precipitation modeling and quantitative analysis

However, accurate estimate of surface rain rate is diffi cult due to the fact that precipitation processes are nonlinearly asso-ciated with the dynamic, thermodynamic, cloud microphysica

Springer Atmospheric Sciences

For further volumes:

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Precipitation Modeling and Quantitative Analysis

Xiaofan Li

NOAA/NESDIS/Center for Satellite

Applications and Research

5200 Auth Road, Camp Springs,

MD 20746

USA

Xiaofan.Li@noaa.gov

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

gst@mail.iap.ac.cn

ISBN 978-94-007-2380-1 e-ISBN 978-94-007-2381-8

DOI 10.1007/978-94-007-2381-8

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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 precipi-tation 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-to-day planning by individuals, longer-term decision making by institutions and gov-ernments, 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 pro-vide detailed derivations of the salient equations, along with quantitative analyses of the effects of sea-surface temperature, vertical wind shear, cloud-radiation interac-tion, 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 effi ciency

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

National Center for Atmospheric Research

Precipitation is one of the most important quantities in meteorology and hydrology Because fl oods 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 signifi cant economic and social implications in rainfall-rich countries However, accurate estimate of surface rain rate is diffi cult due to the fact that precipitation processes are nonlinearly asso-ciated with the dynamic, thermodynamic, cloud microphysical and radiative pro-cesses 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 related 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 effi ciency; the sensitiv-ity of precipitation modeling to the uncertainty of initial conditions; and to develop

water-vapor-a new rwater-vapor-ainfwater-vapor-all pwater-vapor-artitioning 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 pre-summer rainfall event over southern China in 2008 The material in this book has

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 effi cient 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

1 Cloud-Resolving Modeling of Precipitation 1

1.1 Cloud-Resolving Model 2

1.2 Weather Events and Large-Scale Forcing for Precipitation Modeling 6

1.2.1 Experiment COARE 6

1.2.2 Experiment SCSMEX 6

1.2.3 Experiment BILIS 8

1.2.4 Experiment PSR 9

1.3 Comparison Between Simulations and Observations 9

1.3.1 Temperature and Specifi c Humidity 9

1.3.2 Surface Rain Rate 12

1.3.3 Refl ectivity 15

1.4 Equilibrium Simulations with Zero Large-Scale Vertical Velocity 20

1.5 Comparison Between 2D and 3D Model Simulations 22

References 23

2 Precipitation Equations and Process Analysis 27

2.1 Precipitation Equations 27

2.2 Equilibrium Model Simulation with Zero Large-Scale Vertical Velocity 32

2.2.1 Time-Mean Analysis 32

2.2.2 Analysis of Diurnal Variation 35

2.3 Simulation of Rainfall Event During SCSMEX 38

2.4 Simulation of Torrential Rainfall Event During the Landfall of Severe Tropical Storm Bilis (2006) 40

2.5 Simulation of Pre-summer Heavy Rainfall Event over Southern China in June 2008 58

References 60

xii Contents

3 Tropical Precipitation Processes 63

3.1 Model Domain Mean Analysis 63

3.1.1 Effects of Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of Mean Water Vapor Convergence and Mean Local Atmospheric Drying 64

3.1.2 Effects of Mean Local Atmospheric Drying/ Moistening on Mean Rainfall 71

3.1.3 Effects of Mean Local Atmospheric Drying/Moistening and Mean Hydrometeor Loss/Gain on Mean Rainfall in the Presence of the Mean Water Vapor Divergence 73

3.2 Grid-Scale Analysis 74

3.3 Tropical Rainfall Responses to the Large-Scale Forcing 82

3.4 Effects of Time-Dependent Large-Scale Forcing, Solar Zenith Angle, and Sea Surface Temperature on Time-Mean Tropical Rainfall Processes 92

3.5 Diurnal Cycle 101

References 108

4 Effects of Sea Surface Temperature 111

4.1 Introduction 111

4.2 Time-Mean Analysis 111

4.3 Analysis of Diurnal Variation 116

References 124

5 Effects of Vertical Wind Shear 125

5.1 Introduction 125

5.2 Effects of Vertical Wind Shear on Severe Tropical Storm Rainfall 126

5.3 Effects of Vertical Wind Shear on Pre-summer Heavy Rainfall 133

References 136

6 Microphysical and Radiative Effects of Ice Clouds 137

6.1 Introduction 137

6.2 Effects of Ice Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity 139

6.2.1 Time-Mean Analysis 139

6.2.2 Diurnal Analysis 141

6.2.3 Vertical Structures of Thermal and Water Vapor Budgets 150

6.3 Effects of Ice Clouds on Severe Tropical Storm Rainfall 159

6.4 Effects of Ice Clouds on Pre-summer Heavy Rainfall 166

References 172

7 Cloud Radiative Effects 175

7.1 Introduction 175

7.2 Radiative Effects of Water Clouds on Rainfall in the Simulations with Zero Large-Scale Vertical Velocity 176

7.2.1 Time-Mean Analysis 176

7.2.2 Analysis of Diurnal Variation 178

8 Precipitation Effi ciency 209

References 218

9 Sensitivity of Precipitation Modeling to Uncertainty

of Initial Conditions 219

9.1 Introduction 2199.2 Sensitivity of Precipitation Modeling to Uncertainty

of Initial Conditions of Temperature, Water Vapor,

and Clouds 2209.3 Sensitivity of Precipitation Modeling to Uncertainty

of Vertical Structures of Initial Conditions 225 References 234

Index 237

2D Two-dimensional

3D Three-dimensional

AIRS Atmospheric Infrared Sounder

AMSU Advanced Microwave Sounding Unit

ARM Atmospheric Radiation Measurement

CAPE Convective available potential energy

CFAD Contoured frequency with altitude diagram

COARE Coupled Ocean-Atmosphere Response Experiment

CMPE Cloud-microphysics precipitation effi ciency

EQ Equator

GCE Goddard cumulus ensemble

GDAS Global Data Assimilation System

GSFC Goddard Space Flight Center

HSB Humidity Sounder for Brazil

IFA Intensive Flux Array

IMET Improved Meteorological

IOP Intensive Observing Period

IR Infrared

IWP Ice Water Path

LFC Level of free convection

LSPE Large-scale precipitation effi ciency

LST Local standard time

LWP Liquid Water Path

MSPPS Microwave Surface and Precipitation Products System

NASA National Aeronautics and Space Administration

NCEP National Centers for Environmental Prediction

xvi Abbreviations and Acronyms

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

PSU Practical salinity units

PV Potential vorticity

PW Precipitable water

RMPE Rain Microphysics Precipitation Effi ciency

RMS Root-mean-square

SCSMEX South China Sea Monsoon Experiment

SST Sea surface temperature

TOGA Tropical Ocean Global Atmosphere

TMI TRMM Microwave Imager

TRMM Tropical Rainfall Measuring Mission

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

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 scientifi c 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 environ-ment 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 benefi cial to the improvement

of quantitative precipitation forecast However, important information such as cloud microphysical processes is not conventionally available, which make observational analysis rather diffi cult

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 fi ne horizon-tal 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, specifi c humidity, surface rain rate, refl ectivity, and cloud hydrometeor mixing ratios (Sect 1.3) Equilibrium simulations with zero large-scale vertical

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 signifi cantly improved by Tao and Simpson ( 1993 ) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) and was modifi ed by Sui et al ( 1994, 1998 ) for studying tropical convec-tion 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 ), specifi c humidity ( q v ), and fi ve cloud hydrometeor mixing ratios The 2D non-hydrostatic governing equations with anelastic approximation can be expressed by

4 1 Cloud-Resolving Modeling of Precipitation

Here, q c , q r , q i , q s , and q g , are the mixing ratios of cloud water, raindrops, cloud ice,

snow, and graupel, respectively; p = (p/p 0 ) k , k = R/c p ; R is the gas constant; c p is the

specifi c heat of dry air at constant pressure p , and p o = 1,000 hPa; T is air temperature, and T = 0°C, T = −35°C L , L , and L are latent heat of vaporization, sublimation,

and fusion at 0°C, respectively, and L s = L v + L f Q R in ( 1.1d ) is the radiative heating rate due to convergence of the net fl ux of solar and infrared radiative fl uxes calcu-lated 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 param-eterization schemes (Lin et al 1983 ; Rutledge and Hobbs 1983, 1984 ; Tao et al

1989 ; Krueger et al 1995 ) , which are defi ned in Table 1.1 w Tr in ( 1.1g ), w Ts in ( 1.1i )

and w Tg in ( 1.1j ) are terminal velocities for raindrops, snow, and graupel, tively; 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

P GMLT Growth of raindrops by melting of graupel RH84

P SMLT Growth of raindrops by melting of snow RH83

P RACI Growth of raindrops by the accretion of cloud ice RH84

P RACW Growth of raindrops by the collection of cloud water RH83

P RACS Growth of raindrops by the accretion of snow RH84

P RAUT Growth of raindrops by the autoconversion of cloud water LFO

P IDW Growth of cloud ice by the deposition of cloud water KFLC

P IACR Growth of cloud ice by the accretion of rain RH84

P IHOM Growth of cloud ice by the homogeneous freezing of cloud water

P DEP Growth of cloud ice by the deposition of supersaturated vapor TSM

P SAUT Growth of snow by the conversion of cloud ice RH83

P SACI Growth of snow by the collection of cloud ice RH83

P SACW Growth of snow by the accretion of cloud water RH83

P SFW Growth of snow by the deposition of cloud water KFLC

P SFI Depositional growth of snow from cloud ice KFLC

P SACR Growth of snow by the accretion of raindrops LFO

P SDEP Growth of snow by the deposition of vapor RH83

P GACI Growth of graupel by the collection of cloud ice RH84

P GACR Growth of graupel by the accretion of raindrops RH84

P GACS Growth of graupel by the accretion of snow RH84

P GACW Growth of graupel by the accretion of cloud water RH84

P WACS Growth of graupel by the riming of snow RH84

P GDEP Growth of graupel by the deposition of vapor RH84

P GFR 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)

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 spe-cifi c humidity over land and the observed sea surface temperature over ocean are uniformly imposed on each model grid to calculate surface sensible heat fl ux and evaporation fl ux The model details can be found in Gao and Li ( 2008a )

1.2 Weather Events and Large-Scale Forcing

for Precipitation Modeling

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

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) radio meter 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 briefl y interrupted by a few downward motion events, in particular, in the mid and lower troposphere The southerly winds start to diminish with the strengthened

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

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 )

8 1 Cloud-Resolving Modeling of Precipitation

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°

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 )

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 advec-tions (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 west-erly winds of 4–12 m s −1 are maintained during the rainfall event

1.3 Comparison Between Simulations and Observations

1.3.1 Temperature and Specifi c Humidity

Gao and Li ( 2008b ) compared the vertical profi les of simulated temperature and specifi c humidity in COARE with observations through the analysis of their differ-ences in experiment COARE (Fig 1.5 ) Compared to the observations, the simula-tions 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 profi le shows regular diurnal signals The difference in specifi c 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

1993 when the dry atmosphere is associated with large-scale downward motions (Fig 1.1a ) The difference in specifi c 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 profi les of temperature and specifi c humidity from NCEP/GDAS (Fig 1.6 ) The simulated

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 large-

scale forcing Upward motion in ( a ) and westerly wind in ( b ) are shaded (After Wang et al 2009 )

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

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 )

12 1 Cloud-Resolving Modeling of Precipitation

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 km 2 area, which is based on radar refl ectivity 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

Fig 1.5 Time-height distributions of ( a ) temperature difference between the simulation in

COARE and observation (°C) and ( b ) specifi c humidity difference (g kg −1 ) Positive differences are

shaded (After Gao and Li 2008b )

coeffi cient between simulated and observed rain rates is 0.45 A Student’s t -test on

the signifi cance of the correlation coeffi cients is further conducted and a critical relation coeffi cient at the 1% signifi cant level is 0.128 Thus, the correlation between simulated and observed rain rates is statistically signifi cant But the simulated ampli-tudes 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

cor-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 calcu-lated 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 observa-tion, the simulation generates the moderate rain rate on late 19 and 20 July 2006

b

Fig 1.6 Time-height distributions of ( a ) temperature difference (°C) and specifi c humidity

differ-ence (g kg −1 ) between experiment PSR and NCEP/GDAS data (After Shen et al 2011 )

14 1 Cloud-Resolving Modeling of Precipitation

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

Fig 1.7 Time series of model domain-mean surface rain rate ( P S ) 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 ( P S ) simulated in BILIS ( solid ) Unit

is mm h −1 (After Wang et al 2009 )

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 pre-summer 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 signifi cantly 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 differ-ences 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 observa-tions 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 Refl ectivity

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

Fig 1.9 Surface rain rates ( P S ) simulated in PSR ( solid ) and from rain gauge observation ( dash )

Unit is mm h −1 (After Wang et al 2010 )

16 1 Cloud-Resolving Modeling of Precipitation

where G is a Gamma function, n 0r , n 0s , and n 0g are the intercept values of raindrop, snow, and graupel size distributions, respectively; l r , l s , and l g are the slopes of

raindrop, snow, and graupel size distribution, respectively; | K w | 2 is the dielectric

fraction of water (0.93), and | K i | 2 is the dielectric fraction of equivalent ice spheres

(0.176) Then, the effective radar refl ectivity ( Z e ) can be calculated by

Wang et al ( 2007 ) also calculated model hydrometeor density in SCSMEX using a difference refl ectivity method (Golestani et al 1989 ) for mixed phase precipitation and a method proposed by Bringi and Chandrasekar ( 2001 ) for pure rain and com-pared 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 refl ectivity decreases signifi cantly 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 refl ectivity maximum is much higher than that of the observed refl ectivity 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

Fig 1.10 Meridional-vertical (Y-Z) cross section of radar refl ectivity ( shaded ) and system-relative

wind fl ow ( arrow vector ) along a specifi c horizontal line at 0800 LST 20 May 1998 from

observa-tions (After Wang et al 2007 )

Fig 1.11 Model-derived meridional-vertical (Y-Z) cross sections of refl ectivity (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

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 refl tivity [Ze (dBz)] converted from the model calculated hydrometeor density in BILIS with observed refl ectivity (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,

Distance north of CPOL radar(km)

Distance north of CPOL radar(km)

2.5

2.5 3.0 3.5 4.0 4.5

Fig 1.12 As Fig 1.10, but for ( a ) differential refl ectivity (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 refl ectivity and polarimetric parameters (After Wang et al 2007 )

whereas simulated vertical profi le is calculated by taking model domain mean in 15 July 2006 Both vertical distributions show maximum refl ectivity around 4 km while the simulated refl ectivity is larger than observed refl ectivity below 8 km, in particu-lar, near the surface This implies that the model may produce a large amount of water clouds

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 )

20 1 Cloud-Resolving Modeling of Precipitation

1.4 Equilibrium Simulations with Zero

Large-Scale Vertical Velocity

The large-scale vertical velocity may include effects of SST and its diurnal tion, 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, respec-tively These experiments are used to study the effects of SST on rainfall SST29D

varia-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

Fig 1.14 Vertical distributions of radar refl ectivity (dBz) from observation ( dash ) and simulation

in BILIS ( solid ) averaged in 15 July 2006 (After Wang et al 2009 )

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 thermo-

dynamic 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 signifi cantly colder and drier

and ice clouds SST29NIR Time-invariant (29°C) No for ice clouds Yes

SST29NWR Time-invariant (29°C) No for water

SST29D −3.6 44.6 SST29NCR −8.1 37.5 SST29NIR −7.4 35.7 SST29NWR −3.4 44.0 SST29NIM −5.9 41.4

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

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 radia-tive 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 equilib-rium thermodynamic states

Further analysis of mass-weighted mean heat budgets and precipitable water gets in seven equilibrium experiments shows that a warmer temperature in SST31 produces a higher surface evaporation fl ux 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 sim-ulation 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 equilib-rium 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 tem-perature, stronger air-sea fl ux 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 inclu-sion 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 trans-ports of mass, sensible heat, and moisture, thermodynamic fi elds, surface heat fl uxes, surface precipitation, precipitation effi ciency, and convective and moist vorticity vec-tors (e.g., Tao and Soong 1986 ; Tao et al 1987 ; Grabowski et al 1998 ; Tompkins

during the Atmospheric Radiation Measurement (ARM) and found that the ences 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 dom-inant 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

differ-in dynamics between the 2D and 3D models whereas they showed similarities differ-in thermodynamics and precipitation

Gao S (2007) A three dimensional dynamic vorticity vector associated with tropical oceanic vection 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 ated convective and stratiform regions to the large-scale forcing Q J R Meteorol Soc 134:2127–

associ-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 dimensional cloud-resolving modeling study J Atmos Sci 64:656–664