings a careful analyculties

it is

sis of errors.

Statislical Studies of the

General Circulation. Me-

teorology has always been a fertile field for statistics. It contains numbers of observations perhaps equal to or in excess of those in any science. The number of combinations of elements making use of different places and different time intervals is well nigh infinite. Partly for

meteorology has encouraged the use of the correlation technique for discovering significant rela-

this reason,

tionships between meteorological elements or between one and the same element in space or in time. While this

procedure has its secure place in meteorit has probably been the cause of more heated controversy among meteorologists than any other research tool. Owing to the amazingly large mass of correlations to be found in the literature and statistical

ological research,

the lack of general agreement as to tests of significance to apply to such statistics,

it

becomes exceedingly

dif-

time to portray or evaluate the role of statistical studies of the general circulation. Perhaps the most indefatigable worker along these lines has been Sir Gilbert Walker, whose statistical studies of conficult at this

temporaneous and lag correlations form the basis of many interesting and informative papers [52]. For the most part these papers have been reviewed at length elsewhere [40] and thus the present brief survey will not attempt to treat this work but instead will concentrate on the work of Willett [57, 59] who, perhaps next to Walker, has given the atmosphere its most vigorous statistical workout. Besides, Willett had the

having hemisphere-wide maps and could thereby obtain integrated indices of the general circulation which Walker had to estimate by values of elements chosen at selected points. Moreover, Willett's work is of particular interest inasmuch as it ties in with, and indeed, forms distinct

advantage and

at the surface

of

aloft

some of the basis of, the material discussed in earlier portions of this article.

The principal meteorological material upon which work was based consists of daily analyzed charts

this

and at 10,000 ft over the entire Northern Hemisphere for the cold months of the year from October through March for the seven years 1932-39. From these charts, five-day mean maps were prepared twice a week (so that there was one or two days overlap between five-day periods) as well as a host of statistical at sea level

A

list of the complete number of these "indices" of the general circulation would in itself occupy considerable space, even without the addition

derivatives.

of the vast

number of correlations computed between The principal indices considered on a

pairs of indices.

hemisphere-wide scale can be relegated to three types: zonal, meridional, and solenoidal. The zonal indices have been defined on page 555.

The meridional indices used by Willett express the mean (over space and time) of the north-south component

of geostrophic flow

averaged for each of the

and 60°N. This quantity was necessarily obtained from values taken from daily synlatitudes 30°N, 45°N,

optic charts and, as in the case of the zonal indices,

was obtained

for

both sea-level and 10,000

ft.

The solenoidal index measures the poleward gradient of mean virtual temperature between sea level and

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS 10,000

ft in

the 20° latitude

band

of greatest

northward

rate of change.

With

these indices (and

many more)

Willett pro-

ceeded to look for contemporary and lag correlations, Ordinary linear after removing the seasonal trend. (Pearsonian) coefficients of correlation were computed from fifty-two overlapping five-day mean periods for each six-month period (October-March) during each of the seven years and for the seven years as a whole. The terms "significant" and "highly significant" were applied to those correlations which had less than five per cent and less than one per cent probability, respectively, of occurring by chance. Of the contemporary correlations one of the most significant was the negative one ( — 0.54) found with fair year-to-year consistency between the average pressure along latitudes 70°N and 35°N. This negative correlation is, on a global scale, the same phenomenon that Sir Gilbert Walker stressed in his North Atlantic and North Pacific oscillations, when he pointed out the opposing reactions of Aleutian and Icelandic lows to North Pacific and Azores subtropical anticyclones, respectively. These results stress the important fact that the polar-cap anticyclone grows at the expense of the subtropical highs, the shifts in mass being associated with an expanded circumpolar vortex of low index described above on page 561.

Largely as a result of this negative correlation the sealevel polar easterlies correlate insignificantly with sealevel zonal westerlies in spite of the fact that these two indices possess the latitude 55°N in common. But the sea-level polar easterlies correlate significantly

and con-

from year to year in a positive sense with the

sistently

zonal westerlies at the 10,000-ft level, indicating that sea-level polar easterlies are strong, the poleward temperature gradient in the 10,000-ft layer above the surface is also strong. This is also borne out by significant negative correlation between solenoid index and

when the

zonal westerlies and positive correlation between sole-

noid index and 10,000-ft westerlies. The correlation between the strength of the maximum 3-km westerlies and their latitude, while not significant, is consistently negative from year to year, suggesting the observed fact that the jet stream at times intensifies as it expands equator ward. The meridional index computed for 45°N shows a tendency (though not quite significant) for strong meridional circulations to be associated with weak zonal components. The meridional exchange at 45°N also appears to be related to the latitude of the maximum 3-km westerlies, since a significant negative correlation exists between these

two

quantities.

Again

this

reflects the meridional {e.g., cellular) character of the low-index pattern as compared with the high-index

pattern.

From

these correlations Willett [57] concludes that

.the low index circulation pattern, in contrast to the high index pattern, is characterized by: 1. A relatively strong poleward temperature gradient, at least between sea-level and the 3-km level. 2. Relatively weak zonal westerlies at sea-level which in.

.

565

crease to relatively strong aloft, with a tendency to be dis-

placed equatorward, that is, an intensified and expanded circumpolar vortex in the upper troposphere. 3. Strong polar easterlies as a result of a relatively strong sea-level polar anticyclone, which in turn is produced primarily from a weakening of the sub-tropical high pressure belt.

In middle latitudes a relatively strong meridional circuwhich tends to weaken with height as the zonal westerlies become relatively stronger. 4.

lation at sea-level

The step from contemporaneous to lag correlations involving features of the genei'al circulation appears to be of a high order of difficulty. In earlier decades, particularly the 1920's, a popular form of research aimed at long-range forecasting consisted of correlating, with different lags, weather or circulation elements at various points over one or both hemispheres. One such ambitious program, undertaken at the U. S. Weather Bureau under Weigh tman [53], involved correlations between pressure, temperature, and rainfall for lags of three, six, and nine months. It was hoped that these supposedly fact-finding and purely statistical studies would lead to a better understanding of the general circulation and provide a basis for long-range weather forecasting. But the technique was apparently too crude to bring to light any very revealing secrets behavior and evolution of atmospheric circulaand concomitant weather. Similarly, in their vast undertaking Willett and his associates, working with data described previously, were unable to detect any of the

tion

reliable predictors of the general circulation in its zonal

or meridional branches or in regional divisions, aside of persistence. From these negative

from a small degree results Willett [57]

concluded that the general circu-

no internal mechanism of operation and that there was apparently no one way that a subsequent state could dynamically and thermodynamically evolve from an initial state. From this conclusion it was apparently not a difficult step for Willett to join

lation possessed

that group of meteorologists who maintain that controls of nonseasonal variations in the general circulation lie in the sun. One can, of course, question the fundamental premise upon which this latter conclusion was based. Indeed, Willett himself is quite aware of the possibility that the correlation technique, applied as he has applied it, is too crude to unveil the secrets of a highly

atmosphere. The restrictions by fixed time and placed upon space intervals, in the opinion of the present authors, are much too severe to fasten upon an evasive atmos-

complex organism

like the

correlation techniques

phere notoriously resistant to strait jackets. In this semiphilosophical question seems to lie one of the principal deficiencies of research in the problem of general circulation. Admittedly, all meteorologists aim for objectivity. But in the quest for objectivity it is sometimes forgotten that adequate statistical tools may not yet be developed to treat many complex problems. The problems of time series, so common yet so annoying to meteorology, serve as an example. It thus be-

hooves the meteorologist to encourage the development of statistical tools which are by definition objective

THE GENERAL CIRCULATION

566

and are

at the same time not overly restrictive. Perhaps the way out of this dilemma is offered by new electronic high-speed computing equipment.

all levels will

CONCLUSIONS In the

brief

summary

of recent

moisture, should be taken from high atmospheric levels. The idea of the "polar year" or "aerological days" should be extended so that a global supply of data at

be available for at least one year.

REFERENCES

work on the general

circulation presented above, three basic aspects

have

been stressed. The first deals with what is linowu of the observed fields of atmospheric mass and motion, both in their normal state and in their week-to-week or month-to-month variations. While there is a fair delineation of the pressure field in the Northern Hemisphere and in the lower troposphere for a short period of years, there are considerably less systematic analyses of wind and moisture on a hemispheric scale. The second aspect concerns certain quantities such as divergence, vertical motion, heat sources and sinks, transport of mass and momentum, and other factors which can be derived from the fundamental fields of wind and pressure. Finally, there has been some discussion of the physical interpretation of this great mass of observations. It is this interpretation which provides a basis for long-range forecasting. Much work remains to be done in all three aspects of the problem, especially in the last. At present there is no completely quantitative utilization of theoretical findings in forecasting. Perhaps the closest approach to this is confined to certain relatively simple applications of the classical hydrodynamical concept of conservation of vorticity. This meager result is due largely to the fact that, just as in other sciences, advances in theoretical meteorology must go hand-in-hand with advances in observation. For example, there appears to be much promise in the application of electronic machines and numerical integration methods to the problem of short- and long-range forecasting. However, even this will be of little avail unless it is accompanied by a better understanding of atmospheric processes through more intensive studies of existing data and improvement in observational techniques. In various places throughout the text the authors have suggested several ways in which further progress in observational studies can be made. Perhaps the most important of these are the completion of the historical Northern Hemisphere map project for the war years 1939 through 1945. With a complete and improved supply of historical data, further attempts can be made to obtain a more accurate picture than we now have of the normal state of the circulation at many levels, and to study such things as the characteristics of atmospheric waves and circulation indices. Clearly many other projects in addition to those mentioned can be suggested which will lead to better utihzation of our existing supply of data. In addition to utilizing existing data more effectively, meteorologists have the responsibility of seeing that future supplies of hemispheric data are improved. This improvement appears to be more necessary in quality rather than in quantity. Thus, observational networks should be chosen so that there is a more even distribution over the globe. Observations, including winds and

1.

2.

3.

AiE Weatheb Service, Northern Hemisphere Historical Weather Maps, Sea Level and 500 Millibar. October 1945 to September 1946 (to be completed through December 1948). Washington, D. C. Berggren, R,, BoLiN, B., and Rossbt, C.-G., "An Aerological Study of Zonal Motion, Its Perturbations and Break-Down." Tellus, Vol. 1, No. 2, pp. 14-37 (1949). Berry, F. A., Jr., Bollay, E., and Beers, N. R., ed.. Handbook of Meteorology. New York, McGraw, 1945. (See pp. 451-453)

5.

J., and Holmboe, J., "On the Theory of Cyclones." J. Meteor., 1:1-22 (1944). Bjerknes, V., and others, Physikalische Hydrodynamik.

6.

Bohtman, R.

4.

Bjerknes,

Berlin, J. Springer, 1933. (See pp. 668-702) S., "Empirical Corrections to Constant Absolute Vorticity Trajectories." Trans. Amer. geophys.

i7M., 7.

8.

9.

10.

11.

29:324-330 (1948).

The Interrelationship of Wavelength, Amplitude, and Wind Speed in Upper-Air Flow Patterns. Unpubl. Rep., Extended Forecast Sect., U. S. Weather Bureau, Washington, D. C, 1949. Brooks, C. E. P., "The Variation of Pressure from Month to Month in the Region of the British Isles." Quart. J. R. meteor. Soc, 52:263-276 (1926). and others, "Upper Winds over the World." Geophys. Mem., No. 85, 149 pp. (1950). Charney, J. G., "On the Scale of Atmospheric Motions."Geofys. Publ, Vol. 17, No. 2 (1948). "On a Physical Basis for Numerical Prediction of Large-Scale Motions in the Atmosphere." J. Meteor., 6:371-385 (1949).

and Eliassen, A., "A Numerical Method

12.

for Pre-

dicting the Perturbations of the Middle Latitude Westerlies." Tellus, Vol. 1, No. 2, pp. 38-54 (1949). 13.

14.

Clapp, p. F., Further Empirical Studies of Wave Motion in the Westerlies. Unpubl. Rep., Extended Forecast Sect., U. S. Weather Bureau, Washington, D. C, 1948. Cressman, G. p., "On the Forecasting of Long Waves in

Upper Westerlies." J. Meteor., 5:44-57 (1948). "Some Effects of Wave-Length Variations of the Long Waves in the Upper Westerlies." /. Meteor., 6:66the

15.

60 (1949). 16.

Defant,

a., "DieZirkulationder Atmosphare in

den gemas-

sigten Breiten der Erde." Geogr. Ann., Stockh., 3:209-266 (1921).

18.

Deutscher Wetterdibnst, Current Daily Sea-Level and 500-Mb Analyses. Bad Kissingen, 1949 et seq. Dines, W. H., "The Characteristics of the Free Atmos-

19.

DoESEY, H. G.,

20.

U. S. Weather Bureau, Washington, D. C, 1944. Dryden, H. L., "A Review of the Statistical Theory

17.

21.

phere." Geophys. Mem., 2:45-76 (1919). Jr., and Brier, G. W., "An Investigation of a Trajectory Method for Forecasting Flow Patterns at the Ten-Thousand-Foot Level." Res. Paper FR-08 in A Collection of Reports on Extended Forecasting Research. of

Turbulence." Quart, appl. Math., 1 :7-42 (1943). (See p. 9) Elliott, R. D., and Smith, T. B., "A Study of the Effects of Large Blocking Highs on the General Circulation of the Northern-Hemisphere Westerlies." J. Meteor., 6:67-85 (1949).

OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS 22.

Flohn, H., "Grundziige der allgemeinen atmospharischen Zirkulation

auf

SiidhalbkugeL"

der

Arch.

Oeophys. Biokl., (A) 2:17-64 (1950). 23.

25.

26.

27.

28.

29.

30.

31.

Hess, S. L., "Some New Mean Meridional Cross Sections through the Atmosphere." J. Meteor., 5:293-300 (1948). Jacobs, W. C, "Sources of Atmospheric Heat and Moisture over the North Pacific and North Atlantic Oceans." Ann. N. Y. Acad. Sci., 44:19-40 (1943). "The Energy Acquired by the Atmosphere over the Oceans through Condensation and through Heating from the Sea Surface." /. Meteor., 6:266-272 (1949). Jeffreys, H., "On the Dynamics of Geostrophic Winds." Quart. J. R. meteor. Soc., 52:85-104 (1926). Joint METEOROiiOGiCAL Committee, Daily Synoptic Series, Historical Weather Maps, Northern Hemisphere, Sea Level, 1899-1939. Washington, D. C. Daily Synoptic Series, Historical Weather Maps, Northern Hemisphere, 3,000 Dynamic Meters, 1933-1940. Washington, D. C. Normal Weather Maps, Northern Hemisphere, Upper Level. Washington, D. C, 1944. Klein, W. H., "The Unusual Weather and Circulation of the 1948-49 Winter." Mon. Wea. Rev. Wash., 7:99-113

44.

— and Collaborators, "Relation between Variations in

34.

35.

J., Extended Forecasting by Mean Circulation Methods. U. S. Weather Bureau, Washington, D. C, 1947.

the Intensity of the Zonal Circulation of the Atmosphere and the Displacements of the Semi -permanent Centers of Action." J. mar. Res., 2:38-55 (1939). 45.

RossBY, C.-G., and Willett, H. C, "The Circulation of the Upper Troposphere and Lower Stratosphere."

46

Serra, a.

Science, 108:643-652 (1948).

Role in the General Circula-

tion." /. Meteor., 7:130-139 (1950). 36.

and Clapp, P. F., "Studies of the Motion and Development of Long Waves in the Westerlies." /. Meteor., 1:57-77 (1944).

37.

"Normal Fields

of

Convergence and Divergence at

the 10,000-Foot Level." /. Meteor., 3:14^22 (1946). 38.

"Confluence Theory of the High Tropospheric Jet Stream." /. Meteor., 6:330-336 (1949).

39.

Pagava, S. T., Basic Principles of the Synoptic Method of Long-Range Weather Forecasting, 3 Vols. Leningrad, Hydrometeor. Publ. House, 1940. (Translation prepared by Weather Information Service, Headquarters, Army Page, L.

F.,

Methods 41.

of

49

Tannehill, I. R., Draft Notes on Weather of Future Years. Mimeogr. Rep. U. S. Dept. of Commerce, Weather Bureau, Washington, D. C, Part I, September 1944;

50

42.

RossBY, C.-G., "Planetary Flow Patterns

Part II, May 1945. U. S. Weather Bureau, Normal Weather Maps, Northern Hemisphere, Sea-Level Pressure. Washington, D. C, 1946.

— Daily Series, Synoptic Weather Maps, Northern Hemisphere, Sea-Level and 500-Millibar Charts with Synoptic Data Tabulations. Washington, D. C, January 1949 et seq.

52.

Walker, G. T., and Bliss, E. W., "World Weather, IV— Some Applications to Seasonal Foreshadowing." Mem.

53.

Weightman, R,

R. meteor. Soc, 3:81-95 (1930). H., "Preliminary Studies in Seasonal Weather Forecasting." Mon. Wea. Rev. Wash., Supp. 45 (1941).

Wbxler,

H., "Determination of the Normal Regions of Heating and Cooling in the Atmosphere by Means of Aerological Data." J. Meteor., 1:23-28 (1944). 55 and Namias, J., "Mean Monthly Isentropic Charts and Their Relation to Departures of Summer Rainfall." Trans. Amer. geophys. Un., 19:164-170 (1938). 56 Willett, H. C, Descriptive Meteorology. New York, Academic Press, 1944. (See pp. 131-135) 57. "Patterns of World Weather Changes." Trans. Amer. 54.

geophys. Un., 29:803-809 (1948). 58.

"Long-Period Fluctuations of the General Circulation of the Atmosphere." J. Meteor., 6:34-50 (1949).

Atmos-

of the Weather Bureau Extended Forecasting Project for the Fiscal Year 1946-July 1, 1947. Mimeogr., Cambridge, Mass.,

I. T.

July

1,

1947. 60.

Final Report of the Weather Bureau

—M.

30, 1949.

Mimeogr., Cambridge, Mass.,

Yeh, T.-c, "On Energy Dispersion /. Meteor., 6:1-16 (1949).

T Extended

I.

Forecasting Project for the Fiscal Year July 61.

in the

—

and others. Final Report

59.

and others, "Reports on Critical Studies of Long-Range Weather Forecasting." Mon.

(1949).

—

of Meteorology. Vol. II Comparative Meteorology, 2nd ed. Cambridge, University Press, 1936. 48. Starr, V. P., "An Essay on the General Circulation of the Earth's Atmosphere." J. Meteor., 5:39-43 (1948).

M.

Wea. Rev. Wash., Supp. 39 (1939). Priestley, C. H. B., "Heat Transport and Zonal Stress between Latitudes." Quart. J. R. meteor. Soc, 75:28-40

1873-1909. Rio de

Shaw, N., Manual

Air Forces.) 40.

Meteorologia,

47

"Evolution of Monthly Mean Circulation and Weather Patterns." Trans. Amer. geophys. Un., 29:777-788 (1948). Its

B., Atlas de

Janeiro, Servigo de Meteorologia e Conselho Nacional de Geografia, 1948.

Namias,

"The Index Cycle and

"On the Propagation of Frequencies and Energy in Certain Types of Oceanic and Atmospheric Waves."

J. Meteor., 2:187-204: (1945).

(1949).

33.

(Supp.) :68-87

—

Lettau, H., "Luftmassen und Energieaustausch zwischen niederen und hohen Breiten der Norhalblvugel wiihrend des Polarjahres 1932-1933." Beitr. Phys. frei. Atmos., 23:45-84 (1936).

66

43.

51. 32.

Soc.,

(1940).

FuLTZ, D., "Upper-Air Trajectories and Weatlier Forecasting." Dept. Meteor. Univ. Chicago, Misc. Rep., No. 19 (1945).

24.

phere." Quart. J. R. meteor.

Meteor.

567

.

1,

1948-June

1949.

in the

Atmosphere."

APPLICATIONS OF ENERGY PRINCIPLES TO THE GENERAL CIRCULATION By VICTOR

P.

STARR

Massachusetts Institute of Technology

INTRODUCTION

form of energy. In the energy balance is re-examined. It is of course true, as has already been stated, that it is also possible to study the global balance of other individual forms of energy such as geopotential and internal heat energy. A beginning in this direction has been made by Van Mieghem [10]. of the study of one individual

last section the total

Theoretical hydrodynamics and thermodynamics furnish the basic equations of energy which in the end describe the energy transformations which take place in the atmosphere. These equations in themselves are not capable of furnishing a sufficient rational ex-

must

the causes of atmospheric processes, but provide a guide to systematic exploration of finding empirically important facts conbehavior of the atmosphere. Thus their much enhanced if consideration is given to

planation of nevertheless for purposes cerning the utility is

GLOBAL BALANCE OF KINETIC ENERGY General Considerations. One of the basic problems meteorology relates to the manner in which thermal energy received by the atmosphere through short-wave solar radiation becomes in part transformed into kinetic energy of motion relative to in the science of

observational data.

The most important problem which confronts us

in

not one of merely stating the several pertinent equations in a formally complete manner, but rather one of discussing atmospheric processes as given by observations in terms of these relationships. To this end the principles involved must be moulded and recast in such a form as to permit the desired applications to be made. In this procedure the failure to give proper cognizance to the special circiunstances characteristic of the atmospheric processes dealt with can only lead to endless complications and needless con-

such an

effort is therefore

the rotating earth. Plausible estimates show that the fraction of the total energy so transformed is very small, but must nevertheless be sufficient to account for all air motions, in the absence of any other significant energy sources. Since the kinetic energy of organized motions is continually degraded and ultimately dissipated by turbulence and viscosity, the process of kinetic energy production must be a continuous one with, probably, certain fluctuations about a mean rate

Much ject

is considered. The purpose examine this production process from a hydrodynamical point of view. Changes in the kinetic energy of a particle or system of particles can result only from the action of mechanical forces, and hence the rate of kinetic -energy production can be discussed in terms of the joint action of such forces and the kinematics of existing motions. In this light it is not essential to inquire how systems of such forces and such motions in the atmosphere are related to the thermodynamical processes which are ultimately responsible for their existence. In order to dem-

when

fusion.

what has been written concerning this subhas been deficient in two respects. In the first place,

the whole atmosphere

of this discussion is to

of

investigators have been prone to liunp together various

diverse forms of energy, thereby losing the advantages

to be gained from the fact that each form of energy is produced from and converted to other forms in its own characteristic fashion, permitting individual study.

Likewise for each form there exist specific modes of transfer and redistribution. Unless these specific characteristics are subject to scrutiny in detail, only very broad generalizations can be reached. Even here, however, the implications of the balance of total energy for the globe have not yet been studied in sufficient detail as will be discussed later. In the second place, the modes of energy transfer within the atmosphere are so effective that no feature such as a cyclone can be treated independently without due allowance for exchanges of energy between it and the remaining atmosphere. It is therefore inappropriate to treat such a feature as in any sense a closed system. Modern trends are beginning to give proper cognizance to this circumstance, although much of the too restricted point of view permeates meteorological thought. In the present discourse only certain phases of the subject are discussed by way of illustrating a general approach. Thus the discussion which follows treats only the global balance of kinetic energy as an example

onstrate the particular point in question as simply as possible we shall first consider an example of fluid motion under circumstances which are somewhat artificial, but which still have theoretical interest. In view of the fact that the kinetic energy of vertical motions in the

568

atmosphere is very small compared with the kinetic energy of the large-scale horizontal motions we shall consider only the latter.

The approach used

is one suggested by the beautiful paper of Osborne Reynolds [6] entitled "On the D3Tiamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion." Since Reynolds was concerned only with the dissipation of kinetic energy, his treatment must be modified in order to envisage also the process which creates kinetic energy. For this reason his assumption of incompressibility will be abandoned. Also, our restriction to the study of the

classic

,

1

APPLICATIONS OF ENERGY PRINCIPLES kinetic energy of horizontal motions introduces certain

changes, although these changes are not actually in the nature of approximations. Study of a Simple System. Let it be supposed that a mass of gas is confined in a chamber with a plane bottom and vertical walls, under the action of gravity which we assume to be acting vertically do^vnward. If the chamber is of sufficiently great height, it is not necessary that it have a top. Likewise, the gas need not be an ideal one, since for the time being no use will be made of an equation of state. Coriolis forces will, for the present, be omitted. Let it be supposed further that the gas is in some state of motion induced by differential heating and cooling. If we take x, y, and z to be a Cartesian coordinate system with the positive z-axis vertical, we may write the equations of motion for the horizontal directions in the form

Idp

du It

+F., (1)

dv

1

di

P

3p dy

„

,

Here u and v are the velocity components in the directions X and y; p is the density; p the pressure; t time; and Fx and Fy are the components of the viscous forces in the x and y directions. Generally speaking, the motions in the chamber might be turbulent. If we wish to regard the dependent variables in equations (1) as representing mean values free of the turbulence components, we shall assume that the only change necessary is to include eddy-stress effects in the quantities F^, Fy

manner of Reynolds. More will be said concerning this point later. The kinetic-energy equation corresponding to the

after the

system

left-hand side of (3) is the divergence of the (threedimensional) kinetic energy transport vector EV. The quantity in the first parenthesis on the right is the di-

vergence of the horizontal vector pV^. If equation (3) is integrated over an arbitrary volume, both of these quantities may be represented as surface integrals with the aid of the divergence theorem. Thus, if the limits are fixed,

we may

E

dx dy dz

///

—

'

dt 2

+

pu

4 =

/

EVn

the term

ond mode

d.

+

ble to rewrite (2) in the following form: "^

dEu

dEv

dEw

dx

dy

"di (3)

(dpu

= -[-d^

dpv\

.

+

^) +

where use has been made

(du dv\ ^[d-x+d-y)-''' ,

,

dpu

dpv

dt

dx

dy

.

dpW dz

is

mode

of redistribution

—

11

p{v dx

—

u dy)

dz.

This

is

a sec-

of redistribution of kinetic energy.

A

production of kinetic energy within the volume This is represented by the term

( du

-Hi ^^6^+^)^^'^^^^'

The

of kinetic energy. action of frictional forces. This effect would

ordinarily consist of a dissipation

the term

D=

1 1 1

and

is

represented by

d dx dy dz.

If the limits of integration include all of the fluid in the fixed chamber, it is clear that the surface integrals must vanish, so that in a mechanically closed system (5) reduces to

(6)

Z).

dt

_

(4)

'

in any case must be true, and where E — Vl the horizontal kinetic energy per unit volume. The quantity represented by the last three terms on the

which

W=

dK = 5 -

,

of the continuity equation

dp

then one

which contains the primary source

We use the symbol d to represent the rate at which the turbulence and viscosity are decreasing the kinetic energy per unit volume, and Vl = u^ v^. It is possi-

dt

is

dp\

.

4.

dE_

dS. This

2. The performance of work by pressure forces at the boundary in virtue of the displacements due to the horizontal velocity components. This is represented by

S

dp

(

dz,

of kinetic energy.

dy 2

d Vl

d dx dy

///

taken to be the inward component of velocboundary, and dS is a surface element. Equation (5) may now be given the following interpretation. The total horizontal kinetic energy (T) in a fixed region may be changing in consequence of: L An advection of new fluid having kinetic energy across the boundary. This is represented by the term

(2) ,

u dy) dz

is

—d vl + py T-d Vl dx

-

ity at the

itself.

dVl

p{v dx

(5)

3.

(1) is

write

= j EVn dS jl

where F„

dx

p

569

'jy'2

Since for such a system the frictional effect would ordinarily lead to dissipation, it follows that

>"

591

\

d a"

3

Ao I-

3 O

(3

MECHANICS OF PRESSURE SYSTEMS

592

streamlines in the col over the central United States on November 7, 1500Z, fulfill that condition fairly well. The mentioned geostrophic departure towards low pressure on the warm side of the col also favors the

transportation of the isotherms towards the axis of dilatation. As a result of these processes a surface front has formed on November 8, 1500Z, over the region previously occupied by the col, while frontogenesis is in progress over the Great Lakes region where the col has now arrived. A frontal wave has already formed over the state of Missouri and is represented in the pressure field by a small elongated low. During the

RAP

LBF

FTW

NORTH

DDC DODGE

OKC

RAPID CITY

OKLA.

FORT

PLATTE

CITY

CITY

WORTH

the foehn air over Dodge City. The foehn on the warm side of the col gives the frontogenesis a good start in the layers below the level of the continental divide, but the process also takes place higher up, as shown by the isothermalcy between 600 and 560 mb at Rapid City. The thermodynamics of upgliding in the sloping frontal zone can be tested through an inspection of the 293° dry-isentrope which has been inserted in Fig. 11. It shows that a particle could be brought dry-adiabatically along the profile from near the ground in Oklahoma to the tropopause at 350 mb over Montana without being subject to stabilizing gravity effects. If

40°

NOV. 7,1948

(zflj-

500 mb

5^ rr^^^^ Y> 45°

"S"i~ -4 0.1 10

40° NOV. 7, 1948

1500 H

—

Fig. 11. Profile of early frontogenesis, November 7, 1948, 1500Z, and part of the SOO-mb sec"', full barb 10 uations of 2fii — dvJS-i] below diagram. Upper winds: Half barb 5

following twenty-four hours the

m

new cyclone deepens

and moves along the front northeastward. A new field of deformation is active on November 9 along the cold front of that cyclone and helps maintain the frontal temperature contrast.

The described frontogenetical development near the ground conforms with the advective rules set forth by Bergeron [1] and Petterssen [25]. We shall here add a study of the dynamical conditions for isentropic upgliding in the free atmosphere, which is an important part of the process of frontogenesis. The rate of frontogenesis near the ground is increased considerably if the air of the lower part of the frontal

zone

is

100°

110°

35° ,

I500H

-I

sec

removed by upgliding. The dynamical

we take

map

same time. Sample evaltriangular barb 50 sec"'.

for the

m sec"',

into account that condensation Avould begin

mb, the ascent from there on would follow the saturation isentrope of 282°, which climbs more steeply than the dry-isentrope and likewise reaches the tropopause. Actually no single particle in such a particle at 700

undergoes such far-reaching isentropic displacements inside the profile; but the isentropes can still be used as indicators of the direction of the component of stable upgliding (see p. 585), which the particles may have in addition to their much stronger geostrophic component of motion normal to the profile. study of the values of the isentropic upgUding

A

(equation (11)),

possibili-

that process are considered in Fig. 11, which contains a profile across the zone of frontogenesis during its early stage on November 7, 1500Z. At that time no clear-cut front was yet discernible on the surface map, but on the 850-mb map there is great crowding of isotherms between the cold air over North Platte and

m

dVg

ties for

dx 2fi,

dt

-

dVg dr)

along the different sections of the inserted isentropes, will reveal the

dynamical

possibilities for frontogenesis.

EXTRATROPICAL CYCLONES The denominator

in the expression above can be determined uniquely from the data contained in the profile, whereas the numerator depends on derivatives of the geostrophic wind normal to the profile and derivatives in time. Let us consider the denominator first. Along the lower part of the 293° isentrope the geostrophic shear dVg/di) is negative, and hence 20^ — dvg/dri is large.

Between the points

of intersection of

m

sec~' and the 293° isentrope with the isovels of 20 10 sec~' the value of 2Q^ — dvg/d-q can be computed to be 1.6 X 10~^ sec^S as indicated at the bottom of the profile. Farther up along the 293° isentrope, dVg/dri

m

changes sign and 20^ — dvg/dri decreases despite the northward increase of 20^ In the baroclinic field between Rapid City and Glasgow 22^ — dVg/dT] has de.

creased to 0.8

X

10~* sec~\ Still smaller values are

found along the 282° saturation isentrope, and a negative 2Qs — dVg/d-q results in the section near Rapid City.

The

dynamic

latter value indicates

instability or,

in other words, the condition of upgliding

without dy-

namic brake action. Actually only small volumes of saturated air (altostratus and cirrus) occur in the region under consideration during the early stage of frontogenesis, and friction of such air against the dry environment probably exerts enough of a brake action to preclude violent developments. The dry-adiabatic upgliding thus still applies to the greater part of the baroclinic upper-tropospheric air. The numerator in the expression for y, can be judged from an inspection of the 500-mb map (in Fig. 11). If Vx dVg/dx is measured on the map just north of Rapid City, 10~*

it

m

amounts to 20 sec~^.

The

X

2.6

X

IQ-^

m sec-^

=

5.2

5.2 0.8

m

X X

10~* 10-^

=

6.5

msec

dvg/dt has been neglected as insignificant in comparison with VxdVg/dx. The corresponding v^ would be

about one-hundredth of v„ responding determinations

hence 6.5

cm

Corthe frontal slope result in smaller values, and consequently dvjdi] is positive. With dvjdr\ and dVx/dx both positive in the frontal zone, there is stretching in both the

and the

progresses under

,

of v„ lower

sec~'.

down on

x-direction, so that frontogenesis

optimum

conditions.

In the upper troposphere south of the maximum westerlies dVg/d-q assumes large values approaching those of 2Qz In Fig. 11, 2fi^ - dvg/d-r] measured at 300 mb over Oklahoma City is only 0.1 X 10"'' sec~^ However,

also small at that place (see Fig. 9)

is

(directed towards high pressure) at all reporting upper-

wind

stations. This is an example of the systematic nongeostrophic wind components at the "delta" of an upper jet stream derived in Fig. 8. The horizontal convergence resulting in the southern half of the delta is instrumental in providing the pressure rise ahead of the moving high in the southeastern United States (Fig. 10).

Figure 12 shows a profile through the zone of frontoThe frontal slope has become steeper (^io in the lowest portion) and the frontal shear —dvx/dy is now characterized by a sharp 180° wind shift. Negative Vg values (northeast wind) stronger than 10 sec~' now occur in the lower part of the cold wedge near the front. Applying the w,formula to particles in the northeast current, we find conditions set for isentropic downgliding because the numerator VxdVg/dx dVg/dt is now negative. A numerical estimate of the downgliding along the 281° genesis twenty-four hours later.

m

+

isentrope near the cold edge of the frontal zone at 850 mb follows: 3y,g

Vv

=

I

dVg

dx

dt

dVg

2fi.

- -^ drj

X X

-10

comes from the 500-mb contours and that

Here

7;-direction

dVg/dt

large value of the term

m

=

-\-

no great ?;,-component results. Farther east near the Atlantic, where the anticy clonic isentropic shear is equally great and Vxdv„/dx has a large negative value, w, is observed to have a large negative value so that

X

the convergence of feature, in turn, is inherent in the structure of the large pressure trough to the west with its central area of weak pressure gradient bordering on strong pressure gradients to the south. The large value of dVg/dx is, of course, also corroborated by measured wind velocities, which increase from 10 sec~' to 50 sec~' along the streamline from northern Wyoming to Green Bay, Wisconsin. In addition, the 300-mb map (Fig. 9) shows the same convergence of contours a little farther north. An evaluation of w, at the 500-mb level just north of Rapid City gives v„

Vx()Vg/dx

593

0.96

The

resulting

X 10" - 0.1 X

1.4

10-^

dry-isentropic

10"

=

10-^

descent

—2.8 msec traverses

the

component from the cold to the This nongeostrophic component towards

frontal zone with a

warm

side.

the frontal trough, together with the frictional flow component in the same direction, accounts for the subgeostrophic displacement of warm fronts in general. In some cases the nongeostrophic component normal to the front may permit the cold wedge to advance against a moderate geostrophic component from warm to cold. In the upper part of the frontal zone, isentropic upgliding continues on November 8 just as on November 7, as can be seen from the convergence of contours between Omaha and Bismarck on the 500-mb map (Fig. 12). The same contour convergence is found right over Omaha on the 700-mb map (not reproduced). In the profile the 284° saturation isentrope approximately fol-

lows the warm edge of the frontal zone; dvg/di) measured along that isentrope gives values greater than 29,z from the condensation level up to 700 mb. This lower portion of the frontal zone is thus dynamically unstable; while higher up, where the 284° isentrope turns parallel to the Vj-isovels, finite speeds of upgliding can be determined. An estimate of the upgliding on the saturation isentrope of 284° at the 500-mb level gives

.

y„ '

=

23 (1.0

X — -

X 10"' = O.n X 10-'

1.4

^

„ „ 3.6

m sec-1

.

MECHANICS OF PRESSURE SYSTEMS

594

Exploring the whole frontal zone for nongeostrophic we find the conditions for downgliding limited upwards by the zero isovel, while upisentropic motion,

BIS

BISMARCK

OMA OMAHA

CBI

COLUMBIA

about }io in the upper portion, and it is quasian intermediate portion around 700-800 mb tilts only by Kso- The general zone

is

vertical near the ground, while

BRR NASHVILLE

1000

NOV. 8,1948

1500 Z

—

Fig. 12. Profile of the warm front of the incipient wave on November 8, 1948, 1500Z, and part of the 500-mb map for the sec"'. sec"', full barb 10 time. Sample evaluations of 2Q: — dvg/dri below diagram. Upper winds Half barb 5

above that line. Moreover, we find that the dry-isentropes indicate a downgliding with a horizontal component across the front from cold to warm, while the upgliding along saturation isentropes remains almost parallel to the frontal slope. The frontal profile therefore must begin to bulge forward from cold to warm in the lower layers while remaining rather unchanged higher up. That is what happens when the apex of the frontal wave goes by, as will be discussed in connection with the maps in Fig. 14. The anticyclonic shear south of the westwind maxihas growTi to the state of dynamic instability as shown in Fig. 12 by means of the differentiation of Vg along the 333° isentrope. Shears rather close to the instability limit also extend down to the 500-mb level and make possible the rather large and systematic wind component towards low pressure observed on the 500mb map southeast of the jet stream. Figure 13 shows a profile across the cold front from Dodge City (Kansas) to Maxwell Field (Alabama) on November 9, 1500Z. The corresponding sea-level and 850-mb maps are to be found in Fig. 10. The profile shows that strong horizontal temperature gradients have formed all the way to the top of the diagram. The frontogenetical process by horizontal advection has actually been operating through the whole troposphere (in Fig. 14 the resulting frontal zone shows up well even at the 300-mb level). The inclination of the frontal gliding begins

m

m

:

same

shape of the profile can be understood as the result of the bulging forward of the lower portion of the cold wedge after the passage of the frontal wave apex. The

mum

'Z

d-q 4>

37°

is the latitude. Usually, separate maps of u and v are constructed and analyzed, and the partial derivatives are approxi-

where

Determination of Vertical Velocities

methods of meason thunder-

article

storms. ^ In addition, instantaneous vertical velocities near the ground have been measured by many investigators of turbulence. Large-scale vertical velocities

(horizontal

area

>

10" cm^) must be determined indirectly. The two principal methods which have been suggested for estimating these small vertical velocities involve computations (1) from horizontal velocities and the equation of continuity (kinematic method), and (2) from the effect of vertical velocities on temperature, potential temperature, or wet-bulb potential temperature (adiabatic

method) The Kinematic Method of Determining Vertical Velocities. On the scale under discussion here, the vertical velocity at level h can be found from the equation of continuity in the form 1

Wh

t

p div

/

N dz

-\-

w^ El

Pk J s

(5)^

Ph'

Here s stands for surface. The integral can be approximated by a sum, and Ws can be estimated from the horizontal wind field and the slope of the terrain. A more elegant form of this method is obtained if equation

(5) is

transformed to

:

divV =

= ——

Wi,

Ydz.

div

ph

A.

«/

(6)

8

vector 1] V dz is the "resultant vector" which is equal to the horizontal distance from the observer to the position of the pilot balloon at level h, multiplied by the speed of ascent of the balloon. This distance is available directly from the original pilot-balloon runs. The divergence of the resultant vector is computed by one of the techniques described above. The kinematic method yields instantaneous values of vertical velocities, usually averaged over considerable areas. A dense network of actual wind observations is needed, so

The where Si and S2 are the distances between two streamlines, measured along orthogonals to the streamlines; V2 and Vi are the average velocities of outflow and inflow across Si and S^; and A is the area enclosed by the two bounding streamlines. Si and S2 (Fig. 2).

vertical velocities

have been computed by this method ft and in regions of good weather.

only up to 10,000

Radar and radio Fig.

2.

— Illustration

for

definition

of

mean divergence

in

natural coordinates.

Mantis (see [16]) showed that both the "component technique" (Cartesian coordinates) and the streamline technique (natural coordinates) are about equally inaccurate; even for large areas and good wind coverage the sign of the divergence can be trusted only for relatively large observed magnitudes, for example, greater than 5 X 10~^ sec~^ Recently, an objective method proposed by Bellamy [2] has been used extensively. This procedure is based on a determination of divergence from observations at the corners of a triangle. (For another, much more tedious, objective method see [21].)

direction-finder pilot balloons should

and applicability of the method. The Adiabatic Method of Computing Vertical Velocities. The adiabatic method, which is completely independent of the kinematic method, is based on the assumption that rising and sinking air will cool or warm at a known rate. Then a measured temperature change will permit computation of the vertical velocity. We start from the mathematical identity increase the range

where

T

is

dT

ar

dt

dt

,

„ „ „

temperature and V„

,

dT dz'

is

the vector differential

2. Equation (3) is essentially the same as equation but applies only for horizontal ground.

(5),

LARGE-SCALE VERTICAL VELOCITY AND DIVERGENCE operator applied in the horizontal direction. If temperature changes are adiabatic, dT/dt is given by —ivjad where jad is the adiabatic lapse rate. Then

dT

w = —

641

MECHANICS OP PRESSURE SYSTEMS

642

motion, the equation of continuity requires horizontal convergence at the surface (Fig. 4). Quantitative computations [8] show that divergence in and above the tropopause almost exactly compensates the surface convergence. The same is true for surface divergence and stratospheric convergence. The observations are too crude to permit the exact location of a level of "nondivergence" in the upper troposphere. For several months, synoptic vertical velocity charts were constructed at New York University at 10,000 ft or 700 mb along with the regular analysis of standard maps. Aside from the correlation between vertical velocities and meridional flow at the same levels, the followheight

duces convergence in the northward flow, and (2) the curvature term in the gradient wind equation produces faster motions at the wedge than at the trough lines, hence, for sinusoidal isobars, there is convergence with flow from the north. The curvature term depends on the square of the wind speed, the latitude term on the

power. Thus the curvature term is relatively more important at high than at low levels. Quantitative computations show that near the surface the latitude term determines the distribution of divergence, and that above a critical level the curvature term takes the upper hand. This theory, again, leads to qualitative agreement with Fig. 4. Quantitatively, however, the first

km i5r £1

-1 1

I

1

1

1

CONVERGENCE

If

1

1

I

1

I

DIVERGENCE

f

LARGE-SCALE VERTICAL VELOCITY AND DIVERGENCE that Wh, the vertical velocity at the top of the friction is given by

layer,

Wh

curl„ to,

Pf

the surface stress acting on the boundary and ground in the direction of the wind, p the density, subscript v denotes the vertical component, and / is the Coriolis parameter. It is difficult to evaluate the surface stress quantitatively over land; but since the surface stress is in the direction of the wind and the wind blows counterclockwise about low-

where 'Co between

is

air

pressure centers, this formula also indicates

upward

divergence term, and in (9) the low-level divergence almost exactly compensates high-level divergence. Therefore neither equation can be applied to determine pressure changes from measured divergence. Moreover, most theories of divergence are not sufficiently accurate to permit estimates of pressure changes from these equations. Divergence and Change of Vorticity. Another reason for interest in divergence is the effect it has on the individual change of absolute vorticity. The vorticity equation may be written (if we neglect solenoidal fields, friction,

may be asked whether a similar relation-

east to west. It

ship would hold

when the isotherms run

in

some other

direction.

Charney's theory is based on the assumption that the isotherms run from east to west. According to the Bjerknes-Holmboe theory the distribution of divergence depends on sinusoidal air motion superimposed on an east-west channel; upper-level streamlines behave in this way only when the isotherms run from east to west. Consequently both these theories show a relation between vertical and meridional velocities only if the isotherms are parallel to the latitude circles. In general, both theories would predict a relation between vertical motion and the horizontal wind component at right angles to the isotherms, or between vertical motion and horizontal temperature advection. Only when the isotherms run from east to west is a relation expected between vertical and meridional motion.

and terms depending on the horizontal varia-

tion of vertical velocity)

motion above pressure minima. Since nonfrictional theories predict upward motion in the southerly flow above low-pressure centei's, friction has the effect of increasing the absolute magnitudes predicted by these theories. Possibly a combination of the Bjerlcnes-Holmboe theory and the theory of friction would account for the observed distribution of divergence and vertical velocity in the troposphere. The relation between meridional and vertical motion has been observed so far only in the United States and England, where the isotherms run essentially from

643

d^

1

t

+ fdt

'E(f

+ /)

divV,

(10)

30

is the vertical component of vorticity and v the meridional velocity component. Rossby's trajectory method was derived from the vorticity equation on the basis of negligible divergence.

where f is

Some

investigators attribute the systematic errors of the method in certain regions to the omission of divergence [18]. Studies at New York University seem to indicate that the divergence term is at least of the same order of magnitude as the term containing the variation of the Coriolis parameter with latitude, even for very large scales (areas of the order of 10^^ cm^). The omission of the divergence term is justified only near the level of nondivergence or when equation (10) is integrated vertically through the whole atmosphere. Divergence and Change of Stability. Local changes of

can be brought about by three factors [6]: (2) different horizontal temperature advection at different levels, and (3) vertical advection of lapse rate. Since vertical divergence almost stability (1)

vertical divergence,

equals the negative horizontal divergence, the latter may be considered as a factor producing stability changes. Fleagle [6] found that the effect of horizontal divergence on stability changes is of the same order of magnitude as that of differential advection; he also

noted that accurate forecasts of local stability changes based on measured divergence and differential advection are inaccurate, probably due to the large errors in

measurements

of divergence.

Effects of Divergence

Effects of Vertical Velocity

Divergence and Pressure Change. One of the reasons why meteorologists have been interested in divergence is that it is related to pressure change through the

Bjerknes pressure-tendency equation:

^

\dt)

^SP'^^''

~

9J

r where

-' ly'^""'''-

9

ly ''''''''

(9)

stands for the surface which is assumed hori[8] showed that the vertical velocity term in equation (8) almost exactly compensates the s

zontal. Fleagle

-— =

— + V-VffV + w -—.

dt

dl

dz

Charney [5] indicated that the term containing w should be one order of magnitude smaller than the other terms in the expression. This conclusion, based on a dimensional argument, is at variance with results obtained at New York University. Vertical velocities average about

1

cm

sec~'; the vertical shear of horizontal

wind

MECHANICS OF PRESSURE SYSTEMS

644 is

near 5

X

X

10~' sec~^ Hence, the

term averages around about half as large

cm 5 as the other acceleration terms. Neglecting the vertical 10~'

sec~^ in magnitude,

advection terms may lead to considerable errors. Vertical Advection of Temperature and Potential Temperature. Vertical advection of temperature and po-

temperature

tential

by the tained

fact that reasonable values of

by the

was shown have been ob-

also important, as

is

effect of vertical

w

motion on the tempera-

Again, the effect of vertical motion on local temperature changes averages about half the effect

ture

field.

of horizontal advection

[7,

the acceleration of gravity, hi and hi are fc is the ratio of the gas constant to the specific heat at constant pressure, and E is the stability {yad — i)IT This equation avoids the lowlevel, high-level compensation of the Margules-Bjerknes tendency equation. However, the vertical velocity is

where g

.

not

gral with respect to height of local density changes.

density changes in turn are computed from horizontal advection and the effect of vertical motion.

The

it; on used this equation to compute the vertical velocity from the pressure tendency. Later Fleagle [8] discussed the relative importance of vertical and horizontal motion on pressure changes in

the contrary, Panofsky

selected situations,

v-v„,

dz (11)

©to

O

r-h-i

wpE dz

[9]

considered the con-

on the basis of a These studies indicated that vertical motion has effects on local pressure changes of the same order of magnitude as horizontal motion. Vertical Velocities and Changes in Cloudiness. Largescale vertical velocities have their most conspicuous similar equation.

effect in the

when

it rises,

production of cloudiness. Since air cools increasing cloudiness should be associated velocities.

and Miller and others

[17]

Panofsky and Dickey showed that middle

+

g

{I

and decrease along the trajectories of sinking However, vertical velocities do not seem to discriminate between overcast with or without precipitation. Figure 5, taken from Miller [15], shows this effect rising air

J 1,0 /

and Godson

cloudiness tends to increase along the trajectories of

nh2

.hi

g

[19]

ditions favorable for cyclogenesis,

[22]

+

sufficiently well to permit forecasts of pres-

with positive vertical

The equation can be written

dt

known

sure tendencies from (11) or a modification of

19].

Motion and Pressure Changes. Since the vertical velocity has an important effect on the temperature field, and since changes in the temperature field are associated with pressure changes, Raethjen [24] first suggested a pressure-tendency equation in which the pressure tendency is expressed in terms of an inteVertical

dp\

is

arbitrary levels,

-

k)

pdp -'^ P

dt

dz.

air.

©

(to

cm /sac

O

P

to

O

to

LARGE-SCALE VERTICAL VELOCITY AND DIVERGENCE graphically. According to this figure, clear weather at

the end of the trajectory was usually preceded by slightly negative vertical velocities, and cloudy weather or precipitation by vertical velocities averaging about 1 cm sec~^ These values reflect average conditions only; the figure shows instances where the final weather

+

was clear with upward vertical and 2 cm sec~', and a few cases

velocities

between

1

of final precipitation

with slightly negative vertical velocities. Apparently, the relation is not perfect, largely due to errors in constructing trajectories, and errors in the vertical velocities.

Vertical Velocities as a Forecast Tool

The

relation

between vertical

velocities

and changes meas-

in cloudiness suggests the possibility of applying

ured vertical velocities to forecasting weather changes objectively. If the air has an upward component of motion, we might expect bad weather soon. One difficulty suggests itself immediately. If vertical velocities are computed by the adiabatic method, observations at the end of a 12-hr period are needed in order to compute average vertical velocities for that period. These vertical velocities are centered in the middle of the period and are therefore already 6 hr old at the time the analysis is started. A further lag is caused by transmission time, analysis and computation, so that the vertical velocities are at least 8 hr late when they are ready for application to "forecasting." As Fig. 5 indicates, cloud changes are related to the average vertical motion along the air trajectory. If a 24-hr forecast is desired, a 24-hr air trajectory must be forecast and the average vertical velocity along the trajectory must be estimated from quantities at the beginning of the trajectory. Since the forecasting method was to be objective, it was necessary to devise a method of forecasting trajecIt would require too much space here to describe the method finally applied; but it is clear that errors in the forecast trajectory will lead to inaccurate future positions of the air and hence to additional errors in the forecast. Experiments with different variables indicated that an estimate of the mean vertical velocity along the trajectory could be made from the initial vertical velocity and the initial meridional velocity. The multiple correlation coefficient of mean vertical velocity on initial vertical velocity and meridional wind components was 0.64 [15]. Clearly, an estimate of the mean vertical velocity based on these two variables is subject to considerable error.

tories objectively.

In practice it was possible to side-step the computation of the average vertical velocity along the trajectory. Since the average vertical velocity of initial vertical

and the change

is

a function

and meridional velocity components, weather

a function of the average weather changes should be directly related to the initial meridional and "ertical velocity components. Charts were constructed for me fir.st half of December 1945, which showed the final weather and cloudiness as a function of initial of

is

645

weather and of the vertical and meridional components of velocity. In certain regions of these charts clear sky (cloudiness 0.4 or less) was predominant; in other regions overcast and precipitation predominated. A line was drawn which separated the sections of predominantly clear sky from sections of sky mainly overcast. It was quite difficult to find dividing lines between overcast and precipitation on these charts. Such lines were drawn, however, under the assumption that precipitation should occur with large upward vertical velocalong the trajectories. Forecasts were made from these charts for the last half of December 1945. The total percentage of correct forecasts was 69.9 per cent. The chance score was 57.3 per cent. ities

A more severe test is the comparison of the percentage of successful forecasts with those obtained from "low skill" forecasts. For example, if "clear" had been forecast all the time, the score would have been 69.2 per cent; if no change of local weather had been forecast, the percentage of hits would have been 59.7 per cent. The same forecasts were repeated by two graduate students who had considerable forecasting experience. These forecasters

had no knowledge of the The two forecasters

vertical velocities at the time.

scored 63.4 per cent and 69.8 per cent correct, respectively.

Altogether, the objective

method

of forecasting verti-

not perform badly, in spite of the many sources of error. Later studies [16] showed the method considerably less successful. Moreover, Miller showed that equally good forecasts could be made by a very similar method, if the initial vertical velocities were not known at all, but the forecasts were based solely on the initial weather and meridional velocity component. Therefore the laborious computation of vertical velocities for forecasting purposes is possibly unnecessary. Apparently, the meridional velocity component is a sufficiently good indicator of the direction of the vertical air motion. The relation between meridional motion aloft and weather is known to many meteorologists, and has been incorporated, indirectly, into other objective forecasting methods. Some attempts were made to use vertical velocity patterns qualitatively. On daily vertical velocity charts the "unusual" features that did not conform to the simultaneous weather were noted. For example, an area of upward motion over an east coast wedge was judged significant. Such unusual features were followed sometimes, but not always, by unusual developments; for example, unusual centers of upward motion were associated with cyclogenesis. Several forecast rules based on unusual "\'ertical velocity patterns were suggested, but none of them proved reliable. Whether this was due to errors of the vertical velocities cannot yet be decided. cal velocity did

vertical velocity along the trajectory,

Suggestions for Future Research Since most of the studies of vertical velocity were completed the network of radio and radar wind observations has been greatly extended. As a result, de-

MECHANICS OF PRESSURE SYSTEMS

646

termination of divergence and vertical velocity by the kinematic method would seem possible in forecasting techniques. The advantage of the kinematic method is the possibility of computing vertical velocities within only a few hours after the time to which they apply. This and the rather indecisive results of the earlier forecast studies might make it desirable in the future to study forecasting techniques based on vertical

9.

"A New Tendency Equation and

L.,

Its

Ap-

plication to the Analysis of Surface Pressure Changes." /. Meteor., 5: 227-235 (1948). 10.

Graham, R. C, "The Estimation

of Vertical

Motion

in

the Atmosphere." Quart. J. R. meteor. Soc, 73: 407-417 (1947). 11.

Hewson, E. W., "The Application of Wet-Bulb Potential Temperature to Air Mass Analysis." Quart. J. R. meteor. Soc, 62: 387-420 (1936); 63: 7-29 (1937); 64: 407-418

velocities.

Another

Godson, W.

(1938).

possibility,

which has been only partially

the application of the vorticity equation (10) to the forecast of changes of vorticity from observed divergence. So far, systematic work on vertical velocities has been restricted to middle latitudes in the Northern Hemisphere. It is quite possible that the observed relation between vertical and meridional velocities, for example, is not valid everywhere. Studies in other parts of the world are desirable in order to determine whether there exists a general relation between vertical and meridional motion or vertical velocity and advection. Moreover, a study of the relation between vertitested thus far,

is

cal velocities, divergence,

and weather

is

desirable in

Holmboe,

E., and Gtjstin, W., Dynamic York, Wiley, 1945. (See p. 143) 13 Houghton, H. G., and Austin, J. M., "A Study of Nongeostrophic Flow with Applications to the Mechanism of Pressure Changes." J. Meteor., 3: 57-77 (1946).

12

Forsythe, G.

J.,

Meteorology.

New

14.

Longley, R. W., "Subsidence and Ascent of Air as Determined by Means of the Wet-Bulb Potential Tempera-

15

Miller,

ture." Quart. J. R. meteor. Soc, 68: 263-276 (1942). J. E., Application of Vertical Velocities to ObWeather Forecasting. Prog. Rep., Mimeogr., College of Engineering, New York University, 1946.

jective

16

"Studies of Large Scale Vertical Motions of the Atmosphere." Meteor. Pap., N. Y. Univ., No. 1, 48 pp. (1948).

17

and others,

A

Study of Vertical Motion in

the

Atmos-

other sections of the globe. In general, a better understanding of vertical motion will presumably arise out of the work which Dr. Jule Charney and his collaborators are doing at The Institute for Advanced Study on numerical forecasting

18.

Namias,

based on the physical equations.

19.

Panofsky, H. a., "The Effect of Vertical Motion on Local Temperature and Pressure Tendencies." Bull. Amer.

phere. Prog.

New York

J. K., "The Estimation of Large Scale Vertical Currents from the Rate of Rainfall." Quart. J. R.

meteor. Soc, 74: 57-66 (1948).

21.

Bannon,

3.

Soc, 30: 45-49 (1949). Bjehknes, J., and Holmboe,

"Objective Calculations of Divergence, Vertical Velocity and Vorticity." Bull. Amer. meteor. J.

clones." J. Meteor., 4.

Charney,

J.

G.,

1:

J.,

"On

22.

"The Dynamics

of

Long Waves

in a

Vertical Motion in the At45-49 (1946).

"Objective Weather-Map Analysis." J. Meteor., 6:

and Dickey, W. W., "Vertical Motion and Changes Amer. meteor. Soc, 27: 312-313

"On the Scale of Atmospheric Motions." Geofys. Publ, Vol. 17, No. 2 (1948). Fleagle, R. G., "A Study of the Effects of Divergence and Advection on Lapse Rate." J. Meteor., 3: 9-13

S.,

and others, "An Investigation

of

Sub-

Soc,

73: 43-64 (1947).

24

Raethjen, p., "Advektive und konvektive, stationare und gegenlaufige Druckanderungen." Meteor. Z., 56:

25

Sawyer,

133-142 (1939). J. S., "Recent Research at Central Forecasting Dunstable," in a discussion, "Large Scale Vertical Motion in the Atmosphere." Quart. J. R. meteor. Soc, 75: 185-188 (1949). Spilhaus, a. F., Schneider, C. S., and Mooke, C. B.,

Office,

"The Fields of Temperature, Pressure, and ThreeDimensional Motion in Selected Weather Situations." "Quantitative Analysis of Factors Influencing Pressure Change." J. Meteor., 5: 281-292 (1948).

Petteessen,

sidence in the Free Atmosphere." Quart. J. R. meteor.

/. Meteor., 4: 135-162

J. Meteor., 4: 165-185 (1947). 8.

3:

(1946). 23.

(1946). 7.

Computing

386-392 (1949).

the Theory of Cy-

1-22 (1944).

(1947).

6.

of

in Cloudiness." Bull.

Baroclinic Westerly Current." 5.

"Methods

mosphere." /. Meteor.,

C,

Bellamy,

and Clapp, P. F., "Normal Fields of Convergence and Divergence at the 10,000-Foot Level."

meteor. Soc, 25: 271-275 (1944). 20.

2.

University, 1946.

J.,

/. Meteor., 3: 14-22 (1946).

REFERENCES 1.

Rep., Miemogr., College of Engineering,

26

"Controlled-Altitude 130-137 (1948).

Free Balloons." /. Meteor., 5:

THE INSTABILITY LINE By U. S.

J.

R.

Weather Bureau, Washington, D. C.

Introduction and General Features

The synoptic meteorologist frequently encounters nonfrontal squall lines, particularly in the warm sectors of certain types of extratropical cyclones. These nonfrontal squall lines, now designated by the International Meteorological Organization as instability lines, are relatively frequent in the United States east of the Rockies and may be severe in character. Some are accompanied by tornadoes and presumably extreme vertical instability through a relatively deep layer of the atmosphere. A well-developed instability line is marked by squalls or thunderstorms along a line that is usually several hundred miles in length, and in the typical case fifty to three hundred miles ahead of a surface cold front. Or, where scattered showers or general rains are already occurring, the instability line represents a sharp intensification of squall conditions and rainfall, lasting usually for about an hour at any one location. Since these conditions may occur, for the most part, between regular synoptic reports, the best evidence is often in the reported time, character, and amount of rainfall, or in frequent intermediate reports. The pattern of reported thunderstorms is usually also an indication of the existence and location of an instability line, but in some situations scattered thunderstorms occur before and after its passage. By convention the line is taken to be the leading edge of the band, usually thirty to fifty miles in width, of greatest convective activity. In more complicated cases, there may be several bands of squalls. Aircraft encounter marked and sometimes dangerous turbulence in flying through an instability line. The term instability line is also applied to the incipient condition, when synoptic factors indicate that a nonfrontal squall line is forming, and may be applied to the line of instability in the dissipating stage when squalls

in character, usually developing to maximum intensity within a period of twelve hours or less and then dissipating within about the same period of time. Although by definition it is nonfrontal in character, it may cross a front. Often the line extends from the warm sector of a low northward across the warm front and is associated with a line of squalls in the northeastern quadrant of the low. Harrison and Orendorff [5] in 1941 studied the "precoldfrontal squall line," especially from the standpoint of airline operations. In addition to describing the squall line and associated conditions, they examined physical factors possibly contributing toward its development. Without attempting to reach definite conclusions they presented data which suggested a pseudo-cold front of rain-cooled air moving against a rainless zone in the same air mass, and convergence within a potentially unstable air mass, as being at least possible causative factors in most of the cases studied. One of the significant facts they reported was that activity along the cold front decreases during the active stage of the squall line but regenerates as the squall line dissipates. Their

study was confined to the Cheyenne-New York airway (between April 1939 and May 1940) and probably was not fully representative of squall-line conditions elsewhere; for example, they reported no sustained temperature change through the squall line aloft. The heights of upper levels considered were not fully specified; presumably they were flight levels and thus often below heights at which cooling is frequently observed in the general region of the instability fine.

Lloyd

[6],

in his studies of tornadoes, attributed at

an and the

least the tornado-producing squall-line condition to

upper cold front. Advection

of colder air aloft

resulting decrease of temperature, as would be required existence of an upper cold front, is observed in many

by

have ceased.

Alternately, the term instability line

FULKS

is

defined as a

pseudo-cold front for which the cold air

is presumably produced by precipitation falling from a line of accompanying showers. While the pseudo-cold front marking the leading edge of the outflowing rain-cooled air from instability showers is observed in most nonfrontal squall lines, it appears to be normally a secondary effect, other factors probably being more important in forming and maintaining the line of squalls. However, there are some cases where thundershowers develop over

a localized region of, say, 10,000 or 20,000 square miles forming a surface layer of cool air which flows outward in all directions, new thundershowers then tending to develop along the resulting pseudo-cold front where the wind direction in the warm air is favorable to lifting over the cooler surface air. Unlike a true front, the instability line is transitory 647

cooling aloft also takes place, in some inof the squall condition, indicating that near the leading edge of the instability the degree of cases.

But

stances,

ahead

cooling aloft

is

not always sufficient for convective

Back from the leading edge, temperatures aloft may be lower, and surface temperatures higher, so that at some point the critical lapse rate necessary for convection may be realized. The exact distance between activity.

the squall condition and the leading edge of the colder air aloft is difficult to determine by observation, but

appears to vary from a few miles (possibly less) to hundreds of miles. Where the leading edge of advection of colder air aloft is very close to the squall condition, and there is evidence of a discontinuity in density as required for a front aloft, the condition is not properly classified as "nonfrontal."

In

many

instances, however,

the existence of a discontinuity aloft along or near the

MECHANICS OF PRESSURE SYSTEMS

648 squall condition

is difficult

or impossible to determine

from synoptic data and the only practical recourse for the synoptic meteorologist

is

to follow the instability

line.

Synoptic Aspects and Figiu'e

marked

1

Some Associated Physical Factors

represents diagrammatically a typical wellwarm sector of an extra-

instability line in the

1000 miles-

—Model

with instability line in warm Shading indicates areas of active squalls, and hatching shows warm-front precipitation. Fig.

1.

of cyclone

sector.

The line CD is the center of a extends roughly at right angles to the given vertical section. Thus, any constant level or constant pressure surface cutting the vertical section will have a warm tongue, the axis of which intersects the line CD. Generally the horizontal temperature gradient to the right of CD is less than to the left of CD. As the system moves from left to right (normally eastward) cooling aloft over any fixed point will begin as the line CD passes, and since the cooling takes place first at the higher levels, there will be a progressive decrease in vertical stability until the arrival of the instability line. Often, at least in the central and eastern United States, there is a stable layer or inversion at approximately 1}4 km above the surface and to the east of the instability line; this inversion disappears with the arrival of the instability line. It is probable that this stable layer, when it exists, plays an important part in the mechanism of the instability line, because it provides a "cap" under which the temperature and moisture content may increase until, combined with any cooling aloft, the vertical instability is sufficient for vertical convection. This effect is made possible by slower eastward movement of the surface air as compared to the system as a whole, and is enhanced by conditions usually favorable for low-level advection northward of moisture and warmer air, as pointed out by Means [7]. Apparent warm advection is in some cases, however, indicative of lifting rather than lowpotential temperature.

warm tongue which

level

warming.

The

cooling aloft, as illustrated in Fig. 2, is in part the result of horizontal advection, as may readily be verified by inspection of constant-level or constantpressure charts. The typical condition is one of cooling

and thunderstorms (shaded shown as a nearly solid band along the instability line and at scattered points elsewhere in the warm sector and within the area of warm-front precipitation (hatched). In this type of low, and at this stage of

by advection by advection

at lower levels.

at low levels

is

development, precipitation

cooling aloft, but cooling aloft

tropical cyclone. Squalls

area) are

is

rarely observed behind

the portion of the cold front following the instability line.

Figure 2

AB

of Fig.

is 1.

a vertical cross section through the line Thin solid lines represent isotherms of

I6000FT 12000 FT

8000 FT 4000 FT

300'

A

COLD

—

B

Fig. 2. Vertical cross section through cyclone with warm sector instability line. The section is taken along the line AB of Fig. 1 and is on the same horizontal scale; the vertical scale is indicated roughly in feet on the right-hand side. Thin quasi-horizontal lines are potential temperature, labeled in °K on the left. The dashed line CD is the axis of warm air, temperatures decreasing or changing but little horizontally to the right, and decreasing to the left of CD (except near the ground where temperature decreases sharply with onset of instability line squalls). Shading indicates cloud masses, and hatched lines show active precipitation; the double horizontal line indicates a stable layer.

where there is warming The warming by advection

aloft over a region

generally greater in magnitude than the is significant in that it

permits vertical convection to extend to higher levels than would otherwise be possible, thus becoming an important factor in the intensity of resulting convective activity. It seems certain, however, that factors other than advection are also important in the cooling which takes place aloft over the warm sectors of many lows. An early example of cooling aloft ahead of a surface cold front, accompanied by warm-sector precipitation was presented by J. Bjerknes [1] in 1930. This study was based on a detailed examination of frequent soundings at Uccle, Belgium, during the period December 26-28, 1928. The cold front as shown in Fig. 2 does not extend far surface. When the instability line is well developed, there is usually little or no evidence of the existence of the associated cold front at more than two or three thousand feet above the ground. The position of the cold front at the ground is usually quite well

above the

marked by a wind

shift,

of moisture content (dryer

there

is little, if

pressure trough, and change on the cold air side). Usually

any, temperature change immediately

across the front, but there is a horizontal temperature gradient toward colder air to the rear, suggesting that,

THE INSTABILITY LINE in

many

cases at least, there

is

no true discontinuity

of density but rather a discontinuity in the gradient of

customary, however, this hne as a cold front, because at a later stage in the history of the low the instability line tends to dissipate and the "front" again takes on the characteristics of a true cold front. Along the instability line, when it is well developed, there is marked cyclonic wind shear at low levels, associated with a pressure trough. At higher levels, as in extratropical cyclones generally, there is a pressure trough which roughly parallels the surface cold front. In many cases of well-marked instability lines, the pressure trough aloft coincides with the instability line. In density. In synoptic practice to continue to carry

it is

and designate

some cases it is back of the surface cold front, as is normal in lows which do not have an instability line. As with shower conditions generally, surface temperawith the arrival of the instability line, and this fact, combined with the cyclonic wind shear, suggests a surface frontal structure. However, the temperature often rises after passage of the instability line and remains high until after passage of the cold front; moisture content also remains high until after passage tures usually

fall

of the cold front.

The

fact that cyclonic

wind shear

is

observed at the

649

weather along the

line tends to vary from station and there are corresponding irregularities in the reported tendencies. The tendencies are, however, a useful guide if viewed with caution and if

of the

to station,

allowances are made for known squall activity at individual stations. Their use as a guide to location of the instability line should be looked upon as subordinate to the more direct location of the pressure trough or line of wind shear, or the observed onset of squalls at individual stations. Upper winds, when available, are useful in locating the line of wind shear at the gradient level if reports are not too far apart. Surface winds are similarly helpful if allowance is made for local topographical effects and for the fact that isolated squalls may occur ahead of or behind the instability line.

There is no clear guide to the speed of movement of the instability line other than its past history and the known speed of movement of a low with which it may be associated. The pre-coldfrontal squall line moves slightly faster than the cold front which it precedes. The movement of the instability line is at about the same speed as the axis of the warm tongue aloft, which is normally along or ahead of the instability line and moves with a speed somewhat less than that of the

The movement

surface along a well-developed instability line provides

wind speed

one clue to its location on the surface synoptic chart. Or, when a line of squalls is not yet in existence, the appearance of a line of cyclonic wind shear within a warm moist air mass, particularly in the warm sector of a low, may indicate the existence of an incipient

not particularly useful for forecasting the movement of the instability line once the line is in existence, but for longer-period forecasting its movement is some guide to the time and location of possible future squall-line developments. Over the western Great Plains and the Mississippi Valley, a cold front aloft or the advection of colder air aloft often has its inception as a surface cold front over the western mountain region. The surface front, marking the arrival of fresh maritime polar (mP) air from the Pacific, moves across the Plateau region. The shallower portion of the cold air, near the leading edge, becomes heated by the warmer ground over which it moves, and also by compression as it flows downward along the east slope. The heating effect is less within the deeper portion of the cold air so that a horizontal temperature gradient is established within the cold air. The leading edge of the cold air while over the Plateau region remains colder than the surface air ahead of the front, but as the front moves do\Mi the

instability line.

The

instability line

is

either in a pres-

is along a discontinuity in pressure gradient. The wind shear in the horizontal is similar to that along a front, but unlike a

sure trough, or

if

parallel to the isobars,

wind discontinuity is more nearly vertical except along the outrush of cooler air at very low levels ahead of individual squalls. With the density of reporting stations in the United States, the position of the line of shear can ordinarily be located on the synoptic chart only within a range of fifty or one hundred miles, using only reported pressures

front, the

and winds.

A more

exact location of the instability line of individual reports, particularly for the time of onset of squalls associated with the line and for the time of the wind shift. Since the instability line is associated with a horizontal discontinuity in pressure gradient moving with the line, it might be expected to exhibit a tendency field similar to any pressure trough, that is, falling pressure ahead and rising pressure behind, or falling ahead and falling less rapidly behind, etc. When there is a sharp pressure trough, a tendency field of this type can be detected, but in general the three-hour tendencies represent a confused pattern that may be misleading if not considered with caution. When the line is accompanied by severe squalls, there may be rapidly falling pressure ahead of the line, a sharp rise with the onset of squalls, then a rapid fall within an hour or so, all of which may take place within the three-hour period for which the tendencies are reported. Also, the severity requires detailed examination

normal to the

aloft

of the axis of

warm

axis.

air aloft is

east slope of the Plateau

it

encounters maritime tropical

(mT) air which overlies the western plains region and which may intersect the east slope at an elevation of from three to five thousand feet above sea level. Typiunder these conditions, there is a stable layer near mT air, and the mT air below this stable layer has a potential temperature lower than that of the leading edge of the cold air, so that the leading edge of the cold air seeks out a level within the moist mT air or above it where the potential density is the cally,

the top of the

same

as at the base of the cold

edge of the

mP

air.

Thus the leading

air overrides the surface

casionally there in the overriding

is

mP

air for

mT

air.

Oc-

and moisture the development of high-

sufficient instability

MECHANICS OF PRESSURE SYSTEMS

650 level

showers or thunderstorms entirely within the

polar air aloft.

Somewhere within the mP air mass, usually between and three hundred miles from its leading edge aloft,

fifty

the potential density is equal to the potential density of the inT air at theground over the Great Plains region. The air at that point begins to displace the air at the ground. The line thus formed between surface and surface air has in general the characteristics of an occlusion of the warm-front type, though temperatures at the ground are usually the same immediately on either side of the line. There is usually a marked temperature gradient toward colder air on the side, and a sharp difference in moisture content between the moist and the dryer air. This "front" is not accompanied by precipitation but may mark the end of showers in the air mass. As the system moves eastward or northeastward across the western Plains and Mississippi Valley a more important surface cold front normally becomes evident in the system between the air and a colder cP air mass to the north.

mP

mT

mP

mT

mP

mT

mP

mT

mP

The

conditions thus produced as a result of the eastof cold air off the Plateau become somewhat

ward flow

similar to those pictured in Figs.

marked

1

and

2,

instability line tends to develop.

and a

well-

The height

at which the cold air aloft advances farthest ahead is, however, considerably lower than is shown in Fig. 2. Above that level the boundary of cold air slopes upward to the left as with a conventional cold front. The existence in the United States of an extensive area of low elevation open on the south to a plentiful supply of warm moist air and bounded on the west by a plateau, combine to make the United States east of the Rockies a favorable region for the production of well-marked instability lines. This is not only because of the tendency for cold air off the Plateau to override mT air, but apparently also because the Rockies provide a north-south barrier to lower-level air masses, favoring southward flow of cold air and northward flow of warm air, the zone of interaction between the pure mT air and the cold air being most often within the latitude of the United States. Unique geographical and topographical conditions are, however, by no means necessary to the formation of the instability line. It may be found anywhere in middle or subtropical latitudes and perhaps in other regions. But tornadoes in the United States appear to develop most often with the type of instability line that results when cold air from the Plateau overrides mT air over the Great Plains.

Further Discussion of Physical Processes

The pseudo-cold front, suggested by Harrison and Orendorff [5] as important in formation of the pre-coldfrontal squall line, is observed in nearly all cases. Unquestionably its relation to other factors involved must be considered in any complete explanation of the mechanism. However, it seems equally certain that this factor must be secondary to other initial causative factors, because the existence of the shallow layer of

rain-cooled air in the proper location appears to be the result of showers already occurring. The same authors suggested that convergence within a potentially

unstable air mass might act together with the formation of the pseudo-cold front as a pair of factors to produce the squall line. This might be taken as a suggestion that convergence first produces the line of squalls and that the resulting pseudo-cold front then assists in maintaining the squalls and perhaps in keeping them along a line rather than allowing them to disperse in a disorganized manner. Low-level convergence is of course a necessity along the instability line and needs, itself, to be explained in terms of other factors. Are there other factors which first act to produce low-level horizontal convergence and upper-level divergence, or is vertical motion merely the result of vertical instability and thus the full cause of the convergence-divergence pattern?

The

Olivers

[9],

in discussing forecasting of frontal

weather from winds

aloft, stated that if the wind component perpendicular to a cold front increases with height through the frontal surface, no weather is produced by the front, but that convergence in the frontal trough may produce weather in the warm sector which ceases abruptly on passage of the surface cold front. They extended this argument further as an explanation

of the pre-coldfrontal squall line, that

is,

the air flowing

downslope over the frontal surface may extend to near the ground for some distance ahead of the front and, being dry as a result of subsidence, would prevent shower conditions from forming along or immediately ahead of the cold front, while convergence in the trough would continue to produce showers in the mT air. This explanation, as far as it goes, seems to agree well with observation, and if some of the rain falls through the dry subsiding air the condition would be favorable for formation of a pseudo-cold front in the warm sector as envisioned by Harrison and Orendorff. A difficulty is that air at the ground back of the squall line is indistinguishable from the mT air at the ground ahead of the line, except for cooling which can be accounted for by rain. However, this difficulty is not serious if the dry air does not extend all the way to the ground, or if its moisture content is increased sufficiently by the rain falling through it. It has also been suggested by various persons that, from vorticity considerations, the stronger flow of air above the frontal surface will tend to form a pressure

trough as it flows into the warm sector, the argument being that subsidence will be greater at low than at high levels, resulting in vertical stretching and therefore increased cyclonic vorticity along and immediately ahead of the surface cold front. This argument is strengthened by its analogy to the explanation of the pressure trough which normally forms in the lee of extensive mountain ranges. H. B. Wobus (U. S. Weather Bureau, Washington, D. C.) suggested to the author some years ago that the existence of a warm tongue in the mean temperature through a deep layer is favorable for the production of instability along a line near the axis of the tongue, if

THE INSTABILITY LINE it is assumed that the wind at all levels is instantaneously adjusted to the gradient value. Instability lines normally occur near the axis of a warm tongue as represented in the horizontal distribution of mean virtual temperature through a layer, say, 20,000 ft in depth. The cui'vature of the component of gradient wind flow perpendicular to the axis of the warm tongue must, because of this temperature distribution, become

more anticyclonic (or less cyclonic) with height. The component of gradient flow across the axis must therefore tend to increase with elevation, and to carry the upper colder

air

warm

air,

over the lower-level position of the thus decreasing the vertical stability. Also, in a manner pointed out by Rossby [10], a decrease of mean virtual temperature northward along the axis, as is generally observed, must cause an increase of geostrophic wind from the west and thus normally act in the same direction as the effect of curvature to produce greater eastward advection of colder air aloft as compared to lower levels. These considerations do not, of course, take account of important nongradient components of flow that must exist. Conditions near the center of a warm tongue are also favorable for upward vertical motion if the energy of the solenoidal field can be realized, and these same conditions provide a means for eviction of air aloft because of nongeostrophic components of flow as pointed out by Durst and Sutcliffe [2]. Release of latent heat of condensation tends to maintain the solenoidal field. Some low-level convergence into the warm axis can be accounted for by frictional effect in the pressure trough. Further low-level convergence is a possibility in the layer above surface frictional effects in the presence of dynamic instability as pointed out by Solberg [12]. However, it is not known from observation that the axis of

horizontal

component

of

dynamic

instability (as first

discussed in this country by Fulks [4]) is of general importance in the case of instability lines, the requirement being that there is appreciable anticyclonic vorticity in the horizontal wind field. Probably this factor is

important in the immediate vicinity of the squalls

but, in general, instability in the vertical appears to

be predominant.

Some Remarks on Tornadoes Tornadoes occur normally along instability

must therefore involve some

of

lines

and

the same dynamic

though not all instability lines are accompanied by tornadoes. Studies or discussions of the mechanics of tornadoes by Bigelow, Humphreys, Jakl, Showalter, and others in this country, Wegener in Germany, some Russian investigators, and others have given some hint of the factors involved, but much more work remains to be done. Basically, there are two main factors to factors,

be explained: 1. Source of energy. This has usually been assumed to be vertical instability, such as is known to exist in the vicinity of instability lines. This explanation is, however, not sufficient unless it can be shown that the difference between instability lines which produce tornadoes and those which do not is a matter of degree

651

of vertical instability, or that other factors are absent

and not the other. Showalter [11] suggested that precipitation carried aloft and falling ahead of the squalls, cooling the air at higher levels, might be a means of producing a high degree of instability more or less spontaneously. In any case some nearly spontaneous local release of energy seems necessary. Another possible means of creating a vertically unstable lapse rate is for the convectively unstable air mass in one case

would some source of energy and seems less likely than the cooling by precipitation aloft for which con. ahead

itself

of the squall line to be lifted bodily. This

require

vective instability is also important in producing a steep vertical lapse rate. An important possible source of energy other than vertical instability, which cannot be ruled out without further study, is that of the al-

ready existing wind circulation in the vicinity of tornado formation. Existing kinetic energy fed into the whirl would appear to be at least a contributing factoi once the tornado is formed. 2. Source of rotation. It seems necessary that the rotation of the tornado results from low-level horizontal convergence within an already existing field of cyclonic (or occasionally anticyclonic) vorticity.

The

convergence appears to take place first in the upper portion of the warm moist air, roughly 2000-5000 ft above the ground (above surface frictional effects), and the whirl appears to extend rapidly upward and to bore downward to the ground. Tornadoes normally occur along or near a line of cyclonic shear, but this shear line is usually between the warm air moving rapidly northward and the wedge of rain-cooled air moving eastward. Since the required vorticity, to be effective, must be entirely within the warm air because any injection of cooler air at lower levels would tend to damp out convection, it is unlikely that the line of cyclonic shear is a direct source of the vorticity. A more likely source of vorticity is in the interaction between the warm and cool air, especially in warm tongues that must break off from the northward-moving warm air mass and flow into individual convective This turning from northward to westward would produce cyclonic curvature in the warm air as well as some shear, cyclonic on the southern side of the tongue and anticyclonic on the northei'n side, the latter being a possible factor in producing the rarely observed anticyclonic rotation. In this connection it is also necessary to consider the irregular nature of outflowing tongues of cold air as described by Williams [15] and their possible effect on warm air flow. Another source of rotation that has long been considered is that of the roll cloud of the thunderstorm, the roll being presumed to extend down to the ground, resulting in a cyclonic whirl on one end, or an anticyclonic whirl if the other end should reach the ground; this theory has not been fully refuted or confirmed, but appears unlikely in the cells.

light of descriptive reports.

Some Recent

Studies

Tepper [13] recently proposed that a "pressure-jump is an important part of the mechanism of squall

line"

MECHANICS OF PRESSURE SYSTEMS

652 lines.

A

sudden

rise of pressure is

normally observed

upon arrival of the wedge of rain-cooled air. However, Tepper further theorizes that the "pressure jump" is associated with a gravitational wave aloft (following a suggestion by Freeman [3]), and he suggests that the wave originates from an acceleration of the cold front.

No

convincing evidence has been presented in support seems extremely unlikely that there can be any close association between the leading edge of outflowing cold air at low levels and a gravitational of this theory. It

wave aloft, as would be required. The most substantial work to date

ical areas.

that based on observations of the recent Thunderstorm Project. Williams [15] made a microanalysis of selected squall lines passing through the Wilmington net. The official report is

the Thunderstorm Project [14] further discusses some of the factors observed in connection with squall lines, and a still more recent paper by Newton [8] attempts to give a more detailed picture of their physical structure and mechanics, based on Thunderstorm Project data. The latter two studies are too recent to have been taken into account in the preceding discussion. Newton's examples probably do not embody the of

salient characteristics of all types of squall lines

shed light on the type included

in

methods based only on the use of data which are available synoptically. Synoptic data are at best very incomplete, so that he must interpolate to a great extent; better basic knowledge of the phenomenon would aid in this interpolation. There is a large and relatively untouched field for synoptic studies, particularly from a statistical standpoint, in which only synoptically available data are used. There are important geographical differences involved so that similar types of studies need to be made for different geographbetter forecasting

his studies.

2.

levels

is

He

down from

"Exploration de quelques perturbations atmosphgriques k I'aide de Bondages rapprochfe dans le temps." Geofys. Publ., Vol. 9, No. 9 (1930). Durst, C. S., and Stjtcliffb, R. C, "The Importance of Vertical Motion in the Development of Tropical Revolving Storms." Quart. J. R. meteor. Soc, 64:75-84

4.

FuLKS,

J.,

.

C,

"An Analogy between

the Equatorial Easterlies and Supersonic Gas Flows." /. Meteor., 5:138J.

Jr.,

146 (1948).

5.

7.

8.

J. R., Some Aspects of Non-gradient Wind Flow, unpublished. Paper presented before Joint Meeting of Amer. Meteor. Soc. and Amer. Inst, of Aero. Sciences, New York, January, 1946. Harrison, H. T., and Orendobff, W. K., "Pre-coldfrontal Squall Lines." United Air Lines Meteor. Dept. Circ.

No. 16 (1941). Lloyd, J. R., "The Development and Trajectories of Tornadoes." Mon. Wea. Rev. Wash., 70:65-75 (1942). Means, L. L., "The Nocturnal Maximum Occurrence of Thunderstorms in the Midwestern States." Dept. Meteor. Univ. Chicago Misc. Rep., No. 16 (1944). Newton, C. W., "Structure and Mechanism of the Prefrontal Squall Line." J. Meteor., 7:210-222 (1950).

9.

Future progress toward a better understanding of the physical structure and mechanics of the instability line will require both the collection of more adequate detailed observational data and the analysis of existing

and future data. Undoubtedly there is much to be gained by further analysis of the Thunderstoim Project data, though this project was not aimed so much at the problems of the instability line as of the thunderstorm. More observational data for upper levels in the immediate vicinity of tornadoes is especially needed; this is difficult to obtain but will be very important because of the frequent association of tornado conditions with the instability line. A more adequate theory of the mechanics of the tornado would be an important step toward understanding the instability line. From the practical standpoint of the synoptic meteorologist, whose primary problem is to forecast developit

occurs,

much

remains to be done. His problem is somewhat different from that of basic research in that he must develop

Oliver, V. J., and Oliver, M. B., "Forecasting the Weather with the Aid of Upper-Air Data" in Handbook of Meteorology, F. A. Berry, Jr., E. Bollay, and N. R. Beers, ed., pp. 813-857. New York, McGraw, 1945. (See pp. 815-817)

10.

11.

specific

instability line before

of forecasting the dissipation of the

(1938).

Future Research

of the

BjERKNEs,

Freeman,

squall-line activity.

ment

and means

3.

6.

sughigher an essential source of energy for maintaining solenoidal circulations.

of the line is

important to

REFERENCES 1.

this "front"

gests that kinetic energy brought

also

line.

line activity

and augmented by

is

of rainfall, surface Avinds, icing, likelihood of tornadoes, etc.)

He

can be accounted for partly as a result of and partljr by the continuous generation of new thunderstorms as a result of convergence-divergence patterns produced by the vertical transfer of horizontal momentxim in pre-existent thunderstorms

it

develop criteria for determining the individual characteristics of each instability line (turbulence, intensity

but

suggests that squall lines in some cases appear to form first over the cold-front surface and subsequently to move into the warm sector, and he confirms by observation the existence of a pseudo-cold front along the warm-sector squalls. He further suggests that squall-

While forecasting development

main synoptic problem,

the

RossBY, C.-G., "Kinematic and Hydrostatic Properties

of

Certain Long Waves in the Westerlies." Dept. Meteor. Univ. Chicago Misc. Rep., No. 5 (1942). (See pp. 32-37) Showalter, a. K., and Fulks, J. R., Preliminary Report on Tornadoes. U. S. Weather Bureau, Washington, D. C, 1943. (See pp. 20-28)

12.

Solberg, H., "Le mouvement d'inertie de I'atmosphere stable et .son role dans la th^orie des cyclones." P. V. Meteor. Un. geod. giophys. int., Edimbourg, 1936. II,

13.

Tepper, M., "A Proposed Mechanism

14.

The Pressure Jump Line." /. Meteor., 7:21-29 (1950). U. S. Weather Bureau, The Thunderstorm, 287 pp.

pp. 66-82 (1939). of Squall

Lines:

,

Washington, D.

C,

U.

S.

Govt. Printing

Office,

1949.

(See pp. 122-130) 15. Williams, D. T., "A Surface Micro-study of Squall-Line Thunderstorms." Mon. Wea. Rev. Wash., 76:239-246 (1948).

I

LOCAL CIRCULATIONS Local

Winds

by Friedrich Defant

65 5

Tornadoes and Related Phenomena by Edward M. Brooks

673

Thunderstorms

681

by Horace R, Byers

Cumulus Convection and Entrainment by James M, Austin

694

1

:

LOCAL WINDS* By FRIEDRICH DEFANT University of Innsbruck

INTRODUCTION AND DEFINITION The terms

of the complete equation of atmospheric

motion are determined by a number of forces which, through their interplay, cause the movements of the atmosphere. These effective forces are gravity, hydrostatic pressure, friction, and the Coriolis force. If the Coriolis and friction terms are negligibly small, we deal with Eulerian wmd equations in which the acceleration can be measured by the pressure gradient. However, if the Coriolis term is large as compared to the acceleration and friction terms, so that the pressure gradient is balanced only by the deflective force of the earth's rotation, we speak of geostrophic winds. As a third possibility, the friction terms may be so large that they are of the same order of magnitude as

the pressure gradient term, and the Coriolis and acceleration terms may be neglected. In that case the wind blows approximately in the direction of the pressure gradient

The

and

antitriptic

an

wind [42]. wind introduces the field of winds it is

called

antitriptic

restricted to relatively small areas. Their range

is

of

the order of 100 km or less. In this category belong the land and sea breezes, the mountain and valley winds, the jet-effect {Duseneffekt) winds, and, at least in so far as their characteristics are determined by the orog-

raphy winds

of the ground, the

foehn and bora winds. These

of locally restricted influence are classed

under

the general name local winds. They are an elementary yet meteorologically very interesting part of the movement of the atmosphere and a phenomenon which always attracts the attention of the layman. In the following sections the basic principles of these local winds will be discussed. These winds very closely fulfill almost all conditions of the antitriptic wind since they blow roughly at right angles to the isotherms and isobars and are limited in the vertical to a relatively

low altitude.

LAND AND SEA BREEZES Phenomenon. In coastal areas, on tropical coasts and on the shores of relatively large lakes, we can observe in the course of a day Description of the

especially

and offshore winds, called land The phenomenon takes the following

the reversal of onshore

and sea

breezes.

course

A few

hours after sunrise, depending on location and season, a sea breeze develops, particularly on calm summer days. This sea breeze usually has a noticeable cooling effect, particularly in the tropics; it continues throughout the daylight hours and dies down around sunset. After that the seaward-blowing land breeze appears. This phenomenon, which is restricted to the *

Translated from the original German,

and which extends only in tropical 100-km range, must be attributed to the heat response between land and water. On

coastal area proper

regions over a difference in

warm,

summer

days, the horizontal tempera^ between land and water provides the energy that leads to the development of vertical and clear,

difference

ture

horizontal air currents of strictly circulatory characTo the ground observer, only the horizontal parts of

ter.

the circulation are noticeable; the vertical branches can be observed only indirectly, for example, through the formation of clouds over the land. The daytime sea breeze considerably surpasses in intensity the nocturnal land breeze. This is understandable because of the greater daytime arc of the sun during summer and the increased instability and consequently increased vertical austausch in daytime. The nocturnal cooling, on the other hand, produces an immediate stabilization of the air layers

near the ground. It is noteworthy that the direction of the sea breeze does not remain constant in the course of the day, and that this breeze often sets in with considerable gustiness, sometimes in the form of a protrusion similar to a cold front.

determined weather situation, should be superimposed on this local wind system and should at times obscure or even conceal it completely. As an example of a typical day with land and sea breezes, the wind, temperature, and humidity recordIt

is

by the

logical that the gradient wind, as

over-all

Danzig airfield, 3.35 km inland from the Baltic Sea coast, from June 3 to Jime 5, 1932, are reproduced in Fig. 1. This diagram clearly shows the onset of the sea breeze from the northeast and northnortheast, respectively, at 1420 on June 3, and at 1430 on ings of the

5, while on June 4 a gradient wind from westsouthwest-west-northwest completely conceals the sea breeze. After a calm from 1930 to 2245 on June 3, and from 2100 to 2220 on June 5, the land breeze sets in from southwest and west, respectively, and continues as a mild breeze until 0600 the following day. During the night of June 4-5, a calm from 0030 to 0130 and a shift in wind direction to the southeast are the only indications of the onset of the land breeze, but here also a gradient wind that subsequently appears hinders its development until 0600 in the morning. The tem-

June

perature and humidity curves of Fig. acteristic

irregularities in their

1

show char-

normal trend at the

onset and cessation of the sea breeze. Figure 2 gives an example of the above-mentioned change in velocity of land and sea breezes in the course of the day, as observed at Hoek van Holland on July 31, 1938. We can see from this figure the increase in

the speed of the sea breeze up to the daily maximum between 1300 and 1400 and a concurrent steady shift 655

LOCAL CIRCULATIONS

656 to the right, which will be explained later.

down and continued

The dying

shifting to the right takes place

in similar fashion.

sought in the different behavior of land and water under the influence of an equal external heat supply. Water, as compared to soil, has a larger thermal capacity and

MEAN TIME

LOCAL

JUNE 4 0600

0600

1200

1800

N

W 10 s 01

llJ

o Z2

5

L

6

S

G

S

G

C

C

G

C

L

1420 1430

0400 20° 15°

10°

100

- 80 > eo

2 40 20

L—

Pig. Registrations of wind speed and direction, temperature, and relative humidity during the characteristic land- and sea-breeze days from June 3 to June 5, 1932, at Danzig (L = land breeze, S = sea breeze, G = gradient wind, C = calm). {After Koschmieder

[54].)

As an example of the tropical form of the land and sea breezes the diagram of velocity isopleths by van Bemmelen of the land and sea breezes at Batavia is reproduced in Fig. 3. It is also an example of the vertical velocity distribution during the course of a day. Explanation of the Land and Sea Breezes. The cause of

the land and sea breezes must undoubtedly be 1300

heat per unit volume reaches a value 40 per cent larger than that of soil. Although water should have a smaller temperature variation for the first reason, the amplitude of these periodic variations would be 1.414 that of the land for the second reason. This difference is equalized through the much smaller heat conductivity of water, and measurements reveal that the surfaces of water and sandy or rocky ground have temperature variations of comparable order. The depth to which radiation penetrates can also not be considered responsible for large temperature differences since the infrared radiation is immediately absorbed in the upper its specific

water layers.

1800

SEA

—

Fig. 2. Hourly variation of relative wind velocity on a land- and sea-breeze day at Hoek van Holland as recorded on July 31, 1938. {After Sleeker and Schmidt [67].)

However, if we direct our attention to the turbulent mixing of the water by wind and waves, which effects a continuous downward transport of surface heat through large masses of water, we recognize that this mixing is the cause of the relatively small temperature variations. It is now clear that the complete absorption of radiant heat in the surface layers of the ground and the weaker influence of this form of energy on the deeper layers result in an entirely different thermal behavior of land and of water. Thus the temperature conditions of the ground are determined almost exclusively by its physical properties, whereas those of

LOCAL WINDS

657

At the beginning

of the day, the air pressure at higher

altitudes over the land rises, while there

is only a negliover the water. As a consequence a drainage of the upper air from the land toward the sea takes place, and during forenoon the pressure close to the surface of the sea begins to rise, while it starts to fall over the land. This developing sea-land pressure gradient is accompanied by an air current in the same direction, that is, the sea breeze. A countercurrent, blowing toward land, is established at upper levels above the surface sea breeze. The circulation in day-

gible

increase

time is completed by cumulus-forming convection over land and cloud-dissolving subsidence over water. In the evening the land and the overlying air cool faster than the sea and its overlying air, and a reverse nocturnal circulation develops. This circulation must be of smaller intensity and vertical extent because of the 0600 DAY Fig.

3.

1800

1200

SUNSET LOCAL MEAN TIME

2400 NIGHT

0600

— Velocity

isopleths for the land and sea breeze in Batavia. {After van Bemmelen [70].)

lack of instability and convection. The land-sea pressure gradient near the surface at night and toward morning, as compared to a sea-land

gradient during the day,

clearly discernible in Fig. 4.

LOCAL MEAN TIME 1200 0600

the water are governed also by apparent conduction or turbulent mixing. In contrast with the strong heating of the air over the coastal region, the air over the strip

water offshore is only mildly warmed, and, as a a temperature difference between land and water develops. This difference diminishes toward sunset and reverses during the night. Temperature Differences, Pressure Differences, and Pressure Distribution during Land and Sea Breezes. The maximum temperature differences {M) are given in the literature as follows Kaiser [46] gives a range of A< from 1.6C to 10. 9C over a distance of 130 km between Wiistrow and Adlergrund Lightship (anchored in the middle of the Baltic Sea, about 100 km out of Swinemiinde) as averages of a period of twenty summer days. Grenander [31] found differences in temperature between 3.6C and 7.6C at 1400, and between 1.4C and 3.1C at 0700 and 2100. These measurements, taken on the Swedish east coast, involved a distance between

is

1800

2400

of

result,

:

land and sea stations of 115 km. However, maximum values were as high as IOC or more; on the other hand,

very small temperature differences occurred on some

Measurements of A< at lakes, as for Lake of Constance, likewise show a large range of temperature differences, namely values between 0.9C and 4C at 1400. We may conclude from these few measurements that covers a wide range of values, and it is certain that a temperature gradient from sea to land exists in the morning hours. During forenoon a reversal takes place, and in the afternoon an sea-breeze days.

instance at the

M

increasing

which

is

land-sea

temperature

gradient

develops

the driving force in the formation of the sea

Over inland lakes, where opposite shores show this same behavior, the center of the lake must be a neutral zone. In general it may be assumed that the heating over land during daytime can reach a value five times that over water. Such temperature differences force the development of a pressure gradient and cir-

breeze.

culation system.

LAND BREEZE

SEA BREEZE

—

Average daily period of the air pressure on twenty Fig. sea-breeze days at the Baltic Sea. The solid line refers to Swinemiinde; the dashed line, to Adlergrund Lightship. {After Kaiser [46].) 4.

It is to be expected that the air current, according to the pressure distribution, is, at first, nearly at right angles to the coast line; only later, during the afternoon, a gradual change in the direction of the sea breeze

appears because of the effect of the Coriolis force. However, the influence of the Coriolis force remains slight because of the short distances that these winds travel. Conditions are somewhat complicated by the addition of a gradient wind associated with the over-all weather situation. A gradient wind blowing parallel to the coast line has no particular influence, since the pressure gradient causing it also acts normal to the coast line and thus only weakens or strengthens the pressure gradient associated with the land or sea breeze. However, a pressure gradient parallel to the coast line with, for example, an offshore gradient wind causes a mass transfer of air seaward. In that case a kink appears in the isobars where they protrude over the sea. Then the condition of gradient force plus Coriolis force equal to zero, which was valid in the previously discussed is no longer fulfilled, and unbalanced shoreward components of the gradient wind create a possibility for the development of a strengthened sea breeze. In

case,

simple schematic cases these conditions can also be

LOCAL CIRCULATIONS

658

demonstrated numerically by superimposing the pressure fields of land and sea breezes and gradient wind [54].

Development

of

Land and Sea Breezes as a Function

of Geographical Location, Season, and Time of Day. On tropical coasts, the land and sea breezes appear with great regularity [9, 11, 53, 70], because the clear sky there causes large variations in temperature over the

land in the course of the day. Also the usually weak general air motion does not interfere ^\dth the development of local winds. It is only in India that the land breeze is completely obscured from May to September by the strong monsoon, which acts as a steady sea breeze during that season. Partial superimposition of mountain and valley winds on land and sea breezes may

wind conditions, as for instance on the coast of Samoa. In higher latitudes these local \vinds appear almost exclusively, or at least preferably, during also cause peculiar

the warmer seasons, since only then can sufficiently large temperature or pressure differences develop. In the cooler climates of higher latitudes, as for instance at the shores of the Baltic Sea [46], we can expect land and sea breezes, even in summer, on not more

than about 20 per cent of the days. The role of solar radiation becomes apparent in a brief summary (Table I) of

Table

the probability of a sea-breeze day for different I.

Relationship between Cloudiness and Seabreeze Probability

LOCAL WINDS toward the coast, but is foi-med on the boundary line between sea and land and progresses seaward. It is caused by the different heating processes on the flat, sandy beach. This minor sea breeze precedes the major sea breeze, the beginning of which is somewhat retarded by it until the air over the land has become considerably warmer than that over the water. The border line between warm land air and cool sea air, which has been displaced seaward by the minor sea bi'eeze, is eventually overrun, and the cool sea air reaches the coast with an impact. This minor sea breeze, designated as a sea breeze of the first kind, will occur wherever strong pressure gradients connected with the large-scale weather situation do not hinder its development. The Cold Front-Like Sea Breeze, or Sea Breeze of the Second Kind. The character of the sea breeze having a normal, front-free, and steady development is modified if a wind determined by the general weather situation hinders its regular course. This sea breeze, which develops in opposition to the gradient wind, is characterized by its retarded beginning (usually as late as 1500 to 1600), by its formation at sea and its slow progress toward the coast, and finally by a pronounced break-through of a cold front-hke character (distinct gust with wind shift of 180 degrees). The development of this cold-air invasion can be considered to take place in the following

way:

In the morning, the offshore gradient wind carries warmed air from the land out to sea and thus displaces seaward and weakens the pressure gradient between land and sea. An air-mass boundary is thus formed at sea against the cool sea air. The warmed land air, which accumulates in a nearly adiabatic layer, is highly turbulent and is able to carry along some of the stably stratified, cold sea air and is forced to rise with it. For a while, a stationary equilibrium between the two air masses may be maintained by an increasingly steepening frontal surface as is depicted in Fig. 5. However,

SEA

LAND

—

Fig. 5. Stationary condition before outbreak of the sea breeze. The dash-dotted line is the boundary layer between currents of opposite direction in the cool air mass. (After

Koschmieder

[54].)

with further heating this equilibrium breaks down, the system becomes unstable, and the sea air now breaks through toward the land in the form of a front. This sufficiently explains the gusty onset and the cold-air character. If we consider that the largest vertical temperature gradients are not reached until 1200 to 1400, the retarded onset of the sea breeze is also understandable.

659

Land and Sea Breezes. A complete theory and sea breezes must necessarily consider addition to the gradient force caused by land-water

Theory

of

of the land (in

temperature difference) (1) the influence of the vertical turbulent heat exchange, (2) the turbulent friction of the air motion, and (3) the influence of the earth's rotation. In all existing theories these contributory factors receive only partially satisfactory consideration. Usually, the land and sea breezes are treated as simple, antitriptic currents caused by the unequal heating of land and water. An older treatment of a stationary circulation is that

by

Jeffreys [42],

who

applied

it

primarily to the sea

monsoon winds. He considers friction, and Coriolis force and reaches a solution in

breeze and to pressure,

which the daily wind change is in phase with the daily temperature oscillation. This result does not conform to

The application of this theory to the extended monsoon currents allows the calculation of the height of the monsoon reversal as well as of the amplitude of the reality.

surface pressure variations connected with the circulation. The agreement of these calculations with ob-

servation proves to be satisfactory. V. Bjerknes and his collaborators land-

and sea-breeze

circulation

[8]

consider the

a periodic current

isobaric-isosteric solenoids in which the wind is ninety degrees out of phase -with the change in density. Accordingly, the sea breeze would start at the time of the greatest heating and would reach its greatest intensity at the time of the smallest temperature difference between land and sea in the evening. This is not in accordance with observation. Kobayasi and Sasaki [52] as well as Arakawa and Utsugi [2] base their theories on Lord Rayleigh's convection theory [64]. They consider vertical and horizon-

around

tal heat transfer in addition to turbulent friction of the air motion, whereby their basis for calculation becomes more complete than that of Jeffreys. Their solutions of the problem allow a comparison between theory and observation, although in order to reach

complete agreement a heat conductivity one hundred times greater than that derived by Taylor from observations must be assumed. A further shortcoming of the theory is that the height to which the circulation (including the countercurrent) extends must be known, whereas it actually should result from the boundary conditions of the theory. This theory still neglects friction, which, as had already been pointed out by Godske density [30], is responsible for the phase shift between

and wind-velocity

variations.

A

simple elementary theory of land and sea breezes is due to F. H. Schmidt [67]. In this theory he is less concerned with giving a complete explanation of the circulatory movement than with clarifying characteristic phenomena of the land and sea breezes, such as the phase shift between wind and temperature or the influence of the earth's rotation.

A definite

temperature

distribution in accordance with observations is assumed, and the entire system of currents is calculated, taking the compressibility of the air into account. The Coriolis force

is

also introduced into the calculations,

and thus

LOCAL CIRCULATIONS

660

Schmidt succeeds

in explaining quantitatively all facts

of this atmospheric ner.

Most

phenomenon

in a satisfactory

man-

certainly, his theory has greatly contributed

to a better understanding of local winds.

Schmidt's

assumption

by the

characterized

concerning

temperature

is

fact that the entire horizontal

and vertical temperature

distribution

is

given.

He super-

imposes on the normal vertical temperature decrease the daily radiation temperature wave which is assumed to reach its maximum amplitude near the coast at a

wave length of the This amplitude is supposed to decrease exponentially with altitude. However, for reasons of simplicity, he neglects the fact that the maximum amplitude is a function of time which, after all, should be of some importance to the theory. The variation in air density caused by the radiation temperature wave can be calculated; its amplitude also decreases exponentially with altitude. Part of the pressure distance inland amounting to half the

temperature

oscillation.

ascribed to the resulting density variation, is caused by divergence and convergence of the compressible air. This influence of divergence is also assumed by Schmidt to decrease ex-

variation

is

and the remainder

ponentially with altitude. If the pressure gradient is known, the horizontal velocity component can be calculated by application of the Guldberg-Mohn friction formula. Finally, the friction constant is assumed to be a quantity that decreases with altitude according to the expression e^", where r is a constant representing the

decrease of friction with height and z is the height. This is necessary in order to obtain sufficient variation shall with altitude of the sea breeze's starting time. not discuss here how far such assumptions are justi-

We

fied; itself

it would be preferable if the theory would yield the variations with altitude of all

moreover,

these quantities. Nevertheless, the theoretical deter-

mination of the deviation of the wind direction from the perpendicular to the coast and of the shift of the wind in the course of a day gives a satisfactory result. The most recent work on the theory and observation of land and sea breezes has been published by Pierson [61]. In this work the theoretical considerations of F. H. Schmidt are considerably improved. Pierson makes assumptions regarding the temperature contrast

between land and water that closely approximate reality

and he takes

into consideration not only the Coriolis

force but also that type of friction

which

is

u^d

in the

A

solution is given derivation of the Ekman spiral. of the Navier-Stokes equations for laminar flow with consideration of the apparent eddy viscosity. Theoretical hodographs illustrate the variations of land and sea breezes under the influence of this type of friction, the Coriolis force, and the variable pressure-gradient force all altitudes. The temperature contrast between land and water and its periodic variation during the course of a day as well as its variation with altitude are assumed, with due consideration for eddy diffusion (W. Schmidt, see [61, p. 9]), in a manner similar to that employed by F. H. Schmidt. From this the density and pressure distribution can be computed, and the wind field can be obtained from the equations of motion;

at

A

comthe equation of continuity is unnecessary here. parison of the theoretical results with observations made at Boston (42°N), Madras (13.4°N), and Batavia (6°S) shows good agreement. Recently, Haurwitz [37] made an interesting and important contribution to the theory of the land- and sea-breeze circulation. In contrast to pre\'ious investigators, he chooses Bjerknes' circulation theorem as his point of departure. With it he proves that the intensity increases, not only as long as the land-water temperature difference increases, but that it keeps growing until this difference disappears. Thus, the phase shift between temperature difference and wind maximum would be a quarter of the period, that is, six hours. Haurwitz shows that the introduction of frictional influences causes a considerable decrease of this phase shift which leads to a better agreement with observation. The daily shifting of the sea breeze, which was clearly observed in several locations, can be explained without difficulty as an effect of the Coriolis force. Haurwitz' work excels in its logical, all-inclusive consideration of all factors that are of importance for the development of land and sea breezes. However, as in the work by F. H. Schmidt, the theory of the landand sea-breeze circulation is incomplete. In all these investigations the temperature contrast between land and water at the surface and at all levels above it is assumed. A complete theory should furnish the temperature distribution with altitude as well as the circulation from a given temperature contrast at the surface. The temperature distribution with altitude depends not only on the vertical turbulent heat exchange, but also on the circulation itself. For this reason, with a given boundary condition of temperature at the surface, the equation of heat conduction (as in the theory of the slope winds, see p. 666) must be incorporated in

the theory. If

we approach the land and

circulation cell in the sense of

sea breeze as a single Lord Rayleigh's con-

vection theory [64], we come considerably closer to the problem of these local winds. Furthermore, with this method we can take vertical as well as horizontal heat transfer and turbulent friction into account. The solution must yield not only the entire temporal development of the periodic current system, but also its dimensions as a function of heat supply or of the land-

water temperature difference, respectively. I have recently attempted such a solution [18], which actually furnishes the required results in full conformity with observations. For the land-water temperature difference near the surface, which we have assumed as given, I used the simple harmonic function & = Me''°' sin Ix, where x is the normal to the coast, ^ the potential the amplitude of the temperature varitemperature, = 2ir/ (sidereal day) = 7.292 X lO"' sec-^ ation,

M

and the length

of the circulation cell

is

fixed as

L/2

=

This solution permits the utilization of any desired form of the land-water temperature difference, provided it is expressed by a Fourier series; the solution given above then holds for every one of its terms. This solution, based on the assumption that «? is t/1.

LOCAL WINDS proportional to sin

naturally yields a continuous

Ix,

chain of circulations. If a number of such circulations with variable I resulting from the Fourier series are superimposed on one another, we obtain a single circulation of definite horizontal extent. Thus, this extent becomes solely a function of the form of the land-water

temperature difference. When the influence of friction (Guldberg-Mohn's friction equation, where o- is the coefficient of friction) and the Coriolis parameter (/ = 2Q sin 1.6 a) in central Europe, 1752-1947; {g) yearly ( number of cold winter months ( departure >4.5F) for Chicago St. Louis, 1847-1946, Qi) departure of the mean annual temperature in J^oC for ]4 (Apia Colombo), 1890-1945. |

I

|

+

For this reason, there can no longer be any doubt that the Grosswetter is dependent on the solar cycle [18; 19; 20, pp. 962-966]. It must be emphasized, however, that this dependency does not appear in the primitive form of a linear relationship AAdth sunspots. Relationships between Grosswetter and Variations in Solar Radiation. It seems surprising, at first, that precipitation and temperature in the tropics show mainly a single oscillation within a solar cycle, whereas in the temperate zones, a double or higher multiple oscillation can be observed. This can, however, be easily explained if we consider that, on the one hand, the sun can exert an influence upon the weather only by way of radiation and that, on the other hand, the sun's radiaprobability.

—The

average course of some meteorological elecj'cle. (The dashed portion of some curves indicates that these cases, because of the relative brevity of the interval, are based on only few years of observaFig.

ments during a sunspot

|

+

EXTENDED-RANGE WEATHER FORECASTING tion

is ail

exti'aordinarily

complex phenomenon. Those

parts of the sun's radiation which emanate from the sun's corona and the uppermost chromosphere fluctuate

with the sunspots, that is, on the average, with an eleven -year period. These radiations (corpuscular rays and electromagnetic waves) are, however, with one exception, absorbed in the ionosphere and hence, according to our present ideas, are of no influence upon the weather. Only the ultrashort electromagnetic waves penetrate to the earth's with a wave length X < 15 surface. Since, according to Kiepenheuer [35], ultra-

m

short waves act upon colloidal processes, it is possible that the single fluctuation of precipitation in the tropics is caused bj^ a solar influence on the condensation and sublimation of the water vapor, whereas the temperature fluctuation is secondarily produced by cloudiness and precipitation. In agreement with this assumption is the fact that the correlation of sunspots with temperature is of opposite sign and of less significance than is the correlation of sunspots with the amount of precipitation or with the water level of large inland lakes. The radiation emanating from the photosphere, that as has been demonstrated is, the heat radiation, shows several times [7, 9, 26] no single oscillation in or out of phase with the sunspots. However, when the different mean annual trends in the time intervals 1919-23 and 1924-30 are eliminated [9], the curve of the solar constant for the period from July 1918 to February 1937 shows minimum values at about the time of sunspot extremes, and maximum values IJ^ to 2)4, yr before the sunspot extremes [19; 20, pp. 967-968]. These fluctuations agree quite well with the double oscillation of the meteorological elements as presented in the preceding section. However, it must be conceded that the double fluctuation in the most recently revised monthly means of the solar constant no longer appears so clearly [1]. An increase in the total energy radiated from the sun would mean an increase in the heat supply, particularly for low latitudes during winter. The temperature difference between the tropics and the polar region would thereby be increased, resulting in an increase of the general circulation of the atmosphere and a consequent increase of the pressure gradient between the subtropics and the subpolar low-pressure belt. The reality of the fluctuations of the solar constant is corroborated by the fact that during midwinter (January and February) in the period 1919-37, a strong positive correlation existed between the mean solar constant and the simultaneous mean values of the pressure differences between Valencia (Ireland) -and Spitsbergen

—

maximum

chance value. objection has been raised that the variations of the solar constant are too small to cause fluctuations of the general atmospheric circulation. However, according to the Stefan-Boltzmann law, a variation of an the

which

refers to the entire earth's surface. It is therefore quite possible that, owing to the inequalities of insola-

tion (as a function of the geographical latitude)

The

amplitude of 1 per cent of the solar constant (assuming incoming and outgoing radiation to be equal) causes a temperature change (temperature departure) of 0.7C

and

the different heat capacities of land and ocean, the temperature change caused by a one per cent change of insolation may amount to considerably more than

0.7C in some regions. Results of recent investigations [35, 37] suggest that the fluctuations of the atmospheric circulation within a sunspot cycle are caused not so much by the changes of the entire heat radiation as by the fluctuations of the sun's radiation in the ultraviolet. This idea is supported by the fact that the difference between the areas of the sun's faculae F and those of sunspots L, both relative to their long-established mean values Fa and Lo, undergoes the same double fluctuation within a solar cycle as does the atmospheric circulation [19]; this is shown in Fig. 4. Radiation emanating from the

—

and between Rome (Italy) and Haparanda (Sweden) 97-105]. These correlation coefficients were [17, pp +0.69 and +0.65, respectively, both of which exceed

821

+ 20

- 20

.

'

:

WEATHER FORECASTING

822

phenomena such as the alternation between meridional and zonal circulation in the Northern Hemisphere (see p. 827) and the southern oscillation in the Southern Hemisphere. However, these regulatory phenomena merely shape the macrometeorological events and can-

mean is

next along a latitude circle. The mean zonal air motion (eastward and westward) is expressed by the mean of the meridional pressure gradients at sea level from 40°N to 75°N, averaged over all meridians,

not be regarded as governing complexes of conditions. If they alone were decisive, obvious periods should occur in the course of the weather, whereas in reality one must search for such periods by means of "methods for the discovery of hidden periodicities." The solution of the second fundamental problem is given by the empirical facts briefly sketched in the two preceding paragraphs from which the following conclusions can be derived

Fourth Empirical Theorem the solar radiation represent

1

III.

"

\^pU

-E n

Mt

1

where L is the length of the meridional distance between 40°N and 75°N, Ap |^ is the pressure difference from one extreme value to the next along the meridian between 40°N and 75°N, and n is the number of meridians for which Ap |^ is computed [22]. It should be noted that the mean gradients were first determined for each single day and the monthly means computed |

The fluctuations in complexes of conditions that :

govern the course of the large-scale weather.

Table

and 70°N, where R is the radius of the earth, is the latitude, and |Ap|x the pressure difference from one extreme value to the

for the latitudes 50°N, 60°N,

|

Monthly Means of the Daily Zonal and Meridional Pressure Gradients

in the

Northern Hemisphere

Average of

all meridional pressure gradients (mb per 1000 km)

Zonal pressure gradients* (mb per 1000 km)

Month SO°N

60°N

70°N

1937

1938

40°-75°N

40°-75°N

SO°N

60 °N

70°N

10.7

12.4

10.5

12.0

11.5

11.1

10.5

11.8

10.5

8.9

10.7

11.9

March

9.7

10.6

10.6

9.7

10.6

10.3

April

8.8

10.2

9.8

8.9

9.8

9.0

May

8.0

9.0

8.1

7.6

8.2

7.8

June

6.9

7.6

7.4

7.4

7.2

7.0

July

6.0

7.0

7.3

7.0

6.4

6.5

January. February. .

.

50°N

SO°N

70°N

August .... September.

6.0

7.4

7.9

(6.2)

(7.8)

(7.5)

7.3

7.8

10.0

9.6

(8.0)

(9.8)

(9.0)

8.6

9.0

October.

9.0

10.3

10.0

(8.7)

(11.8)

(12.7)

9.6

10.8

10.1

11.3

10.7

(10.1)

(13.1)

(12.0)

10.3

11.5

11.2

12.3

9.4

(11.2)

(12.2)

(13.1)

10.5

11.8

.

.

November. December.

Mean (Aug. 1937-July Mean (50°N-70°N) *

is

Numbers

8.8

1939).

10.1

40°-7S°N

8.1

9.4

9.5

9.5

in parentheses are uncertain.

Therefore, an intensive promotion of solar physics one of the prime prerequisites for progress in long-

range weather forecasting.

Morphology

of the Grosswetter.

Forms

of the General Atmospheric Circidation. Twenty years ago it was recognized that it is erroneous to consider the west-east cir-

culation as the essential feature of the "general atmospheric circulation" in the temperate zone [8; 33, pp.

215-218]. Without the meridional movements there would not be the exchange between the warm subtropical and cold polar air masses that is the most

important

effect of the general circulation in the temperate zone. The quantitative equivalence of zonal and meridional circulation in the lower troposphere is shown in Table III. Here, the mean meridional air motion (poleward and equatorward) is expressed by the mean of the zonal pressure gradients at sea level,

Z{4>)

=

S

|Ap|x

2R-K cos

from them afterwards. Comparison shows that the between the mean zonal and the mean

differences

meridional gradients by months are much less pronounced than the seasonal trend of both these indices. Sometimes, however, large differences between these indices occur on individual days. Thus the mean zonal gradient at 60°N amounted to only 8.5 mb per 1000 km on January 11, 1949 but, on the same day, the meridional gradients from 50°N to 65°N per 1000 km. The mean gradient for meridians with west-east zonal circulation only, between 50°N and 65°N, (that is, two-thirds of all meridians on that particular day) was 17.5 mb per 1000

average of

was

15.0

all

mb

km. Table IV shows the pronounced

daily fluctuations

of the circulation in addition to the seasonal trend.

On some winter days, values are observed that almost equal the summer normals and on many summer days the gradients correspond closely to the mean values of winter.

The

recently available daily circumpolar

500-mb con-

EXTENDED-RANGE WEATHER FORECASTING tour charts show that a remarkable meridional circulation extends also to the upper troposphere of the middle latitudes.

Even

at the 5-

and 10-km

levels, there

is,

Table IV. Daily Values op the Mean Zonal Gradient along the 60°n latitude circle during the first Six (In

Day

Months of

1949*

mb

km)

per 1000

such a case that within

is

the high-pressure

five

823 cell

at the

5-km

level

days (November 24-29, 1949) moved

from 70°N and 172°W to 78°N and 55°W along an

WEATHER FORECASTING

824

II, and to the northwest for region IV, thus producing a new high-pressure cell in region V, which, according

to the investigations of

mained there

Palmen and Rossby

[53],

re-

until July 6.

ional temperature gradient [47,

52,

53].

Above

this

frontal zone, the isobars of the upper troposphere are

crowded in a comparatively narrow belt, so that the west-east current reaches very high speeds (jet stream). The maximum of this zonal movement is found where the tropopause slopes down most strongly toward the This form of circulation (Fig.

pole.

5) rarely

develops

as an upper circumpolar low as far south as the 55th parallel, as is so in the case illustrated in Fig. 5, and,

according to our present experience, it usually develops in only one or two quadrants, and never in the entire temperate zone around the whole hemisphere. Even in the rare case represented in Fig. 5, the jet stream does not run uninterruptedly around the entire hemisphere, but parts of it are dissipated bj' divergent currents. 2. The meridional circulation strips. An ample heat exchange is effected in these strips; quasi-stationary

warm

tropospheric anticyclones that reach up to the stratosphere and are displaced far poleward alternate with cold tropospheric troughs that reach far equator-

ward and likewise extend to high altitudes (Fig. 6). Whereas these two principal forms occur during all seasons, the two following secondary forms occur only in certain seasons:

The winter anticylcone in the lower troposphere Below the circumpolar low at high altitudes there often exists during the winter an anticyclonic circulation system in the lower troposphere over the interior 3.

[52].

Fig.

7.

— Centers

clones {+) at the

of anticyclones (•), ridges (o), and cylevel from June 21 to July 5, 1949.

5-km

Assuming that the meridional heat transport is the main effect of the general circulation, we can distinguish the following principal forms of the general circulation [8; 17, pp. 49-55].

of the Arctic. When these arctic air masses penetrate to the south, additional cooling occurs through radiation over the continent, and wide regions of stationary cold anticyclones are thus formed. The frontal zone

between these cold air masses and warm air to the south, and the resulting westward drift, are displaced far toward the equator. In Europe this displacement extends to the Mediterranean area, in North America to the northern edge of the Gulf of Mexico. 4. The arctic anticyclone of the stratosphere in midsummer. According to Baur and Philipps [23], the

summer

total insolation during the

at the pole,

and thus the

hkely also to be a

solstice is strongest

ultraviolet radiation

is

most

maximum there. For this reason, in the

upper stratosphere a pressure gradient from the pole to the equator exists during this short season, in strong contrast to midwinter conditions.

Figure 9 shows the average topography of the 41-mb surface (at approximately Fig.

5-km

1.

8.— Centers

level

An

of anticyclones (•) and ridges (o) at the 8, 1949.

from July 23 to August

unordered heat exchange. This occurs in westand lows of the lower troposphere

east-travelling highs

with isobars running approximately from west to east at the 5-km level (zonal circulation). In this case, the southern portion of the troposphere (in the Northern Hemisphere) is warm, the northern portion is cold. As long as the flow equilibrium between warm and cold air remains undisturbed, a "frontal zone" ascending poleward exists in the troposphere with a strong merid-

22-km

height) as

it

exists,

July over the Northern Hemisphere. In the Arctic this high pressure extends in some years to the earth's surface, as in Europe from June 5 to June 13, 1947 (Fig. 10) before the extremely dry summer. according to Scherhag

[47], in

Fifth Empirical Theorem: On

the average for all

meridians and over long periods of time, the zonal and meridional components of the atmospheric circulation in the lower troposphere are nearly equal in

middle latitudes

of the Northern Hemisphere.

Sixth Empirical Theorem: In

the lower

and middle

troposphere on both hemispheres, there are always long

— EXTENDED-RANGE WEATHER FORECASTING zones, extending over

many

meridians, in which

warm

subtropical air borders on cold polar air (polar front). In the upper troposphere above these zones, there is always

a narrow

with extremely strong westerly winds

belt

stream), which reach their

maximum

825

Baur [17; 20, pp. 920-923] established 17 types of Grosswetterlagen for the circulation region of Europe 25 types, if finer subdivisions are included. For the cir-

(jet

velocity at the tro-

popause jet

level. However, neither the polar front nor the stream runs uninterruptedly around the entire North-

ern Hemiphere.

Seventh Empirical Theorem:

A

zonal circulation

on rare occasions over all meridians of the middle latitudes. In most cases, regions with a prevailing zonal circulation and regions with a prevailing meridional exists only

circulation exist simultaneously.

Types of Grosswetter. Since in middle latitudes of the Northern Hemisphere the character of the circulation is seldom uniform over the entire hemisphere, it is necessary to consider a division into separate circula-

which Seilkopf refers to as "special circulations" [52]. Furthermore, it is necessary to define an observational unit which lies between the daily weather tion cells,

and the world weather Hemisphere or even the entire earth. This unit is the Grosswetterlage. Because of the existence of two continents (one of which has a large longitudinal extent) and two oceans on the Northsituation of a smaller region situation over the Northern

ern Hemisphere, there usually exist four or five troughs of ridges in the Northern Hemisphere. Therefore, the most suitable regional delinea-

and the same number

tion of Grosswetterlagen results from a division of the total circulation of the Northern Hemisphere into five

(partly overlapping) special circulation regions [17, pp. 58-62]:

North America North Atlantic Europe

(160°W-60°W) ( 70°W-0°) ( 30°W-45°E)

Asia

( 45°E-150°E) (150°E-135°W).

North

Pacific

At some future time

it might perhaps be useful to combine the overlapping North Atlantic and the European regions into a single circulation region. The temporal limits of a Grosswetterlage result from

the following definition [13]: A Grosswetterlage is the mean pressure distribution (at sea level) for a time interval during which the position of the stationary (steering) cyclones and anticyclones and the steering within a special circulation region remain essentially

unchanged. Here "steering" means the direction of propagation of 24-hr isallobars. The reference to the pressure distribution at sea level is necessary in order to enable one to apply this definition to observations of

when

there were no daily aerological obthe other hand, by requiring constancy of the steering, the pressure distribution in the middle troposphere (5-km level) is indirectly taken into conearlier years

servations.

On

sideration.

The mean pressure distribution during an arbitrary five-day period cannot be considered as a GrosswetterRather, it is possible that by such an arbitrary formation of means, two different Grosswetterlagen might cancel each other.

lage.

—

9. Average topography of the 41 -mb surface for July Northern Hemisphere. (After Scherhag [47]).

FiG. in the

North Atlantic he introduced 16 types of Grosswetterlagen. The 25 European Grosswetter types can be grouped into the following divisions: 1. A high in the northwest region (between Greenland and Scandinavia). culation region of the

^

:

WEATHER FORECASTING

826

(For further details, see [13; 17; 20, pp. 920For the North American circulation region, Krick and Elliott have established a system of weather types. tions.

923].)

Considering the pressure distribution at the 5-km level, we can classify the Grosswetterlagen in all special circulation regions of the temperate zone in the Northern Hemisphere according to the following seven fundamental types based on the circulation 1. Three types with zonal circulation: I. High pressure in the south; low pressure in the north; westerlies and jet stream reach farther south than normally. II. High pressure in the south; low pressure in the north northern boundary of high pressure either in normal or more northerly position; westerlies and jet stream far to the north. III. High pressure in the north; low pressure in the south. 2. Four types with meridional circulation: IV. Subtropical meridional flow; high pressure in the east; low pressure in the west. V. Polar meridional flow; high pressure in the west; low pressure in the east. VI. Meridional ridge. VII. Meridional trough. These seven types occur in all special circulation regions of the temperate zone in the Northern Hemisphere, but with different frequencies. Schematic illustrations of the pressure distribution and air flow in the middle troposphere occurring with these seven types are sho\vn in [21]. Annual Variation of Grosswetterlagen. Frequency Maxima above Chance Limit {Weather Key-Days). The establishment of types of Grosswetterlagen and the determination of the corresponding weather represent only the first steps toward rational macrometeorological research. Further steps must include the following: (1) determination of the seasonal trend of Grosswetter types, (2) investigation to determine whether certain Grosswetterlagen occur at certain times of the year more frequently than according to chance, (3) determination of the persistence and repetition tendency of individual Grosswetter types and their dependence on the seasons and on the general atmospheric circulation, and (4) investigation of the frequency and the circumstances of transition from one Grosswetterlage to another. There are many problems to be solved which require the closest coordination of theory, synoptics, and statistics based on the probability theory. A

each during the year with so high a relative frequency that it cannot be explained as chance fluctuation of a

uniform distribution over the entire year. The number 22 represents only the present state of our knowledge; it is possible that this number will be increased with the further increase of observational data. As an example. Fig. 11 gives a portion of the annual course of

;

clear-cut solution of these problems

rably greater value for

is

extended-range

of

incompa-

forecasting,

15

26

I

5

25

15

JUNE

MAY

—

Fig. 11. Seasonal variation of the relative frequency of the //Af -situation from April 1 to August 1 for the period 1881-1943. The dash-dot line represents the annual mean value of the relative frequency of the //A^ -situation among the other Grosswetterlagen the dashed line represents the upper limit of the range of chance of this relative frequency, where the range of chance is defined in the usual manner as the range which contains 99.730 per cent of all values. ,

the relative frequency of the "i/iV-situation," a Grosswetterlage which is characterized by a "steering high" or "central high" over the northeastern Atlantic Ocean between 30°W to 5°E and 58°N to 75°N. As can be seen from this figure, the relative frequency of occurrence on May 25 and 26, as well as on May 29 to June 3, exceeds the maximum chance limit. In such a sector of better-than-chance occurrence, the day of the greatest relative frequency is called a "weather key-day." The general physical explanation of the annual course of the relative frequency of the European Grosswetter types by means of the annual course of insolation and the general circulation of the atmosphere is given else-

where It

[17; 20, pp. 920-923].

must be emphasized, however,

that the relative

frequency of a given Grosswetter type, at least in Europe, never reaches 50 per cent on any day of the year, and, even when several similar Grosswetter types are combined into one group, it never exceeds 70 per cent (see second empirical theorem).

Eighth Empirical Theorem: The tain

Grosswetter types

is

occurrence of cer-

connected with the annual

course of the general atmospheric circulation in such a manner thai during certain parts of the year certain types occur more frequently than according to chance. However, they do not occur so frequently that, without the aid of other indications,

an extended-range

forecast

particularly for

could he based on them.

taken at several institutes. The determination of the annual course of the relative frequency of European Grosswetter types in a 63-yr period showed [16] that in Europe one or more types of Grosswetterlagen occur in 22 intervals of several days

Weather Key-Days and Weather Development. The weather key-days indicate, so to speak, the rhythm of the normal seasonal trend of the atmospheric circulation in the special circulation region under consideration. The term "rhythm," however, is not to be interpreted as a periodic or quasi-periodic process, but

Consult "Extended-Range Forecasting by Weather Types" by R. D. Elliott, pp. 834-840 in this Compendium.

pendence upon time. The basic cause of this rhythm is the annual course of the incoming and outgoing

medium-range forecasting, than are the many harmonic and rhythm analyses still under-

its 2.

meaning

in this connection

is

only a defined de-

EXTENDED-RANGE WEATHER FORECASTING The irregularity of the rhythm probably has cause in the irregular distribution of land and water and in the variation of the period of the possible free oscillations. This latter variability results from the continuous change of temperature in the course of the year. The occurrence or nonoccurrence of the atmospheric phenomena pertaining to the weather key-days of the year is therefore the expression of the circulation character of the season or year in question. It is therefore probable that the weather on weather keydays is connected with the later weather development. In fact, in Europe series of better-than-chance con-

radiation. its

have been found between characteristic weather anomalies occurring around weather key-days and the subsequent or later meteorological situation [15; 17, p. 133]. For example, September 29 is a weather key-day for Europe. On this day, as well as on the nections

preceding and the following day, certain European anticyclonic situations within the period from 1881 to

1943 reach a better-than-chance frequency

September 23 to October

[16].

From

Europe has

in 65 years a so-called Altweibersommer with little cloudiness, infrequent precipitation, and relatively high midday temperatures. Weather of this character occurs in high-pressure regions, stretching from west to east, with a zonal circulation over northern Europe, as well as in the region of high pressure with the center over eastern Europe accompanied by a meridional circulation. In the latter case, the pressure at Moscow is considerably above normal. As is shown in Table V,

per cent of

1,

central

all

Table V. Pressure Anomalies During the European "Altweibersommer" and Temperature Character OF THE Subsequent Winter (Example

of

an unequivocal, significant relation)

827

:

WEATHER FORECASTING

828 circulation changes within limited regions

—

—

of the size

an ocean actually exist and are caused to a large extent, though not exclusively, by the distribution of pressure and temperature within these regions and those immediately adjacent to them. of perhaps a continent or

CRITIQUE OF THE

METHODS OF EXTENDED-

RANGE FORECASTING Medium-Range

Forecasts. It

is

useful to distinguish

between medium-range forecasts (for two to five days) and extended-range forecasts (for six to ten days, for months, or for seasons). The methods of synoptic meteorology play a decisive role in medium-range forecasts. This is possible today, since weather maps of the entire Northern Hemisphere are available every day owing to the improvement of the communication system, However, it is necessary to supplement synoptics by meaningful statistics, partly to enlarge and consolidate our experience, and partly to create objective bases which could be of direct aid to forecasting. The application of rhythm analyses and symmetry points is of little use for the medium-range forecast, since the shorter pressure waves are mostly nonpersistent [20, pp. 933-934]. These methods are therefore discussed in the section on long-range forecasting. Analogue Methods. An aid for the medium-range forecast can be found in the study of the subsequent development of past cases with both similar pressure distributions and similar preceding Grosswetter developments. It is to be noted, however, that such subsequent developments have a definite seasonal trend with frequency maxima in certain rather narrowly limited portions of the year, just as have the types of Grossweiterlagen and the repetition tendency. Therefore, only those days of previous years should be used for comparison whose date is not more than five days removed from th** day in question. As a consequence of this restriction, really useful

and

significantly similar cases

can be found only on rare occasions. This method can be used regularly only when weather map series for 150 yr are available. Combination of Synoptics and Statistics. The only hopeful method of obtaining reliable medium-range weather forecasts is the combination of synoptics and statistics. By synoptics we mean here not only the chartwise representation and analysis of weather and Grosswetterlagen, but also the thorough consideration of subsequent developments from a physical viewpoint. For this purpose, it is necessary to develop the present synoptics, from which forecasts can be made only up to 36 hr in advance, to Grosswetter synoptics. Such Grosswetter synoptics deal with the physical aspects of the sequence of Grosswetterlagen, the forms of transition from one type to another, and the mutual influence of Grosswetterlagen in neighboring circulation regions. With such Grosswetter synoptics, the preceding development which has led to a certain Grosswetterlage must be taken into account to a much greater extent than has been the case with daily synoptics. The multitude of the phenomena and problems that must be taken into account make it absolutely neces-

sary that statistics be used as a broad empirical basis. What a theoretically designed experiment is to the physicist, clear statistics are to the Grosswetter investigator. Investigations of special situations which are favored in the usual synoptics give results which only appear to be proofs and have no value in promoting

knowledge of macrometeorology. Such investigations can be compared to experiments in physics in which uncontrollable secondary effects are not eliminated. Clean-cut statistics must be preceded by definite physical or theoretical formulations of the statistics

must comprise

all

problems; these available observations per-

taining to the problem and they must be compared with suitable control samples to show whether or not

the correlations are statistically significant. Such investigations can serve a double purpose: furthering our

knowledge in a manner similar to a well-designed experiment as well as serving as a basis for forecasting, provided their results are unequivocal and significant (with a significance level of 0.27 per cent). Forecasting the Sea-Level Pressure Distribution for Two to Three Days. The combination of synoptics and statistics makes it possible today to predict in many cases the approximate pressure distribution for the second and third day in those regions for which the necessary data are available. Scherhag [49] has shown how to determine the sea-level pressure distribution for the following day from the movement and intensity change of 3-hr and 24-hr isallobars, from the direction of the isopleths of geopotential, and finally from the divergence and convergence of the isopleths on the 500-

and 225-mb charts. Furthermore, one can compute approximately the change in thickness of the layer between the 500- and 1000-mb surfaces from the surface pressure distribution; by adding the prognostic thickness chart to the prognostic surface pressure chart, the prognostic 500-mb chart for the following day can be obtained. In turn, from this 500-mb chart a forecast of the surface pressure distribution can be obtained for the second consecutive day. Finally, a prognostic

chart of the surface pressure for the third consecutive day can be obtained by repeating this procedure with a consideration of the "steering" of the isallobaric maxima and minima in the upper troposphere by means of the 96-mb chart [17, p. 126]. Of course, the forecast becomes more tmcertain with each successive day because of the propagation of errors. For this reason, it is necessary to supplement the prognosis statistically. If we transform the hydrodjmamic equation of motion so that it includes surface friction, and add to it the equation of continuity, the first law of thermodynamics, and the equation of state, a system of equations is obtained from which the following equation for the pressure change can be derived, as shown in [24]

dp dt

_ V

r [

K

RT 11 -

dg dq

. ,

/

RT

5vA

Kdt div2 V, + '{t+'")]-l^.'^'

where the symbol

div2

gence of the velocity

v stands for the horizontal diverv, k = R/cp = 0.2884, dq/dt is

:

EXTENDED-RANGE WEATHER FORECASTING the amount of heat received per unit time by a unit mass of a moving particle, c is a constant depending on external friction, and the other symbols have their customary meanings. The replacement of the terms on the right-hand side of this equation by quantities which can be statistically interpreted

in the American investigations which can be classed under the name of "mean-circulation methods of extended forecasting" [32, 40, 41, 45, 53, 57]. With re-

Table

Extract from a Multiple-Correlation Table FOB THE Prediction of 48-hr Pressure Changes at Potsdam

VI.

—for these quantities the reader referred —leads to the following variis

(X,

to the original report [10]

(X2

ables which are used as headings in a table of multiple

X2 =

Xz =

=

Xi

mb

reduced to sea level, on the clue day (day of forecast) at 1400 (4 classes), 24-hr temperature change in centigrade degrees from the previous day at 1400 to the clue day at 1400 (4 classes), 24-hr pressure change in mb from the previous day at 1400 to the clue day at 1400 (4 classes), cloudiness in tenths at 1400 on the clue day pressure in

(4 classes),

Xs =

mb from 0700 to 1400 on the clue day (5 classes). In Table VI, a section from a multiple-correlation table is given whose headings include these five vari7-hr pressure change in

The numbers in the blocks are the 48-hr pressure changes from 1400 of the day of the forecast to 1400 two days later, as well as the date of the clue day (in ables.

parentheses). All observations refer to Potsdam (near Berlin). The table is based on observations from June

21 to August 9 of the years 1893-1937. Of the 1280 blocks of the table, 698 are covered with a total of 2250 entries. The boldface numbers of the table represent the mathematical expectation of the 48-hr pressure changes, in mb. Of course, in practice, only those squares are to be used that are most likely to lead to an unequivocal result, as is the case with the blocks of Table VI, marked bj' a black star. If one block contains a pressure change whose sign is different from all the other values of that block, this possibility could be excluded if the weather situation on the day in question (for instance July 12, 1928, in Table VI) were entirely different from that on the day of the forecast. For such comparisons, the method of similar (or, in this example, opposite) cases can be applied even at the present time.

The same table can be used for several climatically coherent places. However, different tables must be computed seasons. ional

for different climatic regions

The

tables can be supplemented

and different by the merid-

and zonal pressure gradients or other physically

important quantities. This, however, is possible only if observations over a longer period at several climatically similar stations can be combined in one table, such that the number of blocks, which increases with every new variable, can be filled with sufficient observations.

On days when

sufficiently reliable results

cannot be

obtained from a multiple-correlation table, it is better not to draw prognostic pressure charts for the second and third consecutive days. Mean-Circulation Methods of Forecasting. A judicious combination of synoptics and statistics is represented

=

=

X5

1019.5 to 1036.5

-f-4.0

(X3

correlations

Xi =

829

=

mb)

to +11.8 cent, deg.) 0.0 to 3.2

mb)

WEATHER FORECASTING

830

order to include these valuable investigations in the total structure of

macrometeorology.

The most important

aspect of these investigations the world-wide point of view of the general circulation, on which they are based. This is Grosswetter synoptics in the true sense of the term. This method of is

consideration, comprising the entire Northern sphere,

is

Hemi-

also applied in Rossby's formula [45]:

c

= U

4x=^

where

c is the eastward velocity of the perturbation (trough or ridge), L is the wave length, U is the zonal velocity of the westerlies, and p is the rate of change of the Coriolis parameter with latitude. This formula (as derived from simplifying assumptions) is of such fundamental importance for the mean circulation methods that it is necessary to conduct rigorous statistical investigations to determine the extent to which it is confirmed by observation, and the conditions under which systematic deviations occur which can be eliminated

by computation. Clapp [41] made such an investigation using fiveday mean 10,000-ft charts covering the period from January 1941 to April 1943. He computed the correlation coefficients between the observed displacements (for half a week and for a full week) of troughs and ridges at 45°N and those computed from Rossby's formula. Clapp used as a representative value of U, the zonal westerlies, the mean west to east geostrophic wind between 40°N and 50°N over the entire range of longitudes from about 130°W to 30°W, known as the 10,000ft index I^. He furthermore defined the wave length L as twice the difference in longitude between a given trough and the ridge to the west of it. Eliminating cases of new trough development, Clapp obtained the following correlation coefficients

r in Full

TV^

cases:

week

r

N

Winter Spring

Summer Fall

For the displacements during a

full week the correlabetter than chance (with a significance level of 0.27 per cent) only in winter; however, for displace-

tion

is

ments during

half a week, three of the four correlation

We can conclude from this, that the Rossby formula, in spite of the simplifications made in its derivation, furnished an approximation of actual conditions. However, the correlations are too small to permit predictions of the displacement of troughs and ridges on the basis of this formula. For this reason, Namias [40] employed additional criteria and methods for the forecasting of circulation patterns. According to Rossby's formula, a westward displacement (retrogression) of a trough or a ridge occurs when the wave length, that is, the distance between troughs, exceeds a certain value depending on the season and the geographical latitude; in other words, when an increased zonal circulation exists. This result is in apparcoefficients are significant.

EXTENDED-RANGE WEATHER FORECASTING correlation of the

monthly means can be interpreted

When

the pressure over Iceland is very low, western Greenland lies within a cold northern flow, whereas to the west of the above-normal Azores High, warm air flows from the south to the north. contrariwise:

In turn, with a strong air-mass exchange between high and low latitudes the temperature difference will diminish. The general circulation shows, after a certain duration of intensified air movement, "fatigue phenomena" which finally lead to a change in the circulation pattern (see Table II and [7]). In order to develop circulation methods so that they can be used as a basis for reliable extended forecasts; a transition is necessary from the statistics of averages, now predominantly in use, to statistics of selected cases which take into account especially the physical pro-

and the special characteristics of the particular case. Examples of "selective statistics" are contained in Tables I and V, which, to some extent, form parts of a multiple-correlation table. Table VI also forms part of cesses,

"selective statistics." for more than days are not possible on a synoptic basis. The multitude of all possible developments no longer permits consideration of the development in all physical details. Here, statistics must be employed if we are to make statements about the future. However, two prerequisites must be fulfilled: (1) the choice of statistical methods must be guided by a physical formulation of the problems and by physical considerations, and (2) long-range forecasts should be given, at least publicly,

Long-Range Forecasting. Forecasts

five

onljr if

better-than-chance statistical relationships are obtained that ensure the success of the forecast with a probability of over 92 per cent. It must be borne in mind that the damage which might result from an incorrect forecast is greater the longer the time interval for which the forecast is made. Therefore all demands for regular issues of

must be declined

monthly and seasonal forecasts

in the present state of our

In order to be on the safe side, it long-range weather forecasts only

is if

Symmetry Points. There are even stronger objections against the use of so-called symmetry points for the pressure curve. In the first place, it was shown that even in a model sample based on chance and persistence tendency only, symmetry points occur with the same degree of approximation as they do for the actual pressure curve [20, pp. 924-926 and 934-936]. In the second place, the existence of a symmetry point can be detected with some degree of certainty only if about 20 days have elapsed. In the third place, even from a very good symmetry during 20-25 days, no sufficiently reliable conclusion can be drawn as to whether and how long the reflected curve of the pressure or any other weather element will persist. As an example, the symmetry point for the pressure curve of Potsdam on 26, 1932, may be cited. The correlation cocorresponding days from the first to the 25th day before and after the symmetry point was -t-0.75; from the 26th to the 50th day it was -0.46. Regression Equations. It is necessary that regression equations which are to be used for long-range forecasts yield a multiple correlation coefficient greater than 0.80, since only then will the standard error of estimate of the correlation be less than ^fo of the standard deviation. Furthermore, the basic single correlations must be stable, that is, they must be approximately the same for subdivisions of the total period. Multiple Correlation Tables. Since most of the Grossv)etter correlations are not linear, it is very rare that multiple-correlation coefficients are obtained for sufficiently long periods which are larger than 0.80. Selective statistics again appear much more promising in this case, since fundamentally they yield parts of multiple correlation tables. As long as their computation is guided by a physical approach to the problem, unequivocal, better-than-chance results can be used as an empirical basis for the further development of the theory as well as a basis for long-range forecasts.

December

efficient of

knowledge.

advisable to issue at least two argu-

ments are available that fulfill the above-mentioned prerequisites and lead to the same expected weather character without contradiction by any other statistical

REFERENCES 1.

2.

argument. Extrapolation of Periods. The extrapolation of periods more helpful for long-range forecasts than for medium-range forecasts. Tests of over a thousand harmonic analyses at the Forschungsinstitut fur langfristige Witterungsvorhersage over a number of years have

3.

is

shown, however, that the percentage

5.

of correct fore-

is too small for these extrapolations to be used as a basis for long-range forecasts. Even the use of rigorous

mathematical criteria permits only the decision as to whether the period has been persistent to date, but it does not yield any clues to its future behavior. Rhythm analyses cannot be used as the basis for any meteorological forecasts as long as we have no physical, statistically sound criteria that would indicate the continuation of the period with an expectancy of over 92

Abbot, C. G., Ann. astrophys. Obs. Smithson. Instn., Vol. 6. Washington, D. C, 1942. (See Table 27) (Also, personal communications through December 1945.) and Fowle, F. E., "Volcanoes and Climate." Smithson, misc. Coll., Vol. 60, No. 29, 24 pp. (1913). Alter, D., "Application of Schuster's Periodogram to Long Rainfall Records, Beginning 1748." Mon. Wea. Rev. Wash., 52:479-483 (1924).

4.

casts

per cent during the forecast period.

831

6.

7.

8.

9.

Angstrom, A., "Teleoonnections of Climatic Changes in Present Time." Geogr. Ann., Stockh., 17:242-258 (1935). Baur, F., "The 11-Year Period of Temperature in the Northern Hemisphere in Relation to the 11-Year SunSpot Cycle." Mon. Wea. Rev. Wash., 53:204-207 (1925). "Statistische Untersuohungen ilber Auswirkungen und Bedingungen der grossen Storungen der allgemeinen atmosphiirischen Zirkulation, III." Ann. Hydrogr., Hamb., 54:227-236 (1926). "Der gegenwartige Stand der meteorologischen Korrelationsforschung." Meteor. Z., 47:42-52 (1930). "Die Formen der atmospharischen Zirkulation in der gemassigten Zone." Beilr. Geo-phys., 34:264-309 (1931).

"SchwankungenderSolarkonstante." 4:180-189 (1932).

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WEATHER FORECASTING

832

"Die Storungen der allgemeinen atmospharischen

10.

Zirkulation in der gemassigten Zone." 437-444 (1937). 11.

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Z.,

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Depant,

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jiihrigen

32.

"tjber die grundsatzliche Mogliohkeit langfristiger Witterungsvorhersagen." Ann. Hydrogr., Hamb., 72: 15-25 (1944). Musierbeispiele europdischer Grossweiterlagen.

13.

U.

34.

Humphreys, W.

Winters zusagen?" Nalurwiss. i?rfsc/t., 1:256-261 (1948). "Zur Frage der Echtheit der sogenannten Singularitaten im Jaliresgang der Witterung." Ann. Meteor.,

35.

KiEPENHEUER, K. O., "Neucre Ergebnisse nenkorona." Neue Phys. Blatter, 1946.

1:372-378 (1948). Einfilhrung in die Grosswetterkunde

36.

J.

"Was kann

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Witterungsgepriige

des

.

kommenden

"Die

18.

doppelte

Sohwankung der atmospharischen

"Zuriickftihrung des Grosswetters auf solare ErscheinArch. Meteor. Geophys. Biokl., (A) 1:358-374

19.

ungen." (1949).

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20.

Meteorologie, J. v. 5.

Aufl. Leipzig,

W.

Keller, 1951.

"Winter Temperature in New England Following Anomalies of Circulation over the North Atlantic in November." Bull. Amer. meteor. Soc., (1951) (in press). u.

a,.,

MitteleuropaischerWitterungsbericht.

burg, Forschungsinst.

f.

BadHom-

(See also "Der Mitteleuropaischer Witterungsbericht." Meteor. Z., 55:142-147 (1938).) 23. Baur, F., und Philipps, H., "Der Warmehaushalt der Lufthiille der Nordhalbkugel im Januar und Juli und zur Zeit der Aquinoktien und Solstitien." Beitr. Geophys., 42:160-207 (1934). 24.

26.

Bebnheimer, W. E., "tJber den angeblichen Zusammenhang der Sonnenstrahlung mit der Fleckenhaufigkeit."

27.

Best, N., Havens, R., and LaGow, H., "The Pressure and Temperature of the Upper Atmosphere," in Upper Atmosphere Research Report IV. Naval Res. Lab., Washington, D. C, 1947. (See pp. 111-115) Bjerknes, J., "On the Structure of Moving Cyclones." Geofys. Publ., Vol. 1, No. 2 (1919); Bjerknes, V., "On the Dynamics of the Circular Vorte.x with Applications to the Atmosphere and Atmospheric Vortex and Wave Motions." Geofys. Publ., Vol. 2, No. 4 (1921); Bjerknes, V., "On Quasi Static Wavemotion in Barotropic Fluid Strata." Geofys. Publ, Vol. 3, No. 3 (1923). Bjerknes, J., and Solbeeg, H., "Life Cycle of Cyclones and the Polar Front Theory of Atmospheric Circulation." Geofys. Publ., Vol. 3, No. 1 (1922).

29.

Lexis, W., Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft. Freiburg, F. Wagner, 1877; also RiETZ, H. L., ed., Handbook of Mathematical StatisBoston, Houghton, 1924. (See pp. 82-88) tics. Maris, H. B., and Hulburt, E. O., "A Theory of Auroras and Magnetic Storms." Phys. Rev., (II) 33:412-431

Meinardus, W., "tJber

;

(1947). 40.

41.

Extended Forecasting by Mean Circulation Methods. U. S. Weather Bureau, Washington, D. C, 1947. and Clapp, P. F., "Studies on the Motion and Development of Long Waves in the Westerlies." J. Meteor., 1:57-77 (1944).

42.

Norton, H. W., "Estimating the Correlation

43.

Amer. meteor. Soc., 27:589-590 (1946). Pettersson, 0., "Ueber die Beziehungen zwisehen hydrographischen und meteorologischen Phanomenen." Me-

Coefficient."

Bull.

teor. Z.,

44.

23:285 (1896).

RossBY, C.-G., "On the Distribution of Angular Velocity in Gaseous Envelopes under the Influence of Large-Scale Horizontal Mixing Processes." Bull. Amer. meteor. Soc, 28:55-68 (1947).

45.

and Collaborators, "Relation between Variations Atmosphere and the Displacements of the Semi -permanent in the Intensity of the Zonal Circulation of the

Meteor. Z., 47:190-191 (1930).

28.

Son-

(See pp. 225-

einige meteorologische Beziehungen zwisehen dem Nordatlantischen Ozean und Europa im Winterhalbjahr." Meteor. Z., 15:85-105 (1898) "Der mitteleuropaische Winter und seine Beziehungen zum Golfstrom." Das Wetter, 16:8-14 (1899). 39. Namias, J., "Physical Nature of Some Fluctuations in the Speed of the Zonal Circulation." /. Meteor., 4:125-133

Behlage, H. p., Jr., "tJber die Verbreitung der dreijiihrigen Luftdruckschwankung tiber die Erdoberflache und der Sitz des Umsteuerungsmechanismus." Meteor. Z., 50:41-47 (1933).

tiber die

(1929). 38.

"Die Bedeutung der Konvergenzen und Divergenzen des Geschwindigkeitsfeldes fiir die Druckanderungen." Beitr. Phys. frei. Atmos., 24:1-17 (1938).

25

37.

langfristige Witterungsvorher-

sage, 1937-39.

J., "Volcanic Dust and Other Factors in the Production of Climatic Changes, and Their Possible Relation to Ice Ages." /. Franklin Inst., 176:131-172

231)

Wiesbaden, Die-

Zirkulation in der gemassigten Zone innerhalb des Sonnenfleckenzyklus." Meteor. Rdsch., 2:10-15 (1949).

Springer, 1925.

(1913).

terioli, 1948.

22.

Weather Bureau, Washington, D. C, 1944. F. M., Dynamische Meteorologie, 2. Aufl. Wien,

Exner,

voraussiohtliciie

21.

S.

33.

baden, Dieterich, 1947. "Ein Beitrag zur Kliirung der Frage eines Einflusses der Planeten auf die Witteruug." Z. Meteor., 2:47-55

15.

17.

6:13^1 (1924). DoBSEY, H. G., Jr., and Brier, G. W., "An Investigation of a Trajectory Method for Forecasting Flow Patterns at the 10,000-Foot Level." Res. Pap. No. 8, pp. 50-58 in A Collection of Reports on Extended Forecasting Research.

Wies-

(1948).

16.

"Die Schwankungen der atmospharischen dem Nordatlantischen Ozean im 25Zeitraum 1881-1905." Geogr. Ann., Stockh.,

a.,

Zirkulation iiber

54:188-189

(1937).

14.

Bjerknes, V., and others, Physikalische Hydrodynamik.

"Zur Frage der Beziehungen zwisehen der Temperatur des Golfstroms und dem naohfolgenden Temperaturcharakter

12.

30.

Meteor. Z., 54:

46.

47.

Centers of Action." /. mar. Res., 2:38-55 (1939). ScHELL, I. I., "Dynamic Persistence and Its Applications to Long-Range Foreshadowing." Harv. meteor. Studies,

No. 8, 80 pp. (1947). ScHERHAG, R., Neue Methoden der Wetteranalyse und Wetterprognose.

48.

Berlin, Springer, 1948.

"Synoptische Untersuchungen iiber die Entstehung der atlantischen Sturmwirbel." Meteor. Z., 54:466-469 (1937).

49.

"Die Verwendung der Hohenkarteu im Wetterdienst." ErfahrBer. Reichs. Wetterd., Reihe B, Nr. 11

Forsch. (1943). 50.

ScHMAUss, A., "Singularitiiten im jahrlichen Witterungsverlauf von Miinchen." Dtsch. meteor. Jb. Bayern, B (1928); "Kalendermassige Verankerungen des Wetters."

EXTENDED-RANGE WEATHER FORECASTING Meteor. Z., 53:72-74 (1936); "Synoptische Singularitaten." il/e«eor. Z., 55:385-403 (1938). 51.

52.

53.

ScHOTT, G., Geographie des Atlaniischen Ozeans, 3. Aufl. Hamburg, C. Boysen, 1942. Seilkopp,H., "SpezielleGrosszirkulationundWitterung."

Ann. Meteor., 1:312-325 (1948). University of Chicago, Dept. Meteob., Staff Members, "On the General Circulation of the Atmosphere in Middle Latitudes." Bull. Amer. meteor. Sac, 28:255280 (1947).

54.

Wagner,

A., Klimadnderungen und Klimaschwankungen. Braunschweig, F. Vieweg & Sohn, 1940. (See pp. 192199)

55.

56.

Waldmeieh, M., Ergehnisse und Probleme forschung. Leipzig, Akad. Verlagsges., 118-120)

der Sonnen-

1941.

(See pp.

833

WiBSE, W., "Die Bedeutung der Eisverhaltnisse im Friihling im Gronlandischen Meere und des Ost-Islandischen Polarstromes

ftir

die Temperaturverhaltnisse des nach-

folgenden Winters in Europa."

Bull. Inst, hydrol. Buss.,

im Barents-Meer und Lufttemperatur in Europa." Nachr. ZentBur. Hydrometeor., UdSSR, 3:1-30 (1924); "Ice in the Polar Seas and the General Circulation of the Atmosphere." /. Geophys. Meteor., 14:52-59 (1925); "Eis

Moscow, 1:78-84 (1924). WiLLBTT, H. C, and others. Final Report of the Weather Bureau .1 .T Extended Forecasting Project for the Fiscal Year 1948-1949. Cambridge, Mass., 1949. 58 WtJNSCHE, W., "tjber die Existenz langsamer Luftdruckschwingungen auf der rotierenden Erde." Veroff. geo57

—M

.

phys. Inst. Univ. Lpz.,

(2)

11:153-199 (1938).

:

.

EXTENDED-RANGE FORECASTING BY WEATHER TYPES By

ROBERT

ELLIOTT

D.

North American Weather Consultants

INTRODUCTION During the

last

and a number

two decades there has been a con-

which

will

be con-

^|

Once the extended-period mean or type pattern is^'

siderable development in the field of extended-range forecasting, that is, forecasts for up to a week in ad-

weather elements for the time interval in question can be predicted. Considerable statistical work has been done relating temperature and precipitation anomalies for an extended period with the weather types [3] and with the mean isobaric pattern at upper levels [17, 20]. In general, extended-period surface temperature anomalies are negative behind mean troughs aloft and positive ahead, ^vith precipitation and cloudiness at a maximum just ahead of the mean trough. The problem of preparing daily prognostic charts for up to seven days in advance is considerably more difficult. It is of course obvious that the sum of the daily prognostic charts should correspond to the extendedperiod prognostic representation; however, there are a great variety of ways in which this pattern may be made up. A prognostic extended-period upper-level chart may be used as a "steering" pattern to fix in a general way the paths of migratory cyclones and anticyclones, the individual systems being extrapolated forward from forecast day with due consideration being given to the predicted strength of the flow aloft. In one technique this is supplemented by various prognostic zonal and meridional indices [20]. Another technique [4] resorts to the use of analogues selected from the archives of weather charts in which the mean flow pattern matches the predicted pattern. Still another method is to use "ideal" weather types [3] giving the characteristic daily surface charts for each day of the weather types as determined through statistical study of past cases. The foregoing paragraphs very briefly outline the features which most extended-range forecasting techniques have in common. These may be summarized as forecast, the anomalies^ for the

vance. While it is known that a modest success in forecasting general weather trends for as much as seven daj^s in advance has been achieved by several groups using techniques of their own development, no particular method has gained the widespread acceptance in meteorological circles enjoyed by the frontal and airmass analysis techniques of short-range forecasting. However, most of the extended-range forecasting methods have a number of points in common and these will be discussed briefly. Meteorologists engaged in effective extended-range forecasting must become accustomed to dealing with certain forms of representation which summarize the circulation characteristics of a given region over a finite period of time. This may take the form of fixed-timeinterval mean charts such as the overlapping five-day mean maps used by the Extended Forecast Section of the U. S. Weather Bureau [20], or more variable and "natural" period representations such as composite maps [21], weather types [3], or steering patterns [26]. In each case the representation involves, basically, the concept of mean circulation patterns at the surface and/or aloft, covering a fixed or variable time interval of several days or more. Even a pure analogue selection technique must involve considerations of this nature in order to be successful. One-map "thumbprint" selection schemes have not proved successful in extendedperiod forecasting, and exhaustive statistical tests by Darling [6] show that persistence is the principal factor taken into account by this method. Ordinarily, the time interval is chosen in such a manner that the local circulation patterns of simple migratory and transitory cyclones and anticyclones ai'e smoothed out, thus delineating the more basic quasistationary and broad-scale features of the circulation pattern which are responsible for the longer-period weather characteristics in a given region. The mean patterns thus revealed are characterized by large-scale cyclones and anticyclones at the surface and by an undulatory pattern aloft having longer wave lengths than those observed on daily upper-level charts. The movements and changes in form of these patterns are on the whole slower than those of the individual migratory systems making up the mean, which at least partly compensates for the difficulty of having to forecast so far in advance. In this country, methods for forecasting these movements and changes in form are based upon statistical weather-type prediction schemes [8], the application of the conservation of vorticity principle [20],

of other techniques

sidered later.

follows

A

1

method

for concise representation of circulation

characteristics during 2.

A

method

an extended period. movement and changes

for forecasting

in form of circulation features delineated in 1, thus permitting the preparation of a prognostic representation. 3.

A

lies of

by

method for forecasting extended-period anomathe weather elements from information provided

2.

A method for preparing daily prognostic charts and forecasts for daily weather elements from 2. 4.

1. The term "anomaly," as used in this article, refers to departure from a long-term average over time and has nothing to do with the departures from means computed for latitude

circles.

834

EXTENDED-RANGE FORECASTING BY WEATHER TYPES Although some investigators who are inchned toward advocate the elimination of one or more of the intermediate steps by going directly from the representation scheme to the forecast of the weather statistical analysis

elements themselves, in the opinion of the author our present knowledge concerning weather processes is so limited that the use of the intermediate steps is required in order that the forecaster can grasp more readily the physical significance of the processes involved. A general discussion of the California Institute of

Technology weather-type technique

is

presented in the

following section.

THE WEATHER-TYPE APPROACH Various sorts of weather types had been developed [2, 14, 23]. Often the earlier attempts at typing were based upon single typical sjoioptic charts and therefore did not truly take into account weather processes occurring during an extended period. After some preliminary investigation during the late thirties [10, 18] a six-day North American weathertype scheme was developed wherein the type itself embraced a sequence of days characterized by certain for different areas in the past

locations

ments

and orientations

of the

semipermanent

ele-

of circulation such as the Pacific anticyclone, the

Aleutian cyclone, the trajectories of polar outbreaks, and cyclone paths. Empirical evidence was discovered which indicated that the mean period between the passages of cyclone famihes past a given point was about three days and that about two-thirds of the time the type characteristics associated with the passage of a given family occurred also in either the preceding or the following cyclone family. Because of this, the types were arranged so as to have a lifetime in any given sector or region of six days plus or minus one day. The instances where the type characteristic was not maintained during the passage of two successive cyclone families were handled by the introduction of the socalled "complex" types in which the first three days had the characteristics of one type and the last three those of another. Considerable work was done on these types over a period of several years, resulting in the development of a weather-type catalogue covering the period 1921-42 [22] and a set of "ideal" types [3] showing the most probable location of frontal systems and centers on successive days of each type, along with other statistical information on the weather element anomalies associated with these "ideal" types. Although these types proved of value, continued study indicated a number of shortcomings, the most important of which seemed to be that forcing the types into a six-day lifetime seemed somewhat arbitrary. Therefore, during World War II, in response to a request from the Army Air Force, which was interested in extended-range forecasting techniques and had contracted with the California Institute of Technology for continued research on the subject, new three-day types [4] were developed wherein the life of the type corresponded to the passage of a single cyclone family across a region. This averaged three days, with con-

835

The three-day weather types included all the essential and well-tested features of the older six-day types plus a number of refinements found necessary as a result of experience in their application. They were developed for each of four synoptic regions siderable variation.

consisting of sectors of forty-five degrees of longitude

extending along the belt of westerlies from 135°E through 180° to 45°W and a fifth region extending from 45°W to 45°E. Some twenty to thirty different types were determined for each region and a catalogue of weather typesfor forty-six years was prepared [4, 5, 15]. It was early recognized that the large-scale and persistent distortions of the upper-level pattern controlled and determined the weather types in each region. With an increasing file of adequate upper-level charts it has been possible to establish in a reliable fashion the upperair patterns associated with each weather type [19]. Because this file does not extend far back historically, it has not been possible to employ upper-air type characteristics in cataloguing, except in recent years. It had early been noted that the weather types for each region could be divided into two distinctive categories and that types in the same category often occurred simultaneously in neighboring regions. These two categories were the meridional and zonal flow types. Meridional flow types are characterized in the mean by upper-level crests and troughs of large amplitude which tend to steer the surface migratory systems along paths far to the north or south of normal, depending upon their location. Most of the large polar outbreaks which penetrate to southerly latitudes occur in this category. Elsewhere, unseasonably warm weather is experienced. Meridional flow patterns are particularly interesting because of the conspicuous anomalies of temperature associated with them. An interesting example may be cited in this connection: during the entire month of January, 1949, in North America there existed an extremely strong and persistent trough aloft in western United States with a persistent crest in eastern United States. As a result, temperatures were far below normal in the West and

above normal in the East. Zonal flow types are characterized by zonal flow aloft. Variations in the strength and latitude of the belt of westerlies lead to variations within this category.

beyond the scope of this article to present the of weather types as delineated by daily or "ideal" charts. However, a set of schematic diagrams representing the major features of the mean flow pattern occurring with a number of the more important wintertime weather types of the North American area is shown in Fig. 1. The types are arranged in two columns; in the left-hand column are meridional flow types, in the right-hand column zonal flow types. In addition, the position of each type in its column is determined by the degree to which it displays the It is

details

of the category. In the case of the meridional flow types, the more the principal mean trough over North America is shifted westward, the stronger the meridional flow character of the type. In the extreme of this category the trough is off the west characteristics

836

WEATHER FORECASTING

EXTENDED-RANGE FORECASTING BY WEATHER TYPES coast of

North America. The depth of the trough as a westward shift. With the zonal

rule increases with the

flow types, the farther southward the westerlies are shifted over a broad sector, the stronger the zonal

flow character of the type. In the extremes of this last category the southward shift occurs over a sector 90° (or

more) wide and

is

accompanied by the formation

of

extensive polar anticyclones to the north of the principal storm path. This storm path is unusually far south.

In the meridional category, the Bn-a type has a trough at about 90°W and a crest over the Great Basin (eastern Washington, Idaho, eastern Oregon, Utah, Nevada, and northern Arizona). Because only minor polar outbreaks occur in this type and because of the presence of a large dynamic anticyclone over the Great Basin which deflects Pacific storms northward, the United States and southern Canada experience relatively warm dry weather. As one proceeds to the Bn-b type, it is found that whereas conditions to the west of the Rockies are nearly identical with those for Bn-a, in the East a polar outbreak occurs as indicated on the diagram. This tends to make the eastern trough aloft deeper than in the case of Bn-a and produces below-normal temperatures east of the Rocky Mountains. In the case of Bn-c type, the meridional character of the flow becomes quite marked with a well-developed trough aloft at about 100°W. Frequently a strong dynamic cyclone remains trapped for several days in the southern Great Basin. The polar outbreak, instead of being confined to the area east of the Rocky Mountains as in the case of Bn-b, flows westward through mountain passes as well as southward along the eastern front of the Rockies and produces much-below-normal temperatures throughout most of western United States. Ahead of the mean upper-level trough, surface temperatures are considerably above normal, and precipitation is likely to be excessive near the mean trough. It is interesting to note that the Great Basin anticyclone, present in the two preceding types, is now weaker and appears to be merged to the west with the Pacific anticyclone, which has shifted northward. A further westward shift of the mean upper-level trough position is exhibited in type A. Here the Basin anticyclone has disappeared from the scene as a semipermanent feature of the definite upper-level

The eastern lobe of the moved unusually far north and

circulation at the surface. Pacific anticyclone has

the polar outbreak associated with this type consists of a mass outflow of cold air moving southward along the Pacific Coast, then southeastward into the Great Basin. In contrast to polar outbreaks over the land areas of North America, this outbreak is characterized by cyclonically curved isobars at the surface. Surface temperatures are below normal along the Pacific Coast and in the Great Basin but are above normal in the East. Because of the interaction of tropical and polar air masses in an area north of normal in the East, precipitation is excessive in the Mississippi and Ohio Valleys. This type and the closely related Bn-c type

837

were responsible for the abnormally cold weather in the West and warm weather in the East during the winter of 1948-49 and also during January, 1937. Type D represents the most extreme of the meridional flow types. In this case the principal trough lies entirely off the West Coast with an unusually intense, northward-displaced Pacific anticyclone, which is merged with the cold anticyclone over Alaska. The principal outbreak of cold air is so far west that a second minor outbreak occurs downstream in eastern North America. There exists a somewhat infrequent, yet important additional meridional flow type not shown in Fig. 1. This is the C type which resembles the Bn-a type except that there is a low-latitude trough aloft just off the southern California coastline. In this way the westerlies are split into two branches, the northernmost branch moving along a crest at about 125°W and the southern branch moving along a trough at this same longitude. The two streams converge downstream. For this reason there are essentially two storm tracks, a northern and a southern track. Very heavy precipitation occurs along the southern track in southern California, Arizona, and New Mexico. The first of the zonal flow types, B, is characterized by a northerly storm track with a belt of well-developed subtropical anticyclones to the south. As a result, relatively dry and warm weather prevails over most of the United States and the southern Prairie Provinces of Canada. In the second zonal flow type, Bs, the upper-level westerlies are farther south in the East but in the West they are as far north as in type B, thus tending to accentuate the western crest. Although the Great Basin anticyclone is actually more persistent in the case of type Bs, it is considered to be more zonal than B because the westerlies are farther south on the average over a broad sector and are definitely stronger as reflected

by the greater rapidity

of

movement

of

migratory systems along the principal storm path. Types Eh, Em, and Eh are each in turn characterized by a more extensively developed polar anticyclone

and a more southerly

shift in the westerlies aloft

and

consequently in the storm tracks. The great masses of cold polar air associated with these types seldom move southward in any form of organized polar outbreak such as occurs with the meridional flow types but merely linger north of the mean frontal zone accentuating the air-mass contrast across the front and leading to excessive precipitation along the mean frontal zone itself. In the extreme Eh type the cold air occupies most of the United States and entirely blocks the eastward progress of Pacific storms beyond the Rocky Mountains.

GENERAL CIRCULATION CONSIDERATIONS

A recent study [13] of broad-scale and long-period weather processes occurring in connection with certain abnormal meridional flow patterns has supplied information providing more justification for the weathertype treatment thus far discussed. Among other things,

WEATHER FORECASTING

838 this

study was aimed at ascertaining the significance

mean flow representations not only with respect to the mean pattern itself but also with respect to the of

and more transitory disturbances going the mean flow. This involved the application of the turbulence principles of fluid mechanics to the circulation of the westerlies. Similar investigasmaller-scale

to

make up

[9, 24] have been undertaken in the past, but no attempt had been made to apply this concept through a more-or-less statistical treatment of a long record of weather data such as the forty-year Northern Hemisphere series [28]. In this treatment the smoothed -out fluctuations, the migratory and transient cyclonic and anticyclonic systems, were treated as turbulent eddies having the property of being able to transport heat

tions

and momentum across large horizontal sheets

of the atmosphere. This analysis indicated that the very large amounts of heat picked up from the oceans off the east coasts of the continents [16] are removed from the westerlies downstream through lateral turbulent diffusion so that equilibrium is maintained. In addition it showed that in years when the north-south thermal gradient is in excess of normal, the lateral mixing in the westerlies is excessive, and the cross-westerly heat transport is also excessive. In connection with excessive lateral mixing there occurred an excess of meridi-

onal flow types. The detailed analysis of the eddy motion in the westerlies indicated the existence of a spectrum of eddy periods with a mean of about six days in the heart of the westerlies and slightly higher values on either side.

The most frequent value was three days, corresponding to the mean period in the passage of cyclone families as used in weather typing. The longer-period eddies even showed a tendency towards durations which were multiples of the three-day period. Eddies of very long duration were associated with larger-than-average distortions from the normal flow pattern, with respect to both

wave length and ampli-

tude. In many cases these large eddies appeared on the surface charts as quasi-stationary anticyclones in the

middle latitudes, with trapped cyclones to the south of them. In the study these were referred to as "blocking highs" because of their action in blocking the normal eastward progress of migratory systems. In cases where such large blocking eddies exist it becomes hardly proper to treat them as eddies in the time and space scales generally involved in the extended-range circulation representation schemes. The smaller and

more frequent short-period eddies characterizing true migratory cyclone and anticyclone activity are steered around or completely blocked by these eddies. Therefore the large eddies merely serve to introduce large-

normal westerly flow on extended-range charts. In effect, these eddies tend to lengthen the closed path of the westerlies around the hemisphere and there is thus provided a longer perimeter along which the smaller eddies can act to transport heat and momentum across the westerlies. This situation corresponds to that existing in the meridional flow category discussed above. These types must then be those for which the cross-westerly heat transport is scale distortions of the

maximum, and the zonal category corresponds to the case where the girdle of westerly winds has a minimum length, at least in the regions where zonal types are in existence, and therefore represents a state of minimum cross-westerly heat transport. It is often apparent that there is a certain time lag between the development of meridional flow types in various regions of the Northern Hemisphere. This observation coupled with the known quasi-periodic alternation between zonal and meridional flow types within one type region suggests that under ordinary circumstances the zonal flow types are incapable of providing the required cross-westerly heat transport needed to balance global radiational effects, whereas the meridional flow patterns are more than adecjuate for this purpose. Since there is no dynamically stable intermediate stage, an alternation between the two circulation types results. At times the alternation seems to be in phase throughout the Northern Hemisphere but at other times this is not true. In view of the rapid dispersion of energy indicated by recent theoretical investigations [25], one might expect the in-phase condition to predominate but there is some evidence of slower modes of energy propagation in the atmosphere. Regardless of this, in any given region the action suggested is analogous to that of a relaxation oscillator, the potential, as represented by the north-south thermal gradient, building up to critical levels from time to time and then relaxing as the flow of the westerlies breaks down into meridional flow patterns. A study by Schwerdtfeger [27] indicated that in a source region for polar outbreaks the polar air may be built up to critical strength from a stage of complete exhaustion through radiation processes within a period of some three weeks. Observation indicates, however, that the at a

pulse period of outbreaks in North America is more on the order of a week (corresponding to rather largesized eddies) with a longer-period fluctuation in the

strength of the pulses on the order of a month. The would correspond to the oscillation in question

latter

but such pulsations are far from systematic and hence it seems that other events, such as perhaps variations in extraterrestrial radiation, may play an important role.

The effect of the irregular geographic distribution of oceans and continents, although complicating matters, should not in itself account for the lack of regular periodicity.

INTERACTION ON A HEMISPHERIC BASIS As was pointed out above, the most difficult step in extended-period forecasting is that involving the prediction of the movement and changes in form of the systems appearing on the extended-period representations. In the weather-type method this amounts to the forecasting of the next weather type or types. This usually involves directly or indirectly the study of large-scale and long-period weather processes on a hemisphere-wide basis. Some of these general processes which can be used in connection with extended-period forecasting by the use of weather types were set down

EXTENDED-RANGE FORECASTING BY WEATHER TYPES

839

by the author during World War II [11]. Since then, additional work has been done upon them [1, 13]. In

analogue elements with different time lags. The analogue scheme thus assumes that weather is a one-dimen-

line with the character of this article, a few very general remarks will be included covering this approach.

sional function of time.

At

times, particularly during meridional flow periods,

movements are apparent. Curiously enough, such motions frequently exhibit a westward displacement or retrogression, not so much of the individual broad-scale crests and troughs aloft but of the amplitude or energy of the disturbance. Thus, following the development of a trough and crest pair, the next major trough or crest-trough pair upstream will increase in amplitude. The rate of the propagation is some seven degrees of longitude per day in winter [1]. Sometimes this upstream effect appears to be propagated mainly through the action of the subtropical easterlies; at other times the polar easterlies appear to be the controlling factor. Other evidence [13] indicates that systematic distortions of the westerlies develop slowly over a period of two or more weeks both upstream and downstream from a major disturbance such as a blocking high. Recent theoretical studies [25, 29] of energy propagation indicate the possibility of a number of modes of energy dispersion and clearly indicate the possibility of interaction on a hemispherewide basis. This confirms much recently obtained synoptic evidence of the dependence of North American weather developments on events occurring elsewhere in the Northern Hemisphere. Considerations of the type just mentioned have been handled statistically through the use of the data appearing in the forty-six-year weather-type catalogue. Naturally the first and simplest statistical aid to be developed from the catalogue was merely the determination of the seasonal expectancies of the various types. Next came the expectancies for various types in one region following a given type. Later, the North American types were arranged in a certain order depending upon such items as the latitude of the Pacific anticyclone, strength and location of polar outbreaks, certain systematic

and natural

statistical relationship,

In statistical investigations using the type catalogue has been found necessary to consider processes of much greater duration than those covered in the usual extended-period considerations. Some rather interesting results have been found in studies of seasonal characteristics. An unpublished study shows that in a normal season the extreme meridional flow types occur frequently in the autumn but that, as winter ap-^ preaches, the frequency of their occurrence drops off it

EXTREME ZONAL FLOW TYPES (WINTER)

\

V f EXTREME MERIDIONAL FLOW TYPES (WINTER) 1

I

and numbers were

assigned in accordance with this order. Then typeprediction regression formulas were developed [8] whereby future types could be predicted on the basis of the past sequence of types in one region. Success was limited. It is believed that the greatest shortcoming of these earlier regression formulas lay in their disregard of present and past types in other zones. More recently the type data for the five zones have been punched on International Business Machine sorting cards [1], and prediction schemes based upon present and past types in each of the five zones will be developed. The use of the type catalogue in analogue selection is of course obvious. It is highly efficient in this respect but selections must be made with extreme care in order to avoid the above-mentioned shortcomings of "thumbprint" analogues. In a theoretical study [8] of "thumbprint" analogue prediction schemes it has been shown that the weakness of this system compared to a generalized prediction scheme lies in the fact that it is not possible to consider direct and cross matches between

1919

1923

1939

TO

TO

TO

1943 TO

1920

1924

1940

1944

YEAR

—

Fig. 2. Curves showing the frequency of meridional (middle curve) and zonal (upper curve) flow types during the winter seasons 1919-20 through 1943-44. The lower curve gives the annual relative sunspot numbers during the same period. rapidljr

and the extreme zonal flow types {E) increase

frequency of the meridional flow types increases and the zonal flow type decreases. Apparently, cross-westerly heat transport and general lateral mixing are greatest in the spring and the autumn. In certain j^ears there is a distinct tendency for the extreme meridional flow types to continue with high frequencies on into the winter season. Since winter meridional flow types exhibit stronger abnormalities than those of autumn and in frequency. Again, in the spring the

spring, this leads to quite exceptional weather {viz., January, 1937 and 1949) and for this reason the phenomenon was studied in detail. The effect can best be

WEATHER FORECASTING

840

demonstrated by graphing the number of days of occurrence of extreme meridional flow types (D, A, Bn-c) in the winter season (December, January, and February) for each year. This appears as the middle curve in Fig. 2. The curve for the extreme zonal flow types {El,, Em, Eh) is the top curve in the figure. These curves show quasi-periodic variations with a period of five or six years and an appreciable amplitude. The

6.

Darling, D. A., Rep. Nos. 5, 7, and Tech.-Army Air Force Res. Unit, 1944.

7.

Relationship between the Analogue Forecast and Other Methods of Forecasting. Calif. Inst. Tech.-Army Air Force Res. Unit, 1944. Report on the Accomplishments of the Statistical Project. Calif. Inst. Tech.-Army Air Force Res. Unit, 1942. Defant, A., "Die Zirkulation der Atmosphare in den gemassigten Breiten der Erde." Geogr. Ann., Stockh.,

8.

9.

two curves are out

of phase. period is suggestive of haK the sunspot cycle, and the curve of sunspot annual relative numbers is shown at the bottom for comparison. The sunspot curve is based upon the annual value corresponding to the year of the January and February portion of the

The

plotted winter-season type characteristics and hence is in effect somewhat lagged in phase from the top two curves. The correspondence between the peaks in the is

striking.

11.

12.

14.

15.

to prospects for the

improvement

of

techniques for extended-range forecasting, it is the author's opinion that two fields of investigation offer the most attraction. One of these is the study of the long-period interaction between broad-scale circulation features in different parts of the Northern Hemisphere and, for that matter, over the whole world. This, it would appear, involves the modes of energy dispersion. A joint theoretical and synoptic attack is in order.

The

ship.

16.

17.

from the viewpoint of a closed system consisting of the atmosphere and the earth, are continually occurring and require a systematic investigation of extra-

20.

21.

23.

American Institute of Aerological Research, Air

2.

3.

Institute

Aerological

Research.

Res.

Rep. No. 3, Part 2, pp. 31-44, 1949. Bowie, E. H., and Weightman, R. H., "Types of Storms of the United States and Their Average Movements." Mon. Wea. Rev. Wash., Supp. No. 1 (1914). California Institute of Technology Meteor. Deft., Synoptic Weather Types of North America.

Pasadena,

25.

5.

Preparation of a Classification Graph of Synoptic Weather Sequences for North America, January 1899 through June 1939. Rep. No. 943, Weather Div., Army Air Force Headquarters, 1945. Preparation of a Classification Graph for East AsiaWest Pacific Synoptic Region. Pasadena, Calif., 1944.

A Dynamical Theory of the Atmospheric Cirand Its UseinWeather Forecasting. Meteor. Dept.,

I. P.,

Lewis, C. H., 3000 Dynamic Meter Ideal Charts Corresponding to the Ideal Surface Types for Zone 3 and 4- Thesis, Meteor. Dept., Calif. Inst. Tech., 1947. Namias, J., Extended Forecasting by Mean Circulation Methods, 57 pp. U. S. Weather Bureau, Washington,

D. C, 1947. Pagava, S. T., and others, Basic Principles of the Synoptic Method of Long-Range Weather Forecasting, 3 Vols. Leningrad, U. S. S. R. Hydrometeor. Publ. House, 1940. (Translation prepared by Weather Information Service,

Army

Air Forces.)

S., Six Day Weather Types of North America. Meteor. Dept., Calif. Inst. Tech., 1943. Reed, T. R., "Weather Types of the Northeast Pacific Ocean as Related to the Weather on the North Pacific Coast." Mon. Wea. Rev. Wash., 60:246-252 (1932). RossBT, C.-G., "Fluid Mechanics Applied to the Study of Atmospheric Circulations." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 7, No. 1,

Paulhus,

J.,

and Blewitt,

pp. 5-17 (1938). "On the Propagation of Frequencies and Energy in

Certain Types of Oceanic and Atmospheric Waves." /. Meteor., 2:187-204 (1945). I. I., "Baur's Contribution to Long-Range Weather Forecasting, Part II." Mon. Wea. Rev. Wash.,

26.

Schell,

27.

Schwehdtpeger, W., "Zur Theorie polarer Temperaturund Luftdruckwellen." Verof. geophys, Inst. Univ. Lpz.,

28.

U. S. Weather Bureau, Historical Weather Maps, Daily Synoptic Series, Northern Hemisphere, Sea Level, Wash-

Supp. No. 39, pp. 79-87 (1940).

Calif., 1943. 4.

Krick,

Headquarters, 22.

24.

— Aiiierican

W. C, "On the Energy Exchange between Sea and Atmosphere." /. mar. Res., 5:37-66 (1942). Klein, W. H., "Winter Precipitation as Related to the 700-Mb Circulation." Bull. Amer. meteor. Soc, 29: 439-

Calif. Inst. Tech., 1942.

REFERENCES Force

(Unpublished re-

Jacobs,

culation

terrestrial effects.

1.

International Meteorological Consultants, Catalogue

453 (1948). 18.

other field involves a thorough study of the

others provide evidence favoring a real relationMeteorological events, seemingly inexplicable

and Smith, T. B., "A Study of the Effects of Large Blocking Highs on the General Circulation in the Northern-Hemisphere Westerlies." /. Meteor., 6:67-85 (1949). Gold, E., "Aids to Forecasting: Types of Pressure Distribution with Notes and Tables for the Fourteen Years 1905-1918." Geophys. Mem., 2:149-174 (1920). of Atlantic-European Weather Types.

radiational properties of the earth

many

Elliott, R. T)., Studies of Persistent Regularities in Weather Phenomena. Meteor. Dept., Calif. Inst. Tech., 1942. Extended Weather Forecasting by Weather Type Methods, 55 pp. U. S. Navy Dept., Long Range Weather Forecasting Unit, Washington, D. C, 1944. "Forecasting the Weather." Weatherwise, 2:15-18, 40-

port)

19.

and its atmosphere and the study of the effects of variations in solar output upon atmospheric motions. The example of a general relationship between solar activity and weather-type frequencies presented above is just one of many such relationships developed from studies of weather types. The works of Abbot, Clayton, and

Inst.

43, 64-67, 86-88, 110-113, 136-138 (1949). 13.

PROSPECTS FOR THE FUTURE With regard

Calif.

3:209-266 (1921). 10.

extreme meridional flow types and the sunspot maxima

and minima

7a,

(2),

29.

4:255-317 (1931).

ington, D. C. Yeh, T.-c, "On Energy Dispersion /. Meteor., 6:1-16 (1949).

in the

Atmosphere."

VERIFICATION OF

WEATHER FORECASTS

By GLENN W. BRIER and

ROGER

A.

ALLEN

U. S. Weather Bureau, Washington, D. C.

INTRODUCTION

widely accepted that this particular purpose of verification no longer is of much importance. However, the effects of this controversy still show their influence by often preventing a realistic attempt to solve some of the problems of forecast verification since some meteorologists object a priori to any scoring system that does not produce high enough figures to make the forecasts appear favorable in the eyes of the public or government appropriating bodies. Economic Purposes of Verification. Since the sole

Verification of weather forecasts has been a controversial subject for

more than

sixty years

and has

affected nearly the entire field of meteorology. This

paper will discuss some of the important reasons for this controversy and attempt to show that much of the existing confusion disappears when a careful analysis is

tion.

made of the objectives of forecasting and verificaA number of verification systems that have been

used will be described, but it is beyond the scope of this paper to make a complete survey of verification practices or of the literature on the subject. For the latter purpose the reader is referred to articles by Bleeker [1], Muller [6], and the U. S. Weather Bureau [10],

which contain extensive bibliographies. Definition of the Problem. Verification

is

is economy of life, would seem that one of the chief purposes of verification is to determine the economic value of the forecasts which have been made. But such an evaluation, especially for the whole economy, is difficult or impossible since the uses and users of forecasts are so diverse and ramified. Forecasts that may have considerable value for one user may have little or no utility for another user or may actually have a

purpose of practical forecasting labor,

usually

understood to mean the entire process of comparing the predicted weather with the actual weather, utilizing the data so obtained to produce one or more indices or scores and then interpreting these scores by comparing them with some standard depending upon the purpose to be served by the verification. In the discussion which follows, it will be assumed that both forecasts and observations have been expressed objectively so that no element of judgment enters into the comparison of forecast with observation, and it will be assumed further that errors of observation are unimportant. These assumptions are discussed in a subsequent section. The selection and interpretation of

an index or score which

will

dollars, it

negative value if their accuracy is low. The measureof the economic value of the forecast is thus a separate project for each user, and this is usually impracticable or impossible because the individual has neither the essential economic data nor the facilities to make such an evaluation. Thus a farmer may feel that an accurate weather forecast enabled him to make some saving in seed cost and planting labor, but he

ment

may be unable to estimate the cost of his o\vn labor, and the total saving might depend upon the value of the harvested crop which is, of course, unknown until harvest time. Sometimes such economic evaluation of the forecasts is possible, the necessary data being found in the cost accounting and financial structure of the particular business [2]. However, since evaluation in

meet the objectives most

of the verification study usually constitute the difficult

and

part of the problem since, as will be shown,

practical considerations often require that the score

a number of requirements and furnish informanumber of different characteristics of the forecasts. Selection of arbitrary scores intended to measure a number of parameters usually leads to difficulty in the last step, interpreting the score. fulfill

tion on a

PURPOSES OF VERIFICATION One of the earliest purposes of forecast verification was to justify the existence of the newly organized national weather services, and thus the question of verification immediately became a football to be kicked around by the supporters and opponents of the national weather services. Some, such as Klein [5], claimed that the official synoptic forecasts had little or no practical value and produced verification figures intended to prove their point. Others, for instance [7], claimed that the weather forecasts could not be subjected to rigorous statistical tests or that the tests that had been performed had no meaning. Today the value of the national weather services is so

Schmauss

841

economic terms is usually impossible, it is most often desirable to determine the reliability of weather forecasts by measuring their approach to the truth and expressing the result in terms of some arbitrary scale such as errors in degrees Fahrenheit or per cent of hits. The user of the forecast can then interpret the information in terms of his operations. Thus an electric power company may want to know when thunderstorms are forecast for a given area

and what the likelihood

is

that

on the other hand, what per cent of observed thunderstorms in an area will be

the forecast will be correct,

or,

correctly forecast.

Admmistrative Purposes of Verification. One of the most useful purposes of verification is to determine the relative ability of different forecasters. In a weather organization the relative ranks of forecasters may be desired for a number of reasons, such as selecting promising personnel for further training in forecasting, selecting able

men

for difficult or specialized forecasting

WEATHER FORECASTING

842

assignments, selecting research personnel, or rating the of the forecaster. The verification scheme adopted may apply only to the regular official forecasts made by the individual or to a special practiceforecast program. Such a program may involve people not assigned to regular forecasting and thus provide a basis for discovering hidden talent. In the classroom a efficiency

program

used to measure the progress of student forecasters and can assist the professor in vocational guidance. A student showing low forecasting ability but high mathematical ability might be encouraged to go into theoretical meteorology rather than into practical forecasting. Numerous other examples of administrative purposes of verification could be given. practice-forecast verification

is

when

applied to the official make a valuable contribution to the control of the quality of the output of the station. In industry it has been found that scientific sampling procedures are necessary to mainVerification procedures,

forecasts of a weather station, can

tain uniformity in the manufacturing process. If the forecasts

made

at a particular station over a period of

fall below the standards of accuracy that have previously been attained, administrative action to investigate the reasons for the falling stand-

time appear to

ards might be desirable. There is also a further advantage that the mere existence of a checking scheme, even if imperfect, tends to keep the forecasters more alert and interested in maintaining the accuracy of forecasts.

Purposes of Verification. One of the goals meteorology is to be able to predict precisely the state of the atmosphere at any time in the future. This goal is a difficult one to attain, but considerable progress has been made in the past several decades in understanding the physics of the atmosphere. Sometimes the question is raised as to whether there has been any increase in the accuracy of weather forecasts over a period of time. The question asked may be quite general, such as whether temperature or precipitation Scientific

of scientific

made by meteorologists in general are more accurate than they were fifty years ago. Sometimes the question may be directed at a specific group of forecasters using special methods on an experimental basis. In both these cases verification statistics can be used to provide information on the trend in forecast accuracy, although the technical difficulties in obtaining accurate

forecasts

statistics

may

be great.

When some new

advance in

meteorological theory which bears on forecasting is proposed, it may be possible to compare the verification scores of experimental forecasts made using the sup-

posed advance with forecasts made without the new theory. In this case verification is equivalent to testing the validity of a scientific hypothesis.

Another scientific purpose of forecast verification is the analysis of the forecast errors to determine their nature and possible cause. This is, in the opinion of some, the most important and most fruitful objective of verification since

it is

more susceptible

of scientific

treatment than some of the other purposes. A search may be made for indicators of forecasting difficulty

which will help to locate the synoptic situations under which forecasts are most likely to be wrong. It is commonly thought, for example, that situations where weather changes are taking place rapidly are more difficult to forecast than other situations, but it should be noted in passing that the literature does not reveal any precise studies to support this view. Likewise, although this is a widespread belief,

it

remains to be shown by

verification figures that the forecasting accuracy for

some element such

as precipitation occurrence

is

lower

which deepening or filling of a low is poorly forecast than for cases in which the deepening or filling is accurately forecast. Such verification as this can b6 for cases in

used to discover the weaknesses of forecasting systems in order to decide where research emphasis is needed.

FUNDAMENTAL CRITERIA TO BE SATISFIED Terminology

of Forecasts.

factory verification

is

One

objectivity,

essential for satis-

which requires that

the forecasts be explicitly stated, either numerically or categorically, thus permitting no element of judgment to enter the comparison of forecast with subsequent observation. But the relation between the forecaster and the public, which depends upon the forecaster's terminology, is usually subjective in nature, since even objective terms and the actual weather are interpreted subjectively by many individuals. Bleeker [1] discusses this point clearly. If every forecast is accompanied by a definition of the terms used, the forecaster sometimes objects on the basis that it hinders his freedom to express himself adequately. At this point it is easy to

about the psychology of forecasters and and many arguments in forecast verification revolve around this point. Although these are practical and very important problems to those raise questions

of the public

attempting to serve the public with weather information, they are in essence outside the field of forecast verification and the goals of verification would be reached much sooner if this were more generally recognized. Only those forecasts which are expressed in objective terms can be satisfactorily verified as forecasts.

The

extent to which public forecasts satisfy the public a different question which can be answered, it appears, only by public opinion polls; and the answer generally will contain little information about the agreement of forecast and actual weather. Meteorologists themselves sometimes advocate subjective verification, particularly in the case of prognostic charts which attempt to portray the pattern of some weather element (such as pressure) rather than to specify the weather at individual points. In some cases this has led to the use of boards of experts who compare the prognostic charts with observed charts. The difficulty in objective comparison arises because of the unsatisfactory state of knowledge as to what are the important parameters of the prognostic pattern; or in other words, the forecaster is unable to specify objectively just what he is trying to represent with a prognostic chart. In effect, the forecaster is trying to verify something which cannot be observed, hence this is

situation does not

meet the

definition of verification.

VERIFICATION OP WEATHER FORECASTS

An

extreme view denying the need for objectivity

that expressed by

Hazen

[3],

who

is

says,

make a proper verification of a weather forecast, and one that shall be rigidly applicable to every case it should one thoroughly acquainted with the average be done by conditions and he should verify from the map on which the prediction was based and not from subsequent maps. If the verification is from a subsequent map, care should be taken to consider what abnormal conditions have occurred which could not have been anticipated. .

.

.

.

,

.

Selection of Purposes of Verification. Before any satisfactory verification scheme is adopted it is necessary to determine the primary purpose or purposes to be served by the verification This may appear to be obvious, but the history of the forecast verification controversy during the past half -century makes it clear that this fundamental point has been forgotten again and again. A

adequate for one purpose may be unsatisfactory for another, just as an automobile is suited for travel over the highway but is quite inefficient for fljnng through the air. Unfortunately, much time has been wasted and much confusion has resulted from attempts to devise a verification method or single score that will serve all purposes. The very nature of weather forecasts and verifications and the way they are used make one single or absolute standard of evaluation impossible. A set of forecasts has many different char-

scheme that

is

acteristics.

Some

knowledge

of the percentage

and which are correct may serve some purposes. Usually the weather occurrences in one part of the range will seem to be more important than those in other parts of the range, and this must be considered in specifying the purpose of the verification. Thus if the set of forecasts are forecasts of temperature in a citrus grove, the characteristic which is most important may be the percentage of forecasts of temperature below freezing which were actually followed by temperature below freezing, and the percentage of forecasts which were correct may be unimportant. The situation is in important respects analogous to measuring an object, for instance a table. The table has length, breadth, height, smoothness of the top, hardness of the top, number of legs, etc. A measure of any such characteristic is of no value unless a way of using the measurement has first been established. of

the forecasts are correct,

In general, if each purpose of verification is exactly specified in advance, in the form of a hypothesi.^, not only will it be much easier to select verification scores to satisfy each purpose, but there will be no doubt as to what action is indicated by any numerical value which the verification score may have. It will often be desirable to select the purpose and the score in such a way that the result will either support or reject an a priori hypothesis.

Specifications of a Scale of Goodness. Another essencriterion for satisfactory verification is that the

tial

scheme should influence the forecaster in no undesirable way. One of the greatest arguments

verification

raised against

which

may

forecast verification

is

of arbitrary scores

may

not be the most useful becomes a question of how to define "best." That there is no unique answer to this question can be seen by considering the following example in which it is desired to verify some forecasts of minimum temperature. Suppose that on some particular occasion the probability of occurrence during the subsequent night of the various integral degrees of minimum temperature is actually known by a forecaster to be as follows: forecasts. Resolving this difficulty

... to

.

system

843

that forecasts

be the "best" according to the accepted

Minimum temperature (°F) Probability of occurrence

31

32

33

34

35

36

37

.05

.10

.15

.25

.30

.10

.05

If the forecaster is required to state a single temperature figure in his forecast for verification purposes, what

figure should

he state on this particular occasion so as

to maximize his score? There are a If the verification

sions

when the

number

scheme counts as

of answers.

hits only the occa-

forecasts are exactly right, he should

forecast 35F, since this value has the greatest probability of occurrence. If he is being verified on the basis

mean

absolute error, he should say 34F, the median frequency distribution, since this will minimize the sum of the absolute deviations. If he is to be verified on the basis of the square or root-mean-square of the error, he should forecast 34.15F, which is the mean value of the frequency distribution. Any number of such arbitrary scoring systems could be devised and they will all influence the forecaster, at least to some extent, or in effect actually do part of the forecasting The verification scheme may lead the forecaster to forecast something other than what he thinks will occur, for it is often easier to analyze the effect of different possible forecasts on the verification score than it is to analyze the weather situation. Some schemes are worse than others in this respect, but it is impossible to devise a set of scores that is free of this defect. There is one possible exception to this which will be discussed in the of

of the

section on verification of probability statements.

VERIFICATION It

METHODS AND SCORES

has been stated above that, in general, different

verification statistics will be required for each different

purpose. The discussion of various verification statistics in the following paragraphs can therefore only hint at

the use which might be made of each of the scores, since so few types of scores appear ever to have been of real value.

Contingency-Table Summaries. When forecasts are in categorical classes a useful summary of the forecast and observed weather can be presented in the form of a contingency table. Such a table does not constitute a verification method in itself, but provides the basis from which a number of useful pertinent scores or indices can easily be obtained An example is given in Table I where precipitation was forecast in three classes, heavy, moderate, or light, for thirty

made

WEATHER FORECASTING

844 occasions. verification

One of the greatest advances in forecast was made when the limits of the various

were chosen

such a

way

that each categorybased on the past climatological record. Thus there is no incentive for a forecaster to choose one class in preference to another because of purely probability (climatological) considerations. This principle, with slight modification, has been used in the verification of the Extended Forecasts of the U. S. Weather Bureau [11], and during the last war the Army Air Forces [8] devised a scheme in which thirty classes (called trentiles) were used, each class representing 3''30 of the frequency distribution based on past records of the particular element being classes

in

had an equal probability

of occurrence,

verified.

Table

I.

Contingency Table for Pkbcipitation Forecasts

Observed precipitation

VERIFICATION OF WEATHER FORECASTS of the range. Thus a forethat the minimum temperature during the night will be near 40F if the cloud cover remains but will be near 30F if the skies clear. If he is being verified on the basis of the RMSE, he might tend to

hedge by playing the middle caster

may

feel

choose 35F in cases of doubt even though he may be quite sure that the temperature will not be close to 35F. These scores can also be used to verify prognostic pressure-patterns by comparing the forecast and observed pressures or pressure gradients at a number of sample stations or points on the map. Correlations. The correlation coefficient is a sta-

which measures association between two sets of values, such as forecast and observed temperatures. One simple formula for the coefficient is tistic

r

—

Vn

NT^FiO,- (Zi^i)(Eo.-) E f\ - (E Fd'- Vn E 0] - (Z

made

correlation coefficient

is

using the other scale.

making operating decisions and is subject to abuse of interpretation, such as attaching too much significance to the value of a coefficient obtained from a small sample. It is influenced by trends that for the purpose of

exist in it

both

series so it is usually desirable to

compute

by using departures from normal.

Verification of Probability Statements. There appears to be one situation where it is possible to devise a verification scheme that cannot influence the forecaster in

any undesirable way. This

is

the case

when the

fore-

casts are expressed in terms of probability statements.

Suppose that on each in

only one of

sion

i, fii,

fi2,

of

N occasions an event can occur and on one such occarepresent the forecast proba-

r possible classes .

.

.

,

fir

bilities that the event will occur in classes 1,2, , r, respectively. If the r classes are chosen to be mutually .

.

.

r

exclusive

A

and exhaustive,

score

P

E

fij

=

1

for

each and every

can be defined by

iV

)-i i=i

En takes the value 1 or according to whether the event occurred in class j or not. For perfect forecasting this score will have a value of zero and for the worst possible forecasting a value of 2. Perfect forecasting is defined as "correctly forecasting the event to occur with a probability of unity or 100 per cent confidence." The worst possible forecast is defined as "stating a probability of unity or certainty for an event that did not materialize" (and also, of course, "stating a probability of zero for the event that did materiahze"). It can be shown that if pi, p2, ps, pr are the where

.

.

.

,

.

.

.

,

2,

r

N

.

.

.

EiP) =

To

illustrate the

1

-

E

p).

procedure consider the following

table of ten actual forecasts of "rain" or "no rain" in

which a probability or confidence statement was made for each forecast.

Table

IV.

Occasion

also difficult to interpret

1,

then in the absence of any forecasting skill the best values to choose for /,y will be p, for all occasions. This will minimize the score P for constant values of /ly = f^j = f^j and the expected value of the score will be 3,

od'

used as a verification score it has the advantage of being relatively free from the fault of influencing the forecaster in an undesirable way. However, it is insensitive to any bias or error in scale that a forecaster may have. Thus the centigrade and Fahrenheit scales are perfectly correlated, but a person would not use one

The

respective climatological probabilities of classes

Example of Forecasts Stated Peobabilitt

When

scale to verify forecasts

845

in

Teems op

:

WEATHER FORECASTING

846

When

made made

a series of forecasts has been

probabihtj^ statements, a study can also be

using to de-

termine whether the forecast probabilities are related to the relative frequency at which the events occur.

An

example of this type of comparison is shown in Table V (based on a more extended series of such forecasts) which suggests a relationship between the forecast and the observed probabilities, but which indicates that the forecaster should modify or adjust his scale to improve the forecasts. Arbitrary Scores for Special Purposes. An infinite number of scores can be devised for verification purposes, but it is beyond the scope of this paper to discuss many of them in detail. In particular cases, such as verifying the forecasts of cloud heights or visibilities, it

may seem

desirable to express errors in terms of

climatological forecasts.

Many

arguments have arisen

over the proper choice (if any) of the blind forecasts to use as a standard. There is no correct answer, of course, since the choice depends not only upon the use that is made of the forecasts but upon the purpose of the verification.

To illustrate these comparisons, let us return now to the skill score defined in the earlier section. The expected number of forecasts correct Er, based on chance or random forecasts for the data in Table I, is computed by the following formula /

Er = where Ri

is

.

RiCi

the total of the i-th row and

for the i-th column. In the

d

example given,

is

the total

this is

per cent and compute a score such as

_ where Fi

is

1

8X15 + 13X8-f-9X7

f IF. -0.1

the forecast value and 0.

9.6,

30 is

the observed

so the skill score based

tingency table

value.

In other instances, verification of selected cases in

which either forecast or observation was

&

of particular

importance may be required, or it may be desired to transform the forecasts into forecasts of change before verifying them. It is common, for example, to want to verify only cases when low visibility either is forecast or occurs, since high values are much less critical for airplane operations. It may be desired to verify only the cases when ceiling changes across the critical value, either in the forecast or in the occurrence.

=

14

30

of the con-

-

9.6

=

0.22.

9.6

If, in this same example, persistence forecasts had been made by pi-edicting a continuation of the preceding precipitation, the expected number right would have been 12, so the skill score would be

Sj,

=

With more

made on the and of the consequences of right or wrong decisions, it would be possible to devise verification scores based on the relative values of different

upon the margins

is

14

30

-

12

=

0.11.

12

intensive study of the decisions which are basis of such forecasts

forecasts, but as

it is,

the climatological frequencies of heavy, moderate,

the expected

number

right E^

is

given by the formula

practically all such specialized

verification systems are arbitrary. This

is

not intended

to discourage the use of such scores, but it should be emphasized that conclusions as to the relative values of two sets of forecasts will always be uncertain so long as the value of any individual forecast cannot be esti-

mated. Innumerable other scores to be used for some special purpose could be mentioned.

CONTROL FORECASTS FOR COMPARISON Chance or Random Forecasts, Persistence, ClimaUp to this point most of the discussion has been concerned with methods of comparing the forecast weather with the actual weather and obtaining some tology.

The final phase of the verification procedure is the interpretation of these scores, which is usually performed by comparing them with some standard. It has long been recognized that a figure such as the percentage of correct forecasts is often meaningless, since the same figure might be obtained by chance or by indices or scores.

some scheme

If

and light precipitation were P;,, Pm, and Fi, respectively,

of forecasting requiring

no meteorological

knowledge. It has been suggested that forecast scores be compared with scores obtained using various "blind" forecasts such as random forecasts, persistence forecasts, or

and E,

=

\ (30)= 10

in the example, since the three classes

were defined as equally likely. Generally, any score which may be devised can be computed for a set of control forecasts a.- well as for the actual forecasts, and a comparison can be made. Adjustment for Difficulty. When the purpose of verification is to compare a number of forecasters, a practical difficulty often encountered is that the forecasts are not comparable because they were made at different times and under different conditions. It is known that different synoptic situations present varying degrees of difficulty and it is invalid to make comparisons between forecasters working at different times unless some attempt is made to take account of this source of variation. This can be partly accomplished by finding parameters dependent on the synoptic situation that are related to the errors in the forecasts. For example, it might be found that there is a high correlation between the verification scores for visibility forecasts made by an individual and the scores obtained

by a

visibility forecast

based simply on persistence.

By

VERIFICATION OF WEATHER FORECASTS means of a regression analysis the scores S made by a mmiber of forecasters can then be adjusted to equivalent "persistence" values before making comparisons by use of the formula Sa where

S,i is

= S

-\-

b (Sp

the adjusted score,

—

S

Sp),

made by each man, but

847 since a logical combination of

it would be far better to consider each score separately. As pointed out in the section on Selection of Purposes of Verification, if it is

scores

is

in general impossible,

decided ahead of time just what measures of accuracy and what will be done with each, the need for combining scores could be largely eliminated. Another practice that may lead to difficulty is the use of overlapping classes for verification purposes. Thus rules may be set up stating that a ceiling forecast of 200 ft will verify if the observation is between 100 and 400 ft, and that a forecast of 400 ft will verify if the observation is between 200 and 800 ft. Although such are needed

the unadjusted score,

Sp the persistence score corresponding to *S, Sp the mean persistence score, and b the average within regression of forecast score on persistence score. This procedure can be generalized to take account of two or more parameters measiu-ing difficulty. Forecast-Reversal Test. useful and simple procedure that can often be used to advantage might be called the "forecast-reversal" test. Suppose that a longrange forecaster claims he can pick out a year in advance the days of the month upon which rain will fall, provided a "tolerance" in timing of one day in either direction is allowed. On this basis some arbitrary verification is proposed which appears to give a relatively good score when applied to some actual forecasts. In the forecast-reversal test the same arbitrary verification procedure would be used, but the forecasts would be reversed with "rain" days being called "no-rain" days and vice versa. If approximately the same verification score were obtained on the reversed forecasts, one would be led to suspect either that the forecasts had no merit or that the verification scheme had no merit, or both. If this procedure were more generally used, especially for long-range forecasts, probably fewer claims would be made by long-range forecasters. It would also probably result in the selection of more sound verification schemes for use in determining the accuracy of such forecasts.

A

PITFALLS OF VERIFICATION There are many pitfalls of verification to entrap both the novice and the expert. One of the greatest dangers lies in attempts to compare the relative abilities of forecasters on the basis of forecasts which are not comparable because of differences of location, season, time of day, length of forecast interval, etc. The reason for this is that the degree of forecasting difficulty varies so much from one circumstance to another that a very large sample of forecasts is needed to assure that the average weather has been approximately the same in the two sets of forecasts being compared. Even if the forecasts being compared are for the same event, there may be other factors to be considered, such as whether equal map facilities were available to each forecaster. Interpretation is made even more difficult when scores on two or more forecast weather elements are arbitrarily combined to form a single index to be used for comparison purposes. It may be true, for example, that

some particular use of a forecast for which an error of 2° in temperature is equivalent to an error of

thei'e is

may seem

reasonable they tend to encourage by choosing the classes having the widest range. Also, the choice of rather wide tolerances in verification limits tends to give rather high and uniform percentage scores to all forecasters, thus failing to discriminate between the better and poorer forecasters. Since the use of a contingency table for comparing forecasts and observations presents the data in one of the most useful forms, the practice of using overlapping classes is to be discouraged because such verification cannot be displayed in this way. rules

forecasters to hedge

FUTURE RESEARCH The preceding

discussion has emphasized that verifi-

than has been thought and that the lack of recognition in the past of the various and diverse objectives of verification has been the real obstacle to progress. One of the most promising fields cation

is less difficult

of study in this connection is that of setting up realistic problems to be solved and selecting scores which would furnish the desired information. Such studies might profitably be conducted in collaboration with administrators who need to select or ranlv forecasters; with economists or business advisors who need to know the effect of weather on operations and who are in the best position to determine what characteristic of the forecasts is related to profit and loss factors, or with meteor-

ologists

who know what

characteristic of the forecast

useful for verifying scientific hypotheses. This appears to be a field of study in which private meteorologists is

should play a very important role, for their knowledge of the real uses which can be made of weather forecasts should be invaluable in specifying the questions which need to be answered by verification. On the scientific side of verification, the relation of forecast error to measures of forecast "difficulty" needs further investigation. If measures relating the synoptic conditions to forecast errors can be found, it would not only assist in the comparison of forecasts made at different times, but would also provide information as to where applied meteorological research is most needed and might contribute to fundamental knowledge of atmospheric processes.

certain that

Investigations regarding the effect of verification sys-

any other) arbitrary weighting is not tz'ue in general Those who must make a selection between forecasters Ijased on verification scores may demand a

tems on the forecaster are needed since very little concrete evidence on this point is available. In this

0.25

in. in

a precipitation forecast, but

it is

this (or

single index to represent the verification of all forecasts

connection the use of probability statements in forecasting needs to be explored in more detail, for if such

'

WEATHER FORECASTING

848

statements can be verified without influencing the forecaster in any undesirable way, an important objection to verification is removed. Furthermore, forecasts expressed in this manner might very well be more useful at the same time. As was stated in the section defining the verification process, it has been assumed that errors of observation are unimportant in practical verification. This is not always the case, and further investigation of the effect of such errors is needed. Most weather forecasting is so far from perfect that forecasting errors far overshadow observational errors, but exceptions may be found, for example in visibility forecasting and perhaps in other cases. There are many other unsolved problems in verification, but on careful analysis it appears that most of them are meteorological in nature. As long as our knowledge of the physics of the atmosphere remains so incomplete this state of affairs will be reflected in the verification problem.

3.

2.

Bleeker, W., "The

Verification of

a.,

Meded. ned. meteor Inst., (B) Deel 1, Nr. 2 (1946). Bbiee, G. W., "Verification of a Forecaster's Confidence and the Use of Probability Statements in Weather Forecasting." U. S. Wea. Bur. Res. Pap. No. 16 (1944).

Verification of

Weather Forecast"'

Heidkb,

7.

p., "Berechnung des Erfolges und der Giite der Windstarkevorhersagen im Sturm warnungsdienst." Geogr. Ann., Stockh., 8: 310-349 (1926). Klein, H. J., "Misserfolge des staatlichen Wetterprognosendienstes in drei Monaten seines Besteiens." Gaea, Koln, 42:641-652 (1906). MuLLER, R. H., "Verification of Short-Range Weather Forecasts (A Survey of the Literature)." Bull. Amer. meteor. Sac, 25: 18-27, 47-53, 88-95 (1944). ScHMATJss, A., "DieTreffsicherheit der Prognosen." Wetter,

8.

U.

4.

5.

6.

28: 68-71, 167-168

9.

S.

(1911).

Army Air Forces Headquarters, Weather

Infor-

mation Branch, Short Range Verification Program. Report No. 602, Washington, D. C, 1943. U. S. Army Air Forces, "Critique of Verification of Weather Forecasts." Air Wea. Serv. Tech. Rep. No. 105-6 (1944). S. Weather Bureau, Methods of Verifying Day-to-Day Weather Forecasts. Report by the Special Committee on Forecast Verification. Washington, D. C, 1940 (un-

10.

U.

11.

WiLLBTT, H. C, Allen, R. A., and Namias, J., "Report of the Five-Day Forecasting Procedure, Verification and Research as Conducted between July 1940 and August 1941." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 9, No. 1, 88 pp. (1941).

published)

Weather Forecasts."

"The

Atner. meteor. J., 8: 392-396 (1891).

REFERENCES 1.

Hazen, H.

.

APPLICATION OF STATISTICAL By

METHODS TO WEATHER FORECASTING

GEORGE

P.

WADSWORTH

Massachusetts Institute of Technology

must seem very odd

to the layman and to the not connected with the field of meteorology that so little practical progress has been made during the last decade in the all-important problem of weather forecasting. This defect is particularly conspicuous when such phenomenal advances have been made in the field of nuclear physics and thermodynamics. However, it is necessary to spend only a moderate amount of time examining observational data of the meteorological elements to understand that the It

scientist

who

It might however be said that it is impossible for dynamics to exist and be really significant and not be brought out by a proper statistical examination of the relevant quantities, and in fact, techniques available in the statistical category have the added advantage that it is unnecessary to make many simplifying assump-

is

tions in order to yield relevant information concerning

problem is much more difficult in many of its aspects than those considered in most allied fields. If we regard the atmosphere as a dynamic model, it soon becomes apparent that the whole process behaves as a complicated mechanism in which past and present values do not determine the future as in most linear processes, but they themselves have an effect upon the system which in turn produces nonlinearity of a very peculiar type. It is with this phenomenon that the meteorologists

,

must contend.

There seem to be only two ways which are available to solve the problem of the motions of the weather systems and therefore the problem of weather forecasting: one is the dynamical approach and the other is the statistical approach. Oftentimes one thinks of these two methods as conflicting programs but actually they are attempting to get at one and the same thing. In the dynamical approach the laws connecting various meteorological phenomena are investigated. These laws are considered to be precise in action even though the data are subject to fluctuations which are random and are thus necessarily incomplete. On the other hand, in the statistical approach the quantities are taken as they are found and the distributions examined both singly and in such combinations as one chooses for the purposes of investigation. In an ideal survey all possible statistical parameters would be considered and not merely a partial selection, but such an undertaking is impractical because of the sheer magnitude of the task. If, however, there exist among the statistical parameters a few which are connected by sharp dynamic laws, then some of the parameters would be determined by a knowledge of the remainder, and the djmamics would be obvious as a statistical fact. The failure to date of statistical methods to contribute markedly to the progress of meteorology may have been due to one

the meteorological phenomenon. At this point it cannot be too strongly emphasized that the use of statistical techniques for the solution of the behavior of the weather systems is equivalent to the setting up of equations of motion and obtaining the solution. The use of generalized harmonic analysis (discussed in a later paragraph) as a method of attack on the problem has the advantage that it automatically takes care of data which have superimposed a random component upon the dynamic motion. In other words, it is a technique which is especially designed to handle situations where, because of ignorance, there has to be omitted a certain number of factors which can be considered in combination as a random phenomenon superimposed on the dynamic movement. There is no doubt that the ideal way to solve any dynamical problem is to set up a physical model in terms of mathematical symbols and, after having solved the resulting mathematical model, to use statistical methods to solve for the basic parameters. However, if the mathematical model does not contain all of the variables which are actually important, the attempt to solve for the parameters

by

result,

statistical

and

it is

methods

^vill

give

an unreliable which

for this reason that a technique

takes account of this unkno^vn group of variables is very appropriate for this problem. An example of such a situation would be one in which the phenomenon in which we were interested had a displacement y given

hy y = A sin kt. Superimposed upon this oscillation might be a group of frequencies which had periods entirely different from those of the phenomenon. This group of frequencies would have been reflected in our observations since they each enter the picture for short periods of time and more or less at random. It would be extremely difficult by observing a small section of the data to fit the parameters A and fc, the constants

However, a statistical analysis would successfid in separating the basic signal

in our equation.

be

much more

from the random

noise.

These parameters have been observed so inac-

perhaps during the last ten years that an added impetus has been given to this method of approach because of the growing conviction on the part of many investigators that the problems of the general circulation and of specific forecasting were not to be solved in the near future by the usual dynamic methods.

curately that they are not in fact the significant parameters of the dynamics.

This is reminiscent of other physical sciences wherein, at the beginning, a conceptual foundation was borrowed

or

more 1.

of three facts:

The parameters

It is

in the analyses to date are

not

the important ones. 2. The parameters considered are number to give us a true picture of the

3.

insufficient

in

operation.

849

WEATHER FORECASTING

850

from physics and mathematics, but it was only after extended programs of experimental work had been carried out that the subjects progressed independently

and produced the astounding developments which have occurred in the last century. A continual succession of experimentation, followed by new theory to explain the results obtained, and then a new period of experimentation, has characterized the development of most of the physical sciences. Unfortunately, meteorology is not in the same position because it is impossible to

conduct experiments with controlled variables since no formal method for the inclusion of all the pertinent variables into a single mathematical system has yet been found as a substitute for experimental control. Thus the most powerful techniques which have been used in the development of other physical sciences are not available to the meteorologist at the present time and he must search elsewhere for his method of attack statistical

methods mean the neglect of root causes and the substitution of shadow for substance. To be sure, statistical methods often lead to useful rules of thumb even when absent, but these rules should never be regarded as anything but makeshift. Doubtless the facility with which empirical recipes can qualitative understanding

is

be invented, together with a natural human tendency to let well enough alone, has engendered a willingness on the part of some statistical practitioners to content themselves with ersatz. But we do not hold medicine in contempt because of quackery, and it would be fallacious to condemn statistics on account of superficiahty. It is perfectly true that at the present time too many meteorologists and statisticians attempt to indulge in an orgy of correlation analysis. Because the processes which they are examining lack the property of being stationary, results are obtained which are inconsistent from one period of time to the next. This difficulty becomes less and less important if a certain

amount

field of

what might be termed

stationary

which motivate the series itself is assumed constant from one period of time to the next. Considering the characteristics of these time series

by themselves, we note that the sequence of observations has certain inherent dynamic properties as well as a superimposed random component. This random component may well be due to other variables not considered. The actual statistical problem is to separate the djTiamics from the random element so that the dynamics can be studied and classified. This situation

is

entirely analogous to a similar one encountered is transmitted by mechanical or elecmethods. In this case, the signal frequently

when information trical

becomes distorted and when this distortion phenomenon is of a purely random statistical nature it is called "noise." Hence, as also in weather phenomena, the thing that

upon

this formidable problem. According to a prevalent misconception,

done in the

time series. In this type of series the actual dynamics

we

observe, or the message, contains the

original signal plus a is

random

to isolate the signal

noise, and the problem from the message.

In the case of pressure,

if

we

consider the sequence

the behavior is analogous to the response of a sluggish oscillator to a series of impulses, where the dynamics are represented by the parameters of the oscillator. Because the oscillator is sluggish, the effect of the impulse at any one time is not immediately worn off but is carried over to affect the pressure at a future time. Even the random components, introduced probably by the variables not considered, affect the future value of the pressure variable since they are equivalent to an additional impulse on the oscillator. The problem of weather forecasting can therefore be thought of in the following terms: In Fig. 1 the solid of values as a continuous function,

of physical reasoning is the basis for the cor-

and as time goes on and more is understood about the phenomenon, this operational approach of examining the physics of the situation will correct much of the condemnation which is now directed at statistical studies. Thus the future of meteorology depends decisively upon an enlightened and energetic use of this important tool.

relation;

The

primarily interested in the beas a function of time, and all his observations are either taken continuously in terms of this variable or are taken at discrete points meteorologist

havior of his

Fig.

is

1.

— Schematic time series.

phenomenon

along the time axis. Each one of the series, therefore, which are considered in the problem of prediction of single meteorological elements or combinations of them can be looked at from the time-series point of view. Since the beginning of World War II, considerable impetus has been given to the development of generalized harmonic analysis because of its importance in the analysis of time series which occur not only in the

some meteormight be past values of the pressure at a single station or even a characteristic of an entire synoptic map. By analyzing this sequence from some period of time in the distant past up to the present time io, the predictable part of this sequence is to be determined. This predictable part represents the true dynamical component, and it is this component which permits one to extrapolate the hne represents the past performance ological phenomenon a. For example,

of it

weather problem but also in

solid line into the future to give a prediction (dotted

is

line).

all fields where prediction important. Unfortunately, most of the work has been

Naturally, the further one extends this prediction

STATISTICAL METHODS

AND WEATHER FORECASTING

the worse the agreement is between the predicted and actual values if there exists a random component. In other words, even after the entire past of all the variables has been exploited, there may exist an upper limit to the attainable accuracy of prediction; this limit

decreases as the forecast period increases. The complete problem, then, is the consideration of an ensemble of such sequences, all of which are known in the past up ,to a specific present time ta, and, regarding them as a group, the evaluation of that component which represents the true mechanism through which the phe-

nomenon

is

operating.

In the theory of generalized harmonic analysis as it affects the prediction of time series, we are approaching the problem from a more general point of view than either that of harmonic analysis, where only certain frequencies or periodicities were assumed to be present, or that of difference equations where a differential relationship is assumed connecting present and past values of the time series. In generalized harmonic analysis, advantage is taken of the entire spectrum of frequencies, and this spectrum in most geophysical phenomena does not consist of a series of discrete lines (exact frequencies) but rather of a continuous distribution of frequencies over the entire range of frequency, usually from zero to infinity. This technique permits us to develop the best linear operator in a very general sense in order to predict the future. Actually, it is this ability to predict which expresses how much dynamics there exists in the series. The linear operator is a weighting function which is applied to past values of a time series in order to obtain estimates of future values, and this weighting function is determined mathematically in such a way that the mean square error of prediction is minimized. Actually, of course, this technique can be extended to more than one variable, and thus many time series can be considered simultaneously.

Unfortunately, the basic arguments and ideas are true only if the process or processes are stationary. This, of course, cannot be true in meteorological phe-

nomena

since the basic movements of the weather systems certainly are different, at least from season to season. To a certain extent this lack of stationary property can be overcome by dividing the data into what might be termed more homogeneous periods, but, nevertheless, this difficulty is inherent in a simple analysis since the seasons themselves do not arrive and leave at any fixed time. Another factor which markedly affects the analysis of time series of this type is the fact that most of the elements have definite trends which are functions of the time of year. It is always possible to compute what might be termed a normal by averaging over a large number of years, but it is extremely doubtful whether this normal has any particular significance for a specific year. The dynamics are determined by the movement above and below a state of equilibrium ^\-hich might be called the noimal for a specific year, although it unquestionably is different from the over-all normal for all years. The shift of this trend line from one year to the next has a very marked effect upon the dynamics. Since it is necessary

851

to deal with relatively short periods of time in order to obtain compatible data,

it is very hard to separate that part of the spectrum which deals with long-period phenomena from the short-period oscillations which tend to dominate a rather minute portion of the entire

record.

Actually, of course, the solution of a nonstationary series has no meaning in the strict sense. The problem is to make the time series approximately stationary through appropriate changes in variables as a function of time. This approach will be increasingly successful as a clearer understanding of the mechanics of the phenomena is attained. In order to appreciate the immensity of the task of solving this problem, let us review briefly what is known about the behavior of

time

basic

some

of the meteorological elements, utilizing the sim-

ple hypothesis of a stationary time series,

what can be gleaned from

and consider

this information as to possible

future courses of fruitful action. One often hears the statement that abnormally warm winters and cold winters recur in a definite cycle. On this basis

one might expect to find long-term effects

in the analysis of the frequency-density function of

average monthly temperatures taken, of course, as deviations from normal. If one considers either the monthly temperature or the daily temperature at any one particular locality, it may be regarded as an individual time series in itself. Actually there exists on the average a correlation of only about 0.35 between the predicted and observed values when one predicts one month in advance. This accounts for only around 10 per cent of the variability, implying merely that there is slightly more than a 50-50 chance that if the present month is above normal the next one vnW also be above nonnal. No matter how far one goes back in the past to obtain iirformation (which means no matter how high an order of a linear differential equation one considers as representing this

phenomenon) no additional

information seems to be available, so that the past of the sequence has practically nothing to do with the future. Naturally other variables exist which might improve this situation, but we are dealing with a phenomenon which in itself shows no statistical regularity as far as long cycles are concerned. On the other hand one may be interested in a daily 24-hr forecast of temperature. 1? one restricts the mechanism to a given month during the year, a developmental sample based on four or five years will give a good estimate of the linear operator. In a 24-hr forecast, a correlation of about 0.75 between the predicted and actual values can easily be realized. Furtheraiore, interestingly enough, this same correlation will be obtained if one picks any other year at random for the same month and applies the operator to this other year. This shows that there exists a certain amount of high-frequency oscillations which are similar from year to year and actually represent dynamics in the time series. In other words there exists a true signal which can be separated from a disturbance which we know nothing about but designate as random noise. The properties of the air mass can be introduced by considering a network of

— 852

WEATHER FORECASTING

and using the entire group as predictors for an individual station. Correlations as high as 0.97 for 24 hr and remaining between 0.80 and 0.90 for 48- and 72-hr intei'vals show that a certain degree of statistical regularity is demonstrably present. Despite these high stations

much to be desired, seems incapable of detecting sudden changes in weather regime. Unfortunately, nonlinear techniques, in the elementary sense, have not yet succeeded so that it is impossible to improve the forecasts without some form of subjective analysis, such as a sjTioptic classification of the regime. Unquestioncorrelations, the forecasts leave

for the linear operator

ably there exist additional variables which, if clearly understood, would change the linear dynamics slightly from year to year and permit better predictions. Equivalent studies have been made on pressure, including daily mean pressures, nonoverlapping fiveday means, and running averages taken over five, fifteen, and thirty-one days. No long-term predictable components in any one of these time series taken at many localities over the Northern Hemisphere ever produced spectra which would indicate any long-term periods. Once again, networks involving a group of stations surrounding the one to be predicted give the best daily predictions. Correlations in the neighborhood of 0.70, which remain stable from year to year, indicate the order of the linear component, while four or five stations surrounding a given station at a distance of about 500 mi seem to produce all of the dynamics of a linear type which is in the network. Thus, increasing the network of stations either in number or in radius seems in no way to increase this predictability. Studies of this nature seem to afford ample proof that the synoptic situation expressed in terms of present temperature, pressure, humidity, etc., does not uniquely determine the future distribution and that the behavior of the pressure distribution outside this ring of 500 mi does not have much influence upon the future of the pressure at the center of the ring. Furthermore, if a forecast is made for 24 or 48 hr in advance by predicting a group of stations individually (considering each one as made up of an individual network), the correlation of the actual predicted map with the observed conditions is not much better than the correlation that one would obtain between predicted and observed pressures at an individual station. This indicates that the errors of forecast are correlated over the entire country and that we are not making a series of individual random predictions. The fact that the errors prove to be highly correlated means, of course, that an outside influence has moved into the picture and that all of the mechanisms fail to predict simultaneously. This brings out rather clearly the concept of changes in regimes in the entire weather pattern, followed again by a stabilization of whatever linear component exists. Once the regime has established itself, pressure changes of considerable magnitude can be forecast quite accurately, but the physical bases for the changes must already exist within the network. Six principal conclusions can be arrived at through a close analysis of

pressure forecasting utilizing straightforward statistical techniques: (1) The performance of the linear forecast

from year to year is stable in that the mean errors of prediction show no significant difference between years and the root-mean-square errors are homogeneous, (2) a small network is adequate, (3) errors cannot be ascribed to improper weighting of the predictors, (4) it is extremely doubtful that linear prediction can be improved upon by using fixed functions of higher deand therefore additional variables not considered

gree,

at the present time are important, (5) the errors in the by a failure to indicate

forecast are not caused primarily

pressure changes as such, but rather

by an inabihty

to

predict extreme values whether they represent changes from the initial situation or not, and (6) statistical

same circumstances that synand apparently for the same reasons. In order to give a little more background to the

forecasts fail under the

optic forecasts

fail

direction that future research should follow, let us

consider for a moment the combined motion of the four major centers of action for the North American continent, namely, the semipermanent highs and lows

the Atlantic high, the Pacific high, the Icelandic low, and the Aleutian low. It is in the motion of these centers of action that one can first observe the fact that considerable dynamics exists in the atmosphere and that it is not a i-andom phenomenon nor anywhere near random. If we consider any one of these cells as the one to be predicted and utilize its past and the present and past of the other three cells as predictors, prediction for a considerable time in advance is possible for any particular year. One can think of this prediction process, of course, merely as a reproduction of the data after the fact, but nevertheless the reproduction of the data by means of the operator is so starthng that it deserves notice. Both the spectra obtained from the autocorrelation functions and those obtained from the cross-correlation functions are extremely active, showing that the density of frequency is located in rather narrow bands. The graphs of these spectra are, however, quite different from year to year, indicating that we are dealing with a phenomenon which has certain specific characteristics at any one time but that these characteristics vary from year to year because of some outside influence. The sharp spectral characteristics which occur in these control cells unquestionably lead oftentimes to the wrong conclusions, namely, that periodicities exist in the atmosphere in the sense of being true line spectra. For periods of time, therefore, one can observe certain fluctuations of these meteorological elements and erroneously conclude that there is a law, perfectly determined, which is influencing their behavior. This is the clearest indication of why it is possible to tie up cycle theory with weather phenomena of various types, particularly for specific short periods of time.

Although a large amount of work has been done by investigators in computing correlations of pressure at one point in the atmosphere with that at another point, correlations of precipitation and tem-

many

STATISTICAL METHODS

AND WEATHER FORECASTING

perature with the forward movement of ice in the North Pole region, etc., the iUustrations set forth in the preceding paragraphs give a picture of about the order of magnitude of the results which one can expect to find in setting up linear hypotheses involving pressure, temperature, humidity, etc., either singly or in combination and at one station or in the network. With this background, I should like to discuss possible future courses which statistical analysis can follow toward the solution of this complicated situation involving

dynamics and thermodynamics. Perhaps one of the greatest contributions which statistical methods can, at the moment, make to the field of meteorology is in the classification of climatological information. It is well known, for example, that the forecasters in the short-range verification program during World War II greatly improved their accuracy

by being given the probability

of the occurrence of the events for which they were forecasting. This climatological information, however, is only part of that which is available to the forecasters to improve their forecasting techniques. There exist certain statistical laws which hold individually for all climatological elements

for all possible locations. These relationships have very profound efi^ects upon the distribution of these elements for a given week or a given month and are entirely different from the over-all distributions that

and

are at present given as the climatological expression of the variability. It is the peculiar behavior of these daily, weekly, monthly, and seasonal distributions at various localities which are the real characteristics of the climatology and could be extremely useful in imderstanding better the weather processes themselves and also in impro\'ing the forecasts at a particular location. Thus a re-evaluation of the whole method of presenting the climatology of various localities and the individual behavior of climate during reasonably short periods of time at a particular locality might do much to increase our knowledge concerning the general behavior of the circulation. In fact, it might be stated

that

if

the basic characteristics of the climatology were

on a Northern Hemisphere map, obvious simultaneous relationships could be studied and the whole forecasting problem could be reduced to a group plotted

of

much more

A

specific questions.

great deal of thought has been given

meteorologists to the use of analogues as a forecasting.

The

basic

by many method of

argument against the use

of

weather never follows exactly the same pattern. However, in the light of past experience in forecasting by statistical methods, it is obvious that in order to progress much further it is going to be necessary to find a way of classifying the dynamics. Dynamic classification might be achieved through the use of analogues, and in that event it should be possible to utilize the correct statistical operator for the prediction mechanism. Many attempts have been made by various people to express the dynamics of a present system in terms of some linear combination analogues

is,

of course, that the

853

of the d3aiamics of past experience or similar situations. This seems to be extremely logical. One can set up a practical analogy. An engineer wishes to determine the dynamics of a particular machine which, for some reason, he is unable to analyze completely. It might, however, be possible for him to analyze three or four machines which are similar to the original machine but differ in some minor details. It is then quite possible that by observing the dynamics of the similar machines he may infer how the machine in question will behave and operate. Actually if the dynamics are changing, in the sense of the series' being nonstationary, about the only way that one can judge what these dynamics might be in the future is through the use of such a technique. Our failure up to this time to extrapolate the dynamics properly from the kno^vn situations is probably due to the fact that the parameters used to express the S3m.optic picture are not dynamic in themselves. It is therefore necessary for us to solve more completely the follo^\ang problems: 1. Parameters must be found that will adequately classify the static picture of the weather situation over a large area. They should represent the general features, particularly the flow patterns, over a region even though they might not bring out every individual detail. The analogue technique calls for a classification in terms of a general fiow pattern, and such a classification would tend to eliminate the influence of extremely random fluctuations which hinder progress in fathoming the dynamics. Whatever parameters are used should maximize the discrimination between different synoptic situations. 2. Parameters should be found which actually classify the dynamic features of large areas. Ha^ang real physical significance, they would have some chance of being associated vnth both the static picture and the dynamic processes of the weather elements over an

area. 3.

The

relationship between the static

and dynamic

properties of the parameters should be distinguishable so that it would be possible to go from one to the other

and realize what is important from both points of view. Because the entire Northern Hemisphere affects the weather patterns at one single locahty, it would seem advisable to attempt to make these parameters of a Northern Hemisphere character. If the characteristics of the general flow could be determined by examining the d3mamics of past situations and extrapolating them in order to obtain the dynamics of the present one in the correct manner, then it is entirely possible that the network theory of simple linear hypothesis would be sufficient to predict the individual \\'eather at various

by the use of an operator fitted to a correct dynamic model. Although none of the problems mentioned above have to my knowledge been solved as yet, there are localities

certain specific conclusions about analogues in general which seem to indicate that the method holds some hope for future development: (1) When the correlations between the seciuence of past and current maps main-

WEATHER FORECASTING

854

Thus

tain themselves with a reasonable value for at least

three days, the analogues are, on the average, synoptically and kinematic ally sound, (2) for the purpose of

making long-range

forecasts

up to ten days' duration

there usually exists one analogue which gives a precipitation forecast as good as, if not better than, the present 24-hr forecast (this, of course, is after the fact,

and at the present time no method is available for detecting such an analogue in advance), (3) there are indications that certain previous temperature distributions aid materially in picking that analogue, and (4) maps which show the same general movement of the good analogues. In order to determine why it is that the major centers of action have such variable dynamics from year to year, it may be desirable to examine more carefully variations in sea-surface temperature. Preliminary studies have indicated that in certain regions the sea surface has undergone rather marked changes in temperatures and that the variation of the difference between the air temperature and the water temperature shows considerable change from year to year. Since the water temperature is a very persistent phenomenon, these long swings of above and below normal over a period of many months may have considerable influence on the behavior of the weather. Also, since about three-quarters of the world is ocean, perhaps too little thought has been given to these variations as potential sources of the fluctuations in the dynamics of the weather system. There are, of course, many variables which should be considered in attempting to get a complete statistical model, particularly in light of the fact that we are dealing with a servomechanism. The low-pressure area produces the clouds, the clouds change the energy input, the change of the energy input causes a change in the energy of the system, and that in turn affects the movement of the low in its future course. Sunspot activity, variations in total pressure over the poles and over the equatoi-ial regions all these must contribute their part. It therefore seems advisable that investigations utilizing the statistical approach be greatly increased so that more and more information will be available, thus clarif3ang the nature of the phenomenon with which we are dealing. As this statistical information establishes the variables which have dynamic properties, it should be possible to set up mathematical models on the bases of reasonable hypotheses inferred from the observational facts, and in this way we may hope that the final solution of the weather forecasting problem will be reached. On the other hand, it might develop that meteorology is faced with a situation analogous to that treated in the kinetic theory of gases, wherein the behavior of an individual molecule is impossible to predict, and only certain average features of all the molecules can be computed. Nevertheless, if the problem has to be reduced to this type of conclusion, it would at least be possible to estimate the respective probabilities for the occurrence of each possible state. essential features are usually

—

it

appears that

if

the general forecasting prob-

lem of meteorology is to progress as rapidly as possible toward its solution, meteorologists and statisticians should combine their efforts in a more united fashion. It is clear from the type of problem with which we are dealing that it is only through the statistician's understanding the meteorological point of view and his being able to understand and utilize the experience of the men who have been watching the progress of weather situations for a long period of time that he can be effective. Reciprocally, the meteorologist cannot take advantage of statistical techniques which would be of great material aid until he himself understands the basic principles upon which the techniques are based and also understands what the statistician wishes to accomplish.

REFERENCES In the following publications the reader will find an account of applications of statistics to weather forecasting. 1.

Baur,

F.,

Einjuhrung in die Grosswetterkunde- Wiesbaden,

Dieterich, 1948. 2.

"Der gegenwartige Stand der meteorologischen Korrelationsforschung." Meteor. Z., 47:42-52 (1930).

3.

"Die Storungen der allgemeinen atmospharischen Zirkulation in der gemassigten Zone." Meteor. Z., 54:437444 (1937).

4.

Darling, D.

A., Report on the Accomplishments of the Statis-

tical Project.

Calif.

Inst.

Tech.-Army Air Force Res.

Unit, 1942. 5.

6.

7.

Relationship between the Analogue Forecast and Other Methods of Forecasting. Calif. Inst. Tech.-Army Air Force Res. Unit, 1944. Elliott, R. D., Extended Weather Forecasting by Weather Type Methods. U. S. Navy Dept., Long Range Weather Forecasting Unit, Washington, D. C, 1944. Haurwitz, B., "Final Report on the Use of Symmetry Points in the Pressure Curves for Long-Range Forecasts." U. S. Air Force, Air Wea. Serv. Tech. Rep. No. 105-7 (1944). J., Extended Forecasting by Mean Circulation Methods. U. S. Weather Bureau, Washington, D. C,

8.

Namias,

9.

ScHELL,

1947.

to

I. I., "Dynamic Persistence and Its Applications Long-Range Foreshadowing." Harv. meteor. Stud., No.

8 (1947). 10.

Schmauss,

a., "Synoptische Singularitaten." Meteor. Z.,

55:385-403 (1938). 11.

Schumann, T. E. W.,

Statistical

Weather Forecasting.

Meteor. Res. Bur., Pretoria, Un. of South Africa, 1947. 12.

Starr, V. P.,

A

Physical Characterization of the General

Circulation. Dept. Meteor., Mass. Inst. Tech., Rep.

No.

General Circulation Project No. AF 19-122-153, Geophys. Res. Lab., Cambridge, Mass., 1949. Wadsworth, G. p., "Short Range and Extended Forecast1,

13.

ing by Statistical Methods." U. S. Air Force, Air Wea.

No. 105-38, 1948. Analogue Techniques in the Forecasting of Rainfall. Geophysical Research Directorate Reps. No. 1, 2, and 3, 1948; Dynamics of the Semi-permanent Pressure Cells, Serv. Tech. Rep.

14.

Rep. No.

4,

1949; Further Analysis of

Pressure Cells, Rep. No.

5,

Dynamics of Major Major Pres-

1949; Position of

STATISTICAL METHODS sure Cells in Relation to Rainfall, Rep. No. 6, 1949;

Search for Pertinent Parameters

AND WEATHER FORECASTING A

Pressure Distributions, Rep. No. 7, 1949; Statistical Prediction of Migratory North American Anticyclones. An Introductory on-Stationary Time Series in Weather, Attack upon the to

Classify

as Aids to Forecasting." Quart. J. R. meteor. Soc, 72:265283 (1946). 16. Wiener, N., Extrapolation, Interpolation, and Smoothing

Time Series. Cambridge, Mass., Technology Press of Mass. Inst. Tech.; New York, Wiley, of Stationary

N

Rep. No. 8, 1950; Preliminary Studies on Variations of Sea Surface Temperatures, Rep. No. 9, 1950. Contract No. W28-099-ac-398, Mass. Inst. Tech., Div. of Industrial Cooperation, Cambridge, Mass. 15.

Walkeh, Sir Gilbert

T.,

"Symmetry Points

in Pressure

855

1950. 17.

C, and others, Final Report of the Weather Bureau-Massachusetts Institute of Technology Extended Forecasting Project for the Fiscal Year 1948-1949, 109 pp. Cambridge, Mass., 1949.

WiLLETT, H.

TROPICAL METEOROLOGY Tropical Meteorology by

C. E.

Palmer

Equatorial Meteorology by A. Grimes

Tropica] Cyclones by Gordon E.

Dunn

Aerology of Tropical Storms by Herbert Riehl

859 881

887

902

TROPICAL METEOROLOGY By

C. E.

PALMER

Institute of Geophysics, University of California

INTRODUCTION: THREE METHODS OF ANALYSIS

from that in higher latitudes only in having a higher temperature and an easterly instead of a westerly mean wind direction. The dynamics, and by this they usually meant the frontal dynamics, remained the same. In the tropics there were fronts, air masses with source regions and modifications as in higher latitudes, an

In 1947, when the University of California established Institute of Geophysics at Los Angeles, one of the research projects initiated with the Institute was an investigation of the synoptic meteorology of the tropical Pacific Ocean. Although the literature contained only scanty references to the topic, it was known that many meteorological data had been collected during World War II and that new ideas had been fermenting in the area throughout the period of conflict. In order to obtain some insight into the general condition of synoptic meteorology in the Pacific as a preliminary to the investigation the Director of the Institute at that time (Dr. J. Kaplan) issued a questionnaire to meteorologists who were known to have been associated with Pacific observation and research during the war, and answers from about half of those addressed were finally received in the Institute. It would serve no good purpose to enter here into a detailed analysis of the replies; however, one striking feature revealed by the survey is relevant, since it turns out to be characteristic of the present state of tropical meteorology in general. The replies fell into three well-marked classes, distinguished by the method of approach to tropical weather problems displayed, in some cases consciously, in others its

unconsciously,

The

equatorial front similar in principle to the polar front, all an occlusion process that resulted in the

and above

formation of typhoons and tropical storms. Small temperature differences became important, and the "slope" of systems a matter of earnest discussion. Finally we have the third group of replies, sent in by workers originating in or influenced by the Institute of Tropical Meteorology at San Juan, Puerto Rico, a school set up by the University of Chicago during World War II but now, so far as I Icnow, no longer active. This group takes its origin from Gordon E. Dunn's paper on easterly waves [25] and its members have at some time been closely associated with the University of Chicago, drawing their theoretical stimulus from C.-G. Rossby. It is natural to term the method followed by this group the pertwbation method. The concepts of the climatological group, referring to a hypothetical general circulation of trades, monsoons, doldrums, etc., identifiable as such on the mean maps, were taken over by these meteorologists. However, the basic currents were now considered to be for the most part zonal but subject to perturbations, and the perturbations to be accompanied by characteristic weather and pressure patterns, identifiable on daily weather maps. This group was much preoccupied with models of various kinds of perturbations. In dynamics, one gets the impression that they considered all dynamical problems connected with the perturbations as already solved

by the authors.

meteorologists whose replies

fell

into the

first

tended to put the greatest emphasis on climatological concepts: even in their approaches to synoptic problems they were dominated by the results of statistical analysis, by mean maps, by statistical notions like the trades, the monsoons, the doldrums, by the conviction that the day-to-day weather in the tropical Pacific differs very little from that revealed by monthly and aimual means. They extended this approach to the forecasting problem. Some felt, for example, that the class

by Rossby 's work and that their great task was to explain the dynamics of the general and zonal circulation.

The significance of the three broad classes of Pacific meteorologists revealed by this survey lies in the fact that, once one Icnows what to look for, the same

best guide to forecasting the tracks of individual ty-

phoons and tropical storms might lie in the study of mean storm tracks. Their dynamic theories, when they had any, were expressed in terms of a hypothetical general circulation of the tropics, and this was the entity whose characteristics were to be explained by physical reasoning from first principles, not the vagaries of the daily weather map. For the purposes we have in mind here, we may term the method of approach which is based upon these conceptions, the climaio-

divisions can be discerned in the

meteorologists. It

The more extreme or less

maintained more explicitly that the tropical atmosphere differed replies of this class

not that they

work

may

of all tropical

be divided into

those whose interests are primarily in climatology, or in synoptic meteorology, or in dynamic meteorology. On the contrary, the division rests upon distinct methods of approach to all branches of tropical meteorology, statistical, dynamic, and synoptic alike. It is therefore convenient to regard writings on tropical meteorological

logical method.

In the second group we must place those meteorologists whose thinking was much under the influence of concepts derived originally from the study of highlatitude weather, the followers of the air-mass method.

is

as emanating from three distinct schools of thought, the climatological, the air-mass, and the perturbation schools, even though it is only in the last

topics

class that the opinions have been common to a locally concentrated group of workers. And, of course, it must be remembered that there will be many borderline cases,

859

860

TROPICAL METEOROLOGY

writings that are hard to place unequivocally in one of the three groups. These things understood, however, we will find it easy enough to survey the present state of tropical meteorology. It will consist of the conflicts of these schools as revealed in the literature. The scope and detail of the confUcts is likely to astonish the meteorologist working on high-latitude problems, accustomed as he is to a large measure of agreement on the fundamental descriptions of temperate and highlatitude weather. In the tropics there is not even agreement on the common forms of tropical clouds or on the meteorological conditions accompanying precipitation. It has become the custom to generalize in haste and to reject inconvenient observations at leisure. Large areas of the tropical atmosphere have not been explored by observation and even the better-known areas have not yet yielded statistics of sufficient scope or reliability to justify the tropical parts of the "models" which are incorporated into the textbook descriptions of the general circulation of the atmosphere. In synoptic meteorology, conditions are little better than in climatology. The role of water substance in the genesis of tropical depressions is a matter of dispute, the existence or nonexistence of fronts the subject of irreconcilable speculations. A dynamical meteorology of the tropics can hardly be said to exist. The assumptions of such work as has been done are usually overlooked, and the results applied in a manner quite beyond the expectation of the original authors. Worse than this, however, is the tendency to apply dynamic theories depending for their validity on assumptions that hold in high latitudes but not in low latitudes. For example, the extent to which reasoning resting implicitly on the geostrophic-wind equation has been applied in equatorial meteorology is disquieting. This state of affairs, however, should not give occasion for pessimism; it is a sign that tropical meteorology, the oldest branch of scientific weather study, is undergoing a new development and that that development is a vigorous one. Each school of thought has had its achievements, has clarified some previously obscure field of knowledge, and has had its defects subject to ^arp criticism. It is our task now to estimate the extent of these achievements and to mitigate the evil of those defects.

THE CLIMATOLOGICAL METHOD

,

There is no doubt that, at least over the oceans, the observed values of the meteorological elements deviate from their monthly, seasonal, and annual means to a far lesser degree in the tropics than in higher latitudes. The mean values therefore can be said, in a special sense, to be more representative of the synoptic values. The steadiness of the wind, for example, has long been known, and the representativeness, in the above sense, of the mean trades and mean monsoons is perhaps the most ancient fact of modern meteorology, antedating in its origin the very notion of a synoptic map. The word "trade" itself is a contraction of "to blow trade," that is, to blow constantly in the same direction, along the same track. The empirical discovery implicit in the expression has, of course, been well confirmed

by scientific

investigation. Gall^,' for example, has given

of the persistence of the wind in various parts of the Indian Ocean. The persistence may be defined as the ratio of the mean vectorial wind speed to the mean speed without regard to direction. If, over

an analysis

the period covered by the means, the wind has the same direction, the persistence would be 100 per cent; on the other hand, if the directions were distributed at random, the persistence would be zero. According to Galle, the persistence of the trade in the square 10°S-20°S, 80°E-90°E does not fall below 69 per cent and for most months lies between 80 per cent and 90 per cent. This can be contrasted with the corresponding figures for the square 35°S-45°S, 70°E-80°E, where the persistence over any month does not rise above 57 per cent and, in the mean, amounts to 45 per cent for the year. But Galle's figures merely give quantitative expression to the conclusion which anyone can draw from the surface-wind maps that are published from time to time by national meteorological organizations [69]. Scrutiny of the wind data on these maps confirms not only the great persistence of the trades but also a similar large persistence, within the seasons of their greatest development, of the monsoons. To a lesser degree the maps also give one the impression of uniformity: over a very large proportion of the tropical oceans, the predominant component of the wind is the east component and this, combined with the Ivnown persistence of the trades, leads even careful workers to fall into the habit of regarding all tropical west winds occurring outside the monsoon regions as anomalous. At first sight the representativeness of the means of meteorological elements other than the wind appears

not to be so striking. Temperature and pressure, for example, show synoptic variations that may depart widely from the monthly, seasonal, or yearly means. However, the periodic nature of these variations is evident, the pressure showing semidiurnal oscillations whose amplitudes are largest at or near the equator, while the temperature has a clear diurnal periodicity whose amplitude becomes less the more closely the conditions of observation approach those typical of the open sea. When allowance is made for the periodicity

and for calculable orographical effects by correction of the synoptic observations, the mean values for a month or a season turn out to be as highly representative of the corrected synoptic values for temperature and pressure as for wind. Further, in the case of temperature, remarkable uniformity is disclosed. Over vast stretches of the western Pacific, forinstance, the temperature of the surface air during the whole "wet season" varies little from 85F [61]. Even in monsoon regions, where we might expect to find large seasonal variations of temperature, remarkable instances of uniformity are known.

At Colombo the mean difference [sicl in surface temperature between the North-East and South-West monsoon seasons is less than 2°F. and just about as much rain falls 1.

Quoted

to me.

in [36, p. 45].

The

original paper is not available

TROPICAL METEOROLOGY during one monsoon as the other, notwithstanding that the North-East monsoon stai-ts out as a cold, dry continental air mass and the South-West monsoon as a warm, maritime air

mass

[46, p. 27].

Connected with the uniformity of surface temperature over the oceans is the well-known uniformity in the height of the base of tropical cumulus. This rarely than 1500 ft or greater than 2000 ft, and departures from these values are so clearly connected with the occurrence of precipitation that the problem of forecasting cloud bases reduces to that of forecasting the presence or absence of precipitation. The persistent and uniform values of the meteorological elements are correlated. Both the trades and the monsoons are more than winds blowing with great regularity. Other elements, such as the precipitation and the cloud amount, the temperature, pressure, and humidity regimes, and the vertical variation of the elements all have structures or values characteristic of the trades or of the monsoons. Bergeron [5] has emphasized these correlated characteristics and has held up the trade and monsoon of the tropical climatologist as paradigms of concepts that should be used in the airmass climatology of higher latitudes. As an example he pointed out that "good monsoon" in India means a complex of heavy rains, strong steady southwest wind, is less

and a

characteristic vertical temperature

distribution.

The term monsoon,

and humidity

therefore,

is

to be

applied to a persistent kinematic and thermodynamic complex. Similarly numerous observations, culminating in the Meteor results [18], have shown that the trade is a persistent complex. Here again we have not only a characteristic and persistent wind, but also a typical associated cloud form, precipitation regime, and lapse rate of temperature and humidity. The "trade-wind inversion" is indeed well known and the equally wellknown trade cumulus owes its peculiarities to the association of the inversion with a typical vertical windshear.

So far we have mentioned the representativeness of the statistical parameters that are derived from observations over the great tropical oceans. At first sight, conditions are different over the land, particularly over the continents. The highly developed land and sea breezes of tropical islands, and the thunderstorms that break out with great regularity in the archipelagos of the East and West Indies are departures from mean conditions that are, through travelogue and fiction, known even to the layman of high latitudes. But these departures are clearly periodic, and synoptic observations may be corrected for them, either quantitatively or qualitatively. The seasonal means for the tropical islands are then representative of these corrected sjoioptic values. Moreover, the diurnal departures from the mean can be so clearly related to astronomical and orographical causes that the short-period forecast seems to depend only upon an adequate knowledge of the statistics and of geography. Upon close examination the same principle seems to apply to forecasting in continental regions. Here we have the added advantage that the seasonal variations themselves appear to be

861

due to the same causes as the diurnal changes, though operating on a larger scale and over longer periods of time. On this view, we may take the slowly varying oceanic conditions as the ground state and regard both diurnal and seasonal variations over the land as perturbations whose causes, orographic and astronomical, are known. The perturbations are thus thermal in their immediate origin and there appears to be no problem of explanation so far as synoptic variations are con-

cerned. Similarly there ought to be no forecasting problem for periods shorter than a season that cannot be

solved with an adequate knowledge of statistics and of orography. In the foregoing account I have outlined an extreme climatological view of tropical meteorology. On this view, there are no sjoioptic problems in the tropics. Synoptic problems become climatological problems; the future advance of tropical meteorology therefore depends on the collection and reduction of longer and longer series of observations from more stations in order to obtain maps of stable statistical parameters and their seasonal variations which are to be combined with a more detailed knowledge of orographical peculiarities.

The remaining problems are then dynamical and relate almost entirely to the "ground state" that was mentioned above. If corrections for diurnal and seasonal variations may be made by assigning them to Imown astronomical and orographic causes, it is clear that we are left with the statistical picture of the "trades" considered as kinematic-thermodynamic complexes to be explained by the methods of mathematical physics. Since the complexes are regarded as the most persistent features of the atmosphere, they represent a steady state in the dynamic sense and the statistics give us a direct insight into

what

is

known

at least for latitudes

plained, therefore,

is

as the general circulation, What has to be ex-

below 20°.

the tropical part of the "planetary and this explana-

circulation" or "winds of the globe"

tion turns out to be one of the easiest ever attempted in

meteorology. If it should appear that I have represented a very extreme view and one which would not be defended in this form by any modern meteorologist, I suggest that almost all textbooks that refer to the tropics at

all

(e.g.

[49]),

and certainly some recent

authors of research papers dealing with the general circulation [45, 56], imply this view in their treatment of the dynamics of the tropical atmosphere. This is

we may rightly classify as belonging to the climatological school but also of those in the frontal and perturbation schools, insofar as they treat the general circulation. Those authors will be true not only of those

dealt with in their proper place.

What kind of picture, then, is obtained by pursuing these principles to their final conclusion? First, let us look at the now-modified empirical laws governing the general circulation in the tropics. Abstracting the data in such a way as to omit the diurnal and seasonal perturbations of thermal and mechanical origin, we are left with a system of trade winds, blowing steadily from the east and toward the equator in the lower

layers of the atmosphere.

The

trades of the two hemi-

;

TROPICAL METEOROLOGY

862

spheres approach one another at the equator, as is clear from the statistics. There, they become hght and variable and this weakening is obviously part of the observed horizontal velocity convergence in the two currents, with a correlated increased vertical component in the motion. The lapse rates of temperature and humidity confirm this conception. At some distance from the equator, the lower atmosphere is characterized by the presence of an inversion of temperature, the tradewind inversion, above which the humidity drops to very low values, both absolutely and relatively. But this inversion, under the influence of the predominantly vertical motions, becomes higher and weaker as the

approached, finally disappearing in the zone of intense upward convection at or near that boundary. At high levels, the motion of the air is predominantly equator

is

and necessarily (on continuity considerations) away from the equator, and at relatively small latitudes it takes on a westerly component to form the antitrades.

The

antitrades are thus westerly winds with a poleward

component and a downward

vertical component that values in the neighborhood of 30°. A circulation cell is thus completed and the composition of the air in it agrees well with the distribution of the vertical component of the steady-state motion. In particular the region of light variable winds near the equator, which we shall now call the doldrums, is, as the statistics show, also a region of large cumulonimbus clouds, with attendant heavy precipitation, the "squalls" of the early navigators. On the other hand the trade-wind zone is the region of trade cumulus, with only light showers or none. The horse latitudes, finally, are regions in which fair-weather cumulus or

reaches

its

maximum

stratocumulus predominate; sometimes they are clear of cloud.

When we come to explain this abstracted picture of the tropical circulation we find the necessary concepts ready to our hands. The equatorward component of the trades was first explained by Halley in 1686; this constitutes, in fact, the first attempt to explain any feature of the general circulation. According to Halley, the equatorward component is to be attributed to the replacement of air that has risen by upward convection at the equator. Surface heating at the equator, supposedly the region receiving the greatest amount of heat from external sources, is sufficient on this view to drive the whole meridional circulation of trades and antitrades. Halley's explanation of the zonal components of the motion, however, was not accepted. In 1735 John Hadley gave the accepted theory, invoking the conservation of absolute angular momentum. Since that time the combined explanation has been handed on from text to text. It Avas, for example, embodied in the earlier dynamic theories of the Chicago group. Rossby [56] specifically has used it under the guise of the "direct cell" in the general circulation. Although little quantitative work has been done, the qualitative use of the assumed, solves the dynamic problem On this assumption, any further work would be directed to improving the theory explanation,

it is

for the tropical atmosphere.

quantitatively,

by

referring to better

and better clima-

tological data.

Summing up the extreme climatological view, we have the following conceptual apparatus the tropical atmos:

composed

wind systems, with their associated composition and thermodynamic properties, the trades and the monsoons. Diurnal variations of the meteorological elements are due to perturbations of these systems, attributable to thermal and orographic disturbances of known origin. The monsoons are seasonal perturbations of the trades due to the same causes. The trades themselves are thermally driven and all phere

is

of persistent

features of that circulation are explicable in terms of

what happens in the doldrums, a region of intense convection and light variable winds coinciding with the equator in the ideal model. Astronomical variations, combined with the different absorptive properties of land and sea, therefore account for everything trades, doldrums, monsoons, land and sea breezes, the regime of precipitation, temperature and humidity, cloudy and fine weather, and lastly (by dynamic functional relations embodied in the equations of motion) the pressure distribution. There are no problems left to solve. On this basis, a large part of the more successful shortrange tropical forecasting in World War II was implicitly conducted the little long-range forecasting that was done was based explicitly on this statistical method on this basis, also, most present-day models of the general circulation incorporate the tropical atmosphere. Two unfortunate circumstances mar the beauty of the picture. The first is a fact that has been known to western science for four hundred years or more. Oceanic tropical regions are not only the seat of steady trades and monsoons, they are also, in their season, notorious for the presence of the most violent storms dealt with by synoptic meteorologists typhoons, hurricanes, and tropical cyclones. How are these storms to be accounted for in terms of the causal theories of the climatological school? The first impulse is to explain their origin in terms of the standard astronomical and orographical variables previously invoked. During the last century, the tendency was to regard tropical cyclones as being perturbations due to local intensifications of convection in the doldrums [43]. Those who wished to advance more explicit causes attributed the convection to local maxima of heating [27]. But this explanation was soon seen to be untenable, since the region of origin of at least some typhoons was discovered to be over the parts of the Pacific Ocean where the temperature gradients in the lower layers were very weak. It must be confessed that the climatological school never successfully dealt with the problem of the origin of tropical storms. The best that could be done was to chart the regions and seasons in which they occurred, to show that the mean tracks generally followed the march of the sun and that there was some justification in the statistics for regarding tropical storms as connected in some way with the only region, in the view of the school, that showed the necessary high variability of the meteorological elements:

—

;

—

TROPICAL METEOROLOGY the doldrums. But even the doldrum origin of tropical storms was not quite general.

At

least

some

of the hurricanes that afflict the

West

Indies and the southern coast of the United States originate in the Caribbean or in the Gulf of Mexico,

and when this happens they appear almost without warning in the trade current, not in the doldrums [25]. The second circumstance that is fatal to the extreme climatological view is that the really steady trades occupy only a small fraction of the total oceanic areas in

the tropics. Further, the antitrades are similarly

comparatively restricted areas. The typimodels of the general circulation, are found only in the eastern parts of the equatorial branches of the great subtropical anticyclones. The regions of high persistence are these same areas. In the western fractions of the tropical oceans the trade wind is variable, not as variable as the belt of the westerlies, it is true, but still subject to perturbations of the wind field, so clearly independent of thermal causes as to belie the classical description. In the western oceans also, the meridional component of the wind may not be directed toward the equator, even in the mean. At Pukapuka (11°S, 166°W), for example, the mean wind at the surface is directed during the summer away from the equator, though this station always lies south of the doldrums [24]. Similarly the antitrade at higher levels is best developed and most easily discovered above the eastern borders of the subtropical highs. To the west, the westerlies are found at higher and higher levels, and in the lower latitudes and near the western borders of the anticyclones they may not be present below the tropopause. The deathblow to the notion of universal antitrades in tropical latitudes was given by J. Bjerknes in his discussion of the subtropical anticyclones [6]. It is clear from that paper that the oceanic anticyclones are major perturbations of the atmosphere with features independent of any direct thermal cause, and that any explanation that leaves them out of account by dismissing the trades as part of a simple "direct cell" symmetrical on all longitudes is artificial. While such explanations may suffice in a discussion that is directed mainly toward clarifying the vagaries of the westerlies, they are too unrealistic to be useful in tropical meteorology. A more serious difficulty arises when, having recognized this oversimplification of the general circulation, we attempt to discuss the details of the observed

found only

in

cal trades, as described in

tropical circulations, daily, seasonal, or annual.

we have an

While

excellent series of observations over the

oceans (excellent, that is, from the climatologists' point of view), we have very few observations and those for comparatively short periods over most of the land masses. India, it is true, has long provided observations from a dense network, but we still lack long and reliable series from Southeast Asia. The data are even more unreliable and sparse from equatorial Africa and from Brazil.

As we

from the

shall see later, the

wartime synoptic data

latter areas strongly suggest that the simple

picture of the

monsoons

in those areas

is

probably a

863

climatological abstraction as misleading as that of the

What good data we have, moreover, consists of surface observations. Upper-air observations are still so widely spaced, even at the present day, that most trades.

high-latitude analysts would refuse to commit themselves to a space analysis of either the synoptic data or

the means. It must be remembered, also, that except for some Indian stations, and a few in the Caribbean and Panama, practically no radiosonde or meteorograph data antedates World War II. Further, the upper winds in India and the East Indies, upon which much emphasis has been placed in some papers [231, are derived from the observations of pilot balloons. Dr. Mintz of the Meteorology Department of the University of California at Los Angeles has pointed out to me how misleading mean winds derived from such observations in the tropics can be. In "The General Circulation of the Atmosphere over India and Its Neighbourhood" [51], for example, are published data giving the mean wind at 4 and 8 km according to the pilot balloons. In the same volume are also given the mean directions of the clouds at and about those levels. The mean circulations for January derived from these two independent sources are directly opposite to one another, that indicated by the balloons corresponding to the east end of an anticyclone situated at the appropriate level, that from the clouds corresponding to the west end. It is clear that the pilot balloons are selective and that mean winds derived from them are probably typical of clear weather; the balloons are very easily lost from view in tropical regions even with small amounts of convective cloiid, since the cloud pillars are so much higher in low than in high latitudes. On the other hand, winds derived from middle and upper clouds are selective in the opposite direction, since such clouds are, in low latitudes, most commonly the result of convection, being formed from the middle and upper parts of cumulonimbus. Such considerations as the foregoing ought to make us hesitate to generalize when discussing the upper parts of the tropical circulations, either in the trade or in the monsoon regions, especially when our point of view leads us to place the greatest emphasis on seasonal and annual means. There are literally not sufficient data to make a single reliable statistical generalization applicable to the upper levels. Our best hope is to allow the lapse of time and the gradual extension of the tropical observing networks to accumulate data that might later give us an insight into the upper circulation in low latitudes. In the meantime, the chief problems seem to be synoptic and dynamic, particularly the dynamic problems growing out of synoptic experience.

THE AIR-MASS METHOD When,

after

World War

I,

meteorologists of the

Bergen group began to extend their application of frontal and air-mass analysis to regions outside Scandinavia, they found the climatological concepts of tropical meteorology already adapted to their purpose. We have already referred to Bergeron's approval of the notions^ trade and monsoon, as modified to include not

TROPICAL METEOROLOGY

864

only the wind structure of those entities but also the associated temperature and humidity distributions and the typical cloud and precipitation regimes. For kine-

matic and thermodynamic complexes of this kind were precisely the new elements the Bergen group had introduced into the synoptic meteorology of high latitudes under the name, "air mass." Both the trade and monsoon of the climatological school of tropical meteorologists fitted the prescription of an air mass perfectly. The trade, for example, had a specific source region: the subtropical anticyclone. Its path from the source was well determined and the character of the surface over it had to pass, the great tropical ocean, had already been investigated and its thermodynamic effect evaluated. These factors together gave to the trade its uniform, persistent features; the relatively steep lapse rate in the lower layers could clearly be attributed to the fact that it moved across the sea-surface isotherms toward the heat equator; it was clearly a cold mass of maritime subtropical origin ("tropical" in the new vocabulary) and the presence and variation of the convective cloud in it confirmed, through indirect aerology, the thermodynamic classification. The trade at its source was a stagnant slowly subsiding mass, almost in equilibrium at all times with the sea surface here there were no clouds or perhaps small amounts of low stratiform cloud. As it moved toward the equator, however, the mass became heated by the warmer waters in lower latitudes so that a relatively steep lapse rate was characteristic of the lower layers, while the air above continued to be warmed by subsidence in the antitrades, thus stabilizing the trade-wind inversion. The closer fhe mass approached the equator, the more intense became the heating from below and the less the subsidence aloft; the result was that a deeper lower layer was overturned by convection, the trade-wind inversion was found at a higher level, and became weaker as it approached the doldrum region corresponding to the heat equator. The clouds used in indirect aerology confirmed this history, for as the mass moved toward the equator the cumulus reached to higher and higher levels and showers associated with cumulonimbus became more frequent. This picture not only fitted the older climatological view of the trade remarkably well, it also removed some of the difficulties of the older theory by emphasizing the role of the subtropical highs as source regions. The most typical trade would be found at the eastern ends of the anticyclones, because there the trade had the largest component toward the equator, and moreover the reconstruction of the vertical motions around a subtropical cell, suggested by J. Bjerknes, required that the predominantly downward motion be confined to the eastern ends. Toward the west the circulation in the cell required an increasingly great upward component in the middle atmosphere it was in those regions, empirical investigations showed, that the trade wind was more variable, the trade-wind inversion frequently weak or absent, and the weather worse than the older theorists could allow.

which

;

—

The monsoon, wherever

it

eastern Asia, or Australia,

occurred, in Africa, South-

was

also

an

air

mass. It

was, in fact, a trade that had passed from one hemisphere to the other, and thus, under the influence of a Coriolis force of opposite sign from that in its place of origin, acquired a westerly, instead of an easterly, component. This mass was accelerated under the influence of a solenoidal field that could be attributed ultimately to the different absorptive properties of land and sea, as required by the older theory. It was considered to be unstable to great heights and to have, in the upper layer, a higher specific humidity than the trade because it had been subjected to the destabilizing influences of the equatorial passage for a long time; further, it was moving on to a continent during the warmest season, and hence might be expected to show cold-mass characteristics to a high degree. What, then, could be said about fronts in the tropics? On the new view, the air masses were tremendous volumes of air, moving away from their source regions and preserving the marks of their origin in their homogeneous properties and of their history in the modifications of their lower layers; ultimately they came into juxtaposition with other air masses along more or less sharp boundaries, the fronts, where the meteorological elements would necessarily show rapid space variations, particularly in the horizontal planes. Were there such boundaries to the trades? This question had already been answered for the Pacific. In 1921 Brooks and Braby [11] had described in the western South Pacific what they called a zone of convergence between the trades of the two hemispheres. The title of their paper, "The Clash of the Trades in the Pacific," is suggestive. In the central Pacific the mean trades from the two hemispheres meet at a small angle along a line that corresponds very well with the mean position of the equatorial low-pressure trough. Farther west, however, the mean trades meet at a larger angle and, in the extreme west, near the Solomons and New Hebrides

during the wet season, the boundary is well marked, separating westerly "monsoons" to the north from easterly trades to the south. Rainfall follows the intensity of the convergence- as judged from the angle of

impact of the currents. In the east, the rain zone is narrow and corresponds in position with the boundary; in the west, the rain zone, while roughly corresponding

with the boundary,

is

broader and, in the mean, the

rainfall is heavier. Finally, the tropical cyclones of the

South Pacific seem to originate near or at the boundary, move along it for a time, but in most cases to curve away from it into higher latitudes. Brooks and Braby had done their work and prepared the paper, it seems, before they had heard of the new polar-front theory; before publication, however, they added a footnote, drawing attention to the similarities of the boundary between the trades and the polar front of higher latitudes of which they had just heard a description by V. Bjerknes at a seminar in England. They then proto

2. In the paper by Brooks and Braby [11], it is clear that "convergence" means convergence of the streamlines, not

horizontal velocity convergence.

;

TROPICAL METEOROLOGY posed to call the new entity they had introduced into tropical meteorology, the equatorial front. The work of Brooks and Braby seems to have been overlooked by the Norwegians, for they proceeded more or less along the same path without referring to it. However, their researches, in which they used the same method of analyzing surface mean winds and rainfall, were more extensive, ultimately covering all the tropics.

They

describe the "intertropical front" in the Pacific

and Atlantic and Indian Oceans, and in addition attempt to trace its course over the land in Africa and [10]

southeastern Asia. Seasonal movements of the front are attributed to different mean temperature conditions in the trades of the winter and of the summer hemispheres. It

is

clear that,

up

to 1933, the

new

tropical meteorol-

ogy still followed, at least implicitly, the assumptions of the climatological school. It was implied that the equatorial or intertropical front, being found on maps of mean winds, pressure, and rainfall, would therefore be found also on synoptic maps. As far as I can discover, this assumption was not questioned at any time; indeed, many authors did not recognize that it was an assumption. After 1933, therefore, there was a concerted attempt to apply frontal and air -mass analysis to S3tioptic maps in the tropics. The movement started slowly, being most active in the Pacific and the Caribbean. By 1939 the standard high-latitude methods of frontal analysis had been adopted by the Philippine Weather Service, by the meteorologists of Pan American Airways [17], in New Zealand [3], Australia [50], and in Martinique and other parts of the Caribbean [31]. World War II brought an immense increase in the amount of forecasting required in the tropics and, with it, a large influx of meteorologists whose training and experience had been largely in high latitudes. The latter applied standard air-mass analysis to their new problems, almost without question the literature at that time gave them every reason for doing this. The only paper that might have thrown some doubt on the accepted view [25] had at that time attracted little attention. Today, as the survey mentioned in the introduction shows, almost half the meteorologists who have had experience in the tropics still adhere to the tenets of the air-mass and frontal school. We are, therefore, entering the most controversial part of this review and it is well to pause and examine our fundamental conceptions closely. For it is often found that an irreconcilable conflict of scientific views concerns not the facts but the explanations; most of the difficulties may be semantic in origin. It must be realized that the complex of ideas advanced by Norwegian meteorologists may be divided into two sections. The first section is concerned with certain readily verified facts. The term front, in empirics, is applied to a set of atmospheric phenomena that are frequently discovered by our instruments and by visual observation to be closely associated. The most striking feature is the occurrence of an organized system of clouds, extending over immense horizontal distances one type of cloud system is called a warm front, another a cold front, and combinations of the two are termed ;

occlusions.

However, these terms are only applied

if,

865

accompanying the cloud system, there is a narrow zone in which the meteorological elements humidity, temperature, and wind show rapid changes whose sense is defined for each of the three different types of cloud systems. Further, in high latitudes, the pressure gradient should have an oppositely directed component

on either side of the system. In this sense an observer on the ground or a pilot in the air may identify a front without ever seeing a synoptic map. It is an observable entity. The Norwegians, however, did not stop at the descriptive stage of meteorology. They had also an explanation, a theory about fronts. This theory accounts for the observed fronts as being boundaries, approxi-

mating atmospheric discontinuities, between masses which possess characteristic and more or

air less

homogeneous values

of the meteorological elements. Further, the theory requires that the fronts can be maintained for any length of time only if there is a density contrast accompanied by cyclonic shear at the discontinuity. Now this theory is not a priori true. There is no general theory of the atmospheric circulation by which we can derive from the principles of physics the result that fronts must form in this maimer. The confidence we have in the theory as an explanation applicable to high latitudes comes not from dynamic meteorology but from experience with synoptic maps,

which we check the contention that the by the airman are in fact boundaries between air masses. This experience leads us to give the name front to regions where certain meteorological elements show steep gradients even in the absence of the typical cloud and weather pattern. This is done because such systems preserve the two most essential features of the theoretical front, viz., the density contrast and the cyclonic wind-shear. The density contrast and the wind shear are essential to the further development of the theory. For, according to the Bergen school, the frontal surface is not always in stable equilibrium. Waves develop in it and some of these waves are dynamically unstable. Such unstable waves give rise to vortical circulations which roll up the surface and form the cyclones of middle and high latitudes. The kinetic energy of these cyclones is derived from the potential energy of the mass distribution at the undisturbed fronts. It is now obvious why both the density contrast and the cyclonic shear are needed at the theoretical front. The first provides the necessary source of energy for the storm, and

by means

of

fronts observed at a single station or

the second

is the destabilizing influence that leads to the occlusion pi-ocess. They, of course, play other roles in the theory, but this is their part in the wave theory

of cyclones.

To emphasize

the independence of the

empirical and theoretical fronts, I should like to remind the reader that line squalls were Icnown long before the frontal theory

was promulgated and that very accurate

descriptions of cold fronts exist, dating back to the last

century [42]. If the theory of extratropical cyclone formation should ever be upset and discredited, cold fronts, warm fronts, and occlusions would continue to

be observed and to be identified on synoptic maps,

:

TROPICAL METEOROLOGY

866

though the explanation of their relations to one another and to the field of motion would be different. I have labored the distinction between the empirical and the theoretical front because it was undoubtedly not made by the early workers of the frontal school in tropical meteorology.

the

following

facts

They succeeded by

observation

in establishing

and

synoptic

In

all

tropical latitudes, organized lines of

cumulo-

nimbus

cloud, closely resembling the cold-frontal cloud systems of high latitudes, are encountered by airmen and are observed to pass over fixed observing stations. 2. In the great majority of cases, these lines of cloud are accompanied by zones of rapid wind change. The total shift is not as pronounced as in high latitudes and is

and

air

major discontinuities of the tropics. First, and most important, came the equatorial or intertropical front, whose synoptic existence was never doubted during this period. But there were other major systems, classify the

particularljr in the western Pacific.

analysis 1.

make

the distinction. Having decided that fronts masses existed in the tropics, the frontal analysts of the decade 1933-1943 were concerned to describe and

ful to

generally

more gradual. The shear

at the shift

is

often

These facts have been emphasized by Deppermann [20], by Harmantas [35], by Frolow [31], and by Alpert [1]. From personal experience I can assui'e the reader that they are facts. 3. Differences of temperature can sometimes be found between the air on either side of the cloud line. This is reported by Sawyer [60] and by Solot [67]. However, in certain oceanic regions, though there is often an abrupt drop in temperature at the surface with the passage of the cloud line, it may recover its former value when the weather clears. 4. There may be very marked differences in specific humidity across the cloud line not, it is true, at the surface, but in the middle atmosphere. 5. The lines are frequently but not always associated with a low-pressure center or trough at the surface, but owing to the weak pressure gradients and the great amplitude of the semidiurnal pressure oscillation, it is difficult to correlate any sharp change in the barogram with the passage of the cloud line, unless a violent thunderstorm occurs at the station. 6. One can sometimes find these cloud and windshift lines day after day in the region of lighter winds around and outside typhoons, hurricanes, and tropical cyclones [21]. Moreover, the storms sometimes appear to originate in the regions where such lines have previously been discovered. To most tropical meteorologists, after 1933, these discoveries were sufficient to identify the lines as fronts, and since they made no distinction between the empirical and the theoretical front, they adopted the entire high-latitude apparatus of frontal and air-mass analysis and forecasting. The way had been prepared, as we have seen, by Brooks and Braby, by Bergeron and, most authoritatively, by the authors of Physikalische Hydrodynamik [10]. The frontal wave theory of storm formation was adopted without question; indeed it seemed to be confirmed by (5) and (6) above. A few meteorologists were concerned by the frequent lack of temperature differences across the fronts and were careful to distinguish "tropical fronts" where the differences were very small (in many cases they were, in fact, absent) from extratropical fronts where there was usually no difficulty in detecting the difference, at least by radiosonde. Deppermann in particular was always carecyclonic.

—

Thus Deppermann

distinguished a "tropical" front between the winter monsoon of eastern Asia and the trade of the North

Other "major fronts" were described in but these are now of only historical interest. In addition, much attention was given to the passage of polar fronts from the belt of the westerlies on into tropical latitudes. Pacific

[20].

different parts of the tropics [17]

Some ricanes

extraordinarily detailed frontal analyses of hurtropical storms were produced during the

and

In the South Pacific the full occlusion process leading to the development of tropical cyclones was illustrated by Kidson and Holmboe [38]. Similar analyses were published for storms in the Caribbean [37, thirties.

64] and in the Bay of Bengal [59]. An elaborate triplepoint theory due originally to Scherhag was applied to North Pacific storms [20]. If one were to judge by the literature up to 1940, one could not doubt that the application of the frontal and air-mass theory to the tropics was completely justified. The chief problem seemed to be, not to account for the origin and development of tropical storms, but to explain why many more than were actually observed did not develop. The tentative theory advanced in Physikalische Hydrodynamik, accounting for the maintenance of the equatorial front in terms of temperature differences between the trades of the winter and the summer hemispheres, was extended to account for this also. The equatorial front, on this view, tended to become a sharp discontinuity, "to become active" in the words of the air-mass school, after the air in a great polar outbreak in the winter hemisphere reached the equatorial regions. This would communicate an impulse of an unspecified kind to the equatorial front which would thereupon become unstable and form a tropical cyclone. As early as 1935 De Monts had published a paper with the significant title "Role catalyseur de I'air polaire dans la g^nese d'un cyclone tropical" [19] describing this process in the South Indian Ocean. Japanese meteorologists seemed particularly attached to this explanation [2]. Later Grimes [33] endeavored to specify the nature of the impulse that would be given to the equatorial front by the arrival of winter-hemisphere air after a polar outbreak. He considered that a "cyclone only forms when there is a surge across the equator of air which in the hemisphere of origin had sufficient anticyclonic vorticity, which is conserved as cyclonic vorticity in the other hemisphere." Since shearing motion at the frontal surface would be the only destabilizing agent leading to waves of increasing amplitude, Grimes was evidently looking for some

process which would bring about a sudden increase in cyclonic shear at the supposed frontal surface.

The

was made to depend upon the conservation of the vertical component of absolute vorticity, which it is process

I

TROPICAL METEOROLOGY

now fashionable to suppose actually occurs in the atmosphere. In "The Movement of Air Across the Equator" [33], he enunciates this principle and applies it, under very restrictive special assumptions as to the nature of the motion. In brief, the motion must be horizontal, nonviscous, and autobarotropic, with a constant meridional component. Although as far as I know no investigation has been undertaken to find out whether vertical motion, frictional forces, solenoids, and variations in the meridional component of the wind can be neglected in the tropics, the results of this paper are frequently quoted without mention of the assumptions and applied as if they were perfectly general. Moreover, the efficacy of the deduction from the principle of the conservation of vorticity, as assigning a cause for cyclone formation in this context, depends upon the validity of the frontal theary in the tropics. If that theory is found to be in-

applicable, the principle of the conservation of vorticity

would have to be invoked

in

some

entirely different

context, with results that cannot at present be antici-

pated.

Although there are

who adhere

ologists

with greater or

still

a large number of meteor-

to the principles outlined above,

lesser modification, the synoptic expei'i-

ences of World War II, especially in the Pacific and the Caribbean, gave a death blow to the air-mass theory in its extreme form. This theory failed to pass the test to all theoretical work in meteorology must finally come (though the evil day may be put off for almost a decade) it was found almost useless as a guide to shortperiod forecasting in low latitudes. The writer can vouch for this through personal experience, through

which

;

conversation with many tropical meteorologists in the Pacific, the Caribbean, and the United States (where people with experience in all tropical areas are now to be found) and through the answers to the questionnaire issued by the Institute of Geophysics. But the reader need not depend on these sources of information; the recent literature reflects the disillusionment of a whole generation of tropical meteorologists. This is shown in attempts to doctor and patch the frontal theory in such a way as to take into account the many anomalous movements and the sudden appearances and disappearances of the fronts, especially of the equatorial front, or in frank abandonment of the air-mass theory altogether. The following modifications of the frontal theory, as previously outlined, have been proposed: 1. The polar front enters the tropics, not as a typical surface front but as a front aloft, in the westerUes. It persists in that situation but may come down to the surface in lower tropical latitudes and at a later time.^ ,

Forsdyke

Waves

[29, p. 82]

says.

in the circumpolar westerlies occur at the surface

on the poleward sides of the subtropical high-pressure belts, and at higher levels they extend to low latitudes where the westerlies overlie the trades. It is tempting to identify these with the upper parts of cold fronts associated with the depressions of middle latitudes. At Mauritius thej' are frequently

and rain which spread from the southwest above the lower current from the eastsouth-east. They should be indicated on the charts as upper fronts. It is possible, therefore, to have in the same part of the chart a lower front moving from an easterly, and an upper front moving from a westerly point, and crossed lower and upper fronts may occur. associated with nimbostratus cloud

3.

See Rep. No. 600-50, Publications of the Weather Divi-

USAAF,

p. 15.

On

2.

entering the tropics, the polar front separates

two portions (a) the density discontinuity or shear line, and (b) the polar trough (see [16, 53, 65]). into

:

3. The polar front is destroyed soon after entering the tropics. The very rational Memo 131/44 of the British Naval Meteorological Branch [46, p. 28], says,

So

we have

considered only discontinuities which orig"What happens to fronts which move into the tropics from higher latitudes? Generally speaking, they lose their well-defined slope and become diffuse: their movement becomes slow and indefinite and by the time they get near the equator, if they get that far, they bear little resemblance to their text-book prototypes. Most of them ultimately lose their identity in the equatorial low pressure trough which is a great leveller of air mass disparities. good many of them get no further than the subsidence zone of the sub-tropical highs where they "dry-out." far

inate in the tropics, notably the I.T.F.

A

4. There is little or no temperature contrast at the equatorial front which is, indeed, simply a more or less narrow zone at which the trades of the two hemispheres

converge and

This represents a return to the origiand Braby, and the climatological school. Brooks and Braby were careful to point out that no temperature contrast could be found across the equatorial front in the regions where, judged by the mean winds and precipitation, it was strongest. Numerous quotations are available on this point [15, Chap. rise.

nal position of Brooks

10; 46, 65]. Garbell [32, p. 70] says,

The discontinuity between the two tropical air masses coming from the two hemispheres usually consists not so much in a difference in surface temperature as in a difference mainly in the vertical distributions of temperature, moisture, stability and wind velocity between the two easterly air streams. 5. 6.

7. 8.

The The The The

many 9.

is

single

equatorial front

is

double

equatorial front

is

equatorial front

equatorial fronts

The equatorial

10.

and continuous

equatorial front

hemisphere

The

atmosphere

[14].

[28, 72].

part single, part double [32]. discontinuous. There are

is

[54].

front

may slope toward the summer

[13].

may

eq^iatorial front

way

in the

in the

upper

slope one

lower atmosphere and the opposite

way

[34].

The equatorial front does not slope at all [46]. The equatorial front moves discontinuously. It may jump from one position to another without passing 11.

12.

through intermediate points 13.

in

sion,

867

The

equatorial front

[29].

may move by

disappearing

one position while another forms in a different

position

The

[17].

list

of suggested modifications to the frontal

TROPICAL METEOROLOGY

868

theory in the tropics could be extended ahnost indefinitely. To anyone, like the writer, who has had to review the literature on tropical fronts pubhshed in the last ten years, the total effect

one of intolerable confusion.

is

confusion exists at the present time, unresolved. Where possible, I have purposely chosen the latest quotations for inclusion in the above list, which is, of course, very incomplete. Thus Garbell's textbook

And

this

in 1947; Forsdyke's summary of tropical meteorology in 1949. Both these works will give the reader some idea of the complexities introduced by members of the air-mass school in an endeavor to remove the difficulties associated with the attempt to

was published

by high-latitude techniques.

forecast tropical weather

Forsdyke, indeed, franldy admits in places the impossibility of using standard methods. On page 37 of his

paper he says.

The

pressure distribution

forecasting the

movement

is

of little or

no assistance in

of the intertropical convergence

the best aid, the frontal zone usually being located at the hne of separation between winds having northerly and southerly components respectively. Over wide areas, however, the surface winds are often the zone.

The streamhne

chart

is

only winds available; hence it is usually the surface front which is so placed, whereas observation shows that the worst weather often occurs up to 200 miles away from the surface front. It may be assumed that the front will move toward the side on which the winds are weaker, but it is difficult to estimate the speed of motion from the observed winds.

Often the front appears to jump.

be wise after the event, but one may on what the history of tropical meteorology would have been, during the last fifteen years, if the distinction between the observed windshift line accompanied by cumulonimbus, the old "line squall," and the theoretical front of the Bergen group had been kept in mind. Would not the early workers, realizing that the empirical front of the tropics was not necessarily a discontinuity in the density field, have also realized that frontal dynamics would not be applicable to it, that new synoptic entities were being investigated and that therefore new explanations were required? That is the position in which we now find ourselves. At a time when the tropical observing networks are beginning to deteriorate, when we have fewer and less accurate observations than at any time since It is easy to

legitimately speculate

1939, we are realizing that tropical meteorology, in investigating these entities, has a contribution to make

to general meteorology. are

we

Nowhere

in the

atmosphere

better able to study the direct effect of horizontal

velocity divergence in the lower atmosphere, free from other effects, than in the tropics. The tropical "fronts,"

have been dismissed as particular, wellunderstood examples of a common atmospheric discontinuity, are now seen to be completely without dynamical explanation. When the explanation is forthcoming, it cannot but react on the theory of high-lati-

which

tude fronts.

THE PERTURBATION METHOD One of the most serious objections to either the doldrum or the frontal explanation of the origin of tropical storms

is that a proportion of the hurricanes that affect the West Indies and the southern United States originate within a comparatively strong east current of great depth prevailing during the wet season over the Caribbean. The storms deepen rapidly and are often of great violence. They are usually of smaller diameter than the hurricanes that move in from the east and which clearly originate in the doldrum region of the eastern Atlantic. In 1940, Gordon E. Dunn published a paper dealing with the origin of these storms [25] and the ideas expressed in it have led to the development of a new outlook on tropical problems. Dunn, using 24-hr isallobars to eliminate the great semidiurnal oscillations of pressure, showed that: 1. The deep easterly belt of the Caribbean in the wet season is subject to pressure waves of small ampli-

tude, 2.

which move from east to west.

Ahead

and

little

wave the trade- wind inversion is and the weather is fine, with small clouds

of the

relatively low,

precipitation.

Behind the trough the trade inversion is high or absent and the region is the seat of many shower-clouds. 3.

He

speaks of this as the "rolling away" of the inversion. Some of the waves, and a proportion that increases as the season advances, grow in amplitude and give rise to small but violent hurricanes. 5. The isallobaric highs and lows associated with the waves, whether hurricanes are formed or not, follow tracks that correspond with the mean hurricane tracks of the appropriate month in the season. Subsequent writers elaborated this picture of the easterly wave. The most active worker was Riehl [53] who investigated the vertical structure of the wave more closely and showed that it was easier to detect in the wind field than in the pressure field and aloft than near the surface. Later the easterly wave analysis was applied to the North Pacific and the North Atlantic. More recently easterly waves have been identified in the Indian Ocean [29] and in West Africa [63]. In opposition to earlier writers on the Caribbean, 4.

such as Kidson [37] and Scofield [64], Dunn insisted that no temperature discontinuity could be found either in the easterly wave or in the developing hurricane. Later research has confirmed his contention and there seems now to be no dispute on this point as far as the West Indian hurricanes are concerned. Radar investigation of the storms as they pass over the southern seaboard of the United States, however, seems to show that there are well-marked cloud and precipitation discontinuities in the mature storm [73]. As this topic will be discussed in the next section, I wish only to point out here that Dunn was explicit only on the absence of tem-perature discontinuities. He admits, however, that the southwest wind at Panama in the wet season may be colder in the lower layers than the easterly on the other side of the equatorial convergence zone. One gets the impression that he is willing to admit a frontal origin

TROPICAL METEOROLOGY for those storms that clearly originate in the

doldrums

but that he denies such an origin in cases where the storm can be traced to an easterly wave. Temperature differences have been reported at the equatorial front in other parts of the world, for example in India [60] and in equatorial Africa [67] this probably predisposed Dunn to concede that a frontal origin of doldrum hur;

ricanes

was

possible.

This concession, either in the form of an outright admission of a frontal origin of some tropical storms, or the lesser concession that storms that originate in the neighborhood of the equatorial low-pressure trough differ fundamentally from those that can be traced back to easterly waves, has been a characteristic of workers of the perturbation school. It has, in fact, done much to prevent their presenting a unified theory of the origin of tropical storms. Apart from this admission,

however, the workers as a group have been rather extreme in denying the existence of fronts in the tropics. They have, rightly I think, insisted on the absence or irrelevance of temperature contrasts in the Caribbean and the western Pacific; but their zeal has also led them to minimize the well-authenticated accounts of cloud systems and wind-shift lines near the equator, lines that look like the cold fronts of high latitudes. As I have said, they may admit that such lines can exist in the equatorial low-pressure trough but deny their presence in the easterly wave in the Caribbean. Yet nothing is easier, with good aircraft reports, than to demonstrate the presence of such lines in certain Caribbean easterly waves. To admit this, perhaps, would seem to them to destroy the value of the contributions they have made; we would be back in the confusion that prevailed during the ascendancy of the frontal theory. The resolution of their difficulty must be left to the next section.

The

detailed structure of the easterly

worked out by Riehl

wave was

He assumes

that the basic undisturbed current in the Caribbean is a deep easterly. If this assumption is conceded, it is a simple matter to define and to detect the chief axes of the easterly wave, both at the surface and aloft, for the axes, horizontal and vertical, along which the wind is easterly will be the "trough" and "wedge" axes. In the Northern Hemisphere we shall find northeast winds ahead of the trough and southeast winds behind it. By the analysis of upper-level wind maps, supplemented by time crosssections at individual stations, it is then possible to discuss the slope of the systems. Riehl showed that the perturbations of the wind field were of greater amplitude than those in the pressure field, and that the amplitude of the former also seemed greater in the middle troposphere than at low levels. Generally, the trough axis slopes toward the east with height. Further, the lower wind fields are positively divergenf ahead of the trough and negatively divergent behind it; with this distribution of the horizontal velocity divergence, [53].

4. Riehl is careful to show that the total horizontal velocity divergence, not merely the streamline divergence, varies in

this

manner. The distinction was never clear to workers

air-mass school.

of the

869

and

(to a high degree of approximation) of the mass divergence, the westward passage of the wave is explained, as is also the "rolling up" of the trade inversion behind the wave axis and the consequent distribution of cloud and precipitation in the perturbation. The

work is that he establishes the correlations of the fields of motion, pressure, composition, and temperature to form a simple integrated picture of the

virtue of Riehl's

perturbation; this has hardly been achieved for any perturbation in high latitudes except, perhaps, the frontal wave.

Riehl also discusses another type of perturbation observed in the Caribbean area, one we have mentioned before. During the winter in that region, the east wind near and at the surface is frequently accompanied aloft by winds with a westerly component; in other words there may be a typical trade-antitrade regime. In the lower easterlies, perturbations that look superficially like easterly waves on the low-level synoptic map appear; however, these disturbances move, not toward the west, but toward the east, against the lower easterly current. It is always possible to show that the trough in the easterlies is continuous with a surface trough in the westerlies of the higher latitudes and with an upperlevel trough in the westerlies of the tropics. This trough Riehl called the polar trough; he accounted for the eastward movement of the system in the lower tropical atmosphere as being a reflection of the movement of the trough aloft in the circumpolar westerlies. This explanation had been advanced before, of course, but in a different form. The older explanations were in terms of an upper front in the westerlies Riehl simply omitted the front, thus effecting a great simplification in this part of the model. However, it is a fact that true surface fronts move southward over the United States in wintertime and that they may move off the continent into the Gulf of Mexico and the Caribbean. The surface front becomes weak, but can often be traced far to the south into Central America. It is then found that it is dissociated from the polar trough (especially in the pressure field) and that the chief cloudiness and precipitation accompany the eastern part of that trough rather than the surface front. This picture has been elaborated by Cressman [16], Simpson, and others. As time goes on more and more complexities are introduced into it; one suspects that all is not well with the polartrough model and that several different synoptic phenomena are being confused under one heading. At present, however, little research is being done on winter disturbances in the tropics and the time seems to be ripe for new investigations. In the meantime, if current synoptic maps from weather stations in the Pacific are a guide, there seem to be two rival explanations of winter disturbances in the higher tropical latitudes: the polar trough explanation and the older one which accounts for all winter precipitation in the trades in terms of classical fronts traveling from higher latitudes

—

toward the equator. In 1948 Freeman periences in the

on the basis of wartime exGuinea area, introduced a new

[30],

New

— 870

TROPICAL METEOROLOGY

type of perturbation into equatorial meteorology. The easterly current near the equator was described by him as being on occasion the seat of a disturbance in the

speed field in the lower atmosphere. The streamlines are not disturbed from their easterly direction, but maxima and minima of speed travel downstream in the current. Freeman places great emphasis on a "jump" in speed corresponding to the passage of the trough in the normal type of wave. However, it is probable that this is merely an extreme form of a longitudinal wave common in the New Guinea area and known to forecasters there since the elaboration of the pilot-balloon network in 1942 and 1943. For convenience in this discussion, I shall call all easterly waves that are detectable in the speed field but not in the streamline field, Freeman waves, without necessarily agreeing with the dynamical explanations advanced by Freeman. As far as I Icnowthis type of wave is found only in the New Guinea area, and there is reason to suspect that the peculiar orography and geographical position of that island play an important part in its genesis. However that may be, we may fairly add a new type of disturbance, independent of fronts or convergence zones, to those already known to affect the homogeneous air streams of low latitudes. It was one of the great advantages of the air-mass theory that it seemed to give a complete or almost complete explanation of a multitude of different weather phenomena in both high and low latitudes. For low latitudes, the climatological school also appeared to have a complete system of explanation. This is not the case, at least explicitly, with the newer concepts advanced by the perturbation school. The ideas are new, the whole movement being less than ten years old. As a consequence there has been a tendency to emphasize methods of analysis, especially synoptic analysis, rather than to attempt complete theories. Further, the workers on perturbations of homogeneous streams have rightly adopted explanations from earlier meteorologists, where these have seemed to them to fit the facts, even though at the time it seemed difficult to reconcile those explanations with the newer outlook. We have already mentioned the fact that the equatorial front was accepted by the perturbation school; it was, of course, regarded as a zone of intense horizontal velocity convergence in the lower atmosphere, and its role as an atmospheric discontinuity was minimized. Nevertheless the newer analyses in the vicinity of the equator were almost indistinguishable in practice from those of the more enlightened members of the air-mass school, such as Deppermann. Similarly, in their treatment of the monsoons of Asia, Africa, and Australia, the group adopted almost without question the explanations of the climatological school. Thus, although no unified theory has yet been presented, we may reconstruct such a theory from these adaptations, from hints in the literature, and from the evident dependence of the group upon the dynamical conceptions of Rossby and his coworkers in Chicago. In this reconstruction, the trade winds, considered as broad streams of air largely homogeneous in the lower horizontal planes, play a major role. Less empha-

than formerly is placed on the meridional components of these winds. They are, indeed, regarded as part of the circumpolar vortex, which happens to be retarded with respect to the earth's surface in low latitudes but which moves faster than the earth in higher latitudes and in the upper air over the tropical zone. The base currents of the general circulation, on this view, are primarily zonal. Meridional circulations arise as perturbations on these currents; the only synoptic problem in tropical regions, with the sole exception of the study of the equatorial front, is to describe and explain the perturbation of the zonal currents in the tropics. After description, the perturbations are classified as we have seen; there are (1) the major "dynamic" perturbations of the zonal motion, the subtropical anticyclones and the semipermanent lows of high latitudes; (2) the great seasonal perturbations of the trades, the monsoons, due to thermal causes, as understood by the climatological school; (3) the perturbations of the trades themselves in winter the polar troughs, in summer the easterly waves and Freeman waves; and (4) the minor diurnal and orographic perturbations, for which an explanation has already been advanced. Hurricanes and tropical storms arise in two ways: (1) as a result of dynamic instability in the trade current, leading to the growth in amplitude of the easterly wave and its transformation into a vortex, and (2) as a result of some unknown process affecting the equatorial front (or, if one wishes to be free of all frontal taint, the intertropical convergence zone). The causes of the instability are unknown, though Riehl has advanced two accounts of the sufficient conditions [54, 55]; of conditions both necessary and sufficient there has been so far no hint in the literature. Whatever may be the difficulties of explaining the origin of hurricanes, typhoons, and other tropical storms, explanation of the major features of the perturbations (again, with the exception of the equatorial front) is achieved by the methods of dynamic meteorology as set forth by Rossby. The central notion of these methods is that the vertical component of vorticity is conserved during the isentropic motion of the air particles in the trade-wind zones. However, in the case of the easterly wave, the horizontal velocity divergence of the lower parts of the trade must be taken into account, and this makes the so-called vorticity equation so intractable mathematically that no quantitative evaluation of the wave characteristics can be carried out the explanation must therefore follow the original qualitative discussion of Bjerknes [7], i.e., in terms of a latitude and a curvature effect. Greater precision was given to this latter explanation by Bjerknes and Holmboe [8], but unfortunately the theory as handled by them leads to the result that all easterly waves of the type described by Riehl must deepen and give rise to vortices.^ Freeman, moreover, has advanced an entirely

sis

—

Bjerknes has directed my attention to the between the theoretical results and the Riehl model by taking into account convergence due to friction in the lowest levels of the divergent part of the wave. He thinks that this might bring about a balance in the integrated mass divergence over the region and thus stabilize 5.

Professor

J.

possibility of effecting a reconciliation

the wave.

:

TROPICAL METEOROLOGY waves he describes; no one has attempted to reconcile the two dynamic explanations. The confusion that results from attempts to explain the dynamics of the perturbations in the tropics is probably temporary; at all events it is negligible comdifferent theory for the origin of the

so

far

pared with the greater confusion of ideas concerning the general circulation in low latitudes. Here the workers have followed Rossby with implicit confidence, and it is in his writings that we find the most complete expression of their views. We shall therefore examine in some detail those parts of his papers that relate to the tropics. In 1941 Rossby published "The Scientific Basis of Modern Meteorology" [56], summarizing his views on the dynamics of the general circulation; presumably he held the same views in 1945, since the same paper was republished in the Handbook of Meteorology [57]. In this paper Rossby gives a masterly exposition of the climatological explanation of the tropical circulation. It is in fact Hadley's explanation in modern dress. First, we have the direct circulation cell, on a nonrotating earth. As the result of the surplus of incoming over outgoing radiation in the lowest layers of the atmosphere near the equator, the temperature in very low latitudes tends to increase, with consequent expansion of equatorial air columns the contrasting radiative regime in higher latitudes produces a tendency to contraction of the vertical air columns. "Thus," says Rossby, "at a fixed level of, say, 5 km (3 miles) above sea level, a greater portion of the total atmospheric air column would be found overhead near the equator than near the poles." A direct circulation converting potential into kinetic energy would result; the air motion would have a component toward the equator in the lower layers and away from the equator aloft. On a rotating earth, zonal components would be introduced. The motion, the same on every longitude, would be subject to the conservation of angular momentum. "A ring of air extending around the earth at the equator ;

at rest relative to the earth, spins around the polar axis with a speed equal to that of the earth itself at the

equator. If

somehow

this ring is

pushed northward over

the surface of the earth, its radius is correspondingly reduced; and it follows from the principle set forth that the absolute speed of the ring from west to east increases." Here we have the origin of the antitrades.

The

trades, in like

manner, acquire their easterly com-

ponent as a result of the conservation of angular momentum. The final result is that though east winds prevail between

"Above 4 vail in all

mean

30°N and 30°S

km

in the lower

atmosphere,

(2i-2

to 3 miles), westerly winds prelatitudes." Thus the observed features of the

to 5

circulation in the tropics, after the abstraction of and orographical perturbations, is

diurnal, seasonal,

completely explained. In 1947 Rossby completely rejected this model of the tropical circulation, for the following reasons [58] 1. He quotes Vuorela [71], Kuhlbrodt [39], and the wartime data from the Marianas and Marshalls as showing that the easterlies near the equator extend farther upward and poleward than would be compatible

871

with the direct-cell theory. He says, "... it is fairly clear that the simple thermal circulation outlined by Hadley cannot be the sole, or even the dominating, feature in the mechanism of the trade winds." 2. He then goes on to point out the great uniformity of the meteorological elements, especially temperature, in the tropics, and the difficulty of reconciling these observations with the simple thermal explanation. 3. He next mentions the "discovery" of Fletcher [28] that in some longitudes there is a mean west, not east, wind near the equator, and this in oceanic regions. Defant also is mentioned in this connection. Further, the well-known zone of divergence in the equatorial central Pacific is cited in support of the thesis that the direct-cell theory is inadequate. 4. "The i-emarkably small annual march of the doldrum belt" seems to Rossby to contradict the directcell

theory.

been known to tropical For example, both van Bemmelen [70] and Kuhlbrodt [39] have emphasized point (1) and it was thoroughly established by 1939 in the Pacific as a

Each

of these points has long

meteorologists.

result of pilot-balloon observations; point (2)

maps (see also by Deppermann

as old

is

point has been discussed [23]; and, further, the explanation of persistent west winds at the equator was first advanced by Piddington and Reid [52] one hundred years ago. The dry zone in the central Pacific has been discussed by Schott [62] and the New Zealand meteorologists, particularly Seelye. All these points, and others I have already mentioned, long ago led many tropical meteorologists to reject the extreme climatological view and some to embrace the frontal and air-mass theory as applied to the tropics. After summing up these objections, Rossby generalizes from them, implying that because the direct-cell theory fails to apply over certain longitudes it fails over as the earliest climatological (3)

[61])

;

all. But this is to commit the typical fallacy of the climatological school: what I may call fallacious generalization from a given longitude. It arises when we become acquainted with new observations restricted to a narrow longitudinal band. Thus, when the older climatologists first became acquainted with the very persistent trade winds typical of the eastern border of the subtropical anticyclones, they generalized to form

a model in which, along every longitude, these winds and the associated antitrades prevailed. We have recently become more aware of the mean state at the

western ends of the subtropical highs, where "double equatorial fronts" and west winds on the equator are common; there is therefore a tendency to generalize from these longitudes to the whole tropical belt. The same remarks apply to the temperature distribution: at the eastern ends of the anticyclones,

horizontal

temperature gradients may be found both on the synoptic and on the mean maps, aloft and at the surface [18, 61].

their

The

model

older climatologists could therefore justify of the trades

by appealing

to observations

from these longitudes. However, if we concentrate our attention on the western parts of the tropical oceans, particularly of the Pacific, and generalize to all longi-

TROPICAL METEOROLOGY

872

of the vertical

ought, however, to make a few general observations on method, deriving our principles from the study, not only of the achievements of the three schools, but of the errors they have committed. 1. Before attempting causal analyses of tropical phenomena, or dynamic explanations, we ought to be sure that our empirical descriptions are correct. This

appealed

principle

we become convinced that there are no horizontal temperature gradients in latitudes below 20°. The new model, then, is open to the same empirical tudes,

objections as the old. But there are also serious objections to the theoretical explanations which have been

advanced, inasmuch as the principle of the conservation

component of the absolute vorticity is Without entering into the details of the new theory, which would take us beyond the limits of this article, we may sum up these objections by saying that it has yet to be shown that the mean motion of the to.

tropical atmosphere

is

autobaro tropic, horizontal,

fric-

and nondivergent to a high degree of approximation. Until this has been shown, we must suspend judgement as to the applicability of Rossby's concepts in low latitudes. Even if we admit them, it will be only in certain longitudes, and not as a general explanation tionless,

of the tropical part of the planetary circulation. It is clear now that the great success of the perturbation school has been in the realm of descriptive synoptic meteorology; the models of the perturbations which they have promulgated have been applied in the field with far greater success than was ever achieved by the air-mass school. In dynamical meteorology and in their treatment of the general circulation, members of this school have been less successful. There have been complaints, moreover, that the model of the easterly wave published by Riehl is far too rigid. In particular, the slope of the actual systems is frequently different from what might be expected from the published accounts and, what is more important, the weather distribution about the wave axes departs widely from the

model But

fallacious generalizations.

THE PRESENT AND THE FUTURE General Observations. Each of the methods of approach to the tropical problems which were described in the preceding sections has something to recommend it; each has contributed something to our empirical knowledge and our understanding. As far as we can see at present, progress will come by pursuing to further lengths, with new and more detailed data, the lines of investigation that have already proved profitable. It is

we

any

unlikely, that

is,

new theory of As a guide to

tropical meteorology in the near future.

that

shall entertain

radically

the assessment of the present state and possible future development of the science we ought therefore to extract from the confusion of present conical

the Pacific; by the air-mass school in describing fronts, since they neglected to describe accurately the temperature and wind changes observed at the supposed discontinuities; and by the perturbation school in omitting all mention of the convergence lines of the frontal school in their description of the model of the easterly wave. The fallacy of generalization from a given longi2. tude should be avoided as far as possible. We ought always to be on guard against it, particularly when dealing with the mean circulation in the tropics. But faulty generalization also enters in other contexts, especially when we have theoretical preconceptions. Thus the frontal school, as soon as it found evidence of empirical "fronts" in the neighborhood of the equatorial low-pressure trough, assumed that the occlusion process would also occur. No evidence was, so far as I know, ever produced to back this up. We ought then to remember at all times that, owing to the fact that we never have as much data as we really need, the habit of hasty generalization is an occupational disease of meteorologists. AU the geophysical sciences suffer from this handicap we ought to be at least as careful as the pure ;

and probably more careful. ought to guard against the statistical fallacy in meteorology. This consists in assuming that a mean motion of the atmosphere, arrived at by the standard physicists, 3.

[26].

these, as we shall see, are not serious objections; they can be removed by a more careful study of the perturbations in low latitudes and by avoiding the tendency to apply models to synoptic maps as if they were rubber stamps. I ought perhaps to point out that my sympathies lie with the perturbation school and that if the criticisms here seem to be harsh, it is because I believe that future advances in tropical meteorology will come through the application of the concepts and methods of this school, provided they are freed from

those concepts upon which the majority of tropmeteorologists would agree. Before we do this we

flicts

was violated by the climatological school in describing the doldrums, particularly the doldrums in

We

methods

of climatology, represents a physically possteady -state motion. Achievements and Future of the Climatological School. There is no doubt that the departures from the mean values of the meteorological elements that are attributable to the diurnal cycle of radiation and to orographical effects can be of great magnitude in the tropics. It is the virtue of the climatological school that they have always emphasized these variations. However, in recent years little research work that might lead to a better understanding of the phenomena has been carried out. It is encouraging to notice that Leopold [41] has entered this field with papers on the so-called sea-breeze fronts in the Hawaiian Islands. Wartime synoptic experience everj^where in the tropics has confirmed the existence of organized lines of cumusible

lus or cumulonimbus, accompanied by wind shifts, which simulate the cold fronts of high latitudes but which are demonstrably due to diurnal and orographical causes. The dynamical problems raised by these "fronts" are among the most interesting problems of tropical meteorology. Their properties, however, can be investigated only on location; it is to be hoped that young meteorologists resident in tropical areas of high relief will, in the future, undertake the investigation. Apart from the theoretical interest of such "fronts,"

:

TROPICAL METEOROLOGY

873

the greater precision that would be given to local forecasting in the tropics by a complete understanding and description of the diurnal variation of orographical organized cumulonimbus well merits military and com-

valid for the longitudes where the trade

mercial support of such investigations. It is difficult to deny that, as far as the most general features of the monsoons are concerned, the climatological school seemed to have analyzed the mean data and to have correctly assigned astronomical and orographical causes to the variations. But it is probable that the monsoons are far more complex in their details than that school supposed. There are several reasons for this conjecture. First, the so-called monsoon lows over the land, whatever may be their properties in the mean, on synoptic maps show day-to-day variations which could be attributed to the westward movement of individual cyclonic circulations through the area. Moreover, where the conformations of the continents are favorable, it can be observed that these minor cyclones come in from the sea, fully formed. They cannot under any circumstances be regarded as "heat lows." These local circulations are known in India, in Australia, in Indo-China and China, and in East Africa. Second, and this is probably correlated with the facts first mentioned, the wartime synoptic observations confirmed what was after all known locally for many years that the weather in the Asiatic monsoons is far more variable than popular and textbook accounts would lead one to suppose. It does not rain continuously for three or four months in the wet season. There are frequent spells, lasting sometimes for days, during which there is little precipitation and sometimes little cloudiness. Third, there are, on certain longitudes, quasipermanent low-pressure areas which migrate to and away from the equator, lagging behind the sun in the same manner as the monsoon lows, and having, on their equatorward borders, belts of winds with a westerly component; they are situated, however, not over the land but over the ocean. There is a very persistent mean low of this type which migrates from eastern New Guinea to the eastern borders of the Philippines and back. There is another west of Mexico and Central America. If these lows had been situated over a land mass, we would have no hesitation in calling them monsoon lows, and in accounting for their movements and the distribution of the meteorological elements about them in the usual manner of the climatological school. We ought, perhaps, to follow up these climatological hints and, combining them with an intense synoptic and dynamic research into subequatorial semipermanent lows in general, improve our understanding and prediction of monsoon weather. Largely because of historical accidents, research has been concentrated in the trade-wind zones of the Pacific and Atlantic. The time is now ripe for a more intensive investigation of those parts of the tropics that show large seasonal variations in the meteorological elements.

aloft, the typical antitrade,

We

should, however, not neglect the oceanic regions.

Particularly

we should not completely

reject the classi-

cal climatological explanation of the trades, as

has done. It

is

possible that that explanation

Rossby is

still

is really a where it shows, in the lower level, great persistence, a large meridional wind component, a com-

trade,

i.e.,

paratively strong meridional temperature gradient and, evidence of persistent and marked subsidence, with a low and strong trade-wind

These conditions obtain, as has been pointed and southeastern branches of the great quasi-permanent anticyclones. Downstream, toward the west, however, factors other than those invoked by the climatological school may dominate the inversion.

out, in the eastern

motion. Here, Rossby's new explanations may hold. Above all, our survey shows, the greatest need is for more complete data, especially from the upper air. At present the distribution of observing stations in all latitudes is largely determined not on scientific, but on economic and military grounds. This, it is to be presumed, will not be changed in the foreseeable future. Nevertheless, it seems to be accepted that improvement

than fortyimprovement in our empirical and theoretical knowledge of the mean circulation of the earth's atmosphere. How this knowledge can be built upon an observing network that is half-way adequate only in North America and in Europe is somein practical forecasting for periods longer

eight hours depends on

my knowledge,

has never been explained. content to advance models of the general circulation based upon the North American atmospheric section and theoretical explanations of this model based upon an obsession with the circular vortex, ignoring the tremendous gaps in our knowledge of the meteorology of the tropics (over half the troposphere), of the high latitudes in the Southern Hemisphere, of Asia, even of Central America then they cannot blame those that hold the purse strings for supposing that all is well with the present setup. The fact that acquaintance with new data is enough to cause a complete volte-face in the theoretical work of an outstanding leader in dynamic meteorology, at least so far as the tropics is concerned, should show that the filling of the gaps mentioned above is an absolutely necessary (although not sufficient) condition of the solution of the long-range forecasting problem. Achievements and Future of the Air-Mass School. The achievements of the air-mass school were two in number. First, they drew attention to the great horizonthing that, to In particular,

if

scientific meteorologists are

—

tal

homogeneity

of the easterly

and the westerly

air

streams found in tropical latitudes, described the sources and modifications of these masses, and accounted for them with varying degrees of plausibility. The work on the trades still goes on, at all events. There has recently been a study of the east wind in the Caribbean by Haurwitz and his collaborators that is a model for all

future

work

of this tj^pe [12]. Similar

work

in the

based on the Panama Canal Zone, would be very welcome, particularly in giving us precise knowledge of the structure of the west winds in that area during the summer. Later, the reseai-ches could profitably be extended to the Far East. The se"cond achievement of the air-mass school is that the earlier frontal workers discovered in the tropics, and

far eastern equatorial Pacific,

:

TROPICAL METEOROLOGY

874

described, the organized lines of cumulonimbus cloud, accompanied by appropriate wind changes, which they identified as fronts. The existence of the lines has been

confirmed, but

it

now

appears that the frontal explana-

must be rejected. The following empirical facts may be regarded as established 1. If an adequate streamline analysis of the lower

tion

wind is

field in

which the cumulonimbus

method

carried out, using the isogon

and

his

collaborators

[9],

line is

embedded

of V. Bjerknes

the line of cumulonimbus

coincides in position with an asymptote of convergence

in the streamline

But not

field.

all

asjmaptotes in the

mogeneity. Orographic lines are rarely more than 200 miles long.

Except on such mountainous islands, the lines show temperature contrast in the lowest layers but may do so in the upper air, as a reflection of different lapse rates in the air on either side of the fine. 3.

rarely

may

The

contrast

both

in space

and

intensify, vanish, or reverse its sign

time but without, as far as can be discovered, affecting the location, movement, or intensity of the cloud line. in

4. By far the greatest number of the lines in the equatorial Pacific, and in the Caribbean in summer,

PILOT

DE-BRIEFING

0745 DBS: ENTERED FRONT LINE OF HEAVY CU TO SE 0815 OBS: PRECIPITATION BEGAN 30 MINUTES BEFORE REACHING POSITION LINE OF HEAVY CU TO SE KWAJ.

S.L.

1300

1330

'•"'!

1

"""I

1

TIME

0815

0915

0845 OBS: PRECIPITATION ENDED 10 MINUTES BEFORE REACHING POSITION LINE OF HEAVY Cu TO NW

1230

0715

WEATHER

KWAJ. EO.

TEMP.

24

R H

88

24 24 SO 72

2!

21

96 96

24 86

May

Fig. 1 .—Streamline and isovel analysis at 1500 ft of an equatorial wave passing the Marshall Islands, 1100 Bikini Time, 26, 1946, with two cloud sections observed by weather reconnaissance aircraft. Speed in knots. (Reprinted from the 7th quarterly report of the Tropical Pacific Project, U.C.L.A., a research supported by funds provided by the Geophysical Research Directorate,

Air Materiel

field

Command.)

are accompanied

by a

ized cloud system only

if,

horizontal velocity divergence

borhood

is an organsame time, the total

"front"; there at the is

negative in the neighft, the cloud

of the line. Aloft, say at 20,000

may correspond to an asymptote of positive divergence in the horizontal wind field. We shall henceforth call organized lines of cumulonimbus (or tall cumulus, on occasion) convergence lines, not fronts. We ought to point out that regions in which there is negative horizontal velocity divergence in the lowest layers are not always the seat of lines of convergence; these occur only if there is also convergence in the streamline along an asymptote. Figures 1 and 2 illustrate some of the properties of convergence lines in the Marshall Islands. 2. Lines of convergence form readily as a result of diurnal and orographic disturbances of the wind field in the neighborhood of large mountainous islands. We may then get temperature contrasts across the line, but these contrasts are confined to the lowest layers of the atmosphere. Aloft there is usually horizontal holine

show no temperature contrast whatever below 20,000 Above this level, temperature gradients across the line may have either sign or be absent. 5. In low latitudes, the vertical component of the ft.

vorticity along the line

may

zero. Cyclonic vonticity is

be positive, negative, or not a necessary condition for

the existence of the line. 6. The convergence line may or may not be accompanied by a trough in the pressure field. 7. Convergence lines may develop within an air mass which is, within the limits of observational error, completely homogeneous. 8. Convergence lines do not move with the wind, nor are pressure changes useful in forecasting the movement. We conclude: Density contrasts and cyclonic shear are conditions which are neither necessary nor sufficient for the formation of convergence lines and hence these lines are not fronts in the sense that that concept is

employed

in the frontal

and air-mass theory. The

B

TROPICAL METEOROLOGY only empirical conditions so far discovered which are necessary and sufficient are the existence of horizontal velocity convergence in the lowest layers of the atmosphere plus the existence of an asymptotic line in the streamline field. This statement, of course, in no sense gives a causal explanation of the lines; it merely gives descriptive correlations.

With these conclusions, we must dismiss the whole body of theoretical explanation developed by the airmass school in the tropics, but at the same time we must incorporate their empirical findings with those of

875

trough in the western Pacific. He comes to the conclusion, a correct one in my opinion, that the western part of the equatorial trough is the seat of a large number of eddies which for the most part move from east to west, either recurving ultimately as hurricanes

and

tropical

storms or passing on to the continent of Asia. But his method of analysis is incapable of showing the relation of the "fronts" that develop pari passu with the vortices to the early stages of their development. From Figs. 16 and 17 in his paper, for example, and from the text, it is clear that Riehl envisages the lines of convergence as 20°

KWAJALEIN 0200 B PRESUMPTIVE NORTHERN HEMISPHERE AIRMASS)

TARAWA 0200 PRESUMPTIVE SOUTHERN HEMISPHERE AIRMASS) JULY 9, 1946

160° EAST

—

Fig. 2. Streamline and isovel analysis at 1500 ft of an equatorial vortex passing the Marshall Islands, 1100 Bikini Time July 1946, with soundings from Tarawa and Kwajalein. Speed in knots. (Reprinted from the 7th quarterly report of the Tropical Pacific Project, U.C.L.A., a research supported by funds provided by the Geophysical Research Directorate, Air Materiel Com-

9,

mand.)

the perturbation school; this we shall attempt in the next section. Achievements and Future of the Perturbation School. The outstanding achievement of this school is undoubtedly the discovery and description of the easterly wave and its relation to Caribbean hurricanes. Its fault lies in an almost complete neglect of the empirical findings of the air-mass school. This is to be attributed to the fact that members of the school have consistently used a streamline technique that is inadequate for the study of detailed features of the wind field. As a result, the school has placed great emphasis on the "trough" in the wind field and has marked it with a heavy line on the map, but at the same time has completely missed the asymptotes of the field which, indeed, are accurately located only by using the standard methods described by V. Bjerlvnes. This weakness in the synoptic methods of the school has recently been emphasized by Riehl's investigation [54] of the structure of the equatorial

existing before the formation of the vortices. Further,

the equatorial westerlies are conceived as being part of the general circulation, so that convergence lines between them and the trades, though not continuous throughout the equatorial low-pressure trough, may nevertheless exist independently of the vortex series. The result is a very complex picture of the normal state of equatorial circulation in the wet season. When the standard methods of streamline analysis are applied to maps from this area, however, a much simpler picture is seen. Upstream, in the central Pacific, the trade winds of the two hemispheres lie side by side most part, forming an extensive easterly current that overlaps the equatorial low-pressure trough in for the

both the Southern and the Northern Hemispheres. This easterly current is subject to perturbations of the same type as the easterly waves of the Caribbean save that they are at much lower latitudes and extend across the low-pressure trough. No lines of convergence are

'TROPICAL METEOROLOGY

876

found in or near the trough so long as the waves are of small amplitude. There is, of course, horizontal velocity convergence in the lower layers, associated with the wave motion, but it may be said to be "unorganized." As the waves move toward the west, some of them at least become unstable, growing in amplitude. The wave in the pressure field can now be detected with good observations, and an asymptote of convergence usually appears behind the "trough" of a wave and a corresponding asymptote of divergence ahead of it. The asymptote of convergence may be detected in flight as a line of cumulonimbus or tall cumulus. With further increase in amplitude of the wave a small vortex appears in the wave pattern, usually, but not always, in the equatorial trough itself. With the formation of this vortex, westerly winds near the equator appear for the

west; there the passage of so many of them north and south of the equator and in both the wet and the dry season results in a mean west wind on the equator in the western part of the ocean. Since this west wind is the statistical result of the vortices it is clearly fallacious to import them into a hypothetical general circulation which is then perturbed to produce the vortices. Our task is to explain the mean maps as the integration of numerous synoptic maps, not to explain the synoptic map in terms of the mean and its perturbations. In other words synoptic models must always be checked by what is known of the mean circulation, but we cannot, except under very special circumstances, infer the synoptic models from the mean map. Figures 3 and 4 show schematically the correct explanation for the tropical Pacific. Neglect of this principle led to the

Fig. 3.— Streamline and isovel analj'sis of the mean resultant surface winds, tropical Paoifio Ocean, Northern Hemisphere autumn. Speed in meters per second. Data derived from Deppermann and Werenskiold, and analyzed by G. A. Dean.

first time.

The vortex proceeds on

its

westward track;

may deepen very rapidly, forming a typhoon storm, or it may remain weak, being accompanied it

this case

by one

or in

of the slight depressions that are

characteristic of the

doldrums

in the western Pacific.

When the vortex is well developed a complicated

system asymptotes accompanies it and the movement of these "equatorial fronts" is dependent not on the winds on either side of them but on the motion of the vortex itseK. This brief summary of the equatorial waves and vortices is based upon recent study of the data collected during the Bikini and Eniwetok bomb tests and the whole subject has been more fully treated in recent of

publications [47, 48]. are now in a position to reconcile the conflicting views that have been held concerning oceanic equatorial

We

meteorology. We see first that the equatorial westerlies, as long ago realized by Piddington and Reid, are merely the mean expression of the fact that the vortices form in the central parts of the Pacific and move toward the

conception of the continuous equatorial front; because can easily be detected on the mean maps, it was assumed that it would be found on the synoptic maps. Recent research has shown that the synoptic convergence lines are quite different from the mean convergence line; the latter, however, can be derived as the statistical result of the properties and positions of the former. The special conditions under which we can pass from the mean map to the synoptic map obviously hold in the eastern parts of the oceans. Here we know that departures from the mean are very small compared with the mean. And it seems that in these regions the thermal effects long ago described by the climatological school must play at least the dominant part in driving the southeast and northeast trades. Here the direct-cell model is probably a good approximation to what actually occurs in the atmosphere. The result of the action of the direct cell, however, is not a mass ascent of the trades at the equator, and their return aloft as antiit

.

TROPICAL METEOROLOGY

A

trades.

large part of the trade air, both

at the passes westward as a solid east current, quite analogous to a jet of fluid being directed into another fluid at rest. Like that jet, the east stream spreads downstream into its surroundings. It is also un-

ground and

aloft,

stable, so that the slightest disturbance of the

stream

waves which grow in amplitude and ultimately form a series of vortices which either move out of the stream into higher latitudes or end stagnating in the "monsoon low" over the land in the extreme west. leads to

Downstream the

air is thoroughly mixed, there are only small temperature gradients, and it is here, if anywhere, that the dynamic mechanisms suggested by

Rossby in his latest paper will be valid (see Fig. 4) We have not, it will be noticed, done more than suggest a working hypothesis to apply to the large-

Fig.

and

its

in

a single ocean. It

this point while

is

we have

data over the land. But a great step forward would be taken if we could explain the main features of the circulation over one ocean. The gap in the data so

little

is

clearly in the eastern oceanic sectors. series of observations in

The only exsuch a sector are those

of the Meteor in the Atlantic [18]. data for the eastern sectors of the Pacific

elucidation of the dynamics of easterly

very low latitudes

is

badly needed

—an

elu-

cidation that, by including vertical motions as well as horizontal, would cover the main features of both the equatorial and the Freeman wave, since the latter is clearly only a limiting case of the former. It is probably too early to ask for a dynamic explanation of the kinematic features we now know attend the transformation of an equatorial wave into a vortex, since these will clearly involve perturbations of large and changing amplitude, with the consequent dilBculty of solving nonlinear equations. But we may fairly ask the dynamic meteorologists for a treatment of the relation between the energy of the equatorial perturbations and that of the east current, particularly as the synoptic evidence suggests that kinetic energy is transferred

of the mean circulation of Fig. 3 in terms of a "general circulation" (trades and equatorial perturbations, stable and unstable.

scale features of the motion premature to advance beyond

first

The in

4.— Schematic explanation

easterlies)

tended

school.

waves

877

We

require similar

North and South and the South Indian Oceans, and clearly the

region to investigate should be the eastern sectors

of the tropical Pacific,

about which

little is

known.

A

fuU program of upper-air soundings in this region would enable us to decide whether the direct-cell model of the trades is to be taken seriously, for, with comparative isolation by the high mountain barriers to the east, it is here that we would expect the most favorable conditions for a direct thermal circulation to develop. There remain other projects which we have suggested in the previous discussion of the perturbation

from the east current to the perturbations as the

move downstream. The approach

of

Kuo

[40]

latter

here

seems the most promising. The problem of tropical-cyclone formation is at present so different in aspect from what it was ten years ago that one is encouraged to think that the rate of progress will be maintained and will result in a complete solution in the near future. It now appears that the problem is that of deciding the sufficient and necessary conditions for the rapid deepening of a vortex already formed from an easterly wave, whether this be in high tropical latitudes, as in the Caribbean, or in low latitudes, as in the eastern Atlantic and the Pacific. We know that this deepening never occurs over the land, in spite of a plentiful supply of vortices; clearly a very moist atmosphere is necessary for the process to occur. But, though we have cause for optimism concerning the future of hurricane research, the problems connected with forecasting the movement, especially the recurvature, of tropical storms, remain as they were

TROPICAL METEOROLOGY

878

twenty years ago, in spite of much work [44, 55, 66]. methods so far suggested suffer from the defect that exceptions to the deduced rules occur too frequently in practice. Some methods suffer from the defect that they merely shift the forecasting problem from one field to another and often more difficult field. Thus all methods based upon isotherm steering suffer from the fact that it is frequently more difficult to forecast the isothermal field at upper levels than to forecast the track of the storm itself. Above all we need an extensive investigation of the necessary and sufficient conditions for the formation of All forecasting

^

rain in the tropics. In spite of published accounts of the precipitation of cumulus clouds whose tops are well

below the zero isotherm, and in spite of the use of fact

by

this

forecasters operating in oceanic tropical

all

by the scepticism high-latitude meteorologists. The

regions, one is constantly surprised

concerning first

it

among

worker to publish a complete atlas of precipitating

tropical clouds will be performing a great service to meteorology, for though he may solve no problems he

draw the attention of the scientific world to the fact that the Bergeron-Findeisen theory of precipitation gives a very incomplete account of the causes will at least

In that atlas, I hope, appear good pictures of the complete precipitation of a cumulus, i.e., precipitation not only from the bottom but also from the sides and overhanging top of the cumulus ^the almost explosive upsetting of the colloidal stability throughout the cloud mass. Deppermann has already published photographs of such clouds, which he calls "melting" cumulus a very descriptive term [22] but apparently he did not realize the great theoretical importance of the phenomenon he was depicting. The problem of precipitation has its s3Tioptic aspects also. The present observations, as transmitted in the international code, give us very little clue to the type of rain that is falling, whether it be from an upper sheet of altostratus, unconnected with cumulonimbus, from altostratus connected with very distant cumulonimbus pillars, from cumulonimbus, from cumulus of great vertical extent, or from comparatively shallow cumulus. The result often enough is that the forecaster cannot tell whether the rain is connected with an extensive region of convergence in the lower atmosphere or whether it is to be attributed to the colloidal instability of cumulus clouds in a region which is in total of colloidal instability in clouds.

will

—

—

—

formative. The lapse rate approaches very closely to the moist-adiabatic over a deep layer, and this can be clearly correlated with existing weather. However, without noticeable change in the weather one may next receive a sounding that differs from the first in the lapse rate both of temperature and of humidity, without apparent reason. It might be suggested that these vagaries are connected with the passage of the apparatus through different parts of cumulus and cumulonimbus clouds and that the soundings reflect the microstructure of the tropical air, not the broad-scale features we wish to study synoptically. Theoretical knowledge of the factors affecting the lapse rates in clouds derived from entrainment studies, together with information on the path of the sonde with respect to existing cloud masses, might do much to remove the perplexity that the present soundings sometimes cause. Conclusion. One would like to conclude as a result of this survey that tropical meteorology, the most ancient branch of scientific meteorology, has shown more progress in the last ten years than in the previous fifty. However that may be, it is certain that it now offers a rich field for research to the climatologist, synoptician, and dynamic meteorologist alike. To the climatologist it offers the challenging task of collecting, reducing, and studying the unique wartime tropical data before they become lost forever; to the synoptician it offers the prospect of new empirical discoveries in a field from which the major errors have just been cleared away discoveries, moreover, that cannot fail to react on the theory of fronts and air masses in high latitudes; to the dynamic meteorologists it presents a series of problems in perturbation theory, applicable to an atmospheric region which, more closely than any other on this earth, resembles his ideal: the homogeneous, horizontally moving, frictionless, and incompressible

J

fluid.

1

—

REFERENCES Alpert,

2.

Aeakawa,

3.

divergent and subsiding.

Connected with this problem is that of the lapse rates and humidity within tropical clouds. It has been claimed that, level for level, tropical clouds are colder than their environment. A recent paper by Barrett and Riehl [4] has, however, pointed out the possible origin of such claims and has rightly emphasized the observational difficulties. More work, howof temperature

ever, needs to be done.

—

426-432 (1945). H., "The Formation of Hurricanes in the South Pacific and the Outbreaks of Cold Air from the North Polar Regions." /. meteor. Soc. Japan, Ser. 2, Vol. 18,

No. 1, pp. 1-6 (1940). Barnbtt, M. a. F., The Cyclonic Storms in Northern New Zealand on the Snd February and the 26th March, 1936. New Zealand Meteor. Off. Note No. 22, 34 pp., Wellington, 1936.

4.

Barrett, E. W., and Riehl, H., "Experimental Verification of Entrainment of Air into Cumulus." /. Meteor.,

5.

Bergeron,

6.

Bjerknes,

304-307 (1948). T., "Richtlinien einer dj^namischen Klimatologie." Meteor. Z., 47: 246-262 (1930). 5:

latitudes

On

the theoretical side, the recent work on entrainment [68] of air in tropical clouds seems to be capable of leading to the solution of an old problem of tropical forecasters the problem of what to do with the radiosonde observations. Many soundings in the tropics seem to be completely unin-

L., "The Intertropical Convergence Zone of the Eastern Pacific Region." Bull. Amer. meteor. Soc, 26:

1.

7.

8.

J.,

"La

circulation

sous-tropicales."

atmosph^rique dans

Scientia,

Sir.

les

phys.-math.,

Paris (1935). "Theorie der aussertropischen Zyklonenbildung." Meteor. Z., 54: 462-466 (1937). and Holmboe, J., "On the Theory of Cyclones." J. Meteor., 1: 1-22 (1944).

9.

Bjerknes,

V.,

and others, Dynamic Meteorology and Hy-

TROPICAL METEOROLOGY

— Kinematics. Washington, D. C, Car-

drography, Part II

34.

negie Institution, 1911. 10.

Physikalische Hydrodynamik.

Berlin,

J.

Springer,

1933. 11.

35.

and Braby, H. W., "The Clash of the the Pacific." Quart. J. R. meteor. Soc, 47: 1-13

Brooks, C. E. Trades in

12.

13.

14.

and others, "Vertical Distribution of Temperature and Huniiditj' over the Caribbean Sea." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 11, No. 1, 82 pp. (1949). Burns, M. C, Frontal Conditions at the Line Islands and other Equatorial Islands. Fleet Weather Central, Navy No. 128, Paper No. 2, p. 7, 1944.

Buxton, E.

Papers prepared for Pan American Airways. U.S. A.A.F. Weather Research Center 4, No. 4, 1942. Ci^TLiAN Staff, Institute of Tropical Meteorology, "Tropical Synoptic Meteorology" in Handbook of Meteorology, F. A. Berry, Jr., E. Bollay, and N. R. Beers, ed. New York, McGraw, 1945. (See pp. 763-803) Chessman, G. P., "Relations Between High and Low Latitude Circulations." Dept. Meteor. Univ. Chicago, Misc. Rep., No. 24, pp. 65-100 (1948). Day, J. A., Synoptic Analysis in the Tropical Pacific.

37.

16.

17.

39.

40.

20.

21.

22.

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pendix to the 5th Quarterly Report of the Tropical ProjCambridge, Mass., 1949. and Ellsaesser, H. W., "Notes on Tropical MeteorolS.,

Introduction

to

1

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:

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Forecasting Weather

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and Ramakrishnan, K.

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General Circulation of the Atmosphere over India and Its Neighbourhood." Mem. Indian meteor. Dept., 26: 190-195 (1939).

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No. 54.

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the Formation of Typhoons." /. Meteor., 5: 247-

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Garbell, M.

131/44, 1944.

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in the Australian Equatorial Regions. Part III

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Petterssen,

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I.,

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Region, Rio Piedras, P. R., 1945. Espy, J. P., Philosophy of Storms. Boston, C. C. Little and J. Brown, 1841. Fletcher, R. D., "The General Circulation of the Tropical and Equatorial Atmosphere." J. Meteor., 2: 167-174

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in

Mintz, Y., "A Rule for Forecasting the Eccentricity and Direction of Motion of Tropical Cyclones." Bull. Amer. meteor. Soc, 28: 121-125 (1947). Namias, J., Methods of Extended Forecasting. Washington, D. C, U. S. Weather Bureau, 1943. Naval Meteorological Branch, Admiralty, London, Tropical Climatology and Forecasting in the Far East.

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(See pp. 277-280)

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Upper Air Circulation over the Philippines and AdjaBureau of Printing, 1940. Directorate of Meteorological Services, Royal New Zealand Air Force, The Climate of Pukapuka Danger Islands. Climatological Notes, South Pacific Region, New Zealand Meteor. Off., Ser. C, No. 3, 1943.

Dunn, G.

Wellington, 1935.

E.,

J. Meteor., 6: 105-122 (1949).

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Kuhlbrodt,

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Depant,

New York,

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Applied Meteor.

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352 (1937). 38.

Coll.

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"Extracts from Notes Derived from in the Manila-Guam Sector."

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Maps and Flights

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B., Notes on Weather Analysis in the Tropics.

Harmantas, Bull.

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Bunker, A.

Notes Concerning the Inter-Tropical Front Between Longitudes 60 E and 160 E. Malayan Meteorological Service. (Written in 1941.)

Synoptic

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and Shafer, R. J., "The Recurvature of Tropical Storms." /. Meteor., 1:42-54 (1944). RossBY, C.-G., "The Scientific Basis of Modern Meteorology" in Climate and Man: Yearbook of Agriculture. U. S. Govt. Printing Office, Washington, D. C, 1941. (See pp. 599-655)

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Amer. geophys. Un.,

pp. 502-529)

"On

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the Nature of the General Circulation of the

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U.

Lower Atmosphere" in The Atmospheres of the Earth and Kuiper, ed.. Chap. IL Chicago, University

Planets, G. P.

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/. Meteor., 4: 91-94 (1947).

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"Klimakunde der

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Handhuch

der Kli-

W. Koppen und R. Geiger, Hsgbr., Bd.

ScoFiELD, E.,

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1938.

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(1918).

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Tropical Atlantic." /. Meteor., 5: 115-117 (1948).

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Teil T. Berlin, Gebr. Borntraeger, 1938. 83. ScHOVE, D. J., "A Further Contribution to the Meteorology of Nigeria." Quart. J. R. meteor. Soc, 72: 105-110 (1946). 64.

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821-844 (1946-1947).

i

I

'

EQUATORIAL METEOROLOGY By A. GRIMES' Farnborough, Hants, England

INTRODUCTION

The

Equatorial meteorology may be regarded as the meteorology of the region about the equator where the Coriolis term in the equations of motion is no longer the only one which is of the same order of magnitude as the pressure term. Indeed, on the equator itself the Coriolis force is zero and the other terms must balance the pressure gradients which undoubtedly exist. One cannot quote any investigation which will indicate the limits of the region thus defined, but the general impression given by most writers is that the Coriolis force ceases to predominate between the latitudes of 15°N and 15°S, and it is to this region, roughly one-quarter of the surface of the earth, that the following discussion will be confined. The region, extending over the central portion of the Atlantic, Pacific, and Indian Oceans, is largely water broken by the land masses of central Africa, Central America and the northern part of South America, the East Indies, southern India, and Ceylon. Generally speaking, the land areas are sparsely populated and meteorological history is comparatively short, extending back only so far as the beginning of international civil aviation for most places in the region. This is not to say that no extended series of meteorological records exists in the region, but the number of stations with reliable records over a period greater than ten to twenty years is pitifully small for the large area

that has to be considered. The situation is steadily improving, because of the pressing needs of international aviation, and the meteorological services in the more backward meteorologically speaking of the countries in the region are being more and more extended as time goes on. Nevertheless, the advancement lags considerably behind the development in the temperate zone. This is principally due to the high cost of meteorological equipment, such as the radiosonde,

—

—

which puts modern methods of observation beyond the resources of the local governments. The number of scientific workers in the region is very small, and since even this small number exist almost entirely for the purpose of issuing forecasts to aircraft, it is not surprising that little meteorological information of any importance has emerged, and it is fairly certain that

emerge until more equipment and more scientists become available to the region. The standard of observing, except at a few stations, is low in many cases because of the poorness of the equipment, and in many more cases because of the shortage of competent observers. Steps are being taken to improve the observations, but it must be many years before adequate and accurate climatological statistics will be available for most of the region. little will

1.

Formerly Director, British West African Meteorological

Services.

881

greatest impetus to the study of meteorology

was given during World War II when the need for developing lines of communication through the region brought an influx of men and equipment far greater than in prewar days. During this period it was realised that our knowledge of the area was meagre, and a large number of reports, both statistical and otherwise, wer? published to remedy this defect. Not all the reports but at least attempts were made to of the equatorial zone on a scientific basis: if little in the way of coherent meteorological theory emerged, there were at least some ideas suggested that might serve as a starting point

were

of great value

explain the

phenomena

for further investigation.

THE AIR MASSES Except for the occasional intrusion of polar air into the South China Sea area, it seems certain that the only air masses affecting the region are tropical and equatorial. The tropical air masses are those of the trade winds giving on an average a belt of northeast winds in the Northern Hemisphere and of southeast winds in the Southern Hemisphere, both derived from the subtropical anticyclones. During the summer of the Northern Hemisphere the trade wind of the Southern Hemisphere crosses the equator everywhere, so far as can be determined, and becomes what is usually known as the monsoon. In the Northern Hemisphere winter the reverse process takes place everywhere except in the Atlantic and West African areas, and it is these annual movements of air which provide the variations in the weather of the equatorial zone. When the tropical air from either hemisphere has passed into the equatorial zone and becomes relatively stagnant it is known as equatorial air and is therefore not an "air mass" as one usually thinks of the term. Such stagnant air, which frequently develops a light anticyclonic circulation over land masses, is invariably moist (or becomes moist) in the lower layers. This air is a common feature of the synoptic situation and is therefore of great importance.

The

properties of tropical air are quite well known or 5 km, but observations are too few above 5

up to 4

km

seems that winds are mainly easterly. Some investigators consider that these winds play a large part in the variation of weather along the equator, but what part they play has not yet been demonstrated with any assurance. It is not in fact clear from the study of daily charts where the trade winds end and the overriding easterlies begin, because in most cases the maximum speed of the trade is reached between above the surface, and there is only a 500 and 1500 gradual variation of speed in the higher levels. When the tropical air has a continental source it is usual to for reliable conclusions to be drawn. It

above

this level the

m

TROPICAL METEOROLOGY

882

regard the top of the haze layer (2-3 km) as the upper surface. This condition is confirmed by the sudden rise in humidity above this level, but when the tropical air has an oceanic source the surface of separation is ill-defined. Upper-air observations with instruments more accurate than ordinary aircraft thermometers might make it possible to define the separation of upper and lower layers with more precision. When the surface air is equatorial, there is frequently a layer of trade or monsoon air before the overrunning easterlies are reached. The lower boundary of the trade or monsoon air is well marked by a rapid increase in wind speed with height, but the separation of trade or monsoon air and the easterlies is still ill-defined. It is quite clear that the day-to-day determination of the vertical structure of the air masses will not be possible until observations are available in greater quantity and with more precision.

FRONTAL PHENOMENA The question

of the existence or nonexistence of true

frontal discontinuities in the equatorial region of the

most controversial

is

one

issues of tropical meteorology.

The majority

of opinion, however, favours the existence but the very fact that many writers disagree makes it important that factual evidence should be produced. The acquisition of convincing evidence is hampered bj' the lack of close networks of upper-air stations, and the main arguments put forward for the

of fronts,

depend on the recognition of wind and the acceptance of such discontinu-

and temporary retreats, each surge being accompanied by typical cold-frontal type phenomena; when the advancing trade dies down temporarily, the frontal

ef-

fect disappears to give place to a region of equatorial air,

or the trade of the

reasserts

itself.

The

summer hemisphere temporarily

retreat

is

a

little

more

regular, until

the intertropical convergence zone has recrossed the equator, and is often accompanied by warm-front phenomena due to the flow of the freshening trade of the

autumn hemisphere over the

retreating trade, but

more

usually the activity of both trades at this period is small, and large areas of stagnant equatorial air appear on

the synoptic chart. The meridional front

the front that forms between distinct anticyclonic cells in the same hemisphere. In the Southern Hemisphere, this takes place usually between a weak ESE/E stream tropical air masses

is

from two

from the more easterly of the two anticyclonic cells and a stronger SE/SSE stream from the more westerly cell. Because of the persistence of such cells during the winters of the respective hemispheres, these fronts are of a semipermanent character and are readily identifiable. In the summer of the hemisphere being considered, the portions of the cells are more variable with a consequent greater variation in the position of the meridional front. Where the air from the other hemisphere crosses the equator the meridional front crosses from the winter to the

summer hemisphere,

giving rise at

its

junc-

tion with the intertropical convergence zone to a "triple

existence of fronts

point." There

is

some evidence

discontinuities

"triple point"

is

associated with the formation of trop-

wind as evidence of discontinuities in the air masses. Three distinct types of discontinuity are normally recognised the intertropical front, the meridional front, and subsidiary fronts. The intertropical front is regarded as being formed in the intertropical convergence zone, the zone comities in

:

which the trade winds from the two hemispheres meet. In earlier days the zone was simply known as the doldrums and all the bad weather associated with the zone was regarded as due to the instability of the moist stagnant air which gave rise to convectional rain and thunderstorms. It is now more common to regard the zone as being one in which true frontal discontinuities between the northern and southern trades exist, interspersed with semistagnant equatorial air masses or doldrum areas. The boundary between the equatorial air masses and the pletely surrounding the earth in

trades will usually orient itself parallel to the direction of the active trade Avind but with an increase or "surge" of the trade wind the relatively cold air will tend to undercut the equatorial air and give rise to frontal phenomena which are well marked and easy to identify. The front between the trades, which is known as the intertropical front, forms most frequently at the times when the trade from the winter hemisphere is beginning its penetration into the summer hemisphere

and when it is receding {i.e., just after the equinoxes). The advance of the trade across the equator is not a steady continuous process but is made up of surges

for the belief that this

ical cyclones.

Subsidiary fronts are of a more local character than the ones already described and are caused by local variations within an otherwise homogeneous air mass. The cause of the local variations may be orographic diversion of one portion of the air stream or the diversion of a portion of the air stream because of the breakdo'svn of geostrophic control as it enters the equatorial region. The diverted portion subsequently meets the undiverted portion again and gives rise to a local zone of convergence, which may be very limited in extent

and

may

fluctuate rapidl}^ in position.

The movements

very difficult to follow since the cause of the movements is not necessarily related to the winds in the neighbourhood of the zone but is related to the previous history of the air mass in which the zone has formed. The slopes of the fronts have been determined in many cases, the criterion almost invariably being the height at which the wind change occurs at various points. Most of the values lie between 1 in 300 and 1 in 500. There is no theoretical value for the slope with which comparison can be made because of the breakdo-wn of the geostrophic equations in the area and the absence of suitable equations to replace them. It has also not been determined satisfactorily to what height of these zones are

the discontinuities extend, the main difficulty here being the similarity between the upper layers of the trade winds and the lower layers of the overrunning! easterlies. Where a front is formed from undercutting!

EQUATORIAL METEOROLOGY by a surge

of the trade wind,

however, the tongue of

fresh air very often does not exceed 1500

m in thickness

so that the frontal surface has a well-marked slope at but trails off horizonthe leading edge up to 1500 tally behind. It is beyond the scope of this article to go into fuller detail in this matter of fronts; a complete account has been given by Forder [3].

steady and frictionless and that there of

many

of the

— 2fio

u =

= A

V

cos

sec

-f B4> -f C,

(1) (2)

,

the latitude, X

is

4)

is

the longitude, a

is

the radius

and A, B, and C are arbitrary constants. The streamlines are given by of earth,

problems

same as those of the tropics generally, the particular problem of finding dynamical equations applicable to the movements of air within the region

of

motion becomes

where

The equatorial region was defined earlier as the region in which the Coriolis term in the equations of motion was no longer predominant in balancing the pressure term, so that although of the equatorial zone are the

no change

is

velocity with longitude, the solution of the equations

m

THE EQUATIONS OF MOTION

883

peculiar to the region. When one examines synoptic charts of the region, particularly during the northern summer, one is struck is

+

A\

22a

-

sin

-

i5

const,

(3)

and the pressure distribution by

-- = ABX + J A P 2B (sin — -1"

The

60.

days days

-

mph

i?t.

.

.

.

.

.and. .and.

... .

.

.

50.01.

.

.

.and.

..?13

^0.05

or570 50.25

or

Days that did not were

procedures it is useful to estimate the danger class of each day and season. This will result in better dispositions for lookout posts, fire-fighting equipment, and personnel. The climatic information serves both for planning purposes and for the anticipation of fire-weather

It

stant so that weather conditions contribute most to the variability of incidence.

fall

into the classes good or poor

classified indifferent, that

is,

the weather would not

contribute to the fire hazard nor would it definitely retard fires. The discrimination of the scale is shown for four test months (January-April =120 days) for four years (total 480 days) (Table VII).

Table VII. Fire Occukrencbs and Fire Danger Glass Fire Class

Good

fire

day

Indifferent

Poor

fire

fire

day

day

Total days

APPLIED CLIMATOLOGY optimally adapted to weather conditions. A be the more economical the better the weather conditions are at the terminals and over the route. Poor terminal conditions, as expressed by weather minimums of combined ceilings and visibilities, prohibit or delay take-offs and landings. Hazardous conditions en route, such as severe icing and severe turbulence due to fronts and thunderstorms, may require detours or delays and hence are not conducive to the

989

flights

and graphical presentation need

flight operatioij will

many

maintenance of a smooth flying schedule. A good flying day can be defined in terms of absence of such limiting weather conditions in sequence at the take-off point, en route, and at the landing terminal. This sequence of events cannot be established readily by spot observations. But it can be obtained on sequences of synoptic weather maps. Statistics of the annual variation of good and poor flying days, the change from year to year, at least in terms of largest and smallest number, will give a plarmer the weather factor for a decision on whether or not a specific air route can be operated profitably.

The

was applied to logistic and other planning problems during World War II. Strategic bombardment operations were a case in question. The limiting weather conditions for take-off and landing in friendly territory, the route conditions, and the availability of targets for visual or blind bombing entered the identical technique

This application of synoptic-climatic techniques has been discussed in more detail by Jacobs picture.

[45,

pp. 20-22].

This type of study for airline operations can be considerably refined by considering, for example, diurnal variations of limiting conditions for each hour at the terminals and en route. There is no reason to elaborate on this because every meteorologist knows that during cei"tain times of the day in various seasons limiting conditions are particularly prevalent at certain airports. It is elementary to expect higher frequency of

dense fogs in the hours before sunrise. Also the high summer frequency of fogs in areas like Newfoundland is notorious. The climatic analysis can place such knowledge on a systematic basis. The same applies to the seasonal variations of air trajectories. These can be obtained from the upper-level synoptic maps and used for laying out the most advantageous routes over great distances in accordance with the principles of pressure pattern flying.

Additional Unsolved Problems

The foregoing review of the state of the art of applied climatology had to point to a great variety of only partially solved problems. In fact, each new application will require its own specific solution. In many respects this part of the Compendium of Meteorology is a series of confessions of ignorance. We have already pointed out in sufficient detail the need for new types of observations, many of which require new instrumental approaches. The requirement for statistical solutions better adapted to the specific problems has also been discussed. These are not the only deficiencies.

The

classical

methods

of

summarization

respects

[55].

radical overhauling in

Some very remarkable advances

of

graphical and pictorial presentation of climatic data, growing out of wartime experiences, have been placed in the scientific record [45, pp. 44-51].

Yet we

still

lack adequate methods for multidimen-

sional representation of data.

We

need more nomo-

graphic charts to simplify the presentation of complex relations and to allow for a quick solution of empirical equations. We have indicated that, in contrast to classical climatology and climatography, applied climatology is a broad, two-way meeting ground between the synoptic meteorologist and the climatologist. A fruitful field for joint efforts lies in the methods of air-mass climatology. There has been insufficient space to discuss these in detail here. This approach, however, has shown increasing promise for problems of bioclimatology [24, 33, 56, 62]. It is likely that further work along this line

can find useful applications. Other advances in applied climatology are intimately tied to progress in microclimatology The research needs in this field have recently been presented by Baum and Court [11]. Their very pertinent remarks can be summarized as follows: There is need for standardization of microclimatic procedures and equipment. More measurements are needed on the vertical distribution of the usual climatic elements in the boundary layer over various forms of terrain and vegetation. Coincidentally, measurements of the following factors should be made:^ .

1.

Temperature gradient

2. Soil

in the soil. conductivity as a variable quantity.

3. Insolation, direct 4.

and

diffuse.

Atmospheric radiation.

5. Terrestrial radiation.

Eddy

conductivity in the air. Evaporation. As basic problems Baum and Court propose studies and causal understanding of the heat balance at the surface of the earth, the existence and extent of laminar layers near the surface, and the interrelation of microclimatic factors and evaporation. Lastly, it should again be stressed that applied climatology should be in each instance a cooperative venture. It deals with borderline fields. Climatology is on one side; on the other side are a great many other disciplines (medicine, ecology, agronomy, hydrology, pedology, architecture, strategy, business management, and various phases of engineering). The solutions to the many joint problems can best be found by teamwork. 6. 7.

Appendix Table VIII

lists

plied climatology,

areas of practical problems in apclasses. Some of these areas have

by

3. Some of these have been mentioned in Table I, above, but are repeated to present Baum and Court's ideas com-

pletely.

.

CLIMATOLOGY

990

been studied and reference is made to pertinent papers that have not ah-eady been quoted. The list is by no means complete, but it indicates what a broad and

Table VIII. List of Topics in Applied Climatology Class of

Field of application

Advertising and marlceting Aerial pliotography Airfield construction Airline operation Air pollution control Architecture and housing

con-

struction

City planning Clothing Crop planning and protection. District heating Forest fires Gas and oil dispatching

.

.

Health resorts Heating and cooling plants

Highway construction Hydroelectric power Insurance

Land

utilization

Lubrication Military operations Open air theater operation Power dispatching

Power

lines

Shipping and transportation Storage (food, oil, photographic material, etc.)

Wind power

APPLIED CLIMATOLOGY Retail Federation, Washington, D.

C,

29.

Deyar,

30.

DuEEST,

31.

Leipzig, Haupt, 1937. EcKERT, W. J., Punched Card Methods in

A.,

II.

25 pp.,

19-16.

53.

Braunschweig, P. Vieweg & Sohn, 1927. Landsberg, H., "On the Relation Between

(19-19).

Compu-

York, The Thomas J. Watson Astronomical Computing Bureau, Columl^ia University, 1940. Fitzgerald, S. E., A Study of the Copper Man, Phase I; Physical Characteristics, Thermometry, Air Clo. Evaluations. Office of the QMG, Clim. Res. Lab., Lawrence,

58.

Ventilating, 48:61-

Causes and Forecasting with Special Reference to Eastern and Southern United States." Bull. Amer. meteor. Soc, 21:135-148, 261-269,

39.

40.

Hand,

41.

Hayes, G.

Biometrika, 36:142-148 (1949). I. F., "Solar Energy for House Heating." Heat. & Ventilating, 44:80-94 (1947).

"Forest Fire Danger" in Yearbook of Agriculture 1949. U. S. Dept. Agric, Washington, D. C. L.,

1949. (See pp. 493-498)

Hill, L., Griffith, O. W., and Flack, M., "The Measurement of the Rate of Heat-Loss at Body Temperature by Convection, Radiation and Evaporation." Phil. Trans, roy. Soc London, (B) 207:183-220 (1916). 43. HoTTiNGER, M., Klima und Gradtage in ihren Beziehungen 42.

44.

45.

46.

47.

zur Heiz- und Liiftungstechnik. Berlin, J. Springer, 1938. Huntington, E., Civilization and Climate, 3d ed. New Haven, Yale University Pre.ss, 1935. Jacobs, W. C, "Wartime Developments in Applied Cli-

matology." Meteor. Monogr., Vol. 1, No. 1, 52 pp. (1947). "Weather Analysis Aid to Business Planning." Dun's Rev., 55:15-18 (1947). Frost Survey of Imperial County, California. 31 pp. Publ. Agri:c. Dept. Imperial Co., El Centro, Calif., Feb.

—

Kestermann,

E.,

"Ueber Luftkorperbestiimnungen."

E., and Mold, W. L., "A Technique for a Synoptic-Climatological Study of an Air Route." Bull. Amer. meteor. Soc, 29: 401-407 (1948).

64.

Mills, C. A., Medical Climatology: Climatic and Weather Influences in Health and Disease. Springfield, 111., C. C.

65.

Neumann,

66.

Nuttonson, M. Y., "International Cooperation in Crop Improvement Through the Utilization of the Concept

Thomas,

1939.

von, and Morgenstern, O., Theory of Games and Economic Behavior, 2d ed. Princeton, N. J., PrinceJ.

ton University Press, 1947.

of

Agroclimatic Analogues." Interagra, Vol.

1,

Nos.

3-4, 8 pp. (1947).

Petersen, W.

F., The Patient and the Weather, Vols. 1-4. Arbor, Mich., Edwards Brothers, 1934-1938. 68. Pollak, L. W., " Charakteristiken der Luftdruckfrequenzkurven und verallgemeinerte Isobaren in Europa." Prager geophysikalische Studien I: Cechoslovakische Statisiik, Bd. 44 (Reihe XII, Nr. 6) (1927).

67.

Ann

69.

and TemperaAir Layers Within and Above Trees and Brush. Los Angeles, Calif., U. of Calif., Dept. of Engng. (ONR Rep., Contract N6-ONR-275, T. 0. VI, NR-082-

PoppENDiEK, H.

F., Investigation of Velocity

ture Profiles in

036) dittoed, 45 pp., 1949. Price, A. G., White Settlers in the Tropics. New York, Amer. Geogr. Soc, Spec. Publ. No. 23, 311 pp., 1939. 71. Putnam, P. C, Power from the Wind. New York, Van Nostrand, 1948. 72. Roth, R. J., "Crop-Hail Insurance in the United States."

70.

Bull. 73.

A.,

"Abklihlungsstudien mit

besonderer

74.

und

,

51.

und Dinies,

Manos, N.

Pfleiderer." Biokl. Beibl. 7 :1-1& (1940).

50.

"Klimatische Anforderungen an einen Kurort."

Amer. meteor. Soc, 30:56-58

Rudder, E. de, Grundriss

(1949).

einer Meteorobiologie des

Men-

schen, 2. Aufl. Berlin, 1938.

Beriicksichtigung des Frigorigraphen nach Biittner 49.

F.,

63.

1941. 48.

Linke,

Z. angew. Meteor., 47: 1-5 (1930).

285-291 (1940).

38.

"Microclimatology."Arc/w'>

3

S,

we

q

or,

The

ihl^^

(20)

V

fco

thickness of the laminar layer 6

depend on the viscosity and the

is

supposed to

by

stress as expressed

the friction velocity:

6

(25)

.

k is

small compared to

^Xfco-^+hi^],

(26)

kopu'*

E =

= X—

(21)

Is

kopyw

(27)

X/co - -(-

In

K

K

Therefore: a

—

+ ln^™* K

Xfc„i: '

K

7

koW*z

introducing w,

•

Ko

+

obtain:

E

-

(19)

where 7 is the resistance coefficient which, according to von Karman, can be obtained from the equation

7

In

(18)

where t is the shearing stress. This is defined as t = A dw/dz and is supposed, near the sea surface, to be independent of height and equal to to, the wind stress at the sea surface. The friction velocity can be expressed by the wind at any level w:

^-+lbl^=5.5 +

K

,

koPW:^

Adding and considering that

Q^ Wit:

-

Qs

(17)

Here the

ratio v/k

(28)

J

independent of temperature {v/k

is

=

0.602), but K increases a little with temperature

(at

OC

K

=

20C

0.22, at

=

k

=

0.24 cm^ sec~^ and a 2 as a function of w.

=

0.25 cm^ sec-i).

800 cm, r^

is

shown

With

k

in Fig.

According to Rossby [19], the sea surface has the of a hydrodynamically smooth surface at wind velocities up to 6-7 sec~^ as measured at a height of about 8 m. At wind velocities exceeding 7-8 sec~^ the sea surface appears to be hydrod3mamically character

m

m

rough.

Over a rough surface the eddy viscosity increases and has, at the surface itself (z = 0), a value which is much larger than that of the .

where X

is

a constant for which von

Karman found

the

value 11.5, whereas Montgomery [16] obtained 7.8. In the following applications we shall use von Karman's value, X = 11.5, but the choice is not of great importance. The picture given above of the variation with height of the eddy viscosity appears fully applicable when turning to the eddy diffusivity. We must indeed expect that next to the sea surface there exists a layer through which the flux of water vapor takes place by molecular diffusion, and it seems reasonable that the thickness of this layer equals that of the laminar layer. In the turbulent layer the eddy diffusivity must then be

pU where k through

is

+

kaWjfZ),

(22)

the coefficient of diffusion of water vapor For values of 2 > > 5 this eddy diffusivity

air.

only imperceptibly from the eddy viscosity. The flux of water vapor through the two layers then

differs

E =

-pK

\dz)i

P

(k

+

is

fd,\ (23)

kliWH:Z)

\dz

Jt'

where the indices I and t indicate that the differentials apply to the laminar and the turbulent layer, respectively. By integration, remembering that 3 = at the

linearly with height

ordinary viscosity:

A = Here

^o is

fcopw* (z

+

(29)

Zo).

the "roughness length" of the surface.

resistance coefficient

7

7

is

The

determined by fco

= z

In

(30)

+ Zo Zo

When this concept is applied to conditions over the ocean the question arises as to where to place the zero level. No wind profiles have been measured at high wind velocities when large waves have been present, and we have, therefore, no knowledge of the wind distribution very close to the sea surface. Using other features ^the angle between surface wind {e.g., wind at about 8 m) and pressure gradient, the Rossby ratio between surface wind and gradient wind arrived at the conclusion that over the ocean the roughness length is independent of the wind velocity and equal to about 0.6 cm. This result is substantiated by the facts that with Zo = 0.6 cm and with 800 cm < z < 1500 cm, equation (30) renders 7 values in agreement with those found by entirely different methods, and that these 7 values have been applied

—

—

EVAPORATION FROM THE OCEANS successfully to such problems as the generation of

waves and the maintenance

wind

of the equatorial currents

1077

At the top of this layer the diffusivity increases abruptly from the molecular value to the value over a rough surface: = kopw^r (5 -f Zo), and for 2 surface.

A

[25].

We

maj^ therefore state that at wind velocities above 6-7 sec~' the eddy viscosity in the lower layer above the sea surface behaves as if the sea surface were a rough surface O'o = 0.6 cm) located about 8 below the level at which ship observations are ordinarily made. The next question is then, How does the eddy diffusivity behave? If z is not small, the eddy diffusivity must be practically equal to the eddy viscosity,

m

m

but what happens when

z

approaches zero? It appears

quite probable that in this case, as well,

>

A =

There

4.

diffusivity cosity,

is

One can

=

win immediately give off its momentum to the surface, but the vapor pressure will not immediately attain the value which is characteristic of the surface. As long as this mass remains at rest, its vapor contents will be increased by processes of ordinary diffusion, supposing that it originally was lower than the equilibrium pressure corresponding to the temperature and salinity of the surface. After a short time the air mass will be removed and replaced by another, and similar processes will be repeated. In order to describe these processes one can introduce a boundary layer, the thickness of which is a statistical quantity representative of the average conditions and within which the transport of water vapor takes place through ordinary diffusion.

A much Millar

[14]

(Sverdrup

2o)

(W*s/W*r)^ [18]. the basis of these assumptions

compute r„

conceive that for a short time a mass of air comes of air

+

On

Ta.

=

r„

2.

The

The eddy eddy

vis-

[24]).

Z

r (xfco

r„

+

^^

w^a

possible to

is

In

^1^)|\

= (Xfc„r+ln^l^'^ K

3.

it

results are:

In- -f.

mass

identical with the

all levels

fcop«;*r(3

of true diffusion.

mediate layer, at z = Z, the vertical flux of water vapor increases abruptly from Eq to E where Eq/E

[23, p. 4]:

to rest in one of the hollows of the surface. This

at

[23].

2o)

no layer

exists

A =

+

kopw*r(z

5. The character of the diffusivity corresponds to that assumed under (1), but at the top of the inter-

we must

introduce a layer next to the boundary surface through which the flux of water vapor takes place by ordinary diffusion. In 1937 the present writer argued as follows

S:

=

(xfco ' K \

(31)

(32)

K

-1-

-^) +

hi

',

(33)

30/

6

(34)

5.

V.„

= fhi^-1.76^T\ \

(35)

W*s/

20

In Fig. 2 five r^ curves, referred to a

shown

as functions of the

wind

to the five sets of assumptions.

=

800 cm, are

velocity, corresponding

The curve marked

(1)

more extreme view has been advanced by and Montgomery [16], who assume that -(5)-

even over a rough surface the laws pertaining to a smooth surface apply to a distance Z from the boundary surface, but that at that height an abrupt transition to "rough" conditions takes place. So far, five different attempts have been made to discuss the evaporation from a rough surface, based on different assumptions as to the character of the diffusivity close to the surface. These assumptions can be described as follows: 1. Next to the surface there is a true diffusion layer followed by an intermediate layer of thickness Z in which the eddy diffusivity corresponds to that over a smooth surface, A = p(k -\- kow^az), where w*s is obtained from equation (20) At Z the eddy diffusivity suddenly increases to the value of the eddy viscosity over a rough surface, and iorz > Z, A = fcopw*r {z Zo) where w*r is obtained from equation (30) [14, 16]. 2. Next to the surface there is a true diffusion layer of thickness 5 = Xc/iu+r, where w*r applies to a rough surface. From the top of this layer the eddy diffusivity increases at the same rate as the eddy viscosity above a rough surface. These assumptions agree with those of Bunker and others [4] if their notations are made to correspond to those that apply to conditions above a rough surface. 3. Next to the surface there is a true diffusion layer of thickness 5 = \v/w*r, where w*r applies to a rough .

+

.15

-(4)-

-ROUGH-

-SMOOTH-

-(3)

-(2)-

05

.05

(I).

6

8

10

12

14

16

18

20

WIND VELOCITY (M SEC-I)

—

Fig. 2. Theoretical values of the evaporation coefficient as function of the wind velocity at 800 cm, computed on the basis of different assumptions, and observed values shown by dots.

plotted according to values given by Montgomery taking into account that here we refer Va to a height of 8 m, whereas he used 4 m. When computing Ta in cases (2) and (3), the question arises as to what value to assign to X. It is not obvious that the value for a smooth surface (X = 11.5) is applicable, but lacking is

[16],

means

may

of determining a better value,

we have used

it.

be observed that, on the basis of Montgomery's humidity measurements, Sverdrup [23] found X = 27.5, but this value seems doubtful because it was derived It

.

MARINE METEOROLOGY

1078

from observations that included many cases of flow over a smooth surface. With X = 27.5, curve (3) would nearly coincide with curve (2) The wide spread of the curves (2) to (5) clearly demonstrates the importance of the assumptions as to the diffusivity near the boundary surface. Assumptions (1), (4), and (5) appear too extreme, but none can be rejected offhand since we have no basis for describing what actually takes place, but are trying to introduce a model which gives results in consistent agreement with observed conditions. In order to advance a step further we have to compare the theoretical conclusions with the empirical results. Our empirical data are of two kinds. On the one hand we have available a few series of measurements of humidity at different heights above the sea surface from which r„ can be found, and on the other hand we have series of accurate ships' observations of meteorological conditions and sea surwe can compute evaporation, using different To values, and we can compare the results with those derived from energy considerations. In order to facilitate computations and comparisons we shall use vapor pressure instead of specific humidity. Approximately, e = gp/0.621 or \vith -p face temperatures from which

=

1000 mb,

in the

e

=

161g.

We

then write equation (15)

form

E

Ka

—

(Cs

Bo)

Wa

(36)

the evaporation factor. We shall use units such that with pressure in millibars and wind velocity in meters per second we obtain the evaporation in millimeters per 24 hours. The curves for Ka

and

{a

shall call

=

Ka

800 cm) are shown in Fig.

3.

The heavy curves

FROM "METEOR" OBSV. USED BY JACOBS -(5)-(4)-

,20

ROUGH-(3)-

quate arguments for accepting one of the many models which at present can be used to describe the character of the eddy diffusion of water vapor close to the sea leads to consistent re-

wind velocities up to 6 m sec^"- for individual cases, or up to 4 m sec~^ for average conditions, but it should be emphasized that this consistency arises behas been accepted that the sea surface is velocities. The empirical evidence for this feature is, however, so meager that its reality is badly in need of confirmation. Should it not be confirmed, we must admit that the theoretical computation of the evaporation factor fails at all wind velocities. The only remaining conclusion is that such a factor can probably be established, either on a theoretical basis (if a new foundation for the development of a theory is found) or on an empirical basis. In trying to do the latter we may follow one of three courses: (a) the evaporation coefficient T may be determined from measurements of humidity gradients over the sea; (b) where accurate meteorological observations are available, and where evaporation can be computed from energy considerations, the evaporation factor may be determined; or (c) where climatological charts are available, based on observations that may contain small systematic errors, such as temperature observations on shipboard, the procedure under (6) can be used. We shall examine these procedures more cause

it

smooth at low wind

closely.

In Fig. 2 the values of T have been plotted which have been derived from observations of humidity gradients. Most of the observations were made at wind velocities below 6 m sec~^ and agree fairly well with the theoretical values for a smooth surface. The few observations at high wind velocities agree quite well with curve (4) for a rough surface, and this feature led the writer [24] to accept that approach although he previously [23] had adhered to different concepts. It will be shown here that the agreement between the empirical r values and the theoretical curve (4) must be accidental because the evaporation factor K, based on curve

-(2)-

The theory apparently

surface. sults at

(4),

gives far too high evaporation values.

The second method

-d)-

6

8

10

12

WIND VELOCITY (M

20

14

SEC."')

K

Fig. 3.— Theoretical valuss of the evaporation factor as function of the wind velocity at 800 cm, computed on the basis of different assumptions, and empirical values shown by dots and a dashed line.

should be used for computing evaporation from single observations. If climatological averages are available, we must use some transition curves in an interval of velocities around 6-7 sec-^, the width of which depends upon the spread of values upon which the averages are based. In Fig. 2, arbitrary transition curves are indicated for the interval 2-11 sec-'. Discussion. The theoretical considerations lead to such different evaporation factors that the theoretical

m

m

approach

is

useless until there can be

advanced ade-

(6), can be used only if very accurate meteorological observations are available for a large area and a sufficiently long time. The Meteor observations in the Atlantic [12] satisfy this requirement, and from these the data in Table II have been obtained. The factor K, which has been plotted in Fig. 3, lies between 0.07 and 0.09, and agrees fairly

well with values derived from curve (2). The result is in sharp contrast to that derived from examination of

humidity gradients and indicates that of the different theoretical assumptions number (2) is the most nearly correct. It should be borne in mind that the computation of the evaporation factor on the above basis is

somewhat uncertain, because the meteorological observations to the

are

extended

over only from

IJ-3

to

3

summer whereas the "energy values" apply whole year. The errors that may be introduced

months

in

because of this circumstance should, however, not be serious, because in the tropics the annual variation in

EVAPORATION FROM THE OCEANS evaporation is small and the same probably applies to the South Atlantic down to latitude 55°S. The third approach has been used by Jacobs [8, 9] in computing the evaporation from the data contained in the Atlas of Climatic Charts of the Oceans [27]. II. Evaporation Factob K [K = E/w {e, — e^)] (Computed from the meteorological observations on board the Meteor and the evaporation rates determined by Wtist)

Table

1079

MARINE METEOROLOGY

1080

evaporation between parallels of latitude. Still, in order to place the results on a firmer basis, it is very desirable to obtain further direct measurements at sea of incoming radiation from sun and sky and of nocturnal radiation. Measurements of the reflectivity of the sea surface under different conditions are also needed, as well as further examination of the Bowen ratio (the ratio between heat losses from the sea surface by conduction and by evaporation). Even with improved knowledge of these conditions, the energy approach cannot render information as to evaporation rates under given meteorological conditions or seasonal and regional values of the evaporation. In order to compute such values the third approach has to be adopted. 3. For the computation of the vertical flux of water vapor from the sea surface several assumptions have been introduced as to the character of the eddy transfer processes near the sea surface. These assumptions lead to different formulas from which the evaporation rate can be obtained from observations of humidity and wind velocity at a standard level above the sea surface and observations of the sea surface temperature from which the vapor pressure at the sea surface can be

character of the formula has been more firmly estaband before it has been shown that the unknown factor is a constant. lished,

REFERENCES 1.

Stockh., 2: 237-252 (1920). 2.

presuppose indifferent stratification or slight instability. This restriction is not very serious, because stable conditions are not common over the open ocean and when they occur, evaporation is small. The different approaches have been reviewed and it has been shown that they lead to widely diverging results. Furthermore, it has been shown that the available empirical evidence is far too scanty and too inconsistent to indicate what assumption may be acall

4.

somewhat different if seasonal and computed from climatological data. In this case it may be assumed that the evaporation can be computed by means of an equation that is based on theoretical considerations, and the unknown factor in this equation may be estabhshed by means of evaporation values that are derived from energy considerations. Such an equation cannot be expected

The problem

BEtJCKNER, E., "Die Bilanz des Kreislaufs des Wassers auf der Erde." Geogr. Z., 11: 436-445 (1905). Bunker, A. F., and others, "Vertical Distribution of Temperature and Humidity over the Caribbean Sea." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 11, No. 1, 82 pp. (1949).

6.

7.

Hann,

from Lakes." Phys. Rev.,

8.

9.

10.

11.

12.

13.

J. v.,

30: 527-534 (1927).

Lehrbuch der Meteorologie,

3.

Aufi. Leipzig,

Tauchnitz, 1915. (See pp. 213-219) Jacobs, W. C, "On the Energy Exchange between Sea and Atmosphere." J. mar. Res., 5: 37-66 (1942). "Sources of Atmospheric Heat and Moisture over the North Pacific and North Atlantic Oceans." Ann. N. Y. Acad. Sci., 44: 19-40 (1943). and Clarke, Katherine B., "Meteorological Results of Cruise VII of the Carnegie, 1928-1929." Carneg. Instn. Wash. Publ. 544, 168 pp., Washington, D. C, (1943). KRtJMMEL, O., Handbuch der Ozeanographie, Band I. Stuttgart, J. Engelhorn, 1907. (See pp. 243-250) KuHLBRODT, E., und Reger, J., "Die meteorologischen Beobachtungen." Wiss. Ergebn. dtsch. Alt. Exped. Forsch. Vermess.-schiff Meteor, 1935-27, Bd. 14, 2. Lief., Abschnitt B, SS. 215-392 (1938). McEwEN, G. F., "Some Energy Relations between the Sea Surface and the Atmosphere." J. mar. Res., 1: 217238 (1938).

14.

15.

16.

Millar, F.

G., "Evaporation from Free Water Surfaces." Canad. meteor. Mem., 1: 41-65 (1937). Mohn, H., Meteorology (The Norwegian North-Atlantic Expedition 1876-1878, II). (Translated into English by J. Hazeland). Christiania, Gr0ndahl & Sons, 1883. Montgomery, R. B., "Observations of Vertical Humidity Distribution above the Ocean Surface and Their Relation to Evaporation." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 7, No. 4, 30 pp. (1940).

17.

MosBY, H., "Verdunstung und Strahlung auf demMeere." Ann. Hydrogr., Berl., 64: 281-286 (1936).

18.

Norris, R., "Evaporation from Extensive Surfaces of Water Roughened by Waves." Quart. J. R. meteor. Soc, 74: 1-12 (1948).

19.

is

regional values are to be

to give accurate results before the correctness of the

S., "The Ratio of Heat Losses by Conduction and by Evaporation from any Water Surface." Phys.

Cherubim, R., "tjber Verdunstungsmessung auf See." Ann. Hydrogr., Berl., 69: 325-335 (1931). CuMMiNGS, N. W., and Richardson, B., "Evaporation

5.

ceptable.

In order to advance our knowledge, it is necessary to carry out a large number of detailed measurements of conditions directly above the sea surface. These should comprise measurements of wind profiles in order to examine the validity of the concept that at low wind velocities the sea surface is hydrodynamically smDoth, measurements of humidity in order to examine the validity of the logarithmic law for the decrease of water vapor with height, and measurements of temperature in order to establish the stability under which the observations are made. It is possible that such extended observations may show that one of the suggested theoretical equations is applicable, but it is also possible that new concepts have to be introduced and more variables considered in order to arrive at a satisfactory basis for the computation of evaporation during short time intervals.

Bowen, L

Rev., 27: 779-787 (1926). 3.

derived.

These theoretical equations

Angstrom, A., "Applications of Heat Radiation Measurements to tiie Problems of the Evaporation from Lakes and the Heat Convection at Their Surfaces." Geogr. Ann.,

20.

RossBY, C.-G., "On the Momentum Transfer at the Sea Surface, I." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Instn., Vol. 4, No. 3, 20 pp. (1936). Schmidt, W., "Strahlung und Verdunstung an freien Wassenflachen." Ann. Hydrogr., Berl., 43: 111-124, 169178 (1915).

21.

"Zur Frage der Verdunstung." Ann. Hydrogr.,

Berl.,

43: 136-145 (1916). 22.

Sutton, O. G., "Wind Structure and Evaporation in a Turbulent Atmosphere." Proc. ray. Soc, (A) 146: 701722 (1934).

EVAPORATION FROM THE OCEANS 23.

SvERDRUP, H. U., "On the Evaporation from the Oceans."

Oceans.

J. mar. Res., 1: 3-14 (1937).

"The Humidity Gradient over the Sea Surface."

24.

26.

27.

/.

"The Wind and the Sea." P. V. Ass. Ocean. Phys., No. 4, pp. 37-55 (1949). Johnson, M. W., and F1|Eming, R. H., The Oceans, Their Phijsics, Chemistry and General Biology. New York, Prentice-Hall, Inc., 1942. (See pp. 99-100) S. Weather Bureau, Atlas of Climatic Charts of the

U.

1247, 130 pp.,

Washington, D.C.,

1938. 28.

Meteor., 3: 1-8 (1946). 25.

W. B. Publ. No.

1081

Wagner,

A.,

"Zur Frage der Verdunstung."

Beitr. Geo-

phys., 34:85-101 (1931). 29. WtJST,

G.,

"Die Verdunstung auf dem Meere." Veroff. Neue Folge, Reihe A, Heft 6,

Inst. Meeresh. Univ. Berl.,

30.

95 SS. (1920). "Oberfiachensalzgehalt, Verdunstung und Niederschlag auf dem Weltmeere." Landerkundliche Forschimg, Festschrift Norbert Krebs, SS. 347-359 (1936).

FORECASTING OCEAN WAVES' By W. H.

MUNK

and R.

S.

ARTHUR

UniversUy of California, Scripps Institution of Oceanography

Introduction

One result of the interaction of wind and ocean is the generation of surface waves. Prior to 1940 a few inadequate empirical rules formed the only basis for the concentrated effort prediction of wind-induced waves. under the stimulus of wartime demands has resulted in

A

the development of relationships which make possible the forecasting of ocean waves from synoptic meteorological data.

As an introductory example, reference is made to the meteorological situation north of the Hawaiian Islands January 1947. An intense low-pressure center remained virtually stationary 1000 miles to the northeast of the islands for a period of more than 72 hours (Fig. 1). On January 1 and 2, the winds in an area exin early

characteristics of the wind waves which are in the process of generation in such a fetch are referred to as state of sea or simply sea. After the wind waves left this particular area of direct influence of intense winds,

they continued onward as swell through a region of relatively weak winds, and reached Hawaii in 28 hours after having traveled a distance of 600 nautical miles. Over this decay distance the height of the significant waves decreased and the period and length increased. Computations yield a swell of height 22 ft and period 14 sec, and available observations compare favorably with these calculations. Further computations show the swell reaching Palmyra Atoll, which is 900 miles south of Hawaii, with a height of 12.5 ft and a period 17 sec after an additional travel time of 29 hours. The damage in Hawaii was estimated at between one and two million dollars. Three waves are reported to have inundated low-lying Cooper Island in the Palmyra group. Although these wave conditions are extreme for Hawaii and Palmyra, wave damage in general is by no means rare. Damaging waves may even move from one hemisphere to another. In April 1930, more than 20,000 tons of superstructure stone were displaced from ihe. Long Beach, California, breakwater by the action of swell which in all probability had its origin in the "Roaring Forties" of the South Pacific Ocean. The "rollers" of St. Helena and Ascension, which cross the equator after moving from the North Atlantic, have been famous since at least 1846, when thirteen vessels were driven from their moorings and wrecked on the shores of St. Helena. Reports of the disaster indicate that waves broke seaward of the vessels at a depth of which denotes that breaker height was around 20 approximately 50 ft. The primary motivation for the development of a wave-forecasting method has been the fact that waves are a nuisance. This problem came into particular prominence during the planning in 1942 of the invasion of North Mvicsi. In that year. Instructor Commander C. T. Suthons, R. N., began an investigation of waveforecasting techniques in England, and the same problem was studied in the Oceanographic Section, Directorate of Weather, Headquarters, Army Air Forces. The study was continued at Scripps Institution of Oceanography under Air Force and, later, Navy support, and in 1943 the method which was used throughout the war had in essence been developed [8]. Although oceanographers played an important role in the development of forecasting methods, the application is best carried out by meteorologists. Since waves represent the effect of the wind integrated over time and distance, forecasts of waves can be made from a laiowledge of only the large-scale fea-

m

JANUARY

1,1947 1330 HST 160'

Fig.

1.

—Weather map for 1330 Hawaiian Standard Time, Janu-

ary

1,

1947.

The shaded area

represents the fetch.

tending from 500 to 1200 miles north of the islands were force 8-10 and direction N-NNW for a period of 36 hours. This area comprised the fetch and computations based on wind velocity, duration, and the forecasting relationships give a wave height of 38 ft and a period of 11.3 sec at the southern boundary [1]. The 1. Contribution from the Scripps Institution of raphy, New Series No. 511. Many of the results here are based on research supported by the Office Research, Navy Department, under contract with

versity of California.

Oceanogdiscussed of

Naval

the Uni-

tures of the wind distribution. 1082

Such forecasts are

likely

—

;

FORECASTING OCEAN WAVES to be

made more

most types

easily

and with greater certainty

tlian

of meteorological forecasts.

The present

wave

circulation [19], including rip currents, on orbital velocities,

that there are available methods which permit useful predictions of certain wave characteristics from synoptic meteorological observations. The theoretical basis of the methods does not adequately explain the physical mechanism of wave generation and decay. We shall consider wave forecasting, the deficiencies of the methods, and some status of

forecasting

is

of the unsolved problems.

1083

and on the important

played by waves, and in the design

role

particularly breakers, in beach erosion of engineering structures.

Although a number predictable

if

of characteristics of surf are

the deep-water

wave

characteristics

and

the bottom topography are known [9], it must be noted that the basic relationships apply only approximately, and even large deviations are to be expected. More research on surf is indicated, particularly on the problem of the mechanism of breaking.

Sea, Swell, and Surf

The

categories sea, swell,

division of the topic of

wave

and

surj

form a natural

forecasting.

The

latter, or

waves in shallow water, is dealt with by methods which are somewhat different from those used in the study of sea and swell. The essential features of the surf problem have been

more

generally, the transformation of

Forecasting Significant

The notations given below will be used in the discussion which follows.

F—length of wind

H—

system of currents, called rip currents [19], which include narrow zones of fast flow away from shore. Active research is being conducted on the near-shore

D

denotes value of

distance (subscript

variable at end of decay distance); wave height;

— E—mean energy wave per unit area; X — horizontal distance coordinate; —time —duration time wind; of

t

of

td

U—wind

i8

C/U

velocity at about 8

m above surface;

(wave age);

wind on sea surface; —tangential —mean surface mass transport velocity; enei'gy transfer to wave as a Rn—mean rate normal wind pressure; energy transfer to wave as a Rt—mean rate tangential wind gravity; g— acceleration — sheltering p— density —resistance applicable to wind. stress of

T

Mo'

of

crests

period [22]. An exception occurs where the waves travel over great stretches of shallow water such as exist along the coast of the Gulf of Mexico and the shelf east of Long Branch, New Jersey. In such cases the effects of bottom friction [14] and percolation [13] should be taken into account. As the waves approach the breaking jjoint the height increases rather suddenly, and the wave breaks at a depth approximately equal to ^^ the wave height. Adequate predictions can be based on the application of the solitary -wave theory [12]. Waves breaking at an angle to the shore set up longshore currents ^^'hose average velocity can be roughly estimated when bottom contours are straight and parallel [15]. In the case of nearly normal wave approach, longshore currents are variable in direction and fomi an integral part of a

F denotes value of

C—phase velocity of wave; T—wave period; L wave length; 5 H/L (wave steepness);

and wave velocity decrease. Waves moving at an angle to the bottom contours are subject to refraction. The tend to orient themselves parallel to the bottom contours. Changes in wave-crest orientation are associated with convergence and divergence of energy along the crest [11]. As a result, waves over a submarine canyon are relatively low compared to waves on either side of the canyon; the pattern is reversed for a submarine ridge. These changes can all be quantitatively accounted for by the linear-wave theory, assuming conservation of energy and constancy of wave

fetch (subscript variable at end of fetch);

D— decay

accounted for physically, whereas this is not the case for sea and swell, as previously mentioned. Sea is determined by the nature of the winds, and the forecasting of sea depends therefore upon the current and predicted synoptic meteorological situation. Swell depends to a lesser extent upon the synoptic situation, but its characteristics can still be altered by a following or an opposing wind during the course of decay. Surf is determined by factors which are largely nonmeteorological, and we confine our consideration of surf to this section, where we note some of the important physical factors in the problem. As waves move into shallow water the wave length

wave

Waves

result

of

of

of

result

stress;

of

s

coefficient;

of air;

7"

coefficient

The outstanding irregularity,

characteristic of sea

and a complete description

and

swell

is its

of the sea sur-

requires the introduction of statistical terms. Nevertheless, a practical purpose can be served by dealing only with the most prominent, or "significant," waves. A definition of the term "significant" is given in the following section. One of the major achievements face

wartime wave forecasting was the development of operationally useful methods, one with a theoreticalempirical basis [24], and the other primarily empirical of

[20]. We next consider the results and basis of the first method, and make a brief comparison with the second. Observers have noted that as the wind blows over a limited fetch, the wave height and period over the upwind part of the fetch reach a steady state after a

limited interval of time.

As time

passes the steady-

expands over the whole fetch. The wave height and period at the end of the fetch ai'e determined from the wind velocity, fetch, and duration. The relationships given below, in terms of nondimensional parameters, follow from the forecasting theory. state region

:

MARINE METEOROLOGY

1084

The assumption is made that energy is transferred from wdnd to waves by normal pressure and tangential

Steady state: (1)

C,/U = MgF/U');

Following Jeffreys, the expression used for the

stress.

mean

(2)

rate of energy transfer per unit area as a result of

normal wind pressure

is

Transient state

gH,/U' = h{gU/U),

(3)

Cf/U = h{gU/U).

(4)

±^ sp{U -

Rn=

Cy

8'C,

C8)

where the sign is positive ior U > C and negative for U < C. Thus, a transfer expression which depends upon

Height and period of swell at the end of the decay distance and travel time are determined from the decay

variations in pressure along the surface

is

introduced,

60

50

40

30

20

10

LINES LINES I

1

I

_J

I

OF EQUAL WAVE HEIGHT, H.IN FEET OF EQUAL WAVE PERIOD, T, IN SECONDS' L__]

I

L_J

I

DURATION, tj

Fig

2

L_J

\

I

I

L_

40

30

20

10

,

IN

50

—Transient state wave-generation relationships in practical form for use in forcasting.

distance and the period at the end of the fetch according to:

although use is made of hydrodynamical theories which assume constant pressure along the surface. For the tangential stress, the form

(5)

T

T^IT,

= MD/gTF^),

(6) (7)

Relationships (l)-(7) are translated into practical

graphs for use in forecasting^ (examples are presented in Figs. 2

The

and

3).

basis of the theory is the

development

of

equa-

wind from two hydrodynamical theories of irrotational waves: (1) the Airy theory of waves of small amplitude, and (2) Stokes' theory of waves of finite amplitude. Certain constants which occur in the solution are evaluated empirically. tions which express the energy budget between

and waves. Use

is

made

of results

Arthur, "Revised Wave Forecasting Graphs and Procedures." Scripps Institution of Oceanography Wave Report No. 73, March 1948 (unpublished). These forecasting relationships, as revised according to [24], are to be included in a forth2.

R.

S.

coming manual on wave forecasting to be issued by the Hydrographic Office.

60

HOURS

=

=

7Vf/^

(9)

2.6 X is introduced with the underwhere standing that wind velocities are great enough so that the sea surface is hydrodynamically rough. The expression for Rn is derived using the horizontal component of particle velocity at the surface from the Airy theory, but on this basis no energy is transferred by tangential stress. However, if the average surface mass transport velocity, mq' = tt^S^C, from the Stokes theory is utilized, the mean rate of energy transfer per unit area by 7^

10"^

tangential stress

R,

is

=^ L Jo I

T uo

dx

= T py 5 CU

(10)

and on the basis of this expression a transfer of energy from wind to waves is possible even if the waves move the wind. Further investigation of this indicated because if the difference between the wind velocity and the horizontal component of particle velocity is introduced in the expression for t, seemingly faster than

point

is

:

FORECASTING OCEAN WAVES

the wind is divided in a certain fixed manner between the energies required to increase wave height and wave period. The solution of the resulting system of differential equations leads to a relationship between wave steepness and wave age.

a more accurate formulation of the transfer expression, no energy is added on the basis of either the Airy or the Stokes theory if the waves move faster than the wind. The validity of Stokes' expression for mass transport in the case of waves on a rotating globe has also been questioned.' If the waves are conservative, that is if they maintain their identity, the knowledge from theory of the way in

200

400

200

400

600

800

800

600

1000

1000

1200

1200

3.

m

(13)

and, finally, to the relationships (l)-(4) above. 1800

1600

1400

which energy advances with the wave form leads to the

CdE

=

D,

1600 IN

1800

2000

2000

2200

2200

2400

2400

NAUTICAL MILES

—Wave-decay relationships in practical form for use in forecasting.

following differential equations:

Steady state

5

1400

DECAY DISTANCE, Fig.

1085

2600

2600

2800

2800

30Q«

3000

MARINE METEOROLOGY

1086

attenuation. The comparison suggests that travel time be computed on the basis of the decay distance and the group velocity of the swell at the end of the decay distance. The effect of a following wind during decay is to give lower swell arriving earlier, and the effect of an opposing wdnd is the opposite. The results for travel WAVE STEEPNESS AGAINST RATIO WAVE VELOCITY TO WIND VELOCITY '

1

U) uj

6

°-

5

Z

FORECASTING OCEAN WAVES waves gives a useful description

of the that tlie daily average height of the highest ten per cent of the waves bears a relatively constant rek. lonship to the significant height at the locations on the Pacific Coast of the United States. significant,

record.''

Wiegel

This fact

is

[25] finds

of practical

importance because

less

time

is

required to compute the average for the highest ten j^er cent. A good correlation between the maximum waves

recorded each day and the significant waves is also noted, and Seiwell [17] finds at Cuttyhunk and Bermuda that the ratio of the daily average height of all waves to the highest one-third is relatively constant. These results (Table II) taken collectively indicate that in gen-

Table II. Ratios of Mean Wave Height and op Average OF Highest 10 Per Cent to Significant Wave Height

1087

.

MARINE METEOROLOGY

1088

the spectrum is the important one. In the problem of storm tracking we are most interested in the longest periods present, as those travel most rapidly.^ It is therefore desirable to divorce from the problem of wave forecasting the selection of that particular portion of

the spectrum which happens to be important to a defi-

ods has been carried out for west-coast situations. Forecasting for an east coast offers some special problems, and these are being investigated by the Department of Meteorology, New York University, under the sponsorship of the Beach Erosion Board, and by the Woods Hole Oceanographic Institution [6].

-

nite application.

REFERENCES

The

derivation of the physical laws governing the of the component wave trains under wind action remains the outstanding theoretical problem in the

growth

development of a method for forecasting the wave spectrum. The problem promises to be a difficult one for at least two reasons: (1) the limitations on the growth of the shorter waves imposed by stability considerations introduce a nonlinearity into the problem; (2) to the extent to which the lower, shorter waves are sheltered from the wind by the large waves, the energy budgets of the component wave trains are not mutually inde-

1.

Arthur, R. ary 2 to

5,

"Forecasting Hawaiian Swell from Janu1947." Bull. Amer. meteor. Soc, 29: 395-400

S.,

(1948) F., and Ursell, F., "The Generation and Propagation of Ocean Waves and Swell. I. Wave Periods and Velocities." Phil. Trans, roy. Soc. London, (A)

2.

Barber, N.

3.

Bates, C.

4.

240; 527-560 (1948).

C, "Utilization of Wave Forecasting in the Invasions of Normandy, Burma, and Japan." Ann. N. Y. Acad. Sci., 51: 545-569 (1949).

of forecasting the transformation of the

5.

Deacon, G. E. R., "Recent Studies of Waves and Swell." Ann. N. Y. Acad. Sci., 51: 475-482 (1949). "Waves and Swell." Quart. J. B. meteor. Soc, 75: 227-

decay also resolves itself into the problem of forecasting the change in the spectrum of the swell. The observed increase in the

6.

DoNN, W.

period of the significant swell is the result of the relatively rapid attenuation of the short-period components.

7.

Groen, P., and Dorrestein, R., "Ocean Swell; Its Decay and Period Increase." Nature, 165; 445-447 (1950). Hydrographic Office, United States Navy, Wind Waves and Swell — Principles in Forecasting. H. O. Misc. 11,275,

pendent.

The problem

238 (1949).

swell traveling through the region of

One

mechanism

provided by the viscous which the dissipation of energy is inversely proportional to the fourth power of the wave period. It can, however, easily be demonstrated that the effect of viscosity is several orders of magnitude too small to explain the observed transformation. Sverdrup [21] has, however, demonstrated that the selective attenuation resulting from the air resistance on waves traveling through regions of calm (equation (8) with U = 0) provides a possible mechanism for selective attenuation. Groen and Dorrestein possible

is

(1949).

8.

effects of the water, according to

suggest that selective damping by eddy viscosity is the mechanism. Further study is indicated. It should also be noted that laws governing the generation of waves at low wind speed can be expected to differ from those governing the generation at moderate and high speeds. The reason lies in the character of the sea surface, which appears to be hydrodynamically smooth at wind speeds less than 6 sec~S and hydrodynamically rough at wind speeds exceeding 7 sec~^

m

61 pp., 1943. 9.

Hydrographic Office, United States Navy, Breakers and Surf— Principles in Forecasting. H. O. No. 234, 55

10.

J. D., and Saville, T., Jr., "A Comparison Between Recorded and Forecast Waves on the Pacific Coast." Ann. N. Y. Acad. Sci., 51 502-510 (1949). Johnson, J. W., O'Brien, M. P., and Isaacs, J. D., "Graphical Construction of Wave Refraction Diagrams." V. S. Hydrogr. Off. Tech. Rep. No. 2, H. O. Publ. No. 605, 45 pp. (1948). Munk, W. H., "The Solitary Wave Theory and Its Application to Surf Problems." Ann. N. Y. Acad. Sci., 51:

pp., 1944.

12.

376-424 (1949). 13.

30:349-356 (1949). 14.

from a Tropical Storm." Scripps Institution Wave Report No. $9, Nov. 1944 (unpublished).

and Johnson, J. W., "The Dissipation of Wave Energy by Bottom Friction." Trans. Amer. geophys. Un., 30: 67-74 (1949).

15.

H., and Traylor, M. A., "The Longshore Currents." Trans. Amer. geophys. Un.,ZO: 337-345 (1949). RossBY, C.-G., and Montgomery, R. B., "The Layer of Frictional Influence in Wind and Ocean Currents." Pap. phys. Ocean. Meteor. Mass. Inst. Tech. Woods Hole ocean. Insln., Vol. 3, No. 3, 101 pp. (1935). Seiwbll, H. R., "Sea Surface Roughness Measurements in Theory and Practice." Ann. N. Y. Acad. Sci., 51: 483-

Putnam,

J. A.,

Prediction

16.

17.

Munk, W.

of

500 (1949).

Consult "Ocean Waves as a Meteorological Tool" by

W. H. Munk, pp. 1090-1100 in this Compendium. 6. W. J. Francis, Jr., Commander, USN, "Waves and

J. A., "Loss of Wave Energy Due to Percolation Permeable Sea Bottom." Trans. Amer. geophys. Vn.,

Putnam, in a

18. 5.

Isaacs,

;

11.

m

Equation (9) and all subsequent development is based on the assumption of a rough sea surface. In addition to the more fundamental problems mentioned above, there remain many problems of practical applications. Among the more important ones is the prediction of waves and swell from a tropical storm. The rules of thumb which have been estabhshed^ do not in all cases lead to adequate forecasts. Most of the actual testing of wave forecasting meth[16].

L., "Studies of Waves and Swell in the Western North Atlantic." Trans. Amer. geophys. Un., 30: 507-516

19.

Swell

of Oceanography 20.

and Wadsworth, G. P., "A New Development in Ocean Wave Research." Science, 109: 271-274 (1949). Shepaed, F. p., and Inman, D. L., "Nearshore Water Circulation Related to Bottom Topography and Wave Refraction." Trans. Amer. geophys. Un., 31: 196-212 (1950). Suthons, C. T., The Forecasting of Sea and Swell Waves.

FORECASTING OCEAN WAVES Naval Meteorological Branch Memo, No.

135/45, Oct.

Sea,

1945. 21.

22.

23.

SvEBDRUP, H. U., "Period Increase of Ocean Swell." Trans. Amer. geophys. Un., 28: 407-417 (1947). and Munk, W. H., "Theoretical and Empirical Relations in Forecasting Breakers and Surf." Trans. Amer. geophys. Un., 27: 828-836 (1946). "Empirical and Theoretical Relations between Wind,

and Swell." Trans. Amer. geophys. Un.,

1089 27: 823-827

(1946). 24.

"Wind, Sea, and Swell: Theory of Relations for Forecasting." U. S. Hydrogr. Off. Tech. Rep., No. 1, H. 0. Publ. No. 601, 44 pp. (March 1947).

25.

Wiegel, R. L., "An Analysis of Data from Wave Recorders on the Pacific Coast of the United States." Trans. Amer. ,geophys. Un., 30: 700-704 (1949).

OCEAN WAVES AS A METEOROLOGICAL TOOL' By W. H.

MUNK

University of California, Scripps Institution of Oceanography

Introduction

The

first attempt to apply this ancient art as an aid weather forecasting appears to have been made in New Zealand around the turn of the century .^ Yet no quantitative methods were developed until World War II. We shall describe the three general methods which present themselves at this time. Each of these has its advantages and disadvantages, but it is too early to state whether these methods will find widespread appli-

in

cation.

The Height-Period Method Applied

to Visible

Swell

based on the relationships established for forecasting sea and swell from weather maps [15, 16].^ It consists of computing the wind speed C/ in a storm area, the distance D from the storm area, and the travel time io of a swell, making use of measurements of the swell height Hd and period To. A discussion of these quantities is found in another paper.' Wave height and period refer to deep water, and to the significant waves, that is, the average of the highest one-third of all waves present.^ Observations from shipboard can therefore be taken without further modification. In the case of land-based observations the wave is

1. Contribution from the Scripps Institution of Oceanography, New Series No. 512. Many of the results discussed here are based on research carried out for the Hydrographic Office, the Office of Naval Research, and the Bureau of Ships of the Navy Department, under contract with the University of Cali-

fornia. 2. Prof. C. E. Palmer, in a letter to the author, writes, "In the early days of weather forecasting in New Zealand (towards the end of the last century) no information from Australia was available, consequently the only meteorological warning of storms coming from the west was the local fall in the barometer. In an endeavor to get more advanced warnings. Captain Edwin,

who was then

in charge of a very small weather forecasting organization in the Marine Department, used the observations of sea and swells from light houses to supplement the data on the synoptic maps. These old maps are still in the archives of the New Zealand Meteorological Service and I have studied

them with some

Institute of Geophysics

any depth since it does not change as waves enter shallow water. Along steep coastlines or exposed beaches with simple bottom topography the deep water wave height can, for practical purposes, be taken as the wave height one or two wave lengths outside the breaker zone. Otherwise it is necessary to period can be determined at

Since ancient times seafaring men have recognized the significance of ocean waves as a sea-borne storm warning. However, their interpretation was intuitive, based upon the experience gained in a hfetime at sea.

This method

and

interest because the reconstruction of the

storm positions and tracks by means of the ocean observations seems remarkably good." 3. Consult "Forecasting Ocean Waves" by W. H. Munk and R. S. Arthur, pp. 1082-1089 in this Compendium. In estimating wave heights from visual observations is a tendency to arrive at values well in excess of the mean heights for all waves present. The definition of significant 4.

there

waves given above has been found of most observers.

in accord

with the estimates

take into account, by means of specially constructed "refraction diagrams" [7, 12], the effect of bottom topography and of the configuration of the coastline. The nondimensional relationships given below follow from the forecasting theory [16]:^ [72

OCEAN WAVES AS A METEOROLOGICAL TOOL tained become increasingly uncertain as the distance

between storm and observer becomes greater. For a discussion of the assumptions underlying the foregoing equations the reader

paper

[16].

The advantage

is

referred to the original

of this

method

is

1091

In the first place, the forerunners travel considerably faster than the vi.sible swell. On the basis of instrumental observations now available [1] the period of the forerunners may reach 25 sec, compared to 12-13 sec

that for

9

10

II

12

13

14

PERIOD OF SWELL, Tp,

16

IN

16

17

IS

19

ZO

17

8

19

ZO

SECONDS

—

Fig. 1. Plot of equations (5) and (6) relating wave steepness S (height/length), wave age /3 (wave velocity/wind velocity), wind speed U and wind duration t. Subscript "F" refers to values at end of fetch. (From Sverdrup and Munk [16], Figs. 5 and 7.)

9

10

M

12

13

14

15

16

,

shipboard observations, or for exposed and steep coasts, permits a rapid determination of the storm distance and a rough estimate of the storm intensity without the need of special wave-measuring equipment. In this sense the method was first used during World War II by Capt. D. F. Leipper, AAF, as an aid in forecasting the arrival of intense storms in the Aleutian area. In many instances the arrival of heavy swell preceded all other indications of the storm. From a climatological point of view this method can be applied by "mapping" on an D,T D-di'dgram typical meteorological situations associated with wave conditions in certain areas (Fig. 3). The principal disadvantage of this method is the slow velocity of the significant waves. As a result the information concerning storm location and intensity may be several days old before the waves reach shore. it

H

The Frequency-Spectrum Method Applied

to

Fore-

runners of Swell

The limitations outlined above can be overcome in part by dealing with the low, long, imperceptible waves which precede the visible swell. Since these waves are only a few inches high it is not possible to apply simple, visual methods of observation, but the advantages involved often appear to justify the use of special instrumental techniques.

PERIOD OF SWELL, T;,,

IN

SECONDS

—

Fig. 2. Distance from which swell comes, travel time, and wind velocity in generating area as functions of observed height and period of swell. The upper figure is drawn for a long-lived storm, the lower figure for a short-lived storm. The assumed relation between wind speed and duration for these two cases is shown in the inset. (From Sverdrup and Munk [16].)

as a typical

maximum

period for the swell.

The

corre-

sponding group velocities with which the disturbance created by a storm is effectively propagated by surface wave motion are of the order of 900 nautical miles per

Table I. Sample Calculations for a Storm of Unusual Duration (Case A) and a Short-lived Storm (Case B) (ft)

MARINE METEOROLOGY

1092

Most of the older instruments recorded the elevation of the sea surface against time by some suitable arrangements of floats. During World War II very effective methods were developed which derive from the underwater pressure fluctuations induced by the surface waves. It

is

curious that this

mode

of attack should

have been initiated independently in Great Britain and the United States. An early model developed by the

120*

130°

140°

150°

160*

170'

IBO'

—

been developed at the College of Engineering, University of CaHfornia [6], and these have been installed at Quillajoite River, Washington; Heceta Head, Oregon; Point Cabrillo, Point Sur, Point Arguello, Oceanside, and La JoUa, California; and on the island of

Guam.

differ in many important aspects, the following principles are common, to

Although the various instruments

170°

160°

150°

140°

130°

IZO*

110°

Fig. 3. Origin of waves reaching La Jolla, California. The capital letters on the large chart represent typical meteorological situations, which give rise at La Jolla to waves of heights and periods shown in inset B. Inset is a chart of the region near La Jolla on an enlarged scale. The shaded areas on the large chart represent typical fetches, that is, areas where the waves are generated. The isobaric pattern and the nature of the meteorological fronts are also indicated. The large open arrows represent typical paths of the storm systems. The wavy arrows indicate the direction of the waves leaving the storm systems. The figure cannot represent the nature of the meteorological situations with any degree of accuracy, but it is supposed to illustrate how different meteorological situations can be identified by the height and period of the waves with which they are associated. {From Munk and Traylor [12].)

Mine Design Department,

British Admiralty, has been Pendeen, near Lands End, England, since 1944. In the United States the development of wave instruments has been carried out chiefly at the Woods Hole Oceanographic Institution and at the Department of Engineering of the University of California. In an early model designed by M. Ewing the recording apparatus was contained directly in the underwater unit. Later, units recording on shore were installed near Cuttyhunk, Massachusetts, and on the island of Bermuda [8]. A number of shore recording models have in operation at

A

most wave instruments of the underwater pressure type and should be understood for a proper interpretation of the records. Surface waves induce pressure fluctuations in the entire column of water between the surface and the sea bottom (Fig. 4). For any given wave height and depth of water, the amplitude of these fluctuations depends on the wave period in such a manner that waves of very short period are virtually eliminated, The underwater unit measures the deviation of the fluctuating pressure at the sea bottom from the mean hydrostatic pressure. A "slow leak" in the underwater unit elimi-

OCEAN WAVES AS A METEOROLOGICAL TOOL nates the effect of tides and other very long waves. The pressure fluctuations are converted into electrical modu-

which are transmitted through a cable to a shore recorder. Finally the records are subjected to a harmonic analysis by a special instrument [2]. The natural lations,

wave spectrum waves

is

therefore modified in three stages:

removed by hydrodynamic removed by the slow leak in the underwater unit; (3) the remaining record is broken down further by harmonic analysis. Hydrodynamic filtering is particularly adapted for extracting the low forerunners from the complex pat(1)

of short period are

filtering; (2)

waves

of very long period are

tern of the sea surface. this filter can

The response

characteristics of

be expressed by the ratio

AP/APo

of the

amplitude of the pressure fluctuation at the bottom to

1093

equations (8) and (9) are in error by approximately 20 per cent.^ Ewing and Press [4] have suggested that this discrepancy might be related to the nonrigidity of the sea bottom. Folsom [5] obtains about half this discrepancy in laboratory experiments employing metal wave tanks, thus indicating that the discrepancy might also be related to other factors. Two methods for determining wave direction are being investigated. At the Department of Engineering, University of California, Berkeley, J. D. Isaacs has measured wave direction by means of a Rayleigh disk attached to the underwater unit. The orientation of this disk is recorded ashore by means of a Selsyn motor. In the case of a simple wave train the disk will align itself normal to the plane of orbital motion. In the case of an

SHORE RECORDER

Fig. 4.— Recording mechanism. The pressure is transmitted through an outer bellows into a second bellows inside the instrument casing, so that the pressure of the air inside the two bellows always equals the pressure in the water outside. The air inside the bellows can pass through a slow leak into the instrument casing, and the average pressure inside the casing equals the average pressure in the water, that is, the hydrostatic pressure. The leak is so slow that the pressure inside the instrument does not change appreciably during one wave period, yet it permits pressure equalization related to tides. The total displacement of the inner bellows depends on the difference in pressure between the inside and the outside of the bellows and therefore measures the deviations of pressure (amplitude AP) from the hydrostatic mean.

that just beneath the surface. Let h designate the water depth, L the wave length, T the wave period, and g the acceleration due to gravity. The length L can be eliminated between the equations

AP

MARINE METEOROLOGY

1094

analyses obtained by the methods discussed above.' first indications of the storm on the wave record were some "low-frequency noises" at 1400, 14 March

velocity appropriate to their period:

The

1945.

At that time

Pendeen re10-sec and 12-sec waves

gT V= 4x

visual observations at

vealed only the presence of

from another source; the long forerunners of the swell were too low to be visible. The band of gradually diminishing periods was the result of an intense storm which formed on 10 March off the coast of Cuba, 3000 miles from Pendeen, and

(10) by)

Ls

Xy, and x, represent the location of a point disturbance and the wave station, respectively; U and ts the time of the disturbance and the time at which waves

Here

T arrived at the wave station. Equation (10) has a simple geometric interpretation on a time-distance of period

20 24 30

—

Fig. 6. Surface weather map for 10 March 1945. Fronts are represented in the conventional manner, and isobars are labeled in millibars. Point P denotes the wave station at Pendeen, England. Figs. 6-9 show the passage across the Atlantic Ocean of the storm for which the wave spectrograms are

shown

in Fig. 5.

{From

Munk

[9].)

Rays through the point source wave periods, the value of each period being determined by the slope of the ray. The measurement of two periods, Ti and T^, arriving at times iio.i and ^^,2, suffices to determine distance and diagram

(Fig.

10):

represent the paths of

>MjJWi^

'°°i

20 24 30

WAVE PERIOD

8 IN

10

12

15

time of the source. .

i 20 24 30

SECONDS

—

Fig. 5. Spectrograms of waves recorded during 14-16 March 1945 at Pendeen, England [1]. Each spectrogram gives the distribution of energy among wave periods for a 20-minute record. The records were taken at 2-hourIy intervals.

traveled in a general northeast direction, passing west of the British Isles. Four representative weather maps are shown in Figs. 6-9. The positions indicated for the

"fetches" were determined according to the rules developed for wave forecasting.^ It should be noted that the fetch lengthened during the time interval between 1830, 11 March,

and

1830, 12

March.

The spectrogram in Fig. 5 can be interpreted in terms of the classical wave theory, according to which component wave trains travel independently with the group

A

different type of analysis

based on the autocorrelation function has recently been applied to ocean waves by Seiwell and Wadsworth [14]. 7.

Fig.

7.

— Surface weather map for 11 March 1945.

Figure 11 shows the propagation diagram used by Barber and Ursell [1]. For each spectrogram (Fig. 5) the maximum and minimum periods were determined, and

OCEAN WAVES AS A METEOROLOGICAL TOOL lines of

appropriate slope drawn. It

is

apparent from the

figure that the foregoing interpretation of the

servations vations.

graph

is

consistent with

tlie

The author has found

[9,

Fig.

meteorological obser-

it

convenient to use a

Fig. 5] with a special coordinate

8.

wave ob-

system on

1095

forward edge of the fetch; D, E, and F were computed from conspicuous features near the upper limit of the period band and give the approximate position of the rear edge of the fetch. It can be seen, however, that focus A in the upper part of Fig. 12 is located 500 miles

—

— Surface weather map for 12 March 1945.

Fig. 10. Schematic presentation of propagation of wave periods on a time-distance diagram. Xs and t, represent the position and time of a point disturbance x„ is the position of a wave-recording station, showing the arrival of waves of periods Ti and T2 at times U.i and t-^.i, respectively. ;

single disturbance fall along

which periods from a

a

straight line. In this manner certain outstanding features on the spectrogram (such as the upper and lower limits) were used to determine the distance and time of

the source region with which they are associated.

Fig.

9.

— Surface weather map for

13

March

DISTANCE FROM PENDEEN

2000

3000

IN

SEA MILES

1000

1945.

The information taken from the weather maps and the periods recm-ded at the wave station have been replotted in Fig. 12 to emphasize the similarity, with regard to both shape and width, between the storm

path and the period band. The computed positions, designated hy A, B, F, agree fairly well with the information on the weather maps, especially if it is remembered that these "foci" were obtained from theory without the introduction of any arbitrary constants. The foci A, B, and C were computed from the lower limit of the period band and seem to correspond to the .

.

.

16

—

for 11-16

MARCH

March

1945

1945, using

Propagation diagram Fig. winds estimated from the pressure distribution, flowing within 30° of a line of the recording station. {From Barber and Ursell 11.

[1].)

MARINE METEOROLOGY

1096

behind the storm front, and the other two foci about 200 miles behind the front. These discrepancies must be expected, since waves generated at the front itself could not gather sufficient energy to be perceptible at the wave station; furthermore, the distance between the point of wave origin and the storm front must be larger for the farthest disturbance, which is almost 3000 miles from Pendeen.

Pendeen came under the influence of the fetch which remained at about the same distance from Pendeen. In the meantime the fetch in the warm sector of the second storm moved slowly eastward, and on 18 February this and the fetch remaining from the first storm appeared as a single generation area. By 19 February the first storm had undergone complete frontolysis. The only remaining fetch was that Iceland,

in the cold sector,

—

Fig. 12. Comparison of storm path with period band. The shaded band in the upper part shows the movement of the storm system toward the wave station. The forward and rear edges of the storm were determined by 6-hourly weather maps, of which every fourth map is shown in Figs. 6-9. The computed storm positions (foci) are marked 4, B, F. The limits of the period band in the lower part were determined from the wave spectrograms shown in Fig. 5. (From Munk [9].) .

Figure 13 illustrates the application of the method to

a more complex meteorological situation. Two storm systems which existed simultaneously could be identified and traced separately. On 15 February 1945 the development of a cyclone started off the east coast of the United States. On 17 February the center of the cyclone had reached mid-Atlantic, and an unusually well-defined 1000-mile fetch in the warm sector was pointing directly toward the wave station. At the same time a new low-pressure area had just moved off the east coast of the United States and formed a second fetch immediately north of Bermuda (Fig. 13, upper right). As the first storm stagnated and veered northward toward

.

in the cold sector of the second storm,

.

which was mov-

ing northward toward Iceland. The spectrograms sho^vn in Fig. 13 are more complicated than those in the preceding examples, and the interpretation foci fall in lantic.

Foci

the

is

much more

first

The first three moved across the Atassociated with wave trains that

storm as

DtoH are

difficult. it

first storm veered northward and was joined with the fetch of the second storm. Only by that time had the main-period band moved

were formed as the its

fetch

sufficiently into the lower periods to

tion of a

Foci

J

to

wave

N

permit identifica-

from the distant second storm. originated from the joint fetch existing from train, F,

,

OCEAN WAVES AS A METEOROLOGICAL TOOL x\\

WAVE SPECTROGRAM IS

:o

t4

30 I

'^stA^'iL^^jLi

-^^yi|i

^^l. ttoo ji

^

j^iLiAi

7 J^^'.

.^j^m .^

j^

^^ufe

i.

\

\mK

«0°

ipo

\\\\\KW::sik^-4^

1097

MARINE METEOROLOGY

1098

hope

for are of the order of 1000 nautical miles per day.

Not until many more

situations

have been analyzed

will

method be posobtained demonstrate the feasibility of locating and tracking storms at distances exceeding 3000 miles and of making rough estimates regarding the size and character of these storms. an evaluation

sible.

The

of the usefulness of the

results

so

far

Should it be possible to use storm surges in locating storms at sea, they would have the advantage of relatively high speed, s/gh in water of depth h, or 10,000 nautical miles per day in mid-ocean. It is hoped, therefore, that they may eventually provide a tool to the S3Tioptic meteorologist.

Discussion and Conclusions

The Storm Surge Method

The

The preceding

discussion has indicated that the swell spectrum, visible or invisible, is limited by the maxi-

mum

velocities of the

clusion

is

winds in a storm area. This con-

in accord with the hypothesis that swell

originally caused

by the normal and tangential

was

stresses

applied by the ^vind to the sea surface, but it does not preclude the existence of other types of waves from storm areas of much longer period than those of the swell. To explore this possibility an instrument [11] has been built which is sensitive to waves whose periods lie between those of the swell and tides. It is essentially a modified tide gauge, and the filtering of the swell and tides is

accomplished by means of capillaries and

Table

II.

Feb. 9-10 Feb. 21-23 Feb. 27-29

methods involving the propagation of sound waves through the sea bottom (microseisms) and electromagnetic waves through the atmosphere (radar and spherics).

Instrumentation.

The

height-period (HT)

quires no special instrumentation.

trum

analysis

r (ft)

(min)

Date and time

method

re-

The frequency -spec-

(FA) method requires an underwater

recording unit connected

by a

cable to a shore recorder.

Along rocky coasts and coral reefs the chafing of the cable may create quite a serious problem and the use of

Maximum

(1948)

Date and time

methods involving

Data for Five Severe Storms off the California Coast

Earliest storm surges

Date

air

relative merits of the three

the propagation of ocean surface waves are summarized below. We shall also point out some of the disadvantages and advantages of these methods as compared to

Maximum swell

storm surges

H

r

(ft)

(min)

Date and time

9:0500

.04

14

9:2230

.12

15.5

10:1500

21:1800

.06

15

22:1100

.15

15.5

.06

12

14

.10

20

28:0600 30:1600

.12

Mar. 30-31

27:1400 30:1000

23:0400 29:1200

.14

12

Apr. 22-24

22:0800

.08

18

22:2200

.09

13

31:1200 24:0700

H

OCEAN WAVES AS A METEOROLOGICAL TOOL

1099

mination of wave height. In the determination of wave height the response characteristics of the instrument enter as an important factor, and it may be necessary to take into account, by means of specially constructed "refraction diagrams" [7, 12], the effect of bottom topography and of the configuration of the coastlines. Wave periods, on the other hand, are relatively easy to ascertain from wave records and are not subject to the complex changes in wave pattern that occur as waves come into shallow water. Determination of wave direction by means of a Rayleigh disk or a two-unit waVe

type, acceleration, and other characteristics. In view of the close "coupling" between the wind pattern and

station are being investigated.

this connection it is

It is not likely that the sible to

SS method

will

make

it

pos-

compute the storm distance from records at a

The distance determination for the FA method depends upon the high dispersiveness of ocean swell, and storm surges are almost nondispersive. In single station.

view of the great length of storm surges they will also be subject to considerable refraction. The principal hope lies in the determination of the arrival time of identical phases at two or three stations, and the location of storms from special charts based on the propagation at

\/gh

velocity.

HT

Range. It is estimated that the method can be used to distances up to 3000 nautical miles, the FA method to distances exceeding 3000 miles. The range of the SS method is not known. The values given above are in excess of those that have been obtained by seismic and electromagnetic methods. Group Velocity. The group velocities applicable for the HT, FA, and SS methods are of the order of 400, 900, and 10,000 nautical miles per day respectively. The relatively long interval between the time the waves are generated and the time they are recorded at the wave station is a disadvantage in the application of the and FA methods. Their practical use will, therefore, be largely to verify or modify the interpretation already made on the basis of meteorological information. In the case of compact meteorological disturbances, such as young hurricanes, these waves may well provide the first clue as to the existence of the storms. The methods should be particularly useful over the southern oceans [3] and for other regions where the network of observing stations is widely spaced. The group velocity of the storm surges, although slow compared to the seismic and electromagnetic waves, is sufficiently large to permit synoptic application. Storm Intensity. The HT method gives an estimate of the storm intensity. In the case of the FA method an estimate of wind speeds from the maximum recorded period is suggested by Fig. 14. It is also hoped that studies dealing with the propagation of energy by the forerunners will lead to an interpretation of the spectrogram ordinate, which has received no attention so far but must be related to the storm intensity. The relationship between storm intensity and storm surges has not been studied. Other Storm Characteristics. The application of the methods employing ocean surface waves is further enhanced by the possibility of determining not only the location and intensity of the storm, but also its size,

HT

the sea surface waves one might expect a better chance by the methods described in this report than

for success

by those based on

seismic

and electromagnetic waves.*

With regard to the HT method the research requirements coincide with those pertaining to the problem of forecasting ocean waves and are discussed in another paper.' Of particular imDesirable Future Studies.

portance

is a better understanding of the decay of swell traveling through an area of calm or cross winds. In

planned to establish a wave

re-

corder in the equatorial Pacific, possibly on the Marquesas Islands. These islands lie 2400 miles and about 6 days "up-swell" from California, and a comparison

wave records obtained

there with those at Oceanwould give information concerning the attenuation of swell over large distances. It is hoped that these studies may help to bring about, on a scienof

side, California,

a revival of the ancient art of judging weather of the sea surface. The FA method appears to have reached a stage of development where it will be possible to work with records from a network of stations, rather than from a single station. We may expect marked progress as a consequence. Our present experience is almost entirely confined to stations in the eastern Atlantic toward which the storms were moving.^ Development and standardization of suitable recording and analyzing equipment is urgently needed. The determination of wave direction is an essential requirement in making use of wave records for tracking storms. The SS method is at such an early stage of development that further work along instrumental and theoretical lines is required before it is possible to make any definite recommendations. An improved instrument has been installed at the end of the Scripps Institution Pier, in La Jolla, California, and similar units will be installed during 1950 at Oceanside, California, 30 miles north of La Jolla (for direction determination) and in Hawaii. By means of this network of long-period-wave stations it is hoped that research on the generation and propagation of storm surges can be vigorously pushed. In conclusion it must be emphasized that it would be most unfortunate if study were to be limited to the three methods with which we have been chiefly concerned here. A sj^stematic exploration of the spectrum of ocean waves is likely to lead to surprising new developments. In this connection it should be remembered that the sea surface wave pattern provides a complete picture, though a distorted one, of the entire wind distribution over the ocean, and our interpretation of this tific basis,

from the appearance

[3] indicates that some of tlie microcaused by the interference pattern of the surface waves in the storm area. Apparently a second-order effect inherent in such a pattern is associated with pressure fluctuations which do not disappear at great depth. 9. Lt. R. L. Miller, USAF, has successfully applied the method to a storm over the Bering Sea, using wave records taken at Guam, located to the rear of the moving storm (Scripps Institution Wave Report No. 90, unpublished).

8.

Recent evidence

seismic activity

is

MARINE METEOROLOGY

1100

picture should improve with the advance of instruments, of theoretical studies, and of empirical ex-

8.

perience. 9.

REFERENCES 1.

F., and Uksbll, F., "The Generation and Propagation of Ocean Waves and Swell I Wave Periods and Velocities." Phil. Trans, roy. Soc. London, (A) 240:

Barber, N.-

;

Darbyshire,

11.

J.,

and Tucker, M.

J.,

"A Frequency

5.

6.

EwiNG, M., and Press, F., "Notes on Surface Waves." Ann. N. Y. Acad. Sci., 51: 453-462 (1949). FoLSOM, R. G., "Sub-surface Pressures Due to Oscillatory Waves." Trans. Amer. geophys. Un., 28: 875-881 (1947). "Measurement of Ocean Waves." Trans. Amer. geoJ. W., O'Brien, M. P., and Isaacs, J. D., "Graphical Construction of Wave Refraction Diagrams." V. S. Hydrogr. Off. Tech. Rep. No. 2, H. O. Publ. 605, 45 pp. (Jan. 1948).

Recording Ultra

"An Instrument Low Frequency Ocean Waves."

Instrum., 19: 654-658 (1948). H., and Traylor, M. A., "Refraction of Ocean Waves: A Process Linking Underwater Topography to Rev.

sci.

13.

Seiwell, H. R., "Sea Surface Roughness Measurements in Theory and Practice." Ann. N. Y. Acad. Sci., 51: 483-

Beach Erosion." /. GeoL,

55: 1-26 (1947).

500 (1949).

14.

15.

phys. Un., 30: 691-699 (1949). 7.

"Surf Beats." Trans. Amer. geophys. Un., 30: 849-

MuNK, W.

Land., 158: 329-332 (1946).

4.

of Swell."

12.

Deacon, G. E. R., "Storm Warnings from Waves and Microseisms." Weather, 4: 74-79 (1949).

by Forerunners

854 (1949). Iglesias, H. v., and Folsom, T. R., for

Analyser Used in the Study of Ocean Waves." Nature, 3.

533-544 (1949). H., "Tracking Storms /. Meteor., 4: 45-57 (1947).

MuNK, W.

10.

—

527-560 (1948). 2.

Klebba, a. a., "Details of Shore-Based Wave Recorder and Ocean Waves Analyzer." Ann. N. Y. Acad. Sci., 51:

Johnson,

16.

——

and Wads worth, G. P., "A New Development in Ocean Wave Research." Science, 109: 271-274 (1949). Sverdrup, H. U., andMuNK, W. H., "Empirical and Theoretical Relations between Wind, Sea and Swell." Trans. Amer. geophys. Un., 27: 823-827 (1946). "Wind, Sea and Swell: Theory of Relations for Forecasting." U. S. Hydrogr. Off. Tech. Rep. No. 1, H. O. Publ. 601, 44 pp. (March 1947).

BIOLOGICAL Aerobiology by Woodrow

Physical Aspects of

C.

Human

AND CHEMICAL METEOROLOGY

Jacobs

1

Bioclimatology by Konrad J. K. Buettner

Some Problems of Atmospheric Chemistry

by H. Cauer

103

1112

1

126

L_

AEROBIOLOGY By

WOODROW

C.

JACOBS

Headquarters, Air Weather Service, Washington, D. C.

INTRODUCTION The field of extramural aerobiology is concerned with the distribution of living organisms by the exterior atmosphere and with some of the consequences of this distribution. It includes within its sphere of interest a study of the dispersion of insect populations, fungiis in fact, spores, bacteria, viruses, molds, and pollens all forms of life, both plant and animal, that are borne aloft and transported wholly or in large part by the atmosphere. The present-day field of aerobiology had its origin in the pioneer experiments of Spallanzani in 1776, and in the work of Pasteur, Tyndall, and others who used the method of the aerobiologist in combating the theory of the spontaneous generation of life and in developing the germ theory of disease. It has been only within the last fifteen or twenty years, however, that aerobiology has emerged as a specialized field of investigation. An examination of the very extensive literature on the subject accumulated during these later years reveals that activity in the field has been largely confined to the biologist and has seldom included the meteorologist. Few of the biological data appear to have been analyzed from the standpoint of fluid mechanics which leaves the quantitative meteorological approach, based on theory and supported by meteorological-biological observations, as something that remains largely for the

—

future.

The biologist has directed his attention primarily to the problems of entrapment, identification, and enumeration of organisms carried by air, but has more recently become interested in the atmosphere as the medium for the dispersal of the organisms. The meteorologist, on the other hand, has as yet shown comparatively little interest in the results of aerobiological investigation as a possible

means

for acquiring

new

knowledge on the nature of mixing processes in the atmosphere and on the movements of air masses. Nevertheless,

the ever-increasing concern of the botanist,

zoologist, geneticist, agriculturist, allergist, the general

public, and,

more

recently, the militarist, in the results

atmospheric dissemination of organisms, whether the latter be injurious insects, allergens, or pathogens, shows clearly that the subject is one of great importance and of wide general interest. of the

BIOLOGICAL FACTORS Methods and Problems

From

of

For those microorganisms which may be by their shape or superficial surface characteristics and which cannot be grown on culture media, the adhesive-coated slide is widely used as a sample trap. A glass collecting slide is normally exposed horizontally to the air and, although particles are deposited by the combined action of turbulent air motion and by gravity, the technique is commonly re-

volume

Sampling and Counting.

the standpoint of the biologist the ultimate quantitative goal of atmospheric biological research is the determination and/or prediction of the type and number of viable organisms suspended in a given

of air.

readily identified

the "gravity slide" method of several important disadvantages from the meteorological point of view. First, comparatively long exposures are required 24 hours being the time vmit conmionly used. The method, therefore, does not afford a means for determining the degree of atmospheric contamination at a given moment or through a given short time interval which, of course, limits the use of the data in the "synoptic" sense. The second, and principal, criticism of the gravity method, however, lies in the fact that the catch does not represent recovery from a definite volume of air. Attempts to convert gravity slide figures into volumetric terms have not been too successful. In spite of the obvious disadvantages of the method, a large proportion of our present statistics on pollen and fungus-spore distribution has been obtained from these gravity slide samples. For the study of mold spores and bacteria which are too small for convenient direct microscopic examination, it is necessary to examine cultiu-ed specimens and count the colonies of each type of specimen. This type of sample is obtained by exposing standard Petri dishes containing suitable culture media to the air for periods ranging from two minutes to one-half hour. This is the ferred

to simply as

collection.

The method has

—

so-called "plate

method"

of collection

and

suffers

from

the same disadvantage as the gravity slide technique in that the results cannot be interpreted in volumetric terms. The samples obtained by this method represent organisms released from the air during the brief period

sampling and no record whatsoever is obtained during the long gaps between exposures. The method is also time-consuming and expensive, and to secure reasonof

abl,v

complete data from only a few collecting locations

requires the support of a large staff of laboratory technicians.

Because it is necessary to identify and count the microorganisms after they have been captured, it appears that some sort of impingement-slide method of collection offers the greatest promise of adaptability to aerobiological work. For surface collecting the equipment should be economical, simple to operate, and capable of sampling known volumes of air. Above all, the equipment, the techniques of its use, the method of counting, and the units of measure for reporting results

1103

BIOLOGICAL AND CHEMICAL METEOROLOGY

1104 should be standardized nicians as far as

is

among

observers and tech-

practicable.

Several types of volumetric sampling devices (such Owens dust counter) are available in some quan-

as the

but most

tity,

air

of

them handle an

to be adaptable

to

insufficient

aerobiological

volume

of

investigation.

While Durham [8] has reported the development of an apparatus which impinges the particles from a measured quantity of air on a slowly moving slide, thus affording both a record of organisms and of the volume of air sampled throughout the 24-hour period, the results of collections by this method have not been reported upon in detail. In a study of various types of air filters for trapping microorganisms, DallaValle and Hollaender [5] found that the relative efficiency of a viscous impinging surface tested was approximately 70 per cent. They report that the highly efficient Greenburg-Smith impinger, used as a dust-sampling apparatus by the U. S. Public Health Service, is not particularly adaptable to aerobiological work. It is the opinion of the writer, however, that the efficiency of the collector, itself, is not nearly so important as the condition that the relative efficiency be a known factor and approximately a constant. For sampling the upper atmosphere the collecting equipment should be compact, light in weight (particularly if it is to be supported aloft by balloon, parachute, or special atmospheric sounding device), and fully automatic in operation; it should be designed to exclude the possibility of contamination^ and to provide for the multiple sampling of measured volumes of air at known temperatures (and humidities) between specified small pressure intervals (or at known altitudes).

Proctor [23] has perfected an apparatus for upper-air sampling by aircraft which, in addition to securing operation independent of the pilot, simultaneously records certain meteorological data. In addition, variation in air flow is recorded to permit comparative counts in known volumes of air. As in his previous models of collecting instruments, provision is made for photomicrography and subculture of the microorganisms with the exclusion of contamination or cross innoculation of the separate samples. As would be expected, the problem of collecting and identifying the larger organisms and insects is simpler than the sampling and counting of air-borne microorganisms. The most common methods for collecting these larger forms at or near the surface involve the use of nets, flight or baited traps of some sort, or simply entail the visual counting of insects on the wing or as they alight on some object. None of these methods, however, serve to give the true population of organisms in the air at any given time, although it is possible, under certain conditions, to convert flight-trap collections into rough volumetric terms. Kites and balloons were naturally the earliest devices 1.

tion

The element of contamination is an important considerawhen sampling the upper atmosphere, the air over the

used for sampling insect populations in the upper air, but few of the results of collections by either method appear to have been published. The most successful collections appear to have been obtained through the use of aircraft. Perhaps the most extensive study made of the insect population of the atmosphere was conducted at Tallulah, La., during a five-year period between 1926 and 1931 by the Bureau of Entomology and Quarantine of the U.S. Department of Agriculture. The results have been reported upon in considerable detail by Glick [9, 10]. In these collections some 28,739 specimens were taken, from altitudes as low as 20 ft above the ground to as high as 15,000 ft with specially de-

signed traps fitted to the wings of several types of aircraft. The results are given in volumetric terms (average volume of air per insect) although desirable details concerning the testing and calibration of the collecting

instrument are lacking. It is unfortunate that similar data are not more generally available for other regions.

Methods and Problems of Identifying Organisms and Locating Sources. Perhaps the greatest difficulty that confronts the aerobiologist in sampling the atarises from the fact that many species of organisms are so similar in appearance that important differences which serve to separate species defy description or pictorial representation. Even in the cases of some economically important plant pathogens, the spores cannot be identified by morphological characteristics alone. In the cases of other forms, such marked variations in size, shape, and septation exist within the species that identification is impossible unless many spores are examined. Because it is certain that many closely related species within the same genus differ greatly in cultural characteristics, allergenic or biochemical effects and pathogenicity, the solution to the

mosphere

problem of rapid and precise identification of organisms is an essential step toward the full development of an applied aerobiology. The greatest difficulty that confronts the meteorologist in his investigations of the local and long-distance dissemination of organisms lies in his lack of knowledge concerning the exact (or even approximate) sources of the collected specimens. In the case of the more commonly collected spores and pollens, the parent plants or fungi may be so universally distributed that it is wasted effort even to attempt speculation as to the origin of the air-borne forms. In the case of bacteria in the atmosphere the problem is even more difficult, for here the entire earth's surface (including the oceans)

must be considered

as a potential source. It is unfortunate for the meteorologist that the organisms most fi-equently collected and identified are those whose sources are most cosmopolitan. It is true that the surface of the earth itself can be considered the source of specimens collected in the is far too broad a classianything beyond gross analyses of the atmospheric factors involved in the vertical

upper atmosphere but

this

fication of origin to allow

and horizontal transport

oceans, or in other situations where population densities of

line of reasoning,

microorganisms are low.

water

may

of organisms.

By

the shore line of a large

be considered a

line source for

same body of

the

land forms

AEROBIOLOGY over water or for aquatic forms collected latter technique has been successfully employed by ZoBell and Mathews [40], Rittenberg [26], and Jacobs [14] in their analyses of data on the microbial populations of marine air. In the investigation of the local dissemination of organisms the problem of identification of origin is usually less difficult. In such cases the collections can frequently be made near or above a source which is readily identified because of a local anomaly in surface cover or because the spore formers or pollinators can be isolated with a reasonable degree of fineness. Proctor and Parker [24] have suggested the artificial introduction into the atmosphere of an easily identified organism for studying dispersion but, because of the rapidity with which small organisms are dispersed throughout large volumes of air and the concurrent impracticability of introducing sufficiently large numbers of organisms to allow reasonable chance for a sample recovery, it appears that such a method would be limited to studies of purely local transport. The use of stained insects has been employed for the latter purpose with some success [30]. From the standpoint of the meteorologist, who is primarily concerned with the atmospheric processes involved in the dissemination of organisms and less interested in the results of such dissemination, it appears that the most pressing need in aerobiologic research is the establishment of a standard list of "biological indicators" or "markers" (as they are called by Stakman [31]). This- list should contain properly described and representative spores, pollens, molds, bacteria, and, perhaps, insects that can be easily identified and whose local sources have been determined. The sources represented by the type specimens should be mutually exclusive as to character of surface and/or geographic location. In the case of fungi, considerable care must be exercised in selecting species that produce a vast number of spores in a relatively short time they should not multiply on dead vegetation or survive in a given region from one year to another [3]. From the standpoint of agriculturists, medical recollected

inland.

The

;

searchers,

and workers in related

fields,

who

are

more

interested in the results of dissemination than in dis-

semination processes, the primary need in aerobiology is the perfection of techniques for collecting and identifying organisms of pathogenic importance and in the determination of circumstances governing their survival and multiplication after they cease to be airborne. This segregation of interest is meant as no reflection upon the attitude of the meteorologist, for it is taken without question that the physical processes governing the distribution of pathogenic and allergenic forms by the atmosphere are identical to those governing the distribution of the nonpathogenic and nonallergenic species.

The Atmosphere as an Environment

for Organisms.

From

the pathological standpoint the viability of organisms transported by air currents is as important a consideration as carried.

is

the distance to which they are

As stated by Stakman

[31],

"To show that

1105

propagative bodies of pathogens are disseminated by the wind is only the first step in finding out what needs to be known. Are they viable at the end of their trip; how long will they remain viable, even if on the host plant, if conditions are not favorable for germination and entrance into the host soon after their trip; do they belong to a virulent race; is the host plant in susceptible condition; are [meteorological] conditions favorable for rapid multiplication and spread if initial infection occurs? These are only a few of the most important questions that must be answered if the problem is to be studied in its broadest aspects." It is, first of all, obvious to the meteorologist that the organisms must be able to withstand great extremes of temperature, pressure, humidity, and solar radiation if they are to survive transport over great distances. From the standpoint of temperature it may be argued that because solid particles (thus all organisms) in the air radiate and absorb very nearly as a black body, they must undergo extreme temperature changes which are not represented by temperature changes within the air mass. However, the heat capacity of the organism, or a particle with which it is associated, must be very small, thus it can be assumed that the temperature of the organism at any instant must be very nearly the temperature of the ambient atmosphere. It is therefore doubtful if such organisms are ever subjected to excessively high temperatures. Certain organisms probably succumb to the very low temperatures that exist at high altitudes [34] although there are some fonns which survive temperatures approaching absolute zero [39].

Bacteriologists

have shown that exposure to

violet radiations for short periods is lethal to

bacteria. In this connection, however, interest to note that bacteria

it is

which are

ultra-

most

of particular killed

when

suspensions (or agar plates streaked with suspensions) are exposed directly to sunlight are the same organisms which have been recovered from air by exposing agar plates for different periods of time. It appears that at least the air-borne parent cells are relatively resistant to sunlight.

Whether

this resistivity is

or intrinsic conditions

is

not

clear.

due to extrinsic

Some

results [29]

indicate that certain individual bacteria within a species survive dosages of ultraviolet radiation which are ordinarily lethal to the species, but that the resistivity of the individual bacterium does not persist in the

subculture progeny. On the other hand, the show later that many bacteria suspended mosphere must be associated with a dust some sort (such as surface debris or sea

writer will in the at-

particle of

salt) or a water droplet, and this particle may afford sufficient protection against the lethal type of radiation. Nevertheless, the bacterial counts should show a diurnal

variation due to this cause. There is the possibility that desiccation of the organism in dry air may render it nonsusceptible to ultraviolet radiations because of its reduced water content.

There appears to

difference of opinion

exist,

among

however,

a marked

investigators concerning

the effect of humidity. Rentschler

[25]

concludes from

1106

BIOLOGICAL AND CHEMICAL METEOROLOGY

laboratory experiments that high relative humidity of the air does not increase the resistivity of air-borne bacteria. Wells [35] and Whisler [36], on the other hand, maintain that ultraviolet radiations are ten to twenty times more germicidal in dry air than in humid air. These antithetical results strongly suggest that the differences in germicidal effects were in some way related to differences in the number or character of condensation nuclei present in the several experiments. In this connection it should be stressed that soil or sea-salt particles play a possible dual role in the maintenance of viability in the organism. In addition to

containing aggregates of microorganisms they may, under certain circumstances, act as condensation nuclei (if hygroscopic) for water vapor in the atmosphere and in so doing provide favorable conditions of moisture for the persistence of organisms in the viable state. If this reasoning is valid, then the consideration of

variations of atmospheric moisture should be important. Wellington [34] has reported upon a series of labora-

tory experiments designed to determine the effects of substantial decreases in pressure, temperature, and

humidity upon certain species of insects common in Canada. Attempts were made to simulate those combinations of pressure, temperature, and humidity that an organism might experience upon being lifted from the surface to a height of around 20 km. He concludes that the decrease in atmospheric pressure may be safely neglected as either a limiting or lethal factor among the elementary environmental changes experi-

enced by insects distributed at higher levels; he does show, however, that most of the species tested become insensible at pressures below 120 mb. He found, also, that the flight activity of the insects varied somewhat with pressure, remaining constant for most insects up to simulated altitudes of about 7.5 km, then decreasing to zero at about 16 km. In the cases of Coleoptera and Diptera, however, there was a distinct increase in activity down to a pressure equivalent to 1.5 km where it again approached normality. This latter finding is significant from the standpoint of the actual vertical distribution of these orders. That the responses are barotactic and not due to distress occasioned by the lowered oxygen pressure was also proved by the experiment. The effects of reduced pressures on microorganisms appear not to have been similarly investigated but, because of their small size and simple internal structure, it is assumed that the effect can be neglected in the cases of these groups also. There appear to be few, if any, actual quantitative data concerning the fraction of organisms that are able to survive significant transport. Proctor [21], in his investigation of the number of bacteria at high levels,

and counted the number of dust particles. found the ratio of microorganisms (bacteria and molds) to dust particles to be 1 to 108 for all levels and 1 to 118 above 9000 ft. As the writer has previously pointed out [14], this would show about eight per cent fewer bacteria per particle for the higher levels, which might indicate that this proportion was killed, since the physical factors governing their removal from the air also collected

He

would be the same as

for the dust particles. Proctor did not give average values for the layer below 9000 ft; it can therefore be assumed that the proportion that did not survive was somewhat greater than eight

per cent.

METEOROLOGICAL FACTORS The Mechanics

of

Exchange

of

Organisms Between

Earth and Atmosphere. It is assumed that nearly all surfaces, whatever their nature or composition, will contribute organisms to the atmosphere; but that some surfaces, because of greater populations of organisms, more extensive vegetative cover, greater mobility of surface materials, or more intensive atmospheric turbulence, will contribute far more than others. In the case of bacteria, it is a statistically remote possibility that any single organisms in the soil will be lifted by themselves into the air; in all probability they are most frequently associated with debris of some kind, such as bits of organic matter, dust motes, or, in the case of marine forms, with salt particles or droplets jof concentrated sea water. These organisms must therefore exist most frequently as- colonies rather than as individuals.

The laboratory method

of plating

and count-

ing the bacteria and molds permits of no distinction between individuals and groups. Because the number of bacteria in a cubic centimeter of soil may be numbered in the millions or hundreds of millions, the potential supply of these organisms must be considered almost

unlimited.

By this reasoning, the processes governing the exchange of soil bacteria between the earth and atmosphere are the same as for the exchange of other terrigenous materials. The quantity of material exchanged will be greatest in those areas where ample supplies of loose particles exist on the surface, surface winds are strong enough to stir up these materials, and steep lapse rates exist in the atmosphere to favor the vertical transport of the particles. The supply of microorganisms should be greatest where the surface is dry due to deficient rainfall, where there is an abundance of oi'ganic matter in the soil, where intensive cultivation is practiced, and in and near wooded areas. A spring maximum of dust in the atmosphere is noted in the solar radiation measurements in the United States. This is to be expected since the soil is driest at this season, cultivation is most extensive, surface winds are strongest, and the vertical temperature lapse rates are steepest. It can be assumed that the population of soil microorganisms in the atmosphere will be greatest during this season for the same reasons. It has previously been pointed out that Proctor [21], during his determinations of the number of bacteria at high levels, also collected and counted the number of dust particles. Although he made no volumetric calculations, rough computations by the writer indicate that he collected approximately 510 visible and collectable dust particles per cubic meter of air averaged for all levels. Above 9000 ft there were approximately 25 per cent fewer particles than the general average. His ratio of 1 microorganism to 108 dust

AEROBIOLOGY an average for all levels gives a figure of only 4.7 collectable bacteria (or molds) per cubic meter of air. If one considers the great number of bacteria that must exist in the lowest layers of air, these results show that either a very small percentage of the organisms survive or that the original number is dispersed rapidly throughout exceedingly large volumes of air. It is, perhaps, also possible that the processes governing the removal of organisms from the atmosphere are more effective than has previously been assumed. The processes governing the exchange of spores and pollens between the earth and atmosphere are not wholly analogous to those governing the exchange of particles as

bacteria and molds between soil and air. The pollens and spores of fungi present a wide range of types with respect to their morphology, physiology, and mode of production and liberation [15]. Consequently they vary greatly in adaptation to aerial dissemination. In the case of certain fungi, very elaborate

mechanisms from

for the forcible ejection of the fungus spores

exist

their

sporophores or spore mother-cells into the air. The force with which the spores are ejected varies greatly with different species, the most common ejection distances being of the order of one or two millimeters to several centimeters. Although many fungi produce an almost incomprehensibly large number of spores,- none of the latter appear to be provided with special adaptations for flotation as is the case with some seeds and insects. Of the various classes of organisms so far discussed, only the insects are capable of aerial locomotion. Their initial presence in the lower layers of the atmosphere and, to some extent, their vertical distribution and local dissemination are due to the flight activity of the insects themselves. Even here, however, the activity of the insect is dependent in some degree upon such meteorological factors as temperature, wind, and humidity [10, 20, 33, 37]. Some nonflying insects are

specially adapted to aerial dissemination, good examples being several species of spiders whose young spin webs from some elevated object to be later carried with the wind. Click reports that at times great masses of such webs are found floating in the air, even at altitudes of 7000 to 10,000 ft. A large number of seeds are particularly well adapted to aerial dissemination through very effective struc-

tures that increase

theii'

frictional

resistance to air.

Because of the size of the seeds and their very common occurrence, knowledge regarding them is more general than is true of smaller organisms. Viruses which are produced within the tissues of plants or animals do not appear particularly well adapted to aerial dissemination except as they may be carried by insect vectors or birds. There is the possibility, however, that such virus material may ocChristensen [3] cites as an example of the remarkable of reproduction of many plant pathogens, that Ustilago zeae (corn smut) in two weeks may produce a gall of 20-40 cubic inches, each cubic inch of which contains about six billion spores. One acre of corn with 10 per cent infection would produce 5 X 10" spores during the same period. 2.

power

1107

casionally be associated with bits of organic matter or microorganisms in the atmosphere. Additional research

on the possible (free) aerial dissemination of virus substances is needed. In the case of marine bacteria, it is only when the sea surface

mechanism

is

stirred sufficiently to

produce spray that a

exists for the introduction of the sea-surface

organism into the atmosphere. The spray droplets will, of course, include any bacteria present in the sea water and subsequent evaporation of the droplet will leave the organism associated with a salt particle or droplet of concentrated sea water. Since such particles are extremely effective nuclei for the condensation of water vapor in the atmosphere, they are more readily removed than are the nonhygroscopic dust particles which may contain soil bacteria. Since the number of marine bacteria in a cubic centimeter of sea water seldom exceeds 500, it can be computed (on the basis of data concerning evaporation from spray)' that the populations of marine bacteria in the air must be sparse everjrwhere except, perhaps, at times of rough sea or in the vicinity of a coastal "breaker zone." An understanding of the physical processes which serve to remove organisms from the atmosphere once they have become air-borne is as important to the aerobiologist as is a knowledge of the mechanism governing the lifting of the organisms into the atmosphere in the first place. Most investigators in the field of aerobiology have taken great pains to point out the usual small size and mass of air-borne organisms, and data concerning the computed or observed free rates of fall under the influence of gravity (in still air)

appear in almost every analytical paper.^ The present author has no desire to minimize the importance of small size and mass in furthering the dissemination of microorganisms for those are their primary adaptations to aerial transport. It should be pointed out, however, that of all the forces tending to move the single microorganism vertically, the gravitational factor is merely another component of force additive to others usually of greater magnitude. The possibility that a single pollen grain, spore, or bacterium carried through convection to an altitude of several kilometei's will ever be allowed to settle back to earth through the efl^ects of gravity alone is exceedingly remote. Some organisms of near colloidal dimensions could be considered to I'emain almost permanently in the atmosphere were they not brought down to the surface again through turbulence or through capture by condensation or precipitation products. Many investigators have made note of the fact that rainfall is an extremely effective mechanism for clearing 3.

On

the basis of determinations of the sea-salt content of

author has previously computed that the marine bacteria near the sea-surface source averages per cubic meter of air [14].

marine

air [13], the

number

of

about 4.

five

The

free rates of fall of the largest fraction of bacteria,

spores, and pollens (at sea-level air densities) are within the

mm

range of 0.1 to 20 sec"'. In some cases the velocities approach those predicted by Stokes' law and in other cases substantially reduced velocities are indicated.

BIOLOGICAL AND CHEMICAL METEOROLOGY

1108

the atmosphere of organisms. The comparatively large number of microorganisms found in rain water by various investigators

is

further evidence that at least a sizeable

have been captured and removed from the atmosphere by falling raindrops. While it has not been definitely proved that micro-

fraction of the air-borne organisms

organisms ever act directly as condensation nuclei in the atmosphere, at least one investigator has noted that the rate of fall of spores in moist air is several times greater than in dry air, presumably because the organism has increased its mass through the absorption of water vapor.

would thus appear that the condensation and prevapor are the important mechanisms for removing microorganisms from the atmosphere. The transport to the surface through the effects of turbulence with subsequent settling or impingement appears to be the secondary process. This reasoning, of course, does not apply to the larger organisms whose free rates of fall are appreciable and which are supIt

cipitation of water

ported aloft only within strong convective currents or through their own flight activity. Vertical and Horizontal Transport of Organisms. Turbulence in the atmosphere tends to create a uniform distribution of properties throughout the air mass. This action, however^ is of far greater magnitude than the mere diffusion of properties between layers; apparently the mixing takes place through the motions of eddies or discrete parcels of air which are pushed from their original surroundings at irregular intervals. Thus, it would be expected that air-borne microorganisms, whose source is at the surface of the earth, would be distributed throughout the entire depth of at least the troposphere,* but that the density of organisms would decrease the greater the distance from the source. Biological work to date shows this to be true. Proctor [21] notes a general decrease in both dust particles and bacteria with elevation and an increase in the bacterial

count in the vicinity of wooded areas, while Rittenberg [26] has presented data which show a general decrease in the mold count over the oceans with increasing distance from shore. It would appear that the horizontal distance over which the individual microorganism may be transported is almost limitless and is largely determined by its ability to survive the atmospheric environment.^ The meteorologist, of course, is interested in the total distribution of microorganisms; the biologist, on the other hand, concerns himself only with what he terms the effective distribution. The effective distribution is a function of the virulence and concentration of organisms and of the conditions bear5. Living spores of several common molds were caught in a spore trap released from the balloon Explorer II at 72,500 ft

and

set to close at 36,000 ft [27].

Living spores of various fungi have been caught from aeroplanes above the Caribbean Sea 600 miles from their nearest possible source [17], while allergens have been identified at least 1500 miles from their probable origins. In spite of the usual low concentrations at the source, marine bacteria 6.

have been collected 80 miles inland from the nearest seacoast [40],

upon their multiplication and spread at the -place and time of deposition. As an example of the sometimes complex meteorological circumstances that must precede the effective

ing

long-distance dissemination of important plant pathogens, Stakman and Christensen [32] cite the spread of stem rust on wheat through the North Central States

during 1942 and 1943. In both years, barberry bushes (the secondary host) in the Virginias became heavily infected about May 15 because of favorable weather circumstances during the preceding period of development. Throughout the first half of June, southeast winds, accompanied by rains (favoring multiplication), carried the rust spores west-northwestward, causing heavy infection through much of Ohio and Indiana and as far as southern Michigan and northeastern Illinois. While the south-to-north air movement was not unusual, the destructive epidemics resulted only when all meteorological factors favorable for rust development operated in conjunction. Supporting evidence on the long-distance dissemination of plant pathogens is given by data collected in Canada which show that urediniospores of leaf and stem rust of wheat are regularly introduced each spring into Manitoba by spores from the United States. These rusts do not overwinter in Canada, but the urediniospores are invariably found in the air in advance of the infection of the wheat crop. Of even greater interest is the fact that the rusts do not survive the hot summers of the south and every fall must be reintroduced by wind-borne spores from the north. The meteorologist cannot help but note how the maintenance of such a biological cycle is favored by the normal seasonal change in the general atmospheric circulation over these areas. Numerous similar examples of the long-distance dissemination of organisms appear in the very extensive literature on aerobiology. A large fraction of the papers contain aerobiological data which should be further analyzed by the meteorologist. Although turbulence tends to create uniformity of properties throughout an air mass, at any given instant this air mass must contain variously large and small masses (eddies) with somewhat different properties from those of the surrounding air. This no doubt accounts for at least part of the extreme variability in bacterial counts within small areas, or over short intervals of time, which has been noted by various investigators. The more intense or prolonged the turbulent action, however, the more nearly will uniformity of properties be approached. At the same time, however, there must be a general decrease in the density of the property relative to the total air mass as the distance between the observation and the source area increases. If this "uniformity of properties" were actually attained in a given region (which would be the case were the process one of pure diffusion), the spatial distribution of microorganisms would approximate a frequency distribution of the Poisson type, and the ratio of the variance {i.e. mean squared deviation) of the counts to the mean of the counts made in the region should approximately equal 1.00. A higher ratio indi-

i

1

AEROBIOLOGY cates the presence of eddy masses which properties derived from their sources.

still

retain the

However, the longer the elapsed time since such an eddy mass left its source, the more completely will its population become equalized with that of diffusion

its

surroundings because of

and small-scale turbulence; hence,

for

any

the ratio referred to above should diminish with distance from the source. The writer has previously analyzed data obtained by class of microorganisms,

Rittenberg [26] on the distribution of molds' over the ocean from shore to a distance of 400 miles westward from the Southern California coast. The mold samples represent collections made on shipboard at oceanographic stations at approximately equal distances along courses normal to the coastline. The region off the coast of California presents unusually stable conditions throughout practically all months, therefore it is not expected that the mixing processes are as effective here as in some other areas. Nevertheless, the data accumulated by Rittenberg show the reasoning in the preceding paragraphs to be valid. His collections give an average mold count per hour of 155.6 for the region from 0-100 miles off the coast and a count of 29.0 for the region from 100-400 miles off the coast. If the mean of the differences in count between individual collecting stations is taken as a measure of the variability, a value of 250.1 molds per hour is found for the coastal region and 30.8 molds for the region beyond the 100-mile zone. These figures are interesting in that they give ratios between the mean differences in count and mean counts of 1.61 for the first region and 1.06 for the second. However, the actual mixing processes are probably best represented if the ratio of the variance to the mean of the counts is taken. In this case, the ratio is 402.0 in the first region and 32.7 in the second. As suggested, if the mixing were accomplished solely by pure diffusion, the ratios would approach 1.00 in both areas. Approximately the same number of counts were obtained in each of the areas under consideration. One may speculate as to the origin of the molds. The prevailing winds in the Southern California area are from the sea, and thus the air masses usually present over the coastal region are essentially marine in character and may have passed over several thousand miles of sea surface without contact with land. Since the mold collections were made by Rittenberg at intervals of varying length and on several cioiises, it may be assumed that a large fraction of the counts were made within truly marine air masses. If the molds are primarily of land origin, they must have originated either over the continental land masses to the east or over the far removed land areas bordering the North Pacific Ocean on the west or north. The fact that Rittenberg notes a decrease in the mold counts from shore seaward appears to rule out the latter possibility which indicates that these organisms actually originated from 7. Rittenberg assumes that all the molds are of land origin regardless of whether they develop on sea-water media or tap-

water media, although it is admitted that at least a portion of the molds collected may have had a temporary sojourn in the sea.

1109

the land surface of the United States but were transported westward across the prevailing wind stream through lateral mixing. Whether the effect is the result of a more or less continuous mixing process or is brought about by sporadic incursions of continental air masses over the ocean is a matter for further speculation.

Considerations such as these suggest the use of baccounts in the identification of air masses and in the study of large-scale mixing processes in the atmosphere. The identification of the origins of species of organisms found in the atmosphere should give information concerning the origin of the air masses, while the study of the ratios (at the surface and aloft) between organisms representing two or more source areas should give additional information concerning the nature and effectiveness of lateral and vertical mixing. Few of the available aerobiological data, however, are complete enough to allow this type of analysis. Many observers have reported great irregularities in concentrations of organisms collected at different levels in the atmosphere, often finding heavier concentrations at higher altitudes than at lower levels. In some cases the investigators have reported encountering clouds of spores or bacteria several thousand feet above the surface of the earth, seemingly borne along by the wind as more or less discrete, sharply bounded units. However, it should be pointed out that such collections have been obtained through the use of aircraft, and it is quite probable that in many cases the variations in samples merely represent the passage of the aircraft from and into convective (rising) columns of air which would be expected to have greater populations of organisms than the surrounding (and perhaps descending) portions of the atmosphere. Wellington [34] has suggested the use of the helicopter for the purpose of "selective sampling" a technique which could be used to obtain more meaningful data on the vertical distribution of organisms in the atmosphei'e. Several investigators have noted that increased counts of microorganisms are obtained in airplane collections upon entering clouds and have ascribed the condition to the fact that the cloud is a more favorable terial

—

envirormient for the organisms than is clear air, although Durham [7] ascribes the increase to the loss of electrostatic charge and the consequent dislodging of particles which adhere to the plane. It does not seem to have occurred to the investigators that the vertical cloud boundary probably also represents the vertical boundary of a rising air column which should contain a heavier concentration of organisms than the sur-

rounding clear (nonconvective) area. The discussion so far is intended to indicate the importance of the horizontal and vertical mixing in distributing organisms throughout the atmosphere. The

may be transported depends upon the degree of stability (or instability) near the surface and upon the height of the turbulent or

height to which the organisms

convective layer of air. The presence of a stable layer at the surface will prevent or retard the introduction of surface organisms into the upper atmosphere but will,

BIOLOGICAL AND CHEMICAL METEOROLOGY

1110

same time, maintain higher concentrations of organisms in the surface layers; the presence of a discontinuity surface in the upper air will limit vertical at the

transport in either direction resulting in the concentration of organisms above or below such a surface. There are several recorded instances of such biologic stratification. For example, Durham [8] has noted that abrupt spore ceilings are often marked by a cloud layer or by a visible haze line. He noted one instance in which a detached cloud of fungus spores, almost 100 per cent AUernaria, was encountered about 1000 feet above a visible 4000-ft haze line that marked the ceiling for ragweed and the ground cloud of other spores. An analysis of the meteorological conditions that existed near New Orleans on September 12, 1940 (the date and

E is the calculated number or coacentration of organisms, a is the position on the graph and b and c are factors determining the slope of the curve as influenced by the logarithm or reciprocal of the distance X from the source. He presents the completed formulas for 251 separate plots of data. For example he finds, from one set of data, that the number of codling moths caught at a distance of x feet from an infested orchard can be given approximately by the expression: where

E =

5.2904 (log x)

Nearly

all

investigators

who have

studied the vertical

distribution of organisms in the atmosphere have noted

the importance populations at over a region is a maximum in

thermal convection in increasing the higher altitudes. Thermal convection

of

a diurnal phenomenon and is usually at the early afternoon; as a result, the maximum altitude populated by organisms should be highest at this time of day. Nearly all the data on insect populations verify this conclusion. In general, the horizontal transport of organisms will be determined by the general stream flow in the at-

mosphere, but lateral mixing will transport the organisms laterally away from the trajectories indicated in the general wind observations. In temperate latitudes, the greater transport will be from west to east and, considering the greater carrying power of polar air masses, from north to south. As an example of the latter, Durham [8] calls attention to a remarkable mold-spore shower that occurred October 6-8, 1937, over the eastern half of the United States. During this period, extremely high slide counts of AUernaria and Hormodendrum were recorded at all collection points between southern Minnesota and Louisiana with somewhat increased counts in the tier of states between North Dakota and Texas. He presents a map of the area which shows, for each of the three days, the line along which the concentration of the organisms was a maximum. The writer has referred to the synoptic charts for those dates and finds it interesting to discover that Durham's lines of maximum spore concentration on each date coincide almost exactlj' with the daily positions of an extensive and rapidly-moving dry cold front.

A number of investigators have attempted to describe mathematically the vertical and horizontal distributions of organisms as functions of space or time but none appear to have been too successful. Wolfenbarger [38] has prepared regression formulas for the plots of a very large number of series of data on the spatial variations in organism counts all are based on the form ;

E = a+ E = a+

20114.0849 (l/.x)- 18.0628.

Since the formulas nowhere take into account meteorological conditions or other factors governing distribution, the writer fails to appreciate the great amount of effort that must have gone into their preparation.

place of collection), might prove interesting, particularly if the source of the "cloud" of AUernaria could be identified.

+

CONCLUDING REMARKS No

attempt has been made in these pages to cover in

detail the list of specific possibilities for research in the field,

either

from the standpoint

the meteorologist.

The

of the biologist or of

principal gaps in the research

programs conducted by aerobiologists have been pointed out, and suggestions for general lines of research have been offered in the several sections. The writer hopes that the discussion will serve as an added stimulus toward future investigations in the field by both groups and that it will, in some measure, give guidance to the biologist. It is the problem of the biologist to develop certain and rapid methods for identifying the organisms with respect to type and place of origin; it will be the problem of the meteorologist to apply the results of the biological investigations to a study of the atmosphere.

The author

is

indebted to Drs. B. E. Proctor, E. C.

Stakman, J. J. Christensen, R. P. Wodehouse, G. W. Keitt, and P. A. Glick for their assistance in locating recent materials on the subject of aerobiology and to Mrs. Marguerite Gleeck of the Air Weather Service, for her careful reading of the manuscript.

The

writer

acknowledge his extensive use of the volume Aerobiology, published by the American Asalso wishes to

sociation for the

Advancement

of Science, as a source

for biological information.

REFERENCES No attempt is made here to cover the list of important papers concerned with aerobiologieal subjects. Care has been taken to include the more recent titles, those which, themselves, contain extensive bibliographies, and all titles which have been specifically referred to in the text. A valuable bibliograph}', which was published after this list of references was prepared, is that by JMiss H. P. Kramer, "Cumulative Annotated Bibliography on Aerobiolog.y and Its Applications to Meteorology." Meteor. Abstr. 1.

Beeland, M.

&

Bibliogr., 1: 119-135 (1950).

"L'exploration biologique de I'atmosphere en avion, et I'emploi possible de cette methode en m^t(5orologie." LaMHeor., Ser. 3, No. 1, pp. 28-35 (1936). L.,

2.

Chester, K. S., "Airplane Spore Traps for Studying the Annual Migration of Wheat Rust." Proc. Okla. Acad.

3.

Chbistensen,

b(\n x), or

Sci., 19: 101-104 (1939).

6(ln x)

+

c{l/x),

J.

J.,

"Long Distance Dissemination

of

AEROBIOLOGY Pathogens" in Aerobiology (publ. by Amer. Assoc. Adv. No. 17, pp. 78-87, 1942. Committee on Apparatus in Aerobiology, Nat. Res. CoMM., "Techniques for Appraising Air-Borne Populations of JNIicroorganisms, Pollen and Insects." Phijlo-

21.

Sci.),

4.

22.

6.

7.

S.

DallaValle,

10.

23.

M., and Hollabnder, A., "The Effectiveness of Certain Types of Commercial Air Filters against Bacteria." Publ.Hlth. Rep., Wash., 54: 695-699 (1939). Darling, C. A., andSiPLB,P. A., "Bacteria of Antarctica." /. Bad., 42: 83-98 (1941). Dueham, O. C, "Methods in Aerobiology." /. Aviai. Med., 12: 153-161 (1941). "Air-Borne Fungus Spores as Allergens." Aerobiology (publ. by Amer. Assoc. Adv. Sci.), No. 17, pp. 32-47, J.

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Rentschlee, H. C, "Bactericidal Ultraviolet Radiation and Its Uses." Trans. Ilium. Engng. Soc, N. Y 35: Rittenberg, S. C, "Investigations on the Microbiology of Marine Air." J. mar. Res., 2: 208-217 (1940). Rogers, L. A., and Meier, F.C., "The Collection of Microorganisms above 36,000 Feet." Nat. Geogr. Soc, Contrib. Tech. Papers, Stratosphere Ser., No. 2, pp. 146-151 (1936). ScHRiEBER, E. A., "1946 Aerobiological Survey for Ann Arbor, Michigan." Univ. Hosp. Bull. Ann Arbor, 13:

Sharp, D. G., "The Effects of Ultraviolet Light on Bacteria Suspended in Air." /. Bad., 39: 535-547 (1940). Smith, G. E., Watson, R. B., and Crow:ell, R. L., "Observations on the Flight Range of Anopheles quadrimaculatus Say." Amer. J. Hyg., 32: 102-113 (1941). Stakman, E. C, "The Field of Extramural Aerobiology." Aerobiology (publ. by Amer. Assoc. Adv. Sci.), No. 17,

and Christensen, C. M., "Aerobiology

in Relation

A., "A Sampling Apparatus for Aeroplankton." Proc. Acad. Sci. Amst., 39: 981-990 (1936). Wellington, W. G., "Conditions Governing the Distribution of Insects in the Free Atmosphere." Parts I-III. Canad. But., 77: 7-15; 21-28; 44-49 (1945). Wells, W. F., "On Air-Borne Infection. II Droplets and Droplet Nuclei." Amer. J. Hyg., 20: 611-618 (1934). Whisler, B. a., "The Efficacy of Ultra-Violet Light Sources in Killing Bacteria Suspended in Air." Iowa

Van Ovbreem, M.

—

38.

2,

pp. 152-153 (1936).

M., Kelly, C. D., and Polunin, N., "Arctic Aerobiology. II Preliminary Report on Fungi and Bacteria Isolated from the Air in 1947." Nature, 162:

39.

379-381 (1948).

T.,

"The Microbiology

bot. CI., 70:

of the

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Bull.

1-14 (1943).

Wolpenbarger, D.

O., "Dispersion of Small Organisms." Amer. Midi. Nat., 35: 1-152 (1946). ZoBell, C. a., "Microbiological Activities at Low Temperatures with Particular Reference to Marine Bac-

teria." Quart. Rev. Biol., 9: 460-466 (1934).

and Alaskan Insects. Environmental QMG, Lawrence, Mass., Rep. No. 156,

L., Weather

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Wolf, F. Torrey

S.

Pratt, R.

17,

St. Coll. J. Sci., 14: 215-231 (1940).

37.

—

20.

No.

to Plant Disease." Bot. Rev., 12: 205-253 (1946).

"Effects of Conditions in the Stratosphere on Spores of Fungi." Nat. Geogr. Soc., Contrib. Tech. Papers, Strato-

Pady,

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pp. 1-7, 1942.

26: 102 (1936). 18.

Amer. Assoc. Adv.

35-37 (1947).

32.

Keitt, G. W., "Local Aerial Dissemination of Plant Pathogens." Aerobiology (publ. by Amer. Assoc. Adv. Sci.), No. 17, pp. 69-77, 1942. McCubbin, W. a., "Relation of Spore Dimensions to Their Rate of Fall." Phytopathology, 34: 230-234 (1944). Meier, F. C, "Collecting Microorganisms from Winds above the Caribbean Sea." (Abstract) Phytopathology,

—

Air Investigations." /. Bad., 36: 175-185 (1938). "Microorganisms in the Upper Air." Aerobiology

.,

Jacobs, W. C, "Preliminary Report on a Study of Atmospheric Chlorides." Mon. Wea. Rev. Wash., 65: 147Discussion of Physical Factors Governing the Distribution of Microorganisms in the Atmosphere." /. mar. Res., 2: 218-224 (1940).

Air. II." J. Bad.,

960-975 (1940).

Gregory, P. H., "The Dispersion

151 (1937). 14.

25.

29

pathology, 28: 10 (1938). 13.

Upper

and Parker, B. W., "Microbiology of the Upper Air. An Improved Apparatus and Technique for Upper

(publ. bjf

pp.

of Air-Borne Spores." Trans. Brit, mycol. Soc., 28: 26-72 (1945). Humphrey, H. B., "Relation of Upper-Air-Mass Movement to Incidence of Stem Rust." (Abstract) Phyto-

of the

Air. I."

1942.

27.

88-98, 1942. 11.

24.

Click, P. A., "The Distribution of Insects, Spiders, and Mites in the Air." U. S. Dept. Agric. Tech. Bull. No.

biology (publ.

"The Microbiology

Ill

1942. 9.

Proctor, B. E., "The Microbiology of the Upper Proc. Amer. Acad. Arts Sci., 69: 315-340 (1934). 30:363-375(1935).

patholoijy, 31: 201-225 (1941). 5.

nil

25 pp., mimeogr., August, 1949.

40.

and Mathews, H. M., "A Qualitative Study

of the

Bacterial Flora of Sea and Land Breezes." Proc. nat. Acad. Sci., Wash., 22: 567-572 (1936).

,

PHYSICAL ASPECTS OF By

KONRAD

HUMAN BIOCLIMATOLOGY* J.

K.

BUETTNER

Randolph Field, Texas According to the classical definition by Humboldt the term climate designates all changes in the atmosphere that noticeably affect human physiology, With this definition, upon which the present article is based, the meteorological elements must be evaluated in a manner different from that used, for instance, in connection with an airway meteorological service or with plant geography. Thermal elements of the climate

become the most

decisive, specific radiations

come

next,

whereas pressure, wind direction, and similar basic weather data play only an indirect role.

HEAT BALANCE Heat Production. The body gains the energy necessary for maintaining its internal temperature by combustion of converted food. This energy is given off by conduction, convection, radiation, and evaporation from the skin, as well as by advection to, and evaporation from, the respiratory organs. A maximum of 20 per cent of the heat produced (less basal metabohsm) may be used for external work. The excretion of stool, urine, etc., merely presents a decrease in the body's heat capacity. Unfortunately, metabolism, which is essential for the life of every cell, takes place in both hot and cold environments; however, it cannot be regulated beyond

An

:

heart.

Rapid variations of the thermal environment produce temperature fluctuations first in the skin, then in larger portions of the body, until a new equilibrium is established. This involves a stock-piling of heat, using the body's heat capacity. The values of specific heat are: .

o 77 Fat.^^. ............ .... ...... 0.55

Muscle

pressure of oxygen in the lungs. This partial pressure determined almost exclusively by the atmospheric pressure because the fraction of oxygen in the air is very nearly constant. Pressure variations caused by

is

weather, however, are too small to be significant in this relation. Consequently, only the well-known variation of pressure with altitude needs to be considered. The combustion end products, CO, and H,0, are removed by breathing and metabolism. Excessive CO, content of the inspired air is harmful; it occurs only near volcanoes and in artificial climates (crowded rooms, submarines, etc.), but in such cases the coexistent sultriness is often more important than the presence of fiQ

The base value

of

heat production (at

fortable" climate)

is

about 40 Cal m"^

fever, or cold increase this value

by more than one order

of

up

rest,

"com-

hi--^ Exercise,

to a rate larger

.„

,

,

room

O

l

-' rd

k

,

"

,

,

^

,

Pl-i

"

'

0.91 ,

,

-2

•_,

,

j

without Roughly, the entire body can lose j Cal in discomfort if its heat metabolism amounts to j Cal the true body "^^ }^^- ^"^^ corresponding drop "^ temperature is composed of 65 per cent core temper-

m

f

^^^ ^^ *T^ J^'^"*"^) This ratio may vary

[24].

^

;

P^^' ?,^* ^^"^P^'^t ^^t^. nevertheless, the mean body

temperature is usually not equal to the rectal tempera ure. t,, ,1 Heat Loss by Convection In the simplest case, the , temperature of a room may be used as a measure of its ''l™^*^- However, thermal environments are rarely as humidity «'°^p!^ ^^ "^?'^*^°^' "" 1 simultaneously. The total rate of heat loss can be f\ determined only synthetically from these weather elements. ^he known laws of heat transfer by convection have

,^ '

^^''"^^f S^/ }^^ ^9]. The ^"^^

•,,

.

T^ll T.

^'^^^ .^PP^'^^ *° *??

T?

human body

[13

16,

surrounded by a laminar boundary millimeters thick (m the case of calm

skm

'a^f /^^T^l

magnitude.

starting with "comfortable" conditions, the

temperature decreases by IOC, the heat production of the body increases by about one half. This heat production would have to double if the skin temperature were to remain constant. Actually, however, the latter decreases by about 7C because of a decrease in the advection of warm blood to the skin, particularly to that *

the other hand, it may rise to 120 Cal m~^ hr~i (deg C)"^ for portions of the sliin heated separately and may drop almost to zero for cold extremities [7, 19, 84]. This complex of phenomena corresponds to variations in blood circulation which, in both extremes, constitute a severe load on the heart since the temperature gradient between heart and skin is small in the case of warm surroundings, the heart must pump large quantities of blood to the periphery in order to rid the body of the heat it produces. In the case of cold surroundings, on the other hand, the necessary heat must be produced by arduous muscular activity which, again, strains the

On

certain limits.

adequate oxygen supply to the blood through

diffusion in the lungs' surface requires a certain partial

If,

whose temperature then drops almost

of the extremities

to that of the air. The thermal conductance (taken between the interior of the body and the average skin) decreases from about 50 to 10 Cal m~^ hr~i (deg C)"^.

[50],

is

^^""^

""{^^'^

^^^\ *'^'?f.^^' f^)' ^\ steady transition takes place by pure conduction. A^^f to turbulent austausch takes place towards the outside on wind ^he dependence of surface conductance velocity . diameter d, and density of the air p is expressed by the followmg formula:

Translated from the original German.

P^'^^^o'^^

'

K

j

i

fc

1112

:

PHYSICAL BIOCLIMATOLOGY where vpd/ix,

fc is the thermal conductivity of the air; U = Reynolds number; n is the viscosity of the air,

and d is the diameter of the cylinder or sphere, or the trunk width of the human body. The exponent n depends on the structure of the air flow. For the range which is of interest to us (10' < U < 10^) the following values have been found: c Cylinder, normal to axis.

«

0.35 Sphere 0.70 Human body, supine, nude. 1.0

Under normal

.

References

0.56 0.52

[13, 16, 19]

0.5-1

[13, 16, 19]

[72]

I

\{la) J

conditions, for the supine adult,

we

find approximately [13]: /la

=

6.3

VJ; Cal m~' hr"' (deg C)"',

(2)

where

v is expressed in kilometers per hour and is greater than 2 km hr~\ In these measurements [13], the exposed surface is taken as fifty per cent of the

More

recent measurements made and standing persons [63] showed values of 5.b-\/v and S.O-v/w, respectively. The scatter in the factors (6.3, 5.5, and 3.9) is caused by differences in the methods used for determining the area from which heat is lost.

geometrical surface.

for sitting persons [84]

Siple [27, 79] used the heat of fusion of water to

"wind chill" which, actually, is the cooling power at sub-zero temperatures. In his antarctic experiments he found the formula. determine the

h

=

lQ. and 6. The beam width is usually defined as the angle subtended at the antenna between points across the beam where the power density is onehalf that along the axis. When using this term it must be understood that an appreciable amount of power is actually present beyond this angle. However, the power beyond the half-power point decreases rapidly with increasing angle, so for most purposes this definition is probably sufficient. If the beam is circular in cross section, it may be depicted as a cone with the apex at the radar antenna. Cross-section figures of radar beams may be in a variety of shapes, depending upon the use for which the radar is designed [49, pp. 22-28]. Most common shapes are circular and elliptical, especially for radars useful for storm detection purposes. Elliptical sections are employed when high directional accuracy or resolution is desii'ed in one dimension and good coverage in the other. For example, a radar used for height determination would require excellent elevation angle dis;

them

into exact focus. It

beam would have

is

not

to be precisely

pointed at a target in order for the radar to detect it, if the target were small in size. For storm detection this would be no particular drawback because of the extent of most storm cells. However, the difficulty and expense of construction and control of large-size parabolas rules out beam widths much less than about 1° for radars with wave length of operation of about 3 cm. For a 10-cm wave length radar this angle is at least doubled. The subjects of beam width and pulse length (which follows) are worthy of careful study by radar meteorologists, for these two factors define the volume of space which is analyzed and strongly influence interpretation of the scope presentations of precipitation. There' are distortions resulting from the finite beam width in the nature of azimuth and elevation angle errors, and from the pulse length in the nature of a range error [65, pp. 20-22]. Pulse Length, h. As beam width affects azimuthal and elevation angle resolution, so pulse length affects range resolution. Pulse length may be defined either in terms of time or length; a pulse one microsecond in duration

m

long. Two has a wave-train of energy about 300 targets in the beam of the radar will be resolved if and only if their range separation exceeds one-half the pulse length [65, pp. 17-20]. Extension of the analysis to storm detection results in the corollary that energy from the particles in only one-half the volume illuminated by the pulse can reach the receiver at the same

—

—

time.

The volume illuminated by the pulse is determined by the pulse length and the linear distance across the beam. The greater the number of scattering particles lying within this volume the stronger will be the echo. By increasing this volume the signal power of the echo may be strengthened, provided this increase in volume does not result in a decrease in the transmitted power density per unit area normal to the beam. However, loss of resolution results both from widening the beam and from lengthening the pulse. Therefore, a designer of radar equipment for storm-detection purposes must balance these factors in order to achieve the best possible

presentation of the storm. Wave Length, X. The evaluation of a radar as a storm detector depends to a major extent upon the operating wave length. Wave length and frequency are used interchangeably in radar discussion, one being related to the other

by the simple formula f

where/

= = =

=

-

(4)

frequency (cycles sec~Oi

(cm sec~0, electromagnetic wave length (cm). Roughly speaking, a wave length of 10 cm correc

X

velocity of light

RADIOMETEOROLOGY

1268

spends to a frequency of 3000 mc sec~^ During the war, radar wave length of operation was highly confidential information, since radar countermeasure development

by the enemy was considerably facilitated if this was to him. Accordingly, wave lengths on which radars operated were designated by letters: S-band for 10 cm; X-band for 3 cm; and K-band for about 1 cm. Thus, a radar with an operating wave length of 10 cm was called an "S-band" radar. These designations have persisted since the war, and are utilized in this article

known

to familiarize the reader with terms widely encountered in the literature.

The radar energy back-scattered toward the receiver by a raindrop is inversely proportional to the fourth power of the wave length if Rayleigh scattering [48] applies. However, absorption and attenuation of the scattered energy may become great enough at very short wave lengths to restrict maximum range seriously, and a compromise value of wave length must be used. Speaking in general terms, we may say that for use in areas of very heavy rainfall a wave length of about 10 cm is best, while in regions where the average drop size is somewhat smaller, a wave length of about 3 cm is desirable [15,16]. From an analysis of this problem it seems that a storm-detection radar should be designed for the climate in which it is to be used [68]. Many authorities agree that the best "all-round" frequency for storm-detection radar equipment would probably be about 6000-7000 mc sec~\ corresponding to a wave length near 5.5 cm. Reflectivity Per Unit Volume of the Storm Region, ij. This is a measure of the energy back-scattered by particles in the storm. It is a function of the number of particles per unit volume, their size distribution, the frequency of the energy scattered [65, pp. 30-34], the composition of the particles, and their shape and aspect. The process of electromagnetic scattering by hydrometeors is similar to that of the scattering of visible radiation by large molecules, by which the color of the sky is explained. Fundamental laws of scattering developed by Rayleigh [48] and Mie [45] were apphed by

Ryde

[50]

tering

and

to the special case of electromagnetic scatdiffraction by raindrops. It was found that a

is small relative to the wave length of radiation falling upon it scatters the energy proportionally to the sixth power of its diameter [49, pp. 33-66]. This indicates that if the size of a drop is

spherical particle which

doubled, its scattering efficiency is increased by a factor of 64. Therefore it is evident that size is of much greater importance than number in the determination of reflectivity. Reflectivity per unit volume turns out to be a function of NR^ where is the number of drops and R is their radius. However, when the drops become large compared to the wave length (222 > X/10), "Rayleigh scattering" no longer applies and the exact dependence of the scattering cross section upon X is

N

a complex function. The composition of the particle affects properties,

and therefore

its efficiency

its dielectric

as a scatterer.

For example, water has a greater dielectric constant than ice, hence for two spheres of equal diameter, one of

water and the other of ice, the water sphere will scatter about five times as much electromagnetic radiation of 3- or 10-cm wave length. Shape and aspect are important for nonspherical particles, therefore the probof evaluating the power of the echo from snow is

lem

difficult.

If

the rainfall intensity

is

known and one assumes a Laws and

drop-size distribution in accordance with

Parsons' data [38], it is possible to compute the reflectivity per unit volume [6]. It is necessary, however, to assume that this reflectivity remains constant throughout the area covered by the radar beam (or fills a known fraction of it). The fact that reflectivity per unit volume is not a unique function of drop-size distribution greatly complicates the problem of determination of rainfall intensity by radar. At present, measurement of a given level of echo-signal power indicates only that the rainfall at that point lies within certain limits of intensity. This conclusion becomes evident when one realizes that a few large drops can give an echo signal equal to that from many small drops. An additional factor which should be mentioned in connection with reflectivity is the variability of the back-scattered energy. This energy fluctuates rapidly with time because of interference between the electromagnetic waves scattered by a large number of moving drops. The received power Pr is the average power of a number of individual precipitation echo signals [49, pp. 81-85]. Attenuation Factor, k. During passage through the atmosphere between anteima and storm the electromagnetic energy radiated by the transmitting antenna and scattered by the precipitation particles suffers attenuation due to several causes: (1) water-vapor and oxygen absorption, (2) molecular scattering by atmospheric gases, and (3) hydrometeor scattering and absorption

,

I

,1

'

j

I

[51, 63, 65].

The problem

of electromagnetic atmospheric attenu-

ation, being a question not confined to the field of radar,

has received the attention of a number of investigators [18]. Tables have been constructed giving attenuation in the free atmosphere and in rain in terms of decibels, as a function of path and wave length [49, pp. 58-62]. Precipitation attenuation is not a serious factor until drop sizes become appreciable in comparison to the wave length (about }{o or larger). Because large drops are frequently present in thunderstorms and tropical rain, X-band (3-cm) radar may sometimes not be the best for observation of storms of these types [13]. Rain attenuation and atmospheric absorption are seldom observed with S-band (10-cm) radars. DetermiFraction of the Beam Filled by the Storm, nation of the magnitude of this factor under certain conditions is difficult or impossible, but its significance cannot be minimized. The echo signal from a weak storm which fills the beam may equal that from a strong storm which only partially fills it, but at present it is not possible to tell from signal characteristics alone what the true condition is. The distances between halfpower points at various ranges for beams of different angular widths are listed in Table I; it will be seen that \j/.

I I

RADAR STORM OBSERVATION these distances are considerable even with respect to the heights of thunderstorms. In the determination of rainfall intensity by radar, it

must be assumed that the Table

I.

Beam Width Between Half-Power Points (in ft)

Range

reflectivity per unit vol-

(miles)

1269

RADIOMETEOROLOGY

1270

The R Scope. The R scope presents the same information as the A scope, but greatly expands the horizontal coordinate so that instead of some 100 miles being represented on the scope, only 5 or 10 miles of

any

Another version of the PPI scope

be controlled

may

A scope is displayed. Figure 3 appearance of this presentation.

PRECIPITATION

LOCATION OF

RADAR IN CENTER OF GROUND CLUTTER

"NOISE"

g- (EAST)

(WEST)

R

dis-

(NORTH)

ECHO

ELECTRON

—

be

placed from the center in any direction to distances of

desired portion of the

illustrates the

may

so that the indicated position of the radar

SCR

615B radar (modified), Fig. 3. Diagram of scope of illustrating difference in appearance of aircraft and precipitation echo signals. RANGE MARKS

The Plan Position Indicator

or

PPI

Scope.

The PPI

popularly kno^vn, is one of the most favored scopes for storm detection purposes because of its graphic and easily interpreted display. The presentation is circular and therefore employs the entire area of the cathode ray tube face in contrast to the rather scopes. When small portion utilized by the A and the radar beam is directed horizontally and rotated in azimuth, the PPI display takes the form of a circular map with the position of the radar represented at the center of the scope. Targets are displayed in position relative to the radar as if viewed from an infinite height directly above the radar. Range from the radar to any target may be determined from the relative distance from its echo signal to the center of the scope. To aid in range determination, an electronic circuit injects marks at proper intervals which correspond to range increments of 1, 10, or 20 miles or any other number and unit of length desired. As the sweep rotates, these marks draw concentric circles about the center of the scope. The appearance of the scope is illustrated in Fig. 4. The electron beam is so controlled that if the radar is not detecting a target at a given position, the face of the scope is not brightened at the corresponding point. When a target is detected, the electron beam is intensified so that it brightens the face of the scope at the proper position in azimuth and range from the radar. This process of target indication is called "intensity modulation" of the electron beam, as contrasted to the beam deflection method employed by A and R scopes, the beams of which are always on and are of constant intensity. If the antenna is directed horizontally, the indicated range will correspond closely to the actual horizontal distance between target and radar, and its geographical position may be determined by reference to a map of the area. If the map is drawn on transparent material and is of proper scale, it may be laid directly over the face of the scope and geographical positions of targets can be determined directly. scope, as

it

10 OR 20 MILE INTERVALS

AT

(SOUTH)

is

Fig.

4.

— Diagram

of features of a

PPI

scope.

Some

detail

has been omitted to clarify the drawing. In all PPI-scope photographs which follow, north is at the top of the scope, east to the right, etc. Elevation angle in all cases is zero degrees.

R

about two diameters of the scope face. This scope is called an "off-center PPI" and enables close examination of selected areas by virtue of the great sweep expansion which can be employed. The Range-Height Indicator or RHI Scope. This scope is

particularly valuable for storm-detection purposes, is found only on radars designed to scan a vertical

but

The electron beam is intensity-modulated like that of the PPI scope. The radar antenna scans cyclically from the horizon upwards to any angle, depending upon control settings or the design of the radar. In order for the display on the scope to be intelligible, the azimuth of the beam must remain nearly constant during the scanning process. Targets in the vertical cross section along a given azimuth are displayed on the face of the scope in coordinates of range versus altitude or elevation angle. Because practically all targets, whether plane.

storms or aircraft, will be found at altitudes less than 10 miles, and since the horizontal range of the radar is nearly always more than 50 miles, it is usually desirable to expand the vertical scale in order to utilize the maximum available area of the scope face. This results in more precise altitude determination due to the vertical

For this reason, RHI scopes are usually designed to have an altitude distortion of about 10:1. The appearance of the scope of a typical height-finding radar (AN/TPS-lOA) is shown in Fig. 5. It will be noted that the range and height of a target may be determined directly from this scope by means of properly calibrated scales. In order to fix the target in space, its bearing or azimuth must also be known. This information cannot be obtained from the RHI display alone; consequently it must be read from a dial scale increase.

J

RADAR STORM OBSERVATION or other indicator operating in synchronism with the

antenna azimuth control. This R-scope azimuth readings.

is

also true for

A- and

1271

during the past few years and need little explanation, especially when accompanied by a synoptic map showing position and orientation of the surface front in the

PRECIPITATION ECHOES

30,000 -

RANGE MARKS AT 10

MILE

NTERVALS

/ 60

5,000

50

40

LOCATION 0^

RADAR

30

RANGE (MILES)

—

Fig. 5. Diagram illustrating features of RHI scope of AJ^/TPS-lOA radar (X-band) Photographic images (and this diagram) are reversed from normal presentation because of the design of camera used to obtain RHI-scope pictures which follow. Vertical distortion of scope about 10:1. Diagram illustrates appearance of mature thunderstorm at range of 40 .

to 55 miles.

.

Appearance of Scopes During Storms.^ Precipitation

may

be divided into various types, using basic causes

as the

means

of classification, as follows:

A. Frontal precipitation. 1.

Cold front.

2.

Warm

front.

Occluded front. B. Orographic precipitation. C. Hurricanes or typhoons. 3.

D.

Instability showers.

Air mass. Thunderstorms. This breakdown is convenient for the purposes of this discussion because the horizontal and vertical distribution of hydrometeors is indicative of the motivating cause. This distribution in space can easily be observed with radar. A. Frontal Preci-pitation. 1. Cold front. Perhaps the most striking and easily understood of all radarscope displays is that of echo signals from the squalls associated with an active cold front. Photographs of PPI scopes similar to Fig. 6 have been widely published 1.

2.

2. It should be noted that a single radar system cannot incorporate all the characteristics necessary for all types of radar weather observations. For example, the cloud-detection radar cannot be used for rain and snow observation because of severe attenuation of its energy when the size of the hydrometeors becomes appreciable with respect to its wave length of operation. In fact, this radar cannot even be used for cloud

detection

—

Fig. 6. Photograph of PPI scope showing echo signals from showers accompanying cold front approaching Boston from the northwest. Isolated warm sector precipitation at azimuth 0°, range 79 miles, and at azimuth 310°, range 20-40 miles. (1730 EST, 3/27/48, S-band radar, range 120 miles, 20-mile markers.) {M.I.T Weather Radar Research.)

when the

precipitation becomes moderate or heavy.

conventional manner. Over fairly smooth terrain a wellsited radar with sufficient power will detect the precipitation

accompanying an active cold front at

dis-

tances in excess of 200 miles, depending upon the heights of the squalls. Close examination of the precipitation pattern shown in Fig. 6 will reveal the distortion caused by finite beam width. This is a photograph of the PPI scope of an SCR 615B-type radar operating on a wave length of 10 cm and a beam width of 3° between half-power points. Notice that the individual cells have circumferential elongation [43]. This is not due to the meteorological situation, but is caused by the comparatively wide beam of this radar. Actually, the cells are usually almost as wide as they are long. This fact can be verified by observation with a radar which has a much

narrower beam. An important restriction on radar storm detection is the limited extent of the front which will pass within the range of this radar. As stated before, during favor-

maximum range of detection may be more than 200 miles, but large portions of the average-sized cyclone will still escape detection by any single radar. This limitation is not due to the lack of power of radar systems, but rather to the curvature of the earth [49, pp. 53-55]. Under standard atmospheric conditions, the height h (in feet) of a horizontally directed beam above the surface of the earth at a range able conditions the

R

(in miles) is

approximately

h

=

W,

(6)

RADIOMETEOROLOGY

1272

from which it may be seen that at a range of 200 miles the lowest portion of a horizontally directed beam of a radar located at sea level is about 20,000 ft above sea level

During more unstable warm-frontal condiwill show stronger echoes from individual storm cells. Absence of uniform or systematic

in Fig. 7.

tions the

PPI scope

[2].

One

of the finest practical applications of radar storm detection is made when radar-equipped aircraft use it to avoid violent convective activity while flying through

an active cold front is far from being a

As mass

[11, 46].

Fig. 6 shows, the front

solid

of storms of

altitudes. This application

is

moderate

especially useful at night restricted by clouds. re-

A

or when the pilot's vision is cent development has been shown to have value in selection of the least turbulent portions of storms when it is impossible to avoid them completely. This will be dis^^ussed in the section concerning echo-signal analysis.

Radar observations of the approach show the following sequence of events

of a cold front

[67]: Scattered storm-echo signals are first detected at maximum ranges (100-300 miles) depending upon the activity of the front. These echoes are caused by hydrometeors in the upper portions of the tallest cumulonimbus along the front, and generally lie in an arc which may be closely identified with the position of the front as reported by surface observation stations. As the front approaches, the radar detects precipitation at successively lower levels and the original cells appear to increase in size

and

When

the nearest portion of the front is about 50 miles away, a large part of it appears to be a solid line of precipitation if the antenna elevation angle is kept at or near zero degrees. The inexperienced observer will sometimes conclude that the front is actually intensity.

intensifying, whereas the radar

simply detecting rain at lower levels which is almost invariably more widespread. This trend continues until the front passes over the radar, at which time echoes from the more distant storms along the front may disappear from the scope entirely because of rain attenuation. At this time the precipitation may appear to be almost evenly distributed around the radar for a distance of many miles. After frontal passage, the above sequence of events is

reversed until the front passes beyond the maximum range of detection or dissipates. While the line of storms taken as a whole appears to approach the radar, close examination reveals that the individual cells have a component of motion in the direction of the warm air movement ahead of and over the front. Thus, if the front appears to approach from the northwest and the warm air movement is from the southwest, the cells will show a movement just about due eastward, depending on the relative velocities of the cold and warm air masses. 2. Warm front. Interpretation of radar displays resulting from warm-front precipitation is considerably more difficult than the interpretation of echoes from cold -front precipitation. This is a result of the larger area covered by the precipitation and the possible variation of conditions. The precipitation causing the echo signals exhibits varying degrees of convective activity depending upon stability and convective stability conditions in the air masses involved. When conditions are stable in both air masses, the return appears as shown is

—

Fig. 7. Stable warm-frontal precipitation echo signals on a PPI scope. Uniform snow echo signals are present at all azimuths. (1010 EST, 2/20/47, range 20 miles, 5-miIe markers.) {M.I.T. Weather Radar Research.)

frequently observed. However, some sort of is nearly always observed, and determination of the velocity and direction of cellular movement is usually straightforward. The movement of prepatterns

is

cellular structure

cipitation cells seems to be controlled

by

several factors,

among which are the circulation within the system and the movement of the entire system itself. Attempts have been made to relate precipitation-cell movements to the winds aloft, but only rather general correlations have been found, and sometimes even these fail completely [29]. It is entirely probable that there is no simple relationship between the winds aloft and cell movement which can be applied to all storms. In order for a given precipitation cell to maintain itself it must have a continuous supply of moisture. This implies that air moves through the system at some speed different from that of the system itself. At times it has been noted that the precipitation nearest to the radar is rain, while that detected at greater distances must be in the form of snow because of the increase in height of the beam with i-ange (see

equation

(6)).

As

yet,

no technique has been developed

for positive determination of the nature of the precipi-

tation, except in special cases, for example,

when

the

known. The appearance of rain and snow echo signals on the PPI scope may be identical when both are present. However, differentiation is sometimes possible by R-scope inspection, as shown in Fig. 11. The approximate height of the frontal surface may sometimes be determined by the presence of shear conheight of the freezing level

is

RADAR STORM OBSERVATION shown by an RHI scope. This spectacular phenomenon is best detected when the pi-ecipitation is due to convective causes as was the case when the photograph shown in Fig. 8 was obtained. Where the ditions as

— Photograph

RHI

scope showing tall (snow) shower with abrupt shear below the altitude of 9000 ft. Lack of shear in showers more distant from the radar can best be explained by nonuniformity of the wind field. Storms are approaching the radar; shear therefore indicates decreasing wind velocity with altitude (in the plane of the picture) up to the point where echo signal edges become nearly vertical. Actual slope of shower in shear zone about 80° from the vertical (X-band radar). {M.I.T. Weather Radar Research.) Fig.

8.

of

the cell is embedded in air moving with constant velocity and direction. Where the echo signal slopes, the precipitation particles are descending into air moving at a different velocity along the direction of the radar beam. This difference may be due to a velocity differential with height, a direction differential, or a combination of both. The slope of the precipitation is a function of the fall velocities of the particles giving the echo and the wind velocities and directions involved. Unless the

precipitation echo signal

fall

velocity

is

is vertical,

known, only

relative

wind

velocities

and

may

directions be calculated from observations of this type [21, 41]. In Fig. 8 it will be noted that in the actual

storm the trajectory of the particles was almost horizontal in the shear zone the 10 1 vertical expansion increases the slope on the scope by this factor. ;

With

:

use of narrow-beam radars for weather observation, hitherto unsuspected phenomena have been observed in conjunction with warm-front precipitation. Precipitation is occasionally observed to form in narrow, closely spaced parallel bands as shown in Fig. 9. The formation is suggestive of billow clouds formed by shear waves, and is in all likelihood partially due to the same action as that which causes clouds of this type. The phenomena are rather transient, usually persisting for only ten or fifteen minutes in any particular area. Observation of this occurrence usually reincreasing

quires narrow

1273

beam width

radars (less than 2°) and

careful adjustment of antenna elevation angle

and

gain.

Also, rather short pulse lengths must be employed for best presentation. It is interesting to note that perfectly

—Photograph

of PPI scope showing striking forparallel bands. precipitation echoes formed Radial spokes are "shadows" cast by buildings and chimneys near the radar. Bands are suggestive of billow clouds, but are actually rain showers oriented north-south. Note the even, light rain echo signal which occupies the northern half of the scope. (1220 EST, 12/7/49, X-band radar, range 120 miles, 10-mile markers.) {M.I.T. Weather Radar Research.)

FiG.

9.

mation

of

m

uniform precipitation conditions are seen, though rarely over any extended area. Finer and finer detail becomes evident as the resolving power of radars is increased by employment of narrower beam widths. It may be that reasonably uniform rain can extend only over an area of a few tens or hundreds of square meters. Another phenomenon observed in conjunction with warm-front precipitation (and also under other conditions), is the descriptively designated "bright band." receives this name from its appearance on RHI scopes; a typical example is illustrated in Fig. 10. FigIt

R

scope of a radar ure 11 shows its appearance on the with a vertically directed antenna. It may be seen that the bright band is an approximately horizontal layer of exceptionally strong echo signal. The RHI scope has shown the following conditions to exist during bright-

band detection: 1. The band may be the only precipitation return detected by the radar. 2. Precipitation may be seen below the band with no return above (and occasionally vice versa). 3. The bright band may be accompanied by precipitation echo signals both above and beneath it. While certain detailed processes of bright-band formation are the cause of dispute, all investigators agree that state

some way connected with the change which occurs at the freezing level. The band

it

is

in

of is

invariably observed nearly at or slightly below this

:

RADIOMETEOROLOGY

1274

determined by radiosonde and aircraft (and sometimes surface) observation [22, 25, 26]. The observed thickness of the band can never be less than the level as

dence that the thickness of the band may vary from as as a few tens of meters to several hundred meters in thickness or more. It has been observed in connection with thunderstorms after convective activity has subsided [10, 19]. Two theories have been advanced to little

explain this phenomenon 1. The region of strong echo

is

due to drop formation

in the colloidally unstable layer of heterogeneous ice-

Any precipitation detected above that would therefore probably be caused by con-

water mixture. altitude

vective transport 2.

Snow

[19].

particles, too small to give

more than a weak

echo, fall to the zero degree isotherm, and melt at or just below this level. While melting, they have the low velocity of snowflakes, but the high reflectivity of water. Coalescence, often observed near melting temperatures, also serves to increase the reflectivity. After the snowflakes have completely melted, the fall velocity increases and the drops become widely spaced. The result is a region of weaker echo below the level of meltfall

—

Fig. 10. Photograph of RHI scope showing horizontal layer of strong echo signal (bright band) at altitude of about 11,000 ft. Tall vertical showers are indicative of convective activity. (1930 EST, 9/25/47, X-band radar.) {M.I.r. Weather Radar Research.)

pulse resolution of the radar used to observe it, and since it has occasionally been determined to be no more than this amount for a given radar system, there is evi-

ing [10, 24, 52]. Most investigators are inclined to favor the latter theory, which the weight of observational evidence seems to support. There is little doubt that, in the ab-

sence of other observations, the bright band provides an excellent indication of the approximate height of the freezing level. To a lesser extent, it is also an indicator of the stability of the atmosphere; a thin band is indicative of relative stabihty, and a thick one (or the absence of a band) suggests convective activity near the freezing level [10]. At the present time, however, this

is

only a rough qualitative measure. conditions, the warm front provides the

Under some

closest approximation to uniform precipitation rates which are so necessary at present for measurements made to study the relationship between rainfall intensity and the power of the echo signal. Efforts are being made to monitor the received power of storm echo signals continuously on two different frequencies [12, 42] (see Fig. 16). The radars are directed and ranged over a recording rain gage to estabHsh relationships between rate of rainfall and echo-signal power. Best correlations between the two have been found

during steady rainfall associated with warm-frontal conditions. 3. Occluded front. Little has been published concerning radar storm detection during occluded frontal conditions. Because of the complexity of the frontal system few generalizations can be made concerning precipita-

tion types or patterns. Some situations show widespread stratified precipitation, others show just as widely spread convective cells. An excellent place to study fronts of this type would be in Norway or in British

Columbia, where radars sited near the coast could be directed westward over the oceans, and observations could be made of fronts unmodified by topography. FiG. 11.

— Photograph

when antenna

illustrating appearance of

R

scope

directed vertically and echoes are received from rain and snow. The weaker echo signal of the snow is due to its greater range and lower dielectric constant. The echo from rain shows much greater intensity variations because of the wider range of fall velocities of the water particles. (Xband radar, range 5 miles, 1-mile markers.) (M.I.T. Weather Radar Research.) is

B. Orographic Precipitation. This type of precipitation, being associated

with uneven terrain,

is

somewhat

observe on PPI scopes if the antenna is directed horizontally. Increase of the antenna elevation angle is necessary to eliminate echo signals from the terrain causing the precipitation. There are no unique difficult to

RADAR STORM OBSERVATION features in this type of precipitation except that, on

By

can be fairly uniform. Because of this factor, this type of precipitation might be useful for relating storm echo signals to precipitation intensity. C. Hurricanes and Typhoons. Radar detection of hurricanes and typhoons is even more dramatic than radar

radars,

occasion,

it

detection of cold-front squall lines [66]. The rain-distribution pattern as seen on a PPI scope is illustrated in Fig. 12. It is startling in its similarity to the symbol §

1275

the time a hurricane its

direction

is

within range of land-based

and speed are usually well known.

However, these radars are useful for precise determinaany instant, and provide very valuable up-to-the-minute data on the storm [58]. It has been found by experience that the best wave length for use in hurricane detection is about 10 cm, at least from the standpoint of rain attenuation. Eventually it may be possible to measure wind speed in different portions of hurricanes by means of radar, and tion of the storm's position at

to obtain other clues concerning the structure of these

severe storms. The great decrease in loss of life from hurricanes in the southeastern United States is due to highly accurate data concerning movement and velocity of the storms and the early warning of their existence.

The importance of the part radar plays in the joint Air Force, Navy, and Weather Bureau hurricane program cannot be minimized. The importance of radar as a research tool for studying the structure of hurricanes should not be overlooked.

The

Fig. 12.— Hurricane of 18-21 Sept., 1948. PPI-scope photograph made just prior to passage of the eve over the radar at Key West, Florida. (0900 EST, 9/21/48, range about 125 miles.") (flfficial U. S. Navy Photo.)

possible use of this

new

presentation of the storm, wind and pressure distribution may be known, should greatly enhance our understanding of hurricanes. Much work is yet to be done; for example, few, if any, RHI-scope photographs of hurricanes have yet been taken. These would give inin

which the rain

relative to the

formation concerning convective activity, and whether or not there are shearing forces present as indicated by sloping of the rain cells. It may well be that some of the spiral patterns shown in Fig. 12 are due to the shear and not entirely an indication of the shape of the convective

D.

cell.

Instability Showers.

1.

Air mass. Air-mass pre-

cipitation, being largely convective in nature, generally

which has been chosen to indicate the position of hurricane centers on weather maps. The spiral rain bands visible in Fig. 12 have been observed in all hurricanes and typhoons detected by radar. These bands move slowly around the center; the cells in the bands move along the bands and into the center in a counterclockwise direction (in the Northern Hemisphere) [37]. As yet, no relationships between the band movement and winds aloft have been estabbecause of the difficulty of obtaining winds-aloft observations during storms of this type. It is possible that radar will also provide the solution to this problem. lished,

From Fig. 12, it will be noted that a very definite position can be found for the center of rotation as far as the rain is concerned. There is evidence that this center detected by radar does not always coincide with the center of low pressure. Also, a clear "eye" may or

may

not be

pi'esent,

depending upon the intensity of

precipitation at this point.

Radar hurricane detection is probably of greatest value in connection with aircraft hurricane reconnaissance. Early detection of the storm, while it is still far from land and out of range of land-based radars, is considerably facilitated by the use of air-borne radar equipment. It is not necessary for the aircraft to penetrate the storm in order to locate the position of the eye; this often eliminates the^ necessity of flying under extremely hazardous conditions [57].

shows somewhat

PPI scope

echo signals on the than does warm-frontal precipita-

finer detail in its

(Fig. 13)

,

•J*".,

.vriiiiiiii, ',''..

?n

'sii

RADIOMETEOROLOGY

1276

because winds aloft are usually fairly uniform. Determination of the direction and speed of the cells is generif the cells are fairly well defined so that their positions may be determined at ten or fifteen minute intervals. It has been observed in the northeastern United States that warm-sector precipitation, besides being

ally quite simple, especially

broken into small convective

cells,

The is

best presentation of thunderstorm echo signals RHI scope, as shown in Fig. 15. Again,

found on the

the reader

is

cautioned to keep in mind the 10

:

1

vertical

usually consists of

rather large, isolated areas. That is, a precipitation Tea of roughly elliptical shape, perhaps 100 miles in ex+ent, will be broken up into small-size cells of 1-5 miles diameter. The large areas follow each other

through the region covered by the radar sweep, with almost no isolated showers occurring between them or on the fringes of the main groups. 2. Thunderstorms. The appearance of a thunderstorm echo signal on PPI and RHI scopes is similar to that shown in Fig. 6. These storms, because of their great height, are detectable at greater distances than any other type of precipitation. Well-developed storms have been detected at distances over 300 miles, although for a radar less than 100 ft above the surrounding country, the usual maximum range is nearer 200 miles. Radar played an important role in the extensive research program on thunderstorms in Florida and Ohio

—

[60-62].

Using radar

it is

possible to determine

when a given

convective cell reaches the thunderstorm stage. Lightning gives a characteristic echo signal on A and R scopes as shown in Fig. 14 [39]. The echo signal from

— Photograph

R

of scope showing lightning echo intensity echo signal from precipitation to- right and left of lightning echo signal which persisted for about Ji sec. (1510 EST, 7/20/49, S-band radar, azimuth 320°, range 50-58 miles, 2-mile markers.) {M.I.T. Weather Radar Research.)

Fig. 14.

signal.

Low

transient, usually lasting less than 3^^ seceasy to detect visually on the scopes. Reflection or scattering evidently takes place from the dielectric gradient established by the stroke, but the mechanism is somewhat uncertain. It should be made clear that it is an actual radar echo signal which is detected, not a radio-static signal emitted by the stroke itself. This is proven by the fact that the lightning indication always occurs on the scope at the range and azimuth of the storm echo signal.

lightning

is

ond, but

is

Fig. 15. Cross section along an azimuth through a thunderstorm. Height of top about 20,000 ft. Note multiple towers at the top, and weak echo signal about 15,000 ft. (1645 EST, 7/31/47, X-band radar, azimuth 350°, range 60 miles, 10-mile markers.) (M.I.T. Weather Radar Research.)

expansion of this particular scope. Since this is a fairly representative example of the well-developed mid-latitude thunderstorm, it may be concluded that the precipitation core of such thunderstorms is approximately cylindrical in shape, and is about as wide as it is high. When analyzed by means of accelerated time-scale moving pictures, the RHI-scope echo signals of thunderstorms show discrete volumes of hydrometeors which may move upwards as well as downwards. These probably correspond to the heavy bursts of rain or hail which are occasionally experienced at the surface during intense thunderstorms. Precipitation strong enough to give intense echo signals at appreciable distances from the radar has occasionally been detected at heights exceeding 50,000 ft in mid-latitude thunderstorms. Somewhat rarely the precipitation echo signal will form in the typical anvil shape which the thundercloud itself assumes. Aircraft have encountered hail in the regions giving intense echo signals, but as yet no reliable means exists for distinguishing the hail from rain or snow by means of radar. A recently developed technique of signal fluctuation analysis, which is discussed in detail imder the section on analysis of the storm echo signal, has promise of being a powerful method of detecting the more turbulent regions in thunderstorms. General Remarks. Because of the comparative recency of applications of radar as a meteorological observation instrument, questions concerning detection of some meteorological phenomena must remain unanswered for the present. Eventually it may be ex-

RADAR STORM OBSERVATION pected that descriptions of radar detection of such phenomena as tornadoes, waterspouts, dust storms, and other atmospheric anomalies will be available. Forest fires sometimes appear as areas similar to weak rainecho signals on PPI scopes. The lack of vertical development, coupled with other meteorological information, is usually sufficient to provide correct identification. It is unknown at present whether the temperature gradients or the cinders and ash carried aloft by convective currents cause the echoes.

The small droplet size in fogs and drizzle make these hydrometeors poor targets for radar detection at 3- and 10-cm wave lengths. However, detection by radars operating on wave lengths near 1 cm (K-band) is common. Because of the scarcity of K-band radar, which has not been developed much beyond the laboratory stage, little

information

is

available concerning radar fog

drizzle detection. This

equipment

and

may eventually prove

valuable for reporting the rate of approach or develop-

ment of coastal fogs. The use of radar for determining meteorological conditions in the troposphere has been suggested by Friend [27]. An interesting application of K-band radar to meteorology has recently been developed by the Weather Radar Section of the United States Army Signal Corps Engineering Laboratories [7, 28]. This highly specialized radar system was designed with a vertically directed beam for the purpose of cloud base and top detection. The radar is equipped with an A scope, but in order to provide a permanent record the video signal is fed into a special slow-rate facsimile recorder in such a manner that a vertical time cross section of the clouds is plotted.^ Radar provides an ideal means of studying the results produced by seeding of clouds with CO2, silver iodide, etc. If the seeding is done by aircraft, the position of the plane is known, and if particles of precipitable size form, such vital information as time of formation, height, and position are readily available from the radar scope indications [56]. Another type of echo which has been ascribed to atmospheric conditions [23] has been given the picturesque designation of "angel." "Angels" are most commonly seen with the cloud-detection radar described above and are strong echo signals with no visible cause. They occur most frequently in the lower levels of the atmosphere, preferring heights near inversions. They have been ascribed to insects too small to be seen, strong temperature and moisture gradients, and regions of high ionization. Their cause is not yet known.

ANALYSIS OF THE RADAR STORM-ECHO SIGNAL Besides visual inspection of the scopes, there are other very powerful methods of studying the echo signals resulting from storms. Most of this work is still in 3. For records showing typical results, see Figs. 8 and 9 in the article, "Instruments and Techniques for Meteorological Measurements" by M. Ference, Jr., pp. 1207-1222 in this Com-

pendium.

1277

the preliminary stages, but enough has been accomplished to warrant description of present techniques. The Pulse Integrator. Echo-signal intensity may be measured at the radar in at least three different ways: (1) by the intensity of the spot on a PPI or RHI scope; (2) by the amount of vertical deflection on an A or scope [32]; and (3) by the echo-signal voltage returned to the radar before it is presented on the

R

The first method must be rejected at present because of fundamental difficulties as well as technical problems. The second method is commonly used, but some doubt exists as to the accuracy of this method and the possibility of observer bias. The third method employs a device designated as the "pulse integrator." The pulse integrator [70] measures electronically the average strength of the pulsating, fluctuating storm echo signals over a short interval of time. This interval, M^hich determines the number of pulses averaged, may be varied to suit conditions, but from two to four seconds has been found satisfactory. The output of the pulse integrator may be fed into any of several types of visual meters or recorders so that a permanent record is made. The precipitation -echo pulse integrator scopes.

records are calibrated by feeding signals of known strength into the antenna and comparing the readings.

This method of echo-signal intensity measurement is entirely free of observer bias and variability, but results obtained so far have not been satisfactorily correlated with rainfall intensity measurements in an absolute

o o ^

REFLECTIVITY TIME SCALE

^

O

00000 CVJ

CD

CO

—

.

SCR

tDCOO(M,^^^^^^ Fig.

5.

— Samples

from a record made at the Bermuda U. S. Navy, September 6, 1949, show"group" effect. Time intervals, 15 sec.

tripartite station of the ing the swell and decay

KILOMETERS Fig.

7.

—Position of the U. S. Navy tripartite station MNS at

Corpus Christi, Texas.

:

.

APPLICATION OF MICROSEISMS TO FORECASTING underneath the Avind system would challenge the resources of an}' but a goveriunental organization. Another tj^De of microseisms is found in a band whose dominant period lies in the neighborhood of two seconds (Fig. 6). Much less is known about these microseisms than about those of longer period. For some time the U. S. Navy maintained a tripartite station near Corpus Christi, Texas (Fig. 7). A preliminary study of the records was made by Jennemann. There were times when this type of microseisms dominated the records sufficiently to permit a determination of the direction of arrival at the station.

They

appeai'ed

This means that these microseisms were coming not from the Gulf of Mexico to

come from

Avest of north.

1315

with three components at each comer of the triangle and separated by distances considerably less than a wave length with a view to determining how, if at all, they are related to weather conditions and whether they have forecasting value (Fig. 9) There are other bands of frequencies in the spectrum of microseisms but their possibilities for weather forecasting have not been tested. Conclusions. There is a limit to what can be done with statistical studies of microseisms.

The

record of more

than three quarters of a century of such studies shows what great care must be taken in their plamiing and in the interpretation of results. Quite contradictory conclusions have been dra^vn from parallel correlations. Much the same may be said of vectorial analysis of microseismic records. A very fruitful line of research has been opened up by the use of tripartite stations whose dimensions are less than one wave length. This method is independent of all assumptions except the successive arrival of an identical

wave

front at the

three corners of the tripartite station. It gives a completely independent determination of the direction and

speed of wave travel. Cross bearings between two or tripartite stations locate the source of the microseisms and thus furnish a clue for the investigation of the point of origin within the storm provided there are a sufficient number of tripartite stations available for the observation of one storm. Research on the origin of the microseisms or the mechanism by which they are produced is difficult but very necessary. The possibility of air oscillations acting as a hammer may be investigated by means of microbarographs disposed on small islands in the path of typhoons and hurricanes. A similar system for the investigation of standing waves, or of the oscillations of a water vortex, would be much more difficult and costly. One might think of pressure gauges on a submarine cable laid in a path frequently followed by tropical storms and terminating at a recording station somewhere on land.

more

wmuB

W»'»"'^^

r,,,,,iB»w>i«lplN9>«Mi«iat(

Ni

>««

Fig.

—

8. Short-period microseisms. Wood-Anderson record, Florissant station. Time marks everj^ half-minute.

but from the continent.

It

was

possible to correlate

these microseisms tentatively with disturbed weather conditions existing to the northward of the station. At Fordham University a tripartite station has been set

REFERENCES Fig.

9.

—Three-tenth-second microseisms

as recorded

by a

The following papers contain extensive surveys

1.

and their relation to the weather: Gutenberg, B., "Untersuchungen iiber die Bodenunruhe mit Perioden von 4 bis 10 Secunden in Europa." Veroff.

2.

Macelwane, J.

3.

Ann. Geophys., 2:281-289 (1946). Ramirez, J. E., "An Experimental Investigation of the Nature and Origin of Microseisms at St. Louis, Missouri."

up

disturbances.

Preliminary studies are in progress on quite another type of microseisms of frequency of two to three cycles per second on a contract between Saint Louis University and the Office of Naval Research (Fig. 8). They are being studied with a tripartite station equipped

of

literature on microseisms

Sprengnether-Volk seismograph. for the express purpose of studying these two-second microseisms on contract mth the Office of Naval Research. Other preliminary studies have been made by Leet and Gutenberg. While it is too early to form a positive judgment, the results so far seem to hold promise for forecasting of conditions related to frontal

the

I.

ZentBur.

int. seism. Ass.,

B.,

106 SS., Strasbourg (1921).

"Storms and the Origin

of Microseisms."

Bull, seism. Soc. Amer., 30:35-84, 139-178 (1940). II.

4.

Important papers on hurricane and typhoon forecasting

by means of microseisms are GiLMORE, M. H., "Microseisms and Ocean Storms." Bull. seism. Soc. Amer., 36:89-119 (1946).

5.

and Hubert, W. E., "Microseisms and Pacific Typhoons." Bull, seism. Soc. Amer., 38:195-228 (1948).

—

—

INDEX (References

Absorbers, effect on effective terrestrial radiation, 39 Absorbing layers, upper atmosphere, heights of, 271 Absorption coefficients, 265 as a function of pressure, 40 oxygen, 275 ozone, 275 Absorption cross section, 265 Absorption functions, 36 Absorption laws, 34 for diffuse radiation, 35 for parallel radiation, 34 Absorption of solar radiation, 19

measurement, 50 spectral evidence, upper composition, 270

atmosphere

Absorption spectrum, 264 Actinograph, Robitzsch, 54 Actinometer, Michelson, 53 Actinometric equipment at

meteoro-

logical stations, 63 instruments, 52 Actinometric measurements, 50 accuracy, 50 atmosphere analysis, 50 critique of routine, 55 effect of absorption on solar radiation, 50 effect of molecular scattering on solar

radiation, 50 varying distance between sun and earth on solar radiation, 50 heat exchange at earth's surface, 50 solar constant, 50 special problems, 55 Actinometric observatory, central, equipment, 54 Actinometric stations, second order, equipment, 54 third order, equipment, 55 Actinometry, 50 biological problems and, 62 Actinon, source, 166 Activation energy, 270 Advective-adiabatic extrapolation, prognosis of relative hypsography by, 782 effect of

Advective models, barotropic models, 473

dynamic forecasting and, 471 Kibel's method, 473 as

environment

appear in bold face.)

Air -continued earth electric current, 113 effect on scintillation, 68 electrical conductivity, 102 ionization of, 102 total oxidation, 1130 tropical, properties, 881 Air current, modifications, forecasting, 779 Air density distribution, 360 Air density, from meteor deceleration, 360 seasonal variations, 360 Air masses, Antarctic, 923 Artie, 948 in equatorial meteorology, 881 modification, 973 forecasting, 779 use for description of climate, 968 Air motion, effect on ozone, 283 Air pressure, effect on downcoming radiation, 40 Air transport, by slope winds, 666 Aircraft, electrification of, flying through precipitation, 133 meteorological instruments, 1223 Aircraft icing, analysis of formation, 1190 at low temperatures, 194 availability of liquid water, 1190

cloud-drop

diameter,

measurement,

1198

cloud-drop size, 1201 concentration of liquid water in clouds, 1199 conditions for formation, 1192 effect on airplane components, 1193 forecasting, 793 forecasting icing conditions, 1201 icing conditions, physical characteristics, 1197 intensity, 1198 liquid-water concentration, measurement, 1198 meteorological aspects, 1197 meteorological conditions, research needed, 1202 operational aspects, 1190 physical aspects, 1190 physical characteristics of icing conditions, 1197 research needed, 1195 special cases, 1193

water impingement, 1191

Aerobiology, 1103

atmosphere

to titles of articles

for

or-

ganisms, 1105 biological factors, 1103

counting, methods and problems, 1103 exchange of organisms between earth and atmosphere, 1106 identifying

organisms, methods and problems, 1104 locating sources, methods and prob-

lems, 1104 meteorological factors, 1106 origin of molds, 1109 sampling, methods and problems, 1103 thermal convection, 1110 transport of organisms, 1108 Aerology of extratropical disturbances, 599 Aerology of tropical storms, 902 Agriculture, and applied climatology, 987 and microclimatology, 998 Air, albedo of pure dry, 25 atmospheric, composition of, 3

Airglow, 269 Airline operations, and instability lines, 647 Airplane, thunderstorms and, 690 Aitken dust counter, 165 Aitken-nuclei, 183; see also Condensation nuclei destruction processes, 188 effect of pressure changes on, 186 form, 184 formation in smoke, 186 growth, 184 horizontal distribution, 184 mechanical sources, 187 optical effects, 188 physical state, 184 size, relation to electrostatic charge, 187 vertical distribution, 184 Albedo, 25 of cloudless atmosphere, 25 of dust, 26 of earth's surface, 27 of planet Earth, 27

1317

Albedo

continued

of pure dry air, 25 of the Earth, 31 of various cloud types, 26 of various surfaces, 27 of water vapor, 26 total atmospheric, 26 Alpine tree line, 953

Alpine tundra, 963 Alps, air circulation during daytime, 663 Altimeter, 1226 Altitude (s), effect on electrical conductivity of air, 104 extreme, pressures at, 308 temperatures at, 308

Ammonia

content of atmosphere, 7 ions, effect on condensation nuclei formation, 186 Amorphous frost, 207 Anafront, 771 Angels, 1277 Angstrom compensation pyrheliometer,

Ammonium

52

Angstrom pyrgeometer, 55 Antarctic, air exchange, 936 air masses, 923 anticyclone, 918 atmosphere, exchange, 936 oxygen content, 933 atmospheric circulation, 917 blizzards, 919 circulation, 925 prospects for study, 937 cyclones, 922 exploration, 917 frontal zones, 922 geography, 917 glaciation, 934 ice, recession, 934 thickness, 933 interior, summer winds, 921 weather conditions, 921 precipitation, 933 pressure waves, 926 characteristics, 926 movement, 926 theories, 927 seasons, 920 snow surface, altitude, 934 soundings, 930 storms, 924 stratospheric warming, 931 surges, 926 temperatures, 929 march of, 932 summertime, 931 wintertime, 930 upper winds, 920 water temperature, 932 weather observation stations, 708, 918, 937 winds, 919 Anticorona, 71 Anticyclogenesis, 770 Anticyclones, 621 and forecasting, 626 and summer showers, 626 Antarctic, 918 "back-door" cold fronts and, 627 definition, 621

degeneration, 778 high level, formation, 612 generation, 778

Indian summer, 626 motion, 625 origin, 621

^

—

— INDEX

1318 Anticyclones

Atmosphere

continued conductivity, measurement of, 146 constituents, diffusion coefficients, 321 molecular properties, 321 of variable concentrations, 6 contrast, reduction by, 92

continued

polar, 621

forecasting motion of, 625

transformation to dynamic, 625 role in general circulation, 621 temperature structure, 621 thermal structure, 621, 627

by water-vapor radiation, 43 density, from meteor deceleration, 360

water-vapor structure, 316 westerlies and, 623 Anticyclonic shear, upper atmosphere, 585 _

upper limit, 604 Antioyolosis, 780 Antitrades, air motion, 862 Anti-twilight arch, 73 Arago point, 79 distances, effect of ground reflection on, 82 position, 82 Arctic, air, seasonal variations, 947 winter, 948 atmospheric circulation studies, 942 Baffin Bay, 960 central basin, circulation pattern, 943 circulation patterns, 944 concepts, 943 typical, 949 variations, 949 climate and tree growth, 954 climatic control, 953 climatological problems, 952 climatology, ecological, 953 general literature, 952 in Greenland, 961 Eurasian, air, seasonal variations, 948 expedition studies, 944 extent of, 956 climatology, Greenland literature, region, 952 in North America, 952 Northern Russia, 952 over Arctic Ocean, 952 meteorological problems, 950 meteorology, 942 700-mb contour patterns, 946 North America, air, seasonal variations, 947 North Water, 960 observational data, 944, 950 permafrost distribution, 958 reconnaissance flights, 944 sea ice, scope for research, 960 sea-ice distribution, 958 sea-level pressure, 945 sea-level pressure charts, 944 soundings, 930, 947 tree growth, 954 tree line, 955 vegetation, zonal divisions, 955 weather observation stations, 708, 944 Argon, content of, in atmosphere, 5 Aspiration condenser, 147 Aspirator, Gerdien, 147

environment for organisms, 1105 hydrodynamic fluid, laboratory investigations, 1235

carbon dioxide content, 3, 4 carbon monoxide content, 7

of, 1

variations in, 3 compressible, wave motions in, 414

middle, origin of high temperature in, 253 mold distribution, 1109 neon content, 5 Neptune, 394 nitrogen content, 5 nitrogen dioxide content, 7 nitrous oxide content, 5 of other planets, 391 ozone content, 6, 275 radio waves in, refraction of, 1290 radioactive substances in, 155 radioactivity, 155 measurement, 155

157

problems, 159 radon, decrease with height, 158

radon balance, 158 radon content, 158 variations, 157

removal of organisms from, 1107 Saturn, 394 scattering of light in, 76 solar radiant energy modification by, 13

sound propagation in, 366 sound wave energy in, 368 stability of permanent, horizontal,

radiation, 44

content, 7 analysis of, 50 argon content of, 5

composition

methane content, 5

temperature change, by water-vapor

ammonia

phenomena

Mars, 392

isobaric motion, 446 subjective phenomena, 61 sulphur dioxide content, 7 suspensions, 146

Weger, 147 Astronomical refraction, 64 Atmosphere, albedo of cloudless, 25

cloud-free, refraction 64

dispersion of light rays by, 67 downcoming radiation from, 38 electric field, in fair weather, 107 measurement, 148 electrical resistance of vertical column, 108 energy transfer within, modes of, 544 exchange of heat with sea surface, 1057 free, electrical measurements of, 150 free oscillations in, 306 future developments, 9 gases of constant percentage, 5 heat gain through convection, 1065 helium content of, 5 hydrogen content, 6 ion concentration, measurement, 146 ion mobility, measurement, 146 ionizers, 146 ions, 120 isotopic composition of gases, 8 Jupiter, 394 kinetic energy balance, 544 krypton content, 5 light behavior in, 91 major planets, circulation, 395

by emanometry, 155 by induction method,

in,

Atmospheric

air continued disturbances, classifying, 457 large-scale, stability properties 454

of,

electricity see Electricity, atmospheric flow, circular vortex, 455

hydrodynamic equations, 454

cooling, 41

transformation, 625 warm, 622 advective theory, 622 dynamic theory, 622 radiative theory, 622

as as

—

upper see Upper atmosphere Uranus, 394 variation of oxygen content, 3, 933 Venus, 391 water vapor density in, 8 wheat stem rust transport in, 1108 xenon content, 5 Atmospheric air, composition of, 3 chemistry see Chemistry, atmospheric circulation see also Circulation general, studies of, 551 density distribution, 360 density, seasonal variations, 360

gases, escape, 246 isotopic composition, 8 motions, experimental analogies, 1235 oscillations see Tides, atmospheric ozone, theory of, 281 perturbation theory, basic assumptions, 402 perturbations, factors involved in, 445 hydrodynamic instability and theory of, 444 pollution see Pollution, atmospheric stability, effect on atmospheric pollution, 1146 testing, 694 tides see Tides, atmospheric turbulence, heat flux due to, 536 Atomic collisions, types, 267 number, 263 particles, 263 combination, 269 dissociation of, 268 ionization of, 268 spectra, 265 two- and three-body collision, 269 processes, reversibility, 267 transitions, spectra associated with, 264 Attachment energy, 263 Audibility zones, abnormal, sound waves through, 371 Aureole, 71 Aurorae, 345 and magnetic storms, 347, 352 appearance, 347 Birkeland's model experiments, 351 charged corpuscle movement and, 352 corpuscular theory of, 351 E-layer of ionosphere during, 353 F2-layer of ionosphere during, 353 forms, 347 flaming, 347 with ray-structure, 347 without ray-structure, 347 in upper atmosphere, 255 ionosphere and, 352 magnetic disturbances and, 258 position in space, 349 direction of arcs, 349 height statistics, 349 method of height determination, 349 position of radiation point, 349 sunlit aurora, 350 spectrum, 350 Stormer's calculations and, 352 use in studying upper atmosphere, 251 VHF-band reflections from, 354 Aviation medicine, 1121 Avogadro's number, 263

B Babinet point, 79 position, 82 Bacteria" marine, exchange between earth and atmosphere, 1106 soil, exchange between earth and atmosphere, 1106 Ball lightning, 141 Ballo-electricity, 1134 Balloons, 1214 altitude performance, 1214 ascensional rates, 1215 recording, use in determining ozone distribution, 278 studies, in upper atmosphere, 303 on temperature, 303

temperature

effects, 1214

tracking direction finder, 1208

— INDEX Band spectra, 265 Baroclinic disturbances, 457, 463 fluids, hydrodynamic equations, 403 instability, in fluid motion, 468 waves studies, 459 by Charney, 459 by Eady, 459 by Fj0rtoft, 459 Barometric oscillations, use in studying upper, atmosphere, 251 Barometric variations, lunar daily, 515 solar daily, 521 Barometry, tropical cyclones, 888 Barotropic disturbances, 460, 463 Barotropic fluids, hydrodynamic equa'

tions, 403

Barotropic models, advective models, 473 linearized, 474 nonlinear, 478 Barotropic waves, stability of, 462

1319

Breezes, land and sea continued range, 658 single circulation cell, 660 temperature differences during, 657 theory of, 659 tropical, 861 vertical extent, 658 sea, cold front -like, 659 Conrad's minor, 658 direction, 655 effect of cloudiness on, 658 of the first kind, 658 of the second kind, 659 Brewster point, 79 Bright band, and precipitation growth, 1286 on radarscope photographs, 1273 Bright segment, 73 Brooken-specter, 71 Bruckner cycle, 383, 817

Bead

lightning, 141 Bellani pyrgeometer, 55 B^nard cells, 701, 1255 Sutton's theory, 1261 Bifilar electrometer, 144 Wulf's, 145 Biological problems, actinometry and, 52 Birkeland, model experiments of, 351

Bishop's ring, 71 Bioclimatology, human, aviation medicine, 1121

breathing, 1116 clothing, 1115 cooling, 1115 effect of aperiodic weather processes, 1120 effects of extreme cold, 1122 effects of extreme heat, 1122 effect of periodic weather processes, 1120 erythema solare, 1118 general effects of climate, 1117 glare, 1119 heat balance, 1112 heat loss by convection, 1112 heat production, 1112 heat transfer by evaporation, 1113 heat transfer by radiation, 1113 meteorotropism, 1120 ozone and, 287 physical aspects, 1112 radiation effects, 1118 research needed, 1122 space medicine, 1121 sultriness and heat, 1114 sunburn, 1118 total heat balance, 1114 vitamin D, 1119 Blocking waves, in planetary jet stream, 432 Boenregen, electrical characteristics, 128 Bolides, 356 Bora, 669 anticyclonic, 670 cyclonic, 670 Boreal forest, 953, 957 southern limit, 958 Boundary layer, in air flow, 492 Bowen ratio, 1058, 1073 Boys cameras, use in determining mechanism of lightning discharge, 142

Branching, 136 Breezes, land and sea, as function of geographical location, 658 _

description, 655 desirable studies, 670 effect of season on, 658 effect of time of day on, 658 explanation, 656 intensity, 658 phase shift, 661 pressure differences during, 657 pressure distribution during, 657

Cage method, 149 Capillary electrometers, in measurement of

atmospheric electricity, 144

Carbon dioxide, atmospheric content, 3 effect effect

on radiation diagrams, 37 on radiation in stratosphere, 46

infrared spectra, 296 variation in atmospheric content over the sea, 4 variations, effect on climate, 1015 Carbon, isotopic variations in atmosphere, 9

Carbon monoxide content

of atmosphere,

7

Cathode-ray oscillograph, in measure-

ment

lightning characteris-

of

tics, 142

Ceilometers, 1218 pulsed light, 1218 radar, 1218 Cellular convection; see Convection, cellular

Centrifugal instability, in fluid motion, 467 Characteristics, definition of, 421

determination of, 421 envelope of, 423

method

of,

421

mathematical foundations, 421 numerical integration of, 422 quasi-linear 421

differential

equations,

Charge determinations, lightning

dis-

charges, 140 Charney, baroclinic wave studies, 459 Charts, moisture, use in meteorological analysis, 725 use in meteorological analysis, 721 Chemistry, atmospheric, 262 absorption-tube methods for detecting gaseous materials, 1126 absorption-tube method results, 1128

condensation method, for determining traces which form condensation nuclei, 1127 iodine, 1128 methods, 1126 ozone, of air strata near ground, 1129 problems of, 1126 results from condensation method, 1131 total oxidation of air, 1130 gas, general principles, 263 troposphere and, 262

Chinook

ions,

Foehn

see

Chlorine,

atmospheric,

1126, 1131 effect on

determining,

condensation formation, 186

nuclei

Christian era, climatic changes during, 1008

Circuit breakers, reclosing, use in lightning protection, 142 Circular vortex, characteristics, 432 Circulation, Antarctic, 917, 925 cellular character at sea level, 555

comparison between Northern and Southern Hemispheres, 555 general, air drift in middle latitudes, 542 atmospheric, forms of, 822 considerations in long-range forecasting, 837 density and meridional motion, 546 developing cyclone, kinetic energy for, 545 during strong polar vortex, 547 effect of mountain ranges on, 547 energy principles applied to, 568 energy, total, global balance, 572 flow types, and sunspot numbers, 840 horizontal, 543 horizontal kinetic energy, transport, 545 index cycle, 560 internal dynamic consistency, 542 irregular variations, 559 kinetic energy, global balance, 568 kinetic energy balance, 544 kinetic energy balance fluctuations, 546 laboratory investigations, 1240 lag correlations, 565 low-index conditions, 547 mean charts, reasons for use of, 552 meridional circulation strips, 824 meridional indices, 564 meridional transfer of internal heat energy, 546 models, 542 momentum and energy balance, 548 nonseasonal variations, 559

normal state, 551 northward transport, 543 patterns, 551 physical basis, 541 physical climatology, 556 qualitative synoptic studies, 559 quantitative empirical studies, 562 solenoidal index, 564 sources of data, 551 statistical studies, 564 summer arctic anticyclone of stratosphere, 824 trough motion, 563 unordered heat exchange, 824 wave motion, 563 wave speed and time, 562 westward progression, 561 winter anticyclone in troposphere, 824 zonal wind speed and wave lengths, 562 geostrophic zonal wind speed, 555 global, 541 in cell in cumulus stage, 697 indices, 555 jet stream see Jet stream local, 653 maximum index, 555 mean, relationship of precipitation to, 810 meridional and zonal, change between, 827 meridional indices, 555 normal, of lower stratosphere, 553 of troposphere, 553 patterns, Arctic, 944 concepts, 943 general, observational studies, 551 index cycle, 560 observational accuracy, 534 qualitative synoptic studies, 559 quantitative empirical studies, 562 translation into weather anomalies, 810

—

—

— INDEX

1320 Circulation continued prognosis, physical methods in, 806 relationship between weather and, 809 studies, Arctic, 942 tropical, empirical laws governing, 861 undulations in circumpolar vortex, 555 upper -level, effect on weather, 723 zonal, at sea level, 555 variation in speed, 560 zonal indices, seasonal behavior, 555 zonal wind-speed profile, 555 Circumpolar vortex, jet stream of, 559 undulations in, 555 Cirrus, ice crystals in, 222

Climatology aviation,

and microolimatology,

1001 Clicks see Sferics

Climate, air-mass description, 968 difficulties of, 970 as a dynamical problem, 972 as a physical problem, 972 basic requirements for discussion, 974 during geological time, 1004 during ice ages, 1004 early ice ages, 1006 Eocene, 1004 geographic control, 1012 Jurassic age, 1004 mountain building and, 1013 pluvial periods, 1006 synthesis of weather, 967 world, expression of, 967 Climatic change, continental drift, 1012 correlation with glacier changes, 1020 dependent on external influences, theories, 1010 due to terrestrial causes, theories, 1012 during Christian era, 1008 effect of changes in earth's orbit, 1010 effect of solar radiation on^ 1010 geological aspects, 1004 historical aspects, 1004 Palaeozoic ice age, 1014 postglacial, 1007 research needed, 1017 role of carbon dioxide variations, 1015 role of ocean currents in, 1014 role of polar ice caps, 1014 solar-topographic theory, 1016 topographic theory of, 1016 tree-ring indices, 1028 volcanic dust and, 1015 Climatic data, analysis of requirements in various activities, 976 Climatic Optimum, 382, 1007, 1021 Climatological analysis, for operational planning, 980 Climatological material, sources of, 977 Climatological problems, Arctic, 952 Climatology, agricultural, 980 applied, 976 and aerial mapping, 986 and agricultural land usage, 987 and aviation, 988 and clothing design, 983 and deterioration of materials, 985 and flood water run-off, 987 and forest fires, 988 and housing design, 982

and marketing

of "weather goods," 986 and objective forecasting, 986 and solar radiation, 984 and wind for power production, 984 classes of problems, 979 data for, 977 definition, 976 frost hazard, 984 historical note, 976 list of topics, 990 techniques, 981 weather insurance, 981

of,

968

altitude, 44 of electrification, effect on aircraft, 134 classification, need for uniform prac-

centers

tice, 1165

according to form, 1165 convection, 694 classes of, 1261 cross sections, 1174 data, synoptic, aid in forecasting, 1173 droplet, accretion, 205

evaporation

of,

of, 169

phase, 173 liquid-water content, 171

measurement, 171 size, 1201

and liquid water, 171 distribution, 170 by cloud types, 173 in sea fog, 173 distribution curves, 172 in free atmosphere, 172 171

edges, evaporation from, 200 heat conduction from, 200 elements, condensation on, 204 effect of thermal processes on, 204 electrical characteristics, 130 heat exchange between air and, 199 melting processes, 205 sublimation on, 204 -environment mixing, 695 formation, experimental, 1255 applications to atmosphere, 1260

comparison of phenomena in and carbon dioxide, 1260 Lord Rayleigh's theories, 1256 motion in unstable layers of

to

thunderstorm

-to-cloud lightning discharge, 139 transformations, interpretation of observed trends in, 1168 types, drop -size variations in various, 173

Cloudiness, effect on ultraviolet radiation, 1119 Clouds, 163, 1159 albedo, 26 altocumulus, and thunderstorm movement, 1173 altocumulus and rain, 1169

altocumulus castellatus, and rain and thunderstorms, 1169 altocumulus lenticularis, and wet weather, 1170 cirrocumulus, weather conditions with, 1170

adequacies, 1164 assessment of inadequacies, 1164 cirrus, movements, and temperature changes, 1172 motion, use in forecasting cyclone

ice

measurement,

relation

electricity, 687 synoptics, historical summary, 1174

classification of forms, assessement of

204 growth by coalescence, 176 growth formula, 169

growth

continued

structure,

Greenland, 961 human comfort and health, 980, 1117 human pathology and, 981 use of synoptic maps in, 970 Clothing design, applied climatology and, 983 Cloud, and weather types, 1175; see also Clouds boundaries, upper, distribution with

ice nuclei in, 196

City planning,

Cloud

continued

demands

air

air,

1256, 1258 nature of simple convection cell,

1255 research needed, 1261 Sutton's theory of B^nard cells, 1261

forms, classification, 1161 genetical classification, 1162 international classifications, 1161 physical classifications, 1163 radiational influences, 203 indications of new developments, 1175 of passing low, 1175 mass, effect of elevation on, 698 effect of humidity on, 698 effect of temperature on, 698 modification, artificial, relation to production of precipitation, 235 by water, 230 methods, 229 with dry ice, 229 with silver iodide, 230 motions, as wind indicators, 1172 observation, 1167 Physics Project, 236 experiments on stratus clouds, 236 experiments with cumulus clouds, 239 properties, mixing on, 696 radiation, 42 seeding see Seeding, cloud size, aircraft measurement, 1228

movement, 1171 speed, and storm speed, 1172 velocities, and weather changes, 1172 convective, dynamics of, 201 slice method of analyzing, 201 development of ice phase in, 194 direction of motion, use in forecasting, 1170 double cirrus, weather associated with, 1169 drop-size distribution, 170 effect on atmospheric radiation, 42 effect on shape of sky, 61 entrainment of air, 694 formed outside space they occupy, 1162 high-level, ice phase in, 196 ice see Ice clouds in forecasting, research needed, 1176 in short-term forecasting, 1167 interior, heat iridescent, 71

conduction

in,

200

liquid-water concentration, 1200 liquid-water content, effect of elevation, 698 mammatus, weather associated with, 1169 medium-level, ice phase in, 196 microorganisms in, 1109 mixed, physics of, 192 mixing processes and, 200 observed, application of diurnal cycle to, 1167 of advection, 1163 of convection, 1162 of turbulence, 1163 orographic, 1163 physical classification, 1163 physics of, 165 point of convergence, use in forecasting, 1170 proper to space they occupy, 1162 radiation processes and, 43, 200 reflection of solar radiation by, 26 solar radiation absorption by, 21, 31 supercooled, elimination by cloud seeding, 232 factors controlling life cycle of, 227 temperature lapse rate, effect of mixing, 696 thermodynamic analysis, 697

thermodynamics

of, 199 tropical cyclones, 890 undulated sheet, weather associated with, 1169 use in forecasting, 1167 wind-shift line marked by, 1173

—

—

INDEX Coagulation, effect in nuclei destruction, 189 Cold fronts, "back-door," anticyclones and, 627 laboratory investigations, 1238 electrical field conditions Collector, produced by, 149 flame, 148 point, 148 radioactive, 148 water-dropper, 148 measurement of discharge of electrostatic induction by, 148 Collision, de-excitation by, 267 excitation by, 267 -interval, 268

Compatibility, equations of, 422 Compression waves, 425 Condensation, atmospheric, nuclei

of,

Corona, 380

and related phenomena, maxima, 72 Cosmic radiation, and

ions, 103 lunar tidal variations of, 521 Craig, calculations of heating and cooling in ozone layer, 299 Crop yields, weather conditions and, 988 Cryology, 1048 Crystalline frost, 207 cup crystal, 207 dendritic crystal, 207 feather-like form, 207 needle form, 207 plate crystal, 207

phase development

liquid-water concentration, 1199

Cumulus

phase, 169 ice

clouds to, 197 nuclei

see

also

Aitken-

nuclei

Condensation nuclei, 165 and gas reactions, 186 atmospheric, pH, determination, 1131 of small ions with, 123

combination condensation

ice

in, 194

Condensation mechanism, relation of Condensation

71

Corpuscular theory, of aurorae, 351 Cosmical meteorology, 377

Condensation nuclei

below OC, 174 initial

Coriolis force, effect on flow under inversion, 432

Cumulonimbus,

182 see also

1321

effect, 182

destruction processes, 188 determining, 1127 discovery of, 165 distribution of, 168 effect of pressure changes on, 186 electrostatic charges on, 187 formation in smoke, 186 growth, 185 hygroscopic, 166 materials forming, 166 measurement, 148

methods, 182 mechanical sources, 187 nature, 165 nonh3'groseopic, 166 number of, 168, 182 optical effects, 188 physical state, 183 sea salts as, 166 size, 167, 182 measurement of, 167 size distribution, 167 size range, 183 sources, 165 Condensation, on cloud elements, 204 Condenser, aspiration, 147 limiting mobility, 147 Conductivity, atmospheric, measurement, 146 electrical, of air, 102 Cone of escape, 247 Conrad's minor sea breeze, 658 Constant-pressure terminology, 773 Continental drift, hypothesis of, 1012 Contour microclimates, 997 Contrast, reduction by atmosphere, 92 Convection, cellular, 203, 1255 effect of shear, 1258 heat gain by atmosphere through, 1065 heat loss from oceans through, 1064 laboratory investigations, 1255 natural, 507 problem of, 506 theory, 1256 free, laboratory experiments on, 1253 Convergence lines, 874 Cooling power, 1115 Cooling temperature, 1115 Coordinate systems, perturbation equations for, 410

convection, 694 predicting, 700 development, convectively unstable air and, 699 prediction, 699 research needed, 700 surface heating and, 699 effect of cloud seeding on, 239 entrainment, 694 concept, 695 growth, 697 ice phase development in, 194 increased precipitation from, by cloud seeding, 232 liquid-water concentration, 1199 mixing, concept, 695 solid precipitation from, 223 Cup crystal frost, 207 Curie unit, 155 Current, continuous, with lightning discharges, 138 electric, air-earth, 113

lightning discharges, 139 ohmic, 146 peaks, of lightning discharges, duration of, 140 wave shapes of, in lightning discharges, 140 saturation, 147 semi-saturation, 147 vertical, in thunderstorms, 150 Current circuit, for electrometers, 144 Cyclogenesis, 618, 770 in extratropical latitudes, and hydrodynamic instability, 442 Cyclolysis, 780 Cyclones, see also Disturbances and long upper waves, 605 Antarctic, 922 deepening, change of vorticity field, 612 degeneration, 778 developing, kinetic energy for, 545 development, basic equations, 465 of individual, 608 quantitative theory, 464 dynamic instability, 584 extratropical, 577 aerology of, 599 critical eccentricity, 578 dynamics of simplified models, 577 friction layer of closed vortex, 579 frontal wave movement, 582 frontogenesis, 590 inertial motion in isentropic surfaces, 583 instability line in, 648 pressure changes, theory of, 577 profile of cold front, 594 profile of warm front, 594 profile through frontogenesis, 593

Cyclones

continued extratropical continued slowing down, 580 structure of maturing frontal, 595 surface pressure tendency, 577 synoptic evolution of upper layers, 587 synoptic example, 587 temperature distribution, 580 thermal structure, 577 three-dimensional movement in, 610 upper-air divergence, 597 vorticity analysis, 582 westerlies associated with, 579 westerly wave of upper atmosphere, 583 families, 608 frontogenesis, 618 generation, 778 high-level, 616 formation, 612 laboratory investigations, 1236 mature, pressure distribution, 611 movement, forecasting, cirrus-cloud movement and, 1171 problem, remarks on, 618 laboratory investigations, systems, 1238 tropical, see also Tropical cyclones permanent circular vortex and, 448 upper streamlines, decrease of vorticity along, 611 wave, pressure distribution, 611 with instability line, 648 Cyclonic circulation, during occlusion process, 610 perturbations, and long upper waves, 607 wind shear, and instability line, 649

D Dalton's law, 320 Dark and bright segments, movement, 74 Dark segment, 73 height at various sun depressions, 75 schematic version, 75

Dart

leader, 136 De-excitation, by collision, 267 radiation with, 267 Dendritic crystal frost, 207

Dendrochronology, 1024; see also Tree ring indices

changing drought areas, 1028 cycle analysis, 1028 dry and wet years, 1028 errors of interpretation, 1025 history, 1024 long-term climatic fluctuations, 1028 methods, 1025 possible errors, 1025 principles, 1024 relation to neighboring sciences, 1025 research needed, 1029 Deposit gauge, for measuring atmospheric pollution, 1139 Diabatic processes, changes in relative height associated with, 784 Dielectric materials, used in measuring instruments, 144 Diffusion, atmospheric, 320, 492, 1140 eddy, 321, 501 horizontal coefficients of, 330 effect in nuclei destruction, 189 effects of sinks, 325 effects of sources, 325 equation of 322, 503 forced electromagnetic fields and, 323 from continuous point source, 503, 1140 from multiple sources, 503, 1146 in the vertical, steady conditions, 323 unsteady conditions, general equation, 327

— INDEX

1322 Diffusion

continued

in upper atmosphere, 320

laboratory investigations, 1252 matter, in nonadiabatic gradients, 507 maximum mixture, 324 maximum separation, 324 molecular, 320 of particulate matter, 326 partial separation, 324 research needed, 332 small-scale, 503 theory of, 320, 503 three-dimensional, 329, 504 three-dimensional, examples of, 330 general causes, 329 time required for establishing equilibrium, 328 two-dimensional, 503 Diffusion coefficients, observed, 321 Diffusion diagram, 322 Diffusion equilibrium, 320 Diffusion processes, effect of representative wind field on, 330 Diffusion theory, Richardson's, 505 Diffusion velocity, in maximum mixture, 324 vector of, 320 Dissociation energy, 263 Dissociation potential, 263, 269 Dissociative recombination, 270 Disturbances, extratropical, aerology of, 599; see Cyclones

Divergence, and pressure change, 643 direct measurement, 639 distribution of, theory of, 642 effects of, 643 influence of scale on, 639 large-scale, distribution of, 641

elec-

trical charges, 132

Dry

ice, cloud modification by, 229 Dust, albedo, 26

effect in scattering solar radiation, 23 volcanic, effect on skylight polarization, 79

Dust counter, Aitken, 165 Dust devils, 679 Dust particles, measurement, 148 Dynamic forecasting see Forecasting, djmamic Dynamic instability, see also Hydrodynamic instability, 584

E Eady, baroclinic wave studies, 459 Earth, albedo, 27, 31 meteorological parameters, 392 shadow, 73 surface, albedo of, 27 heat exchange at, 50 Ebert ion counter, 147

Eddy

diffusion, 321, 501 horizontal coefficients, 330 in microclimate, 996

Electric charge separation, 116 Electric current, air -earth, 113 density, over thunderheads, 114 Electric field, and droplet size, 133 atmosphere, measurement, 148 effect

on

electrical conductivity of air,

104

atmosphere in

weather, 107 Electrical apparatus, protection against of

fair

lightning, 142 Electrical charges, by adhesion, 1134 free, importance of droplet size in, 132 on individual droplets, 130 observed on precipitation, 128

separation of, 132 Electrical conductivity, of air, 102 variations, 103

supply current and thunderstorms, 113 universal aspects, 101 vertical current, measurement, 149 precipitation, 128 in cloud elements, 130 in continuous rain, 129 in electrical storm rain, 129 in snow, 129 in squall rain, 129 in thunderstorms, 129 practical problems, 128 thunderstorm, cloud structure and, 687 current, 150 field, 150 investigations of, 150 lightning discharges, 150 precipitation charge, 150 radio interference, 150 Electrification, of aircraft flying precipitation, 133 Electrode effect, 108

through

types, 144 use in measuring atmospheric electricity, 144 Electron affinity, 263 Electron volt, 264 Electronic configuration, 263 Electrostatic cgs system, 144 Electrostatic charges, of condensation nuclei, 187 Electrostatic induction, discharge, measurement, 148 Elsasser's diagram, 37 Emanometers, types, 156

Emanometrical measurements, diagram for, 156 Emanometry, 155

circuit

correction of alpha rays, 156 effect of atmospheric pressure and temperature, 156 saturation correction, 156 time correction, 156 Emission-spectral evidence, upper atmosphere composition, 271 Emission spectrum, 264

Emitting

layers,

upper

Energy laws, basic, 485 Energy levels, 263 Energy principles, application

atmosphere,

heights of, 271

Empire State Building, lightning

Energy transformations,

in latent form of water vapor, exchange rate of, 1061 kinetic, law of, 484 potential, conversion to kinetic energy, 458

in the atm.os-

phere, 490 over oceans, 1057 Energy units, 264

Entrainment

of air by clouds, 202, 695 in thunderstorms, 683

Eocene age, climate, 1004 Equations, energy see Energy equations Eulerian, use in dynamic forecasting, 480 Equatorial front, 865 Equatorial meteorology, 881 air masses, 881 equations of motion, 883 forecasting, 885 frontal phenomena, 882 Escape, cone of, 247

Eulerian equations, 405 use in dynamic forecasting, 480 Eulerian sj'stem, perturbation equations, 407

Evaporation at cloud edges, 200 Evaporation, at sea, direct measurements, 1071 history, 1071 detailed study, 505 determining, 1049

on supercooled clouds, 228

factor in hydrology, from oceans, 1071

Bowen

1049

ratio, 1058, 1073

computed from energy considerations, 1073

computed from meteorological

theoretical considerations, 1075 by extrapolations of values from land, 1071 energy available for, 1073 from rough surfaces, theoretical considerations, 1077 of cloud droplets, 204 Evaporation factor, as function of wind velocity, 1078 from climatic data, 1079 from meteorological observations, 1078 Evaporation rates, at various latitudes, 1072 Eve number, 146 Excitation by collision, 267 Excitation energies, 263 Excitation potentials, 263 Excited states, 263 Exosphere, 247 Expansion wave, and pressure jump, interaction between, 428 storm, 432

determined

monochroatmosphere, Exponential matic absorption, 265 Extratropical cyclones see Cyclones, extratropical

Eye, human, light-distinguishing properties, 93 visual range, calculation, 93 hurricane, dynamical aspects, 907 thermal structure, 905 tropical cyclones, 891

total, global balance, 572

basic equations, 572 transmission of, by means of finite disturbances in inversion height, 429 Energy change, 483 Energy equations, 483 applications of, 489 basic, 486 for averaged properties, 488 in barotropic atmosphere, 462 stress values, 490

ele-

ments, 1074

dis-

charges to, 139 Energy, concept of, 483

to general

circulation, 568

effect

Electrograms, 109 Electromagnetic cgs system, 144 Electromagnetic fields, forced diffusion and, 323 Electrometer, circuits, 144

Dobson spectrophotometer, 276 Doldrums, air motion, 862 Droplet size, electric field and, 133 importance in separation of free

Electrical potential gradient of air, 108 Electrical properties of snow, 227 Electricity, atmospheric, 128 instruments for measuring, 144 dielectric materials used in, 144 measurement, 150 measuring equipment, auxiliary, 144 methods for measurement of, 144 outstanding problems, 118 present-day research, 150 space charge, measurement of, 149

Faculae, 379 Fallstreifen, appearance of, 192 trails,

shape, 196

Fata Morgana, 66 Feather-like frost, 207

"Fido," 178 method, 149 Fire -danger meters, 988 Fire day, 988 Fire weather, 988 Filter

Fireballs, 356

—

—

INDEX Fj0rtoft,

baroclinic

wave

studies

by,

459

Flame collector, 148 Flocculi, 379 Flood routing, 1051 storage routing, 1051 Flood water run-off, applied climatology and, 987

Flow,

steady-state,

under

inversion,

equations for, 430 time-dependent, as forecast tool, 430

under an inversion, 424 two-dimensional steady, 431 under an inversion, 424 effect of Coriolis force on, 432

Forecast problem, 731 essential nature, 732 failure to assess, 731 scope, 732

Forecast terminology, 842 Forecast verification, 841

adjustment for

difficulty, 846 contingency-table summaries, 843 control forecasts, 846 correlations, 845 forecast -reversal test, 847 methods, 843 percentage correct, 844 pitfalls, 847 probability statements, 845

Flow patterns, midtroposphere, progno-

problem

810 Fluid currents, incompressible, perturbations in, 412 Fluid motion, baroclinic instability in, 468 centrifugal instability in, 467 generalized vertical-overturning instability, 468 gravitational -centrifugal instability in, 467 gravitational instability, 467 Helmholtz instability and, 468 instability, general theory of, 466 Foehn, 667 clouds associated with, 667 desirable studies, 671 development, 668 free, 668 high, 668 islands, 668 north, 668 nose, 667 pauses, 669 south, 667 thermodynamic explanation, 667 Fog, 1179 advection-radiation, 1184 forecasting, 1186 advective marine, drop size, 170 air-mass, 1183 artificial dissipation, 178 classification, 1183 clearing, forecasting, 1187 cold front, 1184 definition, 1179

purposes, 841 administrative, 841

sis,

dissipation, artificial, economics of, 178 effect of atmospheric pollution on, 1148

forecasting methods, 1185 formation, 1179 drop-size distribution, 1180 liquid-water content, 1180 over snow cover, 1181 physical processes, 1181 research needed, 1182 role of condensation nuclei, 1179 frontal, 1183

land- and sea-breeze, 1183 liquid-water content, relation between visibility and, 1180 mixing-radiation, forecasting, 1187 postfrontal, 1184

pre-warmfrontal, forecasting, 1187 restricted heating, 1185 radiation, 1184 drop size, 170 forecasting, 1185 graph, 1185 sea, cloud drop-size-distribution 173 forecasting, 1185 smog, 1179 smoke, 1179 steam, 1183 synoptic aspects, 1183 upslope, 1183 Fogbow, 70 Forecast districts, 768

in,

of, 841

economic, 841 scientific, 842

selection, 843 research needed, 847 root-mean-square-error, 844 scores, arbitrary, for special purposes,

846 scoring, 843, 844

Forecasters,

demand

for, 731

selection, 743 training, 743 Forecasting see also Forecasts aids, 733 air mass modifications, 779 air current modifications, 779 aircraft icing, 793

conditions, 1201

analogue, 738 anticyclogenesis, 770 anticyclones and, 626, 778 approach, 744 area forecast, 767 by statistical methods, 849 cold air -mass hydrometeors, 789 continental factors, 739 cyclones, 778 cyclogenesis, 770, 1175 diffusion conditions in atmospheric pollution, 1151 dynamic, advective models and, 471 by numerical process, 470 computational stability, 477 frictional effects, 482 geostrophic approximation and, .470 linearized barotropic model, 474 nonadiabatic effects, 482 nonlinear barotropic equation, integration of, 478 objective analysis, 479 use of primitive equations, 480 equatorial, 885 extended-range, 802, 814 by weather types, 834 research needed, 840 critique of methods of, 828 definition, 802 interaction on a hemispheric basis, 838 relationship between circulation and weather, 809 research needed, 812 scientific bases, 814 techniques, common factors in, 834 extrapolation, computational techniques, 738 mathematical techniques, 738 techniques, 734 fog, 1185 front modifications, 779 frontal occlusion, 778 frontal weather, 650 frontogenesis, 770 hydrometeors, general, 788 warm air-mass, 789 forecasting needed, improvements techniques standardization, 741

1323 Forecasting

continued

improvements needed -continued recommendations for, 740 technical, 740

weather observations, 741 linear extrapolation, 736 long-range, 831 extrapolation of periods, 831 extrapolation techniques, 734 multiple correlation tables, 831 regression equations, 831

symmetry

points, 831

synoptic extrapolation, 737 synoptic-statistical techniques, 811 mathematical, 470 medium-range, circulation, physical methods in, 806 upper waves, 806 French methods, 804 mean-circulation methods, 829 methods, 804 method of singularities, 804 methods, analogue, 806 weather type, 806 problems, 802 sea-level pressure distribution, 828 statistical methods, 804 symmetry-point technique, 806 midtroposphere flow patterns, 810 movement of sea-level pressure systems, 776 objective, 796 and applied climatology, 986 combined deductive-empirical methods, 799 investigation goals, 796 limitations, 797 methods of deriving aids, 799 numerical calculation, 798 problems, 796 research needed, 850 statistical methods, 798 testing procedures, 850 types, 798 ocean waves, 1082 oceanographic factors, 740 of various weather constituents, 787 phj-sical factors, 739 physical techniques, 739 practical, general principles, 766 problems, 731 projecting centers of action, 811 regional vs. global approach, 744 river see also River forecasting river, 1048

Rossby's vorticity technique, 739 scientific, problem of, 744 short-range, 747 a procedure of, 766 aids, objective, 762 analogues, 737, 750 basic surface chart, 749 charts and graphs, 748 cloudiness, 760 clouds, 753

constant-pressure charts, 749, 751

movement, 752, 1171 empirical forecast rules tests, 762 fog, 761 climatological -statistical, guides, 762 main centers of action, influence, 759 700-mb chart, preparation, 753 700-mb prognosis, operations in making, 754 observations, 748 organization of, 762 physical techniques, 739 pilot-balloon charts, 748, 753 precipitation, 760, 7;)0, 1168 preforeoast study, 758 present state, 747 cj'clone

——

—

INDEX

1324 Forecasting continued short-range continued pressure-change and other auxiliary charts, 749 pressure charts, 749 problem, 747 processing observational data, 748 prognostic chart preparation, 753 radiosonde diagrams, 750 research needed, 763 snow-on-the-ground chart, 749 statistical aids, 762 steps in, 758

recommended by Petterasen, 759 surface prognostic chart, preparation, 756, 769 temperature, 761, 788 temperature charts, 749 thermodynamic diagrams, 748 tj'pe studies, 750 use of surface data, 749 use of upper-air data, 750 usefulness of various charts, 760 usefulness of various techniques, 760 steps

verification, 762, 841

weather prognosis, 760 wind, 761, 791 zonal index graph, 749 short-term, clouds in, 1167 solar control, 740 statistical, research needed, 852 statistical method, application, 849 statistical techniques of extrapolation, 734

storm swell significance in cyclones, 899 _

storm tide significance in

cyclones,

900 synoptic cloud data as aid in, 1173 synoptic cj'cle, 766 synoptic techniques of extrapolation, 735 techniques, 731, 733 analogues, 737 extrapolation, potentialities, 737 lag-correlation, 734 linear extrapolation, 736 need for standardization, 741 performance, 732 physical, 739 present practice, 732 synoptic extrapolation, 735 thunderstorm, 690, 1170 tools, 731

tornadoes, 678, 792 tropical cyclone movement, 897, 911 unsatisfactory progress, reasons for, 731 upper-air map prognosis, 780 use of clouds in, 1167 use of microseisms in, 1312 use of radar in, 1279 use of sferics in, 1299

use of stationary time series use of surface map in, 769

in,

850

vertical velocities as tool for, 645 771 weather see also Forecasting

wave formation,

weather system movement, dynamical approach, 849 statistical approach, 849 weather-type approach, 835 wind, 791 Forecasts, accuracy of, 769 area, 767

chance, 846 climatological, 846 daily, extended, 733 range, 733 extension to longer periods, 811 general, 767 local, 767

long-range, 733

Forecasts

-continued

medium-range, analogue methods, 828 combination of synoptics and statis828 persistence, 846 precipitation, contingency table for, 844 short-range, 732 time range, 732 types, 732 verification, 841 Forest fires, and applied climatology, 988 Forest tundra, 953 Forest-tundra ecotone, 953, 957 Forestry, and microclimate, 1000 tics,

Fork lightning, 141 Formaldehyde, atmospheric, determining, 1131

Fragmentation nuclei,

effect

on snow

formation, 226 Free-electron density, 334

Freeman waves,

in tropical meteorology,

870 Freezing nuclei, 174, 192 effect on snow formation, 224 Frictional effects, dynamic forecasting and, 482 Fringe region, 247

Front,

cold, 1271

radarscope

photographs,

equatorial, 865

occluded, radar pictures, 1274 warm, radar pictures, 1272 Frontal occlusion, 778 Frontal phenomena, intertropical, 882 intertropical convergence zone, 882 meridional, 882 tropical, 882 Frontal precipitation, radarscope photographs, 1271 Frontal strip, 770 Frontal theory, modifications, 867 tropical meteorologv, 866 Frontogenesis, 432, 590, 770 profile through, 593 Frontolysis, 780 Fronts, modifications, forecasting, 779 Frost, amorphous, 207 crystalline, 207, see also Crystalline frost

-point determination, in lower stratosphere, 313 -point hygrometer, design of, 312 protection, applied microclimatology and, 999

window

see

Window

Fulchronograph, lightning 150

frost measurement of in characteristics, 142,

Gas chemistry, general principles, 263 Gas diffusion in atmosphere see Diffusion Gas particles, kinetic energy of, 268 Gas reactions, condensation nuclei formation from, 186 Gases, atmospheric, escape, 246 General circulation, see Circulation, general Geographic cycles, 1012 Geographical location, effect on land and sea breezes, 658 Geohydrology, 1048 Geological temperature variations, 1017 Geomagnetic lunar tide, 521 Geostrophic approximation, dynamic forecasting and, 470 Geostrophic current, inertial oscillations of, 440 Geostrophic motion, general conditions for stability of, 437 law of, 435 stability of, 434

Geostrophic zonal wind speed, 555 Gerdien aspirator, 147 Gewiiter, electrical characteristics, 128 Glacial periods, climate during, 1004 Glacial sequence. Quaternary Ice Age, 1005 Glaciation, effect of solar radiation variation on, 1010 maximum, climatic conditions in, 381 Glacier research, climatic implications, 1019 Glaciers, as climatic indicators, 1019 research needed, 1022 changes, causes of, 1019 correlation with climatic change,

1020

nature of, 1019 since beginning of Christian era, 1020 within Pleistocene epoch, 1021 within recorded time, 1020 Wisconsin maximum, 1020 Glare, effect on vision, 1119 Glory, 71 Gondwanaland, 1014 Gowan, calculations of equilibrium temperature in ozone layer, 298 Gram-atom, 263 Gram-molecule, 263 Granules, 379 Graupel formation, 205 Gravitational instability, in fluid motion, 467 Green flash, 65 Green segment, 65 Greenland, climatological problems, 961 glacial anticyclone, 961 Hobbs' theory, 961 ice cap, alimentation, 962 radial wind system, 962 wind and weather regime, 961 Grinders, see Sferics Grossturbulenz, 502 Grosswetter, 814 consecutive weather anomalies, correlations between, 817 cosmic influences on, 819 effect of ice conditions, 815 effect of long waves on, 817 effect of moon, 819 effect of ocean currents, 815 of fluctuations of periodic effect climate, 817 effect of planets, 819 effect of polar motion, 816 effect of pressure waves, 816 effect of solar radiation, 820 effect of sunspot cycles, 819 effect of volcanic eruptions, 815 existence of, 814 governing complexes, 815 morphology, 822 problem of rhythms, 816 terrestrial influences, 815 Grosswetterlagen, 803 annual variation, 828 European types, 825 Northern Hemisphere types, 826 types of, 825 Ground, radon exhalation from, 158

Ground Ground

inversions, effect on effective terrestrial radiation, 39 reflection, effect on Arago point,

82 effect

on skylight polarization, 85

Ground Ground

state, 263 wires, use in lightning protection, 142 Grounding, of electrostatic instruments,

145

Hail, growth, physics Hail insurance, 981

of,

178

——

INDEX Hailstorms, effect of cloud seeding on, 232 Half-life, 267 Halo phenomena, genetic features, 70 schematic view, 69 Halos, before rain, 1168 Harmonic analysis, generalized, use in times-series prediction, 851

Haze, 1179 radiation by, 42 Haze content, effect on downcoming radiation, 40 Heat, radiation to space, 42 Heat conduction, at cloud edges, 200 in interior of cloud, 200 Heat conductivity, of different materials, 1116 Heat exchange, at Earth's surface, 50 Heat flux, due to atmospheric turbulence, 536 equation, 506 Heat gain, of atmosphere, through convection, 1065

Heat Heat

from ocean, through con-

vection, 1064 Heating, radiational, of stratosphere, 47 Heating degree days, 983 Height, absolute, 772 relative, 772

associated with transisobaric motion, 783 local changes associated with diabatic processes, 784 Heiligenschein, 71

Helium, content of atmosphere, 5 isotopic variation in atmosphere, 8 Helium escape, problem of, 247 Helmholtz instability, fluid motion and,

144

Hoar

crystals, 208 Hobbs' theory of glacial 942, 943, 961

anticyclone,

Hochtroposhare, 287 Horizon, looming, 66 sinking, 66

Horse latitudes, air motion, 862 Housing design, and applied climatology, 982

Hudson Bay,

freeze-up, 959 bioclimatology see Bioclimato-

human

Humidity, and temperature patterns, small-scale, in free air, 318 effect effect

work on, 421 Hydrodynamic equations, 404 atmospheric flow, 454

boundary conditions, 406 physical, 403 sj^stems of, 403 Hydrodynamic equilibrium, 446

Hydrodynamic instability, 434 and theory of atmospheric perturbations, 444 as function of latitude, 438 cyclogenesis in extratropical latitudes

and, 442 in lower latitudes, 440 quadratic form of Kleinschmidt, 437

phere, 8

Hydrogen content of atmosphere, 6 Hydrogen lines, in spectrum of aurorae, 351

Hydrogen

sulfide, atmospheric, determining, 1127 Hydrologic cycle, relation to meteor-

ology, 1048

schematic diagram, 1049 Hydrology, design problems and, 1050 evaporation factor, 1049 fields, 1048 precipitation factor, 1048 relation to meteorology, 1048 snow factor, 1050

data, 1033

Heterostatic circuit, for electrometers,

logy,

steering principle, 911

radarscope photographs, 1275 Hydration order, importance for mode of charging nuclei, 1133 Hydraulic jumps, in atmosphere, early

Hydrometeorology, depth-duration-area

468

Helmholtz waves, 469

Human

continued continued steering method, 910

movement

Hydrogen, isotopic variation, in atmos-

lightning, 141 loss,

Hurricanes

on condensation, 169 on electrostatic charge

of condensation nuclei, 188 effect on growth of condensation nuclei, 184

on growth of various nuclei, 185 in thunderstorm, 686 effect

at tropopause, 315

measurement by aircraft, 1225 measurement, future research, 319 Humidity field, turbulent air flow, 499

Humphrey's volcanic dust theory, Hurricane rings, characteristics, 432 Hurricane tide, 892 Hurricane wave, 892 Hurricanes, formation, 907 see also Tropical cyclones, convection theorjf, 907 frontal theory, 908 hypothesis of Riehl, 909 hypothesis of Sawyer, 909 synoptic conditions during, 908 frontal analyses, 866 movement, 910 recurvature. 911

1015

empiricism and theory, 1034 future of, 1045 in United States, 1033 moisture, equations of, 1037 physical background, 1034 precipitable water, 1035 rainfall, nonorographic, 1039 orographic, 1038 recurrence interval, 1043 seasonal distribution, 1043 space distribution, 1042 storage equation, 1037 time distribution, 1042 rainfall depth, 1033 rainfall intensity, 1033 rainfall probabilities, 1042 rainfall volume, 1033 research needed, 1046

wind tides and waves, 1045 scope, 1033 snow melt, 1044 special problems, 1042 vertical motion, 1037 water resources, estimating, 1045 Hydrometeors, cold air-mass, forecasting, 789 general, forecasting, 788 warm air-mass, forecasting, 789 Hygrometer, frost-point, design of, 312 Hypsography, relative, 773 geometrical extrapolation, 780 prognosis by advective-adiabatic extrapolation, 782 prognosis by nonadvective and diabatic extrapolation, 784 reservoirs,

Ice ages, climate during, 1004 early, climate during, 1006 Ice caps, polar, effect in climatic changes, 1014

1325 Ice clouds, appearance of, 192 growth, 197 physics of, 192 relation to condensation mechanisms, 197 Ice conditions, effect on Grosswetter, 815 Ice crystals, formation, 207 by sublimation, 207 physics, 177 in cirrus clouds, 222 size, aircraft measurement, 1229 Ice fogs, 193, 1183 Ice nuclei, behavior of, 192 concentration, 224 effect of expansion-chamber experiments on, 193 effect of temperaiure on, 192 foreign-particle, temperature dependence, 224 in high-level clouds, 196 in medium-level clouds, 196 in upper troposphere, 193 spectrum, 193 Ice particles, charging, 1134 collision, 116 Ice phase, development in clouds, 194 Ice splinters, rate of formation, 195 Icing, aircraft see Aircraft icing -rate meter, 1227 Idiostatic circuit, for electrometers, 144 Impact-chemistry, 262 Index cycle, 560, 561 circulation patterns, 560 primary, 561 variations, 561 winter's primary, 561 Indian summer anticyclones, 626 Industry, and microclimatology, 1001 Infrared absorption, pressure effects on, 298

Infrared light, 265 Infrared spectra, of ozone, 296 Insects, exchange between earth and atmosphere, 1107 Instability, dynamic, 584 centrifugal, 467 energy, 436 gravitational, 467 hydrodynamic, 434 Instability lines, 647; see aiso Squall lines and airline operations, 647 and cyclonic wind shear, 649 and pressure gradient, 649 and pseudo-cold front, 650 and thunderstorms, 689 and tornadoes, 647, 651 associated physical factors, 648 cyclone with, 648 general features, 647 physical processes, 650 future research needed, 652 recent studies, 651 synoptic aspects, 648 Thunderstorm Project, 652 Instruments see Meteorological instru-

ments Insulation, wood, use in lightning protection, 142 Insulator, open-air, 145 Inversion, compression waves under, 425 expansion waves under, 425 flow, time-dependent under an, 424 flow under, 424 height, transmission of energy by

means of finite disturbances in, 429 simple waves under, 425 steady-state flow equations under. 43C Iodine, atmospheric, 1128 effect on condensation nuclei forma tion, 186 Ion-capture, 116 Ion clouds, 255

—

INDEX

1326 Jet stream

Ion counter, Ebert, 147 Ion production, measurement, 146 Ion spectrum, measurement of, 147 Ionic equilibrium relation, 103 Ionic mobilities, 120 Ionization, air over earth's surface, 122 meteoric, 257 of air, 102 rate, 121

Ionization energy, 263 Ionization potential, 263, 269 Ionizers, of the atmosphere, 146 Ionosphere, 250, 334 absorption of solar radiation by, 19 aurorae and, 352 D-region, 337 E-layer, during auroral displays, 353 normal, 337 sporadic, 337 Es-region, 337 electrical conductivity of air in, 106 elementary concepts, 335 Fi-region,'337 Fi-layer during auroral displays, 353 Fz-region, 338 G-region, 338 formation mechanisms, 340 ionization, probable distribution of, 336 layers, rise

and

fall,

effect of

atmos-

pheric tides on, 520 methods for studying, 334 principal regions, 335 relations between surface meteorology and, 339 research needed, 340 temperatures, 339 typical data, 335 Ionospheric data, need for more, 257 Ions, atmospheric, problems in field of, 126

chemical adsorption, 130 concentration, atmospheric, measurement, 146 in lower atmosphere, 124 positive to negative ratio, 125 variation with height, 125 cosmic radiation and, 103 formation, rates of, measurements, 147 in atmosphere, 120 large, balance, 123

mean

life,

Lightning,

continued

125

measurement, 147 mobility, atmospheric, measurement, 146 mobility values, 121 recombination, measurement, 147 slow, nature of, 121 small, balance, 122 combination coefficients, 122

combination

with

condensation

nuclei, 123

recombination

of, 123

applied microartificial, Irrigation, climatology and, 999 Isentropio charts, use in meteorological analysis, 725 Isentropic convergence, 586 Isentropic divergence, 586 Isentropic shear, anticyclonic, 586 Isentropic surfaces, dynamic instability, 584 inertial motion in, 583 Isentropio upgliding, 592 Isohypses, absolute, 772 relative, 770 total relative, 772 Isotopes, 263 Israel ion counter, 147

Jet stream, circulation, variations, 560 in upper troposphere, 604

of circumpolar vortex, 560

planetary, blocking waves in, 432 position and strength, 553 variations, 560 Jupiter, atmosphere, 394 research needed, 397 meteorological parameters, 392 Red Spot, 395, 397 spot periods, distribution, 396 Jurassic age, climate, 1004

Kaltlufttropfen, formation, 560, 616, 717 Karandikar, calculations of heating of ozone layer, 299 Katafront, 771 Katallobaric system, 635

Kelvin, theory of atmospheric oscillations, 523 Kern counters, 165, 182 Kibel's method, advective models, 473 Kinetic energy, balance fluctuations, 546 change, 467 dissipation, 571

equation

of,

484

global balance, 568 a simple system, 569 equations for the atmosphere, 570 general considerations, 568 of gas particles, 268 of horizontal motions, transfer, 571

Kleinschmidt, quadratic form, 437 coordinate system, direction cosines 437 Kolmogoroif 's theory, turbulent air flow, 497 Kryophilic surfaces, 225 Kryophobic surfaces, 225 Krypton content of atmosphere, 5 for,

Laboratory investigations, motions, 1235

cloud-to-cloud, 139 cloud-to-ground, phenomena on ground end, 139 composite stroke, 140 continuous current with, 138 current peaks, 139 density, 141

forms

of, 141 investigations, 150 ionization process, 136 leaders, 136 mechanism, 136 cloud to ground, 137 multiple stroke, 138 polarity, 141 potential involved in, 138 protection against, 142 radarscope photograph, 1276 return stroke, 137 stroke current, 139 stroke mechanism for high buildings, 138 total charge, 140 wave shape of current peaks, 140 Lightning protection, 142

Lightning stroke see Lightning discharge Limnology, 1048 Line spectra, 265 Liquid-water content, measurement by aircraft, 1226

Long-wave radiation see Radiation, longwave Long waves, upper and cyclones, 605 Looming, 66 Loschmidt's number, 263

atmospheric

cold fronts, 1238 cyclone systems, 1238 cyclones, 1236 experimental cloud formation, 1255 general circulation, 1240 model techniques, 1249 research needed, 1242 rotating-pan experiments, 1244 spherical shell experiments, 1241 thermal convection, 1239 tornadoes, 1236 Lagrangian equations, 405

Lagrangian system, perturbation equations, 408 perturbations in incompressible fluid currents, 412 Land breezes see Breezes, land and sea Landregen, electrical characteristics, 128 Laplace, theory of atmospheric oscillations, 523 Large-ion balance, 123 Layers, double, electrical waterfall effect,

M Mach

lines,

422

Macrometeorology, basic problems, 814 Macroviscosity, in air flow, 496

Magnetic

link, in

measurement

of light-

ning characteristics, 141 Magnetic storms, aurorae and, 347, 352 Magnetic variations, use in studying upper atmosphere, 251 Maloja wind, 664 Map analysis, pressure jump and, 429 Mars, atmosphere, 392 research needed, 397 meteorological parameters, 392 temperature distribution, 393 winds on, 393 Mean-circulation methods of forecasting,

Mean

809, 829 free path, 268

Melting processes, 205 Meridional circulation, idealized, 456 Meridional indices, 564 Meridional variations, of total ozone, 331

Meteor (s), acceleration formula, 359

131

phenomena,

characteristics, measureof, 141 Lightning arrester, for protection of electrical apparatus, 142 Lightning discharge, 136 branching, 136 channel, 138 characteristics of, 140 charge determination, 140

ments

normal characteristics, 553

Israel, 147

effect of

water purity

on, 131 electrical double, 130 Leaders, 136 characteristic data, 100 continuous, 136 dart, 136 mechanism, 138 Lichtenberg figure, in measurement of lightning characteristics, 141 Light, absorption, 264 behavior in atmosphere, 91 emission, 264 rays, dispersion by atmosphere, 67 scattering, in the atmosphere, 76

astronomical background, 358 atmospheric research, 357 based on observation of, 357 atmospheric temperatures and, 306 deceleration, air density from, 360 data, 361 radio measurement, 363 heights, 357 ion cap, 363 ion trail, earth's magnetic field and, 383 mass determination, 360 mass loss rate, 359 photographic observation, 358 methods, 358

— INDEX Meteor(s) conlinued radio observations, 362 showers, 356 radiants, radar observation, 362 spectra, 357 sporadic, 356

stream velocities, radar observation, 363 streams, 356 study, continuous-wave method, 363 Doppler method, 363 whistling meteor method, 363 terminology, 356 trails, radio echoes from, 257 trains, winds and, 358 upper atmosphere research and, 356 visual observations, 357 Meteoric phenomena, use in studying upper atmosphere, 251 Meteoric process, theory of, 359 Meteorite, 356 Meteoroid, 356 Meteorological analysis, 715 centers, 716 coordination of sea-level and upperair, 720 differential technique, 718 frontal technique, 715 isentropic, 725 moisture charts in, 725 prefrontal squall line, 716 radiosondes and, 726 techniques, 715 transmission, 715 upper air, 717 upper-air technique, 715 use of charts in, 721 use of radar, 717 Meteorological balloons see Balloons Meteorological instruments, 1207 aircraft, 1223 cloud and raindrop size, 1228 humidity measurement, 1225 liquid-water content measurement, 1226 pressure measurements, 1225 special research, 1228 snowfiake and ice-crystal size measurement, 1229 temperature measurement, 1223 wind velocity measurement, 1226 altitude measurements, 1226

automatic weather stations, 1217 balloons, 1214 ceilometers, 1218 parachute radiosondes, 1215 radar -wind systems, 1213 radarsonde systems, 1213

radiosonde-radiowind systems, 1207 techniques, 1207 wire sondes, 1216 general trends, 1219 Meteorological optics, general, 61 Meteorological organization, international, need for, 745 Meteorological problems, nonlinear, method of characteristics, 421 Meteorological recorder, 1213 Meteorological research, model techniques, 1249 Meteorological stations, actinometric equipment, 53 Meteorological tool, ocean waves as, 1090 Meteorology, and river forecasting, 1053 Arctic, 942 cosmical, 377 dynamic, problem of, 401 equatorial see Equatorial meteorology and Tropical meteorology experimental, development, 229 recent advances, 229 relationship of snow to, 221 marine, 1055

perturbation equations in, 401 polar, 915 of open systems, ap-

thermodynamics

plication to, 531 tropical see Tropical meteorology visibility in, 91 Meteorotropism, 1120 Methane content of atmosphere, 5 future developments, 9 Michelson actinometer, 53 Microbarographs, 370

Microclimate, 993 as climate near ground, 994 contour, 997 dependent, 997 eddy diffusion, 996 effect of type of ground, 995 forestry and, 1000 in vegetation layer, 998 independent, 997 moisture conditions, 995 temperature conditions, 994 wind conditions, 996 Microclimatological research, history, 993 origin, 993 Microclimatology, 993 agriculture and, 998 applications, 998 applied, artificial irrigation and, 999 frost protection and, 999 future problems, 998 in city planning, 1001 industry and, 1001 phenolog}' and, 1000 present state of research, 994 research, methodology of, 1001 wind protection and, 999 Microorganisms, counts, 1109 in clouds, 1109 Microseismic storm, 1312 Microseisms, application to forecasting, 1312 causes, 1303, 1314 effect of differences in earth crust on, 1308 effect of distance on period, 1308 effect of earth faults on, 1308 effect of ground on, 1309 energy transmitted from surf, 1305 in tropical cj'clones, 900 observations, 1303 periods of pressure waves in the ocean, theoretical, 1307 research needed, 1310 short-period, 1315 storm, 1313 theory of, 1303 theory of elastic wave propagation in the ground, 1307 theory of wave propagation from surface of ocean to bottom, 1306

theory of wave propagation from water to solid rook, 1306 transmission of energy from meteorological disturbances into the ground, 1304 tripartite studies, 1312

types, 1304 typical records, 1303

wave types observed in, 1307 Midtroposphere flow patterns, prognosis, 810

Mirages, 66 Mistral, 670

Mixing-length hypothesis, in turbulent air

flow, 494

Mixing processes, in clouds, 200 Moazagotl cloud, 669

Model techniques,

in meteorological research, 1249 prototype simulation, 1250 similitude requirements, 1249 typical laboratory investigations, 1251

1327

Mold

transport, in atmosphere, 1109 of, 1109 Moist-adiabatio process, prerequisites for ideal, 199 ascending motions, 201 descending motions, 201 Moisture adjustment, cyclonic-adjustment method, 1040 q-adjustment method, 1040

Molds, origin

thunderstorm-adjustment

method,

1040

Moisture, equations of continuity, 1037 Molecular diffusion, 320

Molecular forces, dipolar, 1132 dispersion, 1133 for condensation, 1132 induction, 1133 polar, 1132 Molecular particles, 263 see also Atomic particles Molecular processes, reversibility, 267 Molecular transitions, spectra associated

with, 264 Molecules, mean free path, 369 MoUer's diagram, 37 Momentum, total angular, conservation of, 460 Momentum-transport theorjr, 496 Monochromatic absorption, in exponential atmosphere, 265 Moon, effect on Grosswetter, 819 enlargement, when near horizon, 62

Mountain theory

building, and climate, 1013

of,

385

N Natural m-sec-v-amp system, 144 Needle circuit, for electrometers, 144 Needle frost, 207

Neon

content of atmosphere, 5 Nephelonieter, polar, 95 Neptune, atmosphere, 394 meteorological parameters, 392

Neutral points, measurement of position, 80

Newton, theory

of atmospheric oscillations, 523

Night-sky, aurora, 345 emissions, altitude, 344 further research needed, 345 intensity, 342 spectrum, 341 wave lengths in, 342 theory, 344 variations, 342 annual, 343 diurnal, 343 latitudinal, 343 twilight effects, 343 with zenith angle, 344 light, variation, 258 luminescence, use in studying upper atmosphere, 251 radiations, from upper atmosphere, 341 spectrum, need for more study, 258 zodiacal light, 345 Nitric acid, atmospheric, determining, 1127 determining, atmospheric, Nitrogen, 1131

bands, in spectrum of aurorae, temperature determination from, 351 content of atmosphere, 5 dioxide content of atmosphere, 7 oxides, effect on condensation nuclei formation, 186 Nitrous oxide content of atmosphere, 5 Noctilucent clouds, use in studying upper atmosphere, 251 Nocturnal cooling process, atmospheric radiation and, 40

Nonadiabatic

effects,

ing and, 482

dynamic

forecast-

INDEX

1328 Nonhomogeneous thermodynamics tem, 534 meteorological Nonlinear

method Nordenskjold

sys-

problems,

of characteristics, 421

line,

955

Ozone— continued in the atmosphere, 275 in undisturbed photochemical equilibrium, 281 infrared spectra, 296

293 radiation flux and, 286

Photopolarimeter, 79, 80 Photosphere, 379 Physical meteorology, 165 Piezotropy, equation of, 404

photochemistry total,

Nuclei, charging, ballo-electricity, 1134 by adhesion, 1134 mode of, order of hydration for, 1133 condensation see Condensation nuclei counters see Kern counters freezing see Freezing nuclei ice see Ice nuclei ice-particle charging, 1134 sublimation see Sublimation nuclei Numerical integration, by method of characteristics, 422 Numerical process, dynamic forecasting by, 470

Ocean

currents,

effect

on

in

climatic

Orossivetter, 815

Ocean waves, as a meteorological

tool,

1090

decay distance, 1082

energy

transformation

layer, 292

calculation of heating of, 296 cooling, 296 calculating, 296 data for calculating, 298

equilibrium temperature, Gowan's calculations of, 298 heating, 294 of,

over,

1011 Oscillations, free, in the atmosphere, 306

Oxygen, absorption, 294 absorption coefficients, 275 atomic, ozone and, 272 content, of atmosphere, future developments, 9 variations in atmosphere, 3, 933 isotopic composition, in atmosphere, 8 Ozone, absorption, 293, 294 absorption coefficients, 275 effect on, 283.

mass center, 281 amount, determination of, 276 altitude of

fluctuations, 278 in upper atmosphere, 278 atmospheric, determining, 1127 theory of, 281 atomic oxygen and, 272 bioclimatology and, 287 conditions in troposphere, 286 constitution of upper atmosphere and,

287 cooling effects, Penndorf's calculations, 299 distribution, effect on heating in ozone layer, 295 in ozone layer, 292 theoretical, 282 effect on condensation nuclei formation, 186 effect on radiation in stratosphere, 46 heating effects, Penndorf's calculations of, 299 height distribution, 262 in stratosphere, 284

of,

Planets, effect on Grosswetter, 819 major, atmospheres, 391 atmospheric circulation, 395 Plate crystal frost, 207 Pleistocene epoch, glacier changes in, 1021

Pluvial periods, 1006 Point collector, 148 Points, neutral, distances of in different colors, 86 Polar air, source region, 600 southern limit, 600 subsiding, in troposphere, 315 Polar trough, in tropical meteorology, 869 Polariscope, Savart, 81 Voss, 81 Polarity, of lightning discharges, 141 Polarization, anomalies during twilight, 87 atmospheric, dispersion of, 86 effects of scattering, 79 skylight, 79 at point of maximum elevation, 81 at zenith for different sun's elevations, 81

degree

Karandikar's calculation of heating

evaporation from, 1071 heat loss through convection, 1064 Open systems, thermodynamics, application to meteorology, 531 Optics, general meteorological, 61 Orbit, earth, effect on climatic change,

motion

305

Ozone

299

1057

air

geographic, 6

Ozone heating, in upper atmosphere,

and cooling, Craig's calculations

fetch, 1082 forecasting, 1082 state of sea, 1082

Oceans,

annual variations, 331

diurnal, 6

changes, 1014 effect

Photometry, photographic, 80

of,

meridional variations, 331 under conditions of disequilibrium, 283 variations with synoptic situation, 284 vertical distribution, 280 determination, 276 in the troposphere, 7 warm layer and, 287 weather and, 284 Ozone content, of atmosphere, 6 during depressions, 6 during thunderstorms, 7 future developments, 9 methods of determination, 6 variations, annual, 6

O Observation, weather see Weather observation Observations, data, processing, 748 Occlusion process, cyclonic circulation during, 610

of lightning characteristics, 142 Photography, of meteors, 358

Photolysis, 268

methods

Northwesterly flow, over Europe, 603 Nucleation, effect on supercooled clouds, 32-nuolei, 193

measurement

of observation, 275 of air strata near ground, 1129

Northers, 670

22S

Photochemistry, of ozone, 293 Photographic surge-current recorder, in

299

ozone distribution in, 292 radiative temperature changes

in,

292

screening effect, 287 solar effect on, 293 temperature changes, further research, needed, 300 temperature distribution in, 292 Ozonosphere, absorption of solar radiation by, 19 origin of high temperature in middle atmosphere, 253

research sequence, Palaeoclimatic needed, 1017 Palaeozoic ice age, climatic changes, 1014 Parasites see Sferics Parcel method, for testing atmospheric stability, 694 Particulate matter, diffusion of, 326 Peat bogs, formation, 1008 Penndorf, calculations of heating and cooling by ozone, 299 Permafrost distribution, 958 Perpendicular velocities, method of, 147 Perturbation equations, 407 Eulerian system, 407 for special coordinate systems, 409 in meteorology, 401 Lagrangian sj'Stem, 408 long waves on rotating globe, 416 long waves on rotating plane, 415 quasi-geostrophic approximations, 417 quasi-static approximations, 417 trough formula, 415 Perturbation method, use of, 411 Perturbations in incompressible fluid currents, 412 Perturbed particle motion, 435 Petterssen, steps in forecasting, 759 Phenology, microclimatology and, 1000 Photochemical processes, in upper at-

mosphere, 262

of, 84 deviations, 79 distribution, 81

effect of ground reflection on, 85 effect of volcanic dust, 79

fluctuations of, measurement, 80

magnitude, 81

maximum,

correlation between turbidity coefficient and, 84 measurement, 80 research needed, 88 theory of, 83 unsolved problems, 88 visual measurement, 80 Pollen, exchange between earth and atmosphere, 1107 Pollution, atmospheric, 1139 annual variations, 1147 basic equations, 1140 by domestic heating plants, 1151 by multiple sources, 1146 by single sources, 1140 climatologicai planning for industry, 1152 concentrations distant from the source, 1143 concentrations near the source, 1143 control, 1149 daily variations, 1147 Donora, 1147 effect of atmospheric stability, 1146 effect of rain on, 1147 effect of stack height, 1149 effect of stack temperature, 1149 effect of topography, 1147 effect of wind, 1146 effect

on

air,

electrical conductivity of

109

effect on fog, 1148 effects on meteorological elements,

1148

on rainfall, 1148 forecasting diffusion conditions, 1151 from elevated sources, 1142 future requirements, 1152 gases and vapors, 1139 effect

—

—

—

INDEX Pollution, atmospheric continued influence of topography, 1144 limitation, 1149 measurement, 1139 meteorological control, 1149 nuclear effluents, 1150 particulate matter, 1139 coagulation, 1145 deposition, 1145 present position, 1152 research needed, 1154 smog control, Los Angeles, 1150 types of contaminants, 1139 weekly variations, 1147 wind-tunnel investigations, 1145 Postglacial climatic changes, 1006 Postglacial rainfall, 1008 Postglacial succession in Europe, 1007 Potamology, 1048 Potential, involved in stroke formation, 138 Power-law profiles, in turbulence, 496 Precipitation, see also Rain, Rainfall aircraft flying through, electrification of, 133 air-mass, radarscope photographs, 1275 amount, forecasting, 760, 790 Antarctic, 933 continuous, radar detection, 1285 drop coalescence theory, 176 during a pressure jump, 427 electrical, association processes, 131 environmental processes, 131 electrification, basic processes, 130 factor in hydrology, 1048 free electrical charge on, 128 horizontal structure, radar detection, 1288 ice-crystal theory, 175 maximum possible, 1033 orographic, radar pictures, 1274 physics, 165 production of, as related to artificial cloud modification, 235 solid, from cumulus clouds, 223 in free atmosphere, 222 in stratus clouds, 223 types, 221 tropical cyclones, 890 Precipitation charge, in thunderstorms, 150 Precipitation electricity, see Electricity, Precipitation Precipitation proce,sses, 175 Precipitation static, 133 Pre-dissociation, 264 Prefrontal squall line, 427 in meteorological analysis, 716 Pre-ionization, 2a4 Pressure, at extreme altitudes, 308 atmospheric, measurement by rocket,

306 differences,

during

land

breezes, 657 distribution, during land breezes, 657 during pressure jump, 427 effect

on

and

sea

and

sea

electrical conductivity of air,

104

on infrared absorption, 298 function of, absorption coefficient as, 40 in thunderstorms, 685 in upper atmosphere, 303 effect

measurement by

aircraft, 1225

sea-level, and 700-mb, 554 Pressure changes, dynamic theory, 631 effect on condensation nuclei, 186 empirical evidence, 636 high-level, 636 high-level processes, 636 historical notes, 630 horizontal advection, 635 mechanism, 630

Pressure changes continued nonadiabatic temperature changes, 633 theories, 630 thermal theory, 631 633 vorticity studies, 633 Pressure gradient, and instability line, 649 Pressure jumps, 426 and expansion wave, interaction between, 428 and tornadoes, 431 lines, interaction between, 431 map analysis and, 429 weather associated with, 427 Pressure systems, mechanics of, 575 sea level see Sea-level pressure systems Pressure tendency equations, 632 utility, 632 Pressure waves, effect on Grosswetter, 816 use in studying upper atmosphere, 251 Pseudo-cold front, and instability line, 650 Pulse integrator, radar storm-echo sig,

nal, 1277

Pulse-packet technique, of radio observation of meteors, 362 Purple light, 73 areal extent, 76

associated with volcanic eruptions, 73 schematic diagram, 76 Pyranometers 55 Pyrgeometer, Angstrom, 55 Bellani, 55 Pyrheliometer, Angstrom compensation, 52 silver-disk, 52 ,

Quadrant circuit, for electrometers, 144 Quadrant electrometer, schematic diagram, 145 use in measuring atmospheric electricity, 144 Quantum relation, 264 Quasi-geostrophic approximations, 417 Quasi -geostrophic equation, simplification, 471 Quasi-linear differential equations, method of characteristics, 421 Quasi-static approximations, 417 Quaternary ice age, glacial sequence, 1005

R Radar, A scope, 1269 antenna gain effect, 1266 aperture of the parabola, effect, 1266

appearance dm-ing storms, 1271 attenuation factor, effect, 1268 bands, tropical cyclones, 891, 1275 beam width, effect, 1267 equipment development need, 1280 fraction of beam filled by storm, effect, 1268 measuring meteor shower radiants by, 362 measuring meteor stream velocities by, 363 plan position indicator scope, 1270 pulse length, effect, 1267

R

scope, 1270

range-height indicator scope, 1270 received power, effect, 1266 reflectivity per unit volume of storm region, effect, 1268

-scope

photographs, air-mass precip-

itation, 1275 bright band, 1273, front, cold, 1271

1286

warm, 1272 frontal precipitation, 1271 hurricane, 1275

1329 Radar

continued

instability showers, 1275 lightning', 1276 precipitation, patterns, 1274 thunderstorms, 1276 scopes, types, 1269

weather phenomena observation on, 1269

storm detection, background, 1265 bright band, 1286 continuous precipitation, 1285 factors, 1266 future, 1279

horizontal structure of precipitation, 1288 microwave attenuation, 1285 observation, 1283 precipitation growth, bright band and, 1286 refraction, 1284 showers, 1285 theory, 1266, 1283 observational verification, 1269 use in forecasting, 1279 storm-echo signal, analysis of, 1277 contouring, 1278 control of polarization, 1279 photography, 1279 pulse: integrator, 1277 spectrograph, 1278 storm observation, 1265 thunderstorm study, 688 transmitted power, effect, 1266 use in Cloud Physics Project, 236 use in meteorological analysis, 717 wave length, effect, 1267 Radarscope photography, 1279 Radarsonde systems, 1213 Radar-wind systems, 1213 Radiation, 11 atmospheric, effect of clouds on, 42 outgoing, 41 relative, scattering of, 38 by haze, 42 calculations, analytical, 45 numerical, 45 cloud, 42 de-excitation with, 267 diagrams, 36 according to Elsasser, 37 according to Moller, 37 diffuse, absorption laws, 35 downcoming, atmospheric, 38 absorption coefficient for, 40 effects, on human bioclimatology, 1118 flux, ozone and, 286 from spectral line, absorption laws, 35 in stratosphere, 46 long-wave, 34 absorption laws, 34 research needed, 47 monochromatic, law, 40 night-sky, from upper atmosphere, 34-1 of free atmosphere, and synoptic situations, 43 parallel, absorption laws, 34 processes, clouds and, 200 solar, effect of absorption, measurement, 50 effect of molecular scattering on, measurement of, 50 effect of varying distance between sun and earth on, measurement, 50 terrestrial, effective, effect of absorbers on, 39 effect of ground inversions on, 39 effect of temperature on, 39 Radiational influences, on cloud forms, 203

Radiative processes, heat transportation by, 465

Radio duct, wave trapping

in, 1293

—

— INDEX

1330 Radio exploration,

of

upper atmosphere,

254 Radio fade-out, 248

Radio interference, by thunderstorms, 150

Radio observation

of meteors, 362 technique, of meteors,

pulse-packet 362 Radio propagation problems, meteorological aspects, 1290 Radio refractive index, formula for, 1291 Radio sounding, of ionosphere, 336 Radio wave propagation, meteorological problem, 1294 Radio waves, in the atmosphere, refraction, 1290 reflections from aurorae, 354 superrefraction see Superrefraction use in studying upper atmosphere, 251 Radioactive collector, 148 Radioactive substances, in atmosphere, 165 Radioactivity, atmospheric, 155 measurement, 155 by emanometry, 155 by induction method, 157 Radiosonde, flight equipment, 1207 humidity measurement, 1209 pressure capsule, 1208 temperature measurement, 1209 transmitter, 1210 ground, wind measurement, 1211 ground equipment, 1211 measurement, of water vapor, 313 method of upper atmosphere exploration, 250 parachute, 1215 -radiowind systems, 1207 shortcomings in cloud observations,

199

Radon,

atmospheric,

decrease

with

height, 158 balance, of atmosphere, 158 content, atmospheric, 158 atmospheric, variations, 157 exhalation, of ground, 158 source, 155 Rain see also Precipitation cloud halos before, 1168 effect on atmospheric pollution, 1147 electrical storm, electrical characteristics, 129 insurance, 982 quiet, electrical characteristics, 129 shower or squall, electrical characteristics, 129 torrential, cloud seeding and, 232 Rainbow phenomena, 70

Raindrop

size,

aircraft

measurement,

1228

measurement, 177 Rainfall, see also Rain, Precipitation atmosphere clearance of organisms, 1107 depth, 1033 maximum, in United States, 1034 effect of atmospheric pollution on, 1148 in thunderstorms, 684 intensity, 1033 isohyetal maps, 1034 mass curves, 1034 nonorographic, 1039 JDarrier height adjustments, 1041 isobar-isotherm relationships, 1041 latitude adjustments, 1041 moisture adjustment, 1040 storm transposition, 1039 orographic, 1038

empirical approaches, 1038 spillover, 1039 theoretical barrier methods, 1038 postglacial, 1008 probabilities, 1042 recurrence interval, 1043

continued

Seeding, cloud

runoff, forecasting, 1052 distribution, 1052 seasonal distribution, 1043

effects effects effects effects effects

Rainfall

storage equation, 1037 tree histories, 1026 tree-ring Indices, 1024 volume, 1033 Rayleigh scattering, 25

Recombination spectrum, 271

Redox

value, determining, 1127 Refraction, astronomical, 64 phenomena due to atmospheric suspensions, 69 due to average density gradient, 64 due to special density gradients, 66 in cloud-free atmosphere, 64 radio waves, 1284, 1290 terrestrial, 65 Replica techniques, for studying snow, 221 Reservoirs, wind tides and waves, 1045 Resonance, 270 Resonance theory, atmospheric oscillations, 524 Return stroke, 136 characteristics of, 137 Reynolds stresses, 493 Ribbon lightning, 141 Richardson's criterion, 506 Richardson's diffusion theory, 505 Ringelmann chart, for measuring atmospheric pollution, 1140 Rip currents, 1083 River flow, tree histories, 1026 tree-ring indices, 1024 River forecasting, see also Hydrology River forecasting, 1048, 1051 flood routing, 1051 rainfall, runoff distribution, 1052 role of meteorology in, 1053 runoff from rainfall, 1052 service, organization, 1051 snow-melt, 1053 water supply, 1053 Road mirages, 995 Robitzsch actinograph, 54

Rocket measurements,

in upper atmos-

phere, 306

Saturn, atmosphere, 394 meteorological parameters, 392 Savart polariscope, 81 Scale domain, of nonturbulent variations, 487 Scattering in the atmosphere, 22, 76, 79 dust, 23 molecular, 22 multiple, 25 water vapor, 23 Schlieren, 67 Scintillation, 67

astronomical, 67

chromatic 67

mechanism

of intensity fluctuations,

67 terrestrial, 68

theories of, 68 Sea, breezes see Breezes, land and sea forecasting, 1083 ice, distribution, 958

Hudson Bay, 959 scope for research, 960 condensation nuclei, 166 surface, exchange of heat with atmosphere, 1057 Sea-level pressure distribution, forecasting, 828 Sedimentation, effect in nuclei destrucsalts, as

tion, 189

Seeding, cloud, effective, 230 effects, 230

on on on on on

continued

cumulus clouds, 239

hailstorms, 232 stratus clouds, 236 thunderstorms, 232 torrential rains, 232 elimination of supercooled clouds by, 232 increased precipitation from cumulus clouds with, 232 limitations, 231 overseeding, 230 possibilities, 231 relation to production of precipitation, 235 silver iodide, 231 use in studying atmosphere, 233

windstorms and, 232 Seismographs, 1313 Sf erics, 1297 direction of arrival, determining, 1297 frequency of occurrence, 1298 reception, 1297 relation to thunderstorms, 1298 research needed, 1299 source, 1297 use in forecasting, 1299 use in meteorology, 1298 Shadow bands, 67 Sheet frost, 208 Sheet lightning, 141

Shimmer, 68 Ships, weather, 707

weather observations from, 706 Showers, convective, data on, 699 instability, radarscope photographs, 1275

radar detection, 1285 summer, anticyclones and, 626 Silver iodide, cloud modification by, 230 use in cloud seeding, 231 Simpson's Ice Age theory, 386 Sinking, 66 Sizzles, see Sf erics

Sky, apparent shape, 61 theories concerning, 63 conditions, effect on apparent shape of sky, 61 shape, effect of cloud amount on, 61, 64 phenomena related to, 62 under various sky conditions, 61 synoptic types of, 1173 Sky light polarization, 79 see also Polarization, skylight Slice method, for testing atmospheric stability, 694 Small-ion balance, 122 Smog, 1179 Smoke, 1179 condensation nuclei formation in, 186 filter, for measuring atmospheric pollution, 1139 shell, use in studying upper atmosphere, 251 Snow, aircraft electrification from, 134 crystals, 209, 222, 223 artificial production, 213 in laboratory, 213 laboratory apparatus, 214 capped column, 212 classification, 209, 221 columnar crystals with extended side planes, 212 dendritic, with small plates attached, natural and artificial, 219 fern-like hexagonal, natural and artificial, 217 form, relation to external conditions, 214 upper-air conditions and, 217 formation, 177, 209, 223 growth, 215

— —

— INDEX

Snow

continued

crystals continued irregular assemblage of columns plates, 212 irregular snow particles, 213

and

malformed, 212

method

for taking photomicrographs, 209 natural and artificial, comparison between, 217 needle crystals, 212 practical classification, 213 principles of classification, 209 rimed crystal, 213 replica techniques for studying, 221 scientific classification, 212 spatial assemblage of radiating type, 212 natural and artificial, 219 spatial hexagonal type, 212 stellar crystal with plates at end of branches, natural and artificial, 217 studies, application to meteorology, 217 with irregular number of branches, 212 with twelve branches, 212 electrical characteristics, 129 electrical properties, 227 factor in hydrology, 1050 formation, effect of fragmentation nuclei on, 226 effect of freezing nuclei on, 224 effect of spontaneous nuclei on, 225 effect of sublimation nuclei on, 224 factors controlling, 223 physics, 177 melt, estimate, 1044 forecasting, 1053 relationship to experimental meteor-

ology, 221 size, aircraft

Snowfiake

measurement,

1229

Sodium, atmospheric, 272 chloride condensation nuclei, growth curves, 168 Soil bacteria, exchange between earth and atmosphere, 1106 Solar activit}', variable, nature of, 379 periodic character, 379 Solar constant, 13, 17, 380 determination, 50, 52

methods

of

measurement,

17

numerical value, 18 value, 380 variation, 18, 380 Solar control, of upper atmosphere, 247 Solar effect, on ozone layer, 293 Solar energy, at earth's surface, 28 average conditions, 29 through cloudless sky, 28 through clouds, 28 extraterrestrial, on horizontal surface, 19 in ultraviolet, 295

variations, research needed, 388

weather changes and, 379 Solar prominences, 379 Solar radiant energy, modification by earth, 13

modification by earth's atmosphere, 13 Solar radiation, see also Sun, radiation absorption, spectral by water vapor, 20 total water-vapor, 21 absorption by clouds, 21, 31 absorption by earth's atmosphere, 19 absorption b3' earth's surface, 22 absorption by ionosphere, 19 absorption by ozonosphere, 19 at ground, 30 effect on glaciation, 1010 effect on Grosswelier, 820

1331

Solar radiation continued factor in climatic change, 1010 outside the earth's atmosphere, 13 scattering, 22 by dust, 23 by liquid water droplets, 24 multiple, 25 spectral, b}' water vapor, 23 spectral molecular, 22 total molecular, 22 total water vapor, 23

Storms, Antarctic, 924 effect on electrical conductivity of electrical state in, 129

observation, radar, 1265 radar appearance during, 1271 surge method, of predicting swells, 1098 tropical, frontal analyses, 866 see Tropical cyclones Stratocumulus, liquid-water concentra-

terrestrial effects on, 19

upper-atmospheric heating, 31 Solar rays, illumination of upper atmosphere by, 248 Solar-topographic tlieory of climatic changes, 1016 Solar

ultraviolet

radiation,

on

effect

upper atmospheric gases, 248 Solenoidal index, 564 Sound pressure, waves, 374 Sound propagation, in the atmosphere, 366 research needed, 375 through upper atmosphere, 304 Sound rays, in moving air, 367 in quiet air, 366 Sound velocity, 366 and temperature, 374 Sound wave energy, absorption, 368 effect of distance between rays, 368 in atmosphere, 368 Sound waves, abnormal audibility zones, 371 in gases, theory, 366 in moving air, 367 in quiet air, 366

natural, observation, 371 observation, interpretation, 371 recording, instruments for, 370 temperatures derived from, 305 through stratosphere, 371 through troposphere, 371 use in studying upper atmosphere, 251 Sounding balloon, use in studying upper atmosphere, 251 Space charge, measurement, 149 Space medicine, 1121 Spectra, atomic, different ranges of wave length, 265

atomic particles, 265 infrared, of carbon dioxide, 296 of water vapor, 296 molecular particles, 265 Spectral line, radiation from, absorption law, 35

Strajrs see Sferics

Streak lightning, 141 Stroke, return, 136

Sturbs see Sferics Sublimation, formation of ice crystals by, 207 nuclei, 174, 192 effect on snow formation, 224 on cloud elements, 204 Sulfur dioxide, effect on condensation

nuclei formation, 186 Sulfur dioxide apparatus, for measuring atmospheric pollution, 1140 Sulfur dioxide content of atmosphere, 7 Sulfuric acid, atmospheric, determining, 1126

Sun, chromosphere, 13 corona, 13 enlargement when near horizon, 62 ionized layers, heights and pressures, 15

photosphere, 13 radiation, see also Solar radiation infrared, 14 fluctuation in far ultraviolet, 15 fluctuations in infrared, 17 fluctuations in near ultraviolet, 16 fluctuations in radio waves, 17 fluctuations in visible, 17 fluctuations of emitted, 15 near infrared, 13 short-wave radio, 14 ultraviolet, 14 unmeasured, 15

Sun, reversing

hydrogen lines, 351 intensity effects, 350 de-

sodium lines, 351 wave lengths, 350

laj'er, 13 ultraviolet intensity, 1119 Sunlight, average spectral distribution, 13 Sunrise, in upper atmosphere, 248

Sunset, upper atmosphere, 248 Sunshine recorders, 55

Sunspot cycles,

effect

on Grosswelier,

819

night-skv, 341 Spicules, 379 Spillover, rainfall, orographic, 1039 Spontaneous nuclei, effect on snow formation, 225 Spores, exchange between earth and atmosphere, 1107 Squall lines, 689 see also Instability lines prefrontal, 716 ;

and pressure jump Stability

tion, 1199 Stratosphere, composition of air in, 8 lower, frost point determination in, 313 normal circulation, 553 ozone in, 284 radiation in, 46 radiational heating of, 47 sound waves through, 371 Stratus, effect of cloud seeding on, 236 solid precipitation in, 223 forecasting time of dissipation, 1187 liquid-water concentration, 1199

visible, 13

Spectrograph, radar signal, 1278 Spectrophotometer, Dobson, 276 Spectrum, aurorae, 350

nitrogen bands, temperature termination from, 351

air,

110

properties

of

lines, 427

large-scale at-

mospheric d sturbances, 454 Standard operative temperature, 1115 Static, precipitation, 134 Steady-state flow, under

equations for, 430 Stooping, 66

Sunspot number, relative, 380 and meridional and zonal flow types, 840 Sunspots, 379 follower, 380 leader, 380 Superrefraction, areas subject description of, 1290 explanation of, 1291 propagation, 1294 radio duct, 1292

to,

1290

Surf, forecasting, 1083 Surface friction, heat transportation,_465

Surface map, geometrical extrapolation, inversion,

769 physical extrapolation, 770 prognosis, 769

INDEX

1332 Swell, correlation between wind strength and, 1097 forecasting, 1083 forerunners of wave frequency-spectrum method applied to, 1091 visible,

wave height-period applied

to,

1090

Synoptic cycle, in forecasting, 766 Synoptic representation, models, 711 techniques, 711

Synoptic upper-air model, 784

Telephotometers, 95 Temperature, and humidity patterns, in free air, 318

Antarctic, 929 at extreme altitudes, 308 atmospheric, free oscillations and, 306 measurement by rocket, 306

meteors and, 306 balloon studies on, 303 based on ultraviolet absorption, 305 changes, radiative, in ozone layer, 292 cloud lapse rates, 696 conditions, microclimate, 994 derived from sound wave velocities, 305 differences, during land and sea breezes, 657 distribution, in extratropical cyclones,

580

ozone layer, 292 west -wind zone, 599 during pressure jump, 427 effect on effective terrestrial radiation, 39 effect on electrical conductivity of air, in in

104 effect field,

on sound propagation through upper atmosphere, 304 turbulent air flow, 498

forecasting, 761, 788 in anticyclone, 627 in geological time, 1017 in ionosphere, 339 in thunderstorms, 685 in upper atmosphere, 303

measurement by aircraft, 1223 sound velocity and, 374 tree-ring indices, 1024 in Arctic, 1027 tropical cyclones, 889 vertical advection, 644 Temperature r&ultant, 1115 Theodolite, electronic, 1211 Thermal convection, laboratory investigations, 1239 Thermal low, 781 Thermal processes, effect on cloud elements, 204 Thermal slope wind see Wind, thermal slope Thermodj'namic analysis, cloud, 697 Thermodynamics of clouds, 199 Thermodynamics of open systems, 531 application to general circulation, 536 homogeneous systems, 531 differences between open and closed systems, 532 first law, 531 poly thermic systems, 533 pseudoadiabatic transformations, 533 second law, 532 temperatures, 533 wet-bulb, 533 equivalent, 533 nonhomogeneous systems, 534 first law, 535 heat flux due to atmospheric turbulence, 535 second law, 535 Thermometer, recording black-bulb, 55 vortex, 1224

Thoron, source, 155 Thunderheads, electric current density,

air preceding, 674

and pressure jump

114

Thunderstorms, 681 and the airplane, 690 cell, life cycle,

Tornadoes, 673

682

circulation, 681 cumulus stage, 682 development of new cells, 686 development, preferred areas, 688 dissipating stage, 683 downdraft, thermodynamics, 683 effect of cloud seeding on, 232 electrical characteristics, 129 electrical cycle, 115 electric structure, 115 electricity see Electricity, thunder-

storm entraining, thermodynamics of, 683 forecasting, 690 hearth, 689 mature stage, 682 movement, altocumulus and, 1173 pressure, 685 Project, 687 instability line, 652 radar pictures, 1276 rainfall, 684 relation of sferics to, 1298 squall lines and, 689 structure, 681 study, by radar, 688 supply current and, 113 temperature, 685 tropical cj'clones, 892 unsolved problems, 691 weather, near surface, 684 wind field, 684 effect of environmental, 688 Tidal variations, in geologic time, 1011 Tides, atmospheric, 255, 257, 306, 510 adiabatic nature, 519 equilibrium solar, 510 geomagnetic lunar, 521 gravitational, 510 Kelvin's theory of, 623 Laplace's theory, 523 lunar, annual mean, 515, 516 annual variation, 515 at Paris, 511 computation methods, 514 daily variations, 510 distribution over North America, 517 geographical distribution, 515, 516 harmonic analysis, 513 harmonic dial, 513 nontropical, 512 probable error, 514 rise and fall of ionospheric layers,

520 search for, 511

temperature

effect on, 519 tropical, 512 lunar tidal variations of cosmic rays, 521 lunar tidal wind currents, 519 Newton's theories, 523

research needed, 527 resonance theory, 524 solar daily barometric variations, 521 solar day variations, 510 solar semidiurnal, harmonic analysis, 513 harmonic dial, 513 oscillation, annual variation, 523 oscillations, 521, 522 theory, 523 Time series, non-stationary, 851 schematic, 850 stationary, 850 Topographic theory of climatic change, 1016

lines, 431

appearance, 675 audibility, 676 axis, 676

building safety, 678 definition, 673 flow pattern, 675 forecasting, 678, 792 frequency, 673 generation, theories on, 676 injuries from, 678 instability lines and, 647, 651 insurance, 678 laboratory investigations, 1236 loss of life from, 678 low pressure in, cause of, 677 maintenance, theories on, 676 motion, horizontal, as energy source, 677 vertical, energy for, 676 paths, 676 preliminary signs, 673 pressure, central, 674 pressure drops and, 674 properties, 674 property damage from, 678 protection of life, 678 protection of property, 678 public safety measures, 678 rain and, 674 related phenomena and, 673 scent, 676 source of energy, 651 source of rotation, 651 synoptic weather situations, 673 thunderstorms and, 674 tracking, 678 tropical cyclones, 892 visibility, 675 weather conditions associated with, 673 wind speed, 674 Towering, 66 Trades, boundaries, 864 Trade-wind inversion, 864 Transference, 270 Transisobaric displacement of air, 783 Transmission lines, protection against lightning, 142 Transmittance meters, 94 Tree histories, rainfall in North America, 1026 river flow in North America, 1026 Tree line, Arctic, 955 Tree-ring indices, see also Dendrochronology Arctic temperatures, 1027 of rainfall, 1024 of river flow, 1024 of temperature, 1024 physiological drought, 1028 Tripartite stations, use in study of microseisms, 1313 Tropical air, source region, 600 Tropical air parcel, movement, 610 Tropical cyclones, 887 aerology of, 902 air-mass arrangement around, 888 barometry, 888 classification, according to development stage, 887 according to intensity, 887 clouds, 890 detection, 896 eye, 891, 905, 907 forecasting movement, 897, 910 frequency, 895 height, 893 information sources, 887 inundations, 892 methods of analysis, 903 microseisms, 900 normal storm track, variation from, 897

—

—

—

—

INDEX Tropical cyclones continued observations, 902 origin, 894 precipitation, 890 pumping, 888 radar bands, 891, 1275 rain area, dynamical aspects, 905 heat transfer, 906

microstructure, 905 thermal structure, 904 upper outflow, 907 wind distribution near surface, 900 region of origin, 895 research needed, 900 schematic development of swells, 899 season of origin, 895 steering currents, 898 storm swell significance, 899 storm tide significance, 900 surface characteristics, 887 surface indications, 896 temperature, 889 theories of formation, 907 thunderstorms, 892 tornadoes, 892 tropopause heights, 893 upper-air indications, 897 vertical structure, theory, 892, 904 wind circulation, 889 Tropical meteorology, 859 see also Equatorial meteorology air-mass method, 859, 863 achievements, 873 analysis methods, 859 climatological analysis method, 859 climatological method, 859, 860 achievements, 872 tropical storms and, 862 convergence lines, 874 cumulus base height, 861 direct circulation cell, 871 easterly wave, 868 equatorial front, 865 Freeman waves, 870 frontal surface, 865 frontal theory, 866 modifications, 867 perturbation method, 859, 868 achievements, 875 polar trough, 869 surface air temperature, 860 temperature discontinuities, 868 wind persistence, 860 Tropics, weather observation, 709 Tropopause, humidity in, 315 Troposphere, anticyclone in, water vapor structure, 316 chemistry and, 262 intrusion of moist air tongues into dry air, 317 normal circulation, 553 ozone conditions, 286 sound waves through, 371 subsiding polar air, 315 upper, jet stream, 604 vertical distribution of ozone, 7 water-vapor distribution, 315 Trough, intensifying, flow pattern in, 458 temperature pattern in, 458 Trough formula, Eossby's, 415 Trough motion, atmospheric, 563 Tundra, 953 maritime, 957 Turbidity coefficient, correlation between maximum polarization and, 84 Turbulence, and diffusion, 492 aerodynamical background, 492 boundary layer, 492

eddy

diffusion, 501 flow near a boundary, 493 heat transfer, 499, 502 influence of density gradient on nature of flow, 506

Turbulence

1333

contimied

Upper atmosphere

in the general circulation, 502

Kolmogoroff's theory, 497 laminar flow, 492

continued

ozone continued and constitution

287

of,

vertical distribution, 280

large-scale processes, 500

ozone heating, 305

macroviscosity, 496 mathematical treatment, 493 microscale of turbulence, 497 mixing-length hypothesis, 494 momentum transfer, 499 momentum-transport theory, 496 nature of, 492 physical features, 498 humidity field, 499 temperature field, 498 velocity field, 498 power-law profile, 496 Reynolds stresses, 493 scale, 497 small-scale diffusion processes, 503 statistical theories of, 496 velocity profile, near a boundary, 495 near rough surface, 495 near smooth surface, 495 vorticity-transport hypothesis, 496 water-vapor transfer, 499 Twilight, polarization anomalies during, 87

Twilight arch, 73 Twilight phenomena, 72

phenomena, 245 photochemical processes, 262 physical features, 249 physics, general aspects of, 245 pressures, 303 radio exploration, 254 reactions, 270 rocket measurements, 306 solar control, 247 sound propagation through, 304 study of meteors, 253 studying, by V-2 rocket, 250 direct methods, 250 indirect methods, 251 sunrise in, 248 temperature distribution, 252 temperatures, 303 unsolved problems, 256 water vapor in, 311 weather and, 256 winds, 255, 358 Upper-air analysis, 717 Upper-air maps, prognosis of, 780 Uranus, atmosphere, 394 meteorological parameters, 392

description, 73

problems, 74 results of observations, 73

V-2 rockets, use in determining ozone

schematic view, 73

distribution, 278 use in studying upper atmosphere, 250 Vacuum tube electrometers, use in measuring atmospheric electricity, 144 Vanishing constant, 148 Venus, atmosphere, 391 research needed, 397 meteorological parameters, 392 Vertical current, atmospheric, measure-

theories, 74

Typhoon

see Tropical cyclones

U Ultraviolet, solar energy in, 295

Ultraviolet

absorption,

temperatures

based on, 305 Ultraviolet

daylight

measuring

integrator, for pollu-

atmospheric

tion, 1140 Ultraviolet intensity, sun and sky, 1119 Ultraviolet radiation, effect of cloudiness on, 1119 solar,

effect

on

upper

atmospheric

gases, 248

Ultraviolet spectrum, use in studying upper atmosphere, 251 Umkehr curves, 277 Umkehr effect, 276 Unifilar electrometer, 144 Wulf's, 145 Upper atmosphere, 245 absorbing constituents, amounts, 272 absorbing layers, heights, 271 anticyclonic shear, 585 aurorae, 255 balloon studies, 303 composition, 7, 251 absorption-spectral evidence regarding, 270 emission-spectral evidence regarding, 271 constituents, 270 diffusion in, 320 diffusive separation, 256 dissociation of atomic particles, 268 emitting constituents, amounts of, 272 emitting layers, heights of, 271 extreme ultraviolet radiation, 256 fast-charged particles in, 255 illumination by solar rays, 248 ionization, 254 meteoric, 257 atomic particles, 268 luminescence, 254 meteor use in research in, 356 molecular escape, 247 night-sky radiations from, 341 origin of structure, 245 ozone, 275 amount, 278

ment, 149 recorder, 149

Vertical-overturning instability, generalized, 468 Vertical velocity, large-scale, and divergence, 639 adiabatic method of computing, 640 as a forecast tool, 645 direct measurement of, 640 distribution of, 641 theoretical explanation, 642 effects of, 643 advection of temperature, 644 advection of velocity, 643 changes in cloudiness, 644 pressure changes, 044 influence of scale on, 639

kinematic method of determining, 640 Virga, appearance of, 192 meteorology, 91 research needed, 95 Visual range, calculation, 93 in practice, 95 instruments for measuring, 94 Volcanic dust, effect on skylight polarization, 79 role in climatic changes, 1015 Volcanic eruptions, effect on Grosswetter, 815 Vortex, circular, atmospheric flow and, 455 permanent circular, application to tropical cyclones, 448

Visibility, in

thermometer, 1224 Vorticity, absolute, for 461 isolines for

mean

vertical

zona! flow,

component

of,

460 analysis of extratropical cyclones, 582 conservation, 461 equation, 458

—

—— INDEX

1334 Vorticity continued transport hypothesis, in turbulent air flow, 496 Voss polariscope, 81

W Warm

—

layer, ozone and, 287

Water, cloud modification by, 230 droplets, liquid, scattering of solar radiation by, 24 -dropper collector, 148 exchange of energy in a latent form of, 1061 purity, effect on double-layer phenomena, 131 resources, estimating, 1045 still, freezing of, 207 supercooled, in clouds, 173 supply forecasting, i053 turbulent, freezing, 207 vapor, absorption spectral, of solar radiation by, 20 albedo, 28 distribution, in troposphere, 315 in upper atmosphere, 314 effect in scattering solar radiation, 22 effect on radiation diagrams, 37 effect on radiation in stratosphere, 46

in upper atmosphere, 311 infrared spectra, 296 radiation, cooling of atmosphere by, 43 structure, of an anticyclone, 316

upper atmosphere, determination by aircraft ascents, 313 measurement, 311 variations, in density, 8 Waterfall effect, 131

Waterspouts, 679

Waves, barotropic,

stability, 462 blocking, in planetary jet stream, 432 complex, under inversion, 425 compression, 423, 425 easterly, structure, 869 expansion, 423 and pressure jump, interaction between, 428 gravity, atmospheric perturbation and, 445

atmospheric perturbation and, 445 long, on a rotating plane, 415 long upper, cyclonic perturbations and, 607 horizontal dimensions, 606 prognosis based on, 786 motions, in compressible atmosphere, 414 number, 264 ocean, as a meteorological tool, 1090 characteristics, predicted and observed, 1086 decay relationships, 1085 inertial,

direction measurement, 1093 forecasting, 1082 problems, 1087

frequency-spectrum method applied to forerunners of swell, 1091 future research needed, 1099 generation relationships, 1084 height, significant, 1086 height-period, applied to visible swell, 1090 instrumentation, 1091 interpretation of records, 1093 measurement, 1091 origin, 1092 period, comparison of storm path with, 1096 significant, 1086 propagation diagrams, 1094 instrumentation, 1098 methods, 1098 range, 1099 storm intensity, 1099 storm location by, 1098

West wind

Waves

continued continued recording meehnnism, 1093

ocean

significant, forecasting, tions, 1083

computa-

spectrograms of, 1094 spectrum, 1086 steepness, relation to wave, age, 1086 storm surge method of forecasting swells, 1098 surface weather map and relation to, 1094 pressure, Antarctic, 926 shape of current peaks, in lightning discharges, 140 shear, atmospheric perturbation and, 445 simple, 423 under inversion, 425 sound, atmospheric perturbation and, 445 Weather, control of, 229 frontal, forecasting, 650 glaoial-interglacial sequences, 381 ozone and, 284 relationship of circulation to, 809 Weather anomalies, consecutive, correlation between, 817 persistence tendencies, 817 repetition tendencies, 817 successive in distant regions, correlations between, 818 Weather changes, anomalous, solar energy variations and, 379 Weather conditions, crop yields and, 988 varying, effect on cloud radiation, 43 prediction of various, 787 Weather fluctuations, abnormal, 383 climatic, 382 daily, 383 geographical pattern, 381 geological, 381 periodic character, 381 secular, 383 Bruckner c,ycle, 383 climatic, solar hypothesis, 386 theories, 385 factors controlling, 384 geological, solar hypothesis, 385 theories, 384 intra-century, solar hypothesis, 386 monthly, solar hypothesis, 387 postglacial, solar hypothesis, 386 seasonal, solar hypothesis, 387 secular, solar h3fpothesis, 386 solar hypothesis, 385 sunspot C3'cle, 383 weekly, solar hypothesis, 387 week-to-week, theories, 385 Weather forecasting see Forecasting Weather insurance, 981 Weather key-days, 826 and weather development, 826

Weather map

analysis, see Meteorological analysis Weather observation, aircraft, 707 Antarctic stations, 708 Arctic stations, 708 ships' reports, 706 tropics, 709

world, gaps

in,

705

world network, 705 Weather spectra, long-term predictable, 852

Weather Weather

continued zone, temperature, 599 wind distribution, 599 Westerlies, and anticyclones, 623 baroolinic, middle latitude, 578 disturbances, formation of, 605 eddy motion, 838 geostrophic, average distribution, 601 mid -troposphere, 561 orographic disturbances, 605 thermodynamic disturbances, 605 waves associated with cyclones, 579 zonal current disturbances, 605 Wet -bulb thermometer temperature and equivalent temperature, 533 Wheat stem rust, transport in atmosphere, 1108 Whirlwinds, 678 Wilson test-plate, 149

Wind

see also

Breeze

bora, 669 circulation, tropical cyclones, 889 conditions, in microclimate, 996 distribution, in west-wind zone, 599 during a pressure jump, 427 effect on atmospheric pollution, 1146

environmental, effect on thunderstorms, 688 in thunderstorms, 684

field,

representative, effect processes, 330 foehn, 667

on diffusion

see also Foehn for power production, 984 forecasting, 761, 791 indicators, cloud motions as, 1172 jet-effect, 670 local, 655

definition, 655 desirable studies, 670

Maloja, 664 meridional circulation, 599 mistral, 670 mountain, 662, 663 circulation, components of, 662 desirable studies, 670

theory

of,

664

night, vector frequency of, 358 northers, 670 orographic influences, 667 protection, applied microclimatology

and, 999 -shift line, marked by clouds, 1173 slope, air transport by, 666 speed, effect on ultraviolet daylight losses, 1146

strength, correlation with ocean swells, 1097 thermal slope, 662 -tunnel investigations, of atmospheric pollution, 1145 upper, Little America, 920 upper atmosphere, 255 meteor trains and, 358 valley, 662, 663 desirable studies, 670 theory of, 664 velocitv measurement by aircraft, 1226 Window frost, 207 Windstorms, cloud seeding and, 232 insurance, 982 Wire sondes, 1216 Wulf's bifilar electrometer, 145 Wulf's unifilar electrometer, 145

stations, automatic. 1217 types, and clouds, 1175

catalogue, 839 use in analogue selection, 839 extended-range forecasting by, 834 meridional flow, 835 schematic diagrams, 836 zonal flow, 835 Weger aspirator, 147 West wind, anticyclonic shear, upper limit, 604

X's see Sferics

Xenon content

of atmosphere, 5

Zodiacal light, 345 mystery of, 258

Zonda

see

Foehn