Precipitation Modeling and Quantitative Analysis

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

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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 − ( rw'q ') − w o − w' ∂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 , ∂t ∂x r ∂z

(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)

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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

Height (km)

12

20 ms−1

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

b

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

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

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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 =- u o v - w o v - w¢ v w ¢ qv ¢ ¶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 , ¶t ¶x r ¶z r ¶z

(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), water vapor convergence (QWVF >0)/divergence (QWVF <0), surface evaporation (QWVE), and hydrometeor loss/convergence (QCM >0) or hydrometeor gain/divergence (QCM <0). (2.3) and (2.6) are combined by eliminating QWVS to derive surface rainfall equation related to thermal processes, PS = SHT + SHF + SHS + SLHLF + SRAD + QCM .

(2.8b)

(2.8b) states that the surface rain rate is related to local atmospheric warming (SHT >0)/cooling (SHT <0), heat divergence (SHF >0)/convergence (SHF <0), surface sensible heat (SHS), latent heat due to ice-related processes (SLHLF), radiative cooling (SRAD >0)/heating (SRAD <0), and hydrometeor loss/convergence (QCM >0) or hydrometeor gain/divergence (QCM <0). Equations 2.8a and 2.8b are respectively referred to as water-vapor and thermally-related precipitation equations in the following discussions. Taking model domain mean on (2.8), the mean surface rainfall equations become, PS = QWVT + QWVF + QWVE + QCM ,

(2.9)

2.1

Precipitation Equations

31

QWVT = QWVF = -[u o

¶[ qv ] , ¶t

¶ qv ¶q ] - [ w o v ], ¶x ¶z

QWVE = Es , QCM = -

¶[ql ] , ¶t

PS = SHT + SHF + SHS + SLHLF + SRAD + QCM SHT = SHF =

cp Lv

[p u o

(2.10a)

(2.10b) (2.10c) (2.10d) (2.11)

c p ¶[T ] , Lv ¶t

(2.11a)

¶q o ¶q + pw o ], ¶x ¶z

(2.11b)

SHS = SLHLF = SRAD = -

cp

Hs ,

(2.11c)

[ P18 ],

(2.11d)

1 [QR ]. Lv

(2.11e)

Lv Lf Lv

Note that in (2.10d) hydrometeor convergence is zero because of periodic lateral boundary conditions. m A variable can be partitioned into a time mean (subscript “ ”) and a diurnal d anomaly (subscript “ ”), i.e., X = Xm + Xd.

(2.12)

Substituting (2.12) into (2.8), taking the time mean on the resulting equations, and subtracting the time-mean equations from the resulting equations, respectively, leads to diurnally perturbed model domain mean water-vapor-related surface rainfall equations: d d d d PS d = QWVT + QWVF + QWVE + QCM ,

d QWVT =-

¶[qvd ] , ¶t

(2.13) (2.13a)

32

2

Precipitation Equations and Process Analysis

¶qvo d ¶q d ¶q m ) ] - [(w o )m v ] - [(w o )d v ] ¶x ¶z ¶z d d ¶q ¶q -[(w o )d v ] + [{(w o )d v }m ], ¶z ¶z

d QWVF = -[(u o

(2.13b)

d QWVE = Esd ,

d QCM =-

¶[qld ] . ¶t

(2.13c) (2.13d)

d d d d d d PSd = SHT + SHF + SHS + SLHLF + SRAD + QCM .

d SHT =

d = SHF

cp Lv +

[p (u o

cp Lv

c p ¶[T d ] , Lv ¶t

[p (w o )d

cp ¶q d ¶q d m ] - [p {(w o )d } ], ¶z ¶z Lv

d =SLHLF

d SRAD =-

2.2.1

(2.14a)

cp ¶q o d c p ¶q d ¶q m ) ] + [(w o )m ] + [p (w o )d ] ¶x ¶z ¶z Lv Lv

d =SHS

2.2

(2.14)

cp

(2.14b)

H sd ,

(2.14c)

[ P18d ],

(2.14d)

1 d [QR ]. Lv

(2.14e)

Lv Lf Lv

Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity Time-Mean Analysis

The time and model domain-mean analysis in SST29 shows that the surface rain rate (PS) is mainly associated with surface evaporation (QWVE) and radiative cooling (SRAD >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

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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

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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)

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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)

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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)

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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) appears as the net condensation occurs (condensation and deposition have opposite signs from Sqv). The vertical velocity profile with strong upward motion in the mid and upper troposphere and weak downward motion in the lower troposphere on 15 July produces a large condensation and deposition rate in the mid and upper troposphere and a weak evaporation rate of rain in the lower troposphere. In the next 2 days, the extension of upward motions to the lower troposphere yields condensation in the lower troposphere that consumes the water vapor. These are the major processes responsible for the local atmospheric drying. On 15 July, the imposed large-scale lower-tropospheric downward motions produce a water vapor source (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.

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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)

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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)

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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)

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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

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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), respectively. F and f denote the mean water vapor convergence (QWVF > 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

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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).

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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)

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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

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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

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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

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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).

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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

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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

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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,

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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

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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 (<−1 m s−1) throughout the troposphere. In the SF phase, the maximum ascending motion of 12 m s−1 occurs around 7 km whereas the maximum descending motion of −4 m s−1 appears throughout the troposphere. More than 50% of vertical motion are weak descending motions (<−1 m s−1) in the lower troposphere and weak ascending motions (<1 m s−1) in the mid and upper troposphere. The magnitudes and vertical distributions of contour of 0.1 of CFAD of vertical velocity are similar to those of domain- and time-averaged maximum ascending and descending motions shown in Johnson et al. (2002, 2007). The distributions of water vapor and cloud hydrometeor mass fluxes are broader in the WF phase than in the SF phase. The maximum water vapor mass flux associated with ascending and descending motions are, respectively, about 0.12 and −0.05 kg m−2 s−1 near the surface in the two phases. The maximum hydrometeor mass flux associated with ascending and descending motions are, respectively, about 0.09 kg m−2 s−1 at 10 km and −0.04 kg m−2 s−1 at 5 km in the WF phase whereas they are, respectively, about 0.07 kg m−2 s−1 at 8 km and −0.02 kg m−2 s−1 at 7 km in the SF phase. Vertical profiles of vertical velocity, water vapor mass flux, and cloud hydrometeor mass flux over whole model domain and different regions are calculated in the two phases and shown in Figs. 3.9, 3.11, and 3.12, respectively. Over convective regions, the ascending motions are much stronger in the lower troposphere than in the mid and upper troposphere in the SF phase whereas the ascending motions are slightly stronger in the lower troposphere than in the upper troposphere in the WF phase (Fig. 3.9). The ascending motions and water vapor mass flux below 4 km are larger in the SF phase than in the WF phase whereas those above 4 km are smaller in the SF phase (Figs. 3.9 and 3.11), suggesting that the vertical structure of water vapor mass flux over convective regions may be controlled by the vertical velocity.

3.3

Tropical Rainfall Responses to the Large-Scale Forcing

87

a

b

c

d

e

f

Fig. 3.10 CFAD of vertical velocity (m s−1) in (a) and (b), water vapor mass flux (10−2 kg m−2 s−1) in (c) and (d), and hydrometeor mass flux (10−2kg m−2 s−1) in (e) and (f). (a), (c), and (e) represent the SF phase whereas (b), (d), and (f) denote the WF phase. Contour intervals are 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively (After Gao and Li 2008)

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b

Fig. 3.11 Vertical profiles of time-mean water vapor mass flux (10−4kg m−2 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)

a

b

Fig. 3.12 Vertical profiles of time-mean hydrometeor mass flux (10−5kg m−2 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)

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Tropical Rainfall Responses to the Large-Scale Forcing

89

Over raining stratiform regions, the descending motions in the lower troposphere and the ascending motions in the mid and upper troposphere in the SF phase have similar magnitudes whereas the magnitudes of descending motions in the lower troposphere are larger than those of ascending motions in the mid and upper troposphere in WF phase (Fig. 3.9). The vertical extent of descending motion is smaller in the SF phase (3.8 km) than in the WF phase (5.2 km). The water vapor mass flux associated with ascending motions in the mid and upper troposphere and water vapor mass flux associated with descending motions in the lower troposphere are stronger in the SF phase than the WF phase (Fig. 3.11). Over non-raining regions, the upward motions occur above 6 km whereas the downward motions appear below 6 km in the SF phase (Fig. 3.9a). In contrast, the downward motions occur throughout the troposphere in the WF phase (Fig. 3.9b). The downward water vapor mass flux below 6 km is larger in the SF phase than in the WF phase, while weak upward water vapor mass flux above 6 km only appears in the SF phase (Fig. 3.11). The hydrometeor mass flux vanishes below 6 km in the two phases, whereas the upward hydrometeor mass flux above 6 km is larger in the SF phase than in the WF phase. The magnitudes of vertical motion over non-raining regions are larger in the SF phase than in the WF phase largely due to larger fractional coverage of non-raining stratiform regions in the SF regions whereas those of descending motion over clear sky regions are smaller in the SF regions than in the WF regions mainly because of smaller fractional coverage of clear sky regions in the SF phase. The cloud hydrometeor mass flux over convective regions dominates in the lower troposphere while the cloud hydrometeor mass flux over convective and raining stratiform regions have similar magnitudes in the mid and upper troposphere in the SF phase (Fig. 3.14a). In contrast, the cloud hydrometeor mass flux over convective regions dominates throughout the troposphere in the WF phase (Fig. 3.14b). The imposed large-scale ascending motions yield upward water vapor advection, which produces condensation and deposition as indicated by analysis of water vapor budgets. The difference in condensation and deposition rates and associated cloud microphysical processes responds to the difference in imposed large-scale forcing. Thus, cloud microphysical budgets over convective and raining stratiform regions are averaged in the two phases and shown in Figs. 3.13 and 3.14, respectively. Over convective regions, vapor condensation (PCND) accounts for microphysics-produced rain rate (Sqr) through the collection of cloud water by rain (PRACW) in the two phases (Fig. 3.13) because ice microphysical processes are much weaker than water microphysical processes. Thus, Sqr » PRACW » 2 PCND/3. The differences in PRACW and PCND between the two phases are less than 10% of PRACW and PCND, respectively, which yields similar microphysics-produced rain rates and thus similar convective rain rates. Over raining stratiform regions, microphysics-produced rain rate is determined by the melting of graupel to rain (PGMLT) and PRACW. PGMLT is significantly larger than PRACW in the two phases (Fig. 3.14). Sqr » PGMLT + PRACW − PREVP. This suggests the important role the conversion from ice hydrometeors to water hydrometeors plays in the production of stratiform rainfall, which is consistent with what were found by

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a

b

Fig. 3.13 Cloud microphysics budgets over convective regions in (a) the SF phase and (b) the WF phase. 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 2.1 (After Gao and Li 2008)

Tao et al. (1995). Vapor condensation and deposition rates are higher in the SF phase (0.286 mm h−1) than in the WF phase (0.094 mm h−1). The collection rate of cloud water by rain and melting rate of graupel to rain are higher in the SF phase than in the WF phase. Thus, microphysics-produced rain rate is larger in the SF phase than in the WF phase.

3.3

Tropical Rainfall Responses to the Large-Scale Forcing

a

0.175 PCND

0.143 Sqr

0.054 Sqc

qc

91

0.114 PRACW

0.002 PRAUT

0.015 PGACW (T>To)

(0.037)

0.226 PREVP

qr (0.090)

0.200 Rain Rate

0.008 PSMLT (T>To)

Units: (mm) mm h–1

0.228 PGMLT (T>To)

0.031 PSACW (T
qi (0.011)

0.003 0.018 PSFI(T
0.050 PSAUT(T
0.072 PDEP

b

0.068 PGACW(T
qs (0.034)

qg (0.072)

0.105 PGACS

0.001 Sqs

0.020 PSDEP

0.054 PCND

0.005 PWACS

0.030 Sqc

0.040 0.014 Sqg PGDEP

0.061 Sqr 0.038 PRACW

qc (0.010)

0.006 PGACW(T>To)

0.107 PREVP

qr (0.034)

0.092 Rain Rate

0.002 PSMLT(T>To)

Units: (mm) mm h–1

0.121 PGMLT (T>To)

0.009 PSACW (T
qi (0.007) 0.022 0.006 PDEP Sqi

0.002 0.010 PSFI(T
0.014 PSAUT(T
0.005 PMLTG

0.030 PGACW (T
qs (0.008)

0.002 PWACS 0.036 PGACS

0.002 Sqs

Fig. 3.14 As in Fig. 3.13 except over raining stratiform regions

qg (0.045) 0.053 0.006 Sqg PGDEP

0.008 PMLTG

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Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle, and Sea Surface Temperature on Time-Mean Tropical Rainfall Processes

From the water-vapor-related surface rainfall budget, interactions between timedependent dynamics and water vapor through water vapor and hydrometeor convergence and surface evaporation directly impacts time-mean precipitation processes. The interactions between time-dependent dynamic, thermodynamic and cloud microphysical processes indirectly affect time-mean precipitation processes through local water vapor and hydrometeor changes. Thus, surface rainfall equation will be applied to evaluate effects of time-dependent forcing on time-mean precipitation processes. Since the effects of the time-dependent interaction processes on time-mean precipitation processes are accumulated with time, a series of sensitivity experiments forced only by either time-dependent LSF, or SST, or SZA and the control experiment (COARE) forced by time-dependent LSF, SST and SZA are conducted and compared to examine effects of time-dependent LSF, SZA, and SST on time-mean rainfall processes during TOGA COARE. The sensitivity experiments are summarized in Table 3.7. In COARE_R, the model is imposed by time-dependent SZA and time-mean LSF (large-scale vertical velocity, zonal wind, and horizontal advection) and SST. In COARE_F, the model is imposed by time-dependent LSF and timemean SZA and SST. In COARE_T, the model is imposed by time-dependent SST and time-mean LSF and SZA. Since vertical velocity is a main component of LSF imposed in the model and may vary when it is derived from different regions and periods or averaged over different sizes of areas, an additional experiment COARE_ R0 imposed by zero large-scale vertical velocity and horizontal advection, and time and height invariant zonal wind is tested. The time and height invariant zonal wind is 4 m s−1 since the minimum wind speed in the calculations of surface heat fluxes is 4 m s−1. The time and model domain mean simulation data are first analyzed. The mean surface rain rates are 0.381 mm h−1 in COARE, 0.324 mm h−1 in COARE_R, 0.386 mm h−1 in C OARE_F, 0.332 mm h−1 in C OARE_T, and 0.175 mm h−1 in COARE_R0 (Table 3.8). The mean surface rain rates in COARE and COARE_F are similar; indicating that time-dependent SZA and SST have no discernable effect on time-mean rainfall. The mean surface rain rates in COARE_R and COARE_T are about 15% smaller than that in COARE. Similar mean surface rain rates in COARE and COARE_F and significant reductions of mean surface rain rate in COARE_R and COARE_T suggest that replacement of time-dependent LSF with its time-mean suppresses mean surface rainfall. The mean surface rain rate in COARE_R0 is about 55% smaller than that in COARE. The LSF only accounts for a half of rainfall and infrared cooling and imposed large-scale upward motions have equally important roles in production of mean surface rainfall. Although the mean surface rain rates in COARE_F and COARE are similar, mean local hydrometeor reduction rate (QCM > 0) in COARE_F is about one order of magnitude smaller and mean water vapor convergence rate in COARE_F is about

3.4

Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle…

Table 3.7 Summary of experiments Experiment Solar zenith angle COARE Time dependent COARE_R Time dependent COARE_F Time-mean COARE_T Time-mean COARE_R0 Time dependent

Large-scale forcing Time dependent Time-mean Time dependent Time-mean Zero vertical velocity and constant zonal wind

93

Sea surface temperature Time dependent Time-mean Time-mean Time dependent Time-mean

Table 3.8 (a) Time and model domain means of surface rain rate (PS), local water vapor change (QWVT), water vapor convergence (QWVF), surface evaporation (QWVE), local hydrometeor change/ hydrometeor convergence (QCM) and contributions from (b) raining stratiform regions and (c) convective regions in COARE, COARE_R, COARE_F, COARE_T, and COARE_R0. Unit is mm h−1 (After Gao and Li (2010a)) COARE COARE_R COARE_F COARE_T COARE_R0 (a) PS 0.381 0.324 0.386 0.332 0.175 QWVT 0.047 0.037 0.060 0.045 0.041 QWVF 0.109 0.080 0.102 0.072 0.000 QWVE 0.207 0.198 0.222 0.210 0.138 QCM 0.018 0.008 0.002 0.006 −0.003 (b) PS QWVT QWVF QWVE QCM

0.139 0.079 −0.080 0.023 0.116

0.107 0.110 −0.157 0.017 0.137

0.140 0.096 −0.106 0.026 0.124

0.108 0.116 −0.162 0.018 0.135

0.058 0.065 −0.064 0.006 0.051

(c) PS QWVT QWVF QWVE QCM

0.242 0.140 0.197 0.015 −0.109

0.217 0.109 0.243 0.016 −0.152

0.246 0.157 0.207 0.017 −0.134

0.225 0.089 0.272 0.017 −0.154

0.117 0.054 0.117 0.005 −0.059

6.4% smaller than in COARE, whereas the mean local atmospheric drying (QWVT > 0) and surface evaporation rates in COARE_F are, respectively, about 27.7% and 7.2% larger than in COARE (Table 3.8a). Replacement of time-dependent SZA and SST with their time means enhances local atmospheric drying and surface evaporation but suppresses vapor convergence and local hydrometeor reduction. The mean surface rain rates in COARE_R and COARE_T are smaller than the surface rain rate in COARE (Table 3.8a). About a half of negative difference in mean surface rain rate for COARE_R-COARE (−0.057 mm h−1) is from the negative difference in mean water vapor convergence (−0.029 mm h−1) and another half is from the negative difference in three other terms of surface rainfall equation. The negative

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differences in QWVT, QWVE, and QCM (~0.010 mm h−1) equally contribute to the negative difference in mean surface rain rate for COARE_R-COARE. In contrast, about 75% of negative difference in mean surface rain rate for COARE_T-COARE is from the negative difference in mean water vapor convergence whereas about 25% is from the negative difference in local hydrometeor reduction. The comparison between COARE_R and COARE shows that replacement of time-dependent LSF and SST with their time means decreases mean surface rainfall through suppressing all precipitation processes, whereas the comparison between COARE_T and COARE reveals that replacement of time-dependent LSF and SZA with their time means decreases mean precipitation mainly through suppressing water vapor convergence and slowing down local hydrometeor reduction. Thus, replacement of time-dependent LSF with its time mean decreases mean surface rainfall mainly through suppressing mean water vapor convergence (QWVF). Model domain mean of QWVF is mainly determined by vertical advection of water vapor (see 2.10b), which is covariance between imposed large-scale vertical velocity and vertical gradient of specific humidity. Thus, the suppression of water vapor convergence by replacement of time-dependent LSF by its time-mean in COARE_R and COARE_T is a result of low correlation between imposed upward motion and water vapor variation. The mean surface rain rates in COARE_R and COARE_T are similar. The comparison in mean surface rainfall budgets between COARE_R and COARE_T reveals that mean local atmospheric drying and surface evaporation rates are, respectively, 17.8% and 5.7% smaller in COARE_R than in COARE_T, whereas mean water vapor convergence and local hydrometeor reduction rates are, respectively, 11.1% and 33.3% larger in COARE_R than COARE_T. When the model is imposed with time-mean LSF, replacement of time-dependent SST (SZA) with its time mean in COARE_R (COARE_T) suppresses (enhances) mean local atmospheric drying and surface evaporation rates and increases (decreases) mean water vapor convergence and local hydrometeor reduction rates. Further, the exclusion of LSF in COARE_R0 leads to a zero vapor convergence rate and a smaller mean surface evaporation rate in COARE_R0 than in COARE_R and COARE, which in turn causes a smaller mean surface rain rate in COARE_R0. The enhancement (suppression) of surface evaporation flux by replacement of time-dependent SZA (SST) with its time mean in COARE_T (COARE_R) suggests that enhancement of surface evaporation flux by replacement of time-dependent SZA and SST with their time averages in COARE_F may be mainly due to replacement of time-dependent SZA with its time mean. The enhancement of surface evaporation flux by replacement of time-dependent SZA with its time mean is consistent with the results from Gao et al. (2007). Gao et al. (2007) showed that the equilibrium simulation with time-mean SZA produces larger surface evaporation flux than the equilibrium simulation with time-dependent SZA does because more water vapor is consumed by more condensation initiated by colder air as a result of smaller solar heating in the equilibrium simulation with time-mean SZA. The more condensation in COARE_F (PS − QCM in cloud budget; 0.386 mm h−1) than in COARE (0.363 mm h−1) consumes more water vapor; it appears to lead to larger surface evaporation flux and smaller water vapor convergence rate in COARE_F.

3.4

Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle…

95

The model domain mean surface rain rate and associated processes are from raining stratiform and convective regions. The convective and stratiform rain rates are similar in COARE_F and COARE (Table 3.8b, c). This indicates that timedependent SZA and SST do not impact time-mean convective and stratiform rainfall. But replacement of time-dependent SZA and SST with their time means affects convective and stratiform rainfall processes. More hydrometeor concentration is transported from convective regions to raining stratiform regions in COARE_F than in COARE; it appears to be compensated by more local atmospheric drying and vapor convergence over convective regions in COARE_F. Compared to COARE, more water vapor divergence over raining stratiform regions is balanced by more local atmospheric drying rate and more transport of cloud hydrometeors from convective regions in COARE_F. The reduction of mean surface rain rate in COARE_R and COARE_T from COARE is from both convective and raining stratiform regions as indicated by the fact that the convective and stratiform rain rates in COARE_R and COARE_T are 7–10% and 23% smaller than those in COARE, respectively. The increase of convective rainfall by replacement of time-dependent SZA and SST with their time means is mainly associated with the decrease of the local atmospheric drying rate over convective regions and the increase of transport rate of hydrometeor concentration from convective regions to raining stratiform regions (Table 3.8c). The reduction of stratiform rainfall by replacement of time-dependent SZA and SST with their time means is mainly related to the enhancement of water vapor divergence over raining stratiform regions (Table 3.8b). The convective and stratiform rain rates are similar in COARE_R and COARE_T. Over convective regions, the water vapor convergence rate is 11.9% smaller in COARE_R than in COARE_T whereas the local atmospheric drying rate is 18.3% larger in COARE_R than in COARE_T (Table 3.8c). The surface evaporation rate and transport rate of cloud hydrometeor to raining stratiform regions are similar in both experiments regardless of whether SZA and SST are time-dependent or not. All terms related to stratiform rainfall have similar rates in the two experiments (Table 3.8b). Thus, replacement of time-dependent SST (SZA) with its time mean in COARE_R (COARE_T) enhances (suppresses) local atmospheric drying rate and decreases (increases) water vapor convergence rate over convective regions. Although the time and model domain mean surface rain rates are smaller in CR0 than CR, 33% and 67% of mean surface rain rates in both experiment are, respectively, from raining stratiform and convective regions. This suggests that the magnitude of rainfall are determined by the LSF but the percentages of convective and stratiform rain rates in total surface rainfall are insensitive to strengths of the LSF. Over convective regions, the local atmospheric drying and surface evaporation are largely used to compensate transport of hydrometeor concentration to raining stratiform regions while the vapor convergence is used to support convective rainfall in both experiments. Over raining stratiform regions, the vapor divergence is largely compensated by the transport of hydrometeor concentration from convective regions and surface evaporation while the stratiform rainfall leads to the local atmospheric drying in the two experiments.

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Fig. 3.15 CFAD of vertical velocity (ms−1) in (a) COARE, (b) COARE_R, (c) COARE_F, (d) COARE_T, and (e) COARE_R0. Contour intervals are 0.0001, 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively. Frequencies of larger than 0.001% are shaded (After Gao and Li 2010a)

3.4

Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle…

97

The analysis of surface rainfall budget shows that important impacts of vapor convergence associated with imposed LSF on time-mean surface rainfall processes. Thus, the vertical structures of vertical velocity, water vapor mass flux, and cloud hydrometeor mass flux in the sensitivity experiments are compared with those in the control experiment by analyzing CFAD. The CFAD is used to show the statistical distributions of the properties of precipitation systems including vertical distributions of updraft and downdraft and associated fluxes. The CFAD of vertical velocity, water vapor mass flux, and cloud hydrometeor mass flux are calculated in the control experiment and sensitivity experiments and shown in Figs. 3.15–3.17, respectively. Figure 3.15 shows that variations of vertical velocity range from −9 to 22 m s−1 in COARE, from −8 to 24 m s−1 in COARE_R, from −9 to 19 m s−1 in COARE_F, from −8 to 18 m s−1 in COARE_T, and from −6 to 10 m s−1 in COARE_R0. Maximum updrafts occur around 11 km in COARE, 12 km in COARE_R and COARE_F, 10 km in COARE_T, and 4, 6, and 10 km in COARE_R0, whereas maximum downdrafts appear around 8 and 11 km in COARE, 12 km in COARE_R, 8 km in COARE_F, 4 km in COARE_T, and 3 km in COARE_R0. CR produces stronger updrafts than COARE does whereas COARE_F and COARE_T generate weaker updrafts than COARE does. This suggests than the time dependent SZA enhances updrafts in the upper troposphere. Maximum updrafts are less sensitive to whether LSF and SST are time dependent or not once the time-mean SZA is calculated during the model integrations. The exclusion of LSF in COARE_R0 leads to a narrow distribution of vertical velocity and cuts half of maximum updrafts. Since water vapor in the lower troposphere has a much larger mixing ratio than that in the upper troposphere, the maximum water vapor mass fluxes occurs in the lower troposphere (Fig. 3.16). The maximum upward water vapor mass fluxes are 0.125 kg m−2 s−1 in COARE, 0.145 kg m−2 s−1 in COARE_R, 0.135 kg m−2 s−1 in COARE_F, 0.165 kg m−2 s−1 in COARE_T, and 0.105 kg m−2 s−1 in COARE_R0 while the maximum downward water vapor mass fluxes are about −0.060 kg m−2 s−1 in all experiments. The time-dependent SST intensifies the upward water vapor mass flux in the lower troposphere. The downward water vapor mass flux is insensitive to whether the LSF, SZA, and SST are time dependent or not. The maximum upward hydrometeor mass fluxes in Fig. 3.17 are 0.075 kg m−2 s−1 at 10 km in COARE, 0.135 kg m−2 s−1 at 11 km in COARE_R, 0.125 kg m−2 s−1 at 5 km in COARE_F, 0.085 kg m−2 s−1 at 7 km in COARE_T, and 0.045 kg m−2 s−1 at 7 km in COARE_R0. The maximum downward hydrometeor mass fluxes are 0.035 kg m−2 s−1 in COARE, COARE_R, COARE_F, and COARE_T, and 0.025 kg m−2 s−1 in COARE_R0. Thus, the time dependent SZA enhances the upward hydrometeor mass fluxes and the exclusion of LSF significantly reduce magnitudes of maximum upward and downward hydrometeor mass fluxes. Over raining stratiform regions, COARE, COARE_R, COARE_F, and COARE_T have downward motions below 4 km and upward motions above 4 km (Fig. 3.18a). The differences among the four experiments are upward motions between 5 and 10 km, where ascending velocities in COARE_R and COARE_T are smaller than those in COARE and COARE_F. Time-mean large-scale forcing suppresses upward motions over raining stratiform regions. The vertical structure of vertical velocity

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Fig. 3.16 As in Fig. 3.15 except for water vapor mass flux (10−2 kg m−2 s−1) (After Gao and Li 2010a)

3.4

Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle…

99

Fig. 3.17 As in Fig. 3.15 except for hydrometeor mass flux (10−2kg m−2 s−1) (After Gao and Li 2010a)

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a

b

c

d

e

f

Tropical Precipitation Processes

Fig. 3.18 Vertical profiles of time-mean vertical velocity (cm s−1) in (a) and (b), time-mean water vapor mass flux (10−4kg m−2 s−1) in (c) and (d), and time-mean hydrometeor mass flux (10−5kg m−2 s−1) in (e) and (f). Left and right panels present profiles over raining stratiform and convective regions, respectively. Solid, short dash, dot, long dash, and dot dash lines denote experiments COARE, COARE_R, COARE_F, COARE_T, COARE_R0, respectively (After Gao and Li 2010a)

3.5

Diurnal Cycle

101

below 12 km in COARE_R0 is similar to those in the four other experiments but the former has significantly smaller magnitudes than the latter due to zero large-scale vertical velocity imposed in COARE_R0. COARE_R0 has downward motions above 12 km. This suggests that the large-scale forcing leads to the extension of upward motions to the model top. COARE and COARE_F generate larger upward water vapor mass fluxes above 4 km than do COARE_R and COARE_T (Fig. 3.18c). The upward hydrometeor mass fluxes above 8 km in COARE_R and COARE_T are larger than those in COARE and COARE_F (Fig. 3.18e). The upward hydrometeor mass fluxes from 4 to 8 km in COARE and COARE_F become as large as those in COARE_T whereas the upward hydrometeor mass fluxes in COARE_R become smaller. The downward hydrometeor mass fluxes below 3 km in COARE_R and COARE_T are slightly larger than those in COARE and COARE_F. Downward water vapor and hydrometeor mass fluxes below 4 km and upward water vapor and hydrometeor mass fluxes above 4 km in COARE_R0 are smaller than those in the four other experiments due to smaller vertical motions in COARE_R0. Over convective regions, COARE, COARE_R, COARE_F, and COARE_T show upward motions with their maxima around 3 km (Fig. 3.18b). Their differences are upward motions from 6 to 10 km, in which ascending velocities in COARE_R and COARE_T are larger than those in COARE and COAREF. Time-mean radiation enhances upward motions over convective regions. These differences in upward motions are major factors in determining differences in upward hydrometeor mass fluxes between COARE_R/COARE_T and COARE/COARE_F (Fig. 3.18f). The maximum upward motion and associated upward water vapor mass flux (Fig. 3.18d) in COARE_R are smaller than those in three other experiments. The maximum upward motions in COARE, COARE_F, and COARE_T are similar whereas the maximum upward water vapor mass flux in COARE_T is smaller than those in COARE and COARE_F. Among the four experiments, COARE and COARE_T produce the smaller and largest maximum upward hydrometeor mass fluxes, respectively. The upward motion in COARE_R0 reaches its maximum around 2 km, decreases with increasing height dramatically, and switches to the weak downward motion around 13 km. The maximum upward water vapor and hydrometeor mass fluxes occur around 1 and 3 km, respectively, which are much affected by vertical structures of specific humidity and water hydrometeor mixing ratio.

3.5

Diurnal Cycle

The diurnal anomalies of surface rain rates in the three experiments (COARE, COARE_R, and COARE_F) are calculated by removing the time means from the diurnal composites (Fig. 3.19). The surface rain rates in the three experiments generally show diurnal signals with positive anomalies during the nighttime and negative anomalies during the daytime. COARE and COARE_F have similar positive rainfall anomalies in the nighttime and afternoon. COARE_R has a larger positive anomaly of rainfall during the hour 4–8 than the two other experiments do. To explain these

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Fig. 3.19 Diurnal anomalies of surface rain rates (mm h−1) simulated in COARE (solid), COARE_F (dash), and COARE_R (dot) (After Gao and Li 2010b)

similarities and differences, the diurnally perturbed surface rainfall Eqs. 2.13 and 2.14 are calculated for the three experiments (Figs. 3.20–3.22). The positive anomalies of rainfall in the afternoon occur in both COARE and COARE_F (Figs. 3.20 and 3.21), which result from the positive anomalies of water vapor convergence and heat divergence associated with diurnally varying imposed large-scale upward motions in the two experiments (Fig. 3.23). The positive anomaly of the afternoon rainfall is absent in COARE_R (Fig. 3.22), which is caused by excluding diurnal variation of imposed large-scale vertical motions in COARE_R. Thus, the imposed upward motions in the afternoon are major processes that account for positive anomalies of afternoon rainfall in both COARE and COARE_F. To explain similar positive nocturnal rainfall anomalies in COARE and COARE_F, the diurnal anomalies of convective available potential energy (CAPE) for reversible moist adiabatic process in the three experiments are calculated and shown in Fig. 3.24. Following Li et al. (2002b), CAPE is expressed by CAPE = g ò

zc LFC

q pcl ( z ) - q env ( z ) q env ( z )

dz.

(3.4)

Here q pcl is the potential temperature of an air parcel lifted from the bottom of the atmosphere to the top of the atmosphere while not mixing with its environment (q env). The air parcel is lifted dry adiabatically until it becomes saturated and then is lifted moist adiabatically thereafter. The level of free convection (LFC) is the height where q pcl > q env , zc is the level where q pcl = q env .

3.5

Diurnal Cycle

103

a

b

d d d Fig. 3.20 Diurnal anomalies of (a) PSd (dark solid), QWVT (light solid),d QWVF (short dash), QWVE d d d d S (dot), QCM (dot dash), and QWVS (long dash), and (b) PS (dark solid), HT (light solid), SHF (short d d d d (long dash), and QCM (long short dash), SRAD (dot), SLHLF (dot dash) in COARE. Unit is dash), SHS −1 mm h (After Gao and Li 2010b)

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a

b

d d d Fig. 3.21 Diurnal anomalies of (a) PSd (dark solid), QWVT (light solid), QWVF (short dash), QWVE d d d d (light solid), SHF (long dash), and (b) PSd (dark solid), SHT (short (dot), QCM (dot dash), and QWVS d d d d (long dash), and QCM (dot dash) in COARE_F. Unit (long short dash), SRAD (dot), SLHLF dash), SHS is mm h−1 (After Gao and Li 2010b)

3.5

Diurnal Cycle

105

a

b

d d d Fig. 3.22 Diurnal anomalies of (a) PSd (dark solid), QWVT (light solid), QWVF (short dash), QWVE d d d d d Q S Q P S (dot), CM (dot dash), and WVS (long dash), and (b) S (dark solid), HT (light solid), HF (short d d d d (dot), SLHLF (dot dash) in COARE_R. Unit dash), SHS (long dash), and QCM (long short dash), SRAD −1 is mm h (After Gao and Li 2010b)

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Fig. 3.23 Diurnal composite of vertical profile of imposed large-scale vertical velocity (cm s−1) (After Gao and Li 2010b)

Fig. 3.24 Diurnal anomalies of CAPE (CAPEd) in (a) COARE (solid), (b) COARE_R (dash), and (c) COARE_F (dot). Unit is J kg−1 (After Gao and Li 2010b)

The CAPE can be calculated here for a reversible moist adiabatic process. In the reversible moist adiabatic process, an air parcel is lifted adiabatically while all condensed water is kept in the parcel. Following Xu and Emanuel (1989), the virtual temperatures (Tvre) for the reversible moist adiabatic process is expressed by

3.5

Diurnal Cycle

107

Tvre = Tp

1+

qvs (Tp )

0.622 , 1 + qvs (Tp )

(3.4a)

where Tp is the temperature of a pseudo-adiabatically displaced air parcel; qvs is the saturation specific humidity. The CAPE for the reversible moist adiabatic process is calculated by using (3.4) and (3.4a). The diurnal anomalies of CAPE in COARE and COARE_F are generally similar although CAPE in COARE_F leads that in COARE by 2 h. Since both cases include the diurnal variation of imposed large-scale upward motion and only COARE has the diurnal variation of radiation, the diurnal variation of imposed large-scale upward motion may determine the diurnal anomalies of CAPE. The increase and decrease in CAPE are, respectively, associated with the increase and decrease in large-scale upward motions. The diurnal anomaly of radiation also produces the diurnal anomaly of CAPE in COARE_R. The positive anomaly of CAPE is highly d correlated with the positive anomaly of SRAD associated with IR radiative cooling (Fig. 3.22b) during the nighttime, indicating the buildup of CAPE by the IR radiative cooling. The positive anomaly of rainfall peak around hour 4–8 in COARE_R, which is significantly larger than in COARE and COARE_F (Fig. 3.19), is phase locking with the local atmospheric change from negative (cooling) to positive d (warming) anomaly and the significant reduction of positive anomaly of SRAD by solar radiative heating. The results imply that the similar nocturnal rainfall peaks in COARE and COARE_F are primarily caused by imposed large-scale upward motions. The diurnal anomaly of radiation plays a secondary role in producing the nocturnal rainfall maximum when the diurnal variation of large-scale circulation is present. The nocturnal rainfall maximum is primarily produced by the positive anomaly of IR radiative cooling in COARE_R while the negative anomaly of the daytime rainfall is mainly associated with the negative anomaly of solar radiative heating (Fig. 3.22b). This indicates that the diurnal variation of radiation is a primary process that is responsible for the diurnal variation of rainfall when the diurnal variation of large-scale circulation is absent. During the nighttime, the positive anomaly of radiation is largely offset by the negative anomaly of heat convergence in COARE (Fig. 3.20b), whereas the heat convergence is absent in COARE_R since the diurnal variation of imposed large-scale upward motion is excluded, which accounts for the larger nocturnal rainfall maximum in COARE_R than in COARE. d In the three experiments, QCM show hourly variations due to the fact that life d d , and cycle of clouds have much short time scale than the diurnal cycle. QWVE , SHS d SLHLF have much weaker diurnal cycles than the other rainfall-related processes. Thus, diurnally-perturbed surface rainfall equations (2.13) and (2.14) can be simplified as d d PS d » QWVT + QWVF ,

(3.5a)

d d d PSd » SHT + SHF + SRAD .

(3.5b)

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The diurnally perturbed cloud budget can be correspondingly simplified as d d PS d » QWVS » QWVOUT .

(3.5c)

In (3.5c), the fact that the diurnal variations of vapor condensation and deposition rates are much larger than those of rain evaporation (not shown) has been included. (3.5) states that diurnally varying water vapor and heat convergence associated with diurnally-varying large-scale circulations and diurnally varying radiative processes produce the diurnal cycles of surface rainfall through the generation of diurnal variations of vapor condensation and depositions.

References Chong M, Hauser D (1989) A tropical squall line observed during the COPT 81 experiment in West Africa. Part II: water budget. Mon Weather Rev 117:728–744 Cui X, Li X (2006) Role of surface evaporation in surface rainfall processes. J Geophys Res. doi:10.1029/2005JD006876 Gallus WA Jr, Johnson RH (1991) Heat and moisture budgets of an intense midlatitude squall line. J Atmos Sci 48:122–146 Gamache JF, Houze RA Jr (1983) Water budget of a mesoscale convective system in the tropics. J Atmos Sci 40:1835–1850 Gao S, Li X (2008) 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, Li X (2010a) Effects of time-dependent large-scale forcing, solar zenith angle, and sea surface temperature on time-mean tropical rainfall processes. Meteorol Atmos Phys 106:95–105 Gao S, Li X (2010b) 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, Zhou Y, Li X (2007) Effects of diurnal variations on tropical equilibrium states: a twodimensional cloud-resolving modeling study. J Atmos Sci 64:656–664 Johnson D, Tao WK, Simpson J, Sui CH (2002) A study of the response of deep tropical clouds to mesocale processes, Part I: modeling strategy and simulation of TOGA COARE convective systems. J Atmos Sci 59:3492–3518 Johnson D, Tao WK, Simpson J (2007) A study of the response of deep tropical clouds to mesocale processes, Part II: sensitivity tests of radiation, surface fluxes and microphysics. J Atmos Sci 64:869–886 Li X, Sui CH, Lau KM (2002a) 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, Sui CH, Lau KM (2002b) Interactions between tropical convection and its embedding environment: an energetics analysis of a 2-D cloud resolving simulation. J Atmos Sci 59:1712–1722 Rutledge SA, Houze RA Jr (1987) A diagnostic modeling study of the trailing stratiform rain of a mid latitude squall line. J Atmos Sci 44:2640–2656 Shen X, Wang Y, Zhang N, Li X (2010a) Roles of large-scale forcing, thermodynamics, and cloud microphysics in tropical precipitation processes. Atmos Res 97:371–384, (c) Elsevier. Reprinted with permission Shen X, Wang Y, Zhang N, Li X (2010b) Precipitation and cloud statistics in the deep tropical convective regime. J Geophys Res. doi:10.1029/2010JD014481, (c) American Geophysical Union. Reprinted with permission

References

109

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, Li X, Lau KM (1998) Radiative-convective processes in simulated diurnal variations of tropical oceanic convection. J Atmos Sci 55:2345–2359 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 Tao WK, Scala J, Ferrier B, Simpson J (1995) The effects of melting processes on the development of squall lines in the tropics and midlatitudes. J Atmos Sci 52:1934–1948 Tao WK, Simpson J, Sui CH, Ferrier BS, Chou MD (1996) Mechanisms of cloud-radiation interaction in the tropics and midlatitudes. J Atmos Sci 53:2624–2651 Xu KM, Emanuel KA (1989) Is the tropical atmosphere conditionally unstable? Mon Weather Rev 117:1471–1479 Yuter SE, Houze RA Jr (1995) Three-dimensional kinetic and microphsycial evolution of Florida cumulonimbus. Part II: frequency distribution of vertical velocity, reflectivity, and differential reflectivity. Mon Weather Rev 123:1941–1963

Chapter 4

Effects of Sea Surface Temperature

4.1

Introduction

SST affects surface rainfall and associated cloud microphysical processes mainly through the change in surface evaporation flux (e.g., Lau et al. 1993, 1994; Wu and Moncrieff 1999; Cui and Li 2006). Lau et al. (1993) studied rainfall responses to SST in the presence of same large-scale forcing in the deep convective regime and found 22% increase of convective precipitation and 13% increase of surface evaporation rate when imposed SST increases from 28°C to 30°C. Costa et al. (2001) studied sensitivity of precipitation to SST with cloud-resolving model simulations that are imposed with the forcing derived from TOGA COARE data, and revealed 6.4% increase of precipitation with 2°C increase of SST, which is associated with 17.8% increase of convective precipitation and 19.0% decrease of stratiform precipitation. Wu and Moncrieff (1999) from their SST sensitivity simulations found 3.3% increase of time mean precipitation when time mean SST increases from 27.4°C to 29.4°C and 5.8% increase of precipitation when the SST increases from 29.4°C to 31.4°C. Cui and Li (2006) analyzed the quasi-equilibrium simulation data (Gao et al. 2007) from the model that is imposed with zero large-scale vertical velocity and found that the increase of SST from 29°C to 31°C causes 19% increase of surface rain rate. In this chapter, sensitivity of time-mean surface rainfall and diurnal variation of rainfall to SST is discussed through the analysis of equilibrium model simulation data based on Zhou and Li (2009, 2011).

4.2 Time-Mean Analysis The analysis of model domain mean water-vapor-related surface rainfall budgets in SST29 (Table 2.1a) and SST31 (Table 4.1a) shows that the increase in mean surface rain rate from 0.130 mm h−1 in SST29 to 0.159 mm h−1 in SST31 is mainly associated

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_4, © Springer Science+Business Media B.V. 2012

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Effects of Sea Surface Temperature

Table 4.1 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 SST31. Units are % for fractional coverage, mm h−1 for the others (After Zhou and Li (2009, 2011)) Non-raining Raining stratiform Convective Model domain (a) regions regions regions mean FC PS QWVT QWVF QWVE QCM

91.8 0.000 −0.001 −0.147 0.145 0.003

4.8 0.061 0.017 0.014 0.004 0.026

3.4 0.098 −0.012 0.133 0.003 −0.026

100 0.159 0.004 0.000 0.152 0.003

(b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.008 −0.156 −0.013 −0.001 0.159 0.004

Raining stratiform regions 0.061 0.012 0.020 −0.001 0.001 0.003 0.025

Convective regions 0.098 −0.015 0.136 −0.001 0.000 0.004 −0.026

Model domain mean 0.159 0.005 0.000 −0.015 0.000 0.166 0.003

with the increase in mean surface evaporation rate from 0.134 mm h−1 in SST29 to 0.152 mm h−1 in SST31. The increase of mean hydrometeor concentration in SST29 (−0.005 mm h−1) and the decrease of mean hydrometeor concentration in SST31 (0.003 mm h−1) also widen the difference in mean surface rain rate between the two experiments. The convective rain rate is 32.4% larger in SST31 than in SST29 whereas the stratiform rain rate is 8.9% larger in SST31 than in SST29. Thus, the larger convective rain rate mainly accounts for the larger model domain mean surface rain rate in SST31 than in SST29. The larger surface evaporation rate associated with the warmer SST over rainfall-free regions is balanced by the larger water vapor divergence rate in SST31 than in SST29. Compared to SST29, the larger water vapor divergence over rainfall-free regions and the larger water vapor convergence over convective regions in SST31 indicate the larger transport of water vapor from rainfall-free regions to convective regions, which leads to the larger convective rain rate in SST31. The analysis of model domain mean thermally-related surface rainfall budget in SST29 (Table 2.1b) and SST31 (Table 4.1b) reveals that the increase in SST from 29°C to 31°C leads to the increase in model domain mean surface rain rate from 0.130 mm h−1 in SST29 to 0.159 mm h−1 in SST31 through the enhancement in radiative cooling term from 0.147 mm h−1 in SST29 to 0.166 mm h−1 in SST31. The decrease in hydrometeor concentration in SST31 and the increase in hydrometeor concentration in SST29 also

4.2 Time-Mean Analysis

113

Table 4.2 As in Table 4.1 except for those in SST29D Non-raining Raining stratiform (a) regions regions FC 91.9 5.1 PS 0.000 0.058 QWVT 0.004 0.016 QWVF −0.133 0.006 QWVE 0.126 0.004 QCM 0.003 0.032 (b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.012 −0.146 −0.015 −0.001 0.145 0.004

Raining stratiform regions 0.058 0.008 0.013 −0.001 0.002 0.004 0.032

Convective regions 3.0 0.088 −0.010 0.127 0.002 −0.031

Model domain mean 100 0.146 0.010 0.000 0.132 0.004

Convective regions 0.088 −0.016 0.132 −0.001 0.000 0.004 −0.032

Model domain mean 0.146 0.004 0.000 −0.016 0.001 0.153 0.004

contribute to the enhancement of model domain mean surface rainfall in SST31. The increase in model domain mean surface rain rate from SST29 to SST31 results mainly from the increase in convective rain rate from 0.074 mm h−1 in SST29 to 0.098 mm h−1 in SST31, which is in turn caused by the increase in heat divergence over convective regions from 0.120 mm h−1 in SST29 to 0.136 mm h−1 in SST31. Over raining stratiform regions, similar transport rates of hydrometeors from convective regions and similar heat divergence rates in both experiments lead to similar stratiform rain rates. Compared to SST29, the increase in heat divergence over convective regions in SST31 is associated with the increase in heat convergence over rainfall-free regions, which is caused by the increase in radiative cooling over rainfall-free regions in SST31. To examine the sensitivity of rainfall to diurnally-varying SST, SST29D is compared to SST29 (Tables 2.1 and 4.2). The time and model domain mean surface rain rate is 0.146 mm h−1 in SST29D, which is larger than that in SST29. Although the time-mean of imposed SST is 29°C for the two experiments, the experiment with diurnally varying SST produces the colder atmosphere than does the experiment without diurnally varying SST (Gao et al. 2007). The mean surface rain rates are about 12.3% larger in SST29D than in SST29. The mean water-vapor-related surface rainfall budgets in Tables 2.1a and 4.2a show that the mean local atmospheric drying and decrease of mean hydrometeor concentration occur in SST29D whereas increase of mean hydrometeor concentration appears in SST29, which accounts for the enhancement of mean surface rainfall in SST29D. Since the stratiform rain rates in SST29 and SST29D are similar, the surface convective rain rate determines the differences in the mean surface rain rate between the two experiments. The experiment with diurnally varying SST generates larger convective rain rates through larger water vapor convergence rates over convective regions than does the experiment without diurnally varying SST.

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Table 4.3 (a) Infrared-cooling component (b) solar-heating component of SRAD over rainfall-free regions, raining stratiform regions, convective regions, and model domain mean averaged from days 31 to 40 in SST29, SST31, and SST29D. Unit is mm h−1 (After Zhou and Li 2011) Rainfall-free Raining stratiform Convective Model domain regions regions regions mean (a) Infrared-cooling component SST29 0.232 0.009 0.007 0.249 SST31 0.253 0.008 0.008 0.268 SST29D 0.238 0.008 0.007 0.253 (b) Solar-heating component SST29 −0.091 SST31 −0.094 SST29D −0.093

−0.005 −0.004 −0.004

−0.004 −0.004 −0.003

−0.100 −0.102 −0.100

The surface evaporation rate over rainfall-free regions is slightly smaller in SST29D (0.126 mm h−1) and in SST29 (0.128 mm h−1). The larger water vapor convergence over convective regions requires the larger water vapor divergence over rainfall-free regions in SST29D (−0.133 mm h−1) than in SST29 (−0.123 mm h−1). As a result, a weak local atmospheric drying (0.004 mm h−1) occurs in SST29D whereas a weak local atmospheric moistening (−0.007 mm h−1) appears in SST29. Meanwhile, the weak local atmospheric drying occurs over raining area (convective plus raining stratiform regions) in the two experiments. The local atmospheric drying over both raining and non-raining regions leads to the mean local atmospheric drying in SST29D whereas the local atmospheric drying over raining regions and the local atmospheric moistening over non-raining regions cancel each other out in SST29. The model domain mean thermally-related surface rainfall budgets in SST29 (Table 2.1b) and SST29D (Table 4.2b) show that the increase of mean surface rain rate from SST29 to SST29D is associated with the increase in radiative cooling in SSST29D, and the hydrometeor concentration change from increase in SST29 to decrease in SST29D. The enhancement of model domain mean surface rainfall in SST29D results mainly from the increase in convective rainfall, which is mainly from the increase in heat divergence over convective regions. The increase in heat divergence over convective regions is balanced by the increase in heat convergence over rainfall-free regions, which is compensated by the increase in radiative cooling over rainfall-free regions in SST29D. The radiative cooling term (SRAD) is a major thermal process associated with surface rainfall. The term contains Infrared (IR)-cooling and solar-heating components. Thus, the components are calculated and shown in Table 4.3. While the solar-heating terms are similar in the three experiments (Table 4.3b), the differences in SRAD between the experiments come from the differences in infrared-cooling component (Table 4.3a). The model domain mean IR-cooling components are mainly determined by the infrared-cooling components over rainfall-free regions. Since the difference in IR-cooling component of SRAD is responsible for the differences in surface rainfall, vertical profiles of IR cooling averaged from days 31 to 40 in SST29,

4.2 Time-Mean Analysis

115

Fig. 4.1 Vertical profiles of infrared cooling rate averaged from day 31 to day 40 in SST29 (solid), SST31 (dash), and SST29D (dot). Unit is °C day−1 (After Zhou and Li 2011)

SST31, and SST29D, which are used to calculate the IR-components of SRAD in Table 4.3b, are shown in Fig. 4.1. In SST29, the IR cooling rate decreases with increasing height below 5 km, reaches maximum around 8 km, decreases again with increasing height from 8 to 13 km. The increase in SST from 29°C to 31°C simply

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Effects of Sea Surface Temperature

enhances emission of IR radiation by shifting vertical profiles of IR cooling upward in SST31. Thus, the IR cooling is stronger in SST31 than in SST29. The inclusion of diurnal variation of SST in SST29D produces slightly stronger IR cooling only in mid and lower troposphere while the IR cooling rates in SST29D and SST29 are similar in the upper troposphere.

4.3

Analysis of Diurnal Variation

SST31 has a larger diurnal anomaly of convective rain rate than SST29 does, in particular, in the second half of day when SST31 produces larger negative anomaly in the afternoon and larger positive anomaly in the evening than SST29 does (Fig. 4.2). The analysis of water-vapor-related surface rainfall budgets over convective regions reveals that the difference in diurnal anomaly in convective rain rate between the two experiments are mainly associated with the difference in water vapor convergence because the diurnal anomalies of local water vapor change rate in the two experiments are nearly zero and the diurnal anomalies of QCM in the two experiments are similar. The positive diurnal anomaly of stratiform rain rate in SST31 is in phase with that in SST29 in the first half of day, but the magnitude of the former is larger than that of the latter (Fig. 4.3). The diurnal anomaly of stratiform rainfall in SST31 is out of phase with that in SST29 in the second half of day, which also widens the difference in diurnal anomaly of stratiform rain rate between the two experiments. The difference in diurnal anomaly of stratiform rain rate is associated with the difference in QWVT, QWVF, and QCM over raining stratiform regions since the diurnal anomalies of stratiform rainfall processes are dominated by hourly fluctuations. Over rainfall-free regions, the difference in diurnal anomaly of water vapor convergence rate between the two experiments is balanced by the difference in local water vapor change rate (Fig. 4.4). The difference in diurnal anomaly of convective rain rate between the two experiments is mainly related to the difference in water vapor convergence over convective regions, which is mainly balanced by the difference in water vapor convergence over rainfall-free regions. Since the diurnal anomaly of rainfall is mainly caused by the diurnal anomaly of IR radiative cooling, the thermally-related surface rainfall budgets in SST29 and SST31 are analyzed. The larger diurnal anomaly of convective rainfall in SST31 is associated with larger diurnal anomaly of heat divergence over convective regions while the magnitudes of diurnal anomalies of SHT and QCM are similar (Fig. 4.5). The larger negative anomaly of afternoon stratiform rainfall in SST31 is mainly related to the negative anomalies of SHT and QCM, whereas the positive anomaly of evening stratiform rainfall in SST31 is related to the positive anomalies of SHF and QCM (Fig. 4.6) The difference in diurnal anomaly of heat divergence over convective regions for SST31-SST29 is larger than the difference over raining stratiform regions and is mainly balanced by the difference over rainfall-free regions. Over rainfall-free regions, the difference in diurnal anomaly of SHF for SST31-SST29 is balanced by the difference in diurnal anomaly of SHT while the diurnal anomalies of

a

b

c

d

e

Fig. 4.2 Diurnal anomalies of (a) PS, (b) QWVT, (c) QWVF, (d) QWVE, and (e) QCM in water-vapor-related surface rainfall budgets over convective regions in SST29 (solid), SST31 (dash), and SST29D1 (dot). Units are mm h−1

118

4

a

b

c

d

e

Fig. 4.3 As in Fig. 4.2 except over raining stratiform regions

Effects of Sea Surface Temperature

4.3

Analysis of Diurnal Variation

119

a

b

c

d

Fig. 4.4 Diurnal anomalies of (a) QWVT, (b) QWVF, (c) QWVE, and (d) QCM over rainfall-free regions in SST29 (solid), SST31 (dash), and SST29D1 (dot). Units are mm h−1

SRAD in the two experiments are similar (Fig. 4.7). The differences in diurnal anomaly of vertical profiles of heat divergence for SST31-SST29 have larger magnitudes below 8 km than the differences in diurnal anomaly of vertical profiles of radiative heating while both differences are smaller above 8 km (Fig. 4.8a, c). The difference in heat divergence for SST31-SST29 in Fig. 4.8c roughly shows three positive centers and three negative centers during 24-hour period; this appears to indicate that the time scale for the difference is about 8 h. This sub-diurnal variation of difference in heat divergence intensifies diurnal anomaly of convective rainfall.

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a

b

c

d

e

Fig. 4.5 Diurnal anomalies of (a) PS, (b) SHT, (c) SHF, (d) SRAD, and (e) QCM in thermally-related surface rainfall budgets over convective regions in SST29 (solid), SST31 (dash), and SST29D1 (dot). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

4.3

Analysis of Diurnal Variation

a

b

c

d

e

Fig. 4.6 As in Fig. 4.5 except over raining stratiform regions

121

122

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Effects of Sea Surface Temperature

a

b

c

d

Fig. 4.7 Diurnal anomalies of (a) SHT, (b) SHF, (c) SRAD, and (d) QCM over rainfall-free regions in SST29 (solid), SST31 (dash), and SST29D1 (dot). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

When diurnal variation of SST is included during the integration, SST29D generally generates negative anomaly of convective rain rate from hour 3 to hour 18 and positive anomaly of convective rain rate in the evening (Fig. 4.2), which is different from SST29. The analysis of water-vapor-related surface rainfall budgets over convective regions reveals that the diurnal anomaly of water vapor convergence is much larger than those of QWVT and QCM. Thus, the difference in diurnal anomaly of convective rain rate for SST29D-SST29 is mainly associated with the difference in

4.3

Analysis of Diurnal Variation

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a

b

c

d

Fig. 4.8 Diurnal anomalies of vertical profiles of radiating heating (SRAD; upper panel) and heat divergence (SHF; lower panel) over rainfall-free regions. (a) and (c) denote SST31-SST29 whereas (b) and (d) present SST29D-SST29. Unit is 10−6 h−1

diurnal anomaly of water vapor convergence over convective regions. The difference in diurnal anomaly of convective rain rate generally is much larger than that the difference in diurnal anomaly of stratiform regions due to similar QWVT, QWVF, and QCM in the two experiments (Fig. 4.3). Over rainfall-free regions, the diurnal anomaly of water vapor convergence in SST29D is positive from hour 4 to hour 18 and negative in the evening (Fig. 4.4), which generally is out of phase with the diurnal anomaly of water vapor convergence over convective regions. Meanwhile, due to negligibly small diurnal anomalies of QWVE and QCM, the difference in difference in diurnal anomaly of water vapor convergence is offset by the difference in diurnal anomaly of local water vapor change. The analysis of thermally-related surface rainfall budgets shows that the diurnal anomaly of convective rain rate in SST29D is mainly associated with the diurnal

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anomaly of heat divergence over convective regions (Fig. 4.5). The diurnal anomalies of stratiform rainfall in the two experiments generally are similar because of similar thermally-related stratiform rainfall processes (Fig. 4.6). The difference in diurnal anomaly of heat divergence over convective regions for SST29D-SST29 is mainly balanced by the difference over rainfall-free regions, which in turn is balanced by the difference in diurnal anomaly of local thermal change over rainfall-free regions (Fig. 4.7). The differences in diurnal anomaly of SRAD are negligibly small. The differences in diurnal anomaly of vertical profiles of heat divergence for SST29DSST29 have larger magnitudes below 10 km than the differences in diurnal anomaly of vertical profiles of radiative heating (Fig. 4.8b, d). Higher (lower) SST in the second (first) half of day in SST29D yields positive (negative) difference in diurnal anomaly of heat divergence and radiative heating for SST29D-SST29 via negative (positive) difference in diurnal anomaly of surface sensible heat flux (not shown). Diurnally varying SST tends to produce the differences for SST29D-SST29 at the diurnal scale; this indicates that diurnal variation of imposed SST regulates time scale of difference in heat divergence over rainfall-free regions. Compare to SST29, lower (higher) SST in the first (second) half of day produces negative (positive) anomaly of convective rainfall.

References Costa AA, Cotton WR, Walko RL, Pielke RA Sr, Jiang H (2001) SST Sensitivities in mulltiday TOGA COARE cloud-resolving simulations. J Atmos Sci 58:253–268 Cui X, Li X (2006) Role of surface evaporation in surface rainfall processes. J Geophys Res. doi:10.1029/2005JD006876 Gao S, Zhou Y, Li X (2007) Effects of diurnal variations on tropical equilibrium states: a twodimensional cloud-resolving modeling study. J Atmos Sci 64:656–664 Lau KM, Sui CH, Tao WK (1993) A preliminary study of the tropical water cycle and its sensitivity to surface warming. Bull Am Meteorol Soc 74:1313–1321 Lau KM, Sui CH, Chou MD, Tao WK (1994) An inquiry into the cirrus cloud thermostat effect for tropical sea surface temperature. Geophys Res Lett 21:1157–1160 Wu X, Moncrieff MW (1999) Effects of sea surface temperature and large-scale dynamics on the thermodynamic equilibrium state and convection over the tropical western Pacific. J Geophys Res 104:6093–6100 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 5

Effects of Vertical Wind Shear

5.1

Introduction

The effects of vertical wind shear on convective development have been examined for decades (e.g., Pastushkov 1975; Corbosiero and Molinari 2002; Lang et al. 2007; Ueno 2007). The delayed initiation of convection is associated with a strong vertical wind shear (e.g., Xu et al. 1992). The vertical wind shear affects convective development through the change in vertical transport of horizontal momentum (e.g., Wu and Yanai 1994). The convection becomes increasingly organized in lines because of a strong lower-tropospheric vertical wind shear (e.g., Robe and Emanuel 2001). Vertical wind shears affect convective development in two ways. First, vertical wind shear change intensity of convective systems through the change in dynamic instability. The degree of dynamic instability can be described by a secondary circulation, which is quantified by the magnitude of perturbation kinetic energy. Vertical structures of large-scale horizontal winds may alter perturbation kinetic energy through the change in energy exchange between perturbation kinetic energy and large-scale kinetic energy, which is determined by covariance between perturbation horizontal wind and vertical velocity in the presence of vertical shear of large-scale horizontal winds (e.g., Peixoto and Oort 1992; Li et al. 2002). Second, vertical structures of large-scale horizontal winds may have impacts on horizontal structures of convective systems. Unicell and multicell convections are associated with the unidirectional and reverse wind shears, respectively (e.g., Tao et al. 2003). In this chapter, sensitivity experiments with vertical wind shear excluded (BILISNWVS, PSRNVWS) are compared with the control experiments with vertical wind shear included (BILIS, PSR) to discuss effects of vertical wind shear on rainfall processes during the landfall of sever tropical storm Bilis (2006) and pre-summer heavy rainfall event over southern China in June 2008, based on Wang et al. (2009) and Shen et al. (2011). These sensitivity experiments are identical to the control experiments except in sensitivity experiments vertically varying large-scale zonal winds are replaced with mass-weighted mean large-scale zonal winds from the control experiments.

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_5, © Springer Science+Business Media B.V. 2012

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Effects of Vertical Wind Shear on Severe Tropical Storm Rainfall

Temporal-zonal distributions of simulated surface rain rate in Figs. 2.11 and 5.1 reveal that the convective systems in both experiments develop over the entire model domain in the afternoon of 14 July 2006. The two experiment show similarities in two aspects: rainfall occupies nearly entire model domain on 15 July, and 1 day later, rain rates become larger while the rainfall coverage becomes smaller. The differences between the two experiments include the following: (1) on 15 July, the individual rainband propagates eastward whereas the rainbands move westward in BILIS. In contrast, only eastward movement of individual rainband is clearly

Fig. 5.1 Time-zonal distribution of surface rain rate (mm h−1) simulated in BILISNVWS (After Wang et al. 2009)

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evident in BILISNVWS; (2) on 16 July, convective systems are much better organized in BILIS than in BILISNVWS; the sizes of rainfall area in BILIS (~200 km) are much larger than those in BILISNVWS (~100 km or less). Ping et al. (2008) analyzed COARE and found that the eastward propagation of individual rainband is responsible for the advection of water hydrometeor mixing ratio by imposed largescale westerly winds in the lower troposphere. The westward movement of rainbands can be explained by a new rainband formed at the west of existing rainband in BILIS. This implies that vertical wind shear with the westerly winds in the lower troposphere and the easterly winds in the upper troposphere may enhance the development of the new cloud at the west of the existing cloud. The rainfall information can be further summarized by calculating fractional coverage for raining stratiform and convective regions (Fig. 5.2). The imposed large-scale vertical velocity with the weak descending motion in the lower troposphere (Fig. 1.3) yields nearly 100% of fractional coverage of raining stratiform regions on the second half day of 15 July, which is insensitive to vertical wind shear. A significant increase in fractional coverage of stratiform rainfall can be seen in BILISNVWS on 16 July in the absence of the vertical wind shear. The daily mean fractional coverage of stratiform rainfall on 16 July is larger in BILISNVWS (64.9%) than in BILIS (46.1%) while those of convective rainfall in the two experiments are similar (30.8% in BILISNVWS and 29.5% in BILIS). Stratiform rain rates are larger in BILISNVWS than in BILIS and convective rain rates are smaller in BILISNVWS than in BILIS (Fig. 5.3) as the imposed large-scale upward motions have their maximum in the lower troposphere in the first half of 16 July (Fig. 1.3). Both experiments have similar stratiform and convective rain rates as the imposed large-scale upward motions have their maximum in the upper troposphere in the second half of 16 July. The lower-tropospheric upward motions cause more surface rainfall than the upper-tropospheric upward motions do in BILIS on 16 July even when they have similar maximum magnitudes (~10 cm s−1). Thus, the exclusion of vertical wind shear enhances stratiform rainfall and suppresses convective rainfall, respectively only when the imposed large-scale upward motions reach their maxima in the lower troposphere. To investigate the effects of vertical wind shear on convective and stratiform rainfall processes, the differences in water-vapor-related surface rainfall budget for BILISNVWS-BILIS are calculated and plotted in Fig. 5.4. On 15 July, the model domain mean surface rain rates are similar in the two experiments because they are mainly associated with the mean water vapor convergence rates as a result of same imposed large-scale vertical velocity. Since the mean surface rain rates come mainly from raining stratiform regions, both experiments have similar stratiform rain rates. On 16 July, the exclusion of vertical wind shear reduces the mean rain rate. The decrease in the mean rainfall is associated with the decreases in the mean local atmospheric drying, water vapor convergence, and hydrometeor loss. The decrease in the mean rain rate results from the reduction in convective rain rate because the exclusion of vertical wind shear increases stratiform rainfall. The reduction in convective rainfall is related to the increases in local atmospheric moistening and the transport of hydrometeor concentration from convective regions to raining stratiform

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a

b

Fig. 5.2 Time series of fractional coverage (%) of (a) raining stratiform regions and (b) convective regions from BILIS (solid) and BILISNVWS (dash) (After Wang et al. 2009)

regions and the slowdown in water vapor convergence. The increase in stratiform rainfall corresponds to the increases in local atmospheric drying and the transport of hydrometeor concentration from convective regions to raining stratiform regions and water vapor convergence. Secondary circulations are directly responsible for cloud development, and cloud microphysical processes directly produce surface rainfall. The intensity of secondary

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Effects of Vertical Wind Shear on Severe Tropical Storm Rainfall

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a

b

c

Fig. 5.3 Time series of (a) model domain mean surface rain rates, (b) stratiform rain rates, and (c) convective rain rates from BILIS (solid) and BILISNVWS (dash). Units are mm h−1 (After Wang et al. 2009)

circulations can be described using perturbation kinetic energy. The major difference between the two experiments is that kinetic energy exchange between large-scale forcing and perturbation circulations are allowed in BILIS but not allowed in BILISNVWS. Compared to those in BILISNVWS, well-organized convective

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a

b

c

Fig. 5.4 Differences in 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 for BILISNVWS-BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1

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clouds and large convective rainfall in BILIS may be associated with enhancement of perturbation kinetic energy in the presence of vertical wind shear as indicated by ¶K ¢ the growth rates of perturbation kinetic energy ( >0) (Fig. 5.5) and significant ¶t increases in convective rainfall (Figs. 5.3c and 5.4c) around the morning of 16 July. Figure 5.5 shows that the growth rates are significantly larger in BILIS than in BILISNVWS in late evening of 15 July and early morning of 16 July. To explain the differences in perturbation kinetic energy ( K¢ ) between the two experiments, budgets of perturbation kinetic energy will be analyzed. Following Li et al. (2002), the equation of K¢ can be derived by multiplying (1.1b) by u¢ and (1.1c) by w¢ and applying the model domain mean and the mass integration on the resulting equation: ¶K ¢ = Cu ( K , K ¢ ) + Cw ( K , K ¢ ) + C ( P ¢, K ¢ ) + Gqv ( K ¢ ) + Gql ( P ¢ ), ¶t

(5.1)

é (u¢ )2 + (w¢ )2 ù K¢ = ê ú, 2 ëê ûú

(5.1a)

é ¶u o ù Cu ( K , K ¢ ) = - ê u ¢ w ¢ ú, ¶z û ë

(5.1b)

é ¶w o ù Cw ( K , K ¢ ) = - ê w¢ w¢ ú, ¶z û ë

(5.1c)

é w ¢T ¢ ù C ( P ¢, K ¢ ) = ê g ú, ë Tb û

(5.1d)

Gqv ( K ¢ ) = éë0.61gw¢ qv ¢ ùû ,

(5.1e)

Gql ( K ¢ ) = - éë gw¢ ql ¢ ùû .

(5.1f)

where

Here, Tb is initial temperature; superscript o is an imposed NCEP/GDAS value; Cu ( K , K¢ ) and Cw ( K , K¢ ) are the barotropic conversion between mean domain mean kinetic energy ( K ) and K¢ , respectively, through covariance between perturbation zonal wind and vertical velocity in the presence of vertical shear of imposed horizontal-mean zonal wind, and between perturbation vertical velocities in the presence of vertical shear of imposed horizontal-mean vertical velocity. C ( P ¢, K ¢ ) is the baroclinic conversion between perturbation available potential energy ( P¢ ) and K¢ through covariance between perturbation vertical velocity and temperature. Gqv ( K¢ ) and Gql ( K¢ ) are the generation terms of K¢ through covariance between perturbation

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a

b

Fig. 5.5 Time series of perturbation kinetic energy budgets (107 J s−1) in (a) BILIS and (b) ¶K ¢ , BILISNVWS. Dark solid, light solid, short dash, dot, long dash, dot dash lines denote ¶t Cu ( K , K¢ ), Cw ( K , K¢ ), C ( P ¢, K ¢ ), Gqv ( K¢ ) , and Gql ( K¢ ), respectively (After Wang et al. 2009)

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Effects of Vertical Wind Shear on Pre-summer Heavy Rainfall

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vertical velocity and specific humidity, and between perturbation vertical velocity and cloud mixing ratio, respectively. Note that C(P′,K′), Gqv(K′), Gql(K′) are derived T from the buoyancy term in the vertical momentum equation { g( + 0.61qv ¢ - ql ¢ )}. Tb Thus the sum of the three terms denotes a generalized baroclinic process in the deep convective system. In late evening of 15 July and early morning of 16 July, C ( P ¢, K ¢ ) and Gqv ( K¢ ) are mainly balanced by Gql ( K¢ ) in the two experiments. The nearly cancellation among C(P’,K’), Gqv(K’), Gql(K’) suggests that the baroclinic process play a minor role in determining the tendency of perturbation kinetic energy. Cu ( K , K¢ ) accounts ¶K ¢ ¶K ¢ > 0 . Cu ( K , K¢ ) = 0 in . Cu ( K , K¢ ) > 0 in BILIS, which leads to for ¶t ¶t ¶K ¢ . This indicates that the negative vertical BILISNVWS, which yields a small ¶t ¶u o wind shear ( < 0 ) with the westerly winds in the lower troposphere and the ¶z easterly winds in the upper troposphere enhances perturbation kinetic energy, which leads to strong development of convective rainfall through the barotropic process when the imposed large-scale upward motions reach their peaks in the lower troposphere.

5.3

Effects of Vertical Wind Shear on Pre-summer Heavy Rainfall

The differences in domain-mean water-vapor-related surface rainfall budget for PSRNVWS-PSR show that the exclusion of vertical wind shear barely alters the mean surface rain rate on 4 June because the mean rainfall processes are insensitive to vertical wind shear (Fig. 5.6). The removal of vertical wind shear decreases the mean rain rate on 6 June, but the reduction in the mean rainfall is less than 2%. The tiny decrease in the mean rainfall is associated with a large offset of the reduction in the mean hydrometeor loss by the increases in the mean local atmospheric drying and water vapor convergence on 6 June. The exclusion of vertical wind shear increases the mean rain rate by nearly 10% on 7 June. The increased mean rainfall caused by the elimination of vertical wind shear is related to the reduction in the mean water vapor divergence and the increase in the mean hydrometeor loss. Rotunno et al. (1988) showed that vertical wind shear allows a spatial separation between the updraft and downdraft, which leads to longer lived systems and more effective secondary initiation from cold-pool outflows. Thus, the exclusion of vertical wind shear may shorten the life span of convective systems, which in turn causes the acceleration of hydrometeor loss. The budgets of K¢ in the two experiments on 7 June are calculated in Table 5.1. C ( P ¢, K ¢ ) and Gqv ( K¢ ) are largely balanced by Gql ( K¢ ) in the two experiments (their sums are −2.9 ´ 105 J s−1 in PSR and −2.1 ´ 105 J s−1 in PSRNVWS). Thus, similar baroclinic processes in the two experiments imply the crucial role the

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a

b

c

Fig. 5.6 Differences in 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 for PSRNVWS-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)

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é ¶K ¢ , Cu ( K , K¢ ), Cw ( K , K¢ ), C ( P ¢, K ¢ ), Table 5.1 Budgets of perturbation kinetic energy ê ë ¶t ù Gqv ( K¢ ) , Gql ( K ¢ )ú in the control experiment (PSR) and the experiment without vertical wind û shear (PSRNVWS). Unit is 105 J s−1 (After Shen et al. 2011)

PSR PSRNVWS

¶K ¢ ¶t

Cu ( K , K¢ )

Cw ( K , K¢ )

C ( P ¢, K ¢ )

Gqv ( K¢ )

Gql ( K¢ )

−4.9 −2.1

−1.9 0.0

0.0 0.0

21.5 13.4

32.3 31.3

−56.7 −46.7

barotropic process plays in determining effects of vertical wind shear on the mean rainfall. This can be demonstrated by the fact that the difference in the local change ¶K ¢ ) between the two experiments is mainly rate of perturbation kinetic energy ( ¶t attributable to the difference in Cu ( K , K¢ ) (a negative value denotes the barotropic conversion from perturbation kinetic energy to domain-mean kinetic energy). The decrease in perturbation kinetic energy in PSRNVWS is suppressed by the exclusion of vertical wind shear through the removal of barotropic conversion from perturbation kinetic energy to domain-mean kinetic energy. On 7 June, 75% and 25% of the increase in model domain mean surface rain rate from PSR to PSRNVWS result, respectively, from the increase in convective and stratiform rain rate (Fig. 5.6) as both convective and stratiform rainfall cover areas that are about 20% larger in PSRNVWS than in PSR. The increase in convective rainfall caused by the exclusion of vertical wind shear is associated with the local atmospheric change from moistening in PSR to drying in PSRNVWS, which is largely offset by the decrease in water vapor convergence. The increase in stratiform rainfall resulting from the removal of vertical wind shear is related to the suppression in water vapor divergence and the increase in the transport of hydrometeor concentration from convective regions to raining stratiform regions, which is largely cancelled out by the reduction in local atmospheric drying. Although the domain-mean surface rain rates are similar in the two experiments on both 4 and 6 June, the convective and stratiform rain rates are, respectively, lower and higher in PSRNVWS than in PSR. The decreases in convective rainfall caused by the elimination of vertical wind shear are associated with the enhanced transport of hydrometeor concentration from convective regions to raining stratiform regions and suppressed water vapor convergence on 4 and 6 June. The increases in stratiform rainfall resulting from the removal of vertical wind shear are related to the increased transport of hydrometeor concentration from convective regions to raining stratiform regions on 4 and 6 June and the enhanced local atmospheric drying on 4 June and increased water vapor convergence.

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References Corbosiero KL, Molinari J (2002) The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon Weather Rev 130:2110–2123 Lang S, Tao WK, Cifelli R, Olson W, Halverson J, Rutledge SA, Simpson J (2007) Improving simulations of convective systems from TRMM LBA: easterly and westerly regimes. J Atmos Sci 64:1141–1164 Li X, Sui CH, Lau KM (2002) Interactions between tropical convection and its embedding environment: an energetics analysis of a 2-D cloud resolving simulation. J Atmos Sci 59:1712–1722 Pastushkov RS (1975) The effects of vertical wind shear on the evolution of convective clouds. Q J R Meteorol Soc 101:281–291 Peixoto JP, Oort AH (1992) Physics of climate. American Institute of Physics, New York, 520 pp Ping F, Luo Z, Li X (2008) Kinematics, cloud microphysics, and spatial structures of tropical cloud clusters: A two-dimensional cloud-resolving modeling study. Atmos Res 88: 323–336. Robe FR, Emanuel KA (2001) The effect of vertical wind shear on radiative-convective equilibrium states. J Atmos Sci 58:1427–1445 Rotunno R, Klemp JB, Weisman ML (1988) A theory for strong, long-lived squall lines. J Atmos Sci 45:463–485 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 Tao WK, Shie CL, Simpson J, Braun S, Johnson RH, Ciesielski PE (2003) Convective systems over the South China Sea: cloud resolving model simulations. J Atmos Sci 60:2929–2955 Ueno M (2007) Observational analysis and numerical evaluation of the effects of vertical wind shear on the rainfall asymmetry in the typhoon inner-core region. J Meteorol Soc Jpn 85:115–136 Wang D, Li X, Tao WK, Wang Y (2009) Effects of vertical wind shear on convective development during a landfall of severe tropical storm Bilis (2006). Atmos Res 94:270–275, (c) Elsevier. Reprinted with permission Wu X, Yanai M (1994) Effects of vertical wind shear on the cumulus transport of momentum: observations and parameterization. J Atmos Sci 51:1640–1660 Xu KM, Arakawa A, Krueger SK (1992) The macroscopic behavior of cumulus ensembles simulated by a cumulus ensemble model. J Atmos Sci 49:2402–2420

Chapter 6

Microphysical and Radiative Effects of Ice Clouds

6.1

Introduction

As an important constituent in the stratiform clouds of precipitation systems, ice hydrometeors play an important role in the development of convective systems and precipitation. Due to scarce cloud observations, effects of ice clouds on precipitation systems have been intensively investigated through the numerical modeling and its analysis in recent decades. Numerical studies have showed that the inclusion of ice microphysical parameterization schemes in the models has led to the improvements in cloud-resolving simulations of squall lines (e.g., Yoshizaki 1986; Nicholls 1987; Fovell and Ogura 1988; Tao and Simpson 1989; McCumber et al. 1991; Tao et al. 1991), in cloud-resolving and mesoscale simulations of tropical cyclones (e.g., Willoughby et al. 1984; Lord et al. 1984; Liu et al. 1997), and in simulations of general circulation models (e.g., Ramanathan et al. 1983; Slingo 1987; Heymsfield and Donner 1990; Fowler et al. 1996). The major conclusion of previous short-term (less than 1 day) cloud-resolving modeling studies on ice effects is that the ice clouds is crucial for better simulation of stratiform development, such as the light precipitation associated with stratiform clouds over the trailing region of precipitation systems. In recent long-term (more than 1 week) cloud-resolving modeling studies, Li et al. (1999) used the improved schemes that parameterize the growth of cloud ice by the Bergeron process and the conversion of cloud ice to snow by Krueger et al. (1995) in a cloud-resolving model and found that the enhancement of the mixing ratio of cloud ice led to better simulations of atmospheric thermodynamic states and surface fluxes. Grabowski et al. (1999) revealed in their 7-day cloud-resolving model simulations during Phase III of Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) that the effects of cloud clouds on the temperature and moisture profiles are always statistically significant whereas the effects on the relative humidity profiles are not significant, and the temperature in the upper troposphere is modified by the effect of cloud microphysics on the anvil clouds when the radiation and clouds are fully

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_6, © Springer Science+Business Media B.V. 2012

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interactive. In their 39-day cloud resolving model simulations during TOGA COARE, Wu et al. (1999) showed that the simulations of cloud radiative properties have improved by the modified ice microphysical parameterization schemes and that the radiative flux, cloud radiative forcing, and albedo are sensitive to the effective radius of ice particles. Li et al. (2005) carried out a sensitivity experiment that excludes the depositional growth of snow from cloud ice and found anomalous growth of cloud ice and more than 20% increase in fractional cloud cover; it appears to suggest that the lack of the depositional snow growth causes an unrealistically large mixing ratio of cloud ice. Grabowski and Moncrieff (2001) and Grabowski (2003) used cyclic lateral boundary conditions and a large model domain in 2D cloud-resolving model simulations to allow cloud-radiation interaction with large-scale circulations and found that the convective systems simulated without ice clouds have a reduced stratiform component, a larger propagation speed, and a shorter life cycle than those simulated with ice clouds. Tao and Simpson (1989) used periodic lateral boundary conditions in a 2D cloud-resolving model to examine effects of ice clouds on large-scale circulations and revealed that the model that includes and excludes ice clouds simulated similar propagation speeds and life cycles of convective systems. Liu and Moncrieff (1997) simulated tropical squall lines using a cloud-resolving model with open lateral boundary conditions and showed that the model without ice clouds simulated a much weaker and less organized convective system than does the model with ice clouds in a weakly unstable environment, whereas ice clouds have important effects on the system-scale structures in a strongly unstable environment. This indicates that the environmental thermodynamics is a major factor in regulating effects of ice clouds on tropical convection. Although effects of ice clouds on large-scale circulations cannot be examined using the model with the imposed large-scale forcing, the effects of ice clouds on model domain mean thermodynamics can be investigated in this framework. Gao et al. (2006) conducted 2D cloud resolving model simulations to study effects of ice clouds on tropical atmosphere and found that the experiment without ice clouds produces a colder and more humid atmosphere, a larger amount of cloud water, and a lower surface rain rate than does the experiment with ice clouds. In this chapter, effects of microphysical and radiative effects of ice clouds on rainfall processes are discussed by comparing sensitivity experiments with the control experiments in an idealized case with zero large-scale vertical velocity and during the landfall of severe tropical storm Bilis (2006) and pre-summer heavy rainfall event over southern China in June 2008. The sensitivity experiments include SST29NIR, BILISNIR, and PSRNIR that exclude radiative effects of ice clouds by setting ice hydrometeor mixing ratios to zero in calculations of radiation and SST29NIM, BILISNIM, and PSRNIM that totally exclude the ice hydrometeor mixing ratio and associated microphysical processes (both microphysical and radiative effects of ice clouds). The microphysical effects of ice clouds here include thermal effects associated with the latent heat release and moist effects associated with the exchange between water vapor and cloud hydrometeors. The comparison of SST29NIR, BILISNIR, and PSRNIR with SST29, BILIS, and PSR shows impacts

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Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

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of exclusion of radiative effects of ice clouds on rainfall responses whereas the comparison of SST29NIM, BILISNIM, and PSRNIM with SST29NIR, BILISNIR, and PSRNIR reveals impacts of exclusion of microphysical effects of ice clouds on rainfall responses in the absence of radiative effects of ice clouds. The following discussions are mainly based on Ping et al. (2007, 2011), Li and Zou (2009), Ping and Luo (2009), Wang et al. (2010a, b), and Zhou and Li (2011).

6.2

6.2.1

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity Time-Mean Analysis

The exclusion of radiative effects of ice clouds produces a larger model domain mean surface rain rate in SST29NIR than in SST29 (Tables 2.1 and 6.1). The fractional coverage of stratiform rainfall decreases by excluding the radiative effects of ice clouds while the fractional coverage of convective rainfall is insensitive to the radiative effects of ice clouds. SST29NIR produces a larger convective rain rate than SST29 does because SST29NIR has a larger water vapor convergence and heat divergence rates than SST29 does. Due to the cyclic lateral boundary conditions, the larger water vapor convergence and heat divergence rates in convective regions are balanced by the larger water vapor divergence and heat convergence rates in rainfall-free regions in SST29NIR that are offset by the larger surface evaporation and IR radiative cooling rates in SST29NIR, respectively, compared to SST29. The larger surface evaporation rate in rainfall-free regions may be caused by drier air and larger fractional rainfall-free coverage in SST29NIR since sea surface temperatures are fixed in the two experiments. The exclusion of microphysical effects of ice clouds yields a smaller mean surface rain rate in SST29NIM than in SST29NIR in the absence of radiative effects of ice clouds (Tables 6.1 and 6.2). The fractional coverage of stratiform rainfall in SST29NIM is about a half of that in SST29NIR, while the fractional coverage of convective rainfall is less sensitive to the microphysical effects of ice clouds. SST29NIM produces both smaller convective and stratiform rain rates than SST29NIR does because it has smaller water vapor convergence and heat divergence rates in convective regions and smaller local atmospheric drying and warming rates over raining stratiform regions and smaller transport rate of hydrometeor concentration from convective regions to raining stratiform regions. Compared to SST29NIR, the smaller water vapor convergence and heat divergence rates in convective regions caused by the exclusion of microphysical effects of ice clouds in SST29NIM are balanced out by the smaller water vapor divergence and heat convergence rates in rainfall-free regions, respectively, which are in turn offset by smaller surface evaporation and IR radiative cooling rates. The smaller surface evaporation rate in SST29NIM is caused by more humid air in rainfall-free regions.

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6 Microphysical and Radiative Effects of Ice Clouds Table 6.1 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 icerelated 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 SST29NIR. Units are % for fractional coverage, mm −1 for the others (After Ping et al. 2007 and Zhou and Li 2011) Non-raining Raining stratiform Convective Model domain (a) regions regions regions mean FC 92.3 4.5 3.2 100 PS 0.000 0.065 0.121 0.186 QWVT 0.004 0.030 −0.024 0.010 QWVF −0.179 −0.018 0.197 0.000 QWVE 0.166 0.007 0.005 0.178 QCM 0.007 0.046 −0.056 −0.003 (b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.015 −0.200 −0.024 0.000 0.202 0.008

Raining stratiform regions 0.065 0.018 −0.006 −0.001 0.003 0.005 0.045

Convective regions 0.121 −0.034 0.206 −0.001 −0.001 0.006 −0.056

Model domain mean 0.186 −0.001 0.000 −0.026 0.002 0.213 −0.003

Table 6.2 Table 6.2 As in Table 6.1 except for those in SST29NIM Non-raining Raining stratiform Convective Model domain (a) regions regions regions mean FC 94.3 2.3 3.4 100 PS 0.000 0.038 0.086 0.124 QWVT 0.001 0.009 −0.008 0.002 QWVF −0.129 0.018 0.111 0.000 QWVE 0.141 0.003 0.003 0.147 QCM −0.010 0.008 −0.021 −0.023 (b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.008 −0.142 −0.017 0.000 0.162 −0.011

Raining stratiform regions 0.038 0.009 0.020 0.000 0.000 0.002 0.008

Convective regions 0.086 −0.018 0.122 −0.001 0.000 0.004 −0.021

Model domain mean 0.124 0.000 0.000 −0.018 0.000 0.167 −0.024

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Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

141

Table 6.3 (a) Infrared-cooling component (b) solar-heating component of SRAD over rainfall-free regions, raining stratiform regions, convective regions, and model domain mean in SST29, SST29NIR, and SST29NIM. Unit is mm h−1 (After Zhou and Li 2011) Rainfall-free Raining stratiform Convective Model domain regions regions regions mean (a) Infrared-cooling component SST29 0.232 0.009 0.007 0.249 SST29NIR 0.294 0.008 0.009 0.311 SST29NIM 0.254 0.003 0.008 0.265 (b) Solar-heating component SST29 −0.091 SST29NIR −0.092 SST29NIM −0.092

−0.005 −0.003 −0.001

−0.004 −0.003 −0.004

−0.100 −0.098 −0.097

The radiative cooling term (SRAD) is a major thermal process associated with surface rainfall. The term contains Infrared (IR)-cooling and solar-heating components. Thus, the components are calculated and shown in Table 6.3. While the solar-heating terms are similar in SST29, SST29NIR, and SST29NIM (Table 6.3b), the differences in SRAD between the three experiments result from the differences in infrared-cooling component (Table 6.3a). The model domain mean IR-cooling components are mainly determined by the infrared-cooling components over rainfall-free regions. Vertical profile of IR cooling is significantly changed when the ice radiative effects (SST29NIR), or ice microphysics (SST29NIM) is excluded in the model simulations (Fig. 6.1). The IR cooling is much stronger below 10 km in SST29NIR than in SST29NIM because the exclusion of ice clouds in SST29NIM consumes less water vapor in the upper troposphere than in SST29NIR and the more water vapor in the upper troposphere in SST29NIM produces weaker IR cooling rate than in SST29NIR by trapping more IR radiation in the mid and lower troposphere. The IR cooling is much stronger below 8 km in SST29NIR than in SST29 because the exclusion of radiative effects of ice clouds in SST29NIR enhances more IR cooling than in SST29 by allowing more IR radiation to space.

6.2.2

Diurnal Analysis

Both convective (Fig. 6.2a) and stratiform rain rates (Fig. 6.3a) in SST29, SST29NIR, and SST29NIM generally show positive diurnal anomalies after sunset and negative diurnal anomalies after sunrise. The diurnal amplitudes of convective rain rates are larger than those of stratiform rain rates. This indicates that the diurnal variation of model domain mean surface rain rate comes mainly from that of convective rain rate. When radiative effects of ice clouds are excluded in the experiment, SST29NIR produces a larger positive diurnal anomaly of convective rainfall in hours 7–9 and evening hours and a larger negative diurnal anomaly in the afternoon than SST29

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6 Microphysical and Radiative Effects of Ice Clouds

Fig. 6.1 Vertical profiles of infrared cooling rate averaged from day 31 to day 40 in SST29 (solid), SST29NIR(dash), and SST29NIM (dot). Unit is oC d−1 (After Zhou and Li 2011)

does. The exclusion of ice microphysical effects yields negative difference in diurnal anomaly of convective rainfall in hours 7–9 and evening hours and positive difference in the afternoon. The stratiform rainfall is less sensitive to both microphysical and radiative effects of ice clouds.

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

143

a

b

c

d

e

Fig. 6.2 Diurnal anomalies of (a) PS, (b) QWVT, (c) QWVF, (d) QWVE, and (e) QCM in water-vapor-related surface rainfall budgets over convective regions in SST29 (solid ), SST29NIM (dash), and SST29NIR (dot). Units are mm h−1 (After Ping and Luo 2009)

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

c

d

e

Fig. 6.3 As in Fig. 6.2 except over raining stratiform regions

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

145

The diurnally perturbed water-vapor-related surface rainfall budgets reveal that the diurnal anomalies of water vapor convergence rates in the three experiments are larger than those of change and convergence of cloud mass over convective regions (Fig. 6.2). Thus, the differences in diurnal anomaly of convective rain rate for SST29NIR-SST29 and SST29NIM-SST29NIR are mainly associated with the differences in diurnal anomaly of water vapor convergence over convective regions. Over raining stratiform regions (Fig. 6.3), the diurnal anomalies of local water vapor change, water vapor convergence, and hydrometeor change/convergence have similar magnitudes in hourly fluctuations in the three experiments, which result in similar diurnal anomalies of stratiform rain rates. The diurnal anomalies of water vapor convergence over convective and rainfall-free (Fig. 6.4) regions are larger than those over raining stratiform regions and they nearly are out of phase. As a result, the diurnal anomalies of water vapor convergence rates over convective regions are approximately balanced by those of water vapor divergence rates over rainfall-free regions. Over rainfall-free regions, the diurnal anomalies of water vapor divergence rates are nearly compensated by those of local water vapor change rates. Since the diurnal anomalies of local water vapor change rates over rainfall-free regions are much larger than those over raining regions, the diurnal anomalies of model domain mean local water vapor change rates result mainly from those of local water vapor change rates over rainfall-free regions. The diurnally perturbed thermally-related surface rainfall budgets show that the differences in diurnal anomaly of convective rainfall for SST29NIR-SST29 are mainly related to the differences in diurnal anomaly of heat divergence over convective regions (Fig. 6.5). The difference in diurnal anomaly of stratiform rainfall between the two experiments is much smaller than that of convective rainfall due to similar stratiform rainfall processes (Fig. 6.6). Thus, the difference in diurnal anomaly of heat divergence over convective regions for SST29NIR-SST29 is mainly compensated by the difference over rainfall-free regions (Fig. 6.7). Over rainfallfree regions, the magnitudes of difference in diurnal anomaly of radiative heating for SST29NIR-SST29 are much smaller than those of difference in diurnal anomaly of local thermal change and heat divergence rates. The exclusion of ice radiative effects in SST29NIR leads to positive difference in diurnal anomaly of radiative heating from 1 to 3 km with maxima during nighttime and positive difference during daytime and negative difference during nighttime from 6 to 17 km (Fig. 6.8a), but the cancellation between positive and negative difference in mass integration causes small difference in diurnal anomaly of radiative heating between the two experiments. The responses of heat divergence to the exclusion of ice radiative effects are limited below 10 km as indicated by Fig. 6.8c, where maximum difference in heat divergence responds to relatively small difference in radiative heating. The difference in heat divergence in Fig. 6.8c roughly shows the time scale of about 8 h. This sub-diurnal variation of the difference over rainfall-free regions by the exclusion of ice radiative effects enhances the magnitude of diurnal anomaly of convective rainfall in SST29NIR. The difference in diurnal anomaly of convective rainfall for SST29NIMSST29NIR is significantly larger than that of stratiform rainfall as a result of similar

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

c

d

Fig. 6.4 Diurnal anomalies of (a) QWVT, (b) QWVF, (c) QWVE, and (d) QCM over rainfall-free regions in SST29 (solid ), SST29NIM (dash), and SST29NIR (dot). Units are mm h−1 (After Ping and Luo 2009)

stratiform rainfall processes in the two experiments (Figs. 6.5 and 6.6). The difference in diurnal anomaly of convective rainfall for SST29NIM-SST29NIR is mainly associated with that of heat divergence over convective regions, which is mainly balanced by the difference over rainfall-free regions (Fig. 6.7). The diurnal anomaly of SRAD in SST29NIM follows that in SST29NIR, indicating no ice microphysical

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

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a

b

c

d

e

Fig. 6.5 Diurnal anomalies of (a) PS, (b) SHT, (c) SHF, (d) SRAD, and (e) QCM in thermally-related surface rainfall budgets over convective regions in SST29 (solid ), SST29NIM (dash), and SST29NIR (dot). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

c

d

e

Fig. 6.6 As in Fig. 6.5 except over raining stratiform regions

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

149

a

b

c

d

Fig. 6.7 Diurnal anomalies of (a) SHT, (b) SHF, (c) SRAD, and (d) QCM over rainfall-free regions in SST29 (solid), SST29NIM (dash), and SST29NIR (dot). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

effects on diurnal anomaly of radiative heating. The difference in diurnal anomaly of vertical profile of radiative heating in Fig. 6.8b shows maximum negative difference during daytime and maximum positive difference during nighttime at 18 km. The difference from 1 to 10 km is out of phase with that from 11 to 19 km but the magnitudes of former are smaller than those of latter. The positive difference appears

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6 Microphysical and Radiative Effects of Ice Clouds

Fig. 6.8 Diurnal anomalies of vertical profiles of radiating heating (SRAD; upper panel) and heat divergence (SHF; lower panel) over rainfall-free regions. (a) and (c) denote SST29NIR-SST29 whereas (b) and (d) present SST29NIM-SST29NIR. Unit is 10−6 h−1

near the surface. The large offset in mass integration makes small difference in diurnal anomaly of SRAD. The difference in diurnal anomaly of vertical profile of heat divergence in Fig. 6.8d reveals maximum difference from 1 to 10 km where relatively small difference in radiative heating occurs. The differences in diurnal anomaly of vertical profile of heat divergence for SST29NIM-SST29NIR (Fig. 6.8d) and SST29NIR-SST29 (Fig. 6.8c) nearly are out of phase.

6.2.3

Vertical Structures of Thermal and Water Vapor Budgets

The difference in temperature tendency for SST29-SST29NIR is positive below 16 km whereas it is negative above 16 km (Fig. 6.9a); it appears to suggest that the inclusion of radiative effects of ice clouds produces a tropospheric warming. The positive difference in temperature is mainly caused by the positive difference in radiation,

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

151

a

b

Fig. 6.9 Vertical profiles of differences in (a) heat budgets (oC day−1) and (b) vapor budgets (g kg−1 day−1) for SST29-SST29NIR. Solid, dash, dot, and dot dash lines in (a) denote differences in local temperature change, latent heat, convergence of vertical heat flux, and radiative heating, respectively. Solid, dash, and dot lines in (b) denote differences in local water vapor change, condensation and convergence of vertical vapor flux, respectively (After Li and Zou 2009)

except near the surface where it is primarily determined by the positive difference in convergence of vertical heat flux. The positive difference in latent heat also plays a role in determining the positive difference in temperature tendency in the upper troposphere. The positive difference in radiation is mainly associated with the positive differences in IR cooling below 8 km and in solar heating from 8 to 14 km (Fig. 6.10). This implies that the radiative effect of water clouds mainly acts on IR cooling whereas the radiative effect of ice clouds mainly acts on solar heating. The positive difference

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6 Microphysical and Radiative Effects of Ice Clouds

Fig. 6.10 Vertical profiles of differences in radiation (solid ), solar heating (dash), and IR cooling (dot) for SST29-SST29NIR. Unit is oCday−1 (After Li and Zou 2009)

in water vapor tendency is mostly caused by the positive difference in the net condensation, except between 8 and 9 km where it is determined by the positive difference in the convergence of vertical water vapor flux (Fig. 6.9b). The negative difference in water vapor tendency is determined by the negative difference in condensation. Compared to SST29NIR, the inclusion of cloud radiative effects in SST29 enhances ice clouds with more deposition and more consumption of water vapor and more latent heat in the upper troposphere, and suppresses water clouds with less condensation and less consumption of water vapor and less latent heat. The difference in water vapor tendency for SST29-SST29NIR is positive below 10 km whereas it is negative above 10 km. The difference in water vapor tendency for SST29-SST29NIR generally follows the difference in net condensation. Over raining stratiform regions, the difference in local temperature change is insensitive to radiative effects of ice clouds because the cancellation between the weakened heat divergence resulting from radiative effects of ice clouds and the reduced latent heat above 8 km and the decreased heat convergence and the weakened latent heat loss due to the evaporation of rain below 6 km (Fig. 6.11a). The differences in convergence of vertical heat flux and radiation are insensitive to radiative effects of ice clouds. The decrease in heat divergence above 8 km over raining stratiform regions is associated with the decrease in heat convergence over clear sky regions. The decrease in local atmospheric drying around 4–7 km and the increase in local atmospheric moistening near the surface are mainly associated with the enhancement in convergence of vertical vapor flux (Fig. 6.11b). The enhanced local atmospheric drying around 1–4 km is related to the weakened convergence of vertical vapor flux and reduced net condensation. Local atmospheric change from drying in SST29NIR to moistening in SST29 near the surface corresponds to the enhanced convergence of vertical vapor flux.

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

153

a

b

Fig. 6.11 Contributions from raining stratiform regions to differences in vertical profiles in (a) model domain mean heat budget (oCday−1) and (b) water vapor budget (g kg−1 day−1) for SST29SST29NIR. Solid, dash, dot, long dash, and dot dash lines in (a) denote differences in local temperature change, latent heat, convergence of vertical heat flux, heat convergence, and radiative heating, respectively. Solid, dash, dot, and long dash lines in (b) denote differences in local water vapor change, condensation, convergence of vertical vapor flux, and water vapor convergence, respectively (After Ping et al. 2011)

Over convective regions, the decreases in heat divergence and latent heat caused by radiative effects of ice clouds are largely balanced out to produce a small difference in local temperature change for SST29-SST29NIR (Fig. 6.12a). The difference in radiation is small. Convergence of vertical heat flux shows a decrease in the mid troposphere and divergence of vertical heat flux has a decrease near the surface, which also contribute to the small difference in local temperature change. The decreases in heat

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

Fig. 6.12 As in Fig. 6.11 except for contributions from convective regions

divergence and latent heat result partly from the decrease in fractional coverage of convective regions from 3.5% in SST29NIR to 3.0% in SST29. The decreased heat divergence over convective regions corresponds to the decreased heat convergence over clear sky regions. The decrease in local atmospheric moistening resulting from radiative effects of ice clouds generally occurs above 1.5 km, which is largely related to the decrease in convergence of vertical vapor flux as a result of the cancellation between the decreases in net condensation and vapor convergence (Fig. 6.12b). Near the surface, there is a decrease in local atmospheric drying, which is mainly associated with the decrease in net condensation due to the cancellation between the decreases in divergence of vertical vapor flux and vapor convergence. The reduction in convergence of vertical vapor flux and the decrease in net condensation are caused by the shrink of convective areas from SST29NIR to SST29.

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

155

a

b

Fig. 6.13 As in Fig. 6.11 except for contributions from non-raining regions

Since the differences in radiation for SST29-SST29NIR are negligibly small over raining regions, the vertical profile of difference in the mean radiation is similar to the vertical profile of difference in radiation over non-raining regions (Fig. 6.13a). Over non-raining regions, the decreases in local atmospheric warming resulting from radiative effects of ice clouds associated with radiative change from heating in SST29NIR to cooling in SST29 above 13 km. The local atmospheric change from cooling in SST29NIR to warming in SST29 from 6 to 13 km is related to the decrease in radiative cooling and the increase in latent heat release. The temperature from 4 to 6 km is less sensitive to radiative effects of ice clouds as a result of offset between the reductions in heat convergence and radiative cooling. The decrease in local atmospheric cooling below 4 km is associated with the decrease in radiative cooling below 4 km and the increase in heat convergence

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

Fig. 6.14 Vertical profiles of differences in (a) heat budgets (oC day−1) and (b) vapor budgets (g kg −1 day−1) for SST29NIR-SST29NIM. Solid, dash, dot, and dot dash lines in (a) denote differences in local temperature change, latent heat, convergence of vertical heat flux, and radiative heating, respectively. Solid, dash, and dot lines in (b) denote differences in local water vapor change, condensation and convergence of vertical vapor flux, respectively (After Li and Zou 2009)

near the surface. The increase in local atmospheric drying caused by radiative effects of ice clouds is related to the enhancement in the net condensation from 10 to 16 km (Fig. 6.13b). The decrease in local atmospheric drying from 2 to 6 km corresponds to the reduction in water vapor divergence. The reduction in local atmospheric moistening is associated with the suppressed convergence of vertical vapor flux. The vertical structure of the difference in temperature tendency for SST29NIRSST29NIM (Fig. 6.14a) is nearly out of phase with that for SST29-SST29NIR.

6.2

Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale…

157

The small negative difference in temperature tendency for SST29NIR-SST29NIM below 13 km is mainly determined by the negative differences in convergence of vertical heat flux below 4 km and radiative heating from 4 to 13 km and latent heat around 10 km. The large positive difference in temperature tendency for SST29NIR-SST29NIM above 13 km is mainly caused by the positive difference in radiative heating. The difference in water vapor tendency for SST29NIRSST29NIM generally is negative and follows the negative difference in net condensation (Fig. 6.14b). Since stratiform clouds mainly consist of ice clouds, the exclusion of ice clouds leads to the significant decay of stratiform clouds as indicated by the fact that fractional coverage of stratiform rainfall in SST29NIM (1.8%) is about a half of that in SST29NIR (3.6%). Fractional coverage of convective rainfall is insensitive to ice clouds. Over raining stratiform regions, the local temperatures are generally unchanged due to the balances between the enhanced heat convergence and the decreased latent heat due to the increased evaporation of rain below 5 km and the increases in latent heat and heat divergence above 5 km (Fig. 6.15a). The enhancement in local atmospheric drying caused by microphysical effects of ice clouds is associated with the increased vapor divergence near the surface and the increased divergence of vertical vapor flux around 4–6 km (Fig. 6.15b). The decrease in local atmospheric moistening above 6 km results from the decrease in convergence of vertical vapor flux around 6–8 km and the increase in net condensation above 8 km. The local atmospheric change from moistening in SST29NIM to drying in SST29NIR near the surface corresponds to the decrease in vapor divergence. Over convective regions, the difference in local heat change is much smaller than the differences in heat divergence and latent heat because large cancellation between the enhancements in heat divergence and latent heat caused by microphysical effects of ice clouds (Fig. 6.16a). The increase in local atmospheric moistening resulting from microphysical effects of ice clouds corresponds to the increased convergence of vertical vapor flux as a result of cancellation between the increases in vapor convergence and net condensation around 4–8 km and the increased vapor convergence around 2 km (Fig. 6.16b). The reduction in local atmospheric moistening around 3 km is related to the weakened convergence of vertical vapor flux due to the offset between the increases in vapor convergence and net condensation. The enhanced local atmospheric drying near the surface is associated with the enhanced net condensation as a result of the balance between the increases in vapor convergence and divergence of vertical vapor flux. Over non-raining regions, the increased local atmospheric warming caused by microphysical effects of ice clouds is associated with the radiative change from cooling in SST29NIM to heating in SST29NIR above 13 km (Fig. 6.17a). The local atmospheric change from warming in SST29NIM to cooling in SST29NIR from 2 to 13 km is related to the increase in radiative cooling from 4 to 13 km and the decrease in latent heat release from 2 to 4 km. The local atmospheric cooling caused by microphysical effects of ice clouds near the surface corresponds to the enhanced radiative cooling. The enhanced local atmospheric drying caused by microphysical effects of ice clouds are associated with the enhanced net condensation

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

Fig. 6.15 Contributions from raining stratiform regions to differences in vertical profiles in (a) model domain mean heat budget (oC day−1) and (b) water vapor budget (g kg−1 day−1) for SST29NIR-SST29NIM. Solid, dash, dot, long dash, and dot dash lines in (a) denote differences in local temperature change, latent heat, convergence of vertical heat flux, heat convergence, and radiative heating, respectively. Solid, dash, dot, and long dash lines in (b) denote differences in local water vapor change, condensation, convergence of vertical vapor flux, and water vapor convergence, respectively (After Ping et al. 2011)

from 10 to 12 km and the increase in water vapor divergence and divergence of vertical vapor flux from 4 to 6 km and the increase in water vapor divergence around 2 km (Fig. 6.17b). The increase in local atmospheric moistening near the surface is related to the enhanced convergence of vertical vapor flux and the reduced water vapor divergence.

6.3

Effects of Ice Clouds on Severe Tropical Storm Rainfall

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a

b

Fig. 6.16 As in Fig. 6.15 except for contributions from convective regions

6.3

Effects of Ice Clouds on Severe Tropical Storm Rainfall

On 15 July, the exclusion of radiative effects of ice clouds increases model domain mean surface rain rate from BILIS to BILISNIR (Fig. 6.18a). The removal of microphysical effects of ice clouds decreases the mean rain rate from BILISNIR to BILISNIM (Fig. 6.19a). Since the increase in the mean rain rate caused by the exclusion of radiative effects of ice clouds is much smaller than the decrease in the mean rain rate resulting from the removal of microphysical effects of ice clouds,

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

Fig. 6.17 As in Fig. 6.15 except for contributions from non-raining regions

the elimination of ice clouds (both radiative and microphysical effects of ice clouds) reduces the mean rain rate from BILIS to BILISNIM (Fig. 6.20a). On 16 July, the exclusion of radiative effects of ice clouds and the removal of microphysical effects of ice clouds decrease the mean rain rate. As a result, the elimination of ice clouds reduces the mean rain rate. The analysis of water-vapor-related surface rainfall budgets shows that the increase in the mean rain rate caused by the exclusion of radiative effects of ice clouds is associated with the decrease in the mean local atmospheric moistening on 15 July, whereas the reduction in the mean rain rate resulting from the removal of

6.3

Effects of Ice Clouds on Severe Tropical Storm Rainfall

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a

b

c

Fig. 6.18 Differences in 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 for BILISNIR-BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1

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6 Microphysical and Radiative Effects of Ice Clouds

a

b

c

Fig. 6.19 As in Fig. 6.18 except for BILISNIM-BILISNIR

radiaitve effects of ice clouds is related to the decrease in the mean hydrometeor loss on 16 July (Fig. 6.18a). The elimination of microphysical effects of ice clouds decreases the mean rain rate primarily through the reduction in the mean hydrometeor loss and the enhancement in the mean local atmospheric moistening in the two

6.3

Effects of Ice Clouds on Severe Tropical Storm Rainfall

163

a

b

c

Fig. 6.20 As in Fig. 6.18 except for BILISNIM-BILIS

days (Fig. 6.19a). Since the rainfall processes are much sensitive to microphysical effects of ice clouds than to radiative effects of ice clouds, the removal of ice clouds decreases the mean rain rate mainly through the suppressed mean hydrometeor loss and the enhanced mean local atmospheric moistening (Fig. 6.20a).

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Table 6.4 Breakdown of daily and model domain means of QCM to QCWM, QRM, and QIWPM in BILIS, BILISNIR, and BILISNIM and their differences for BILISNIR-BILIS, BILISNIMBILISNIR, and BILISNIM-BILIS on (a) 15 July and (b) 16 July 2006. Unit is mm h−1 (After Wang et al. 2010) C CNIR CNIM CNIR-C CNIM-CNIR CNIM-C (a) 15 July QCM 0.073 0.060 −0.258 −0.013 −0.318 −0.331 QCWM −0.020 0.007 −0.306 0.027 −0.313 −0.286 QRM 0.112 0.090 0.048 −0.022 −0.042 −0.064 QIWPM −0.019 −0.037 0.000 −0.018 0.037 0.019 (b) 16 July QCM 0.103 QCWM −0.011 QRM 0.092 QIWPM 0.022

0.050 0.013 0.099 −0.062

−0.010 −0.094 0.084 0.000

−0.053 0.024 0.007 −0.084

−0.060 −0.107 −0.015 0.062

−0.113 −0.083 −0.008 −0.022

The change of QCM in three experiments impacts the mean rain rate. Thus, QCM is further broken down into QCM = QCWM + QRM + QIWPM ,

(6.1)

Here, QCWM, QRM, and QIWPM are hydrometeor change/convergence from cloud water, rain, and ice clouds, respectively. The slowdown in the mean hydrometeor loss resulting from the exclusion of radiative effects of ice clouds is associated with the slowdown in the mean rain hydrometeor loss from 0.112 mm h−1 in BILIS to 0.090 mm h−1 in BILISNIR and the enhancement in the mean ice hydrometeor gain (QIWPM) from −0.019 mm h−1 in BILIS to −0.037 mm h−1 in BILISNIR on 15 July, whereas it is related to the mean ice hydrometeor change from loss in BILIS (0.022 mm h−1) to gain in BILISNIR (−0.062 mm h−1) on 16 July (Table 6.4). The mean hydrometeor change from loss in BILISNIR to gain in BILISNIM caused by the exclusion of microphysical effects of ice clouds results primarily from cloud water hydrometeor (−0.313 mm h−1 on 15 July and −0.107 mm h−1 on 16 July for BILISNIM-BILISNIR). The large mean water hydrometeor gain in BILISNIM is consistent with the results in the sensitivity experiment with the total removal of ice clouds during TOGA COARE when the vapor condensation cannot be consumed by the collection of cloud water by rain and the autoconversion of cloud water to rain (Gao et al. 2006). With the total exclusion of ice clouds, the model produces a large mean water hydrometeor gain, which leads to the decrease in the mean rain rate in BILISNIM. The differences in model domain mean thermally-related surface rainfall budget for BILISNIR-BILIS show that the exclusion of radiative effects of ice clouds increases the mean radiative cooling but it decreases the mean heat divergence and slows down the decrease of the mean hydrometeor concentration (Fig. 6.21a), which leads to the insensitivity of the mean rainfall to radiative effects of ice clouds. The negative difference in the mean rain rate for BILISNIM-BILISNIR on 15 July is primarily associated with the mean hydrometeor change from loss in BILISNIR to gain in BILISNIM and the reduction in the mean heat divergence caused by the

6.3

Effects of Ice Clouds on Severe Tropical Storm Rainfall

165

a

b

c

Fig. 6.21 Differences in 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) (a) BILISNIR-BILIS, (b) BILISNIM-BILISNIR, and (c) BILISNIM-BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1

exclusion of microphysical effects of ice clouds (Fig. 6.21b). The reduction in the mean rain rate caused by the exclusion of microphysical effects of ice clouds on 16 July is related to the slowdown in the mean heat divergence and the decreases in the mean radiative cooling. The decreases in the mean rain rate caused by the exclusion

166

6 Microphysical and Radiative Effects of Ice Clouds

of ice clouds are associated with similar thermal processes except that the exclusion of microphysical effects of ice clouds decreases the mean radiative cooling whereas the exclusion of ice clouds increases the mean radiative cooling (Fig. 6.21b, c). The exclusion of radiative effects of ice clouds decreases stratiform rain rate in the two days (Fig. 6.18b). The decreases in stratiform rainfall are associated with the decreases in water vapor convergence in the 2 days, which are largely offset by the decreases in local atmospheric moistening and the increases in the transport of hydrometeor concentration form convective regions to raining stratiform regions. The removal of microphysical effects of ice clouds decreases stratiform rainfall on 15 July primarily through hydrometer change from loss/convergence in BILISNIR to gain/divergence in BILISNIM whereas it increases stratiform rainfall through the increase in water vapor convergence on 16 July (Fig. 6.19b). The effects of ice clouds on stratiform rainfall are determined by the effects of microphysical effects of ice clouds (Fig. 6.19b, c). The elimination of radiative effects of ice clouds increases convective rainfall through the increases in water vapor convergence in the 2 days (Fig. 6.18c). The removal of microphysical effects of ice clouds decreases convective rainfall through the decreases in water vapor convergence and local atmospheric drying in the 2 days (Fig. 6.19c). The microphysical effects of ice clouds on convective rainfall are larger than the radiative effects of ice clouds on convective rainfall. As a result, the exclusion of ice clouds decreases convective rainfall through the decrease in local atmospheric drying and hydrometeor change from loss/convergence in BILIS to gain/divergence in BILISNIM on 15 July and through the reduced local atmospheric drying and decreased water vapor convergence on 16n July (Fig. 6.20c).

6.4

Effects of Ice Clouds on Pre-summer Heavy Rainfall

The exclusion of radiative effects of ice clouds slightly decreases model domain mean surface rain rate on 4 June, whereas it increases the mean rain rate on 6 and 7 June (Fig. 6.22a). The decrease in the mean rainfall caused by the removal of radiative effects of ice clouds is associated with the reduced mean hydrometeor loss as a result of the offset between the enhanced mean local atmospheric drying and suppressed mean water vapor convergence on 4 June. The increases in the mean rainfall resulting from the elimination of radiative effects of ice clouds is related to the increases in the mean local atmospheric drying and mean hydrometeor loss on 6 and 7 June and the suppressed water vapor divergence on 7 June. The exclusion of microphysical effects of ice clouds decreases the mean rainfall on 4, 6, and 7 June (Fig. 6.23a). The decrease in the mean rainfall caused by the removal of microphysical effects of ice clouds is associated with the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM on 4 June, which is largely offset by the enhanced mean local atmospheric drying. The reduction in the mean rainfall resulting from the elimination of microphysical effects of ice clouds is related to the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM and the decrease in

6.4

Effects of Ice Clouds on Pre-summer Heavy Rainfall

167

a

b

c

Fig. 6.22 Differences in 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 for PSRNIR-PSR on 4 June 2008 (open bar), 6 June (black bar), and 7 June (grey bar). Unit is mm h−1

168

6 Microphysical and Radiative Effects of Ice Clouds

a

b

c

Fig. 6.23 As in Fig. 6.22 except for PSRNIM-PSRNIR

the mean local atmospheric drying on 6 June. The decreased mean rainfall induced by the exclusion of microphysical effects of ice clouds corresponds to the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM and the decrease in the mean surface evaporation flux on 7 June. The removal of ice clouds from the

6.4

Effects of Ice Clouds on Pre-summer Heavy Rainfall

169

a

b

c

Fig. 6.24 As in Fig. 6.22 except for PSRNIM-PSR

model decrease the mean rainfall through the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM in the 3 days and reduced mean water vapor convergence on 4 June and the decreased mean local atmospheric drying on 6 June and the suppressed mean surface evaporation flux on 7 June (Fig. 6.24a).

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6 Microphysical and Radiative Effects of Ice Clouds

The model domain mean thermally-related surface rainfall budgets in the three experiments are analyzed since radiation is a term in the budget. The exclusion of radiative effects of ice clouds enhances the mean radiative cooling whereas it decreases the mean heat divergence during the life span of pre-summer rainfall event (Fig. 6.25a). On 4 June, the decrease in the mean rain rate caused by the exclusion of radiative effects of ice clouds is associated with the increase in the mean local atmospheric cooling, the decrease in the mean heat divergence, and the reduction in the mean hydrometeor loss although the mean radiative cooling is enhanced. On 6 and 7 June, the increases in the mean rain rate are related to the decreases in the mean local atmospheric cooling and the increases in the mean radiative cooling and the mean hydrometeor loss. The decrease in the mean rain rate resulting from the exclusion of microphysical effects of ice clouds on 4 June is small because the reduction in the mean local atmospheric cooling is largely offset by the decreases in the mean heat divergence and the mean radiative cooling and the mean hydrometeor gain in PSRNIM (Fig. 6.25b). On 6 June, the exclusion of microphysical effects of ice clouds significantly reduces the mean rain rate primarily through the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM. On 7 June, the slowdowns in the mean hydrometeor change from loss in PSRNIR to gain in PSRNIM and the mean local atmospheric cooling lead to the significant weakening of reduction in the mean rain rate. The decrease in the mean rain rate caused by the total exclusion of ice clouds on 4 June comes from those caused by the removal of both radiative and microphysical effects of ice clouds (Fig. 6.25c). The total removal of ice clouds decreases the mean rainfall through the decrease in the mean rainfall caused by the elimination of microphysical effects of ice clouds on 6 June. On 7 June, the total elimination of ice clouds slightly increases the mean rainfall through the increase in the mean rainfall caused by the exclusion of radiative effects of ice clouds. The model domain mean surface rain rate consists of stratiform and convective rain rate. On 4 June, the large reduction in the mean rainfall caused by the exclusion of radiative effects of ice clouds results from the reduction in convective rainfall whereas the small reduction in the mean rainfall caused by the exclusion of microphysical effects of ice clouds results from cancellation between the reduced stratiform rainfall and enhanced convective rainfall (Figs. 6.22 and 6.23). The reduced convective rainfall caused by the exclusion of radiative effects of ice clouds is associated with the weakened local atmospheric cooling over convective regions. The reduced stratiform rain rate and enhanced convective rain rate caused by the exclusion of ice microphysical effects are mainly associated with the weakened transport of hydrometeor concentration from convective regions to raining stratiform regions; these also are contributed to by the reduced water vapor convergence over raining stratiform regions and the enhanced water vapor convergence over convective regions. The total exclusion of ice clouds leads to the reduction in stratiform rainfall and enhancement in convective rainfall (Fig. 6.24). On 6 June, the enhanced mean surface rain rate caused by the exclusion of ice radiative effects comes from the enhanced convective rainfall; this appears to be

6.4

Effects of Ice Clouds on Pre-summer Heavy Rainfall

171

a

b

c

Fig. 6.25 Differences in 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) for (a) PSRNIR-PSR, (b) PSRNIM-PSRNIR, and (c) PSRNIM-PSR on 4 June 2008 (open bar), 6 June (black bar), and 7 June (grey bar). Unit is mm h−1

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caused by the weakened transport of hydrometeor concentration from convective regions to raining stratiform regions and enhanced local atmospheric cooling over convective regions. The total exclusion of ice microphysics reduces stratiform rain rate but it barely change convective rain rate due to cancellation between ice radiative and microphysical effects on convective rainfall. On 7 June, the enhanced mean surface rain rate caused by the exclusion of ice radiative effects that is maintained from the previous day comes mainly from the enhanced stratiform rain rate, which is mainly related to the weakened water vapor divergence over the weakened local atmospheric drying. The reduction in the mean surface rainfall caused by the exclusion of ice microphysical effects is significantly slowed down from the previous day; this is mainly caused by the weak enhancement in convective rainfall compared to the significant reduction in convective rainfall on 6 June. This is related to the local atmospheric change from moistening on 6 June to drying on 7 June. The exclusion of ice clouds reduces stratiform rain rate but it enhances convective rain rate.

References Fovell RG, Ogura Y (1988) Numerical simulation of a midlatitude squall line in two dimensions. J Atmos Sci 45:3846–3879 Fowler LD, Randall DA, Rutledge SA (1996) Liquid and ice cloud microphysics in the CSU general circulation model. Part I: model description and simulated microphysical processes. J Clim 9:489–529 Gao S, Ran L, Li X (2006) Impacts of ice microphysics on rainfall and thermodynamic processes in the tropical deep convective regime: a 2D cloud-resolving modeling study. Mon Weather Rev 134:3015–3024 Grabowski WW (2003) Impact of ice microphysics on multiscale organization of tropical convection in two-dimensional cloud-resolving simulations. Q J R Meteorol Soc 129:67–81 Grabowski WW, Moncrieff MW (2001) Large-scale organization of tropical convection in twodimensional explicit numerical simulations. Q J R Meteorol Soc 127:445–468 Grabowski WW, Wu X, Moncrieff MW (1999) Cloud-resolving model of tropical cloud systems during Phase III of GATE. Part III: effects of cloud microphysics. J Atmos Sci 56:2384–2402 Heymsfield AJ, Donner LJ (1990) A scheme for parameterization ice-cloud water content in general circulation models. J Atmos Sci 47:1865–1877 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, Zou CZ (2009) Effects of sea surface temperature, radiation, cloud microphysics, and diurnal variations on vertical structures of tropical tropospheric temperature: a two-dimensional equilibrium cloud-resolving modeling study. Meteorol Atmos Phys 105:85–98 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 Li X, Sui CH, Lau KM, Tao WK (2005) Tropical convective responses to microphysical and radiative processes: a 2D cloud-resolving modeling study. Meteorol Atmos Phys 90:245–259 Liu C, Moncrieff MW (1997) Dynamic influence of microphysics in tropical squall lines: a numerical study. Mon Weather Rev 125:2193–2210 Liu Y, Zhang DL, Yau MK (1997) A multiscale numerical study of HurricaneAndrew (1992). Part I: explicit simulation and verification. Mon Weather Rev 125:3073–3093

References

173

Lord SJ, Willoughby HE, Piotrowicz JM (1984) Role of a parameterized ice phase microphysics in an axisymmetric, nonhydrostatic tropical cyclone model. J Atmos Sci 41:2836–2848 McCumber M, Tao WK, Simpson J, Penc R, Soong ST (1991) Comparison of ice –phase microphysical parameterization schemes using numerical simulations of tropical convection. J Appl Meteorol 30:985–1004 Nicholls ME (1987) A comparison of the results of a two-dimensional numerical simulation of a tropical squall line with observations. Mon Weather Rev 115:3055–3077 Ping F, Luo Z (2009) Microphysical and radiative effects of ice clouds on diurnal variations of tropical convective and stratiform rainfall. Atmos Res 93:862–873, (c) Elsevier. Reprinted with permission Ping F, Luo Z, Li X (2007) Microphysical and radiative effects of ice microphysics on tropical equilibrium states: a two-dimensional cloud-resolving modeling study. Mon Weather Rev 135:2794–2802, (c) American Meteorological Society. Reprinted with permission Ping F, Luo Z, Li X (2011) Regional dependence of microphysical and radiative effects of ice clouds on vertical structures of tropical tropospheric temperature. Meteorol Atmos Phys 112:29–39 Ramanathan V, Pitcher EJ, Malone RC, Blackmon ML (1983) The response of a spectral general circulation model to refinements in radiative processes. J Atmos Sci 40:605–630 Slingo JM (1987) The development and verification of a cloud prediction scheme for the ECMWF model. Q J R Meteorol Soc 113:899–927 Tao WK, Simpson J (1989) Modeling study of a tropical squall-type convective line. J Atmos Sci 46:177–202 Tao WK, Simpson J, Soong ST (1991) Numerical simulation of a subtropical squall line over the Taiwan Strait. Mon Weather Rev 119:2699–2723 Wang D, Li X, Tao WK (2010) Torrential rainfall responses to radiative and microphysical processes of ice clouds during a landfall of severe tropical storm Bilis (2006). Meteorol Atmos Phys 109:115–128 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 Willoughby HE, Jin HL, Lord SJ, Piotrowicz JM (1984) Hurricane structure and evolution as simulated by an axisymmetric, non-hydrostatic numerical model. J Atmos Sci 41:1169–1186 Wu X, Hall WD, Grabowski WW, Moncrieff MW, Collins WD, Kiehl JT (1999) Long-term evolution of cloud systems in TOGA COARE and their interactions with radiative and surface processes. Part II: effects of ice microphysics on cloud-radiation interaction. J Atmos Sci 56:3177–3195 Yoshizaki M (1986) Numerical simulations of tropical squall-line clusters: two-dimensional model. J Meteorol Soc Jpn 64:469–491 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 7

Cloud Radiative Effects

7.1

Introduction

Cloud radiative processes have important impacts on precipitation. The IR radiative cooling increases 14% and 31% of surface rain rate, respectively, in the simulations of squall over midlatitudes and tropics (Tao et al. 1993). The clear-sky IR cooling increases the surface rain rate by 15% whereas the reduction of IR cooling rate by the anvil cirrus decreases the surface rain rate by 10% (Fu et al. 1995). The diurnal variation of oceanic precipitation is insensitive to the cloud-radiation interaction (Xu and Randall 1995). The nocturnal IR cooling leads to the nocturnal rainfall peak through the reduction in saturation specific humidity (e.g., Sui et al. 1997, 1998). Water clouds, which are measured by the sum of mixing ratios of cloud water and raindrops, are a crucial ingredient of precipitation systems and associated radiative processes may impact thermal balance through the changes in radiation and latent heat and alter cloud budget through the change in net condensation and surface rainfall. In this chapter, cloud and water cloud radiative effects on rainfall processes are discussed through the comparison of sensitivity experiments with the control experiments in idealized case with zero large-scale vertical velocity and during the landfall of severe tropical storm Bilis (2006) and pre-summer heavy rainfall event over southern China in June 2008. The sensitivity experiments include SST29NCR, BILISNCR, and PSRNCR that exclude cloud radiative effects by setting total hydrometeor mixing ratios to zero in calculations of radiation, SST29NWR and PSRNWR that exclude radiative effects of water clouds by setting water hydrometeor mixing ratios to zero in calculations of radiation, SST29NIR and PSRNIR, and BILISNCRI that is identical to BILIS except in BILISNCRI the cloud-radiation interaction is not allowed and the vertical profiles of solar radiative heating and IR radiative cooling are replaced with the model domain mean vertical radiation profiles from BILIS. The following discussions are mainly based on the analysis of sensitivity experiments conducted by Ping et al. (2007), Gao and Li (2008), and Zhou and Li (2011) in Sect. 7.2, Wang et al. (2010) in Sect. 7.3, and Shen et al. (2011a, b) in Sect. 7.4.

X. Li and S. Gao, Precipitation Modeling and Quantitative Analysis, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-2381-8_7, © Springer Science+Business Media B.V. 2012

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7.2

Cloud Radiative Effects

Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity

7.2.1

Time-Mean Analysis

The difference in between SST29NCR and SST29NIR shows the radiative effects of water clouds on rainfall in the absence of radiative effects of ice clouds. Although similar cold and dry equilibrium states in SST29NCR and SST29NIR (Table 1.3), water-vapor-related surface rainfall budgets in SST29NCR differ from those in SST29NIR in four ways (Tables 6.1a and 7.1a). First, time and model domain mean surface rain rate is larger in SST9NCR than in SST29NIR because the local hydrometeor loss occurs in SST29NCR whereas the local hydrometeor gain appears in ST29NIR. Second, fractional coverage of convective regions is larger in SST29NCR than in SST29NIR whereas that of non-raining and raining stratiform regions is smaller. Third, surface evaporation rate over non-raining regions is slightly smaller in SST29NCR than in SST29NIR. Fourth, over raining stratiform regions, water vapor divergence rate in SST29NCR is twice larger than in SST29NIR, which leads to a larger water vapor convergence rate over convective regions in SST29NCR because of similar water vapor divergence rates in the two experiments.

Table 7.1 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 divergnece (SHF), surface sensible heat (SHS) , latent heat due to icerelated 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 SST29NCR. Units are % for fractional coverage, mm h−1 for the others (After Gao and Li (2008) and Zhou and Li 2011) Non-raining Raining stratiform Convective Model domain (a) regions regions regions mean FC 91.9 4.3 3.8 100 PS 0.000 0.069 0.129 0.198 QWVT −0.003 0.043 −0.027 0.013 QWVF −0.176 −0.035 0.211 0.000 QWVE 0.162 0.008 0.006 0.176 QCM 0.016 0.053 −0.061 0.008 (b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.012 −0.204 −0.025 0.000 0.201 0.016

Raining stratiform regions 0.069 0.027 −0.019 −0.001 0.003 0.006 0.053

Convective regions 0.129 −0.038 0.223 −0.001 −0.002 0.008 −0.061

Model domain mean 0.198 0.001 0.000 −0.027 0.001 0.214 0.008

7.2

Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero… Table 7.2 As in Table 7.1 except for those in SST29NWR Non-raining Raining stratiform Convective (a) regions regions regions FC 91.1 5.7 3.2 PS 0.000 0.057 0.089 QWVT −0.006 0.020 −0.009 QWVF −0.129 0.004 0.125 QWVE 0.130 0.005 0.002 QCM 0.005 0.028 −0.030 (b) PS SHT SHF SHS SLHLF SRAD QCM

Rainfall-free regions 0.000 0.012 −0.147 −0.014 −0.001 0.145 0.004

Raining stratiform regions 0.057 0.010 0.016 −0.001 0.001 0.003 0.028

Convective regions 0.089 −0.014 0.131 −0.001 0.000 0.003 −0.030

177

Model domain mean 100 0.146 0.005 0.000 0.137 0.003 Model domain mean 0.146 0.007 0.000 −0.016 0.000 0.152 0.002

The difference between SST29NWR and SST29 reveals the radiative effects of water clouds on rainfall in the presence of radiative effects of ice clouds. The time and model domain mean surface rain rate is larger in SST29NWR than in SST29 through the increase in the mean local atmospheric drying and the mean hydrometeor change from gain in SST29 to loss in SST29NWR (Tables 2.1a and 7.2a). The difference in time and model domain mean surface rain rate results from the difference in convective rain rate between the two experiments, which is associated with the difference in water vapor convergence over convective regions. Compared to SST29, the larger water vapor convergence over convective regions is caused by the larger water vapor divergence over non-raining regions in SST29NWR. The analysis of thermally-related surface rainfall budgets in SST29NIR and SST29NCR (Tables 6.1b and 7.1b) shows similar model domain mean radiative cooling terms and their components over rainfall-free regions. The increase in model domain mean surface rainfall in SST29NCR is related to the mean hydrometer change from gain in SST29NIR to loss in SST29NCR while the thermally-related precipitation processes are similar in the two experiments. The increase in the mean surface rainfall results from the increase in both convective and stratiform rainfall. The increase in convective rainfall corresponds to the increase in heat divergence over convective regions, whereas the increase in stratiform rainfall corresponds to the increases in local atmospheric warming and transport of hydrometeor from convective regions. The increase in the mean surface rainfall in SST29NWR is associated with the increase in the mean radiative cooling and the decrease in the mean hydrometeor concentration in SST29NWR and the increase in the mean hydrometeor concentration in SST29 (Tables 2.1b and 7.2b). The increase in the mean radiative cooling in SST29NWR is mainly related to the increase in radiative cooling over rainfall-free

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Table 7.3 (a) Infrared-cooling component (b) solar-heating component of SRAD over rainfall-free regions, raining stratiform regions, convective regions, and model domain mean averaged from days 31 to 40 in SST29, SST29NIR, SST29NCR, and SST29NWR. Unit is mm h−1 (After Zhou and Li 2011) Rainfall-free Raining stratiform Convective Model domain regions regions regions mean (a) Infrared-cooling component SST29 0.232 0.009 0.007 0.249 SST29NIR 0.294 0.008 0.009 0.311 SST29NCR 0.293 0.009 0.011 0.313 SST29NWR 0.237 0.008 0.007 0.252 (b) Solar-heating component SST29 −0.091 SST29NIR −0.092 SST29NCR −0.092 SST29NWR −0.092

−0.005 −0.003 −0.003 −0.005

−0.004 −0.003 −0.004 −0.003

−0.100 −0.098 −0.099 −0.099

regions; this leads to the increase in transport of heat from convective regions to rainfall-free regions and thus to the increase in convective rainfall. The radiative cooling term (SRAD) is a major thermal process associated with surface rainfall. The term contains IR-cooling and solar-heating components. Thus, the components are calculated and shown in Table 7.3. While the solar-heating terms are similar in all seven experiments (Table 7.3b), the differences in SRAD between the experiments come from the differences in infrared-cooling component (Table 7.3a). The model domain mean IR-cooling components are mainly determined by the infrared-cooling components over rainfall-free regions. Vertical profiles of the mean IR cooling show that the IR cooling is much stronger below 8 km in SST29NIR than in SST29 (Fig. 7.1) because the exclusion of radiative effects of ice clouds in SST29NIR enhances more IR cooling than in SST29 by allowing more IR radiation to space. SST29NCR has slightly larger IR cooling below 5 km and slightly smaller IR cooling above 5 km than SST29NIR does, which yields similar mass integrations of IR-cooling component of SRAD in both experiments. SST29NWR has slightly larger IR cooling below 10 km and slightly smaller IR cooling above 10 km than SST29 does, which leads to a slightly larger mass integration of IR-cooling component of SRAD in SST29NWR than in SST29. Note that the model with this horizontal and vertical resolution may not adequately simulate shallow cumulus clouds, which may be the reason why vertical profiles of IR cooling may not be very sensitive to radiative effects of water clouds.

7.2.2

Analysis of Diurnal Variation

The exclusion of cloud radiative effects mainly produces positive difference in diurnal anomaly of convective rainfall for SST29NCR-SST29 in hours 1–5 and negative difference in hours 14–18 (Fig. 7.2), which are mainly associated with

7.2

Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero…

179

Fig. 7.1 Vertical profiles of infrared cooling rate averaged from day 31 to day 40 in SST29 (solid), SST29NIR (short dash), SST29NCR (long dash), and SST29NWR (dot). Unit is °C day−1 (After Zhou and Li 2011))

the positive difference in diurnal anomaly of water vapor convergence in hours 1–5 and the negative difference in diurnal anomaly of water vapor convergence in hours 14–18, respective, over convective regions from the analysis of watervapor-related surface rainfall budgets in the two experiments. The negative difference in diurnal anomaly of QCM largely offsets the positive difference in diurnal anomaly of water vapor convergence in hours 1–5 whereas the positive difference in diurnal anomaly of QCM partially cancels the negative difference in diurnal anomaly of water vapor convergence in hours 14–18. The difference in stratiform rain rate between the two experiments is smaller than the difference in convective rain rate due to cancellation between the differences in diurnal anomalies of QWVT, QWVF, and QCM over raining stratiform regions (Fig. 7.3). The differences in diurnal anomaly of water vapor convergence over raining stratiform and rainfallfree regions (Fig. 7.4) between the two experiments have similar magnitudes;

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Cloud Radiative Effects

a

b

c

d

e

Fig. 7.2 Diurnal anomalies of (a) PS, (b) QWVT, (c) QWVF, (d) QWVE, and (e) QCM in water-vaporrelated surface rainfall budgets over convective regions in SST29 (solid), SST29NCR (short dash), SST29NIR (dot), and SST29NWR (long dash). Units are mm h−1

they balance the difference in diurnal anomaly of water vapor convergence over convective regions. The analysis of diurnally perturbed thermally-related surface rainfall budgets in SST29NCR and SST29 reveals that the positive difference in hours 1–5 is mainly

7.2

Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero…

181

a

b

c

d

e

Fig. 7.3 As in Fig. 7.2 except over raining stratiform regions

associated with positive differences in diurnal anomaly of SHF and SHT, which is largely offset by the negative difference in diurnal anomaly of QCM (Fig. 7.5) Similar convective rain rates in the two experiments during hours 6–11 are associated with similar convective rainfall processes, whereas similar convective rain rates during hours 12–14 is associated with cancellation between the negative difference in

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Cloud Radiative Effects

a

b

c

d

Fig. 7.4 Diurnal anomalies of (a) QWVT, (b) QWVF, (c) QWVE, and (d) QCM over rainfall-free regions in SST29 (solid), SST29NCR (short dash), SST29NIR (dot), and SST29NWR (long dash). Units are mm h−1

diurnal anomaly of SHT and positive differences in diurnal anomalies of SHT and QCM. The negative difference in convective rain rate during hours 14–18 is mainly related to the negative difference in diurnal anomaly of SHF. Similar convective rain rates in the two experiments during evening hours also are associated with similar convective rainfall processes. Stratiform rain rates in the two experiments are similar because of the offset between diurnal anomalies of SHF and QCM over raining stratiform regions (Fig. 7.6). The difference in diurnal anomaly of SHF over convective regions is significantly larger than that over raining stratiform regions, and is nearly balanced by that over rainfall-free regions (Fig. 7.7). The difference in diurnal

7.2

Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero…

183

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b

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e

Fig. 7.5 Diurnal anomalies of (a) PS, (b) SHT, (c) SHF, (d) SRAD, and (e) QCM in thermally-related surface rainfall budgets over convective regions in SST29 (solid), SST29NCR (short dash), SST29NIR (dot), and SST29NWR (long dash). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

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Cloud Radiative Effects

a

b

c

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Fig. 7.6 As in Fig. 7.5 except over raining stratiform regions

anomaly of SRAD for SST29NCR-SST29 is much smaller the diurnal anomalies of SRAD. The difference in diurnal anomaly of SHF is balanced by that of SHT over rainfall-free regions. Although the differences in diurnal anomaly of vertical profile of SRAD for SST29NCR-SST29 and SST29NIR-SST29 are similar (Figs. 7.8a and

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Fig. 7.7 Diurnal anomalies of (a) SHT, (b) SHF, (c) SRAD, and (d) QCM over rainfall-free regions in SST29 (solid), SST29NCR (short dash), SST29NIR (dot), and SST29NWR (long dash). SHS and SLHLF are not shown due to negligibly small diurnal anomalies. Units are mm h−1

6.8a), the responses of diurnal anomaly of SHF to the exclusion of cloud radiative effects in SST29NCR are different from the responses to the exclusion of radiative effects of ice clouds in SST29NIR. The positive difference in diurnal anomaly of SHF for SST29NCR-SST29 extends to hour 6 (Fig. 7.8c). The positive difference for SST29NCR-SST29 is weaker than that for SST29NIR-SST29 during hours 7–12. The difference for SST29NCR-SST29 becomes stronger than that for SST29NIRSST29 in late afternoon and evening hours. The different responses of heat divergence over rainfall-free regions to the exclusion of radiative effects of ice clouds in SST29NIR and cloud radiative effects in SST29NCR implies important responses

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Fig. 7.8 Diurnal anomalies of vertical profiles of radiating heating (SRAD; upper panel) and heat divergence (SHF; lower panel) over rainfall-free regions. (a) and (c) denote SST29NCR-SST29 whereas (b) and (d) present SST29NWR-SST29. Unit is 10−6 h−1

of diurnal variation to radiative effects of water clouds, which can be demonstrated by the comparison between SST29NWR and SST29. The exclusion of radiative effects of water clouds in SST29NWR produces negative difference in diurnal anomaly of convective rainfall for SST29NWRSST29 in hours 2–5 and 11–17 and positive difference in hours 19–21 (Fig. 7.2). The difference in diurnal anomaly of convective rainfall for SST29NWR-SST29 is mainly associated with the difference in diurnal anomaly of water vapor convergence over convective regions. The difference in diurnal anomaly of stratiform rainfall for SST29NWR-SST29 is generally smaller than that of convective rainfall because of offset between the differences in water-vapor-related stratiform rainfall processes in the two experiments (Fig. 7.3). The difference in diurnal anomaly of water vapor convergence over convective regions for SST29NWR-SST29 is offset by the differences in diurnal anomaly of water vapor convergence over both raining stratiform and rainfall-free regions (Fig. 7.4). The difference in diurnal anomaly of convective rain rate is mainly associated with the difference in diurnal anomaly of heat divergence over convective regions (Fig. 7.5), whereas the small difference in diurnal anomaly of stratiform rain rate is related to similar thermally-related surface rainfall processes (Fig. 7.6). Thus, the difference in diurnal anomaly of heat divergence over convective regions is mainly balanced by the difference over

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rainfall-free regions (Fig. 7.7). Over rainfall-free regions, the water radiative process does not have significant effects on diurnal anomaly of vertical profiles of radiative heating (Fig. 7.8b), whereas it affects the diurnal anomaly of heat divergence below 8 km (Fig. 7.8d). The difference in heat divergence over rainfall-free regions with the sub-diurnal scale of about 8 h slightly increases the diurnal magnitude of convective rainfall.

7.3

Effects of Cloud Radiative Process and Cloud-Radiation Interaction on Severe Tropical Storm Rainfall

Wang et al. (2010) showed similar temporal-zonal distributions of simulated surface rain rates in the three experiments (BILIS, BILISNCRI, and BILISNCR) on 15 July 2009 (Fig. 7.9). The heavy rainfall bands over 0–200 km were well organized earlier in the experiment without cloud-radiation interaction (BILISNCRI) than in the control experiment (BILIS) (Fig. 7.9a, b) during the late evening of 15 July – early morning of 16 July. The zonal length of rain rate of higher than 25 mm h−1 is shorter in BILISNCRI than in BILIS. In contrast, the heavy rainfall bands of higher than 25 mm h−1 in the experiment without cloud radiative effects (BILISNCR) split into three bands with the much shorter zonal lengths during the late evening of 15 July – early morning of 16 July (Fig. 7.9c).

Fig. 7.9 Time-zonal distributions of surface rain rates (mm h−1) simulated in (a) BILIS, (b) BILISNCRI, and (c) BILISNCR (After Wang et al. 2010)

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Fig. 7.10 Differences in 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 for BILISNCRI-BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1 (After Wang et al. 2010)

The time and model domain mean surface rain rates show that the exclusion of cloud-radiation interaction in BILISNCRI decreases the rainfall whereas the removal of cloud radiative effects in BILISNCR increases the rainfall compared to BILIS on 15 July (Figs. 7.10a and 7.11a). The exclusion of cloud radiative effects in BILISNCR and cloud-radiation interaction in BILISNCRI reduces the mean rainfall on 16 July. The difference in the mean surface rain rate between the sensitivity experiments

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Fig. 7.11 As in Fig. 7.10 except for BILISNCR-BILIS

(BILISNCRI and BILISNCR) and the control experiment (BILIS) are less than 3.2%, which is much smaller than the 52.3% of increase in the mean surface rain rate in the experiment without cloud radiative effects from the experiment with cloud radiative effects when the model is imposed by zero large-scale vertical velocity (see comparison between SST29NCR and SST29 in Sect. 7.2.1). The same large-scale forcing is imposed in the model for BILIS, BILISNCRI, and BILISNCR whereas zero large-scale vertical velocity is imposed in the model SST29 and SST29NCR. This indicates that the imposed large-scale forcing suppresses cloud radiative effects on the mean surface rainfall.

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Fig. 7.12 Differences in 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 (SLHLF), and radiation (SRAD) (a) BILISNCRI-BILIS and (b) BILISNCR-BILIS on 15 July 2006 (open bar) and 16 July (black bar). Unit is mm h−1 (After Wang et al. 2010)

The time and model domain mean water-vapor-related surface rainfall budgets on 15 July show that the mean hydrometeor loss occurs in BILIS whereas the mean hydrometeor is barely changed in BILISNCRI; this appears to cause the lower surface rainfall in BILISNCRI than in BILIS. The exclusion of cloud radiative effects in BILISNCR suppresses the mean local atmospheric moistening, which leads to the mean rainfall increase in BILISNCR. On 16 July, the exclusion of cloud-radiation interaction and cloud radiative processes, respectively, suppresses the local atmospheric drying in BILISNCRI and water vapor convergence in BILISNCR, which causes the mean rainfall decrease. The time and model domain mean thermally-related surface rainfall budgets reveal that the decreases in the mean rain rate caused by the exclusion of cloudradiation interaction are primarily associated with the slowdown in the mean hydrometeor loss on 15 July and the increase in the mean local atmospheric cooling on 16 July (Fig. 7.12a). The removal of cloud radiative effects increases the mean rainfall through the reduction in the mean radiative cooling on 15 July, whereas it decreases the mean rainfall through the suppressions in the mean local atmospheric cooling and the mean heat divergence on 16 July (Fig. 7.12b).

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Since the mean surface rain rate comes from raining stratiform and convective regions, the partitioning analysis for water-vapor-related surface rainfall budget is further conducted. On 15 July, the difference in the mean surface rain rate for BILISNCRI-BILIS comes mainly from convective regions (Fig. 7.10) whereas the difference for BILISNCR-BILIS results mainly from raining stratiform regions (Fig. 7.11). The reduction in convective rainfall caused by the exclusion of cloudradiation interaction is mainly associated with the enhancement in the transport of hydrometeor concentration from convective regions to raining stratiform regions. The increase in stratiform rainfall resulting from the exclusion of cloud radiative effects is related to the reduction in local atmospheric moistening and the enhancement in the transport of hydrometeor concentration from convective regions to raining stratiform regions. On 16 July, the differences in the mean surface rain rate for BILISNCRIBILIS and for BILISNCR-BILIS come mainly from raining stratiform regions. The decreases in stratiform rainfall in BILISNCRI and BILISNCR are mainly associated with the significant reductions in water vapor convergence over raining stratiform regions; these appear in turn to be caused by the increases in water vapor convergence over convective regions due to the similar mean water vapor convergence associated with the same large-scale upward motions imposed in the model in the three experiments. Over convective regions, the increase in water vapor convergence in BILISNCRI nearly offsets the increase in local atmospheric moistening and the increase in transport of hydrometeor concentration from convective regions to raining stratiform regions; causing the similar convective rainfall in comparison with the control experiment. The enhancement in water vapor convergence in BILISNCR overcomes the increase in local atmospheric moistening, which increases convective rainfall. To understand how cloud radiative processes affect surface rainfall processes, cloud radiative effects on responses of vertical structures of vertical velocity, water vapor mass flux, and hydrometeor mass flux to the large-scale forcing will be analyzed by plotting CFAD and vertical profiles of time and model domain mean and contributions from convective and stratiform regions. The large value of CFAD of more than 10% displays the statistics of the storm properties whereas the small value of about 0.001% shows the maximum of the storm properties. On 15 July, the exclusion of cloud-radiation interaction in BILISNCRI weakens the maximum upward motions in the upper tropospheric and strengthens maximum upward motions in the mid and lower troposphere and maximum downward motions in the upper troposphere (Fig. 7.13a, c); strengthened mid and lower-tropospheric upward motions in BILISNCRI produce the enhancement in upward water vapor mass fluxes in the mid and lower troposphere (Fig. 7.14a, c). The removal of cloud-radiation interaction causes maximum upward hydrometeor mass fluxes moving downward with the enhancement around the mid troposphere (Fig. 7.15a, c). The elimination of cloud radiative effects in BILISNCR enhances maximum upward motions in the mid troposphere and maximum downward motions in the upper troposphere (Fig. 7.13a, e) whereas it strengthens and weakens maximum water vapor mass fluxes, respectively, in the mid troposphere and lower troposphere (Fig. 7.14a, e).

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Fig. 7.13 CFAD of vertical velocity (m s−1). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Contour intervals are 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively (After Wang et al. 2010)

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Fig. 7.14 CFAD of water vapor mass flux (10−2 kg m−2 s−1). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Contour intervals are 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively (After Wang et al. 2010)

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Fig. 7.15 CFAD of hydrometeor mass flux (10−2 kg m−2 s−1). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Contour intervals are 0.001, 0.01, 0.1, 0.3, 0.5, 1, 10, 40, and 50%, respectively (After Wang et al. 2010)

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The maximum upward hydrometeors are insensitive to the cloud-radiation interaction (Fig. 7.15a, e). On 16 July, the exclusion of cloud-radiation interaction significantly reduces maximum upward and downward motions in the upper troposphere and strengthens downward motions in the mid troposphere (Fig. 7.13b, d) while it does not affect maximum upward and downward water vapor mass fluxes (Fig. 7.14b, d). The exclusion of cloud-radiation interaction significantly enhances maximum mid-tropospheric upward hydrometeor mass fluxes whereas maximum downward hydrometeor mass fluxes are insensitive to cloud-radiation interaction (Fig. 7.15b, d). The exclusion of cloud radiative effects in BILISNCRI significantly enhances maximum mid-tropospheric upward motions and reduces the downward motions (Fig. 7.13b, f). The exclusion of cloud radiative effects in BILISNCR significantly strengthens maximum upward water vapor mass fluxes in the mid and lower troposphere and maximum upward hydrometeor mass fluxes in the mid troposphere as well as maximum downward water vapor mass fluxes near the surface but it weakens maximum downward hydrometeor mass fluxes in the mid troposphere (Figs. 7.14b, f and 7.15b, f). BILIS shows dominant upward motions over raining stratiform regions on 15 July and over raining stratiform regions in the upper troposphere and over convective regions in the lower troposphere on 16 July (Fig. 7.16a, b). Since the specific humidity is much larger in the lower troposphere than in the upper troposphere, the time and model domain mean water vapor mass fluxes come mainly from convective regions on 16 July (Fig. 7.17b). The time and model domain mean water vapor mass fluxes on 15 July come mainly from raining stratiform regions in the upper troposphere and from convective regions in the lower troposphere (Fig. 7.17a). On 15 July, the exclusion of cloud-radiation interaction in BILISNCRI and cloud radiative effects in BILISNCR has limited impacts on vertical velocities over raining stratiform regions and model domain mean water vapor mass fluxes but it affects vertical velocities and associated water vapor mass fluxes over convective regions and water vapor mass fluxes over raining stratiform regions (Figs. 7.16c, e and 7.17c, e). Over convective regions, the exclusion of cloud-radiation interaction in BILISNCRI suppresses the maximum upward water vapor mass fluxes in the lower troposphere (Fig. 7.17c) whereas the exclusion of cloud radiative effects in BILISNCR mainly enhances the upward water vapor mass fluxes in the mid and upper troposphere (Fig. 7.17e). The maximum upward water vapor mass fluxes over raining stratiform regions are reduced in BILISNCRI and BILISNCR compared to BILIS, which leads to the decreases of mass-integrated water vapor convergence over raining stratiform regions in BILISNCRI and BILISNCR from BILIS. On 16 July, the exclusion of cloud-radiation interaction in BILISNCRI enhances the upper-tropospheric upward motions whereas the exclusion of cloud radiative effects in BILISNCR strengthens maximum upward motions over convective regions (Fig. 7.16d, f) but both intensify maximum upward water vapor mass fluxes over convective regions (Fig. 7.17d, f). On 15 July, the exclusion of cloud-radiation interaction in BILISNCRI does not have significant impacts on model domain mean upward hydrometeor mass fluxes but it suppresses upward hydrometeor mass fluxes over raining stratiform regions and enhances upward hydrometeor mass fluxes over convective regions (Fig. 7.18a, c).

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Fig. 7.16 Vertical profiles of daily and model domain mean imposed large-scale vertical velocity (solid) and components from raining stratiform regions (dash) and convective regions (dot). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Unit is cm s−1 (After Wang et al. 2010)

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Fig. 7.17 Vertical profiles of daily and model domain mean water vapor mass flux (solid) and contributions from raining stratiform regions (dash) and convective regions (dot). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Unit is 10−4 kg m−2 s−1 (After Wang et al. 2010)

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Fig. 7.18 Vertical profiles of daily and model domain mean hydrometeor mass flux (solid) and contributions from raining stratiform regions (dash) and convective regions (dot). (a), (c), and (e) present BILIS, BILISNCRI, and BILISNCR on 15 July, respectively, and (b), (d), and (f) present BILIS, BILISNCRI, and BILISNCR on 16 July, respectively. Unit is 10−4 kg m−2 s−1 (After Wang et al. 2010)

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Cloud Radiative Effects on Pre-summer Heavy Rainfall

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The exclusion of cloud radiative effects in BILISNCR significantly strengthens upward hydrometeor mass fluxes over both raining stratiform and convective regions (Fig. 7.18e). The hydrometeor mass fluxes are not sensitive to cloud radiation interactions (Fig. 7.18b, d). The exclusion of cloud radiative effects in BILISNCR does not affect maximum upward hydrometeor mass fluxes over convective regions and over model domain but it lowers the height of the maximum upward hydrometeor mass flux (Fig. 7.18f).

7.4 7.4.1

Cloud Radiative Effects on Pre-summer Heavy Rainfall Cloud Radiative Effects

On 4 and 6 June, the differences in the domain-mean surface rain rate caused by cloud radiative effects are less than 3.3% (Figs. 7.19 and 2.22). The differences in the mean local atmospheric drying rates are largely offset by the differences in the mean water vapor convergence rate and the rate of the mean hydrometeor loss. On 7 June, the exclusion of cloud radiative effects increases the mean rain rate by 12.8%. The increase in domain-mean surface rain rate caused by the removal of cloud radiative effects is associated with the increases in surface evaporation and local atmospheric drying and the mean hydrometeor loss. The analysis of the mean thermally-related surface rainfall budgets shows that the increases in the mean rainfall caused by the exclusion of cloud radiative effects are associated with the increases in the mean radiative cooling on 4 and 7 June and the decrease in the mean local atmospheric warming and the increase in the mean hydrometeor loss on 7 June (Fig. 7.20). The decrease in the mean rainfall caused by the removal of cloud radiative effects is related to the reduction in the mean heat divergence, which is largely offset by the increase in the mean radiative cooling. The increases in the mean rainfall induced by the increase in the mean radiative cooling on 4 and 7 June are consistent with the nocturnal rainfall peak associated with the decrease in saturation specific humidity caused by the IR-cooling-induced decrease in temperature proposed by Sui et al. (1997, 1998). The increase in the mean radiative cooling cannot always increase the mean rainfall in the presence of non-zero large-scale vertical velocity because the decrease in the mean heat divergence may be larger than the increase in the mean radiative cooling as indicated by the comparison in the mean thermally-related surface rainfall budget between PSR and PSRNCR on 6 June. On 7 June, the exclusion of cloud radiative effects increases convective and stratiform rain rates are, respectively, by 11.3% and 15.2% (Figs. 7.19 and 2.22). The stratiform rainfall covers 10.8% larger areas in PSRNCR than in PSR whereas the convective rainfall occupies similar sizes of areas in the two experiments. The enhancement in convective rain rate caused by the exclusion of cloud radiative effects is mainly associated with the local atmospheric change from moistening in PSR to drying in PSRNCR over convective regions. The increase in stratiform rain rate

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Fig. 7.19 Differences in 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 for PSRNCR-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. 2011a)

caused by the removal of cloud radiative effects is related to the enhanced transport of hydrometeor concentration from convective regions to raining stratiform regions and the weakened water vapor divergence over raining stratiform regions. The cloud radiative process generally affects convective and stratiform rainfall budgets on 4 and 6 June. The stratiform and convective rainfalls cover, respectively,

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Fig. 7.20 Differences in 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 (SLHLF), and radiation (SRAD) for PSRNCR-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. 2011a)

more and less areas in PSRNCR than in PSR. On 4 June, the exclusion of cloud radiative effects increases stratiform rain rate by 11.3% whereas it barely alters convective rain rate. The increase in stratiform rain rate caused by the exclusion of cloud radiative effects is mainly associated with strengthened local atmospheric drying over raining stratiform regions. The insensitivity of convective rain rate to cloud radiative effects is related to the cancellation between weakened local atmospheric drying and strengthened water vapor convergence. On 6 June, the exclusion of cloud radiative effects increases stratiform rain rate by 5.9% whereas it decreases convective rain rate by 6.3%. The decrease in convective rain rate resulting from the exclusion of cloud radiative effects is associated with weakened water vapor convergence over convective regions and strengthened transport of hydrometeor concentration from convective regions to raining stratiform regions. The increase in stratiform rain rate caused by the exclusion of cloud radiative effects is primarily related to the strengthened transport of hydrometeor concentration from convective regions to raining stratiform regions.

7.4.2

Radiative Effects of Water Clouds

The comparison between PSR and PSRNWR reveals that in the presence of radiative effects of ice clouds, the exclusion of radiative effects of water clouds increases the mean rainfall by 19.5% on 7 June, whereas it decreases the mean rainfall on 4 and 6 June. The comparison between PSRNIR and PSRNCR shows that the exclusion of radiative effects of water clouds enhances the mean surface rain rates in the absence of radiative effects of ice clouds on 4 and 7 June, whereas it suppresses the mean rainfall on 6 June. The maximum increase of 12.4% occurs on 7 June.

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Fig. 7.21 Differences in 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 for PSRNWR-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. 2011b)

On 4 June, the decrease in the mean rain rate resulting from the exclusion of radiative effects of water clouds in the presence of radiative effects of ice clouds from PSR to PSRNWR is primarily associated with the mean local hydrometeor change from loss in C to gain in PSRNWR (Fig. 7.21). In contrast, the increase in the mean rain rate in the absence of radiative effects of ice clouds from PSRNIR to PSRNCR is mainly related to the increases in the mean net condensation and the mean local

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Cloud Radiative Effects on Pre-summer Heavy Rainfall

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Fig. 7.22 As in Fig. 7.21 except for PSRNCR-PSRNIR

hydrometeor loss (Fig. 7.22). The enhanced mean net condensation leads to the intensified local atmospheric drying in the water vapor balance. On 6 June, the decreases in the mean rainfall from PSR to PSRNWR and PSRNIR to PSRNCR correspond primarily to the decreases in the mean net condensation. The suppressed mean net condensation is related to the decrease in the mean local atmospheric drying and water vapor convergence in the water vapor balance. On 7 June, the increases in the mean rainfall from PSR to PSRNWR and PSRNIR to PSRNCR are primarily associated with the enhanced mean net condensation. The enhanced mean net condensation mainly increases the mean local atmospheric drying in the water vapor balance.

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Fig. 7.23 Vertical profiles of model domain mean differences in local temperature change (black), heat divergence (green), convergence of vertical heat flux (orange), latent heat (red), and radiation (blue) for PSRNWR-PSR averaged in (a) 4 June 2008, (b) 6 June, and (c) 7 June. Unit is °C h−1 (After Shen et al. 2011b)

Radiative processes of water clouds directly impact radiation in heat budget. The change in latent heat release may correspond to the change in radiation in thermal balance. The net condensation and surface rain rate may change as a response to the change in latent heat release. Thus, vertical structures of the mean heat budgets are analyzed. On 4 June, in the presence of radiative effects of ice clouds, the exclusion of radiative effects of water clouds increases the mean radiative cooling from PSR to PSRNWR below 3 km and from 8 to 11.5 km whereas it decreases the mean radiative cooling from 3 to 8 km and above 11.8 (Fig. 7.23a).

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Cloud Radiative Effects on Pre-summer Heavy Rainfall

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Fig. 7.24 As in Fig. 7.23 except for PSRNCR-PSRNIR

The decrease in the mean latent heat release corresponds to the decrease in the mean radiative cooling from 3 to 8 km. The decrease in the mean net condensation is associated with the decrease in the mean latent heat release, but it is much smaller than the mean hydrometeor change from loss in PSR to gain in PSRNWR in the cloud budget. When radiative effects of ice clouds is turned off, the removal of radiative effects of water clouds enhances the mean radiative cooling in PSRNCR below 4 km whereas it suppresses the radiative cooling above 4 km (Fig. 7.24a). The increase in the mean latent heat release corresponds to the enhancement in the mean radiative cooling. The mean net condensation is enhanced and the surface rainfall is increased.

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On 6 June, the decrease in the mean latent heat release corresponds mainly to the decrease in the mean radiative cooling in the mid and upper troposphere as radiative effects of water clouds are removed from the model, while the difference in the mean heat divergence for PSRNWR-PSR is largely offset by the difference in the mean convergence of vertical heat flux (Fig. 7.23b). The decrease in the mean net condensation is associated with the decrease in the mean latent heat release. The reduced mean rainfall corresponds primarily to the suppressed mean net condensation. Compared to PSRNWR-PSR the absence of radiative effects of ice clouds enhances the decrease in the mean radiative cooling caused by the exclusion of radiative effects of water clouds for PSRNCR-PSRNIR (Fig. 7.24b). The decreases in the mean net condensation and the mean rain rate for PSRNCR-PSRNIR become larger than that for PSRNWR-PSR. On 7 June, the exclusion of radiative effects of water clouds from PSR to PSRNWR and from PSRNIR to PSRNCR strengthens the mean radiative cooling in the lower troposphere whereas it reduces the mean radiative cooling in the mid troposphere (Figs. 7.23c and 7.24c). The increase in the mean latent heat release in the low troposphere corresponds to the increase in the mean radiative cooling, which leads to the increase in the mean net condensation and surface rain rate. The difference for PSRNWR-PSR and PSRNCR-PSRNIR mainly occurs near the surface, where the mean latent heat release is increased from PSR to PSRNWR whereas it is decreased from PSRNIR to PSRNCR. Such difference in the mean latent heat release leads to the larger increase in the mean net condensation and the mean surface rain rate for PSRNWR-PSR than for PSRNCR-PSRNIR. The analysis of convective and stratiform rainfall shows that the decrease in the mean rainfall from PSR to PSRNWR comes primarily from the decrease in stratiform rainfall, which is associated with the decrease in water vapor convergence over raining stratiform regions on 4 June (Fig. 7.21). The increase in the mean rainfall from PSRNIR to PSRNCR results from the enhancement in convective rainfall due to the increase in water vapor convergence over convective regions (Fig. 7.22). On 6 June, the decreases in the mean rainfall from PSR to PSRNWR and PSRNIR to PSRNCR come from the decreases in convective rainfall, which are respectively associated with the decrease in local atmospheric drying from PSR to PSRNWR and the slowdown in water vapor convergence from PSRNIR to PSRNCR over convective regions. On 7 June, the increases in the mean rain rates from PSR to PSRNWR and PSRNIR to PSRNCR result from the decreases in convective rain rates, which corresponds to the local atmospheric change from moistening in PSR to drying in PSRNWR and the increase in local atmospheric drying from PSRNIR to PSRNCR while the decreases in water vapor convergence prevail over convective regions.

References Fu Q, Krueger SK, Liou KN (1995) Interactions of radiation and convection in simulated tropical cloud clusters. J Atmos Sci 52:1310–1328 Gao S, Li X (2008) Cloud-resolving modeling of convective processes. Springer, Dordrecht, 206 p

References

207

Ping F, Luo Z, Li X (2007) Microphysical and radiative effects of ice microphysics on tropical equilibrium states: a two-dimensional cloud-resolving modeling study. Mon Weather Rev 135:2794–2802, (c) American Meteorological Society. Reprinted with permission Shen X, Wang Y, Li X (2011a) Effects of vertical wind shear and cloud radiatve 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 Shen X, Wang Y, Li X (2011b) Radiative effects of water clouds on rainfall responses to the largescale forcing during pre-summer heavy rainfall over southern China. Atmos Res 99:120–128, (c) Elsevier. Reprinted with permission Sui CH, Lau KM, Takayabu YN, Short D (1997) Diurnal variations in tropical oceanic cumulus convection during TOGA COARE. J Atmos Sci 54:639–655 Sui CH, Li X, Lau KM (1998) Radiative-convective processes in simulated diurnal variations of tropical oceanic convection. J Atmos Sci 55:2345–2359 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 D, Li X, Tao WK (2010) Cloud radiative effects on responses of rainfall to large-scale forcing during a landfall of severe tropical storm Bilis (2006). Atmos Res 98:512–525, (c) Elsevier. Reprinted with permission Xu KM, Randall DA (1995) Impact of interactive radiative transfer on the macroscopic behavior of cumulus ensembles. Part II: mechanisms for cloud-radiation interactions. J Atmos Sci 52:800–817 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 8

Precipitation Efficiency

Precipitation efficiency is an important physical parameter in convective systems and has been applied to determine the rainfall intensity in operational precipitation forecasts (e.g., Doswell et al. 1996). Since Braham (1952) calculated precipitation efficiency with the inflow of water vapor into the storm through cloud base as the rainfall source more than half century ago, precipitation efficiency has been defined as the ratio of the precipitation rate to the sum of all precipitation sources. This definition of large-scale precipitation efficiency (LSPE) has been modified and widely applied in modeling studies and operational forecasts (e.g., Auer and Marwitz 1968; Heymsfield and Schotz 1985; Chong and Hauser 1989; Doswell et al. 1996; Ferrier et al. 1996; Li et al. 2002; Tao et al. 2004; Sui et al. 2005). Due to the fact that prognostic cloud microphysical parameterization schemes are used in cloud-resolving modeling of convective processes, precipitation efficiency is also defined through cloud microphysical budgets as cloud microphysics precipitation efficiency (CMPE; e.g., Weisman and Klemp 1982; Lipps and Hemler 1986; Ferrier et al. 1996; Li et al. 2002; Sui et al. 2005). The inclusion of water vapor divergence leads to a negative LSPE. The exclusion of local atmospheric drying associated with nocturnal IR cooling as a precipitation source yields more than 100% of LSPE. The exclusion of the decrease of hydrometeor concentration as a precipitation source causes more than 100% of LSPE and CMPE. These precipitation efficiencies fall within the normal range of 0–100% through the inclusion of all rainfall sources and the exclusion of all rainfall sinks from the water-vaporrelated surface rainfall budget (Gao et al. 2005) for LSPE and the cloud microphysical budget for CMPE (Sui et al. 2007). The estimates of precipitation efficiency from these definitions should be similar. However, the precipitation efficiency in the previous studies has been defined in water-vapor-related surface rainfall budget (LSPE) derived from water vapor and cloud budgets and in cloud microphysical budget (CMPE) derived from the microphysical budgets of five cloud species (cloud water, rain, cloud ice, snow, and

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graupel) could be very different (e.g., Li et al. 2002; Sui et al. 2007). What is the “true” precipitation efficiency? What causes the difference in the estimate of precipitation efficiency? While cloud information is usually unavailable from conventional data, water vapor processes can be estimated with available conventional data. Can water vapor process data be used to estimate precipitation efficiency? These questions will be discussed through the analysis of a COARE simulation from Gao and Li (2011). The precipitation efficiency can be defined only in the primitive budget where precipitation rate is a diagnostic term. An example of such a primitive budget is the rain microphysical budget in the tropics. Thus, the rain microphysical budget is used to define rain microphysics precipitation efficiency (RMPE) and its estimate from grid-scale simulation data serves as the “true” precipitation efficiency. The mass-integrated rain microphysical budget in the tropics can be written as 12

PS - QRM = å RPI ,

(8.1)

I =1

where ¶[qr ] ¶q ¶q - [u r ] - [ w r ], ¶t ¶x ¶z

QRM = -

(8.1a)

Here, RPI denotes rainfall source/sink terms from rain microphysical processes, which are defined in (1.2k); Thus, RMPE is defined as RMPE =

PS , RSRB

(8.2)

+ H (QRM )QRM ) is the rainfall source from rain microphysical where RSRB ( = RSR 12 budget; RSR ( å H ( RPI ) RPI ) is the rainfall source from rain microphysical I =1

processes; H is the Heaviside function, H(F) = 1 when F >0, 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)

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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)

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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)

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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)

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b

c

d

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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)

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(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

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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)

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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)

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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 (<250 m) is required to realistically reproduce the development of boundary-layer clouds. Cheng and Xu (2006) studied the effects of turbulence closures on cloud simulations and found that fully prognostic quasi-Gaussian based third-order closures produce more and deeper shallow cumuli but smaller and narrower convective clouds than intermediately prognostic double-Gaussian based third-order closures do. Khairoutdinov and Randall (2003) showed that the uncertainties of precipitation simulations are much more sensitive to the uncertainties of initial conditions than the uncertainties of cloud microphysical parameterization schemes. Li et al. (2006) and Gao and Li (2008) conducted 2D cloud-resolving model simulations with the perturbed initial PW and temperature conditions and compared these perturbed experiments with the control experiment. They found significant differences in cloud and precipitation simulations with the given precipitation water perturbations. The further budget analysis indicates that the errors of initial conditions affect cloud and precipitation simulations through a biased condensation process. Temperature and water vapor are key quantities that control precipitation processes through cloud microphysical processes. However, temperature and water

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vapor that serve as initial conditions for numerical model simulations may contain large uncertainties. Grody et al. (2001) conducted a comparison study of PW between the radiosonde observations and satellite retrievals from NOAA 15 Advanced Microwave Sounding Unit (AMSU) and found the biases ranging from 0.44 to 1.86 mm and a RMS difference of 3 mm. Aires et al. (2002) developed a principal component analysis neural network to simultaneously retrieve temperature, water vapor, and ozone atmospheric profiles from the high spectral resolution Infrared Atmospheric Sounding Interferometer spaceborne instrument and showed that temperature is retrieved with error of smaller than 1 K and PW is retrieved with an error of 5–7%. Susskind et al. (2003) revealed the RMS error of 1 K for retrieved temperature at different vertical layers in the presence of clouds from the Atmospheric Infrared Sounder (AIRS)/AMSU/Humidity Sounder for Brazil (HSB). Thus, evaluation of impacts of uncertainty of initial conditions on precipitation simulations is important. Li et al. (2006) showed that the magnitudes of PW in both the simulated and the satellite-retrieved differ markedly. Satellite-retrieved PW is from NOAA/ NESDIS/Microwave Surface and Precipitation Products System (MSPPS). The RMS differences of PW between the simulated and the satellite-retrieved are 2.5 mm over the clear-sky regions and 4.5 mm over cloudy regions (the sum of LWP and IWP is larger than 5 × 10−4 mm). The standard deviations of PW in MSPPS are 6.5 and 6.0 mm over the clear-sky and cloudy regions, respectively, as compared to the respective 6.4 and 5.1 mm in GDAS. The RMS differences of PW between MSPPS and GDAS are smaller than its standard deviations over both the clear-sky and cloudy regions. The RMS differences over cloudy regions are significantly greater than those over clear-sky regions. To statistically measure the PW error relative to its mean, Li et al. (2006) defined the statistical PW error of GDAS with respect to MSPPS as the ratio of the RMS difference between MSPPS and GDAS to the area-averaged values of PW. The area-averaged values of PW are 42.3 mm in MSPPS and 43.2 mm in GDAS over the clear-sky regions whereas they are 51.7 mm in MSPPS and 52.1 mm in GDAS over cloudy regions. Thus, the PW statistical error in the GDAS product is 6% over clear-sky regions and 8.5% over cloudy regions. In this chapter, sensitivity of precipitation modeling to uncertainty of initial conditions of temperature, water vapor, and clouds is discussed in Sect. 9.2 (Gao and Li 2009) and sensitivity of precipitation modeling to uncertainty of vertical structures of initial conditions of temperature and water vapor is examined in Sect. 9.3 (Li and Shen 2010).

9.2

Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions of Temperature, Water Vapor, and Clouds

Gao and Li (2009) conducted a series of sensitivity experiments to study model precipitation responses to uncertainty of initial conditions of temperature, water vapor, and clouds. The model is imposed by the large-scale forcing (large-scale vertical velocity, zonal wind, and sea surface temperature) averaged over 150–160oE,

9.2 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions…

221

a

b

Fig. 9.1 Temporal and vertical distributions of (a) vertical velocity (mb h−1) and (b) zonal wind (m s−1) obtained from GDAS for a selected 8-day period. Downward motion in (a) and westerly wind in (b) are shaded (After Gao and Li 2009)

EQ from 1100 LST 18 to 1700 LST 26 April 2003 (Fig. 9.1). The large-scale vertical velocity and zonal wind are obtained from 6-hourly NCEP/GDAS data, whereas the daily-mean sea surface temperature is retrieved from TRMM TMI radiometer with a 10.7 GHz channel. The control experiment is integrated with the large-scale forcing. The five perturbation experiments are identical to the control experiment, but different initial conditions are used in the preturbation experiments. The two perturbation experiments are perturbed by ± 0.5oC of mass-weighted mean temperature whereas the two other perturbation experiments are perturbed by ± 1 mm of PW. The initial temperature and specific humidity are perturbed uniformly in vertical direction. The additional perturbation experiment is conducted by setting cloud mixing ratios to zero after a 6-hour spin up. The simulation data are first averaged over different spatial and time scales and are used to calculate RMS difference and standard deviation. The ratio (RS ratio) of the RMS difference to standard deviation is then calculated to measure the sensitivity of cloud and precipitation simulation to the initial condition. When the RS ratio is smaller than 1, model sensitivity to the uncertainty of the initial condition is weak and the simulation is considered as accurate. When the RS ratio is larger than 1, the model simulation is strongly sensitive to the uncertainty of the initial condition and model simulation cannot capture the variation. The RMS difference in PW between the perturbation experiments and control experiment varies with the time scale for average of data whereas it is insensitive to

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9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

a

b

c

d

e

f

g

h

Fig. 9.2 RMS differences between perturbation experiments and control experiment (contours) and the ratios of RMS difference to standard deviation (background) of (a) PW, (b) IWP, (c) LWP, (d) Ps, (e) QWVT, (f) QWVF, (g) QWVE, and (h) QCM as functions of time and spatial scales for average of data. The contour intervals of RMS differences are 0.05 mm for PW, IWP, and LWP, 0.1 mm h−1 for PS, QWVT, QWVF, and QCM, and 0.01 mm h−1 for QWVE (After Gao and Li 2009)

9.2 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions…

223

the spatial scale for average of data (Fig. 9.2a). The RS ratio of PW is nearly a constant (~0.23). This indicates that the initial conditions barely alter PW in the perturbation experiments. The RMS differences in IWP, LWP, and PS increase as time and spatial scales decrease (Fig. 9.2b–d). The accurate cloud and rainfall simulations, in which the RS ratios of IWP, LWP, and PS are smaller than 1, require a small spatial scale (~300 km) for daily averaged data and a much larger spatial scale (>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

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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

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9 Sensitivity of Precipitation Modeling to Uncertainty of Initial Conditions

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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…

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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)

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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…

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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)

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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…

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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,

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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…

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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.

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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

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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