Precipitation Modeling and Quantitative Analysis [1 ed.] 9400723806, 9789400723801

Citation preview

Precipitation Modeling and Quantitative Analysis

Springer Atmospheric Sciences

For further volumes: http://www.springer.com/series/10176

Xiaofan Li • Shouting Gao

Precipitation Modeling and Quantitative Analysis

Xiaofan Li NOAA/NESDIS/Center for Satellite Applications and Research 5200 Auth Road, Camp Springs, MD 20746 USA [email protected]

Shouting Gao Laboratory of Cloud-Precipitation Physics and Severe Storms Institute of Atmospheric Physics Chinese Academy of Sciences Chaoyang District, Beijing 100029 China [email protected]

ISBN 978-94-007-2380-1 e-ISBN 978-94-007-2381-8 DOI 10.1007/978-94-007-2381-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2011941660 © Springer Science+Business Media B.V. 2012 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To my wife Qin for her encouragement and support Xiaofan Li To my wife Rongyu for her patience and support Shouting Gao

Foreword

Precipitation is interlinked with atmospheric dynamics and thermodynamics through the latent heat released during phase changes of water, and the heat absorbed during the evaporation of precipitation. The nonlinear relationships involved with precipitation processes coupled to atmospheric dynamics are major sources of uncertainty for all prediction models. Floods caused by torrential rainfall, along with weather hazards, cause enormous economic loss and affect livelihood around the world. Understanding precipitation processes and how these interact with dynamics is a vital step towards improving the skill of prediction models. This will help day-today planning by individuals, longer-term decision making by institutions and governments, and foster an improved relationship between science and society. Improving our knowledge of precipitation processes requires the formulation of quantitative relationships between microphysics, clouds, water vapor, latent heating and dynamics. During the past 7 years, along with their research groups, Professor Shouting Gao of the Institute of Atmospheric Physics in Beijing, China and Dr.Xiaofan Li of NOAA’s National Environmental Satellite, Data, and Information Service (NESDIS) have made considerable progress with precipitation modeling. In number of publications they have derived diagnostic equations involving clouds, water vapor and energy. They applied these equations to enhance our understanding how water, atmospheric dynamics, cloud processes interact in precipitation systems. This well-written book by Dr. Xiaofan Li and Professor Shouting Gao updates and reviews precipitation modeling and quantitative analysis through the effects of physical processes. Their approach is focused on two-dimensional precipitation modeling of selected periods during the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE), the landfall of severe tropical storm Bilis (2006), and pre-summer rainfall over southern China in 2008. This includes the validation of numerical models against observations. They provide detailed derivations of the salient equations, along with quantitative analyses of the effects of sea-surface temperature, vertical wind shear, cloud-radiation interaction, and ice clouds on heavy rainfall. They evaluate the sensitivity of the numerical models to uncertainties in the initial conditions, and describe basic concepts such as precipitation efficiency. vii

viii

Foreword

The authors provide a solid foundation for the quantitative analysis of precipitation processes and lay a basis for future three-dimensional precipitation modeling pertinent to weather and climate. Senior Scientist National Center for Atmospheric Research

Mitchell Moncrieff

Introduction

Precipitation is one of the most important quantities in meteorology and hydrology. Because floods resulting from torrential rainfall associated with severe weathers and storms can cause tremendous economic loss, the accurate measurement and the quantitative estimate and forecast of precipitation have significant economic and social implications in rainfall-rich countries. However, accurate estimate of surface rain rate is difficult due to the fact that precipitation processes are nonlinearly associated with the dynamic, thermodynamic, cloud microphysical and radiative processes. While many previous studies have contributed to the qualitative analysis of precipitation processes, quantitative analysis of precipitation processes has seldom been conducted simply because diagnostic precipitation equations associated with heat and water vapor processes have not been available. Facing this challenge, in 2005, the authors combined water vapor and cloud budget to derive a water-vaporrelated diagnostic precipitation equation for quantitatively identifying dominant water vapor and cloud processes associated with precipitation. In 2010, the authors combined heat and cloud budgets to derive a thermal-related precipitation equation for quantitatively identifying dominant thermal and cloud processes associated with precipitation. This set of precipitation equations has been widely used to study the effects of sea surface temperature (SST), vertical wind shear, radiation, and ice clouds on torrential rainfall and diurnal cycle, precipitation efficiency; the sensitivity of precipitation modeling to the uncertainty of initial conditions; and to develop a new rainfall partitioning scheme. The material in this book is based on our research work in the last 7 years. This book starts with precipitation modeling with the two-dimensional version of the Goddard Cumulus Ensemble Model and an evaluation of modeling with available observations. The book details the derivation of precipitation equations and covers many research aspects on the effects of sea surface temperature, vertical wind shear, radiation, and ice clouds on rainfall in idealized cases without large-scale vertical velocity, in a tropical rainfall case during the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE), and in torrential rainfall cases associated with severe tropical storm Bilis (2006) and a presummer rainfall event over southern China in 2008. The material in this book has ix

x

Introduction

been used in part of a graduate course at the Graduate School, Chinese Academy of Sciences, Beijing, China. Therefore, this book can be used as both reference and as a textbook for graduate students, researchers, operational forecasters and those whose research interests include precipitation modeling, analysis, and forecasts. This book is comprised of nine chapters. Chap. 1 presents and evaluates precipitation modeling with available observations. Chap. 2 gives detailed derivations of a set of precipitation equations and their applications to the analysis of precipitation processes in idealized rainfall cases and torrential rainfall cases in Bilis and presummer rainfall events. Chap. 3 discusses tropical rainfall processes during TOGA COARE. The effects of SST, vertical wind shear, ice clouds, and cloud radiative processes on the development of rainfall are respectively discussed in Chaps. 4–7. Precipitation efficiency is analyzed in Chap. 8, and the sensitivity of precipitation modeling to uncertainty of initial conditions is studied in Chap. 9. We would like to thank Dr. Mitchell W. Moncrieff, the senior scientist of the National Corporation for Atmospheric Research who read the book draft and wrote the preface for this book. Our sincere thanks also go to Dr. Wei-Kuo Tao at NASA/ Goddard Space Flight Center (GSFC), Professor Ming-Dah Chou at National Taiwan University, and Professor Minghua Zhang at the State University of New York, Stony Brook for providing the two-dimensional Goddard Cumulus Ensemble (GCE) model, the radiative transfer code used in GCE model, and TOGA COARE forcing data, respectively. We also thank Dr. Hsiao-Ming Hsu at the National Center for Atmospheric Research and Prof. Xiaoqing Wu at the Iowa State University for their comments, Drs. Fan Ping, Xiaopeng Cui, and Yushu Zhou at the Institute of Atmospheric Physics, Chinese Academy of Sciences, Dr. Donghai Wang at the China Meteorological Administration, Prof. Xinyong Shen at the Nanjing University of Information Science and Technology, Dr. Jian-Jian Wang at the Goddard Center for Earth Science and Technology, University of Maryland, Baltimore County, and Mr. Yi Wang at the Jiangsu Weather Bureau for efficient and productive research collaborations, and Miss Di Li at the University of Pennsylvania Law School, Philadelphia for editing this book. We are also indebted to Dr. Robert K. Doe of Springer for his editorial efforts. This work was supported by the National Key Basic Research and Development Project of China No.2009CB421505, the National Natural Sciences Foundation of China under the Grant No.40930950 and 41075043. Camp Springs, Maryland, USA Beijing, China

Xiaofan Li Shouting Gao

Contents

1

2

Cloud-Resolving Modeling of Precipitation ........................................... 1.1 Cloud-Resolving Model ..................................................................... 1.2 Weather Events and Large-Scale Forcing for Precipitation Modeling ................................................................. 1.2.1 Experiment COARE............................................................... 1.2.2 Experiment SCSMEX ............................................................ 1.2.3 Experiment BILIS .................................................................. 1.2.4 Experiment PSR ..................................................................... 1.3 Comparison Between Simulations and Observations ........................ 1.3.1 Temperature and Specific Humidity....................................... 1.3.2 Surface Rain Rate ................................................................... 1.3.3 Reflectivity ............................................................................. 1.4 Equilibrium Simulations with Zero Large-Scale Vertical Velocity ................................................................................. 1.5 Comparison Between 2D and 3D Model Simulations ....................... References ................................................................................................... Precipitation Equations and Process Analysis ....................................... 2.1 Precipitation Equations ...................................................................... 2.2 Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity ................................................................................. 2.2.1 Time-Mean Analysis .............................................................. 2.2.2 Analysis of Diurnal Variation................................................. 2.3 Simulation of Rainfall Event During SCSMEX ................................ 2.4 Simulation of Torrential Rainfall Event During the Landfall of Severe Tropical Storm Bilis (2006) ........................... 2.5 Simulation of Pre-summer Heavy Rainfall Event over Southern China in June 2008 ..................................................... References ...................................................................................................

1 2 6 6 6 8 9 9 9 12 15 20 22 23 27 27 32 32 35 38 40 58 60

xi

xii

Contents

3

Tropical Precipitation Processes .............................................................. 63 3.1 Model Domain Mean Analysis .......................................................... 63 3.1.1 Effects of Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of Mean Water Vapor Convergence and Mean Local Atmospheric Drying ............................................................... 64 3.1.2 Effects of Mean Local Atmospheric Drying/ Moistening on Mean Rainfall................................................. 71 3.1.3 Effects of Mean Local Atmospheric Drying/Moistening and Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of the Mean Water Vapor Divergence ........... 73 3.2 Grid-Scale Analysis ........................................................................... 74 3.3 Tropical Rainfall Responses to the Large-Scale Forcing ................... 82 3.4 Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle, and Sea Surface Temperature on Time-Mean Tropical Rainfall Processes ....................................... 92 3.5 Diurnal Cycle ..................................................................................... 101 References ................................................................................................... 108

4

Effects of Sea Surface Temperature ........................................................ 4.1 Introduction ........................................................................................ 4.2 Time-Mean Analysis .......................................................................... 4.3 Analysis of Diurnal Variation............................................................. References ...................................................................................................

111 111 111 116 124

5

Effects of Vertical Wind Shear................................................................. 5.1 Introduction ........................................................................................ 5.2 Effects of Vertical Wind Shear on Severe Tropical Storm Rainfall ... 5.3 Effects of Vertical Wind Shear on Pre-summer Heavy Rainfall ........ References ...................................................................................................

125 125 126 133 136

6

Microphysical and Radiative Effects of Ice Clouds ............................... 6.1 Introduction ........................................................................................ 6.2 Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity ............................................ 6.2.1 Time-Mean Analysis .............................................................. 6.2.2 Diurnal Analysis..................................................................... 6.2.3 Vertical Structures of Thermal and Water Vapor Budgets ..... 6.3 Effects of Ice Clouds on Severe Tropical Storm Rainfall .................. 6.4 Effects of Ice Clouds on Pre-summer Heavy Rainfall ....................... References ...................................................................................................

137 137

7

Cloud Radiative Effects ............................................................................ 7.1 Introduction ........................................................................................ 7.2 Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity ............................................ 7.2.1 Time-Mean Analysis .............................................................. 7.2.2 Analysis of Diurnal Variation.................................................

139 139 141 150 159 166 172 175 175 176 176 178

Contents

7.3 Effects of Cloud Radiative Process and Cloud-Radiation Interaction on Severe Tropical Storm Rainfall................................... 7.4 Cloud Radiative Effects on Pre-summer Heavy Rainfall ................... 7.4.1 Cloud Radiative Effects.......................................................... 7.4.2 Radiative Effects of Water Clouds ......................................... References ...................................................................................................

xiii

187 199 199 201 206

8

Precipitation Efficiency............................................................................. 209 References ................................................................................................... 218

9

Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions .................................................................................. 9.1 Introduction ........................................................................................ 9.2 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions of Temperature, Water Vapor, and Clouds.......................................................................................... 9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures of Initial Conditions ........................................ References ...................................................................................................

219 219

220 225 234

Index ................................................................................................................. 237

Abbreviations and Acronyms

2D 3D

Two-dimensional Three-dimensional

AIRS AMSU ARM

Atmospheric Infrared Sounder Advanced Microwave Sounding Unit Atmospheric Radiation Measurement

CAPE CFAD COARE CMPE

Convective available potential energy Contoured frequency with altitude diagram Coupled Ocean-Atmosphere Response Experiment Cloud-microphysics precipitation efficiency

EQ

Equator

GCE GDAS GSFC

Goddard cumulus ensemble Global Data Assimilation System Goddard Space Flight Center

HSB

Humidity Sounder for Brazil

IFA IMET IOP IR IWP

Intensive Flux Array Improved Meteorological Intensive Observing Period Infrared Ice Water Path

LFC LSPE LST LWP

Level of free convection Large-scale precipitation efficiency Local standard time Liquid Water Path

MSPPS

Microwave Surface and Precipitation Products System

NASA NCEP

National Aeronautics and Space Administration National Centers for Environmental Prediction xv

xvi

Abbreviations and Acronyms

NESDIS NOAA

National Environmental Satellite, Data, and Information Service National Oceanic and Atmospheric Administration

PSU PV PW

Practical salinity units Potential vorticity Precipitable water

RMPE RMS

Rain Microphysics Precipitation Efficiency Root-mean-square

SCSMEX SST

South China Sea Monsoon Experiment Sea surface temperature

TOGA TMI TRMM

Tropical Ocean Global Atmosphere TRMM Microwave Imager Tropical Rainfall Measuring Mission

Chapter 1

Cloud-Resolving Modeling of Precipitation

Precipitation has important impacts on people’s daily life and torrential precipitation could bring tremendous losses in economy and cause fatalities. Thus, precipitation always is one of the top priorities in operational forecast and scientific research. Precipitation is a result of convective development under a favorable environment. The unstable energy is accumulated with favorable environmental thermodynamic conditions when the clouds and associated precipitation are absent. The release of unstable energy drives the growth of clouds that eventually leads to precipitation. The development of clouds and precipitation has important feedback to the environment by redistributing temperature, water vapor, and momentum via radiative, cloud microphysical and dynamic processes. The precipitation processes are determined by environment thermal and water vapor conditions through cloud microphysical processes. The analysis of thermal, water vapor, and cloud microphysical budgets will enhance understanding of precipitation, which is beneficial to the improvement of quantitative precipitation forecast. However, important information such as cloud microphysical processes is not conventionally available, which make observational analysis rather difficult. The cloud-resolving models provide a practical tool for process studies associated with surface rainfall processes (e.g., Gao and Li 2008a). The model has fine horizontal resolution to simulate individual cloud and includes radiative and prognostic cloud microphysical schemes to simulate cloud-radiation interaction processes (Sect. 1.1). In this chapter, two-dimensional (2D) cloud-resolving model simulations of tropical convective events during the Tropical Ocean Global Atmosphere Coupled Ocean– atmosphere Response Experiment (TOGA COARE) (Experiment COARE; Gao and Li 2008b) and South China Sea Monsoon Experiment (SCSMEX) (Experiment SCSMEX; Wang et al. 2007), torrential rainfall event during the landfall of severe tropical storm Bilis (2006) (Experiment BILIS; Wang et al. 2009), and pre-summer heavy rainfall event over southern China in June 2008 (Experiment PSR; Wang et al. 2010; Shen et al. 2011) will be discussed in terms of large-scale forcing (Sect. 1.2), temperature, specific humidity, surface rain rate, reflectivity, and cloud hydrometeor mixing ratios (Sect. 1.3). Equilibrium simulations with zero large-scale vertical X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_1, © Springer Science+Business Media B.V. 2012

1

2

1 Cloud-Resolving Modeling of Precipitation

velocity are introduced in Sect. 1.4. Comparisons between 2D and three-dimensional (3D) simulations are discussed in Sect. 1.5.

1.1

Cloud-Resolving Model

The cloud-resolving model was originally developed by Soong and Ogura (1980); Soong and Tao (1980) for studying convection at the timescale of shorter than a day. This model was significantly improved by Tao and Simpson (1993) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) and was modified by Sui et al. (1994, 1998) for studying tropical convection and associated hydrological cycles at the timescale from weeks to months and tropical equilibrium states. The model was named the Goddard cumulus ensemble (GCE) model. The model includes prognostic equations for perturbation zonal (u) and vertical (w) winds, potential temperature (q), specific humidity (qv), and five cloud hydrometeor mixing ratios. The 2D non-hydrostatic governing equations with anelastic approximation can be expressed by ∂u' 1 ∂( rw ') + = 0, ∂x r ∂z

(1.1a)

∂ u' ∂ 1 ∂ = − (2u'u o + u'u') − r ( w'u o + w o u' + w'u' − w'u') ∂t ∂x r ∂z − cp

∂(qp ') + Du − Du , ∂x

(1.1b)

∂w' ∂ 1 ∂ = − (u'w o + u o w' + u'w') − r (2 w'w o + w'w' − w'w') ∂t ∂x r ∂z − cp

∂(qp ') q' + g( + 0.61qv ' − ql ') + Dw − Dw , ∂z qo

(1.1c)

∂q ∂(u'q ') ∂q ' 1 ∂ ∂q ' ∂q =− − uo − − w' ( rw'q ') − w o ∂t ∂x ∂x r ∂z ∂z ∂z +

Qcn QR ∂q o ∂q + − uo − wo + Dq , pc p pc p ∂x ∂z

(1.1d)

∂qv ∂(u' qv ' ) ∂q ' ∂q ' ∂q 1 ∂ =− − u o v − w o v − w' v − rw' qv ' ∂t ∂x ∂x ∂z ∂z r ∂z − Sqv − u o

∂qv' ∂q − w o v + Dqv , ∂x ∂z

(1.1e)

1.1 Cloud-Resolving Model

3

∂qc ∂(uqc ) 1 ∂( rwqc ) =− − + Sqc + Dqc , r ∂t ∂x ∂z

(1.1f)

∂qr ∂(uqr ) 1 ∂ =− − r (w − wTr )qr + Sqr + Dqr , ∂t ∂x r ∂z

(1.1g)

∂qi ∂(uqi ) 1 ∂( rwqi ) =− − + Sqi + Dqi , r ∂z ∂t ∂x

(1.1h)

∂q s ∂(uqs ) 1 ∂ r (w − wTs )qs + Sqs + Dqs , =− − r ∂z ∂t ∂x

(1.1i)

∂q g ∂t

=−

∂(uqg ) ∂x

−

1 ∂ r (w − wTg )qg + Sqg + Dqg , r ∂z

(1.1j)

where 20

Qcn = ∑ CNPI ,

(1.2a)

I =1 7

Sqv = ∑ PI ,

(1.2b)

I =1 9

Sqc = ∑ CWPI ,

(1.2c)

I =1 12

Sqr = ∑ RPI ,

(1.2d)

I =1 9

Sqi = ∑ CIPI ,

(1.2e)

I =1 15

Sqs = ∑ SPI ,

(1.2f)

I =1 14

Sqg = ∑ GPI ,

(1.2g)

I =1

CNPI = ( Lv PCND − Lv PREVP ), Ls PDEP , Ls (1 − d1 )PSDEP (T < To ), Ls (1 − d1 )PGDEP (T < To ), − Ls PMLTS (T > To ), − Ls PMLTG (T > To ), L f PSACW (T < To ), L f PSFW (T < To ), L f PGACW (T < To ), L f PIACR (T < To ), L f PGACR (T < To ), L f PSACR (T < To ), L f PGFR (T < To ), − L f PRACS (T > To ), − L f PSMLT (T > To ), − L f PGMLT (T > To ), L f PIHOM (T < Too ) − L f PIMLT (T > To ), L f PIDW (Too < T < To )),

(1.2h)

4

1 Cloud-Resolving Modeling of Precipitation

PI = ( PCND , PDEP , (1 − d1 ) PSDEP (T < To ),(1 − d1 ) PGDEP (T < To ), − PREVP , − PMLTG , − PMLTS ),

(1.2i)

CWPI = ( − PSACW , − PRAUT , − PRACW , − PSFW (T < To ), − PGACW , PCND , − PIHOM (T < Too ), PIMLT (T > To ), − PIDW (Too < T < To )),

(1.2j)

RPI = ( PSACW (T > To ), PRAUT , PRACW , PGACW (T > To ), − PREVP , PRACS (T > To ), − PIACR (T < To ), − PGACR (T < To ), − PSACR (T < To ), − PGFR (T < To ), PSMLT (T > To ), PGMLT (T > To )),

(1.2k)

CIPI = ( − PSAUT (T < To ), − PSACI (T < To ), − PRACI (T < To ), − PSFI (T < To ), − PGACI (T < To ), PIHOM (T < Too ), − PIMLT (T > To ), PIDW (Too < T < To , PDEP )),

(1.2l)

SPI = ( PSAUT (T < To ), PSACI (T < To ), PSACW (T < To ), PSFW (T < To ), PSFI (T < To ), PRACI (T < To ), − PRACS (T > To ), − PGACS , − PSMLT (T > To ), − PRACS (T < To ), PSACR (T < To ), PSDEP (T < To ), − PMLTS (T > To ), PIACR (T < To ), − PWACS (T < To )),

(1.2m)

GPI = ( PRACI (T < To ), PGACI (T < To ), PGACW (T < To ), PSACW (T < To ), PGACS , PIACR (T < To ), PGACR (T < To ), PRACS (T < To ), PGFR (T < To ), PWACS (T < To ), − PGMLT (T > To ), PGDEP (T < To ), − PMLTG (T > To ), PSACR (T < To )).

(1.2n)

and d1 = 1, only if qc + qi > 10 −8 gg −1 , T < To ,

(1.2o)

d 2 = 1, only if qs + qr < 10 −4 gg −1 , T < To ,

(1.2p)

d 3 = 1, only if qr > 10 −4 gg −1 , T < To ,

(1.2q)

d 4 = 1, only if qs ≤ 10 −4 gg −1 , qc > 5 × 10 −4 gg −1 , T < To

(1.2r)

Here, qc, qr, qi, qs, and qg, are the mixing ratios of cloud water, raindrops, cloud ice, snow, and graupel, respectively; p = (p/p0)k, k = R/cp; R is the gas constant; cp is the specific heat of dry air at constant pressure p, and po = 1,000 hPa; T is air temperature, and To = 0°C, Too = −35°C. Lv, Ls, and Lf are latent heat of vaporization, sublimation,

1.1 Cloud-Resolving Model

5

Table 1.1 List of microphysical processes and their parameterization schemes Notation Description Scheme PMLTG Growth of vapor by evaporation of liquid from graupel surface RH84 PMLTS Growth of vapor by evaporation of melting snow RH83 PREVP Growth of vapor by evaporation of raindrops RH83 PIMLT Growth of cloud water by melting of cloud ice RH83 PCND Growth of cloud water by condensation of supersaturated vapor TSM PGMLT Growth of raindrops by melting of graupel RH84 PSMLT Growth of raindrops by melting of snow RH83 PRACI Growth of raindrops by the accretion of cloud ice RH84 PRACW Growth of raindrops by the collection of cloud water RH83 PRACS Growth of raindrops by the accretion of snow RH84 PRAUT Growth of raindrops by the autoconversion of cloud water LFO PIDW Growth of cloud ice by the deposition of cloud water KFLC PIACR Growth of cloud ice by the accretion of rain RH84 PIHOM Growth of cloud ice by the homogeneous freezing of cloud water PDEP Growth of cloud ice by the deposition of supersaturated vapor TSM PSAUT Growth of snow by the conversion of cloud ice RH83 PSACI Growth of snow by the collection of cloud ice RH83 PSACW Growth of snow by the accretion of cloud water RH83 PSFW Growth of snow by the deposition of cloud water KFLC PSFI Depositional growth of snow from cloud ice KFLC PSACR Growth of snow by the accretion of raindrops LFO PSDEP Growth of snow by the deposition of vapor RH83 PGACI Growth of graupel by the collection of cloud ice RH84 PGACR Growth of graupel by the accretion of raindrops RH84 PGACS Growth of graupel by the accretion of snow RH84 PGACW Growth of graupel by the accretion of cloud water RH84 PWACS Growth of graupel by the riming of snow RH84 PGDEP Growth of graupel by the deposition of vapor RH84 PGFR Growth of graupel by the freezing of raindrops LFO The schemes are Lin et al. (1983, LFO), Rutledge and Hobbs (1983, 1984, RH83, RH84); Tao et al. (1989, TSM), and Krueger et al. (1995, KFLC)

and fusion at 0°C, respectively, and Ls = Lv + Lf. QR in (1.1d) is the radiative heating rate due to convergence of the net flux of solar and infrared radiative fluxes calculated by solar and thermal infrared radiation parameterization schemes (Chou et al. 1991, 1998; Chou and Suarez 1994). The cloud microphysical terms in prognostic cloud Eqs. 1.2h–1.2n are calculated by single-moment cloud microphysical parameterization schemes (Lin et al. 1983; Rutledge and Hobbs 1983, 1984; Tao et al. 1989; Krueger et al. 1995), which are defined in Table 1.1. wTr in (1.1g), wTs in (1.1i) and wTg in (1.1j) are terminal velocities for raindrops, snow, and graupel, respectively; overbar denotes a model domain mean; prime is a perturbation from model domain mean; and superscript o is an imposed observed value. The model uses cyclic lateral boundaries and has a horizontal domain of 768 km with 33 vertical levels, and its horizontal and temporal resolutions are 1.5 km and 12 s, respectively. The top

6

1 Cloud-Resolving Modeling of Precipitation

model level is 42 hPa. The vertical grid resolution ranges from about 40–200 m near the surface to about 1 km near 100 hPa. The observed surface temperature and specific humidity over land and the observed sea surface temperature over ocean are uniformly imposed on each model grid to calculate surface sensible heat flux and evaporation flux. The model details can be found in Gao and Li (2008a).

1.2

1.2.1

Weather Events and Large-Scale Forcing for Precipitation Modeling Experiment COARE

The cloud resolving model in experiment COARE is forced by large-scale vertical velocity, zonal wind, and horizontal advections derived using 6-hourly TOGA COARE observations within the Intensive Flux Array (IFA) region from Professor M. Zhang of the State University of New York at Stony brook and hourly SST at the Improved Meteorological (IMET) surface mooring buoy (1.75°S, 156°E) from Weller and Anderson (1996), (Gao and Li 2008b). The model is integrated from 0400 Local Standard Time (LST) 22 December 1992 to 0400 LST 08 January 1993. Figure 1.1 shows the time-height cross sections of the large-scale vertical velocity, zonal wind, and the time series of SST from 0400 LST 22 December 1992 to 0400 LST 8 January 1993, which are imposed in the model. On 22–27 December 1992, the strong upward motions with a maximum of 8 cm s−1 are associated with westerly winds of 10 m s−1. From 28 December 1992 to 2 January 1993, the downward motions of −1 cm s−1 occur while the westerly winds reach a maximum of 16 m s−1. In the last few days, the moderate upward motions occur as westerly winds weaken. Except for the last 4 days, the SST has only a weak diurnal variation with a slowly decreasing trend.

1.2.2

Experiment SCSMEX

The forcing (Fig. 1.2) averaged over the area of 16°–23°N, 116°–117°E using 6-hourly observational data from SCSMEX Intensive Observing Period (Johnson and Ciesielski 2002) and daily-mean SST data (not shown) retrieved from NASA/ Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer with a 10.7 GHz channel (Wentz et al. 2000) are imposed in the model in Experiment SCSMEX (Wang et al. 2007). The model is integrated from 0200 LST 20 May to 1400 LST 24 May 1998. Downward motions occur in early morning of 20 May 1998, followed by the strong upward motions around early afternoon of 20 May. The upward motions continue to dominate the rest of the integration period, while they are briefly interrupted by a few downward motion events, in particular, in the mid and lower troposphere. The southerly winds start to diminish with the strengthened

1.2 Weather Events and Large-Scale Forcing for Precipitation Modeling

7

Fig. 1.1 Time-height distributions of (a) vertical velocity (cm s−1) and (b) zonal wind (m s−1), and (c) time series of sea surface temperature (°C) observed and derived from TOGA COARE, which are used in Experiment COARE as the large-scale forcing. Upward motion in (a) and westerly wind in (b) are shaded (After Gao and Li 2008b)

northerly winds, which propagate downward. The southerly winds regain strengths in the mid and lower troposphere on the last day of the integration period, although the northerly winds remain strong in the upper troposphere.

8

1 Cloud-Resolving Modeling of Precipitation

Fig. 1.2 Temporal and vertical distributions of (a) vertical velocity (cm s−1) and (b) meridional wind (m s−1) during selected SCSMEX period, which are used in Experiment SCSMEX as the large-scale forcing. Upward motion in (a) and southerly wind in (b) are shaded. The arrows above (a) indicate the analysis period in this study (After Wang et al. 2007)

1.2.3

Experiment BILIS

The reanalysis data from National Centers for Environmental Prediction (NCEP)/ Global Data Assimilation System (GDAS) that have a horizontal resolution of 1° × 1°

1.3

Comparison Between Simulations and Observations

9

and a temporal resolution of four times per day are used to construct large-scale forcing (vertical velocity, zonal wind, and horizontal temperature and vapor advection) in Experiment BILIS (Wang et al. 2009). Bilis made its second landfall in Fujian, China early on July 14, and then weakened into a tropical depression over land the next day. It brought a torrential rainfall over the areas of southeast China (Fujian, Guangdong, Guangsi, and Hunan provinces) during 15–17 July 2006, and dissipated on 18 July 2006. The model is integrated from 0800 LST 14 July to 0800 LST 20 July 2006 with the forcing averaged in a rectangular box of 108–116°E, 23–24°N (Fig. 1.3). Figure 1.3 shows the temporal-vertical cross sections of the large-scale vertical velocity and zonal wind that are imposed in the model during the integration. Upward motions are dominant during most of integration period except that weak downward motions occur during 18–20 July 2006.

1.2.4

Experiment PSR

The data from NOAA/GDAS are used to calculate the forcing data for the model over a longitudinally oriented rectangular area of 108–116°E, 21–22°N over coastal areas along southern Guangdong and Guangxi Provinces and surrounding northern South China Sea in Experiment PSR. The model is imposed by large-scale vertical velocity, zonal wind (Fig. 1.4), and horizontal temperature and water vapor advections (not shown) and is integrated from 0200 LST 3 June to 0200 LST 8 June 2008 during the pre-summer heavy rainfall in experiment PSR. The imposed large-scale vertical velocity shows that upward motions increase from 3 June to 6 June with a maximum upward motion of 18 cm s−1 around 9 km in the late morning of 6 June. The upward motions decrease dramatically on 7 June. The lower-tropospheric westerly winds of 4–12 m s−1 are maintained during the rainfall event.

1.3 1.3.1

Comparison Between Simulations and Observations Temperature and Specific Humidity

Gao and Li (2008b) compared the vertical profiles of simulated temperature and specific humidity in COARE with observations through the analysis of their differences in experiment COARE (Fig. 1.5). Compared to the observations, the simulations yield 1–2°C warmer upper troposphere and 1–2 g kg−1 more humid lower troposphere in December 1992 and 1–2°C colder mid and lower troposphere and 1 g kg−1 drier atmosphere in January 1993. The model tends to produce a cooling bias while the observed vertical temperature profile shows regular diurnal signals. The difference in specific humidity between the simulation and observation can be as high as 2–3 g kg−1 in the lower troposphere from 31 December 1992 to 3 January

10

1 Cloud-Resolving Modeling of Precipitation

Fig. 1.3 Time-pressure cross sections of (a) vertical velocity (cm s−1) and (b) zonal wind (m s−1) from 0800 LST 14 July to 0800 LST 20 July 2006, which are used in Experiment BILIS as the largescale forcing. Upward motion in (a) and westerly wind in (b) are shaded (After Wang et al. 2009)

1993 when the dry atmosphere is associated with large-scale downward motions (Fig. 1.1a). The difference in specific humidity results partially from the phase shift and the duration difference in drying between the simulation and observation. Shen et al. (2011) compared the simulations in PSR with vertical profiles of temperature and specific humidity from NCEP/GDAS (Fig. 1.6). The simulated

1.3

Comparison Between Simulations and Observations

11

Fig. 1.4 Temporal and vertical distributions of (a) vertical velocity (cm s−1) and (b) zonal wind (m s−1) from 0200 LST 3 June to 0200 LST 8 June 2008, which are used in Experiment PSR as the large-scale forcing. The data are averaged in a rectangular box of 108–116°E, 21–22°N from NCEP/GDAS data. Ascending motion in (a) and westerly wind in (b) are shaded (After Wang et al. 2010)

temperature and specific humidity are, respectively, −1°C and −1 g kg−1 smaller than the temperature and specific humidity from NCEP/GDAS, and their root-meansquared (RMS) differences are 0.61°C and 0.39 g kg−1.

12

1 Cloud-Resolving Modeling of Precipitation

Fig. 1.5 Time-height distributions of (a) temperature difference between the simulation in COARE and observation (°C) and (b) specific humidity difference (g kg−1). Positive differences are shaded (After Gao and Li 2008b)

1.3.2

Surface Rain Rate

The simulated surface rain rates in COARE generally follow the observations (Fig. 1.7). The observed surface rain rate is derived by taking an average over a 150 × 150 km2 area, which is based on radar reflectivity data taken from the Massachusetts Institute of Technology Doppler radar and the TOGA radar located within the Intensive Flux Array (IFA) region (Short et al. 1997). The linear correlation

1.3

Comparison Between Simulations and Observations

13

a

b

Fig. 1.6 Time-height distributions of (a) temperature difference (°C) and specific humidity difference (g kg−1) between experiment PSR and NCEP/GDAS data (After Shen et al. 2011)

coefficient between simulated and observed rain rates is 0.45. A Student’s t-test on the significance of the correlation coefficients is further conducted and a critical correlation coefficient at the 1% significant level is 0.128. Thus, the correlation between simulated and observed rain rates is statistically significant. But the simulated amplitudes are generally larger than the observed amplitudes and there are some phase differences. Gao et al. (2006) showed that in a zero-order approximation the surface rain rate is determined by vertical moisture advection in the model domain mean mass-integrated water vapor budget. Li et al. (1999) revealed that the difference in rain rate between simulations and observations is partly caused by an inconsistency between the imposed vertical velocity and the observed rain rate. The prognostic cloud scheme used in the cloud-resolving model produces larger condensates than do the observations (Li and Weng 2004) and may contribute to a relatively large simulated rain rate. Wang et al. (2009) compared domain-mean simulated surface rain rate in BILIS with observed surface rain rate in Fig. 1.8. The observed surface rain rate is calculated using the rain gauge data in the model domain (108–116°E, 23–24°N). The simulated and observed surface rain rates show a similarity, in particular, during the period of 16–17 July 2006. The simulated rain rate differs from the observed rain rate. First, the simulated rain rate leads the observed rain rate by 3–5 h. Second, the simulated rain rate is generally higher than the observed rain rate, in particular, in late afternoon of 16 July and early morning of 17 July 2006. Third, the simulation does not produce the small rain rate on 18 July 2006. Fourth, unlike the observation, the simulation generates the moderate rain rate on late 19 and 20 July 2006.

14

1 Cloud-Resolving Modeling of Precipitation

Fig. 1.7 Time series of model domain-mean surface rain rate (PS) simulated in COARE (solid). The dashed line denotes observed surface rain rate. Unit is mm h−1

Fig. 1.8 Time series of model domain-mean surface rain rate (PS) simulated in BILIS (solid). Unit is mm h−1 (After Wang et al. 2009)

The differences may result partially from the inconsistent calculations of phase and magnitude of the imposed vertical velocity from the 6-hourly NCEP/GDAS data and partially from the sampling and accuracy of observed rain gauge data.

1.3

Comparison Between Simulations and Observations

15

Fig. 1.9 Surface rain rates (PS) simulated in PSR (solid) and from rain gauge observation (dash). Unit is mm h−1 (After Wang et al. 2010)

The observational rain rate is averaged by hourly rain gauge data collected from 17 rain gauge stations over the model domain (108–116°E, 21–22°N) in PSR during presummer heavy rainfall event over southern China in June 2008 (Fig. 1.9). The RMS difference (0.97 mm h−1) between model domain mean rain rate in PSR and observed rain rate is significantly smaller than the standard derivations of simulated (1.34 mm h−1) and observed (1.26 mm h−1) rain rates (Shen et al. 2011), indicating that the simulated rain rate in PSR captures the variation of observed rain rate. There is a similarity in the peak rainfall period, whereas the differences between observed and simulated rain rate could be up to 2 mm h−1, particular at the beginning and end of the period. The differences may result partially from the comparison of small hourly local sampling of rain gauge observations over 35% of model domain over land and no rain gauge observations over 65% of model domain over ocean with large model domain averages of model simulation data in PSR with imposed 6-hourly large-scale forcing.

1.3.3

Reflectivity

Wang et al. (2007) converted the model hydrometeor density into the effective radar reflectivity [Ze (dBZ)] and compared it with the CPOL radar measurement (Figs. 1.10 and 1.11). The effective reflectivity factor (ze) can be written by ze =

nog | K i |2 n n Γ (7)( or7 + os7 + 7 ), 2 | Kw | lr ls lg

(1.3)

16

1 Cloud-Resolving Modeling of Precipitation A’ 10 ms−1

A 15

12 −1

Height (km)

20 ms

9

6

dBZ 10 20 30 35 40 45 50

3

0

-20

0 10 -10 Distance north of CPOL radar(km)

20

Fig. 1.10 Meridional-vertical (Y-Z) cross section of radar reflectivity (shaded) and system-relative wind flow (arrow vector) along a specific horizontal line at 0800 LST 20 May 1998 from observations (After Wang et al. 2007)

where G is a Gamma function, n0r, n0s, and n0g are the intercept values of raindrop, snow, and graupel size distributions, respectively; lr, ls, and lg are the slopes of raindrop, snow, and graupel size distribution, respectively; |Kw|2 is the dielectric fraction of water (0.93), and |Ki|2 is the dielectric fraction of equivalent ice spheres (0.176). Then, the effective radar reflectivity (Ze) can be calculated by Z e = 10 log10 (z e ).

(1.4)

Wang et al. (2007) also calculated model hydrometeor density in SCSMEX using a difference reflectivity method (Golestani et al. 1989) for mixed phase precipitation and a method proposed by Bringi and Chandrasekar (2001) for pure rain and compared model hydrometeor density with observed hydrometeor density (Figs. 1.12 and 1.13). The similarity between the observation and simulation shows stable positions of convective system. The reflectivity decreases significantly with increasing height above the melting layer, while it generally shows little tilt in vertical direction. The updraft maximum and convective center are collocated, and convective center is surrounded by convective downdrafts. The weak convective cold pool is caused by expanded updraft area. The difference between the observation and simulation reveals that the simulated updraft is much stronger than the observation partially because of 2D model framework. The altitude of model reflectivity maximum is much higher than that of the observed reflectivity center. The maximum model hydrometeor density appears in the mid troposphere but the maximum observed hydrometeor density occurs near the surface. The model hydrometeor density is

1.3

Comparison Between Simulations and Observations

17

Fig. 1.11 Model-derived meridional-vertical (Y-Z) cross sections of reflectivity (dBz) and wind vectors (m s−1) from SCSMEX at (a) 0700 LST, (b) 0800 LST, and (c) 0900 LST 20 May 1998 (After Wang et al. 2007)

18

1 Cloud-Resolving Modeling of Precipitation

a

A’

A 15

dB 12

Height (km)

0.5 1.0

9

1.5 6

2.0 2.5

3

0

-20

-10 0 10 Distance north of CPOL radar(km)

b

A 15

20 A’ g/m3

6

0.0 0.5 1.0 1.5 2.0 2.5 3.0

3

3.5 4.0 4.5

12

Height (km)

9

0

-20

-10 0 10 Distance north of CPOL radar(km)

20

Fig. 1.12 As Fig. 1.10, but for (a) differential reflectivity (dB), and (b) rainwater density (shaded; g m−3) and ice water density (contoured at 0.1, 0.5, 1.0 g m−3) retrieved from radar reflectivity and polarimetric parameters (After Wang et al. 2007)

larger than the observed hydrometeor density. These differences are associated with the overestimation of updrafts in the model simulation. Following Wang et al. (2007), Wang et al. (2009) compared the effective radar reflectivity [Ze (dBz)] converted from the model calculated hydrometeor density in BILIS with observed reflectivity (Fig. 1.14). Observed vertical distribution is constructed by averaging data over the model domain (108–116°E, 23–24°N) in 15 July 2006,

1.3

Comparison Between Simulations and Observations

19

Fig. 1.13 Model-derived meridional-vertical (Y-Z) cross sections of rainwater density (shaded; g m−3) and ice water density (contoured at 0.1, 0.5, 1, 2, 3, 4 g m−3) from SCSMEX at (a) 0700 LST, (b) 0800 LST, and (c) 0900 LST 20 May 1998 (After Wang et al. 2007)

whereas simulated vertical profile is calculated by taking model domain mean in 15 July 2006. Both vertical distributions show maximum reflectivity around 4 km while the simulated reflectivity is larger than observed reflectivity below 8 km, in particular, near the surface. This implies that the model may produce a large amount of water clouds.

20

1 Cloud-Resolving Modeling of Precipitation

Fig. 1.14 Vertical distributions of radar reflectivity (dBz) from observation (dash) and simulation in BILIS (solid) averaged in 15 July 2006 (After Wang et al. 2009)

1.4

Equilibrium Simulations with Zero Large-Scale Vertical Velocity

The large-scale vertical velocity may include effects of SST and its diurnal variation, cloud radiative and microphysical processes. To examine effects of SST and its diurnal variation, cloud radiative and microphysical processes on rainfall, a series of experiments are conducted using the 2D model that is imposed with zero vertical velocity and constant zonal wind (Gao et al. 2007a; Ping et al. 2007; Gao 2008). The sensitivity experiments are summarized in Table 1.2. SST29 and SST31 are identical except that different time-invariant SSTs of 29 and 31°C are used, respectively. These experiments are used to study the effects of SST on rainfall. SST29D is identical to SST29 except diurnally-varied SSTs with a mean of 29°C and diurnal amplitude of 1°C in SST29D. The comparison of SST29D with SST29 shows the effects of diurnal variation of SST on diurnal variation of rainfall. Experiments SST29NIR, SST29NWR, and SST29NCR are identical to SST29 except that

1.4

Equilibrium Simulations with Zero Large-Scale Vertical Velocity

Table 1.2 Summary of seven equilibrium experiments Experiment SST SST29 Time-invariant (29°C) SST31 Time-invariant (31°C) SST29D Diurnally-varied with mean of 29°C and maximum diurnal difference of 1°C SST29NCR Time-invariant (29°C) SST29NIR SST29NWR

Time-invariant (29°C) Time-invariant (29°C)

SST29NIM

Time-invariant (29°C)

Table 1.3 Mass-weighted mean temperature (°C) and precipitable water (mm) averaged over model domain from day 31 to day 40 in seven equilibrium experiments

21

Radiation Yes Yes Yes

Ice microphysics Yes Yes Yes

No for both water and ice clouds No for ice clouds No for water clouds

Yes Yes Yes No

Experiment SST29 SST31 SST29D SST29NCR SST29NIR SST29NWR SST29NIM

Mass-weight mean temperature −3.0 0.1 −3.6 −8.1 −7.4 −3.4 −5.9

Precipitable water 44.9 52.5 44.6 37.5 35.7 44.0 41.4

SST29NIR, SST29NWR, and SST29NCR exclude the radiative effects of ice clouds, water clouds, and clouds (both ice and water clouds) by setting the mixing ratios of ice, water, and cloud hydrometeors to zero in the calculations of radiation, respectively. The comparisons between SST29NCR and SST29, between SST29NIR and SST29, and between SST29NWR and SST29, respectively, reveal cloud, ice, and water radiative effects on rainfall. The comparisons between SST29NWR and SST29 and between SST29NCR and SST29NIR show radiative effects of water clouds on rainfall in the presence and absence of radiative effects of ice clouds, respectively. Experiment SST29NIM excludes ice-cloud variables and associated ice microphysical and radiative processes by turning off the ice microphysics scheme during the model integration. The comparison between SST29NIM and SST29NIR shows microphysical effects of ice clouds in rainfall in the absence of ice radiative effects. All the experiments are integrated to quasi-equilibrium thermodynamic states during the 40-day integrations. Mass-weighted mean temperature and precipitable water (PW) averaged over model domain from day 31 to day 40 in seven equilibrium experiments in Table 1.3 reveal that higher SST in SST31 produces a warmer and more humid equilibrium state whereas the inclusion of diurnal variation of imposed SST in SST29D causes a slightly colder and drier equilibrium state compared to SST29. The exclusion of radiative effects of ice clouds in SST29NIR generates significantly colder and drier

22

1 Cloud-Resolving Modeling of Precipitation

equilibrium state than the inclusion in SST29 does. The exclusion of microphysical effects of ice clouds in SST29NIM yields warmer and moister equilibrium state than the inclusion in SST29NIR under the conditions that both experiments exclude radiative effects of ice clouds. The differences in equilibrium thermodynamic states between SST29 and SST29NWR and between SST29NCR and SST29NIR are much smaller than the differences between SSTNIR and SST29 and between SST29NCR and SST29NWR; indicating the minor role of water clouds in determining equilibrium thermodynamic states. Further analysis of mass-weighted mean heat budgets and precipitable water budgets in seven equilibrium experiments shows that a warmer temperature in SST31 produces a higher surface evaporation flux that causes a moister atmosphere than is found in SST29 (Gao et al. 2007a). The moister atmosphere in SST31 leads to a warmer atmosphere through more condensation and associated latent heat than in SST29. The simulation with the diurnally-varied SST in SST29D produces colder temperatures through less condensational heating and larger IR cooling than the simulation with time-invariant SST in SST29 does. The exclusion of ice radiative effects produces a colder and drier equilibrium state in SST29NIR than in SST29 through more IR cooling and more consumption of water vapor in SST29NIR, whereas the exclusion of ice microphysical effects generates a warmer and more humid equilibrium state in SST29NIM than in SST29NIR through less IR cooling associated with water clouds and less consumption of water vapor in SST29NIM (Ping et al. 2007). The comparison of heat and water vapor budgets between SST29NCR and SST29 indicates that SST29NCR generates a colder and drier equilibrium state through more IR radiative cooling than SST29 does (Gao 2008). A further comparison of radiation budgets between SST29NCR and SST29 shows that SST29NCR emits more IR radiation into space than SST29 does. The IR cooling causes colder temperature, stronger air-sea flux exchanges, lower air capacity to hold water vapor, and thus consumes more water vapor to produce more condensates and surface rainfall in SST29NCR than in SST29. The exclusion of ice radiative effects in both SST29NCR and SST29NIR leads to the smaller IR-induced temperature difference and the inclusion of ice radiative effects in both SST29NWR and SST29 also yields the smaller IR-induced temperature difference. The similar IR emission leads similar cold and dry equilibrium states in SST29NCR and SST29NIR and similar warm and humid equilibrium states in SST29NWR and SST29.

1.5

Comparison Between 2D and 3D Model Simulations

It should be noted that the results included in this book come only from the analysis of the 2D model simulation data. The 2D and 3D models produce differences while they show similarities in collective thermodynamic feedback effects, vertical transports of mass, sensible heat, and moisture, thermodynamic fields, surface heat fluxes, surface precipitation, precipitation efficiency, and convective and moist vorticity vectors (e.g., Tao and Soong 1986; Tao et al. 1987; Grabowski et al. 1998; Tompkins

References

23

2000; and Khairoutdinov and Randall 2003; Gao et al. 2004, 2005, 2007b; Sui et al. 2005). Moncrieff and Miller (1976) argued that the 3D cross-over flow pattern associated with propagating tropical squall lines can be only simulated in the 3D framework whereas Rotunno et al. (1988) found that the basic dynamics associated with longlived squall lines in strong low-level shear can be captured in the 2D model framework. Xu et al. (2002) carried out an intercomparison study of cloud-resolving models during the Atmospheric Radiation Measurement (ARM) and found that the differences between 2D and 3D model simulations may be caused by the differences between 2D and 3D dynamics. Gao et al. (2005) and Gao (2007) revealed that the horizontal and vertical components of dynamic vorticity vector are highly correlated with cloud hydrometeors, respectively, in 3D and 2D model framework because dominant components in horizontal 3D dynamic vorticity vector are excluded from the 2D model framework. Stephens et al. (2008) revealed the difference in spatial scales of precipitable-water variability between 2D and 3D model simulations while they showed similarities in the equilibrium states and the feedbacks related to radiative processes. Thus, the previous cloud-resolving modeling studies revealed differences in dynamics between the 2D and 3D models whereas they showed similarities in thermodynamics and precipitation.

References Bringi VN, Chandrasekar V (2001) Polarimetric Doppler weather radar: principles and applications. Cambridge University Press, Cambridge, 636 pp Chou MD, Suarez MJ (1994) An efficient thermal infrared radiation parameterization for use in general circulation model. NASA Tech Memo 104606, 3 Chou MD, Kratz DP, Ridgway W (1991) IR radiation parameterization in numerical climate studies. J Climate 4:424–437 Chou MD, Suarez MJ, Ho CH, Yan MMH, Lee KT (1998) Parameterizations for cloud overlapping and shortwave single-scattering properties for use in general circulation and cloud ensemble models. J Climate 11:202–214 Gao S (2007) A three dimensional dynamic vorticity vector associated with tropical oceanic convection. J Geophys Res. doi:10.1029/2006JD008247 Gao S (2008) A cloud-resolving modeling study of cloud radiative effects on tropical equilibrium states. J Geophys Res. doi:10.1029/2007JD009177 Gao S, Li X (2008a) Cloud-resolving modeling of convective processes. Springer, Dordrecht, 206 pp Gao S, Li X (2008b) Responses of tropical deep convective precipitation systems and their associated convective and stratiform regions to the large-scale forcing. Q J R Meteorol Soc 134:2127– 2141, (c) Royal Meteorological Society. Reprinted with permission Gao S, Ping F, Li X, Tao WK (2004) A convective vorticity vector associated with tropical convection: a two-dimensional cloud-resolving modeling study. J Geophys Res. doi:10.1029/2004JD004807 Gao S, Cui X, Zhou Y, Li X, Tao WK (2005) A modeling study of moist and dynamic vorticity vectors associated with 2D tropical convection. J Geophys Res. doi:10.1029/2004JD005675 Gao S, Ping F, Li X (2006) Tropical heat/water vapor quasi-equilibrium and cycle as simulated in a 2D cloud resolving model. Atmos Res 79:15–29 Gao S, Zhou Y, Li X (2007a) Effects of diurnal variations on tropical equilibrium states: a twodimensional cloud-resolving modeling study. J Atmos Sci 64:656–664

24

1 Cloud-Resolving Modeling of Precipitation

Gao S, Li X, Tao WK, Shie CL, Lang S (2007b) Convective and moist vorticity vectors associated with tropical oceanic convection: a three-dimensional cloud-resolving simulation. J Geophys Res. doi:10.1029/2006JD007179 Golestani Y, Chandrasekar V, Bringi VN (1989) Intercomparison of multiparameter radar measurements. Preprint. In: 24th international conference on Radar conference, Boston, Am Meteorol Soc, 309–314 Grabowski WW, Wu X, Moncrieff MW, Hall WD (1998) Cloud-resolving model of tropical cloud systems during Phase III of GATE. Part II: effects of resolution and the third spatial dimension. J Atmos Sci 55:3264–3282 Johnson RH, Ciesielski PE (2002) Characterstics of the 1998 summer monsoon onset over northern South China Sea, J Meteorol Soc Japan 80: 561–578 Khairoutdinov MF, Randall DA (2003) Cloud resolving modeling of the ARM summer 1997 IOP: model formulation, results, uncertainties, and sensitivities. J Atmos Sci 60:607–625 Krueger SK, Fu Q, Liou KN, Chin HNS (1995) Improvement of an ice-phase microphysics parameterization for use in numerical simulations of tropical convection. J Appl Meteorol 34:281–287 Li X, Weng F (2004) An operational cloud verification system and its application to validate cloud simulations in the operational models. In: 13th conference on satellite meteorology and oceanography, Norfolk, 20–24 Sept 2004 Li X, Sui CH, Lau KM, Chou MD (1999) Large-scale forcing and cloud-radiation interaction in the tropical deep convective regime. J Atmos Sci 56:3028–3042 Lin YL, Farley RD, Orville HD (1983) Bulk parameterization of the snow field in a cloud model. J Climate Appl Meteorol 22:1065–1092 Moncrieff MW, Miller MJ (1976) The dynamics and simulation of tropical cumulonimbus and squall line. Q J R Meteorol Soc 102:373–394 Ping F, Luo Z, Li X (2007) Microphysical and radiative effects of ice clouds on tropical equilibrium states: a two-dimensional cloud-resolving modeling study. Mon Weather Rev 135:2794–2802 Rotunno R, Klemp JB, Weisman ML (1988) A theory for strong, long-lived squall lines. J Atmos Sci 45:463–485 Rutledge SA, Hobbs RV (1983) The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. Part VIII: a model for the “seeder-feeder” process in warm-frontal rainbands. J Atmos Sci 40:1185–1206 Rutledge SA, Hobbs RV (1984) The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude clcones. Part XII: a diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. J Atmos Sci 41:2949–2972 Shen X, Wang Y, Li X (2011) Effects of vertical wind shear and cloud radiative processes on responses of rainfall to the large-scale forcing during pre-summer heavy rainfall over southern China. Q J R Meteorol Soc 137:236–249, (c) Royal Meteorological Society. Reprinted with permission Short DA, Kucera PA, Ferrier BS, Gerlach JC, Rutledge SA, Thiele OW (1997) Shipboard radar rainfall patterns within the TOGA COARE IFA. Bull Am Meteorol Soc 78:2817–2836 Soong ST, Ogura Y (1980) Response of tradewind cumuli to large-scale processes. J Atmos Sci 37:2035–2050 Soong ST, Tao WK (1980) Response of deep tropical cumulus clouds to mesoscale processes. J Atmos Sci 37:2016–2034 Stephens GL, van den Heever S, Pakula L (2008) Radiative-convective feedbacks in idealized states of radiative convective equilibrium. J Atmos Sci 65:3899–3916 Sui CH, Lau KM, Tao WK, Simpson J (1994) The tropical water and energy cycles in a cumulus ensemble model. Part I: equilibrium climate. J Atmos Sci 51:711–728 Sui CH, Li X, Lau KM (1998) Radiative-convective processes in simulated diurnal variations of tropical oceanic convection. J Atmos Sci 55:2345–2359 Sui CH, Li X, Yang MJ, Huang HL (2005) Estimation of oceanic precipitation efficiency in cloud models. J Atmos Sci 62:4358–4370 Tao WK, Simpson J (1993) The goddard cumulus ensemble model. Part I: model description. Terr Atmos Ocean Sci 4:35–72

References

25

Tao WK, Soong ST (1986) The study of the response of deep tropical clouds to mesoscale processes: three-dimensional numerical experiments. J Atmos Sci 43:2653–2676 Tao WK, Simpson J, Soong ST (1987) Statistical properties of a cloud ensemble: a numerical study. J Atmos Sci 44:3175–3187 Tao WK, Simpson J, McCumber M (1989) An ice-water saturation adjustment. Mon Weather Rev 117:231–235 Tompkins AM (2000) The impact of dimensionality on long-term cloud-resolving model simulations. Mon Weather Rev 128:1521–1535 Wang JJ, Li X, Carey L (2007) Evolution, structure, cloud microphysical and surface rainfall processes of a monsoon convection during the South China Sea monsoon experiment. J Atmos Sci 64:360–380, (c) American Meteorological Society. Reprinted with permission Wang D, Li X, Tao WK, Liu Y, Zhou H (2009) Torrential rainfall processes associated with a landfall of severe tropical storm Bilis (2006): a two-dimensional cloud-resolving modeling study. Atmos Res 91:94–104, (c) Elsevier. Reprinted with permission Wang Y, Shen X, Li X (2010) Microphysical and radiative effects of ice clouds on responses of rainfall to the large-scale forcing during pre-summer heavy rainfall over southern China. Atmos Res 97:35–46, (c) Elsevier. Reprinted with permission Weller RA, Anderson SP (1996) Surface meteorology and air-sea fluxes in the western equatorial Pacific warm pool during TOGA COARE. J Climate 9:1959–1990 Wentz FJ, Gentemann C, Smith D, Chelton D (2000) Satellite measurements of sea surface temperature through clouds. Science 288:847–850 Xu KM, Cederwall RT, Donner LJ, Grabowski WW, Guichard F, Johnson DE, Khairoutdinov M, Krueger SK, Petch JC, Randall DA, Seman CJ, Tao WK, Wang D, Xie SC, Yio JJ, Zhang MH (2002) An intercomparison of cloud resolving models with the atmospheric radiation measurement summer 1997 intensive observation period data. Q J R Meteorol Soc 128:593–624

Chapter 2

Precipitation Equations and Process Analysis

Precipitation is the production of cloud microphysical processes, which is governed by cloud budget. The cloud microphysical processes are associated with thermal and water vapor processes, which are governed by thermal and water vapor budgets. The diagnostic surface rainfall equations are derived from the combinations of cloud budget with water vapor and thermal budgets in Sect. 2.1 (Gao and Li 2010). The precipitation equations are applied to the analysis of surface rainfall processes in SST29 in Sect. 2.2 (Zhou and Li 2009, 2011), SCSMEX in Sect. 2.3 (Wang et al. 2007), BILIS in Sect. 2.4 (Wang et al. 2009, 2010), and PSR in Sect. 2.5 (Shen et al. 2011).

2.1

Precipitation Equations

The environmental temperature and water vapor, and clouds play important roles in precipitation processes. The clouds grow as environmental thermodynamic conditions are favorable for convective development (Fig. 2.1). The cloud microphysical processes along with dynamic updrafts and downdrafts produce precipitation. A 3D precipitation physical space is defined with three basic prognostic variables (Fig. 2.2). They are water vapor (specific humidity; qv), temperature (T), and clouds (cloud hydrometeor mixing ratio; ql = qc + qr + qi + qs + qg). There are three basic relations in the precipitation physical space. They are water vapor, heat, and cloud budgets. From (1.1d–1.1j), the budgets in the 2D framework can be written as ¶q v ¶(u¢ qv ¢ ) ¶q ¢ ¶q ¢ ¶q 1 ¶ r w ¢ qv ¢ =- u o v - w o v - w¢ v ¶t ¶x ¶x ¶z ¶z r ¶z ¶q ¶q - Sqv - u o v - w o v , ¶x ¶z

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_2, © Springer Science+Business Media B.V. 2012

(2.1a)

27

28

2

Precipitation Equations and Process Analysis

Fig. 2.1 A schematic diagram of a precipitation system

Fig. 2.2 Three-dimensional precipitation physical space

¶T ¶ ¶q o ¶ ¶q = - (u o + u¢ )T ¢ - p u o - p w o (q + q ¢ ) - p w¢ ¶t ¶x ¶x ¶z ¶z Qcn QR p ¶ ( r w ¢q ¢ ) + c + c , p p r ¶z ¶ql ¶(uql ) 1 ¶ 1 ¶ r wql + =ρ (wTr qr + wTs qs + wTg qg ) + Sqv , r ¶z r ¶z ¶t ¶x

(2.1b)

(2.1c)

where 18

P18 = å P18 I , I =1

(2.2a)

2.1

Precipitation Equations

29

P18 I = ( PDEP , PSDEP , PGDEP , - PMLTS , - PMLTG , PSACW (T < To ), PSFW (T < To ), PGACW (T < To ), PIACR (T < To ), PGACR (T < To ), PSACR (T < To ), PGFR (T < To ), - PRACS (T > To ), - PSMLT (T > To ), - PGMLT (T > To ), PIHOM (T < Too ), - PIMLT (T > To ), + PIDW (Too < T < To )).

(2.2b)

(2.1) shows that Sqv links the water vapor, heat, and cloud budgets. Following Gao et al. (2005) and Sui and Li (2005), the cloud budget (2.1c) and water vapor budget (2.1a) are mass integrated, which can be, respectively, written as PS - QCM = QWVS = QWVOUT + QWVIN ,

(2.3)

QWVT + QWVF + QWVE = QWVS ,

(2.4)

PS = Pr + Ps + Pg ,

(2.5a)

Pr = ρ wTr qr |z = 0 ,

(2.5b)

Ps = ρ wTs qs |z = 0 ,

(2.5c)

Pg = r wTg qg |z = 0 ,

(2.5d)

¶[ql ] ¶q ¶q - [u l ] - [ w l ], ¶t ¶x ¶z

(2.5e)

where

QCM = -

QWVOUT = [ PCND ] + [ PDEP ] + [ PSDEP ] + [ PGDEP ],

(2.5f)

QWVIN = -[ PREVP ] - [ PMLTG ] - [ PMLTS ],

(2.5g)

¶[ qv ] , ¶t

(2.5h)

¶q o ¶q ¶ o ¶ (u + u¢ )qv ¢ + u o v + w o (qv + qv ¢ ) + w¢ v ], ¶x ¶x ¶z ¶z

(2.5i)

QWVT = QWVF = -[

QWVE = Es .

(2.5j)

Here, PS is precipitation rate and PS = Pr as Ps = 0 and Pg = 0 in tropics; Es is zt [()] () = r surface evaporation; òzb dz, zt and zb are the heights of the top and bottom of the model atmosphere, respectively. Following Gao and Li (2010), the heat budget (2.1b) is mass integrated and the mass-integrated heat budget becomes SHT + SHF + SHS + SLHLF + SRAD = QWVS ,

(2.6)

30

2

Precipitation Equations and Process Analysis

where SHT =

SHF =

c p ¶[T ] , Lv ¶t

cp ¶ o ¶q o ¶ ¶q + p w o (q + θ ¢ ) + p w¢ [ (u + u¢ )T ¢ + p u o ], L v ¶x ¶x ¶z ¶z SHS = -

SLHLF = SRAD = -

cp Lv

Lf

Hs ,

(2.7a)

(2.7b) (2.7c)

< P18 >,

(2.7d)

1 < QR >, Lv

(2.7e)

Lv

Hs is surface sensible heat flux. The Eqs 2.3, 2.4, and 2.6 indicate that the surface rain rate (PS) can be resulted, respectively, from favorable environmental water vapor and thermal conditions via cloud microphysical processes (QWVS = QWVOUT + QWVIN). (2.3) and (2.4) are combined by eliminating QWVS to derive surface rainfall equation related to water vapor processes, PS = QWVT + QWVF + QWVE + QCM .

(2.8a)

(2.8a) states that the surface rain rate is associated with local atmospheric drying (QWVT >0)/moistening (QWVT 0)/divergence (QWVF 0) or hydrometeor gain/divergence (QCM 0)/cooling (SHT 0)/convergence (SHF 0)/heating (SRAD 0) or hydrometeor gain/divergence (QCM 0) (Table 2.1). Thus, the mean surface rainfall equation in SST29 can be approximately expressed by PS = QWVE ,

(2.15a)

PS = SRAD .

(2.15b)

2.2 Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity

33

Table 2.1 Time means of (a) fractional coverage (FC), surface rain rate (PS) , minus vapor storage (QWVT), water vapor convergence (QWVF), surface evaporation (QWVE) , and hydrometeor convergence minus storage (QCM) and (b) surface rain rate (PS) , local heat change (SHT), heat divergence (SHF), surface sensible heat (SHS) , latent heat due to ice-related processes (SLHLF), radiative cooling (SRAD) and hydrometeor convergence minus storage(QCM) over non-raining regions, raining stratiform regions, and convective regions, and their sums (model domain means) in SST29. Units are % for fractional coverage, mm h−1 for the others (After Zhou and Li (2009, 2011)) Non-raining Raining stratiform Convective Model domain regions regions regions mean (a) FC 91.0 5.8 3.2 100 0.000 0.056 0.074 0.130 PS QWVT −0.007 0.019 −0.011 0.001 QWVF −0.123 0.007 0.116 0.000 QWVE 0.128 0.004 0.002 0.134 QCM 0.002 0.026 −0.033 −0.005 (b) PS SHT SHF SHS SLHLF SRAD QCM

0.000 0.007 −0.135 −0.014 −0.001 0.140 0.003

0.056 0.011 0.016 −0.001 0.001 0.004 0.025

0.074 −0.015 0.120 −0.001 0.000 0.003 −0.033

0.130 0.003 0.000 −0.015 0.000 0.147 −0.005

Model domain consists of raining and non-raining regions. The model domain mean surface rainfall comes from convective and raining stratiform regions. Convective precipitation differs from stratiform precipitation in four ways. First, convective rain rate is higher than stratiform rain rate. Second, convective rainfall is associated with stronger horizontal reflectivity gradients than stratiform rainfall. Third, ascending motion associated with convective rainfall is much stronger than that associated with stratiform rainfall. Fourth, the accretion of cloud water by rain via collisions in strong updraft cores and the vapor deposition on cloud ice particles are primary microphysical processes for the development of convective and stratiform rainfall, respectively (Houghton 1968). To study convective and stratiform rainfall, the convective-stratiform rainfall partitioning scheme that was originally developed by Tao et al. (1993) and modified by Sui et al. (1994) are used in this book. In this modified scheme, each vertical column containing rainfall is partitioned into convective or stratiform based on the following criterion. Model grid points in the surface rainfall field that have a rain rate twice as large as the average taken over the surrounding four grid points (two grid points at left and two grid points at right in the 2D framework) are identified as the cores of convective cells. For each core grid point, the one grid point on either

34

2

Precipitation Equations and Process Analysis

side (in the 2D framework) is also considered as convective. In addition, any grid point with a rain rate of 20 mm h−1 or more is designated as convective regardless of the above criteria. All nonconvective rainfall points are regarded as stratiform. Since the above separation criterion is strictly based on surface precipitation, the stratiform region may actually include areas with tilted convective updrafts aloft. It may also include light- or non-precipitating convective cells that are initiated ahead of the organized convective system. Therefore, grid points in the raining stratiform regions are further checked and classified as convective if in the precipitating stratiform regions, cloud water mixing ratio below the melting level is greater than 0.5 g kg−1or the maximum updraft above 600 hPa exceeds 5m s−1 or if in the non-precipitating stratiform regions, cloud water exists (cloud water mixing ratio is greater than 0.025 g kg−1) or the maximum updraft exceeds 5 m s−1 below the melting level. The convective-stratiform rainfall partitioning analysis in SST29 shows that 57% and 43% of domain-mean surface rain rate come, respectively, from convective and raining stratiform regions, while convective and stratiform rainfall only covers 3.2% and 5.8% of model domain, respectively. Although the surface evaporation flux and radiative cooling are the two largest contributors to the mean rain rate, about 95% of the mean surface evaporation flux and radiative cooling rate come from nonraining regions that occupy 91.0% of the model domain. Over non-raining regions, the surface evaporation flux and radiative cooling are major water vapor source and heat sink that nearly offset the water vapor divergence (QWVF < 0) and heat convergence (SHF < 0) associated with subsidence, respectively. Thus, water vapor pumped by the surface evaporation in non-raining regions is transported from non-raining regions to raining regions (convective and raining stratiform regions) for the production of rainfall, whereas heat is transported from raining regions to non-raining regions to compensate heat loss associated with radiative cooling due to rainfall. Convective rain rate is mainly associated with water vapor convergence and heat divergence over convective regions. The water vapor convergence also supports the transport of hydrometeor concentration from convective regions to raining stratiform regions (QCM < 0) as well as it moistens the local atmosphere (QWVT < 0) over convective regions. The local atmospheric cooling (SHT < 0) over convective regions also corresponds to heat divergence. From (2.3) to (2.6), PS-QCM in thermally-related surface rainfall budget mainly is latent heat since SLHLF is negligibly small over convective regions. Thus, latent heat over convective regions is transported out by heat divergence. Stratiform rain rate is associated to the transport of hydrometeor concentration from convective regions to raining stratiform regions (QCM > 0), the local atmospheric drying (QWVT > 0) and warming (SHT > 0), and water vapor convergence and heat divergence over raining stratiform regions. The surface evaporation and radiative cooling over raining stratiform and convective regions play minor roles in the production of precipitation. The water vapor convergence and heat divergence rates over raining stratiform regions generally are one order of magnitude lower than those over convective regions. The analysis indicates different convective and stratiform precipitation processes. In summary, surface evaporation pumps water vapor into non-raining regions and the water vapor is transported from non-raining regions to convective regions,

2.2 Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity

35

which supports the convective rainfall. The heat is transported from the convective regions to non-raining regions, which nearly balances radiative cooling over nonraining regions.

2.2.2

Analysis of Diurnal Variation

To study diurnal variation of rainfall, the diurnal anomaly of model domain mean rain rate is calculated by removing time and model domain mean from diurnal composite of rain rate. The diurnal anomaly of the mean rain rate (PdS) in SST29 shows positive anomalies during nighttime and negative anomalies during daytime (Fig. 2.3). The analysis of thermally-related surface rainfall budget shows that the diurnal anomaly of the mean rain rate is generally phase Locking with that of the mean radiative cooling (SdRAD), but the magnitude of former is much smaller than that of the latter (Fig. 2.3b). The diurnal anomaly of the mean local thermal change rate (SdHT) is out of phase with those of the mean radiative cooling and surface rain rate. Thus, the nocturnal infrared (IR) radiative cooling produces rainfall peak and local atmospheric cooling during nighttime. The analysis of diurnal anomaly of watervapor-related surface rainfall budget reveals that the diurnal anomaly of the mean rain rate is generally associated with that of the mean local vapor change rate (QdWVT) (Fig. 2.3a). Thus, the diurnally-perturbed mean surface rainfall budgets have following approximate forms: d PSWV d » QWVT ,

(2.16a)

d d PSHd » SHT + SRAD .

(2.16b)

From cloud budget (2.3), we derive diurnally-perturbed form: d PS d » QWVS .

(2.16c)

(2.16a) to (2.16c) suggest that the nocturnal rainfall peak is related to the local atmospheric drying through the net condensation. The diurnal anomaly of convective rain rate in SST29 generally shows positive anomalies during nighttime and negative anomalies during daytime (Fig. 2.4). The diurnal anomaly of stratiform rain rate lags that of convective rain rate by about 2 h and the magnitude of diurnal anomaly (maximum minus minimum of diurnal anomaly) of convective rain rate is about twice as large as that of stratiform rain rate. The diurnal anomaly of convective rain rate is similar to the diurnal anomaly of heat divergence (SdHF) over convective regions in magnitude and phase since the diurnal anomalies of SdHT, SdRAD, and QdCM are smaller than those of SdHF. The diurnal anomalies of SdHT, SdHF, SdRAD, and QdCM over raining stratiform regions have similar magnitudes; they contribute to the diurnal anomaly of stratiform rainfall. Over rainfall-free regions, SdRAD and SdHT have similar magnitudes but they are out of phase. SdHF is

36

2

Precipitation Equations and Process Analysis

a

b

d

Fig. 2.3 Diurnal anomalies of model domain means of (a) PSd (dark solid), QWVT (light solid), d d d d QWVE (dot), and QCM (dot dash), and (b) PSd (dark solid), SHT (light solid), SHS (long short dash), d d d (dot dash) in SST29. Unit is mm h−1 SLHLF (dot), SRAD (dash), and QCM

2.2 Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity

37

a

b

c

Fig. 2.4 Diurnal anomalies of PdS (dark solid), SdHT (light solid), SdHF (long dash), SdRAD (dash), and QdCM (dot dash) over (a) convective regions, (b) raining stratiform regions, and (c) non-raining regions in SST29. SdHS and SdLHLF are not shown because they are negligibly small. Unit is mm h−1

38

2

Precipitation Equations and Process Analysis

mainly associated with the large cancellation between SdRAD and SdHT. The negative (positive) SdHF and SdHT correspond to the positive (negative) SdRAD over rainfall-free regions during nighttime (daytime). Thus, the diurnal anomaly of convective rain rate is mainly associated with the diurnal anomaly of heat divergence over convective regions, which is nearly balanced by the diurnal anomaly of heat divergence over rainfall-free regions. SdHS and SdLHLF are not shown in (Fig. 2.4) because they are negligibly small. The diurnal anomaly of convective rainfall is primarily associated with that of water vapor convergence over convective regions whereas the diurnal anomaly of stratiform rainfall is related to those of local vapor change, water vapor convergence, and hydrometeor change/convergence over raining stratiform regions (Fig. 2.5). Over rainfall-free regions, the diurnal anomaly of water vapor convergence is nearly offset by that of local water change.

2.3

Simulation of Rainfall Event During SCSMEX

Wang et al. (2007) plotted a time-horizontal distribution of surface rain rate (Fig. 2.6) and calculated water-vapor-related surface rainfall budgets (Table 2.2) and cloud microphysical budgets (Fig. 2.7) during a selected area and period of rainfall event in SCSMEX. A major rainband initiates around 670 km after 0500 LST as started by the enhanced water vapor convergence. The water vapor convergence plus surface evaporation is used to moisten local atmosphere. At 0600 LST, water vapor convergence rate increases significantly, which supports local atmospheric moistening, the growth of clouds and surface rainfall. Only water microphysical process occurs at this time. The vapor condensation produces rainfall mainly through the collection of cloud water by rain (PRACW). At 0700 LST, surface rain rate reaches its maximum (21.9 mm h−1) as the water vapor convergence rate reaches its peak (30.8 mm h−1). Meanwhile, the local atmosphere continues to be moistened and clouds keep growing. Although the water microphysical process dominates in the production of rainfall, the melting of graupel (PGMLT) also contribute about 10% to the rainfall mainly through the accretion of cloud water by graupel (PGACW(T < 0)) since vapor deposition rates are negligibly lower compared to the vapor condensation rate. The surface rainfall show a significant reduction as the water vapor divergence appears at 0800 LST. The rainfall is associated with the local atmospheric drying and the decrease of hydrometer concentration. The melting of graupel becomes a primary microphysical source for rainfall mainly through the consumption of graupel (Sqg < 0). The surface rainfall nearly stops as the local atmospheric drying and the decrease of hydrometeor concentration are offset by the water vapor divergence at 0900 LST. The melting of graupel that consumes precipitation ice hydrometeor (Sqs < 0 and Sqg < 0) is largely offset by the evaporation of rain (PREVP), which leads to a low rain rate. New rainbands form around 660, 653, 647, 640 km at hour 7, 8, 9, 10, respectively, and propagate southward while the individual rainband barely moves.

2.3 Simulation of Rainfall Event During SCSMEX

39

a

b

c

Fig. 2.5 Diurnal anomalies of PdS (dark solid), QdWVT (light solid), QdWVF (long dash), QdWVE (dot), and QdCM (dot dash) over (a) convective regions, (b) raining stratiform regions, and (c) non-raining regions in SST29. Unit is mm h−1

40

2

Precipitation Equations and Process Analysis

Fig. 2.6 Temporal and horizontal distribution of surface rain rate (mm h−1) simulated in SCSMEX on 20 May 1998. Contour intervals are 0.05, 1, 3, 5 mm h−1 (After Wang et al. 2007)

Table 2.2 PS, QWVT, QWVF, QWVE, QCM (mm h−1) during a life span of convection averaged in 669–672 km from 0500 LST to 0900 LST 19 May 1998 (After Wang et al. 2007) Stage Case LST PS QWVT QWVF QWVE QCM Pre-formation Formation Mature Weakening Dissipating

2.4

A B C D E

0500 0600 0700 0800 0900

0 6.7 21.9 12.1 0.2

−2.6 −2.3 −7.2 11.7 2.8

2.4 16.0 30.8 −11.8 −4.5

0.2 0.2 0.2 0.2 0.2

0 −7.2 −1.9 12.0 1.7

Simulation of Torrential Rainfall Event During the Landfall of Severe Tropical Storm Bilis (2006)

Wang et al. (2009) showed the difference in temporal-horizontal distribution of simulated surface rain rate in BILIS between 15 and16 July 2006 (Fig. 2.8) because of different vertical structures of imposed large-scale vertical velocity (Fig. 1.3a). The strong upward motions in the mid and upper troposphere and weak downward motions in the lower troposphere around noon of 15 July produce a strong stratiform rainfall (Figs. 1.3a and 2.9). The change from downward motions on 15 July to upward motions on 16 July in the lower troposphere enhances convective rainfall and suppresses stratiform rainfall on 16 July. The daily and domain mean analysis on 15 July shows that surface rain rate is primarily associated with water vapor convergence and heat divergence

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

41

(Figs. 2.10a and 2.11). The heat divergence cools down the local atmosphere while the water vapor convergence moistens the local atmosphere. The daily means of fractional coverage show that the model domain is mainly covered by stratiform rainfall (Table 2.3). The mean stratiform rainfall is mainly related to the mean water vapor convergence over raining stratiform regions. The mean convective rainfall is mainly associated with the mean water vapor convergence over convective regions. The mean cloud microphysical budget on 15 July 2006 (Fig. 2.12a) reveals that 73% of cloud source comes from vapor condensation rate (PCND = 2.331 mm h−1). The collection of cloud water by rain (PRACW = 1.516 mm h−1) and the melting of graupel to rain (PGMLT = 1.320 mm h−1) are equally important rain sources (Sqr = 2.573 mm h−1); this appears to suggest important water microphysical processes and the ice-water conversion processes for rainfall as a result of the dominance of stratiform rainfall. The daily and domain mean analysis on 16 July 2006 shows that the rain rate is primarily associated with water vapor convergence and heat divergence (Figs. 2.10a and 2.11). The mean surface rain rate on 16 July is larger than that on 15 July 2006,

a

b

Fig. 2.7 Cloud microphysical budgets averaged in 669–672 km at (a) 0600 LST, (b) 0700 LST, (c) 0800 LST, and (d) 0900 LST 20 May 1998. Units for hydrometeors and conversions are mm and mm h−1, respectively (After Wang et al. 2007)

42

2

Precipitation Equations and Process Analysis

c

d

Fig. 2.7 (continued)

mainly due to the fact that the local atmospheric changes from moistening on 15 July to drying on 16 July. The fractional coverage of stratiform rainfall significantly reduces from 88.8% on 15 July to 46.0% on 16 July whereas the fractional coverage of convective rainfall increases from 5.8% on 15 July to 29.4% on 16 July (Table 2.3). The mean stratiform rainfall (1.11 mm h−1) is associated with the mean water vapor convergence (0.54 mm h−1), the transport of hydrometeor concentration from convective regions to raining stratiform regions (0.32 mm h−1), and local atmospheric drying (0.24 mm h−1). Over convective regions, the mean water vapor convergence

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

43

Fig. 2.8 Time-zonal distribution of surface rain rate (mm h−1) simulated in BILIS (After Wang et al. 2009)

(2.25 mm h−1) support the convective rainfall (1.99 mm h−1) and the transport of hydrometeor concentration from convective regions to raining stratiform regions (−0.22 mm h−1) and slightly moisten the local atmosphere (−0.04 mm h−1). The daily and domain mean cloud microphysical budget on 16 July 2006 (Fig. 2.12b) shows that 84.3% of cloud source comes from vapor condensation rate (3.013 mm h−1). In the rain budget, the collection rate of cloud water by rain (2.271 mm h−1) is twice as large as the melting rate of graupel to rain (1.114 mm h−1), indicating that the water microphysical processes play a primary role in the production of rain. The vertical structures of imposed large-scale vertical velocity affects horizontal patterns because of strong upward motions in the upper troposphere and weak downward motion in the lower troposphere on 15 July and upward motions throughout the

44

2

Precipitation Equations and Process Analysis

Fig. 2.9 Time series of fractional coverage (%) for stratiform (solid) and convective (dash) rainfall simulated in BILIS (After Wang et al. 2010)

entire troposphere on 16–17 July. The responses of vertical velocity structure to the large-scale forcing can be examined through the calculations of extremely low frequencies (~0.001%) in contoured frequency-altitude diagrams (CFAD) developed by Yuter and Houze (1995). Here, the CFAD differences in vertical velocity structures, water vapor mass flux and cloud hydrometeor mass flux in Fig. 2.13, and specific humidity perturbation and cloud hydrometeor mixing ratio in Fig. 2.14 between 15 July and 16–17 July are compared. Although the upper-tropospheric upward motions are weaker on 16–17 July than on 15 July, the moderate lower-tropospheric upward motions on 16–17 July and the weak lower-tropospheric downward motion on 15 July yield a broader distribution of vertical velocity during 16–17 July than on 15 July. Maximum upward motions of 15–16 m s−1 and maximum downward motions of −7 m s−1 occur at 4 km and 13 km on 16–17 July. Maximum upward motions of 12 m s−1 and maximum downward motions of −5 m s−1 occur at 13 km on 15 July. The broader distribution of vertical velocity during 16–17 July along with maximum specific humidity near the surface leads to a much broader distribution of water vapor mass flux on 16–17 July than on 15 July. Maximum water vapor mass fluxes associated with upward and downward motions are, respectively, about 0.15 kg m−2 s−1 and −0.055 kg m−2 s−1 near the surface on 16–17 July, and about 0.065 kg m−2 s−1 and −0.035 kg m−2 s−1 near the surface on 15 July. The broader distributions of vertical velocity and total hydrometeor mixing ratio on 16–17 July generate a much broader distribution of cloud hydrometeor mass flux on 16–17 July than on 15 July. The maximum hydrometeor mass flux associated with upward motions is about 0.035 kg m−2 s−1 in the upper troposphere, whereas maximum hydrometeor mass flux associated with downward motions is about −0.01 kg m−2 s−1 throughout the

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

45

a

b

c

Fig. 2.10 Daily means of surface rain rate (PS), local water vapor change (QWVT), water vapor convergence (QWVF), surface evaporation (QWVE), local hydrometeor change/hydrometeor convergence (QCM) averaged over model domain mean in (a), and contributions from (b) raining stratiform regions (c) and convective regions in BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1

46

2

Precipitation Equations and Process Analysis

Fig. 2.11 Daily and model domain means of surface rain rate (PS), radiative heating (SRAD), local heat change (SHT), heat convergence (SHF), surface sensible flux (SHS), ice-related latent heat release (SLH), and radiation (SRAD) in BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1 Table 2.3 Daily means of fractional coverage (%) of stratiform and convective rainfall in BILIS on 15 and 16 July 2006 (After Wang et al. 2009) Stratiform rainfall Convective rainfall 15 July 88.8 5.8 16 July 46.0 29.4

troposphere on 16–17 July. The maximum hydrometeor mass fluxes associated with upward and downward motions are about 0.1 kg m−2 s−1 at 5 km and −0.03 kg m−2 s−1 at 6 km on 15 July. The distributions of specific humidity perturbation and cloud hydrometeor mixing ratio are much broader on 16–17 July than on 15 July. Maximum specific humidity perturbations are 0.65 g kg−1 around 2–4 km and −0.65 g kg−1 near the surface on 16–17 July and 0.35 g kg−1 near the surface and −0.35 g kg−1 around 5 km on 15 July. Maximum total hydrometeor mixing ratios are 11 g kg−1 in the mid and lower troposphere on 16–17 July and 7 g kg−1 in the mid and upper troposphere on 15 July. Imposed large-scale downward motions in the lower troposphere on 15 July reduce the maximum hydrometeor mixing ratio, which leads to small disturbances of specific humidity. The extension of imposed large-scale upward motions into the lower troposphere enhances the maximum hydrometeor mixing ratio and specific humidity perturbations. The responses of convective and stratiform rainfall to the large-scale forcing, vertical velocity structures, water vapor and hydrometeor mass fluxes, and water vapor and heat budgets are further analyzed. The vertical velocity profile over raining stratiform regions is nearly identical to the imposed large-scale vertical velocity profile on 15 July (Fig. 2.15). This demonstrates that the large-scale vertical velocity profile with strong upward motions in the mid and upper troposphere and weak downward motions in the lower troposphere accounts for the production of the dominant stratiform clouds and rainfall on 15 July. During the next 2 days, the large-scale

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

47

a

b

Fig. 2.12 Time and model domain mean cloud microphysical budgets simulated in BILIS in (a) 15 July and (b) 16 July 2006. Units for cloud hydrometeors and conversions are mm and mm h−1, respectively. The definitions and schemes of cloud microphysical processes can be found in Table 1.1 (After Wang et al. 2009)

a

b

c

d

e

f

Fig. 2.13 CFAD of vertical velocity (m s−1) in (a) and (b), water vapor mass flux (10−2 kgm−2 s−1) in (c) and (d), and hydrometeor mass flux (10−2 kgm−2 s−1) in (e) and (f). (a), (c), and (e) represent the 15 July case whereas (b), (d), and (f) denote 16–17 July case. Contour intervals are 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively (After Wang et al. 2010)

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

49

a

b

c

d

Fig. 2.14 As in Fig. 2.13, except for CFAD of specific humidity perturbation (g kg−1) in (a) and (b), and total hydrometeor mixing ratio (g kg−1) in (c) and (d) (After Wang et al. 2010)

vertical velocity profile is attributable to the raining stratiform and convective regions; this appears to suggest that the extension of large-scale upward motions to the lower troposphere basically enhances upward motions, with the lower-tropospheric maxima over convective regions where water hydrometeor microphysical processes are dominant. The upward water vapor mass fluxes from the surface to 8 km over convective regions significantly respond to the upward water vapor mass fluxes associated with imposed large-scale ascending motions in the lower troposphere on 16–17 July (Fig. 2.16). The upward water vapor mass fluxes from 3 to 10 km over raining stratiform regions mainly respond to the upward water vapor mass fluxes associated with imposed large-scale ascending motions in the upper troposphere on 15 July. The upward hydrometeor mass fluxes from 2 to 9 km on 16–17 July are much larger over

50

2

Precipitation Equations and Process Analysis

Fig. 2.15 Time-height distributions of (a) imposed vertical velocity and contributions from (b) raining stratiform regions and (c) convective regions. Units are cm s−1 (After Wang et al. 2010)

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

51

Fig. 2.16 Time-height distributions of (a) model domain mean water vapor mass flux associated with imposed vertical velocity and contributions to the domain mean from (b) raining stratiform regions and (c) convective regions. Units are 10−5 kg m−2 s−1 (After Wang et al. 2010)

52

2

Precipitation Equations and Process Analysis

Fig. 2.17 Time-height distributions of (a) model domain mean hydrometeor mass flux associated with imposed vertical velocity and contributions to the domain mean from (b) raining stratiform regions and (c) convective regions. Units are 10−6 kg m−2 s−1 (After Wang et al. 2010)

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

53

convective regions than over raining stratiform regions and the upward hydrometeor mass fluxes from 3 to 14 km on 15 July are larger over raining stratiform regions than over convective regions (Fig. 2.17). The upward hydrometeor mass fluxes on 16–17 July are much larger than on 15 July, indicating a massive transport of water hydrometeor concentration from convective regions to raining stratiform regions on 16–17 July. The model domain mean water vapor and heat budget can be calculated by taking model domain mean over (2.1a) and (2.1b). Thus, the local water vapor change is determined by water vapor advection, convergence of vertical water vapor flux, and net water vapor sink in the water vapor budget, and the local temperature change is determined by temperature advection, convergence of vertical heat flux, latent heating, and radiative heating in the heat budget. The model domain mean water vapor budget (Fig. 2.18) shows that except for the local atmospheric moistening in the lower troposphere in the morning of 15 July, the local atmosphere in the mid and lower troposphere experiences drying on 15–17 July. The local atmospheric moistening in the morning of 15 July is associated with the advective moistening. The local atmospheric drying on 15–17 July is related to the condensation and divergence of vertical water vapor flux. The imposed large-scale vertical velocity determines the vertical structure of condensation and deposition rates (see Figs. 2.15a and 2.18b). A net water vapor sink (Sqv 0) through the enhancement of the evaporation of rain in the lower troposphere over raining stratiform regions (Fig. 2.19b), which moistens the local atmosphere (Fig. 2.19a). On 16–17 July, the imposed large-scale upward motions extend to the lower troposphere and significantly enhance condensation over convective regions (Fig. 2.20b) while the nearly unchanged imposed large-scale upper-tropospheric upward motions support condensation and deposition over raining stratiform regions (Fig. 2.20b). The enhancement of condensation over convective regions on 16–17 July consumes a plenty amount of water vapor, which dries the local atmosphere over convective regions (Fig. 2.20a). The vertical velocity profile displays weak lower-tropospheric downward motions over raining stratiform regions and generates an advective drying in the lower troposphere on 16–17 July (Fig. 2.20d), which dries the local atmosphere (Fig. 2.20a). The model domain mean heat budget reveals that the advective cooling is nearly offset by the latent heating on 15 July and becomes stronger on 16–17 July (Fig. 2.21). The model domain mean local atmospheric cooling on 16–17 July is generated from both raining stratiform and convective regions (not shown), and is determined by the advective cooling over the two regions.

54

2

Precipitation Equations and Process Analysis

Fig. 2.18 Time-height distributions of (a) local water vapor change, (b) condensation, (c) convergence of vertical water vapor flux, and (d) water vapor advection in model domain mean water vapor budget. Units are 10−1 g kg−1 h−1 (After Wang et al. 2010)

2.4

Simulation of Torrential Rainfall Event During the Landfall of Severe…

55

Fig. 2.19 As in Fig. 2.18, except for the contribution to the domain mean water vapor budget from raining stratiform regions (After Wang et al. 2010)

56

2

Precipitation Equations and Process Analysis

Fig. 2.20 As in Fig. 2.18, except for the contribution to the domain mean water vapor budget from convective regions (After Wang et al. 2010)

57

Fig. 2.21 Time-height distributions of (a) local temperature change, (b) latent heat, (c) convergence of vertical heat flux, (d) radiative heating, and (e) temperature advection in model domain mean heat budget. Units are 10−1°Ch−1. Contour intervals are −18, −12, −6, 0, 6, 12, and 18 × 10−1 °C h−1 in (b) and (e), −3, −2, −1, 0, 1, 2, and 3 × 10−1 °C h−1 in (c) and (d), and −6, −4, −2, 0, 2, 4, and 6 × 10−1 °C h−1 in (a) (After Wang et al. 2010)

58

2.5

2

Precipitation Equations and Process Analysis

Simulation of Pre-summer Heavy Rainfall Event over Southern China in June 2008

Shen et al. (2011) showed that the time and model domain mean surface rain rate in PSR increases from 4 June to 6 June 2008, reaches its maximum on 6 June, and then decreases significantly on 7 June (Fig. 2.22a). These 3 days represent the onset, mature and decay phases of pre-summer heavy rainfall events over southern China. June 4 is characterized by moderate large-scale upward motions with the mean water vapor convergence and heat divergence. June 6 has strong large-scale upward motions with the mean water vapor convergence and heat divergence. 7 June has weak large-scale upward motions with domain-mean water vapor and heat divergence. In water-vapor-related surface rainfall budget, the increase in the mean surface rain rate from 4 June to 6 June is largely associated with the enhanced mean water vapor convergence, which is consistent with the dominance of large-scale water vapor convergence found in the total vapor source from tropical equilibrium cloud-resolving model simulation (Sui et al. 1994) and in BILIS. The decrease in the mean surface rain rate on 7 June is mainly related to the change to the water vapor divergence from the water vapor convergence on the previous day. The mean surface rain rate is primarily associated with the mean local atmospheric drying rate as the domain-mean water vapor divergence occurs on 7 June. There is an increase in heat divergence from 4 to 6 June 2008 when surface rainfall increases and there is a decrease in heat divergence from 6 to 7 June as surface rainfall decreases (Fig. 2.23). The mean heat divergence cools down the mean local atmosphere. Although the mean water vapor divergence cannot support rainfall on 7 June, the mean heat divergence balances out latent heat (not shown) for rainfall. Thus, the mean local atmospheric drying is a result of consumption of water vapor by condensation. The convective-stratiform rainfall separation analysis shows that convective rainfall contributes more to the model domain mean surface rainfall than stratiform rainfall does. The fractional coverage of stratiform and convective rainfall increases from 4 June to 6 June whereas it decreases from 6 June to 7 June (Table 2.4). On 4 June, the water vapor convergence appears over convective regions (Fig. 2.22c) whereas the weak water vapor divergence occurs over raining stratiform regions (Fig. 2.22b). The convective rainfall is associated with water vapor convergence and local atmospheric drying over convective regions. The stratiform rainfall is mainly supported by the transport of hydrometeor concentration from convective regions to raining stratiform regions. On 6 June, water vapor convergence is enhanced over both raining stratiform and convective regions. The convective rainfall and the transport of hydrometeor concentration from convective regions to raining stratiform regions cannot be fully supported by the water vapor convergence over convective regions, which lead to local atmospheric drying over convective regions. The stratiform rainfall is associated with the water vapor convergence and the transport of hydrometeor concentration to raining stratiform regions.

2.5

Simulation of Pre-summer Heavy Rainfall Event over Southern China in June 2008

59

a

b

c

Fig. 2.22 Daily means of surface rain rate (PS), local water vapor change (QWVT), water vapor convergence (QWVF), surface evaporation (QWVE), local hydrometeor change/hydrometeor convergence (QCM) averaged over model domain mean in (a), and contributions from (b) raining stratiform regions (c) and convective regions in PSR on 4 June 2008 (open bar), 6 June (black bar), and 7 June (grey bar). Unit is mm h−1 (After Shen et al. 2011)

60

2

Precipitation Equations and Process Analysis

Fig. 2.23 Daily and model domain means of surface rain rate (PS), radiative heating (SRAD), local heat change (SHT), heat convergence (SHF), surface sensible flux (SHS), ice-related latent heat release (SLH), and radiation (SRAD) in PSR on 4 June 2008 (open bar), 6 June (black bar), and 7 June (grey bar). Unit is mm h−1 (After Shen et al. 2011) Table 2.4 Daily means of fractional coverage (%) of stratiform and convective rainfall in PSR on 4, 6, and 7 June 2008 (After Shen et al. 2011) Stratiform rainfall Convective rainfall 4 June 20.4 10.7 6 June 33.2 12.6 7 June 11.1 2.7

The mean water vapor divergence occurs on 7 June. The mean water vapor divergence comes mainly from raining stratiform regions, where the stratiform rainfall is mainly associated with the transport of hydrometeor concentration from convective regions to raining stratiform regions as a result of cancellation between water vapor divergence and local atmospheric drying. Over convective regions, the water vapor convergence support convective rainfall and transport of hydrometeor concentration from convective regions to raining stratiform regions while it moistens the local atmosphere over convective regions.

References Gao S, Li X (2010) Precipitation equations and their applications to the analysis of diurnal variation of tropical oceanic rainfall. J Geophys Res. doi:10.1029/2009JD012452, (c) American Geophysical Union. Reprinted with permission Gao S, Cui X, Zhou Y, Li X (2005) Surface rainfall processes as simulated in a cloud resolving model. J Geophys Res. doi:10.1029/2004JD005467 Houghton HG (1968) On precipitation mechanisms and their artifical modification. J Appl Meterol 7:851–859

References

61

Shen X, Wang Y, Li X (2011) Effects of vertical wind shear and cloud radiative processes on responses of rainfall to the large-scale forcing during pre-summer heavy rainfall over southern China. Q J R Meteorol Soc 137:236–249, (c) Royal Meteorological Society. Reprinted with permission Sui CH, Li X (2005) A tendency of cloud ratio associated with the development of tropical water and ice clouds. Terr Atmos Ocean Sci 16:419–434 Sui CH, Lau KM, Tao WK, Simpson J (1994) The tropical water and energy cycles in a cumulus ensemble model. Part I: equilibrium climate. J Atmos Sci 51:711–728 Tao WK, Simpson J, Sui CH, Ferrier B, Lang S, Scala J, Chou MD, Pickering K (1993) Heating, moisture, and water budgets of tropical and midlatitude squall lines: comparisons and sensitivity to longwave radiation. J Atmos Sci 50:673–690 Wang JJ, Li X, Carey L (2007) Evolution, structure, cloud microphysical and surface rainfall processes of a monsoon convection during the South China Sea monsoon experiment. J Atmos Sci 64:360–380, (c) American Meteorological Society. Reprinted with permission Wang D, Li X, Tao WK, Liu Y, Zhou H (2009) Torrential rainfall processes associated with a landfall of severe tropical storm Bilis (2006): a two-dimensional cloud-resolving modeling study. Atmos Res 91:94–104, (c) Elsevier. Reprinted with permission Wang D, Li X, Tao WK (2010) Responses of vertical structures in convective and stratiform regions to large-scale forcing during the landfall of severe tropical storm Bilis (2006). Adv Atmos Sci 27:33–46 Yuter SE, Houze RA Jr (1995) Three-dimensional kinetic and microphysical evolution of Florida cumulonimbus. Part II: frequency distribution of vertical velocity, reflectivity, and differential reflectivity. Mon Weather Rev 123:1941–1963 Zhou Y, Li X (2009) Sensitivity of convective and stratiform rainfall to sea surface temperature. Atmos Res 92:212–219, (c) Elsevier. Reprinted with permission Zhou Y, Li X (2011) An analysis of thermally-related surface rainfall budgets associated with convective and stratiform rainfall. Adv Atmos Sci 28:1099–1108

Chapter 3

Tropical Precipitation Processes

In this chapter, precipitation equations are applied to the analysis of tropical rainfall event in Experiment COARE. Roles of large-scale forcing, thermodynamics, and cloud microphysics in tropical precipitation processes are discussed through the partitioning analysis of model domain mean simulation data based on watervapor-related surface rainfall budget in Sect. 3.1 (Shen et al. 2010a). Precipitation and cloud statistics in deep tropical convective regimes are investigated through the partitioning analysis of grid-scale simulation data based on water-vapor-related surface rainfall budget in Sect. 3.2 (Shen et al. 2010b). Responses of tropical convective precipitation systems and their associated convective and stratiform regions to the large-scale forcing are examined in Sect. 3.3 (Gao and Li 2008). Effects of time-dependent large-scale forcing (LSF), solar zenith angle (SZA), and SST on time-mean tropical rainfall processes are analyzed in Sect. 3.4 (Gao and Li 2010a). Diurnal variations of tropical rainfall and associated processes are studied in Sect. 3.5 (Gao and Li 2010b).

3.1

Model Domain Mean Analysis

Unlike SST29, non-zero large-scale forcing imposed in the model in COARE produces water vapor convergence and heat divergence in model domain mean surface rainfall budgets. Based on water-vapor-related surface rainfall budget, model domain mean rainfall simulation data are separated into eight rainfall types: TFM, TFm, tFM, tFm, TfM, Tfm, tfM, tfm (Table 3.1). Here, T and t represent the mean local atmospheric drying (QWVT > 0) and moistening (QWVT 0) and divergence (QWVF < 0), respectively. M and m represent the decrease of mean local hydrometeor concentration (QCM > 0) and the increase of mean local hydrometeor concentration (QCM < 0), respectively, because the hydrometeor convergence vanishes as a result of cyclic lateral boundaries. Rainfall occurs in about 80% of the integration hours. X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_3, © Springer Science+Business Media B.V. 2012

63

64

3

Tropical Precipitation Processes

Table 3.1 Summary of rainfall types Type Description TFM Local atmospheric drying, water vapor convergence, and hydrometeor loss/convergence TFm Local atmospheric drying, water vapor convergence, and hydrometeor gain/divergence tFM Local atmospheric moistening, water vapor convergence, and hydrometeor loss/ convergence tFm Local atmospheric moistening, water vapor convergence, and hydrometeor gain/ divergence TfM Local atmospheric drying, water vapor divergence, and hydrometeor loss/convergence Tfm Local atmospheric drying, water vapor divergence, and hydrometeor gain/divergence tfM Local atmospheric moistening, water vapor divergence, and hydrometeor loss/ convergence tfm Local atmospheric moistening, water vapor divergence, and hydrometeor gain/ divergence T and t represent local atmospheric drying and moistening, respectively. F and f represent water vapor convergence and divergence, respectively. M and m represent local atmospheric loss and gain, respectively

Among them, roughly 72% of rainy hours appear in the presence of water vapor convergence associated with imposed large-scale tropospheric upward motions whereas nearly 28% of raining hours occur in the presence of water vapor divergence associated with imposed large-scale lower-tropospheric downward motions (Fig. 3.1). The mean rain rate is larger in TFM than in TFm (Table 3.2). While both rainfall types have the mean water vapor convergence and local atmospheric drying, TFM and TFm have the mean hydrometeor loss and gain, respectively. The effects of mean hydrometeor loss/gain on mean rainfall in the presence of mean water vapor convergence and mean local atmospheric drying are analyzed in Sect. 3.1.1. The mean rain rates are similar in two pairs of rainfall types (in tFM and TfM and in tFm and Tfm). The effects of mean local atmospheric drying/moistening on mean rainfall will be examined in Sect. 3.1.2. The mean rainfall is associated with the mean water vapor divergence in four rainfall types (TfM, Tfm, tfM, and tfm). The effects of mean local atmospheric drying/moistening and mean hydrometeor loss/gain on mean rainfall in the presence of the mean water vapor divergence will be discussed with the analysis of the four cases in Sect. 3.1.3.

3.1.1

Effects of Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of Mean Water Vapor Convergence and Mean Local Atmospheric Drying

Similar imposed large-scale upward motion profiles (Fig. 3.1) produce similar mean water vapor convergence rates in water-vapor-related surface rainfall budgets (2.8a) in TFM and TFm (Table 3.2a, b) and similar vertical profiles of mean water vapor mass fluxes in both cases (Fig. 3.2). Both rainfall types have the same mean surface

3.1 Model Domain Mean Analysis

65

Fig. 3.1 Vertical profiles of composites of model domain mean vertical velocity (cm s−1) in TFM (dark solid), TFm (dark dash), tFM (dark long dash), tFm (dark dot dash), TfM (light solid), Tfm (light dash), tfM (light long dash), and tfm (light dot dash) in COARE (After Shen et al. 2010a)

evaporations rates. Although the mean local atmospheric drying rate is higher in TFm than in TFM, the mean hydrometeor gain in TFm and the mean hydrometeor loss in TFM lead to a lower mean surface rain rate (PS) in TFm than in TFM. The mean hydrometeor change is important in the production of precipitation. The fractional cloud coverage is larger in TFM than in TFm, while their vertical structures are similar (Fig. 3.3).

66

3

Tropical Precipitation Processes

Table 3.2 Model domain means of fractional coverage (FC), PS, QWVT, QWVF , QWVE, and QCM and contributions from non-raining regions, raining stratiform regions, and convective regions in (a) TFM, (b) TFm, (c) tFM, (d) tFm, (e) TfM, (f) Tfm, (g) tfM, (h) tfm in COARE. Units are % for fractional coverage and mm h−1 for the others (After Shen et al. 2010a) Non-raining Raining stratiform Convective Model domain regions regions regions mean (a) TFM FC 75.9 18.3 5.9 100 0.000 0.309 0.586 0.895 PS QWVT −0.133 0.147 0.203 0.217 QWVF −0.031 −0.145 0.520 0.343 QWVE 0.131 0.045 0.023 0.200 QCM 0.033 0.263 −0.160 0.136 (b) TFm FC PS QWVT QWVF QWVE QCM

78.9 0.000 −0.073 −0.071 0.145 0.000

14.9 0.223 0.217 −0.200 0.036 0.170

6.2 0.494 0.194 0.617 0.021 −0.338

100 0.717 0.338 0.346 0.201 −0.168

(c) tFM FC PS QWVT QWVF QWVE QCM

84.6 0.000 −0.425 0.260 0.146 0.019

10.8 0.147 0.100 −0.134 0.027 0.154

4.7 0.212 0.107 0.145 0.016 −0.055

100 0.360 −0.219 0.271 0.189 0.118

(d) tFm FC PS QWVT QWVF QWVE QCM

85.7 0.000 −0.296 0.163 0.137 −0.005

10.4 0.122 0.031 0.008 0.020 0.063

3.9 0.139 0.090 0.178 0.010 −0.138

100 0.261 −0.175 0.349 0.167 −0.080

(e) TfM FC PS QWVT QWVF QWVE QCM

90.3 0.000 −0.046 −0.148 0.165 0.029

6.3 0.105 0.134 −0.176 0.016 0.130

3.3 0.270 0.131 0.173 0.012 −0.046

100 0.375 0.220 −0.151 0.194 0.112

(f) Tfm FC PS QWVT QWVF QWVE QCM

91.2 0.000 −0.226 −0.204 0.175 0.026

4.0 0.057 0.098 −0.118 0.010 0.066

4.9 0.186 0.208 0.190 0.016 −0.227

100 0.243 0.309 −0.132 0.201 −0.135 (continued)

Table 3.2 (continued) Non-raining regions

Raining stratiform regions

Convective regions

Model domain mean

(g) tfM FC PS QWVT QWVF QWVE QCM

88.7 0.000 −0.246 0.010 0.195 0.041

7.1 0.066 0.147 −0.201 0.018 0.101

4.3 0.054 −0.034 0.113 0.017 −0.042

100 0.120 −0.134 −0.077 0.230 0.100

(h) tfm FC PS QWVT QWVF QWVE QCM

91.2 0.000 −0.319 0.093 0.200 0.026

4.6 0.026 0.044 −0.081 0.014 0.049

4.2 0.031 0.197 −0.069 0.018 −0.115

100 0.057 −0.078 −0.058 0.232 −0.039

Fig. 3.2 Vertical profiles of composites of model domain mean water vapor mass flux (10−4kg m−2 s−1) in TFM (dark solid), TFm (dark dash), tFM (dark long dash), tFm (dark dot dash), TfM (light solid), Tfm (light dash), tfM (light long dash), and tfm (light dot dash) in COARE (After Shen et al. 2010a)

68

3

Tropical Precipitation Processes

Fig. 3.3 Vertical profiles of fractional cloud coverage (%) in TFM (dark solid), TFm (dark dash), tFM (dark long dash), tFm (dark dot dash), TfM (light solid), Tfm (light dash), tfM (light long dash), and tfm (light dot dash) (After Shen et al. 2010a)

LWPs are larger than IWPs (Table 3.3a). The cloud microphysical budgets are calculated to explain the mean hydrometeor loss in TFM and the mean hydrometeor gain in TFm. Following Sui and Li (2005), mass-integrated cloud microphysical budgets analyzed here can be approximately expressed as SIWP = PDEP + PSDEP + PGDEP - C (IWP, LWP ) - PMLTS - PMLTG ,

(3.1a)

3.1 Model Domain Mean Analysis

69

Table 3.3 Model domain means of PS, IWP, LWP, SIWP, SLWP, PCND, PDEP + PSDEP + PGDEP , PREVP , PMLTS + PMLTG, and C(LWP, IWP) in (a) TFM, TFm, tFM, tFm, and (b) TfM, Tfm, tfM, and tfm in COARE. Unit is mm h−1 (After Shen et al. 2010a) (a) TFM TFm tFM tFm PS 0.895 0.717 0.360 0.261 IWP 0.274 0.271 0.151 0.131 LWP 0.360 0.320 0.183 0.170 SIWP −0.033 0.075 −0.051 −0.001 SLWP 0.793 0.810 0.292 0.343 PCND 0.989 1.049 0.392 0.418 PDEP + PSDEP + PGDEP 0.224 0.242 0.107 0.119 PREVP 0.436 0.385 0.247 0.190 PMLTS + PMLTG 0.017 0.019 0.011 0.005 C(IWP, LWP) 0.240 0.147 0.147 0.115 (b) TfM Tfm tfM tfm PS 0.375 0.243 0.120 0.057 IWP 0.117 0.086 0.098 0.091 LWP 0.155 0.128 0.096 0.082 SIWP −0.052 0.044 −0.048 −0.010 SLWP 0.314 0.334 0.067 0.104 PCND 0.416 0.469 0.147 0.186 PDEP + PSDEP + PGDEP 0.069 0.069 0.067 0.075 PREVP 0.210 0.153 0.185 0.158 PMLTS + PMLTG 0.012 0.006 0.008 0.007 C(IWP, LWP) 0.109 0.019 0.106 0.077

SLWP = PCND + C (IWP, LWP ) - PREVP ,

(3.1b)

Where C (IWP, LWP ) = - PSACW (T < T0 ) - PSFW (T < T0 ) - PGACW (T < T0 ) - PIHOM (T < T00 ) + PIMLT (T > T0 ) - PIDW (T00 < T < T0 ) + PRACS (T < T0 ) - PIACR (T < T0 ) - PGACR (T < T0 ) - PSACR (T < T0 ) - PGFR (T < T0 ) + PSMLT (T > T0 ) + PGMLT (T > T0 ).

(3.1c)

Here, cloud microphysical processes and their parameterization schemes in (3.1) can be found in Table 1.1. The cloud budget (2.3) can be written as PS - QCM = SIWP + SLWP .

(3.2)

From the mean cloud budget (Table 3.3a), the difference in QCM between TFM and TFm is determined by the differences in PS and − SIWP and − SLWP. Since the

70

3

Tropical Precipitation Processes

Table 3.4 Model domain means of surface rain rate (PS) , local heat change (SHT), heat divergence (SHF), surface sensible heat (SHS) , latent heat due to icerelated processes (SLHLF), radiative cooling (SRAD) and hydrometeor convergence minus storage(QCM) in (a) TFM, (b) TFm, (c) tFM, (d) tFm, (e) TfM, (f) Tfm, (g) tfM, (h) tfm in COARE. Unit is mm h−1 (a) TFM TFm tFM tFm PS 0.895 0.717 0.360 0.261 SHT 0.055 0.264 −0.213 −0.197 SHF 0.570 0.509 0.347 0.475 SHS −0.033 −0.029 −0.030 −0.026 SLHLF 0.011 −0.003 0.010 0.004 SRAD 0.156 0.144 0.126 0.085 QCM 0.136 −0.168 0.118 −0.080 (b) PS SHT SHF SHS SLHLF SRAD QCM

TfM 0.375 0.208 −0.082 −0.030 0.010 0.157 0.112

Tfm 0.243 0.205 0.024 −0.027 0.004 0.179 −0.135

tfM 0.120 −0.058 −0.001 −0.028 0.008 0.098 0.100

tfm 0.057 0.004 0.000 −0.026 0.003 0.114 −0.039

difference in − SLWP (0.017 mm h−1) for TFM-TFm is much smaller than the differences in PS (0.178 mm h−1) and − SIWP (0.108 mm h−1), the difference in QCM results mainly from the differences in PS and − SIWP. The mean cloud microphysical budgets show that SIWP increases in TFm whereas it decreases in TFM since the conversion rate from IWP to LWP is much larger in TFM than in TFm; it appears to be associated with the warmer mass-weighted mean temperature in TFM (−8.14°C) than in TFm (−8.45°C). The mean thermally-related surface rainfall budgets show that SHF and SRAD are larger in TFM than in TFm (Table 3.4a), which account for the difference in mean rain rate between TFM and TFm in thermal aspects. The fractional coverage of convective rainfall is similar in TFM and TFm whereas the fractional coverage of stratiform rainfall is larger in TFM than in TFm (Table 3.2a, b). Both convective and stratiform rain rates are lower in TFm than in TFM. Over convective regions, the larger water vapor convergence rate yields the larger transport rate of hydrometeor concentration from convective regions to raining stratiform regions in TFm than in TFM. The lower stratiform rainfall in TFm than in TFM is associated with a larger water vapor divergence rate and a smaller transport rate of hydrometeor concentration from convective regions to raining stratiform regions in TFm, though the local atmospheric drying rate is higher in TFm than in TFM. The mean hydrometeor loss comes from raining stratiform regions in TFM whereas the mean hydrometeor gain comes from convective regions in TFm. The mean local atmospheric drying in both rainfall types comes mainly from convective regions.

3.1 Model Domain Mean Analysis

3.1.2

71

Effects of Mean Local Atmospheric Drying/Moistening on Mean Rainfall

Imposed large-scale tropospheric upward motions produce the mean water vapor convergence in tFM and tFm whereas imposed large-scale lower-tropospheric downward motions generate the mean water vapor divergence in TfM and Tfm (Fig. 3.1 and Table 3.2c–f). The upward water vapor mass fluxes and fractional cloud coverage in tFM and tFm are significantly larger than the upward water vapor mass fluxes in TfM and Tfm (Figs. 3.2 and 3.3). The mean local atmospheric moistening and drying largely offset the mean water vapor convergence and divergence, respectively, in tFM and tFm and in TfM and Tfm. The similar surface evaporation and mean hydrometeor loss rates mainly account for the similar rain rates in tFM and TfM whereas the similar surface evaporation and mean hydrometeor moistening rates are mainly responsible for the similar rain rates in tFm and Tfm. This indicates that the local changes in water vapor are as important as the water vapor convergence in the production of precipitation. The LWPs are larger than IWPs in the four rainfall types. tFM and TfM show similar SIWP and SLWP (Table 3.3). The vapor deposition rates and the conversion rates from IWP to LWP are higher in tFM than in TfM, which leads to similar SIWP. The similar vapor condensation rates occur in tFM and TfM. The evaporation rate of rain and the conversion rate from IWP to LWP are higher in tFM than in TfM, which yields similar SLWP. Ice hydrometeor concentration barely changes in tFm (SIWP » 0) and it increases in Tfm (SIWP > 0), while similar SLWP appears in tFm and Tfm. The zero SIWP in tFm results mainly from the cancellation between the vapor deposition and the conversion from IWP to LWP. A much lower conversion rate is found in Tfm than tFm, which accounts for the positive SIWP in Tfm. Although the vapor condensation rate is lower and evaporation rate of rain is higher in tFm than in Tfm, the conversion rate from IWP to LWP is much higher in tFm than in Tfm. Thus, similar SLWP occurs in tFm and Tfm. Since TfM (75.9%) and Tfm (71.0%) have more samples than tFM (52.3%) and tFm (36.8%) (Fig. 3.4) during the nighttime, TfM and Tfm have larger mean radiative cooling rates than tFM and tFm, respectively (Table 3.4c, f). The nocturnal radiative cooling reduces saturation specific humidity and increases relative humidity and net condensation (e.g., Tao et al. 1996; Sui et al. 1998). Thus, the mean latent heat rates correspond to the mean radiative cooling rates in TfM and Tfm whereas they correspond to the mean heat divergence rates in tFM and tFm. The mean latent heat rates are also associated with the mean local atmospheric warming rates in TfM and Tfm, whereas they are also related to the mean local atmospheric cooling rates in tFM and tFm, which yields the similar mean latent heat rates and net condensation rates (SIWP + SLWP) in tFM and TfM and in tFm and Tfm (Table 3.3). The mean net condensation caused by the mean radiative cooling in TfM and Tfm leads to the mean local atmospheric drying in the presence of the mean water vapor divergence. The mean water vapor convergence in tFM and tFm produces the mean net condensation and moistens the mean local atmosphere. Thus, the local changes in water

72

3

Tropical Precipitation Processes

a

b

c

d

Fig. 3.4 Diurnal variations of number of samples in (a) TFM (black) and tFM (grey), (b) TFm (black) and tFm (grey), (c) TfM (black) and tfM (grey), (d) Tfm (black) and tfm (grey) (After Shen et al. 2010a)

vapor and the water vapor convergence are equally important in the production of precipitation. The mean surface rain rates are higher in TFM and TFm than in tFM and tFm (Table 3.2a–d). The mean thermally-related surface rainfall budgets reveal that the positive difference in SRAD for tFM- tFm contributes to the positive difference in mean rain rate while the difference in SHF and SHT are negative (Table 3.4a). The differences

3.1 Model Domain Mean Analysis

73

in SRAD, SHF, and SHT for TfM-Tfm are negative (Table 3.4b), which partially offset the positive difference in QCM to cause small positive difference in mean rain rate. Although the fractional coverage of convective and stratiform rainfall is smaller in TfM than in tFM, the mean surface rain rate is slightly higher in TfM than in tFM (Table 3.2c, e) mainly because of higher convective rain rate in TfM than in tFM. The higher convective rainfall in TfM is associated with the higher water vapor convergence and the local atmospheric drying rates over convective regions in TfM than in tFM. While the water vapor convergence over convective regions nearly negates the water vapor divergence over raining stratiform regions in both rainfall types, the mean water vapor divergence in TfM causes the water vapor divergence and the mean water vapor convergence in tFM leads to the water vapor convergence over non-raining regions. The water vapor divergence is offset by surface evaporation over non-raining regions in TfM. The water vapor convergence and surface evaporation moistens local atmosphere over non-raining regions in tFM. The lower stratiform rainfall in TfM is mainly associated with the higher water vapor divergence rate and lower transport of hydrometeor concentration from convective regions to raining stratiform regions, compared to tFM. The comparison in surface rainfall processes between tFM and TfM can be applied to tFm and Tfm. The difference is that the higher convective rainfall and lower stratiform rainfall in Tfm than in tFm mainly result from the higher local atmospheric drying rate over convective regions and the water vapor divergence over raining stratiform regions, respectively, in Tfm (Table 3.2d, f).

3.1.3

Effects of Mean Local Atmospheric Drying/Moistening and Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of the Mean Water Vapor Divergence

In Sect. 3.1.2, the mean local atmospheric drying/moistening and the mean water vapor convergence/divergence are equally important in the production of the mean rainfall. In this subsection, the effects of mean local atmospheric drying/moistening and mean hydrometeor loss/gain on mean rainfall will be examined through the analysis of rainfall types associated with the mean water vapor divergence. The vertical profiles of imposed large-scale vertical velocity show that the upper-tropospheric upward motions and the lower-tropospheric downward motions are stronger in tfM and tfm than in TfM and Tfm (Fig. 3.1). The stronger lower-tropospheric downward motions in tfM and tfm produce the downward water vapor mass fluxes in the lower troposphere (Fig. 3.2). The clouds cover a larger area in tfM and tfm than in TfM and Tfm below 8 km (Fig. 3.3). The mean water vapor divergence rates in tfM and tfm are only half of the divergence rates in TfM and Tfm (Table 3.2e–h). The mean surface rain rates are much lower in tfM and tfm than in TfM and Tfm mainly because of the mean local atmospheric moistening in tfM and tfm and the mean local atmospheric drying in TfM and Tfm. The mean LWPs are larger than IWPs in TfM and Tfm. The mean LWP is similar to IWP in tfM whereas it is smaller than IWP in tfm; it appears to suggest the importance

74

3

Tropical Precipitation Processes

of ice hydrometeors in rainfall systems. The mean vapor condensation rates are much lower in tfM and tfm than in TfM and Tfm, which causes much lower rates of water hydrometeor gain in tfM and tfm (Table 3.3b). The differences in SLWP between tfM and TfM and between tfm and Tfm are much larger than the differences in SIWP. Thus, the local atmospheric drying and moistening are associated with the enhancement and suppression of the surface rainfall through water microphysical processes. Since TfM (75.9%) and Tfm (71.0%) have more nighttime hours than tfM (50.0%) and tfm (26.7%) (Fig. 3.4c, d), TfM and Tfm have larger mean radiative cooling rates than tfM and tfm, respectively (Table 3.4). The large mean latent heat rates correspond to the large mean radiative cooling rates in TfM and Tfm whereas the small latent heat rates correspond to the small mean radiative cooling rates in tfM and tfm. The mean local atmospheric warming rates widen the differences in the mean latent heat between TfM and tfM and between Tfm and tfm. Thus, the net condensation rates are much higher in TfM and Tfm than in tfM and tfm (Table 3.3). The nighttime radiative cooling enhances the net condensation and associated consumption of water vapor in TfM and Tfm; the net condensation and water vapor divergence rates are larger than the surface evaporation rates in these two rainfall types that dries the local atmosphere. In contrast, the net condensation rates and water vapor divergence rates are lower than the surface evaporation rates in tfM and tfm that moistens the mean local atmosphere. The convective rain rates are much lower in tfM and tfm than in TfM and Tfm (Table 3.2e–h). The convective rainfall occupies a larger area in tfM than in TfM whereas it covers a smaller area in tfm than in Tfm. The stratiform rainfall covers a larger area in tfM and tfm than in TfM and Tfm. The lower convective rain rate in tfM is mainly associated with the local atmospheric moistening in tfM and the local atmospheric drying in TfM over convective regions. The lower convective rain rate in tfm is mainly related to the water vapor divergence in tfm and the water vapor convergence in Tfm over convective regions. The stratiform rain rates are lower in tfM and tfm than in TfM and Tfm primarily because the water vapor divergence rate over raining stratiform regions is higher and the transport of hydrometeor concentration from convective regions to raining stratiform regions is lower in tfM than in TfM and the local atmospheric drying rate is lower in tfm than in Tfm over raining stratiform regions. Like TfM-Tfm, the differences in SRAD and SHT for tfM-tfm are negative (Table 3.4b), which against the positive difference in QCM. Thus, these thermal processes decrease the positive difference in mean rain rate.

3.2

Grid-Scale Analysis

Li et al. (2002a) showed that model domain mean rainfall come from convective regions where prevailing upward motions throughout the troposphere produce water vapor convergence and raining stratiform regions where downward motions in the mid and lower troposphere generate water vapor divergence. The collection of cloud water by rain is a dominant microphysical process resulting in rainfall over convective

3.2

Grid-Scale Analysis

75

regions, whereas the collection of cloud water by rain and the melting of precipitation hydrometeors into rain are the major processes responsible for rainfall over raining stratiform regions. The transport of hydrometeor concentration from convective regions to raining stratiform regions is an important source of stratiform rainfall (e.g., Cui and Li 2006). Experiment SCSMEX shows that local atmospheric moistening results from water vapor convergence during the formation and mature phases of monsoon precipitation system whereas the local atmospheric drying is caused by water vapor divergence during the dissipating phase (see Table 2.2). The local atmospheric drying can be caused by the increase in the net condensation resulting from the decrease in saturation specific humidity induced by nocturnal radiative cooling. Thus, the model domain contains different types of rainfall, whose statistics can be studied through the partitioning analysis of grid-scale data based on surface rainfall budget. The questions to be discussed in this section are which rainfall type in grid-scale rainfall calculation plays an important role in contributing to total rainfall and how they differ from the model domain mean analysis from COARE in Sect. 3.1. In this section, grid-scale rainfall simulation data in COARE are analyzed to partition rainfall into eight types (Table 3.1) and to study precipitation and cloud statistics. Among eight rainfall types, the rainfall type associated with local atmospheric drying and hydrometeor loss and water vapor divergence (TfM) has the largest contribution to total rainfall as indicated by 30.8% of percentage of rain amount over total rainfall (PRA) because the fractional rainfall coverage (FRC) is 35.3% (Fig. 3.5). The mean surface rain rate of TfM is 2.833 mm h−1, which is related to the local atmospheric drying rate and the hydrometeor loss/convergence in the presence of water vapor divergence. Hydrometeor change/convergence (QCM) come from water (QCMLWP = PS − SLWP) and ice (QCMIWP = SIWP) clouds. The hydrometeor loss/ convergence of TfM is associated with the loss/convergence of water (76.1%) and ice (23.9%) hydrometeors (Fig. 3.6). The water hydrometeor loss/convergence is related to the precipitation and evaporation of rain that overcome the conversion from the ice hydrometeor to the water hydrometeor, which leads to the ice hydrometeor loss/convergence. IWP is 24.2% smaller than LWP. Although the rainfall in TfM is the largest contributor to the total rainfall, the other rainfall types associated with water vapor divergence play minor roles in total rainfall. The rainfall in Tfm and tfM only contribute to 5.0% and 3.0% of the total rainfall, respectively, because of a small coverage and weak rainfall intensity. The rainfall in tfm is virtually zero due to the very small samples as indicated by small fractional rainfall coverage. In Tfm, the small rain rate corresponds to the local atmospheric drying while water vapor divergence and hydrometeor gain/divergence occur. Hydrometeor gain/divergence comes from both water (71.2%) and ice (28.8%) clouds. The water hydrometeor gain/divergence results from vapor condensation, which is much larger than the surface rainfall. The ice hydrometeor gain/divergence corresponds to vapor depositions. IWP is 20.2% smaller than LWP. In tfM, hydrometeor loss/convergence is responsible for the surface rainfall while it overcomes the water vapor divergence to moisten the local atmosphere. The hydrometeor loss/ convergence comes from both water (73.1%) and ice (26.9%) clouds (Table 3.6b).

76

3

Tropical Precipitation Processes

a

b

c

d

e

f

g

Fig. 3.5 (a) Fractional rainfall coverage (FRC), (b) percentage of rain amount over total rainfall amount (PRA), and means of (c) PS, (d) QWVT, (e) QWVF, (f) QWVE, and (g) QCM in TFM, TFm, tFM, tFm, TfM, Tfm, tfM, and tfm. Units are mm h−1 for PS, QWVT, QWVF, QWVE, and QCM and % for FRC and PRA

3.2

Grid-Scale Analysis

77

a

b

c

d

e

f

g

Fig. 3.6 Means of (a) IWP, (b) LWP, (c) QCM, (d) QCMIWP, (e) QCMLWP, (f) PS, (g) − PCND, (h) − (PDEP + PSDEP + PGDEP), (i) PREVP, (j) PMLTS + PMLTG, and (k) C(LWP, IWP) in TFM, TFm, tFM, tFm, TfM, Tfm, tfM, and tfm. Units are mm for IWP and LWP and mm h−1 for the others

78

3

Tropical Precipitation Processes

h

i

j

k

Fig. 3.6 (continued)

The water hydrometeor loss/convergence result from the surface rainfall and evaporations of cloud water and rain (PCND < 0 when the evaporation of cloud water occurs). IWP is slightly larger than LWP. The rainfall types associated with water vapor convergence (TFM + TFm + tFM + tFm) make significant contributions to total rainfall. 10%, 17.7%, 19.2%, and 14.2% of the total rainfall come, respectively, from the rainfall types associated with local atmospheric drying and hydrometeor loss/convergence in TFM, with the local atmospheric drying and hydrometeor gain/divergence in TFm, with the local atmospheric moistening and hydrometeor loss/convergence in tFM and with the local atmospheric moistening and hydrometeor gain/divergence in tFm in the presence of water vapor convergence. The large contributions of rainfall with the local atmospheric moistening may be associated with the large fractional coverage of rainfall (24.7% in tFM and 15.4% in tFm). Although they cover small area (1.2% in TFM and 6.9% in TFm), the rainfall types associated with local atmospheric drying have large magnitudes in TFM (27.814 mm h−1) and TFm (8.273 mm h−1). In TFM, water vapor convergence, local atmospheric drying, and hydrometeor loss/convergence have equal contributions (~30%) to the rain rate. The analysis of the cloud budget in TFM reveals that the hydrometeor loss/convergence comes only from water clouds. The water hydrometeor loss/convergence corresponds to the

3.2

Grid-Scale Analysis

79

surface rainfall and the evaporation of rain, which is largely offset by vapor condensation. IWP is about 26% of LWP, which is a indicative of the dominance of water clouds. In TFm, the water vapor convergence is nearly offset by the hydrometeor gain/divergence, while rainfall is associated with the local atmospheric drying. The water vapor convergence rate is larger in TFm than in TFM. The cloud budget in TFm shows that the 65% and 35% of hydrometeor gain/divergence come, respectively, from water and ice clouds. The water hydrometeor gain/divergence is primarily associated with vapor condensation, whereas the ice hydrometeor gain/divergence is related to vapor depositions and the conversion from the water hydrometeor to the ice hydrometeor. IWP is about 44% of LWP. In tFM, water vapor convergence is largely used to moisten the local atmosphere. As a result, the rainfall corresponds to the hydrometeor loss/convergence, which comes primarily from water clouds. In water cloud budget, the rain rate and evaporation rate of rain are higher than the conversion rate from the ice hydrometeor to the water hydrometeor. IWP is about 24% smaller than LWP. In tFm, the water vapor convergence is largely used to moisten the local atmosphere and to increase hydrometeor concentration/to advect hydrometeor out, which leads to a low rain rate. The large hydrometeor gain/divergence comes mainly from water cloudsthrough the vapor condensation. IWP is about half of LWP. Contribution of each rainfall type to total rainfall may be affected by large-scale forcing. Such response to large-scale vertical velocity can be examined through the analysis of life span of rainfall event. Thus, a 2-day rainfall event from 2000 LST 23 December to 1800 LST 25 December 1992 is chosen to study precipitation statistics in a life span of precipitation system. The life span of precipitation event is divided into four phases: the onset phase (2000–2200 LST 23 December), the development phase (2300 LST 23 December–1400 LST 24 December), the mature phase (1500 LST 24 December–0900 LST 25 December), and the decay phase (1000–1800 LST 25 December). Model domain mean surface rain rates are 0.16 mm h−1 in the onset phase, 0.36 mm h−1 in the development phase, 0.68 mm h−1 in the mature phase, and 0.19 mm h−1 in the decay phase. During the onset phase, rainfall is largely attributable to TfM, tFm and TFm. TfM makes a significant contribution to total rainfall even though the rainfall associated with water vapor convergence is slightly larger than the rainfall associated with water vapor divergence (Fig. 3.7). The large contributions to total rainfall made by tFm and TFm signify a large growth of clouds. During the development phase, TFM, TfM and TFm mainly contribute to total rainfall. The contribution of TfM to total rainfall is significantly low. The large contributions to total rainfall from TFM and TfM are mainly associated with local atmospheric drying caused by the decrease in saturation mixing ratio, which is induced by the nocturnal radiative cooling. During the mature phase, TfM, tFM, tFm and TFm account for total rainfall. The large contribution of tFM to total rainfall indicates that the rainfall is associated with water vapor convergence and hydrometeor loss/ convergence. During the decay phase, TfM and tFM make the largest rainfall contributions. The rainfall contribution by TfM is increased from the mature phase to the decay phase. Contribution of each rainfall type to total rainfall in grid-scale analysis may be different from that in model domain mean analysis. The four rainfall types associated

80

3

Tropical Precipitation Processes

a

b

c

d

Fig. 3.7 Percentage of rain amount over total rainfall amount (PRA) calculated using grid-scale data during (a) the onset phase (2000–2200 LST 23 December), (b) the development phase (2300 LST 23 December–1400 LST 24 December), (c) the mature phase (1500 LST 24 December–0900 LST 25 December), and (d) the decay phase (1000–1800 LST 25 December) in a rainfall case from 2000 LST 23 December to 1800 LST 25 December 1992. Unit is %

with water vapor convergence account for about 61% of total rainfall in the grid-scale calculation, which is significantly smaller than model domain mean calculation (86.6%) (Fig. 3.8). The large contributions of the rainfall types associated with water vapor divergence are excluded by simple model domain mean calculations for mean rainfall types. In the grid-scale analysis, the rainfall type associated with local atmospheric drying, water vapor divergence and hydrometeor loss/convergence (TfM) contributes to 30.8% of total rainfall, which is about five times as large as the contribution of the same rainfall type to total rainfall (6.2%) found in the model domain mean in COARE. TfM makes the largest contribution to total rainfall among eight rainfall type because TfM is the largest rainfall contributor for each mean rainfall types. Thus, the contribution of each rainfall type to total rainfall in the grid-scale analysis is significantly different from that in the model domain mean analysis. This difference suggests a spatial scale dependence of precipitation statistics.

3.2

Grid-Scale Analysis

81

a

b

c

d

e

f

g

Fig. 3.8 Percentage of rain amount over total rainfall amount (PRA) calculated using model domain mean simulation data for seven mean rainfall types (grey bar) and PRA of rainfall types calculated using grid-scale simulation data for each mean rainfall type (black bar) in TFM, TFm, tFM, tFm, TfM, Tfm, and tfM. Unit is %

82

3.3

3

Tropical Precipitation Processes

Tropical Rainfall Responses to the Large-Scale Forcing

To study the responses of tropical deep convective precipitation systems and their associated convective and stratiform regions to the large-scale forcing, two periods in COARE are chosen for analysis. From 22 to 27 December 1992, the vertical profile of model domain mean vertical velocity shows the strong upward motions with a maximum of 2.81 cm s−1 at 8.8 km (Fig. 3.9a). From 3 to 8 January 1993, the vertical profile of the mean vertical velocity displays the weak upward motions with maxima of 0.71 cm s−1 at 4.8 km and 0.81 cm s−1 at 10.3 km, respectively (Fig. 3.9b). Since imposed large-scale upward motions are much stronger during the period of 22–27 December 1992 than during the period of 3–8 January 1993, the periods of 22–27 December 1992 and 3–8 January 1993 are, respectively, defined as the strongforcing (SF) and weak-forcing (WF) phases. Time and model domain mean surface rain rate is higher in the SF phase (0.481 mm h−1) than in the WF phase (0.364 mm h−1) (Table 3.5). During the SF phase, 41.6% and 58.4% of mean surface rain rate come from raining stratiform and convective regions, respectively. During the WF phase, 25.3% and 74.7% of mean surface rain rate come from raining stratiform and convective regions, respectively. Convective rain rates show similar magnitudes (0.281 mm h−1 in the SF phase and 0.272 mm h−1 in the WF phase) in the two phases, although convective rainfall covers larger areas in the SF phase (4.7%) than in the WF phase (3.5%). Stratiform rain

a

b

Fig. 3.9 Vertical profiles of time-mean vertical velocity (cm s−1) over non-raining regions (short dash), raining stratiform regions (dot), convective regions (dot dash), and whole model domain (solid) in (a) the SF phase and (b) the WF phase (After Gao and Li 2008)

3.3

Tropical Rainfall Responses to the Large-Scale Forcing

83

Table 3.5 Time means of fractional coverage (FC), surface rain rate (PS), local vapor change (QWVT), water vapor convergence (QWVF), surface evaporation (QWVE), hydrometeor change/convergence (QCM), water vapor sink (QWVOUT), and water vapor source (QWVIN) over non-raining regions, raining stratiform regions, and convective regions and their sums (model domain means) in (a) the SF phase and (b) the WF phase in COARE. Units are % for fractional coverage and mm h−1 for the others (After Gao and Li 2008) Non-raining Raining stratiform Convective Model domain regions regions regions mean (a) FC 78.8 16.5 4.7 100.0 0.000 0.200 0.281 0.481 PS QWVT −0.152 0.082 0.133 0.063 QWVF −0.007 −0.078 0.281 0.197 QWVE 0.148 0.045 0.021 0.213 QCM 0.010 0.150 −0.153 0.008 QWVOUT 0.083 0.280 0.483 0.846 QWVIN −0.094 −0.231 −0.048 −0.373 (b) FC 92.0 4.5 3.5 100.0 PS 0.000 0.092 0.272 0.364 QWVT −0.263 0.145 0.143 0.039 QWVF 0.070 −0.186 0.255 0.139 QWVE 0.161 0.012 0.011 0.184 QCM 0.017 0.121 −0.136 0.003 QWVOUT 0.014 0.086 0.470 0.570 QWVIN −0.031 −0.116 −0.061 −0.208

rate is higher in the SF phase (0.200 mm h−1) than in the WF phase (0.092 mm h−1). Three factors may account for the larger stratiform rain rate in the SF phase than in the WF phase. First, stratiform rainfall occupies much larger areas in the SF phase (16.5%) than in the WF phase (4.5%). Second, imposed downward motions appear in the lower troposphere only in the SF phase (Fig 3.9). Third, the vertical shear of imposed large-scale zonal winds is larger in the SF phase than in the WF phase (Fig. 1.1b). The difference in stratiform rain rate between the two phases accounts for the difference in model domain mean surface rain rate. The mean water-vapor-related surface rainfall budgets in Table 3.5 show that 13.1%, 41.0%, 44.3%, and 1.7% of surface rain rate in the SF phase are, respectively, from local atmospheric drying, water vapor convergence, surface evaporation, and hydrometeor loss, whereas 10.7%, 38.2%, 50.5%, and 0.8% of surface rain rate in the WF phase are, respectively, from local atmospheric drying, water vapor convergence, surface evaporation, and hydrometeor loss. Surface evaporation and water vapor convergence associated with imposed large-scale upward motions account for 85–88% of the mean surface rain rate in the two phases, while 11–13% of the mean surface rain rate is associated with the local atmospheric drying in the two phases. QCM only accounts for less than 2% in the production of rainfall in the two phases. All rainfall processes are stronger in the SF phase than in the WF phase. As a result,

84

3

Tropical Precipitation Processes

Table 3.6 Daily and model domain means of surface rain rate (PS), local heat change (SHT), heat divergence (SHF), surface sensible heat (SHS), latent heat due to ice-related processes (SLHLF), radiative cooling (SRAD), and hydrometeor change/convergence (QCM) in (a) the SF phase and (b) the WF phase in COARE Unit is mm h−1 SF phase WF phase PS 0.481 0.364 SHT −0.049 0.029 SHF 0.457 0.196 SHS −0.035 −0.028 SLHLF 0.007 0.002 SRAD 0.093 0.162 QCM 0.008 0.003

the mean surface rain rate is higher in the SF phase than in the WF phase. Because the mean imposed large-scale upward motions are stronger in the SF phase than in the WF phase (Fig. 3.9) and the mean imposed SST is warmer in the SF phase (29.1°C) than in the WF phase (28.7°C), the mean water vapor convergence rate and surface evaporation rate are larger in the SF phase than in the WF phase. About 50% of the difference in the mean surface rain rate for SF-WF (0.117 mm h−1) comes from the difference in the mean water vapor convergence (0.058 mm h−1), about 25% is caused by the difference in the mean surface evaporation (0.029 mm h−1), and about 21% results from the difference in local atmospheric drying rate (0.024 mm h−1). This indicates that the difference in imposed large-scale vertical velocity between the two phases primarily determines the difference in the mean surface rain rate. The mean thermally-related surface rainfall budgets reveal that the surface rain rates are mainly associated with advective and radiative cooling in the two cases (Table 3.6). Over convective regions, the similar water vapor convergence rates (0.281 mm h−1 in the SF phase and 0.255 mm h−1 in the WF phase) lead to similar convective rain rates in the two phases (Table 3.5). Over raining stratiform regions, the differences in PS, QWVT, QWVF, QWVE, and QCM between SF-WF are 0.108, −0.063, 0.108, 0.033, and 0.029 mm h−1, respectively. Thus, the difference in water vapor convergence rate for SF-WF accounts for the difference in stratiform rain rate because the negative difference in local atmospheric moistening is offset by the positive differences in surface evaporation and the transport of hydrometeor concentration from convective regions to raining stratiform regions. From (2.5i), QWVF can be partitioned into three components: QWVF = QWVF 1 + QWVF 2 + QWVF 3 ,

(3.3)

QWVF 1 = -[u o

¶qv o ¶q ] - [ w o v ], ¶x ¶z

(3.3a)

QWVF 2 = -[ w o

¶q v ¢ ¶q ] - [ w¢ v ], ¶z ¶z

(3.3b)

where

3.3

Tropical Rainfall Responses to the Large-Scale Forcing

QWVF 3 = -[

¶ o (u + u¢ )qv ¢ ]. ¶x

85

(3.3c)

In (3.3), QWVF1 is imposed horizontal advection of specific humidity and vertical advection of spatial mean specific humidity by imposed large-scale vertical velocity, QWVF2 is vertical advection of perturbation specific humidity by imposed large-scale vertical velocity and vertical advection of spatial mean specific humidity by perturbation vertical velocity, and QWVF3 is convergence of horizontal flux of perturbation specific humidity . The differences in QWVF1, QWVF2, and QWVF3 for SF-WF are 0.058, −0.040, and 0.090 mm h−1, respectively. This indicates that the larger convergence of horizontal flux of perturbation specific humidity and the larger vertical advection of the mean specific humidity by imposed large-scale vertical velocity lead to the smaller water vapor divergence in the SF phase than in the WF phase. Non-raining regions in the WF phase (92.0%) covers larger areas than in the SF phase (78.8%) (Table 3.5). In both phases, the surface evaporation largely moistens the local atmosphere over non-raining regions while both rates are larger in the WF phase than in the SF phase. The water vapor budgets are used to study the contribution of net condensation to convective and stratiform rainfall in the previous studies (e.g., Tao et al. 1993; Johnson et al. 2007). Since (2.8a) is derived through the combination of the water vapor (2.4) and cloud (2.3) budgets, water vapor and cloud budgets can be separately analyzed. The time and model domain mean analysis shows that the net condensation (QWVOUT + QWVIN) is nearly offset by water vapor convergence and surface evaporation that leads to small local atmospheric drying rates in the water vapor budgets and the net condensation nearly accounts for surface rain rate in the cloud budgets in the two phases because the mean hydrometeor loss is small (Table 3.5). The magnitudes of time and model domain mean QCM are much smaller than those of time mean QCM over convective and stratiform regions in the two phases. The positive QCM over stratiform regions and negative QCM over convective regions in the two phases indicate the transport of hydrometeor concentration from convective regions to raining stratiform regions primarily accounts for stratiform rainfall in the SF phase whereas it is the only source for stratiform rainfall. The net condensation also contributes to stratiform rainfall in the SF phase. The important role of transport of hydrometeor concentration from convective regions to raining stratiform regions in the production of stratiform rainfall is consistent with what were found in tropical and midlatitude precipitation systems in the previous budget studies (e.g., Gamache and Houze 1983; Rutledge and Houze 1987; Chong and Hauser 1989; Gallus and Johnson 1991). Over convective regions, the net condensation is caused primarily by the water vapor convergence in the water vapor budget. In the cloud budget, convective rainfall corresponds to water vapor convergence while water vapor convergence supports the transport of hydrometeor concentration from convective regions to raining stratiform regions in the two phases. Over raining stratiform regions, the net condensation, surface evaporation, and water vapor divergence dries the local atmosphere in the water vapor budget whereas stratiform rainfall is associated with the net condensation and the transport of hydrometeor concentration from convective regions to

86

3

Tropical Precipitation Processes

raining stratiform regions in the cloud budget in the SF phase. In contrast, water vapor divergence dries the local atmosphere in the water vapor budget while stratiform rainfall is associated with the transport of cloud hydrometeors from convective regions to raining stratiform regions in the cloud budget in the WF phase. Over nonraining regions, surface evaporation moistens the local atmosphere in the SF phase, whereas surface evaporation plus weak water vapor convergence moisten the local atmosphere in the WF phase. The analysis of surface rainfall budget and heat budget reveals that the similarity in convective regions and difference in raining stratiform regions between the two phases as convective and stratiform rainfall responses to different large-scale forcing are largely determined by water vapor convergence and heat divergence. Thus, the vertical structures of vertical velocity, water vapor mass flux, and cloud hydrometeor mass flux in the two phases are compared, respectively, over different regions. The CFAD proposed byYuter and Houze (1995) of vertical velocity, water vapor mass flux, and cloud hydrometeor mass flux are calculated, respectively, in the two phases and shown in Fig. 3.10. It reveals a broader distribution of vertical velocity in the WF phase than in the SF phase. In the WF phase, the maximum ascending motion of 17 m s−1 occurs around 11 km whereas the maximum descending motion of −7 m s−1 appears between 3 and 13 km. More than 50% of vertical motion are weak descending motions (To)

0.031 PSACW (T0, and H(F) = 0 when F £ 0. RMPE is calculated using hourly data and accumulating rainfall sources (RSRB) from each model grid over the model domain, which serves as the “true” precipitation efficiency. Sui et al. (2007) used the cloud microphysical budget to define precipitation efficiency (CMPE). The cloud microphysical budget can be expressed by 7

PS - QCM = å PI ,

(8.3)

I =1

where QCM = -

¶[ql ] ¶q ¶q - [u l ] - [ w l ], ¶t ¶x ¶z

(8.3a)

8

Precipitation Efficiency

211

Fig. 8.1 (a) RMPE versus CMPE. Unit is %. RMPE and CMPE are calculated by accumulating rainfall sources from each model grid over the model domain. Diagonal line denotes RMPE = CMPE (After Gao and Li 2011)

Here, PI denotes rainfall source/sink terms from cloud microphysical processes, which are defined in (1.2i). Thus, CMPE is defined as CMPE =

PS , RSC + H (QCM )QCM

(8.4)

7

where RSC ( = å H ( PI )PI ) is the rainfall source from cloud microphysical I =1 processes. Rainfall sources are used to calculate precipitation efficiency, whereas rainfall sinks are excluded, which may lead to the difference between RMPE and CMPE. This is demonstrated in Fig. 8.1 where RMPE is larger than CMPE. RMPE and CMPE are calculated by accumulating rainfall sources from each model grid over the model domain in Fig. 8.1. The difference between RMPE and CMPE can be quantitatively measured by RMS difference, which is 15.3%. The RMS is smaller than the standard deviation of RMPE (18.0%). This suggests that CMPE may capture variation of RMPE. The relationship between CMPE and RMPE is given by CMPE RSR + H (QRM )QRM , = RMPE RSC + H (QCM )QCM

(8.5)

Thus, CMPE and RMPE are exactly same only if RSR + H (QRM )QRM = RSC + H (QCM )QCM .

(8.6)

212

8

Precipitation Efficiency

The difference between RMPE and CMPE in Fig. 8.1 implies that (8.6) can be met. Since RSC + H(QCM)QCM can be expanded into RSC + H (QCM )QCM = RSR + H (QRM )QRM + RSCW + H (QCWM )QCWM + RSCI + H (QCIM )QCIM + RSS + H (QSM )QSM + RSG + H (QGM )QGM ,

(8.7)

(8.6) can be met only if H (QCWM )QCWM + RSCW = 0,

(8.8a)

H (QCIM )QCIM + RSCI = 0,

(8.8b)

H (QSM )QSM + RSS = 0,

(8.8c)

H (QGM )QGM + RSG = 0.

(8.8d)

9

In (8.7) and (8.8), RSCW ( = å H (CWPI )CWPI ) is the rainfall source from cloud I =1

9

water microphysical processes, RSCI ( = å H (CIPI )CIPI ) is the rainfall source I =1

15

from cloud ice microphysical processes, RSS ( = å H (SPI )SPI ) is the rainfall I =1 14

source from snow microphysical processes, and RSG ( = å H (GPI )GPI ) is the rainfall I =1

source from graupel microphysical processes. CWPI, CIPI, SPI, and GPI denote rainfall source/sink terms from microphysical processes of cloud water, cloud ice, snow, and graupel, respectively, which are defined in (1.2j, 1.2l, 1.2m, and 1.2n). Since only rainfall sources are included and all rainfall sinks are excluded in microphysical budgets of cloud water, cloud ice, snow, and graupel, (8.8a)–(8.8d) cannot be met, which may contribute to the difference between RMPE and CMPE. This can be demonstrated in Fig. 8.2, which shows RSC versus RSR, RSCW, RSCI, RSS, and RSG, respectively, and in Fig. 8.3, which shows H(QCM)QCM versus H(QRM)QRM, H(QCWM)QCWM, H(QCIM)QCIM, H(QSM)QSM, and H(QGM)QGM, respectively. Graupel and cloud water microphysical budgets contribute more to the difference in rainfall sources between RMPE and CMPE than cloud ice and snow microphysical budgets do, while cloud microphysical budget is primarily attributable to the rain microphysical budget. Thus, H (QCWM )QCWM + RSCW ¹ 0,

(8.9a)

H (QCIM )QCIM + RSCI ¹ 0,

(8.9b)

H (QSM )QSM + RSS ¹ 0,

(8.9c)

H (QGM )QGM + RSG ¹ 0.

(8.9d)

8

Precipitation Efficiency

213

a

b

c

d

e

Fig. 8.2 (a) Rainfall source from cloud microphysics (RSC) versus rainfall source from rain microphysics (RSR), (b) RSC versus rainfall source from cloud water microphysics (RSCW), (c) RSC versus rainfall source from cloud ice microphysics (RSCI), (d) RSC versus rainfall source from snow microphysics (RSS), and (e) RSC versus rainfall source from graupel microphysics (RSG). Calculations are conducted by accumulating rainfall sources from each model grid over the model domain. Diagonal lines in (a), (b), (c), (d), and (e) denote RSC = RSR, RSC = RSCW, RSC = RSCI, RSC = RSS, and RSC = RSG, respectively (After Gao and Li 2011)

214

8

a

b

c

d

Precipitation Efficiency

e

Fig. 8.3 (a) H(QCM)QCM versus H(QRM)QRM, (b) H(QCM)QCM versus H(QCWM)QCWM, (c) H(QCM)QCM versus H(QCIM)QCIM, (d) H(QCM)QCM versus H(QSM)QSM, and (e) H(QCM)QCM versus H(QGM)QGM. Calculations are conducted by accumulating each term from each model grid over the model domain. Diagonal lines in (a), (b), (c), (d), and (e) denote H(QCM)QCM = H(QRM)QRM, (b) H(QCM) QCM = H(QCWM)QCWM, (c) H(QCM)QCM = H(QCIM)QCIM, (d) H(QCM)QCM = H(QSM)QSM, and (e) H(QCM) QCM = H(QGM)QGM, respectively (After Gao and Li 2011)

8

Precipitation Efficiency

215

(8.9a) and (8.9d) leads to the deviation of CMPE from RMPE. Sui et al. (2007) showed that large-scale precipitation efficiency (LSPE) is defined as LSPE =

PS , RSWV + H (QCM )QCM

(8.10)

3

where RSWV ( = å H (QI )QI ) is the rainfall source from water vapor and cloud I =1

budgets, QI = (QWVT , QWVF , QWVE ) . LSPE (8.10) can be derived from the watervapor-related surface rainfall budget (Gao et al. 2005; Cui and Li 2006), which is in turn derived from the combination of mass integrated cloud microphysical budget (8.3) with mass integrated water vapor budget. The relationship between LSPE and RMPE is given by RSC + H (QCM )QCM RSR + H (QRM )QRM LSPE . = RMPE RSWV + H (QCM )QCM RSC + H (QCM )QCM

(8.11)

Thus, LSPE and RMPE are exactly same only if (8.6) can be met and RSC = RSWV .

(8.12)

(8.11) and (8.12) state that the deviation of LSPE from RMPE comes from the deviation of CMPE from RMPE and difference in rainfall source between water vapor and cloud budgets. Another way to estimate the difference between LSPE and RMPE is to calculate the difference in rainfall source between the rain microphysical budget (RSRB) and the surface rainfall budget ( RSWVCB = RSWV + H (QCM )QCM ), which is shown in Fig. 8.4. RSRB is generally smaller than RSWVCB when the water vapor and cloud microphysical budgets are averaged over areas smaller than 192 km (Fig. 8.4a–d), whereas it is generally larger than RSWVCB when the water vapor and cloud microphysical budget is averaged over areas larger than 384 km (Fig. 8.4e–f). As a result, LSPE is significantly different from RMPE (Fig. 8.5). The RMS differences between RMPE and LSPE are 20.7–37.5% (Table 8.1), which are significantly larger than the RMS difference between RMPE and CMPE (15.3%) and the standard deviation of RMPE (18.0%). The estimate of precipitation efficiency with water vapor process data may not capture the variation of the true precipitation efficiency. Therefore, water vapor process data cannot be used to estimate RMPE.

Table 8.1 RMS differences between RMPE and estimates of LSPE using grid-scale (1.5 km) and model domain mean (768 km) data and data averaged over the areas of 12, 96, 192, and 386 km. Unit is % (After Gao and Li 2011) 1.5 km 12 km 96 km 192 km 384 km 768 km 37.5 31.7 23.1 20.7 21.8 31.0

216

8

a

b

c

d

e

f

Precipitation Efficiency

Fig. 8.4 Rainfall source from rain microphysical budget (RSRB) versus rainfall source from water vapor and cloud microphysical budget (RSWVCB). RSR is calculated by accumulating rainfall sources from each model grid over the model domain with hourly data, whereas RSWVCB is calculated by using (a) grid data (1.5 km), (b) 12 km, (c) 96 km, (d) 192 km, (e) 384 km, and (f) 768 km (model domain) mean data. Unit is mm h−1. Diagonal lines denote RSRB = RSWVCB (After Gao and Li 2011)

8

Precipitation Efficiency

217

a

b

c

d

e

f

Fig. 8.5 RMPE versus LSPE. RMPE is calculated by accumulating rainfall sources from each model grid over the model domain with hourly data, whereas LSPE is calculated by using (a) grid data (1.5 km), (b) 12 km, (c) 96 km, (d) 192 km, (e) 384 km, and (f) 768 km (model domain) mean data. Unit is %. Diagonal lines denote RMPE = LSPE (After Gao and Li 2011)

218

8

Precipitation Efficiency

References Auer AH Jr, Marwitz JD (1968) Estimates of air and moisture flux into hailstorms on the high plains. J Appl Meteorol 7:196–198 Braham RR Jr (1952) The water and energy budgets of the thunderstorm and their relation to thunderstorm development. J Meteorol 9:227–242 Chong M, Hauser D (1989) A tropical squall line observed during the CORT 81 experiment in West Africa. Part II: water budget. Mon Weather Rev 117:728–744 Cui X, Li X (2006) Role of sureface evaporation in surface rainfall processes. J Geophys Res 111, doi:10.1029/2005JD006876 Doswell CA III, Brooks HE, Maddox RA (1996) Flash flood forecasting: an ingredients-based methodology. Weather Forecast 11:560–581 Ferrier BS, Simpson J, Tao WK (1996) Factors responsible for different precipitation efficiencies between midlatitude and tropical squall simulations. Mon Weather Rev 124:2100–2125 Gao S, Li X (2011) Can water vapor process data be used to estimate precipitation efficiency? Q J R Meteorol Soc 137:969–978, (c) Royal Meteorological Society. Reprinted with permission Gao S, Cui X, Zhou Y, Li X (2005) Surface rainfall processes as simulated in a cloud resolving model. J Geophys Res. doi:10.1029/2004JD005467 Heymsfield GM, Schotz S (1985) Structure and evolution of a severe squall line over Oklahoma. Mon Weather Rev 113:1563–1589 Li X, Sui CH, Lau KM (2002) Precipitation efficiency in the tropical deep convective regime: a 2-D cloud resolving modeling study. J Meteorol Soc Jpn 80:205–212 Lipps FB, Hemler RS (1986) Numerical simulation of deep tropical convection associated with large-scale convergence. J Atmos Sci 43:1796–1816 Sui CH, Li X, Yang MJ, Huang HL (2005) Estimation of oceanic precipitation efficiency in cloud models. J Atmos Sci 62:4358–4370 Sui CH, Li X, Yang MJ (2007) On the definition of precipitation efficiency. J Atmos Sci 64:4506–4513 Tao WK, Johnson D, Shie CL, Simpson J (2004) The atmospheric energy budget and large-scale precipitation efficiency of convective systems during TOGA COARE, GATE, SCSMEX, and ARM: cloud-resolving model simulations. J Atmos Sci 61:2405–2423 Weisman ML, Klemp JB (1982) The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon Weather Rev 110:504–520

Chapter 9

Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

9.1

Introduction

The meaningful precipitation simulation and estimate require sophisticate models with accurate cloud microphysical and radiative parameterization schemes. One of such models is cloud-resolving model. The precipitation processes are highly nonlinearly associated with the dynamic, thermodynamic, cloud microphysical and radiative processes, which makes precipitation simulations very sensitive to temperature, water vapor, and parameterization schemes of these physical processes (Grabowski et al. 1998; Donner et al. 1999; Guichard et al. 2000; Xu et al. 2002; Petch et al. 2002, 2008; Petch 2004, 2006; Phillips and Donner 2006; Keil et al. 2008). Petch and Gray (2001) found that the model domain size, horizontal resolution, use of a third dimension, and cloud microphysical parameterization have impacts on the model simulations. Petch et al. (2002) revealed that the finer horizontal resolution (750 km) for hourly averaged data. The RMS differences in Ps, QWVT, QWVF, and QCM have similar magnitudes, which are much larger than those of QWVE (Fig. 9.2d–h). The RS ratio of QCM is always larger than 1 regardless of time and spatial scales, indicating a extremely large sensitivity of cloud model simulation to the uncertainty of the initial conditions. The RS ratio of PS is smaller than 1 when the spatial scale is larger than 350 km and the time scale is larger than 8 h or when the spatial scale is larger than 750 km and the time scale is smaller than 4 h. The accurate precipitation simulation, in which the RS ratio of surface rain rate is smaller than 1, requires a small spatial scale with a large time scale or a large spatial scale with a small time scale. This indicates that accurate precipitation simulation cannot be obtained on both fine temporal and spatial scales, which limits quantitative precipitation forecast. The large RS ratio for QCM and small RS ratio for Ps implies that a larger uncertainty exists in cloud simulations than in precipitation simulations. This does not contradict the result from Khairoutdinov and Randall (2003) because different aspects of model simulations such as QCM and PS are analyzed in this study based on the same simulation dataset whereas differences in same variables (e.g., precipitation rate) between the two sets of ensemble experiments with randomly perturbed initial thermodynamic soundings and same microphysics scheme and with changed microphysics parameters and same initial conditions are examined by Khairoutdinov and Randall (2003). When the spatial scale approaches the length of the model domain (768 km), the RS ratio of QWVF is nearly zero because similar QWVF in all experiments as a result of the same imposed large-scale vertical velocity. The RS ratios of PS, QWVT, and QWVE are smaller than 1while QCM is larger than 1. The water vapor process dominated by the water vapor convergence has stronger impacts on surface precipitation than the cloud process does when the time scale is larger than 3 h whereas the cloud process has dominant effects on precipitation when the time scale is smaller than 3 h. This may be due to the facts that the time scale of water vapor processes in which the dominant water vapor convergence is mainly determined by the imposed large-scale vertical velocity (~a day) is much longer than that of QCM (~an hour). In contrast, the time scales of fluctuations of QCM are much shorter (~hourly) (Fig. 8 in Gao and Li 2008). Thus, QCM is dominated by cloud activity only. The distributions for time and spatial scales of data average of RS ratio of Sqv (Fig. 9.3h) are similar to those of Ps, IWP, and LWP. The RMS differences and RS ratio of PCND determine the RMS differences in Sqv (Fig. 9.3). The vapor condensation that is dependent nonlinearly of temperature is largely determined by the tiny

224

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

b

c

d

e

f

g

h

Fig. 9.3 RMS differences between perturbation experiments and control experiment (contours) and the ratios of RMS difference to standard deviation (background) of (a) mass-weighted mean temperature, (b) PCND, (c) PDEP, (d) PSDEP, (e) PGDEP, (f) PREVP, (g) PMLTS + PMLTG, and (h) Sqv as functions of time and spatial scales for average of data. The contour intervals of RMS differences are 0.04oC for mass-weighted mean temperature, 0.1 mm h−1 for PCND, PREVP, and Sqv, and 0.02 mm h−1 for PDEP, and 0.01 mm h−1 for PSDEP, PGDEP, and PMLTS + PMLTG (After Gao and Li 2009)

9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures…

225

difference between two big terms of specific humidity and saturation specific humidity (Li et al. 2006). The RS ratio of mass-weighted mean temperature is 0.25–0.37. Both RS ratios of mass-weighted mean temperature (Fig. 9.3a) and PW (Fig. 9.2a) are smaller than 1 but the RS ratio of vapor condensation could be larger than 1 when the spatial scale is larger than 350 km and the time scale is longer than 8 h or when the spatial scale is larger than 750 km and the time scale is shorter than 4 h. The results suggest that tiny uncertainties of temperature and water vapor could lead to large uncertainties of vapor condensation, which significantly reduce the predictability of cloud and rainfall.

9.3

Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures of Initial Conditions

To study sensitivity of precipitation modeling to uncertainty of vertical structures of initial conditions, Li and Shen (2010) conducted the twelve perturbation experiments and compared them with the control experiment in Sect. 9.2. The twelve perturbation experiments are identical to the control experiment, but they use different initial temperature or water vapor conditions. The six perturbation experiments are perturbed by ± 0.2°C of temperatures in the upper (above 500 hPa), mid (between 700 and 500 hPa), and lower (below 700 hPa) troposphere. The six other perturbation experiments are perturbed by ± 0.04 g kg−1 of specific humidity in the upper, mid, and lower troposphere. The upper, mid, and lower troposphere defined here contains ice clouds, both ice and water clouds, and water clouds, respectively. The perturbations of initial temperature and water vapor conditions here are significantly smaller than the observed temperature and water vapor errors (~1°C and 1 mm). The reason for choosing such tiny perturbations is to demonstrate that the cloud and precipitation simulations with prognostic cloud microphysical parameterization schemes in current model framework are extremely sensitive to uncertainty of the initial conditions of temperature and water vapor. Thus, the modeling communities face tough challenge in seeking better quality observational data for initial modeling conditions. To measure sensitivity of model simulation of surface rainfall to the uncertainty of the initial condition, the simulation data from the plus and minus perturbation experiments and the control experiment are first averaged for different spatial and time scales and are used to calculate the RMS difference between the perturbation experiments and the control experiment and standard deviations of the perturbation experiments and the control experiment. When the initial temperature condition in the upper troposphere is perturbed, the RS ratio of surface rain rate is generally smaller than 1 when the spatial and time scales for data average are larger than 200 km and 4 h (Fig. 9.4a). When the initial temperature condition in the mid troposphere is perturbed, the spatial scale for the RS ratio of less than 1 is about 400 km (Fig. 9.4b). When the initial temperature condition in the lower troposphere is

226

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

d

b

e

c

f

Fig. 9.4 Ratios of RMS difference between perturbation experiments and control experiment to standard deviation of surface rain rate (Ps) as functions of time and spatial scales for average of data. (a), (b), and (c) present the experiments with perturbed initial temperature conditions in the upper, mid, and lower troposphere, respectively, whereas (d), (e) and (f) present the experiments with perturbed initial water vapor conditions in the upper, mid, and lower troposphere, respectively. Ratios of larger than 1 are shaded (After Li and Shen 2010)

perturbed, the spatial scale for the RS ratio of less than 1 becomes 500 km (Fig. 9.4c). The RS ratio of surface rain rate is generally smaller than 1 when the spatial and time scales for data average are larger than 500 km and 4 h (Fig. 9.4d–f), regardless of which vertical layers the initial water vapor conditions are perturbed in. This suggests that the variability of simulated tropical surface rain rate at the zonal scales of 200–500 km is sensitive to the uncertainty of vertical structures of perturbed initial temperature whereas it may not be sensitive to the uncertainty of vertical structures of perturbed initial water vapor. When the initial temperature or water vapor conditions in the lower troposphere are perturbed, the patterns of RS ratios of local change of water vapor and water vapor convergence are similar to those of surface rain rate (Fig. 9.5). The RS ratios

9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures…

a

e

b

f

c

g

d

h

227

Fig. 9.5 Ratios of RMS differences between perturbation experiments and control experiment to standard deviations of water vapor tendency (QWVT) in (a) and (e), water vapor convergence (QWVF) in (b) and (f), surface evaporation (QWVE) in (c) and (g), and cloud source/sink (QCM) in (d) and (h) as functions of time and spatial scales for average of data. Left and right panels, respectively, present the experiments with perturbed initial temperature and water vapor conditions in the lower troposphere. Ratios of larger than 1 are shaded (After Li and Shen 2010)

228

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

of surface evaporation are smaller than 1 regardless of the spatial and time scales for data average; it appears to suggest that the model simulations of surface evaporation are less sensitive to perturbed initial conditions. The RS ratios of the hydrometeor change/convergence are generally larger than 1 regardless of the spatial and time scales for data average. This implies large uncertainties of cloud simulation that are dominated by cloud activities. Note that the RS ratio of water vapor convergence is much smaller than 0.2 when the spatial scale for data average is 768 km (model domain mean). This is due to the fact that same zonally uniform large-scale vertical velocity is imposed in the control experiment and perturbation experiments. The imposed forcing partially controls the RS ratio for time scale of longer than 4 h for model domain mean surface rain rate but cannot determine the RS ratio for the time scale of shorter than 4 h. The RS ratio for the time scale of shorter than 4 h for model domain mean surface rain rate is mainly affected by the local change of water vapor and hydrometeor change/convergence, which is much affected by cloud activities at very short time scales (~hourly or shorter). The RS ratio increases as the spatial scale decreases. This suggests that the influence of imposed large-scale forcing on precipitation simulation becomes weaker as the spatial scale is smaller. The RS ratio of hydrometeor change/convergence is larger than 1 while the RS ratio of water vapor convergence is smaller than 1 for the spatial scale of larger than 500 km. The patterns of RS ratios of local change of water vapor and water vapor convergence are similar to those of surface rain rate regardless of what initial conditions are and which vertical layers initial conditions are perturbed in (not shown). The RS ratios of surface evaporation are generally smaller than 1. Li et al. (1999, 2002) showed that the vapor condensation is a dominant microphysical source for surface rainfall in the tropical deep convective regime. The patterns of RS ratios of PCND (Fig. 9.6b, f) are similar to those of Sqv (Fig. 9.6a, e), which are similar to those of surface rain rate. This suggests that the uncertainty of precipitation simulation due to the uncertainty of initial conditions stems from the uncertainty of vapor condensation calculation. Since the vapor condensation is the residual between the two large items of specific humidity and saturation specific humidity that is the function of air temperature only, the analysis of variance in vapor condensation between the control experiment and the perturbed experiments, which is similar to Li et al. (2006), is conducted. The results show that the variances in vapor condensation between the control experiment and the perturbed experiments are 4–5 orders of magnitudes smaller than the variances in the items of specific humidity and saturation specific humidity; it appears to suggest that small errors in specific humidity and saturation specific humidity may lead to significant errors in vapor condensation. The results here show that 0.2oC of temperature perturbation and 0.04 g kg−1 of specific humidity perturbation strongly affect model simulations of the variability of condensation and surface rainfall at the spatial scales of smaller than 500 km and time scales of shorter than 4 h. While the RS ratios of surface rain rate can be well above 1 for small time and spatial scales for data average, the RS ratios of temperature (Fig. 9.6c, g) and specific humidity (Fig. 9.6d, h) are well below 1. This indicates

9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures…

a

e

b

f

c

g

d

h

229

Fig. 9.6 Ratios of RMS differences between perturbation experiments and control experiment to standard deviations of water vapor sink (Sqv) in (a) and (e), vapor condensation (PCND) in (b) and (f), mass-weighted mean temperature in (c) and (g), and precipitable water in (d) and (h) as functions of time and spatial scales for average of data. Left and right panels, respectively, present the experiments with perturbed initial temperature and water vapor conditions in the lower troposphere. Ratios of larger than 1 are shaded (After Li and Shen 2010)

230

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

d

b

e

c

f

Fig. 9.7 RMS differences in mass-weighted mean temperature (oC) between perturbation experiments as functions of time and spatial scales for average of data. (a), (b), and (c) present the experiments with perturbed initial temperature conditions in the upper, mid, and lower troposphere whereas (d), (e), and (f) present the experiments with perturbed initial water vapor conditions in the upper, mid, and lower troposphere (After Li and Shen 2010)

that the model simulations of temperature and water vapor are insensitive to the uncertainty of initial conditions of temperature and water vapor. The perturbed initial temperature conditions may cause differences in water vapor simulations whereas the perturbed initial water vapor conditions may cause differences in temperature simulations through radiative, microphysical, and advective processes. The initial temperature conditions perturbed by 0.2oC and the initial water vapor conditions perturbed by 0.04 gkg−1 cause the RMS differences in mass-weighted mean temperature between perturbation experiments and the control experiment (0.15–0.3oC; Fig. 9.7) and the RMS differences in PW (0.55 to 0.9 mm; Fig. 9.8).

9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures…

a

d

b

e

c

f

231

Fig. 9.8 As in Fig. 9.7 except for RMS differences in precipitable water (mm)

Although the RMS differences in PW are smaller than PW itself, the differences might be enough for producing the large uncertainty of cloud and precipitation simulations. The RMS differences in IWP and LWP increase from less than 0.05 mm in the large time and spatial scales to 0.55 mm in the small time and spatial scales (Figs. 9.9 and 9.10), which are smaller than the RMS differences in PW. The RMS differences in temperature and PW are barely changed for the spatial scale for data average, whereas the RMS differences in IWP and LWP increases as the time and spatial scales for data average decrease. Finally, statistical errors of surface rain rate are calculated (Fig. 9.11). Li et al. (2006) defined statistical error as the ratio of RMS difference to the average value. The statistical errors increase from less than 10% in large time and spatial scales for data average to more than 200% in small time and spatial scales for data average,

232

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

e

b

f

c

g

d

h

Fig. 9.9 As in Fig. 9.7 except for RMS differences in ice water path (mm)

9.3 Sensitivity of Precipitation Modeling to Uncertainty of Vertical Structures…

a

d

b

e

c

f

233

Fig. 9.10 As in Fig. 9.7 except for RMS differences in liquid water path (mm)

regardless of which vertical layers the initial conditions are perturbed in. For such small initial temperature and water vapor perturbations, the precipitation simulations with the statistical errors of smaller than 20% cannot be obtained when the time scales are longer than a half day and the spatial scales are larger than 700 km.

234

9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

d

b

e

c

f

Fig. 9.11 Statistical errors (%) of surface rain rate as functions of time and spatial scales for average of data. (a), (b), and (c) present the experiments with perturbed initial temperature conditions in the upper, mid, and lower troposphere whereas (d), (e), and (f) present the experiments with perturbed initial water vapor conditions in the upper, mid, and lower troposphere. Statistical errors of larger than 100% are shaded (After Li and Shen 2010)

References Aires F, Rossow WB, Scott NA, Chedin A (2002) Remote sensing from the infrared atmospheric sounding interferometer instrument, 2, Simultaneous retrieval of temperature, water vapor, and ozone atmospheric profiles. J Geophys Res. doi:10.1029/2001JD001591 Cheng A, Xu KM (2006) Simulation of shallow cumuli and their transition to deep convecitve clouds by cloud-resolving models with different their-order turbulence closures. Q J R Meteorol Soc 132:359–382 Donner LJ, Semen CJ, Hemler RS (1999) Three-dimensional cloud-system modeling of GATE convection. J Atmos Sci 56:1885–1912 Gao S, Li X (2008) Impacts of initial conditions on cloud-resolving simulations. Adv Atmos Sci 25:737–747

References

235

Gao S, Li X (2009) Dependence of the accuracy of precipitation and cloud simulation on time and spatial scales. Adv Atmos Adv 26:1108–1114 Grabowski WW, Wu X, Moncrieff MW, Hall WD (1998) Cloud-resolving model of tropical cloud systems during Phase III of GATE. Part II: effects of resolution and the third spatial dimension. J Atmos Sci 55:3264–3282 Grody N, Zhao J, Ferraro R, Weng F, Boers R (2001) Determination of precipitable water and cloud liquid water over oceans from the NOAA 15 advanced microwave sounding unit. J Geophys Res 106:2943–2953 Guichard F, Redelsperger JL, Lafore JP (2000) Cloud resolving simulations of convective activity during TOGA-COARE: sensitivity to external sources of uncertainties. Q J R Meteorol Soc 126:3067–3095 Keil C, Ropnack A, Craig GC, Schumann U (2008) Sensitivity of quantitative precipitation forecast to height dependent changes in humidity. Geophys Res Let. doi:10.1029/2008GL033657 Khairoutdinov MF, Randall DA (2003) Cloud resolving modeling of the ARM summer 1997 IOP: model formulation, results, uncertainties, and sensitivities. J Atmos Sci 60:607–625 Li X, Shen X (2010) Sensitivity of cloud-resolving precipitation simulations to uncertainty of vertical structures of initial conditions. Q J R Meteorol Soc 136:201–212, (c) Royal Meteorological Society. Reprinted with permission Li X, Sui CH, Lau KM (1999) Large-scale forcing and cloud-radiation interaction in the tropical deep convective regime. J Atmos Sci 56:3028–3042 Li X, Sui CH, Lau KM (2002) Dominant cloud microphysical processes in a tropical oceanic convective system: a 2-D cloud resolving modeling study. Mon Weather Rev 130:2481–2491 Li X, Zhang S, Zhang DL (2006) Thermodynamic, cloud microphysics and rainfall responses to initial moisture perturbations in the tropical deep convective regime. J Geophys Res. doi:10.1029/2005JD006968 Petch JC (2004) The predictability of deep convection in cloud-resolving simulations over land. Q J R Meteorol Soc 130:3173–3187 Petch JC (2006) Sensitivity studies of developing convection in a cloud-resolving model. Q J R Meteorol Soc 132:345–358 Petch JC, Gray MEB (2001) Sensitivity studies using a cloud-resolving model simulation of the tropical west Pacific. Q J R Meteorol Soc 127:2287–2306 Petch JC, Brown AR, Gray MEB (2002) The impact of horizontal resolution on the simulations of convective development over land. Q J R Meteorol Soc 128:2031–2044 Petch JC, Blossey PN, Bretherton CS (2008) Differences in the lower troposphere in two- and three-dimensional cloud-resolving model simulations of deep convection. Q J R Meteorol Soc 134:1941–1946 Phillips VT, Donner LJ (2006) Cloud microphysics, radiation and vertical velocities in two- and three-dimensional simulations of deep convection. Q J R Meteorol Soc 132:3011–3033 Susskind J, Barnet CD, Blaisdell JM (2003) Retrieval of atmospheric and surface parameters from AIR/AMSU/HSB data in the presence of clouds. IEEE Trans Geosci Remote Sens 41:390–409 Xu KM, Cederwall RT, Donner LJ, Grabowski WW, Guichard F, Johnson DE, Khairoutdinov M, Krueger SK, Petch JC, Randall DA, Seman CJ, Tao WK, Wang D, Xie SC, Yio JJ, Zhang MH (2002) An intercomparison of cloud resolving models with the Atmospheric Radiation Measurement summer 1997 Intensive Observation Period data. Q J R Meteorol Soc 128: 593–624

Index

A Accretion, 5, 33, 38 Adiabatic reversible moist adiabatic, 102, 106, 107 Advection horizontal advection, 6, 85, 92 moisture advection, 13 temperature advection, 53, 57 vertical advection, 85, 94 water vapor advection, 9, 53, 54, 89, 94 Anelastic approximation, 2 Ascending motion, 11, 33, 49, 86, 89

B Boundary cyclic lateral boundary, 5, 63, 138, 139 periodic lateral boundary, 31, 138 Budget cloud microphysical budget, 1, 38, 41, 43, 47, 68, 70, 89, 90, 209, 210, 212, 215, 216 heat budget, 22, 29, 46, 53, 57, 86, 151, 153, 156, 158, 204 rain microphysical budget, 210, 212, 215, 216 surface rainfall budget, 34, 35, 58, 63, 64, 70, 72, 75, 83, 84, 86, 92, 94, 97, 111–114, 116, 117, 120, 122, 123, 127, 133, 143, 145, 147, 160, 164, 170, 176, 177, 179, 180, 183, 190, 191, 199, 209, 215 water vapor budget, 13, 22, 27, 29, 53–56, 85, 86, 89, 150–159, 215

C CFAD. See Contoured frequency-altitude diagram Channel, 6, 221 Closure turbulence closure, 219 Cloud anvil cloud, 137 cloud hydrometeor, 1, 2, 21, 23, 27, 44, 46, 47, 86, 89, 90, 95, 97, 138 cloud ice, 4, 5, 21, 33, 137, 138, 209, 212, 213 cloud-radiation interaction, 1, 138, 175, 187–199 cloud water, 4, 5, 33, 34, 38, 41, 43, 74, 75, 78, 89, 90, 138, 164, 175, 209, 212, 213 ice cloud, 21, 22, 79, 137–172, 176–178, 185, 201, 202, 204–206, 225 water cloud, 19, 21, 22, 78, 79, 151, 152, 175–187, 201–206, 212, 225 Cloud microphysical processes, 1, 27, 30, 47, 69, 89, 90, 92, 111, 128, 211, 219 Coefficient correlation coefficient, 12–13 Collection, 5, 38, 41, 43, 74, 75, 89, 90, 164 Condensation, 5, 22, 35, 38, 41, 43, 53, 54, 58, 71, 74, 75, 79, 85, 89, 90, 94, 108, 151–154, 156–158, 164, 175, 202–206, 219, 223, 225, 228, 229 Contoured frequency-altitude diagram (CFAD), 44, 48, 49, 86, 87, 96, 97, 191–194 Convection, 2, 40, 102, 125, 138 Convective, 1, 27, 63, 111, 125, 137, 176, 209, 219

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8, © Springer Science+Business Media B.V. 2012

237

238 Convergence, 5, 30, 63, 112, 127, 139, 176, 223 Conversion, 5, 41, 47, 70, 71, 75, 79, 89, 90, 131, 135, 137 Covariance, 94, 125, 131

D Density, 15, 16, 18, 19 Deposition, 5, 33, 38, 53, 71, 75, 79, 89, 90, 108, 138, 152 Descending motion, 86, 89, 127 Deviation standard deviation, 15, 211, 215, 220–222, 224–227, 229 Dimensional three-dimensional, 2, 22–23, 27, 28 two-dimensional, 1, 2, 16, 20, 22–23, 27, 33, 34, 138, 219 Dissipation, 9, 40, 75 Disturbance, 46 Diurnal diurnal composite, 35, 101, 106 diurnal cycle, 101–108 diurnal variation, 6, 20, 21, 35–38, 63, 72, 102, 107, 108, 111, 116–124, 141, 145, 175, 178–187 Divergence, 30, 33–35, 38, 40, 41, 53, 58, 60, 63, 64, 70, 71, 73–75, 78–80, 84–86, 95, 102, 112–114, 116, 119, 123, 124, 133, 135, 139, 140, 145, 146, 150, 152–154, 156–158, 164–166, 170, 172, 176, 177, 185–187, 190, 199, 200, 204, 206, 209 Downward motion, 6, 9, 10, 40, 43, 44, 46, 53, 64, 71, 73, 74, 83, 89, 97, 101, 191, 195, 221 Draft downdraft, 16, 27, 97, 133 updraft, 16, 18, 27, 33, 34, 97, 133

E Emission, 22, 116 Energy convective available potential energy (CAPE), 102, 106, 107 kinetic energy, 125, 129, 131–133, 135 unstable energy, 1 Environment, 1, 8, 27, 30, 102, 138

Index Equation precipitation equation, 27–60, 63 prognostic equation, 2 surface rainfall equation, 27, 30–32, 92, 93, 107 Equilibrium state, 2, 21–23, 176 Evaporation, 5, 6, 22, 29, 30, 32–34, 38, 45, 56, 59, 65, 71, 73–75, 78, 79, 83–86, 92–95, 108, 111, 112, 114, 130, 134, 139, 140, 152, 157, 161, 167–169, 176, 188, 199, 200, 202, 227, 228

F FC. See Fractional coverage Flux cloud hydrometeor mass flux, 44, 86, 89, 97 evaporation flux, 6, 22, 34, 94, 111, 168, 169 infrared radiative flux, 5 sensible heat flux, 6, 30, 124 vertical heat flux, 53, 57, 151–153, 156–158, 204, 206 vertical water vapor flux, 53, 54, 152 water vapor mass flux, 44, 48, 49, 51, 64, 67, 71, 73, 86–89, 97, 98, 100, 101, 191, 193, 195, 197 Formation, 40, 75 Fractional coverage (FC), 33, 41, 42, 44, 46, 58, 60, 66, 67, 70, 73, 78, 83, 89, 112, 113, 127, 128, 139, 140, 154, 157, 176, 177 Fusion, 5

G Graupel, 4, 5, 16, 38, 41, 43, 89, 90, 210, 212, 213

H Heat latent heat, 4, 22, 30, 33, 34, 46, 53, 57, 58, 60, 70, 71, 74, 84, 112, 138, 140, 151–158, 165, 171, 175, 176, 190, 201, 204–206 Heating condensational heating, 22 radiative heating, 5, 46, 53, 57, 60, 107, 119, 124, 145, 149–151, 153, 156–158, 165, 171, 175, 190, 201 185 Height, 6, 7, 12, 13, 16, 29, 50–52, 54, 57, 92, 101, 102, 115, 199

Index I Ice water path, 68–71, 73–75, 77–79, 164, 220, 222, 223, 231, 232 Imposed, 5, 6, 9, 13–15, 20, 21, 40, 43, 46, 49–53, 63, 64, 71, 73, 82–85, 89, 92, 94, 97, 101, 102, 106, 107, 111, 113, 124, 127, 131, 133, 138, 189, 191, 196, 220, 223, 228 Initial condition, 219–234

L Large-scale circulations, 107, 108, 138 Large-scale forcing, 1, 6–11, 15, 44, 46, 63, 79, 82–101, 111, 129, 138, 189, 191, 220, 221, 228 Level of free convection (LFC), 102 Liquid water path, 233

M Mass-weighted, 21, 22, 70, 125, 221, 224, 225, 229, 230 Mean, 5, 30, 63, 111, 125, 138, 175, 215, 220 Melting, 5, 16, 34, 38, 41, 43, 75, 89, 90 Microwave, 6, 220 Mixing ratio, 4, 21, 34, 79, 97, 101, 127, 133, 137, 138, 175, 221 cloud hydrometeor mixing ratio, 1, 2, 27, 44, 46 Model cloud-resolving model, 1–23, 58, 111, 137, 138, 209, 219 general circulation model, 137 Moist, 22, 102, 106, 107, 138 Moisture, 13, 22, 137 Momentum, 1, 125, 133

N Non-hydrostatic, 2

O Outflow, 133 Overbar, 5

P Parameterization cloud microphysical parameterization, 5, 209, 219, 225 ice microphysical parameterization, 137, 138

239 radiation parameterization, 5 Partition, 31, 33, 34, 63, 75, 84, 191 Pool cold pool, 16, 133 Precipitable water (PW), 21–23, 219–223, 225, 229–231 Precipitation precipitation ice, 38 precipitation water, 219 Precipitation efficiency cloud-microphysics precipitation efficiency (CMPE), 209–212, 215 large-scale precipitation efficiency (LSPE), 209, 215, 217 rain-microphysics precipitation efficiency (RMPE), 210–212, 215, 217 Pressure, 4, 10 Prognostic, 1, 2, 5, 13, 27, 209, 219, 225 Propagation, 127, 138 PW. See Precipitable water

R Rain rainband, 38, 126, 127 raindrops, 4, 5, 16, 175 rainfall, 1, 27, 63, 111, 125, 138, 175, 209, 223 rain rate, 1, 30, 64, 111, 126, 138, 175, 223 Reflectivity, 1, 12, 15–20, 33 Riming, 5 Root-mean-square (RMS), 11, 15, 211, 215, 220–227, 229–233

S Satellite, 220 Saturation, 71, 75, 79, 107, 175, 199, 225, 228 Scale large-scale, 1, 6–11, 15, 20–22, 32–38, 40, 43, 44, 46, 49, 53, 58, 63, 64, 71, 73, 79, 82–102, 106–108, 111, 125, 127, 129, 133, 138–159, 175–187, 189, 191, 196, 199, 209, 215, 220, 221, 223, 228 spatial scale, 23, 80, 222–231, 233, 234 timescale, 2, 107, 119, 124, 145, 221, 223, 225, 226, 228, 233 Sensitivity, 20, 92, 97, 111, 113, 125, 138, 164, 175, 188, 201, 219–234

240 Snow, 4, 5, 16, 137, 138, 209, 212, 213 Specific humidity, 1, 2, 6, 9–13, 27, 44, 46, 49, 71, 75, 85, 94, 101, 107, 133, 175, 195, 199, 221, 225, 228 Storm severe tropical storm, 1, 40–57, 125–133, 138, 159–166, 175, 187–199 Stratiform, 33, 63, 111, 127, 137, 176, Sublimation, 4 Subsidence, 34

T Temperature potential temperature, 2, 102 sea surface temperature, 6, 7, 20–22, 63, 84, 92–101, 111–124, 139, 220, 221 Tendency, 133, 150–152, 156, 157, 227 Thermodynamics, 1, 21–23, 27, 63, 92, 137, 138, 219, 223 Transport, 22, 34, 35, 42, 43, 53, 58, 60, 70, 73–75, 84–86, 95, 112, 113, 125, 127, 128, 135, 139, 166, 170, 172, 177, 178, 191, 200, 201 Tropical deep convective regime, 228 Troposphere, 6, 7, 9, 16, 40, 43, 44, 46, 49, 53, 73, 83, 84, 86, 89, 97, 116, 127, 133, 137, 141, 151–153, 191, 195, 206, 225–227, 229, 230, 234

Index U Uncertainty, 219–234 Upward motion, 6–10, 40, 43, 44, 46, 49, 53, 58, 64, 71, 73, 74, 82–84, 89, 92, 94, 97, 101, 102, 107, 127, 133, 191, 195

V Vaporization, 4 Variance, 228 Vertical velocity, 6–11, 13, 14, 20–22, 32–38, 40, 43, 44, 46, 48–53, 65, 73, 79, 82, 84–87, 92–94, 96, 97, 100, 101, 106, 111, 125, 127, 131, 133, 138–159, 175–187, 189, 191, 192, 196, 199, 220, 221, 223, 228 Vorticity convective vorticity vector, 22 dynamic vorticity vector, 23 moist vorticity vector, 22

W Water vapor, 1, 27, 63, 111, 127, 138, 176, 209, 219 Wind horizontal wind, 125 vertical wind, 125–135