Profiles of Wind Temperature and Humidity Over the Arabian Sea 9780824891251

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I N T E R N A T I O N A L I N D I A N OCEAN E X P E D I T I O N METEOROLOGICAL MONOGRAPHS

Number 6

The International Indian Ocean Expedition Meteorological Monographs, published as An East-West Center Book by The University Press of Hawaii, contain detailed discussions and supporting data on the various components of the general atmospheric circulation over the Indian Ocean, as well as the results from measurements of atmosphere-ocean interaction made as part of the expedition's observational program. Manuscripts are solicited, and should be sent to C. S. Ramage, Department of Meteorology, University of Hawaii, Honolulu, Hawaii, U.S.A. 96822. Editorial

committee

C. S. RAMAGE

M. A. ESTOQUE

MICHAEL GARSTANG

Profiles of Wind, and Humidity

Temperature,

over the Arabian Sea

PROFILES OF WIND, TEMPERATURE, AND HUMIDITY OVER THE ARABIAN SEA

by F. I. Badgley, C. A. Paulson, and M. Miyake

A N EAST-WEST CENTER BOOK

yjf^y

T t i e

U n i v e r s i t y P r e s s of H a w a i i

The publication from

the National

of this

volume

Science

has been aided

by Grant

Foundation.

Copyright © 1972 by The University Press of Hawaii All Rights Reserved International Standard Book Number: 0-8248-0101-6 Library of Congress Catalog Card Number: 70-129539 Printed in the United States of America F i r s t Edition

No.

GA-380

Acknowledgment P a r t One of this work was supported by the National Science Foundation under three grants, GP-571, GP-2270, and GP-2418. The support is gratefully acknowledged. We had the generous cooperation of the staff of the International Meteorological Center of the IIOE, Bombay. The officers of the tug "Oceaan" provided invaluable help with the measurements. P a r t Two was supported by the National Science Foundation under g r a n t s GP-2418, GP-4689, and GA-1099. We are grateful for this support. Our thanks go to Professors R. G. Fleagle and J. A. Businger for their interest in this work and for suggestions made at various times throughout its progress.

F. I. Badgley, University of Washington, Seattle C. A. Paulson, Oregon State University, Corvallis M. Miyake, University of British Columbia

Honolulu, October 3,1968

Contents PART 1: THE OBSERVATIONS

by F. I. Badgley (1) and C. A. Paulson (2) I. II. III.

Introduction

3

Discussion

7

Ship Observations Data

8

Notes and References

29

PART 2: AN ANALYSIS

by C. A. Paulson (1), M. Miyake (2), and F. I. Badgley (3)

I. II.

Abstract

33

Introduction

35

Errors in the Measurements

36

A. E r r o r s C a u s e d by Buoy Motion 36 B. E r r o r s C a u s e d by S t r u c t u r a l I n t e r f e r e n c e 40 C. E r r o r s C a u s e d by S a m p l i n g 4.1

III.

Effect of Wave Generation on the Profiles

45

IV.

Profile Analysis

49

Variation of Drag Coefficient with Wind Speed

55

Turbulent Fluxes of Momentum, Heat, and Water Vapor

58

Summary and Conclusions

59

Notes and References

61

V. VI. VII.

PART Î:

The Observations

PART Î:

I.

The Observations

INTRODUCTION

The tabulated data which are presented here were gathered early in 1964 over the Arabian Sea during the International Indian Ocean Expedition (IIOE). Observations were taken at locations shown in Figure 1. In their present form, the data are intended as a source of basic information on wind, temperature, and moisture in the boundary layer over the ocean. The data are homogeneous in the sense t h a t they were all taken during the winter monsoon when relatively cool air blows f r o m the land toward and over the relatively warm ocean. Some local variations are noticeable, especially near the shore where meso-scale landsea breeze circulations are important. There are a few cases of stable temperature stratification but typically the lapse rates are slightly unstable; in every case the humidity decreases with height, indicating evaporation f r o m the water surface. In almost no case was cloud visible f r o m the observing point; t h a t is, the energy being used for evaporation was transported beyond visual range before being released by condensation of water vapor. A floating instrument carrier, "Mentor" (Figs. 2 - 3 ) , was used for measuring the wind, temperature, and humidity in the 8 m boundary layer immediately over the sea surface. The instrument has been described elsewhere (3). Briefly, it consists of a catamaran-like float carrying a mast about 8.5 m tall in the f o r m of a ladder. The float is stabilized during observations by a weighted underwater tube t h a t projects vertically below the float to a depth of 10 meters. "Mentor" is tethered at its f o r w a r d end to the tending ship at a distance of 150 to 300 meters. The a f t end is fastened to a sea anchor, in this case a large parachute rigged to be open and completely submerged behind "Mentor." The entire rig acts as a large weathercock with the sea anchor upwind and the tending ship downwind. Projecting a f t into the wind f r o m "Mentor's" mast is a horizontal, instrumented boom t h a t is mounted on a carriage t h a t runs up and down the mast. The boom stops at four to six selected levels for sampling times of approximately 15 seconds each. The complete sequence including moving f r o m level to level takes about two minutes, and is repeated as often as possible during a test period t h a t lasts about 40 minutes. The instrument outputs are used to modulate FM carrier signals that are transmitted via wire to a tape recorder and are recorded in FM multiplex form on 0.25 inch magnetic tape.

4

PROFILES

OF

WIND, T E M P E R A T U R E ,

AND

HUMIDITY

OVER

THE

ARABIAN

SEA

FIGURE 2: The "Mentor" buoy with a movable instrumented boom (being serviced) measures wind, temperature, and humidity up and down the 8.5 tn mast. Similar reference measurements are made from the fixed boom. (Note the sonic anemometer at the end of the boom.) Watertight wells in the buoy's pontoons contain electronic equipment. When measurements begin at sea, stability is ensured by filling the cylindrical keel with water and lowering it to a position vertically below the mast. The buoy floats freely 150 m to 300 m upwind of the tug tender. The tender houses recording equipment attached by electric cables to the buoy.

.INDICATES

OBSERVING STAI

FIGURE 1: Positions and dates (day-month) of observations from the buoy, "Mentor','in the Arabian Sea. [After Badgley et al. (3).]

6

PROFILES

OF WIND, T E M P E R A T U R E ,

AND

HUMIDITY

OVER

THE

ARABIAN

SEA

Wind speeds were measured with a modified Beckman-Whitley three-cup anemometer having a distance constant of approximately one meter. A i r temperatures were measured by thermocouple with a reference junction immersed in the sea at a depth of about 30 centimeters. Wet-bulb depression was from a thermocouple having one wet and one dry junction. The thermal junctions were ventilated by the natural wind and were shielded from direct solar radiation. The sea-water surface temperature was measured hourly by bucket samples taken at the stern (and therefore to the windward) of the ship, in the ship's shadow. The measurements were sheltered from the sun and wind during the one-minute period needed to make a reading. The recorder and associated equipment used in the tests reported here were on board the ocean-going tug "Oceaan," of the L. Smit International Towing Service. The upper-wind data were gathered by single theodolite pilot balloon determinations, with the help of officers of the "Oceaan."

150 to 300m

PARACHUTE DRAG F I G U R E 3: The buoy system configuration during measurement.

[After Badgley et •/. (3).]

P A R T I: T H E

OBSERVATIONS

7

II. DISCUSSION The data reported in Table 1 are from 118 test periods corresponding to particular record-rolls of magnetic tape. The tape is used to identify the test period. Data from periods that were incomplete or questionable because of instrumental difficulties have been eliminated. The records have been carefully checked and are believed to be free of major errors. The principal remaining uncertainty results from sampling inadequacy. Since each level was sampled only about one-eighth of the total time, it is conceivable that this could lead to errors large enough to invalidate the results. This possibility has been minimized by comparing the readings of the traveling probe to simultaneous readings made from a fixed probe at a height of 4 meters. Since the data from the fixed boom averaged for the same sampling times were less than or greater than the fixed-boom average for the whole period, the raw data from the traveling probe at any level have been adjusted upward or downward. This assumes that the readings at all levels at any one time are linearly perfectly correlated with each other; experience shows this to be approximately, but not exactly, true. There are many other possible sources of error. Some of them are common to land-based operations as well, while others are unique to sea-borne operations. Concerning the latter, estimates have been made of the effects of buoy motion (pitch, roll, and heave), of instrument orientation (anemometers are not always level), and of position (bobbing carries instruments above and below their average level). These conditions produce errors that theoretically could be corrected by careful use of measured instrument motion, attitude, and position. Our estimates show, however, that as f a r as average profiles are concerned, such errors can be left in the data and lumped together with the others as random errors. The random errors from all sources have been left in the averaged data presented here. They are of the following magnitudes: Wind Temperature Humidity

± 3 cm sec - 1 ± 0.01° C ± 0.03 parts per thousand

Non-random errors, common to all levels in any one run, are not known precisely but may be estimated from measurements made under similar conditions elsewhere. For our data, they a r e : Wind Temperature Humidity

± 2 per cent of average speed ± 0.5° C (due to uncertainties in water temperatures measured by bucket method) ± 0.7 parts per thousand (due to uncertainties in temperature readings)

A thorough critical appraisal of the profiles is not undertaken here but the following generalizations can be checked by the interested user. 1. There are no obvious, qualitative differences between these profiles and those measured over land; they are generally as smooth as those made over flat terrain.

8

PROFILES

OF WIND, T E M P E R A T U R E ,

AND

HUMIDITY

OVER

THE

ARABIAN

2. The effective roughness lengths (z„) are small, in the order of 0.1 centimeter. Wave heights, not reported here, were characteristically in the range of 30 cm to 120 cm trough-tocrest. 3. The effects of stability and instability on the curvature of the wind profiles are qualitatively the same as over land. 4. No peculiarities traceable to the exchange of momentum f r o m wind to wave can be seen in the lower levels of the profiles. If such peculiarities do exist, they are too small or at heights too low to be perceptible in these data. 5. The effects of land, that is, of inhomogeneous surface conditions, are observable at great distances. Some of these effects are due to changes in roughness; others, to thermal inhomogeneities which set up land and sea-breeze circulations. Whatever the cause, observations must be made at distances in the order of tens of kilometers away from land, before the land influence is negligible. 6. There is a marked similarity between the profiles of different variables, especially between those of wind and temperature. Even minor quirks in one are apt to be reflected in the other. This may be due in p a r t to nothing more profound than correlation of the errors in the sampling of the two quantities. Whatever the cause, the correspondence occurs too frequently to be due entirely to chance. There is one real difference existing between air flows over land and over sea that does not show up in these d a t a : the turbulence spectra over water show less energy at small wave numbers — 0.01 cycles per meter and less — than those over land. The difference has no obvious effect on the profiles unless the small roughness lengths can be so construed. An analysis of the data given here appears in (4) • A small part of the data has been used in (5). III. SHIP OBSERVATIONS DATA The surface and upper-air observations in Table 2 were made during the same periods as the profile observations. The codes are international Ship and Pilot Ship Codes (6) summarized below: SURFACE: YQL:1L;1L„ NhCr.hCuCii

L„L„L„GG D s V,app

U P P E R AIR: YQL.,L;lL;1

(FM 21-C) Nddff OT s T s T,iT,i

(FM 33 C)

L„L„L„GG

SHIP VVwwW ld w d w P w H w

PPPTT

PILOT S H I P

OOi h Df ; ,

lddff

2ddff

The only change f r o m standard coding procedure was that a height indicator (1, 2, 3, etc., indicating thousands of feet) was prefixed to each of the wind groups making each of them a fivenumber group. Winds aloft were determined by single optical theodolite using standard U.S. Weather Bureau tables. Both 30 gm and 100 gm balloons were used. An abnormally large number of leaky balloons were found in our stock, and although they were discarded when discovered, some of the data may be in error because of this.

SEA

PART

I: T H E

OBSERVATIONS

9

T A B L E 1: Profiles of Wind, Temperature, and Moisture over the Arabian Sea Water

Ht. a b o v e

Tape

Date

Lat.,

Long.,

Begun, Local

Wind

Temp.,

Water Sfc.,

Wind S p e e d

Temp.,

Humid.,

No.

1964

N

E

Time

Dir.

°C

(cm)

(cm s e c - ' )

(°C)

%

017

2/22

18.9

71.8

1934

N

24.5

018

020

021

029

031

032

035

2/22

2/23

2/23

2/25

2/25

2/25

2/26

18.9

18.8

18.8

18.5

18.5

18.5

18.3

71.3

71.8

71.8

71.9

71.9

71.9

72.0

2024

1134

1221

1045

1530

1715

2115

NW

NW

NNW

NNW

N

N

WNW

24.4

24.6

24.4

24.9

25.1

25.0

25.4

Spec.

815

402

24.08

9.71

578

392

24.11

9.81

413

24.14

9.88

297

386 377

24.16

10.00

213

369

24.20

10.06

157

355

24.22

10.14

815

432

24.06

10.02

578

423

24.10

10.11

413

24.13 24.17

10.23

297

410 402

213

394

24.18

10.52

157

384

24.20

10.62

815

681

578 413 297 213 157

663

24.46 24.50

9.79 9.97

638 624

24.54 24.57

10.10 10.30

24.60 24.64

10.48 10.74

24.06

10.16 10.34

609 583

815 578 413 297 213 157

716 695

815

531

578 413 297 213 157

527

684 659 637 625

24.12 24.17

10.36

24.20

10.53 10.72

24.23 24.26

10.90 11.02

25.52 25.57

11.84 12.00 12.14

496

25.58 25.60

472

25.61

12.40

460

25.63

12.59

815

559

25.48

12.24

578

25.52

12.36

413

545 531

25.54

12.53

297

526

25.55

12.59

213

506

25.59

12.75

157

486

25.61

12.88

815

542

25.34

12.11

578

524

25.36

12.28

413

508

25.38

12.36

297

497

25.40

12.53

213

484

25.42

12.63

157

468

25.43

12.79

815

546

25.08

12.81

413

521

25.18

13.05

297

509

25.25

13.23

213

494

25.30

13.36

157

477

25.34

114

466

25.36

13.43 13,54

505

12.26

10

P R O F I L E S OF W I N D , T E M P E R A T U R E , A N D H U M I D I T Y OVER T H E A R A B I A N

SEA

Table 1 ( C o n t i n u e d ) Begun, Tape No.

Date 1964

Lat., N

Long., E

Local Time

Wind Dir.

Water Temp., °C

Ht. above Water Sfc., (cm)

036

2/26

18.3

72.0

2219

WNW

25.4

815

037

2/26

18.3

72.0

2325

WNW

25.6

Wind Speed (cm sec - ' )

Temp., the roll period. Differentiating with respect to z we obtain

Multiplying through by kz where k is von Karman's constant, neglecting the second term on the right hand side compared to the first, and invoking our assumption of neutral stability, we have

where u-m is the friction velocity computed f r o m the measured profile. This contains only the error under discussion. If we take h to be the geometric mean height of the anemometers above the center of gravity of the buoy and substitute measurements of a-,, T->, and u,„ for each of the 12 runs the effect of roll on the computation of u- is negligible. E r r o r s of less than 0.2 cm sec 1 are introduced in every case, compared to a typical value of u- of 20 cm sec" 1 . A possible source of error in the wind-profile measurement is the non-linear response of the cup anemometer to pitch-and-rollinduced wind speed fluctuations. Curves for estimating the error due to this effect are given in the Handbook of Meteorological Instruments (11) and were used to compute the error in u« for the selection of the 12 runs discussed. The computed errors were less than 0.2 cm sec - 1 in every case. Another possible source of error is t h a t caused by correlation of vertical motions of the cup anemometer (associated with buoy motion) with systematic variations of the wind field along the wave profile. Schooley (12) has reported wind-water tunnel measurements indicating t h a t the mean wind gradient is larger near the crest of a wave than near the trough. These results are qualitatively similar to laboratory measurements by Motzfield (13) over a solid wavy profile. This also indicated t h a t horizontal variations of wind speed associated with the waves decreased with increasing height. In order to understand how differences between measurements f r o m fixed heights and f r o m a moving buoy may occur, let us examine a simple model. Consider wind blowing perpendicular to long-crested sinusoidal waves of constant amplitude a, constant wave length I, and constant phase speed c. We require t h a t the wind field over any par-

SEA

PART

II: A N A N A L Y S I S

39

ticular wave be identical to that over any other. We assume that the mean wind profile, as measured by fixed anemometers, is logarithmic. We place the origin of our coordinate system at mean sea level, z vertical, and x, the direction of air flow. We may write a Taylor expansion about some height z' above mean sea level of the wind speed um, measured with an anemometer moving vertically in phase with the waves. Um

du

+ — ^ Az + • • • •

= u\z,

(4)

dz

where Ax is the vertical displacement of the anemometer. We require that z' > a since the wind speed below the water surface is not defined. We then set Az = -Q, where -Q is the water-surface displacement in the vertical. We choose a particular instant in time such that T] =

a

2-KX

cos —— • L

Then Equation (4) becomes um

. = u\2 f

+

dU , 2ttX — I*' a COS —

dz

[-....

I

I f we average over a wavelength, we obtain um

— u\z>

a

i l du

= I Jo

—

,

dz

2-IRX ,

cos —— I

ax

+ • • • >

(5)

where um — ¿i | is the difference between the mean wind speed measured at a height z' above the water surface and that at a height z' above mean sea level. We must have some knowledge of the horidU

zontal variation of — i..- in order to carry out the integration in DZ

"

du

Equation ( 2 ) . A limiting case is for no correlation between — I.- and cos —j— , in which case the first integral in Equation (5) is zero and the only contribution to um — fij.> comes from higher order terms which can be shown to be small. Indeed, Pond (5) considered the error for this case and concluded that it was negligible. AlternadU

tively, suppose we assume — |2/ to be perfectly correlated with »7. Let dz

dU ,

du

,

,

2irX

- I , ' = - | „ + &cos-r + ---,

(6)

where, following our assumption of a log profile du dz

u* =

kz' ' u*

Suppose we further assume that b = — , from which it follows that the wind gradient will be a maximum over the crest of the waves and zero over the troughs. This wind field, although quite unrealistic, should give us an estimate of the upper limit of the error under consideration. Substituting b in Equation (6) and carrying out the integration we obtain, correct to the first order,

40

PROFILES

OF WIND, T E M P E R A T U R E ,

i

AND

a U

HUMIDITY

OVER

THE

ARABIAN

*

We may replace z' by z, differentiate with respect to z, multiply through by kz, and finally obtain u.m

u* u*

a

= iT" 2z

Equation (8) represents an estimate of the maximum error expected due to a correlation of vertical motion of the anemometer with the wind field. It probably gives an overestimate because (1) there may be attenuation of the correlation between wind field and waves for increasing height, (2) the actual wind-speed variations are unlikely to be perfectly correlated with vertical motions, (3) the amplitude of the vertical motion of the anemometer might be less than the wave amplitude if there is damping of vertical motion as was the case for the buoy under consideration, and (4) the unrealistic assumption of zero wind gradient above the troughs acts to increase the computed error. Applying Equation (8) to the buoy measurements under consideration (a 50 cm, 300 cm), we obtain | {u m — k ) a : 0.08 which, even though probably an overestimate, is of the same order of uncertainty as « due to other sources and therefore may be safely ignored. B. Errors Caused by Structural Interference

During the analysis of the profiles, it became apparent that the wind speed measured at 157 cm above mean sea level was, on the average, anomalously low by about 3 cm sec 1. This anomaly cannot be explained as an effect of wave generation as predicted by Stewart (6), since this prediction called for anomalously high wind speeds for the lower part of the profile. Since the buoy pontoons extend about 9 inches above the water surface and are quite large compared to the other structural elements, it was suspected that they might be the reason for the anomaly. The results of an experiment, shown in Figure 1, comparing profile measurements made from the buoy to those made simultaneously from a stationary mast about 30 m away support this suspicion. The curvatures of the lower sections of the profiles measured from the buoy are probably caused by interference of the pontoons. The motion of the buoy is negligible for the data reported, so it cannot be a factor in the difference. The resolution and quantity of the data are not sufficient to give a quantitative estimate of the error in wind speed for the lowest probe heights of 114 cm and 157 cm used in the Indian Ocean observations. However, they do provide a plausible explanation of the observed anomaly. Note that there are differences in the overall slope of the simultaneous profiles which cannot be ascribed to structural interference. A conclusive explanation for these differences has not been found, although they may be due to the proximity of the observation site to land. The likelihood of structural interference is also supported by model studies in a wind tunnel which indicated that the air flow was disturbed at low levels upwind of the model pontoons at and beyond the location of the anemometer. The error in computing u* from profiles containing the 3 cm sec - 1 anomaly is about 0.6 cm sec - 1 if the lowest and highest measurement

SEA

PART

II: AN

ANALYSIS

41

1000

Z (cm)

100

o -u

A

-U

10 230

250

270

290

u cm sec

•i

F I G U R E 1: A comparison of wind-speed profiles measured simultaneously from the buoy, "Mentor, " and a stationary mast.

heights are used. If data f r o m intermediate heights are also used, together with a curve-fitting technique, the error would be substantially less. We conclude that the anomaly may safely be ignored for purposes of computing it-, since a typical value of u- is 20 cm sec" 1 . C. Errors Caused by Sampling

One of the problems of making profile measurements with fixed instruments is the difficulty of calibrating the instruments well enough to eliminate systematic errors in the profiles. The problem is especially difficult over water where the vertical gradients of wind speed and temperature are typically about one-half as large as those over rough land. In order to eliminate this difficulty, the over-water profiles discussed in this paper have been obtained with an instrumentcarrying probe described by Badgley et al. (H) which makes sequential measurements at selected heights. This technique was used by Fleagle et al. (15) for measuring wet- and dry-bulb temperature profiles. It has gone through several stages of development to the present system which includes the measurement of wind speed by the same technique. However, since the probe does not sample continuously at any level throughout this observation period, sampling error is introduced.

42

PROFILES

OF

WIND,

TEMPERATURE,

AND

HUMIDITY

OVER

THE

ARABIAN

Sampling error prior to the present system was discussed by Willis (7) and Willis et al. (16). The conclusions of these studies were that the optimum sampling time at each level was from 10 sec to 15 sec and that the maximum sampling errors in differences between two levels was 5 cm sec - 1 for wind and 0.02° C for temperature. There was an indication that sampling error was less for stable stratification than unstable stratification, but there was insufficient data for a definitive conclusion. The conclusions were based exclusively on data from observations over inland waters and therefore are of questionable validity over the open sea. A set of instruments similar to those used in the profiling probe was mounted on a stationary arm about 4 m above the sea surface. Measurements from these instruments were sampled simultaneously with the probe samples. It is possible to evaluate the sampling error by comparing the average obtained using all the samples of a particular variable measured at the stationary arm with that obtained using only simultaneous probe samples at a particular level (every sixth sample if 6 probe levels are used). The differences between averages of the first and second type are estimates of the sampling error. Table 1 gives the standard deviations of these differences for different stability classes. There is some indication that the sampling error in wind speed u, is larger for the most unstable cases and that error in wet-bulb temperature T„, may be less for the most stable cases. However, these variations are minor. The overall results indicate that sampling error in wind speed is about 1.3 per cent, the error in temperature about 0.012° C, and the error in wet-bulb temperature about 0.04° centigrade. These results are strictly valid only for the 4 m level, but are probably not very different at any point between the 1 m and 8 m levels. The statistics of turbulence fluctuations of periods longer than 15 sec are nearly constant over the height-range of interest. It is apparent from analysis of the data that 15 sec samples of variables measured on the probe correlated highly with the simultaneous samples measured on the stationary arm. With this observation we may devise a procedure for reducing the sampling error. We assume a linear relationship exists between a variable measured on the probe and the same variable measured from the stationary arm. This implies a perfect correlation between these simultaneous 15 second samples. It also implies that the constant of proportionality in the linear relationship is equal to the ratio of the standard deviations of the probe and stationary arm samples. This model gives the following correction formula for wind speed: uc = us — — (vs - v)

(9)

Vv

where uc is the mean wind speed at a particular probe level corrected for sampling error, us is the wind at the same level computed from the probe samples, o-„ is the standard deviation of the probe samples at the same level, o> is the standard deviation of simultaneous stationary arm samples, vs is the mean wind computed from the simultaneous stationary arm samples, and v is the mean wind computed from all the samples from the stationary arm. Correction equations

SEA

PART I I : AN A N A L Y S I S

T A B L E 1: Sampling Error as a Function of Richardson Number; the subscript s denotes the sampled quantity; the overbar indicates an average; the numbers in parentheses are the number of runs used in the error R a n g e of

Ri

at 358 cm

0.04 ,0.01

0

[(~L5"I,)2JA

0.010(15)

[ C , - T)']'.i TO) [(T u _T U .)']"= " Vc)"

,-0.03

-0.04 ,-0.06

-0.07 ,-0.10

-0.12 ,-0.19

-0.20 ,-1.20

0.013(18)

0.011(21)

0.012(26)

0.011(14)

0.018(15)

0.013(15)

0.011(18)

0.012(17)

0.013(22)

0.011(13)

0.013(14)

0.025 (15)

0.040 (15)

0.048 (17)

0.50 (22)

0.051 (12)

0.040 (15)

T A B L E 2: Average Correlation Coefficients between Variables Measured on the Probe and on the Stationary Arm for Different Stability Ranges and for Different Probe Locations

Probe Height ( c m ) Variable

No. R u n s

160

210

300

410

580

810

0.01

15

0.86

0.88

0.89

0.89

0.90

0.84

,-0.03

16

0.88

0.87

0.91

0.94

0.95

0.90

0.91

0.92

RI R a n g e

u

0.04,

u

0

u

-0.04, -0.06

21

0.85

0.90

0.91

0.94

u

-0.07, 0.10

23

0.86

0.88

0.91

0.94

0.93

0.92

u

-0.12,-0.19

14

0.86

0.87

0.93

0.94

0.94

0.90

u

-0.20,-1.20

15

0.94

0.96

0.96

0.95

0.04, -1.20

43

0.81

0.82

0.83

0.82

0 83

0.81

0.04,-1.20

50

0.75

0.76

0.77

0.77

0.77

0.76

T

0.93

43

44

PROFILES

OF

WIND, T E M P E R A T U R E ,

AND

HUMIDITY

OVER

THE

ARABIAN

similar to Equation (9) may be written for temperature and wetbulb temperature. If we assume that the sampling error remaining in the corrected values due to the imperfection of the model is a function only of Rm, the correlation between probe samples at a particular level and simultaneous stationary arm samples, then