for Full Article
Precipitation equations and their applications to the analysis
of diurnal variation of tropical oceanic rainfall
Shouting Gao
1and Xiaofan Li
2Received 11 May 2009; revised 19 November 2009; accepted 20 November 2009; published 28 April 2010.
[1]
The cloud, water, and heat budgets lay down a foundation for studying relations
between precipitation, clouds, and environmental water vapor and thermal conditions.
The water vapor constrained precipitation equation is derived by combining cloud budget
with water vapor budget, whereas the thermally constrained precipitation equation is
derived by combining cloud budget with heat budget. The precipitation equations are
applied to analyze the diurnal variations of tropical oceanic rainfall using the 21 day
two‐dimensional cloud‐resolving model simulation during Tropical Ocean–Global
Atmosphere Coupled Ocean
‐Atmosphere Response Experiment and two additional
sensitivity experiments. One sensitivity experiment excludes the diurnal variation of
large
‐scale forcing, and the other experiment excludes the diurnal variation of solar zenith
angle. The analysis shows that the diurnal variations of water vapor convergence and
heat divergence associated with diurnally varying imposed large
‐scale upward motions
play a primary role in the development of rainfall peaks in both afternoon and nighttime,
whereas the diurnal variation of radiation is secondary in the formation of nocturnal
rainfall peak. The diurnal variation of radiation associated with diurnally varying solar
zenith angle determines the diurnal variations of tropical oceanic rainfall when the diurnal
variation of large
‐scale circulation is absent. The diurnal variations of rainfall can be
concisely described by simplified diurnally perturbed surface rainfall equations.
Citation: Gao, S., and X. Li (2010), Precipitation equations and their applications to the analysis of diurnal variation of tropical oceanic rainfall, J. Geophys. Res., 115, D08204, doi:10.1029/2009JD012452.
1.
Introduction
[2] 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 ther-modynamic conditions when the clouds and associated pre-cipitation 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 micro-physical, and dynamic processes. The precipitation processes are determined by environment thermal and water vapor conditions through cloud microphysical processes. The anal-ysis of thermal, water vapor, and cloud microphysical
bud-gets 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 makes observational analysis rather difficult.
[3] 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. The cloud‐resolving model simulations have been validated with available observations during the Global Atmospheric Research Pro-gram Atlantic Tropical Experiment [e.g., Xu and Randall, 1996; Grabowski et al., 1996], Tropical Ocean–Global Atmo-sphere Coupled Ocean‐AtmoAtmo-sphere Response Experiment (TOGA COARE) [e.g., Wu et al., 1998; Li et al., 1999], Atmospheric Radiation Measurement [e.g., Xu et al., 2002], South China Sea Monsoon Experiment [e.g., Tao et al., 2003; Wang et al., 2007], and torrential rainfall events over China [e.g., Xu et al., 2007; Wang et al., 2009]. The validated simulation data have been used to study surface rainfall processes [e.g., Gao et al., 2005a; Cui and Li, 2006; Gao and Li, 2008b]; precipitation efficiency [e.g., Li et al., 2002a; Sui et al., 2005, 2007]; cloud clusters and their merging processes [e.g., Ping et al., 2008]; convective, moist, and dynamic vorticity vectors [Gao et al., 2004, 1Laboratory of Cloud‐Precipitation Physics and Severe Storms,
Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China.
2
Center for Satellite Applications and Research, NOAA, NESDIS, Camp Springs, Maryland, USA.
Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2009JD012452
2005b]; and climate equilibrium states [e.g., Gao et al., 2007; Ping et al., 2007; Gao, 2008; Cui and Gao, 2008].
[4] Li et al. [2002a] and Sui et al. [2005] found that the
large‐scale precipitation efficiency (LSPE) that is defined as the ratio of surface rain rate to the sum of water vapor convergence and surface evaporation could be negative or larger than 100%, which is not physically meaningful. The calculation of LSPE should include all water vapor sources that prevent LSPE from larger than 100% and exclude water vapor sinks that prevent LSPE from negative values. Since the surface rain rate is not a term in water vapor budget, it is hard to count all sources and to drop all sinks. Gao et al. [2005a] combined water vapor and cloud budgets to de-rive a diagnostic surface rainfall equation for studying sur-face rainfall processes in a unified framework that links precipitation, clouds, and environmental water vapor con-ditions. Sui et al. [2007] defined a new LSPE based on the surface rainfall equation and found that the new LSPE ranges from 0% to 100%, which is physically meaning. The surface rainfall equation of Gao et al. [2005a] is only based on water vapor constraint. The surface rainfall processes are much affected by the environmental thermal conditions such as infrared (IR) cooling‐induced nocturnal rainfall peak [e.g, Sui et al., 1997, 1998], which requires the thermally con-strained surface rainfall equation.
[5] In this study, precipitation equations with both water
vapor and thermal constraint are derived and applied to study dominant physical processes that are responsible for the diurnal variation of tropical oceanic rainfall. Precipita-tion equaPrecipita-tions are derived in secPrecipita-tion 2. The applicaPrecipita-tion of precipitation equations to the analysis of the diurnal varia-tion of tropical oceanic rainfall is presented in secvaria-tion 3. The summary is given in section 4.
2.
The Physical Space Associated With
Precipitation Processes and Precipitation Equations
[6] The temperature, water vapor, and clouds playimpor-tant roles in precipitation processes. Thus, the three dimen-sions in the physical space associated with precipitation processes are water vapor (specific humidity; qv),
tempera-ture (T), and clouds (total hydrometeor mixing ratio; ql =
qc+ qr+ qi+ qs+ qg, qc, qr, qi, qs, qgare the mixing ratios
of cloud water, raindrops, cloud ice, snow, and graupel, respectively). Correspondingly, there are three basic relations in the precipitation physical space: water vapor budget, heat budget, and cloud budget. The budgets in the two‐ dimensional (2‐D) framework can be written as
@qv @t ¼ @ u0qv0 ð Þ @x uo @qv0 @x wo @qv0 @z w0 @qv @z 1 @ @zw0qv0 Sqv uo @qv @x wo @qv @z; ð1aÞ @T @t ¼ @@xðuoþ u0ÞT0 uo @o @x wo @ @z þ 0 w0@ @z @ @zðw00Þ þ Qcn cp þQR cp; ð1bÞ @ql @t ¼ @ uql ð Þ @x 1 @ @zwqlþ 1 @ @z wTrqrþ wTsqsþ wTgqg þ Sqv; ð1cÞ where
Sqv¼ PCNDþ PDEPþ PSDEPþ PGDEP PREVP PMLTS
PMLTG; ð2aÞ
Qcn¼ LvSqvþ LfP18; ð2bÞ
P18¼ PDEPþ PSDEPþ PGDEP PMLTS PMLTG
þ PSACWðT < ToÞ þ PSFWðT < ToÞ þ PGACWðT < ToÞ
þ PIACRðT < ToÞ þ PGACRðT< ToÞ þ PSACRðT < ToÞ
þ PGFRðT< ToÞ PRACSðT> ToÞ PSMLTðT > ToÞ
PGMLTðT > ToÞ þ PIHOMðT< TooÞ PIMLTðT> ToÞ
þ PIDWðToo< T < ToÞ: ð2cÞ
is the potential temperature; u and w are zonal and ver-tical components of wind, respectively;r is air density that is a function of height; cpis the specific heat of dry air at
constant pressure; Lv, Ls, and Lf are latent heat of
vapori-zation, sublimation, and fusion at To = 0°C, respectively;
Ls = Lv+ Lf,; Too= −35°C; and cloud microphysical
pro-cesses in equation (2) can be found in Table 1. QR is the
radiative heating rate caused by the convergence of net flux of solar and IR radiative fluxes. wTr, wTs, and wTgin
equation (1c) are terminal velocities for raindrops, snow, and graupel, respectively; the overbar denotes a model domain mean; prime is a perturbation from model domain mean; and superscript o is an imposed observed value. Equations (1) and (2) show that the water vapor, heat, and cloud budgets are linked by Sqv.
[7] Following Gao et al. [2005a] and Sui and Li [2005],
the cloud budget (1c) and water vapor budget (1a) are mass integrated, and mass‐integrated cloud and water vapor budgets can be, respectively, written by
PS QCM ¼ QWVS¼ QWVOUTþ QWVIN; ð3Þ QWVTþ QWVFþ QWVE¼ QWVS; ð4Þ where PS¼ Prþ Psþ Pg; ð5aÞ Pr¼ wTrqrjz¼0; ð5bÞ Ps¼ wTsqsjz¼0; ð5cÞ Pg¼ wTgqgjz¼0; ð5dÞ
Table 1. A Summary of Experiments
Experiment Solar Zenith Angle Large‐Scale Forcing Sea Surface Temperature C Time dependent Time dependent Time dependent CF Time mean Time dependent Time mean CR Time dependent Time mean Time mean
QCM ¼ @ ql ½ @t u @ ql @x w @ql @z ; ð5eÞ
QWVOUT ¼ P½ CND þ P½ DEP þ P½ SDEP þ P½ GDEP; ð5fÞ
QWVIN¼ P½ REVP P½ MLTG P½ MLTS; ð5gÞ QWVT¼ @ qv ½ @t ; ð5hÞ QWVF¼ uo@ q@xv wo@ qv @ z @ðu0qv0Þ @x uo@ qv0 @x wo@ qv0 @z w0@ qv0 @z ; ð5iÞ QWVE¼ Es: ð5jÞ
Here, PSis the precipitation rate and PS= Prin the tropics;
Es is surface evaporation; and [()] =
Rzt
zbðÞdz, where zt and zbare the heights of the top and bottom of the model
atmosphere, respectively.
[8] The heat budget (1b) is mass integrated, and the mass‐
integrated heat budget becomes
SHTþ SHFþ SHSþ SLHLFþ SRAD¼ QWVS; ð6Þ where SHT¼ cp Lv @ T½ @t ; ð7aÞ SHF¼ cp Lv @ @xðuoþ u0ÞT0þ uo @o @x þ wo @ @zð þ 0Þ þ w0 @ @z " # ; ð7bÞ SHS ¼ cp Lv Hs; ð7cÞ SLHLF¼ Lf Lv hP18i; ð7dÞ SRAD¼ 1 Lv hQRi: ð7eÞ
Hsis surface sensible heat flux.
[9] Equations (3), (4), and (6) indicate that the surface rain
rate (PS) can be resulted, respectively, from favorable
envi-ronmental water vapor and thermal conditions via cloud microphysical processes (QWVOUT+ QWVIN). Equations (3)
and (4) are combined by eliminating QWVOUT + QWVIN to
derive the surface rainfall equation (PSWV) constrained by
water vapor processes,
PSWV ¼ QWVTþ QWVFþ QWVEþ QCM: ð8aÞ
Equation (8a) states that the surface rain rate (PSWV) is
deter-mined by local atmospheric drying (QWVT > 0)/moistening
(QWVT< 0), water vapor convergence (QWVF> 0)/divergence
(QWVF < 0), surface evaporation (QWVE), and decrease in
local hydrometeor concentration/hydrometeor convergence (QCM > 0) or increase in local hydrometeor concentration/
hydrometeor divergence (QCM < 0). Equations (3) and (6)
are combined by eliminating QWVOUT + QWVIN to derive
the surface rainfall equation (PSH) constrained by thermal
processes,
PSH ¼ SHTþ SHFþ SHSþ SLHLFþ SRADþ QCM: ð8bÞ
Equation (8b) states that the surface rain rate (PSH) is
determined by local atmospheric warming (SHT> 0)/cooling
(SHT< 0), heat divergence (SHF> 0)/convergence (SHF< 0),
surface sensible heat (SHS), latent heat caused by ice‐related
processes (SLHLF), radiative cooling (SRAD > 0)/heating
(SRAD< 0), and decrease in local hydrometeor concentration/
hydrometeor convergence (QCM > 0) or increase in local
hydrometeor concentration/hydrometeor divergence (QCM<
0). Note that PSWV = PSH= PS. Precipitation equations (8a)
and (8b) are, respectively, constrained water vapor and thermal processes.
3.
Application to the Analysis of the Diurnal
Variation of Tropical Oceanic Rainfall
[10] The diurnal variation of tropical oceanic rainfall is
one of the most important tropical variables and plays a crucial role in regulating tropical climate. The dominant diurnal signal is the nocturnal rainfall peak over the tropical open ocean. The tropical oceanic nocturnal rainfall peak has been evident from radar observations over the tropical Pacific during TOGA COARE [e.g., Sui et al., 1997] and Tropical Rainfall Measuring Mission Microwave Imager and precipitation radar measurements over the tropical oceans [e.g., Yang et al., 2008]. The diurnal variations of radiation including solar heating and IR cooling play a pri-mary role in the development of diurnal rainfall variations [Gray and Jacobson, 1977; Tao et al., 1996; Sui et al., 1997, 1998]. The diurnal variations of large‐scale circulations also cause the diurnal variations of tropical rainfall [Petch and Gray, 2001; Dai, 2001; Gao et al., 2009].
[11] The impacts of diurnal variations of water vapor
convergence and heat divergence associated with large‐scale circulations on diurnal rainfall variations can be examined, respectively, with (8a) and (8b), whereas the effects of diurnal variation of radiation on diurnal rainfall variations can be analyzed with (8b). Thus, diurnally perturbed surface rainfall equations are derived. Taking model domain mean on (4) and (5), the model domain mean surface rainfall equations become PSWV¼ QWVTþ QWVFþ QWVEþ QCM; ð9Þ QWVT¼ @½ qv @t ; ð9aÞ QWVF¼ uo@qv @x wo@qv @z ; ð9bÞ
QWVE¼ Es; ð9cÞ QCM¼ @½ql @t ; ð9dÞ PSH ¼ SHTþ SHFþ SHSþ SLHLFþ SRADþ QCM; ð10Þ SHT¼ cp Lv @ T @t ; ð10aÞ SHF¼ cp Lv uo@ o @xþ wo @ @z " # ; ð10bÞ SHS ¼ cp Lv Hs; ð10cÞ SLHLF¼ Lf Lv hP18i; ð10dÞ SRAD¼ 1 Lv hQRi: ð10eÞ
Note that in (9d), hydrometeor convergence is zero because of cyclic horizontal lateral boundary conditions.
[12] A variable can be partitioned into a time mean
(superscript m) and a diurnal anomaly (superscript d), i.e.,
X ¼ Xmþ Xd: ð11Þ
Substituting (11) into (8a) and (8b), taking the time mean on the resulting equations, and subtracting the time‐mean equations from the resulting equations, respectively, lead to diurnally perturbed model domain mean surface rainfall equations: PdSWV ¼ QdWVTþ QWVFd þ QdWVEþ QdCM; ð12Þ QdWVT¼ @½q d v @t ; ð12aÞ QdWVF¼ uo@q o v @x d " # wð Þo m@qdv @z wð Þo d@qmv @z wð Þo d@qdv @z þ f wð Þod@qdv @zg m ; ð12bÞ QdWVE¼ Eds; ð12cÞ QdCM¼ @ q d 5 @t ; ð12dÞ PdSH ¼ SdHTþ SdHFþ SHSd þ SdLHLFþ SdRADþ QdCM; ð13Þ SdHT ¼cp Lv @ Th id @t ; ð13aÞ SdHF ¼cp Lv u o@ o @x !d 2 4 3 5 þcp Lv wo ð Þm@ d @z " # þcp Lv w o ð Þd@ m @z " # þcp Lv w o ð Þd@ d @z " # cp Lv ( wo ð Þd@ d @z )m " # ; ð13bÞ SdHS¼ cp Lv Hds; ð13cÞ SdLHLF¼ Lf Lv hPd 18i; ð13dÞ SdRAD¼ 1 Lv hQd Ri: ð13eÞ
The control experiment (C) and two sensitivity experi-ments from Gao et al. [2009] are revisited with calcula-tions of diurnally perturbed surface rainfall equacalcula-tions. The control experiment is integrated from 0400 local standard time (LST) 18 December 1992 to 0400 LST 09 January 1993 using a 2‐D cloud‐resolving model. The model is forced by large‐scale vertical velocity, zonal wind, and horizontal advections derived using 6 hourly TOGA COARE observations within the intensive flux array region (M. Zhang, personal communication, 1999), and hourly sea surface temperature (SST) at the improved meteorological surface mooring buoy (1.75°S, 156°E) [Weller and Anderson, 1996] (Figure 1). Gao et al. [2009] showed that diurnal variations of radiation and large‐scale forcing can produce a nocturnal rainfall peak through IR and advective cooling, respectively. But they did not fully explain the similarities and difference in the nighttime and afternoon rainfall peaks between these experiments. Thus, the diur-nally perturbed precipitation equations are applied in the analysis of these experiments to examine the similarities and difference in the nighttime and afternoon rainfall peaks between these experiments in the following discussions.
[13] In the control experiment, QWVFd in (12) and SHFd in
(13) are the diurnal variations of water vapor convergence and heat divergence associated with diurnally varying imposed large‐scale upward motions (Figure 2), and SRADd in
(13) is the diurnal variation of radiative processes, which are major factors that drive the diurnal variation of rainfall. To examine the role the diurnally varying large‐scale forcing plays in the diurnal rainfall processes, two additional sen-sitivity experiments are conducted (see Table 1). In exper-iment CF, the model is imposed by temporally varying large‐scale vertical velocity, zonal wind, and horizontal advection, a time‐invariant cosine of solar zenith angle in interactive radiation calculations, and time‐mean SST. Since the diurnal variation of radiation is mainly induced by the diurnal variation of solar radiative heating, imposed time‐ invariant cosine of solar zenith angle suppresses the diurnal variation of radiation (see SRADd in Figure 5b). In experiment
Figure 1. Time‐height cross sections of (a) vertical velocity (cm s−1) and (b) zonal wind (m s−1) and
time series of (c) sea surface temperature (°C) observed and derived from TOGA COARE for the 21 day period.
CR, the model is imposed by time‐dependent interactive radiation and time‐mean large‐scale vertical velocity, zonal wind, horizontal advection, and SST.
[14] The cloud‐resolving model used by Gao et al. [2009]
is the 2‐D version of the Goddard Cumulus Ensemble Model, which was originally developed by Soong and Ogura [1980], Soong and Tao [1980], and Tao and Simpson [1993] and was modified by Li et al. [1999]. The model has prog-nostic equations of potential temperature; specific humidity; mixing ratios of cloud water, raindrop, cloud ice, snow, and graupel; and perturbation momentum. The model also includes the cloud microphysical parameterization schemes from Rutledge and Hobbs [1983, 1984], Lin et al. [1983], Tao et al. [1989], and Krueger et al. [1995] (see Table 2) and interactive solar and thermal IR radiation parameteri-zation schemes from Chou et al. [1991, 1998] and Chou and Suarez [1994]. The model uses cyclic lateral boundaries, a horizontal domain of 968 km, a horizontal grid resolution of 1.5 km, 33 vertical levels, and a time step of 12 s.
[15] The diurnal anomalies of surface rain rates in the
three experiments are calculated by removing the time means from the diurnal composites (Figure 3). The surface rain rates in the three experiments generally show diurnal signals with positive anomalies during the nighttime and negative anomalies during the daytime. C and CF have similar positive rainfall anomalies in the nighttime and afternoon. CR has a larger positive anomaly of rainfall during hours 4–8 than the two other experiments do. To explain these similarities and differences, the diurnally perturbed surface rainfall (equations (12–13)) is calculated for all three experiments (Figures 4–6).
[16] The positive anomalies of rainfall in the afternoon
occur in both C and CF (Figures 4 and 5), 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 (Figure 2). The positive anomaly of the afternoon rainfall is absent in CR (Figure 6), which is caused by excluding diurnal vari-ation of imposed large‐scale vertical motions in CR. Thus, the imposed upward motions in the afternoon are major processes that account for positive anomalies of afternoon rainfall in both C and CF.
[17] To explain similar positive nocturnal rainfall
anoma-lies in C and CF, the diurnal anomaanoma-lies of convective available potential energy (CAPE) for the reversible moist adiabatic process [Li et al., 2002b] in the three experi-ments are calculated and shown in Figure 7. The diurnal anomalies of CAPE in C and CF are generally similar, although CAPE in CF leads that in C by 2 h. Since both cases include the diurnal variation of imposed large‐scale upward motion and only C 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, respec-tively, associated with the increase and decrease in large‐ scale upward motions. The diurnal anomaly of radiation also produces the diurnal anomaly of CAPE in CR. The positive anomaly of CAPE is highly correlated with the positive anomaly of SRADd associated with IR radiative
cooling (Figure 6b) during the nighttime, indicating the buildup of CAPE by the IR radiative cooling. The positive anomaly of rainfall peaks around hours 4–8 in CR, which is significantly larger than in C and CF (Figure 3) and is phase locking with the local atmospheric change from negative (cooling) to positive (warming) anomaly and the significant reduction of positive anomaly of SRAD
d
by solar Figure 2. Diurnal composite of the vertical profile of imposed large‐scale vertical velocity (cm s−1).
radiative heating. The results imply that the similar noc-turnal rainfall peaks in C and CF are primarily caused by imposed large‐scale upward motions. The diurnal anomaly of radiation plays a secondary role in producing the noc-turnal rainfall maximum when the diurnal variation of large‐scale circulation is present.
[18] The nocturnal rainfall maximum is primarily
pro-duced by the positive anomaly of IR radiative cooling in CR, whereas the negative anomaly of the daytime rainfall is mainly associated with the negative anomaly of solar radi-ative heating (Figure 6b). This indicates that the diurnal variation of radiation is a primary process that is responsible for the diurnal variation of rainfall when the diurnal varia-tion of large‐scale circulation is absent. During the night-time, the positive anomaly of radiation is largely offset by the negative anomaly of heat convergence in C (Figure 4b), whereas the heat convergence is absent in CR since the diurnal variation of imposed large‐scale upward motion is excluded, which accounts for the larger nocturnal rainfall maximum in CR than in C.
[19] In the three experiments, QCM d
shows hourly varia-tions attributable to the fact that the life cycle of clouds has a much shorter time scale than the diurnal cycle. QWVEd ,
SHSd , and SLHLFd have much weaker diurnal cycles than the
other rainfall‐related processes. Thus, diurnally perturbed surface rainfall (equations (12) and (13)) can be simplified as
PdSWV QdWVTþ QdWVF; ð14aÞ
PdSH SdHTþ SdHFþ SdRAD: ð14bÞ
The diurnally perturbed cloud budget can be correspond-ingly simplified as
PdS QdWVS QdWVOUT: ð14cÞ
In (14c), 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. Equation (14) 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 via generating the diurnal variations of vapor condensation and deposi-tions. When the diurnal variation of the large‐scale forcing is absent, the diurnally varying solar heating is the only factor driving the diurnal rainfall cycle. Thus, (14) becomes
PdSWV QdWVT; ð15aÞ
PdSH SdHTþ SdRAD; ð15bÞ
PdS QdWVS QdWVOUT: ð15cÞ
The diurnally varying radiative process leads to the diurnal variation of surface rainfall via the diurnal variations of vapor condensation processes.
[20] Note that this analysis differs from that of Gao et al.
[2009] in three ways. First, the thermal processes, including radiative heating, directly link to precipitation processes through new derived precipitation equations in this study, whereas Gao et al. [2009] discussed the diurnal variation of rainfall using the thermal budget. Thus, the analysis in this study and physical explanation of diurnal variation of
rain-Table 2. List of Microphysical Processes and Parameterization Schemesa
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
a
Data are from Rutledge and Hobbs [1983, 1984] (RH83, RH84), Lin et al. [1983] (LFO), Tao et al. [1989] (TSM), and Krueger et al. [1995] (KFLC).
fall are straightforward. Second, the diurnal anomalies of precipitation processes are examined in this study, and a set of precipitation equations associated with diurnal variation of rainfall are derived. In contrast, the diurnal variation of rainfall is analyzed with diurnal composite (diurnal anomaly plus time mean) data in the study by Gao et al. [2009]. Third, with the applications of anomalous precipitation equations, the similarities and differences in nighttime and afternoon rainfall peak between the three experiments, which are not fully understood by Gao et al. [2009], and are clearly explained in this study.
4.
Summary
[21] The precipitation is the product of development of
clouds, which is subject to environmental conditions. The water vapor, heat, and cloud budgets best describe the re-lations between precipitation, clouds, and environmental water vapor and thermal conditions. The surface rainfall is constrained by environmental water vapor and thermal conditions, which can be summarized by the precipitation equations. Thus, the surface rainfall equations are, respec-tively, derived by combining cloud budget with water vapor budget and with heat budget. The water vapor constrained rainfall equation was derived by Gao et al. [2005a]. The rainfall equations are applied to the analysis of diurnal variations of surface rainfall over the tropical deep con-vective regime during TOGA COARE. The three experi-ments with the 2‐D cloud‐resolving model conducted by Gao et al. [2009] are revisited in this study. Since diurnal-ly varying imposed large‐scale forcing and solar zenith angle are two factors that are responsible for the diurnal variations of tropical oceanic rainfall, the control experiment
includes both diurnal variations, whereas the two additional experiments exclude either the diurnal variation of imposed large‐scale forcing or the diurnal variation of solar zenith angle.
[22] Petch and Gray [2001] showed that the simulated
diurnal rainfall cycle of the tropical west Pacific is deter-mined by large‐scale forcing but is not enhanced by radia-tion. Dai [2001] revealed the importance of land‐ocean contrast in the formation of a nocturnal precipitation peak over the coastal areas. The control experiment and sensi-tivity experiment with time‐invariant solar zenith angle conducted in this study show similar nighttime and after-noon rainfall peaks, which is consistent with the results of Petch and Gray [2001]. This suggests that the diurnal var-iation of radvar-iation may play a secondary role in the devel-opment of nocturnal rainfall peak when diurnal variation of large‐scale circulation is present.
[23] Previous studies showed the important role of diurnal
variation of radiation in the formation of diurnal variation of rainfall when the large‐scale forcing is weak or absent [e.g., Sui et al., 1997, 1998]. The analysis of precipitation equa-tions with the experiment of time‐invariant large‐scale forcing reveals that the diurnal variation of radiation mainly associated with diurnally varying solar zenith angle is a major process that accounts for the diurnal variation of rainfall. The calculation of the thermally constrained pre-cipitation equation reveals that the diurnal anomaly of sur-face rainfall is associated with the diurnal anomaly of radiation. The concise diagnostic analysis of diurnal rainfall variations with precipitation equations indicates potential applications of the equations to diagnose the dominant physical processes that are responsible for surface rainfall processes at multiple temporal and spatial scales.
Figure 3. Diurnal anomalies of surface rain rates (mm h−1) simulated in C (solid line), CF (dashed line), and CR (dotted line).
Figure 4. Diurnal anomalies of (a) PSWVd (dark solid line), QWVTd (light solid line), QWVFd (short dashed
line), QWVE d
(dotted line), QCM
d (dot‐dashed line), and Q WVS d
(long dashed line) and (b) PSH d
(dark solid line), SHTd (light solid line), SHFd (short dashed line), SHSd (dotted line), SLHLFd (long short dashed line),
Figure 5. Diurnal anomalies of (a) PSWVd (dark solid line), QWVTd (light solid line), QWVFd (short dashed
line), QWVEd (dot), QCMd (dot‐dashed line), and QWVSd (long dashed line) and (b) PSHd (dark solid line),
SHTd (light solid line), SHFd (short dash line), SHSd (dotted line), SLHLFd (long short dashed line), SRADd (long
dashed line), and QCM
Figure 6. Diurnal anomalies of (a) PSWVd (dark solid line), QWVTd (light solid line), QWVFd (short
dashed line), QWVE d
(dotted line), QCM
d (dot‐dashed line), and Q WVS d
(long dashed line) and (b) PSH d
(dark solid line), SHTd (light solid line), SWVTd (short dashed line), SHSd (dotted line), SLHLFd (long short dashed
[24] Acknowledgments. We thank W.‐K. Tao at NASA/GSFC for his cloud‐resolving model, M. Zhang (The State University of New York at Stony Brook) for his TOGA COARE forcing data, and three anonymous reviewers for their constructive comments. This work was supported by National Key Basic Research and Development Project of China 2004CB418301, National Natural Sciences Foundation of China grant 40775031, Knowledge Innovation Project of Chinese Academy of Sciences grant KCL14014, and“Outstanding Oversea Scholars” project 2005‐2‐17.
References
Chou, M.‐D., and M. J. Suarez (1994), An efficient thermal infrared radi-ation parameterizradi-ation for use in general circulradi-ation model, NASA Tech. Memo., TM‐104606, vol. 3, 85 pp., NASA Goddard Space Flight Cent., Greenbelt, Md.
Chou, M.‐D., D. P. Kratz, and W. Ridgway (1991), Infrared radiation parameterization in numerical climate models, J. Clim., 4, 424–437, doi:10.1175/1520-0442(1991)004<0424:IRPINC>2.0.CO;2.
Chou, M.‐D., M. J. Suarez, C.‐H. Ho, M. M.‐H. Yan, and K.‐T. Lee (1998), Parameterizations for cloud overlapping and shortwave single scattering properties for use in general circulation and cloud ensemble models, J. Atmos. Sci., 55, 201–214.
Cui, X., and S. Gao (2008), Effects of zonal perturbations of sea surface temperature on tropical equilibrium states: A 2D cloud‐resolving model-ing study, Prog. Nat. Sci., 18, 413–419, doi:10.1016/j.pnsc.2007.10.007. Cui, X., and X. Li (2006), Role of surface evaporation in surface rainfall processes, J. Geophys. Res., 111, D17112, doi:10.1029/2005JD006876. Dai, A. (2001), Global precipitation and thunderstorm frequencies. Part II: Diurnal variations, J. Clim., 14, 1112–1128, doi:10.1175/1520-0442 (2001)014<1112:GPATFP>2.0.CO;2.
Gao, S. (2008), A cloud‐resolving modeling study of cloud radiative effects on tropical equilibrium states, J. Geophys. Res., 113, D03108, doi:10.1029/2007JD009177.
Gao, S., and X. Li (2008a), Cloud‐Resolving Modeling of Convective Processes, 206 pp., Springer, Berlin, Germany.
Gao, S., and X. Li (2008b), Responses of tropical deep convective precip-itation systems and their associated convective and stratiform regions to the large‐scale forcing, Q. J. R. Meteorol. Soc., 134, 2127–2141, doi:10.1002/qj.331.
Gao, S., F. Ping, X. Li, and W.‐K. Tao (2004), A convective vorticity vec-tor associated with tropical convection: A 2D cloud‐resolving modeling study, J. Geophys. Res., 109, D14106, doi:10.1029/2004JD004807.
Gao, S., X. Cui, Y. Zhou, and X. Li (2005a), Surface rainfall processes as simulated in a cloud‐resolving model, J. Geophys. Res., 110, D10202, doi:10.1029/2004JD005467.
Gao, S., X. Cui, Y. Zhou, X. Li, and W.‐K. Tao (2005b), A modeling study of moist and dynamic vorticity vectors associated with 2D tropical con-vection, J. Geophys. Res., 110, D17104, doi:10.1029/2004JD005675. Gao, S., Y. Zhou, and X. Li (2007), Effects of diurnal variations on tropical
equilibrium states: A two‐dimensional cloud‐resolving modeling study, J. Atmos. Sci., 64, 656–664, doi:10.1175/JAS3835.1.
Gao, S., X. Cui, and X. Li (2009), A modeling study of diurnal rainfall var-iations during the 21‐day period of TOGA COARE, Adv. Atmos. Sci., 26, 895–905, doi:10.1007/s00376-009-8123-6.
Grabowski, W. W., X. Wu, and M. W. Moncrieff (1996), Cloud‐resolving model of tropical cloud systems during Phase III of GATE. Part I: Two‐ dimensional experiments, J. Atmos. Sci., 53, 3684–3709, doi:10.1175/ 1520-0469(1996)053<3684:CRMOTC>2.0.CO;2.
Gray, W. M., and R. W. Jacobson (1977), Diurnal variation of deep cumu-lus convection, Mon. Weather Rev., 105, 1171–1188, doi:10.1175/1520-0493(1977)105<1171:DVODCC>2.0.CO;2.
Krueger, S. K., Q. Fu, K. N. Liou, and H.‐N. S. Chin (1995), Improvement of an ice‐phase microphysics parameterization for use in numerical simu-lations of tropical convection, J. Appl. Meteorol., 34, 281–287. Li, X., C.‐H. Sui, K.‐M. Lau, and M.‐D. Chou (1999), Large‐scale forcing
and cloud‐radiation interaction in the tropical deep convective regime, J. Atmos. Sci., 56, 3028–3042, doi:10.1175/1520-0469(1999)056< 3028:LSFACR>2.0.CO;2.
Li, X., C.‐H. Sui, and K.‐M. Lau (2002a), Precipitation efficiency in the tropical deep convective regime: A 2‐D cloud resolving modeling study, J. Meteorol. Soc. Jpn., 80, 205–212, doi:10.2151/jmsj.80.205. Li, X., C.‐H. Sui, and K.‐M. Lau (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, doi:10.1175/1520-0469(2002)059<1712:IBTCAI>2.0.CO;2.
Lin, Y.‐L., R. D. Farley, and H. D. Orville (1983), Bulk parameterization of the snow field in a cloud model, J. Clim. Appl. Meteorol., 22, 1065– 1092, doi:10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2. Petch, J. C., and M. E. B. Gray (2001), Sensitivity studies using a cloud‐
resolving model simulation of the tropical west Pacific, Q. J. R. Meteorol. Soc., 127, 2287–2306, doi:10.1002/qj.49712757705.
Ping, F., Z. Luo, and X. Li (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, doi:10.1175/MWR3419.1.
Figure 7. Diurnal anomalies of CAPE (CPAEd) in (a) C (solid line), (b) CR (dotted line), and (c) CF (dashed line). Data are in J kg−1.
Ping, F., Z. Luo, and X. Li (2008), Kinematics, cloud microphysics, and spatial structures of tropical cloud clusters: A two‐dimensional cloud‐ resolving modeling study, Atmos. Res., 88, 323–336, doi:10.1016/j. atmosres.2007.11.027.
Rutledge, S. A., and P. V. Hobbs (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, doi:10.1175/ 1520-0469(1983)040<1185:TMAMSA>2.0.CO;2.
Rutledge, S. A., and P. V. Hobbs (1984), The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. Part XII: A diagnostic modeling study of precipitation devel-opment in narrow cold‐frontal rainbands, J. Atmos. Sci., 41, 2949– 2972, doi:10.1175/1520-0469(1984)041<2949:TMAMSA>2.0.CO;2. Soong, S. T., and Y. Ogura (1980), Response of tradewind cumuli to large‐
scale processes, J. Atmos. Sci., 37, 2035–2050, doi:10.1175/1520-0469 (1980)037<2035:ROTCTL>2.0.CO;2.
Soong, S. T., and W. K. Tao (1980), Response of deep tropical cumulus clouds to mesoscale processes, J. Atmos. Sci., 37, 2016–2034, doi:10.1175/1520-0469(1980)037<2016:RODTCC>2.0.CO;2.
Sui, C.‐H., and X. Li (2005), A tendency of cloud ratio associated with the development of tropical water and ice clouds, Terr. Atmos. Oceanic Sci., 16, 419–434.
Sui, C.‐H., K.‐M. Lau, Y. N. Takayabu, and D. Short (1997), Diurnal variations in tropical oceanic cumulus convection during TOGA COARE, J. Atmos. Sci., 54, 639–655, doi:10.1175/1520-0469(1997)054< 0639:DVITOC>2.0.CO;2.
Sui, C.‐H., X. Li, and K.‐M. Lau (1998), Radiative‐convective processes in simulated diurnal variations of tropical oceanic convection, J. Atmos. Sci., 55, 2345–2359, doi:10.1175/1520-0469(1998)055<2345:RCPISD> 2.0.CO;2.
Sui, C.‐H., X. Li, M.‐J. Yang, and H.‐L. Huang (2005), Estimation of oce-anic precipitation efficiency in cloud models, J. Atmos. Sci., 62, 4358– 4370, doi:10.1175/JAS3587.1.
Sui, C.‐H., X. Li, and M.‐J. Yang (2007), On the definition of precipitation efficiency, J. Atmos. Sci., 64, 4506–4513, doi:10.1175/2007JAS2332.1. Tao, W.‐K., and J. Simpson (1993), The Goddard Cumulus Ensemble model. Part I: Model description, Terr. Atmos. Oceanic Sci., 4, 35–72. Tao, W.‐K., J. Simpson, and M. McCumber (1989), An ice‐water satura-tion adjustment, Mon. Weather Rev., 117, 231–235, doi:10.1175/1520-0493(1989)117<0231:AIWSA>2.0.CO;2.
Tao, W.‐K., S. Lang, J. Simpson, C.‐H. Sui, B. Ferrier, and M.‐D. Chou (1996), Mechanisms of cloud‐radiation interaction in the tropics and
midlatitude, J. Atmos. Sci., 53, 2624–2651, doi:10.1175/1520-0469 (1996)053<2624:MOCRII>2.0.CO;2.
Tao, W.‐K., C.‐L. Shie, J. Simpson, S. Braun, R. H. Johnson, and P. E. Ciesielski (2003), Convective systems over the South China Sea: Cloud‐resolving model simulations, J. Atmos. Sci., 60, 2929–2956, doi:10.1175/1520-0469(2003)060<2929:CSOTSC>2.0.CO;2.
Wang, D., X. Li, W.‐K. Tao, Y. Liu, and H. Zhou (2009), Torrential rain-fall processes associated with a landrain-fall of severe tropical storm Bilis (2006), A two‐dimensional cloud‐resolving modeling study, Atmos. Res., 91, 94–104, doi:10.1016/j.atmosres.2008.07.005.
Wang, J.‐J., X. Li, and L. Carey (2007), Evolution, structure, cloud micro-physical and surface rainfall processes of a monsoon convection during the South China Sea Monsoon Experiment, J. Atmos. Sci., 64, 360– 380, doi:10.1175/JAS3852.1.
Weller, R. A., and S. P. Anderson (1996), Surface meteorology and air‐sea fluxes in the western equatorial Pacific warm pool during TOGA COARE, J. Clim., 9, 1959–1990, doi:10.1175/1520-0442(1996)009< 1959:SMAASF>2.0.CO;2.
Wu, X., W. W. Grabowski, and M. W. Moncrieff (1998), Long‐term evolution of cloud systems in TOGA COARE and their interactions with radiative and surface processes. Part I: Two‐dimensional cloud‐ resolving model, J. Atmos. Sci., 55, 2693–2714, doi:10.1175/1520-0469(1998)055<2693:LTBOCS>2.0.CO;2.
Xu, K.‐M., and D. A. Randall (1996), Explicit simulation of cumulus ensembles with the GATE Phase III data: Comparison with observations, J. Atmos. Sci., 53, 3710–3736, doi:10.1175/1520-0469(1996)053<3710: ESOCEW>2.0.CO;2.
Xu, K.‐M., et al. (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, doi:10.1256/003590002321042117.
Xu, X., F. Xu, and B. Li (2007), A cloud‐resolving modeling study of a torrential rainfall event over China, J. Geophys. Res., 112, D17204, doi:10.1029/2006JD008275.
Yang, S., K.‐S. Kuo, and E. A. Smith (2008), Persistent nature of second-ary diurnal modes of precipitation over oceanic and continental regions, J. Clim., 21, 4115–4131, doi:10.1175/2008JCLI2140.1.
S. Gao, Laboratory of Cloud‐Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Huayanbeili 40 Building, Beijing 100029, China. (gst@lasg.iap.ac.cn)
X. Li, Center for Satellite Applications and Research, NOAA, NESDIS, 5200 Auth Rd., Rm. 712, Camp Springs, MD 20746, USA.
