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Relating Convective and Stratiform Rain to Latent Heating
WEI-KUO TAO
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland

STEPHEN LANG
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Science Systems
and Applications, Inc., Lanham, Maryland

XIPING ZENG
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Goddard Earth Sciences
and Technology Center, University of Maryland, Baltimore County, Baltimore, Maryland

SHOICHI SHIGE
Graduate School of Science, Kyoto University, Kyoto, Japan

YUKARI TAKAYABU
Center for Climate System Research, University of Tokyo, Tokyo, Japan(Manuscript received 5 June 2009, in final form 23 October 2009)
ABSTRACTThe relationship among surface rainfall, its intensity, and its associated stratiform amount is established byexamining observed precipitation data from the Tropical Rainfall Measuring Mission (TRMM) Precipitation
Radar (PR). The results show that for moderate–high stratiform fractions, rain probabilities are strongly
skewed toward light rain intensities. For convective-type rain, the peak probability of occurrence shifts tohigher intensities but is still significantly skewed toward weaker rain rates. The main differences between
the distributions for oceanic and continental rain are for heavily convective rain. The peak occurrence, as
well as the tail of the distribution containing the extreme events, is shifted to higher intensities for continental rain. For rainy areas sampled at 0.58 horizontal resolution, the occurrence of conditional rain rates over
100 mm day21 is significantly higher over land. Distributions of rain intensity versus stratiform fraction forsimulated precipitation data obtained from cloud-resolving model (CRM) simulations are quite similar to thosefrom the satellite, providing a basis for mapping simulated cloud quantities to the satellite observations.
An improved convective–stratiform heating (CSH) algorithm is developed based on two sources of information: gridded rainfall quantities (i.e., the conditional intensity and the stratiform fraction) observed
from the TRMM PR and synthetic cloud process data (i.e., latent heating, eddy heat flux convergence, andradiative heating/cooling) obtained from CRM simulations of convective cloud systems. The new CSH
algorithm-derived heating has a noticeably different heating structure over both ocean and land regions
compared to the previous CSH algorithm. Major differences between the new and old algorithms include
a significant increase in the amount of low- and midlevel heating, a downward emphasis in the level of maximum cloud heating by about 1 km, and a larger variance between land and ocean in the new CSH algorithm.

Corresponding author address: Dr. W.-K. Tao, Laboratory for Atmospheres, NASA GSFC, Greenbelt, MD 20771.
E-mail: wei-kuo.tao-1@nasa.gov
DOI: 10.1175/2009JCLI3278.1
Ó 2010 American Meteorological Society

VOLUME 23

1 APRIL 2010

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1. Introduction
The release of latent heating (LH) during the formation of precipitation is of immense consequence to thenature of large- and small-scale atmospheric circulations,particularly in the tropics where various large-scale tropical modes controlled by LH persist and vary on a global
scale. Latent heat release and its variations are without
doubt the most important diabatic processes within theatmosphere, and thus play a central role in the earth’s
water cycle. Latent heating is dominated by phase changes
between water vapor and small liquid or frozen cloudsized particles. It consists of the condensation of cloud
droplets, evaporation of cloud droplets and raindrops,
freezing of cloud droplets and raindrops, melting of snow
and graupel/hail, and the deposition and sublimation ofice particles. In addition, eddy heat flux convergencefrom cloud motions can also redistribute the heating or
cooling vertically and horizontally. LH cannot be measured directly with current techniques, including current
remote sensing or in situ instruments, which explains
why nearly all retrieval schemes depend heavily on some
type of cloud-resolving model (CRM). However, apparent
heating or Q1, of which LH is an important component,
can be derived indirectly by measuring vertical profiles oftemperature and the associated 3D wind fields from extensive rawinsonde networks through a residual method(known as a diagnostic heating budget; Yanai et al. 1973).
The launch of the Tropical Rainfall Measuring Mission(TRMM) satellite, a joint U.S.–Japan project, in November 1997 made it possible for quantitative measurementsof tropical rainfall to be obtained on a continuous basis
over the entire global tropics. TRMM provides a muchneeded accurate measurement of rainfall as well as an
estimate of the four-dimensional structure of LH (ordiabatic heating) over the global tropics. Over the last
few years, standard LH products from TRMM measurements have become established as a valuable resource forscientific research and applications (see a review by Tao
et al. 2006). Such products enable new insights and investigations into the complexities of convective system
life cycles, diabatic heating controls and feedbacks related to mesoscale to synoptic-scale circulations and theirforecasting, the relationship of tropical patterns of LH to
the global circulation and climate, and strategies for improving cloud parameterizations in environmental prediction models.
Five different TRMM LH algorithms designed to use
satellite-estimated surface rain rates and precipitation
profiles have been developed, intercompared, validated,
and applied in the past decade (see Tao et al. 2006, 2007).
They are the Goddard convective–stratiform heating(CSH) algorithm, the hydrometeor heating (HH) algo-1875

rithm, the Goddard profiling heating (GPROF heating)algorithm,1 the spectral latent heating (SLH) algorithm,
and the precipitation radar heating (PRH) algorithm.
The CSH algorithm only requires information on thesurface precipitation rates, amount of stratiform rain,
and the type and location of the observed cloud systems2(Tao et al. 1993a). A lookup table (LUT), however, isused, which contains stored mean diabatic convective
and stratiform heating profiles that have been normalized respectively by their mean convective and stratiform surface rain rates for various types of cloud systems
in different geographic locations. These profiles aremostly obtained from CRM [i.e., the Goddard Cumulus
Ensemble (GCE) model] simulations but also include
profiles from sounding budget studies. In GPROF, CRMsimulated vertical profiles of hydrometeors (and associated LH) that have radiative characteristics consistent
with a given set of multispectral microwave radiometricobservations are composited to create (retrieve) a best
estimate of the observed profiles (Olson et al. 1999; Grecu
et al. 2009). The HH algorithm3 estimates LH profiles
as a function of the vertical derivative of the retrievedhydrometeor profiles (Yang and Smith 1999). The derivation and evaluation of the HH algorithm is also basedon CRM simulations. It requires information about thevertical profiles of cloud- and precipitation-sized waterand ice particles, all of which can be obtained from passive microwave measurements, including those from the
TRMM Microwave Imager (TMI; Smith et al. 1994). The
terminal (fall) velocities of the large cloud ( precipitating)particles (rain, snow, and graupel/hail) are also required
for the HH algorithm, as is the cloud-scale velocity,which is obtained by applying a regression method toa CRM-simulated database. The SLH algorithm (Shige
et al. 2004, 2007, 2008, 2009) is also based on CRM(i.e., GCE) results. It uses TRMM Precipitation Radar(PR) information (i.e., melting layer, precipitation top
height, rain rate and type) to select the heating profiles from a LUT. The PRH algorithm (Satoh and Noda
2001; M. Katsumata et al. 2008, unpublished manuscript)
also uses PR information but without using any CRMsimulated heating profiles. However, it needs to estimate
the cloud drafts and (standard) thermodynamic structuresassociated with cloud systems. An iteration calculation is

1
The GPROF heating algorithm was recently replaced by the
TRAIN algorithm.
2
The CSH algorithm regularly uses PR echo top heights to include shallow convection.
3
Tao et al. (1990) were the first to put forth a LH algorithm thatwas termed a hydrometeor heating algorithm. Tao et al. (1993a)then improved the performance of their HH algorithm by including
surface rain rates.

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TABLE 1. Summary of the five LH algorithms participating. Data inputs, retrieved products, and salient references included. Note thatthe conventional relationship between Q1 (apparent heat source), LH, and QR (radiative heating) is expressed by Q1 2 QR 5 LH 1 EHT,
where the final term represents eddy heat transport by clouds (noting that vertically integrated EHT is zero; i.e., it provides no explicit
influence on surface rainfall). Note that CSH, SLH, and TRAIN explicitly use CRM-simulated latent heating profiles in their heating
algorithm lookup tables. Both HH and PRH also implicitly use CRM-simulated results (i.e., cloud vertical velocity).

CSH (Convective-stratiform
heating)
SLH (Spectral latentheating)
TRAIN (Trained radiometer
algorithm)
HH (Hydrometeor heating)
PRH (Precipitation radar
heating)

Key references inalgorithm description

TRMM data needed

Heating products

PR, TMI,
PR–TMIPR

Q1, LH
LH, Q1 2 QR

Shige et al. (2004, 2007, 2008, 2009)

TMI (PR training)

Q1 2QR, LH

PR–TMI
PR

LH
LH

Grecu and Olson (2006); Olson et al. (2006);
Grecu et al. (2009)
Yang and Smith (1999); Yang et al. (2006)
Satoh and Noda (2001);
M. Katsumata et al. (2008, unpublishedmanuscript)

applied to match the relationship between rainfall and
LH. The strengths and weaknesses of each algorithm
were discussed in Tao et al. (2006). Table 1 lists the required data, type of heating product, and the key references for each of these algorithms.
In this paper, both TRMM PR and CRM-simulated
results will be used to examine and quantify the relationship among stratiform rain fraction, surface rain intensity,and LH for convective systems of various geographic origins. The results from the GCE model simulations will be
used to calculate each of the major components of theatmospheric heating budget (i.e., LH, eddy transport, andradiation). These simulated results are then used to develop a new CSH algorithm. In section 2, the model, its
setup, and the cases are described. The results are shownand discussed in section 3. In section 4, the performanceof the new CSH algorithm is presented. Finally, the major
results and future work are summarized in section 5.

2. Numerical modeling and data
a. Goddard cumulus ensemble model
The GCE is a CRM and is used to simulate clouds/
cloud systems and their associated heating budget. The
model is nonhydrostatic. It accounts for both absorption
and scattering for solar radiation and both emission andabsorption for infrared radiation and has been used
to study cloud–radiation interactions (Tao et al. 1996,
2003a). Subgrid-scale (turbulent) processes in the model
are parameterized using a scheme based on Klemp andWilhelmson (1978). The effects of both dry and moist
processes on the generation of subgrid-scale kinetic energy have been incorporated (Soong and Ogura 1980).
The sedimentation of cloud ice (Starr and Cox 1985) is
included to better model clouds in the upper troposphere.

Tao et al. (1993a, 2000, 2001)

All scalar variables (i.e., temperature, water vapor, andall hydrometeors) are advected with a positive definite
advection scheme. Results from the positive definite advection scheme are in better agreement with observations
for tropical cloud systems (Johnson et al. 2002).
The model has five prognostic hydrometeor variables:
the mixing ratios of cloud water, rainwater, cloud ice,
snow, and graupel. The model’s bulk microphysics scheme
was recently modified by Lang et al. (2007) to reduce theunrealistically large amount of precipitating ice particles(mainly graupel) in the model and by Zeng et al. (2008,2009) to introduce the ice nuclei concentration into theparameterization of the Bergeron process as an input
factor. The development and main features of the GCE
model were published in Tao and Simpson (1993) and Tao
et al. (2003a). A review on the application of the GCE
model to better understand precipitation processes can befound in Simpson and Tao (1993) and Tao (2003).
In the GCE model, each grid point is designated aseither a cloudy or clear area for each integration time,depending on whether the sum of the cloud water and ice
mixing ratios are larger than 1023 g kg21 at each grid
point (usually an indicator of 100% relative humidity). In
the cloudy area, each grid point can also be designated aseither being in the active or nonactive updraft or downdraft region (Tao et al. 1987). In addition, the cloud
characteristics can be divided into their convective andstratiform components (Tao et al. 1991, 1993b; Lang et al.
2003). In short, convective regions include those withlarge vertical velocities (exceeding 3–5 m s21) and/or
large surface precipitation rates. The stratiform region isseparated into regions with and without surface rainfall.
The model used in this study has the same structure asthat in previous studies (e.g., Soong and Tao 1980; Taoand Soong 1986; Johnson et al. 2002; Tao et al. 2003b,
2004; Zeng et al. 2007; and many others) wherein clouds

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TABLE 2. Field campaigns (ARM, SCSMEX, TOGA COARE, and GATE) including the geographic location, starting time, andintegration length of GCE model simulations. Also included are the previous GCE modeling papers that have simulated the case.
Field campaign

Geographic location

Starting date

Modeling days

ARM-SGP-97
ARM-SGP-02
SCSMEX/NESATOGA COARE(378N, 978W)(218N, 1178E)(28S, 1548E)

18 Jun 1997
25 May 2002
6 May 1998
1 Nov 1992

29
20
44
61

GATE

(98N, 248W)

1 Sep 197418

are simulated under prescribed large-scale forcing. The
default numerical experiment is two-dimensional (2D),using a 1-km horizontal resolution and vertical resolution that ranges from 42.5 m at the bottom to 1 km at themodel top, which is at 22.5 km. The model uses a time
step of 6 s and 512 3 41 grid points for integration.
Please see Zeng et al. (2008, 2009) for more details.

b. Data
1) OCEANIC CONVECTIVE SYSTEMS (GATE,TOGA COARE, AND SCSMEX)The South China Sea Monsoon Experiment (SCSMEX)
was conducted in May–June 1998. Two major convective
events, one prior to and during monsoon onset (18–26
May 1998) and the other post monsoon onset (2–11 June1998), were observed. The SCSMEX forcing data wereobtained from a variational analysis approach (Zhang
and Lin 1997; Zhang et al. 2001) and used to drive the
GCE model for 44 days starting at 0600 UTC 6 May 1998.
The Tropical Ocean Global Atmosphere–Coupled Ocean
Atmosphere Response Experiment (TOGA COARE)
was conducted in 1992/93 over the central Pacific. The
most intense convection during TOGA COARE occurred in mid and late December 1992, prior to the peakin westerly wind bursts around 1 January 1993. Several
major convective events occurred around 11–16 and
20–25 December 1992, mainly due to the low-level, largescale convergence of easterlies and westerlies (Ciesielski
et al. 2003). For TOGA COARE, the large-scale forcing
used in the GCE model was derived from the Intensive
Flux Array (IFA) sounding network (Lin and Johnson
1996). The Global Atmospheric Research Program(GARP) Atlantic Tropical Experiment (GATE) was
conducted in 1974 over the east Atlantic. Cloud systems(nonsquall clusters, a squall line, and scattered convection) for the period 1–8 September 1974 during phase III
of GATE have also been simulated using the GCE model(Li et al. 1999; Tao 2003). Large-scale GATE forcingsfrom Sui and Yanai (1986) were used to drive the GCE
model. The environmental conditions for SCSMEX,TOGA COARE, and GATE can be found in Tao et al.
(2004). The TOGA COARE surface flux algorithm

Tao et al. (2004); Zeng et al. (2009)
Zeng et al. (2007, 2009)
Tao et al. (2003b); Zeng et al. (2008)
Das et al. (1999); Johnson et al. (2002);
Zeng et al. (2009)
Li et al. (2002); Zeng et al. (2009)(Wang et al. 1996) is used to calculate sea surface fluxes
for these oceanic cases.

2) CONTINENTAL CASES (ARM 1997 AND 2002)
The Atmospheric Radiation Measurement (ARM) program established the Southern Great Plains (SGP) site toobserve clouds and precipitation for climate research.
The site is centered at 36.68N, 96.58W. Two summer field
campaigns were conducted at the site in 1997 and 2002
and are referred to here as ARM-SGP-97 and -02. The
ARM forcing data were also obtained from the variational analysis approach of Zhang and Lin (1997) andZhang et al. (2001). Surface fluxes taken from site-wide
averages of observed fluxes from the ARM Energy Balance Bowen Ratio (EBBR) stations are imposed into themodel (Zeng et al. 2007). The ARM-SGP-97 numericalsimulation starts at 2330 UTC 18 June 1997 and lasts for
29 days. The ARM-SGP-02 simulation starts at 2030 UTC
25 May 2002 and lasts for 20 days. For the ARM cases, thesurface wind does not interact with the boundary layer.
The SCSMEX, TOGA COARE, GATE, and ARM
cases were all previously simulated with the GCE model.
Please see Das et al. (1999), Li et al. (1999), and Zenget al. (2009) for the GATE case; Johnson et al. (2002) and
Zeng et al. (2009) for the TOGA COARE cases; Taoet al. (2003b) and Zeng et al. (2008) for the SCSMEX
cases; and Xu et al. (2002) and Zeng et al. (2007, 2009) for
the ARM cases regarding the temporal variation of thewind shear. Table 2 summarizes all of the GCE model
integrations for these cases.

c. TRMM PR
TRMM PR data are available in a variety of forms,
from raw instantaneous pixel-level data (e.g., 1B21) toprocessed instantaneous pixel-level data (e.g., 2A25) toa gridded monthly product containing a complete set ofmeasurement statistics (i.e., 3A25). Although it is not
limited to using rainfall data just from the PR, the original
CSH algorithm (hereafter CSHv1) utilized the monthly
gridded 3A25 product at 0.58 3 0.58 horizontal resolution because of the coincident measurements of echo
top heights available from the PR. However, frequent

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FIG. 1. Hit frequency of the TRMM observations over (a) oceanic and (b) continental regions.

demands for heating data at a higher temporal resolution
to study processes on shorter time scales necessitateda change to another product: 3G68. The 3G68 productblends the convenience of a gridded product at 0.58 3 0.58
resolution with instantaneous values. It also contains rainfall data from all three TRMM rain algorithms: PR, TMI,
and combined. However, it is limited strictly to surface
rainfall information. By combining 3G68 with a separate
dataset on PR echo top heights, CSHv1 heating profiles
were generated on a daily time scale,4 which was wellreceived by users interested in having higher-temporalresolution heating data. Shige et al. (2007) conducted anerror analysis for the SLH algorithm and recommended
that horizontal averaging over ;30 km be used for quantitative heating estimates. This makes the 3G68 gridded
orbital product a suitable target for heating retrieval.

3. Resultsa. PR-estimated relationship between rain intensity
and stratiform rain percentage
Figure 1 shows the relationship between rainfall intensity and stratiform precipitation percentage for ocean andland regions based on gridded instantaneous rainfall datafrom the TRMM PR (i.e., 3G68). Average stratiform rain
percentages and mean rain rates for rainy areas only (i.e.,
conditional rain rates) were computed over each 0.58 3
0.58 grid and then distributed into rain intensity and stratiform rain percentage bins of 20 mm day21 and 5%, respectively. The overall pattern between the two regions isquite similar. For example, for moderate to high stratiform fractions, rain probabilities are strongly skewed

4

Although the 3G68 product contains instantaneous gridded
orbital data, its effective time sampling is approximately daily
when considering the TRMM satellite’s coverage.

toward light rain intensities (i.e., less than 100 mm day21);
for convective type rain, the peak probability of occurrence and the tail of the distribution shift to higher intensities, but overall weaker rain rates still dominate
the distribution in terms of occurrence. These results
imply that there is a general relationship between rainfall intensity and stratiform amount, one that might beused to help formulate a retrieval algorithm. There are,however, differences in the probability distributions
between oceanic and land regions. These differences aremainly in the highly convective region. For highly convective rain, both the peak occurrence and the tail ofthe distribution containing the extreme rainfall rates are
shifted toward higher intensities for continental rain, suchthat for rainy areas the relative likelihood of precipitation
rates over 100 mm day21 is significantly higher over land.
Combined with the fact that there are characteristic differences in continental versus oceanic convection, this
implies that there is and should be a separation between
the treatment of continental and oceanic regions.
Figure 2 shows the TRMM PR observed relationshipbetween rainfall intensity and stratiform precipitation
percentage over the SCSMEX northern enhanced sounding array (NESA) for May–June of 1998.5 It also shows
the relationship for the same SCSMEX region for 10 yr
of May–June observations. Once again, the same general pattern emerges, with light rainfall dominating theprobability of occurrence and peak probabilities andextreme events shifting to higher intensities for themost convective part of the distribution. The SCSMEXNESA distribution, however, appears more similar tothat for land (i.e., Fig. 1b). Johnson et al. (2005) foundthat the stratiform rain fraction during the monsoon
5

Note that Ciesielski and Johnson (2006) stated that ENSO hada strong influence on the rainfall distribution over the South China
Sea during SCSMEX.

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FIG. 2. (a) As in Fig. 1, but for TRMM observations over SCSMEX NESA for May–June 1998. (b) As in (a), but for
10 yr of observations.

onset in SCSMEX was relatively low. They attributed
this to dry conditions aloft and relatively weak instability. In addition to rainfall amount, Table 3 shows thePR-observed mean stratiform rain percentage for the
global tropics and subtropics (52.8%) and its oceanic(55.0%) and continental (47.4%) components. The stratiform fraction is about 7%–8% higher over ocean thanover land. A similar relative difference is reflected in the
SCSMEX versus ARM regions; however, in an absolutesense the SCSMEX region is closer to the overall land
percentage. This agrees with Johnson et al.’s (2005) assessment that the stratiform fraction for SCSMEX wasrelatively low and explains the similarity between the
SCSMEX and land stratiform fraction versus rain intensity distributions.
Schumacher and Houze (2003) examined stratiform
rain in the tropics using the TRMM PR. Their results
showed that stratiform rain accounted for 40% of thetotal rain amount from 208N to 208S for the 3-yr period
1998–2000. They also found that stratiform amounts
were lower over land (ranging from 26% to 38%) thanover ocean (ranging from 41% to 53%). For example,
stratiform rain accounted for 53% of the total rainfall
over the southeast Pacific but only 36% of the rain over
North and South America. These findings are in good
agreement with the current results in terms of land–
ocean contrast. However, since the current results are
based on a 10-yr period over a larger geographic area,
the total stratiform rain percentage is higher in the current study because it encompasses a wider geographic
domain and thus includes many more midlatitude systems (i.e., frontal), which have a higher stratiform rain
percentage, especially during the cold season (e.g., Zenget al. 2009). In addition, there are differences between theversion 5 2A25 algorithm used in the Schumacher andHouze (2003) study and the version 6 PR algorithm usedin this study. Convective rain rates are significantly lower
in version 6.

b. GCE model-simulated relationship between rain
intensity and stratiform rain percentage
To compare against the TRMM 0.58 3 0.58 rainfall
products, the GCE model domain (i.e., 512 km) was
subdivided into eight equal subdomains, each with ahorizontal scale of 64 km (comparable to the resolutionof the TRMM products). Average rainfall rates and stratiform fractions were then calculated in each subdomain
at roughly the same scale as the gridded TRMM products. The average stratiform rain percentage and mean
conditional rain rate for each subdomain were then used
to bin the data as was done with the PR gridded data.
The associated latent, eddy, and radiative heating profiles were also binned using the exact same bins, effectively building the LUT for the new algorithm.
Figure 3 shows the model-simulated probability distribution of rainfall intensity versus stratiform rain percentage over land and ocean regions. The oceanic region
was constructed from a combined total of 123 days ofmodel integration from the SCSMEX, TOGA COARE,TABLE 3. PR-estimated rainfall amount and stratiform % overthe global tropics, land, oceans, SCSMEX (1998), SCSMEX(10 yr), ARM (2002), and ARM (10 yr).

Global tropics
Ocean
Land
SCSMEX (1998)SCSMEX (10 years)
ARM (2002)
ARM (10 years)

Rainfall amount(mm day21)

Stratiform rain
percentage (%)

2.26
2.35
2.06
11.24
3.64
2.59
2.36

52.8
55.0
47.4
42.3
49.8
35.7
41.1

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FIG. 3. As in Fig. 2, but for GCE model simulation for (a) oceanic (TOGA COARE, GATE, and SCSMEX) and(b) continental (ARM 1997 and 2002) cases.

and GATE cases. The land region consists of just 49 daysof model integration for the two ARM cases. This is why
the oceanic distribution is smoother. The model results
have overall features that are similar in many ways to
the PR observations (Fig. 1). For example, light rain rates(less than 100 mm day21) tend to dominate the distributions and more so over ocean and at high stratiform
fractions. Peak probabilities shift to higher intensities forthe most convective portions of the distributions; also,
maximum intensities in the tails of the distributions—andhence the overall widths of the distributions—increase
monotonically with increasing convective fraction forboth land and ocean. The qualitative similarity between
the PR and model distributions suggests that informationfrom the model can be mapped to the observations via
surface rain intensity and stratiform fraction characteristics (i.e., bins), providing the basis for a new algorithm.
However, there are some notable differences between the
PR observations and model simulations. The agreement in
the predominance of light rain rates holds true for bothmoderate and high stratiform fractions for oceanic conditions but only for high stratiform conditions for land. At
moderate to high convective fractions, the model tends tohave more moderate rain, especially over land. Although
not especially prominent, the highest probabilities forthe model fall into the very lowest rain intensity bin,whereas for the observations, the highest probabilities
fall into slightly more intense bins. The reason for thisdiscrepancy is that the minimum detectable return for the
PR is 17 dBZ, which is equivalent to about 0.4 mm h21(or 9.6 mm day21) of rain. Another difference is that theshift in peak occurrence and extreme values to higher
intensities with increasing convective fraction is more
pronounced and begins sooner, especially for land conditions, in the model simulations.
Figure 4 shows the relationship between rainfall intensity and stratiform rain percentage for each of theindividual land and ocean cases. The two summer landcases, ARM-SGP-97 and -02, are similar to each other,with the moderate to strongly convective parts of theirdistributions having probabilities that are shifted to significantly higher intensities than the oceanic cases. The
oceanic cases are also more similar to each other thanthey are to either of the land cases. The overall trend
between land and ocean is similar between the modeland observations with there being an increase in convective fraction and a shift in the distribution to higher
intensities at higher convective fractions for land relative to ocean; however, in addition, superimposed on
this trend is a general shift from lower to higher rain
intensities for the simulated land distributions.
Table 4 shows grid-averaged total rainfall and stratiform rain percentage for each of the GCE simulatedcases. The oceanic cases have more rainfall than the continental. This is due primarily to the fact that the oceanic
environments have higher precipitable water contents(i.e., more moisture) than the continental (see Table 1
in Tao et al. 2004). The vertically integrated water vapor content for the SCSMEX case is very moist (over62 g cm22) compared to the TOGA COARE and GATE
cases. That is why the SCSMEX simulation has thelargest amount of rainfall. However, although the TOGACOARE environment is moister than that for GATE, it
has less rainfall because the model simulation starts in
November, which did not have many active convective
events. In general, the tropical oceanic cases should havea higher stratiform amount (i.e., 40%–50%) than the
midlatitude continental cases. However, the ARM cases
also have a large stratiform rain fraction (from 36%–41%) because they include frontal cases. Houze (1977),
Zipser et al. (1981), and Gamache and Houze (1983) estimated that widespread stratiform rain accounted forabout 32%–49% of the total rainfall during GATE. The
fraction of stratiform rainfall from midlatitude squall1 APRIL 2010

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TAO ET AL.

FIG. 4. As in Fig. 2, but for GCE model simulation.
The three left panels are oceanic cases, TOGACOARE, GATE, and SCSMEX; the right two panels
are continental cases, ARM 1997 and 2002.

lines has been estimated at 29%–43% (Rutledge andHouze 1987; Johnson and Hamilton 1988). The GCE
model-simulated results are in good agreement withthese observations.
Although the GCE model-simulated stratiform rain
percentage for the SCSMEX and ARM-SGP-02 cases

are in excellent agreement with the TRMM PR estimates, comparing the GCE model simulations with
the PR observations (Table 3) shows that the simulated
rainfall amount for the ARM-SGP-02 case is much larger
than was estimated by the PR. Sampling may be the reason
for this difference as the GCE model-simulated rainfall

TABLE 4. CRM-simulated rainfall amount and stratiform percentage for SCSMEX (1998), ARM (1997, 2002), TOGA COARE (1992),
and GATE (1974).

SCSMEX
ARM (1997)
ARM (2002)
TOGA COARE (1992–93)
GATE (1974)

Simulated rainfall
amount (mm day21)

Stratiform rain
percentage (%)

Estimated rainfall
amount (mm day21)

12.31
4.31
4.85
7.72
10.56

42.6
41.3
36.0
47.6
41.4

11.35
4.32
4.77
9.32
11.38

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amounts for the SCSMEX, ARM (1997 and 2002), andGATE cases are in good agreement with those estimated by sounding networks.6 For the TOGA COARE
case, however, the model produced 17% less rainfall
than was estimated from the sounding budget. The GCE
model was previously used to simulate two TOGACOARE cases, 10–17 December and 19–27 December
1992, and the simulated rainfall was in excellent agreement with the sounding estimates (see Table 5 in Tao
et al. 2004). The current difference could be due to thelonger model integration. The longer model integration
could allow for larger error accumulation. In addition,
the longer model integration included less active periods
associated with shallow convection that require a finermodel grid resolution (e.g., 250 m or finer).

c. GCE model-simulated heating budget components
The apparent heat source Q1 can be directly related tothe contributions by cloud effects, which in turn can be
explicitly estimated with the GCE model (Soong and
Tao 1980; Tao and Soong 1986; Tao et al. 1993b, andmany others):›rw9u91$  Vu9 1 [Ly (c e)
Q1 5 pcpr›z
1 Lf (fm) 1 Ls (ds)] 1 QR ,(1)

where the primes indicate deviations from the largescale environment mainly due to small-scale cloud processes. The variable u is potential temperature; r is
air density; p 5 (p/poo )R/cp is nondimensional pressure(where p and poo are dimensional and reference pressures, with poo taken as 1000 hPa); and cp and R represent the specific heat at constant pressure and the gas
constant of dry air, respectively. The variables Ly, Lf, andLs are the latent heats of condensation, freezing, andsublimation, respectively; the variables c, e, f, m, d,and s respectively denote the microphysical mass transfer rates for condensation of cloud droplets, evaporationof cloud droplets and rain drops, freezing of water droplets and rain drops, and the melting, deposition, andsublimations of ice particles (i.e., crystals, snow flakes,
graupel, and hail).
The term (1/cp)[Ly(c 2 e)1Lf ( f 2 m)1Ls(d 2 s)] is
the LH due to microphysical phase changes. As definedin Yanai et al. (1973), Q1 is the apparent heat source,
while QR is the radiative heating/cooling rate. The first6
In addition to the inherent sampling errors, which are likely to
be significant, associated with comparing the PR against the relatively small variational analysis domains, the PR did not cover thenorthern half of the ARM variational analysis domain.

VOLUME 23

two terms on the right-hand side of Eq. (1) are the verticaland horizontal eddy heat flux convergence—p[›w9u9/›z]
and p[$  V9u9]—where the horizontal eddy term is neglected when Eq. (1) is spatially averaged over a large
area suitable for large-scale diagnostic analysis or overthe GCE model if a cyclic lateral boundary condition isapplied. The horizontal eddy term (entrainment and detrainment) may not be negligible over a small area, suchas the GCE model subdomains used in this study.
Figures 5 and 6 show the main components of the simulated heating structures (i.e., latent, eddy, and radiative)
derived from composites of the land and oceanic cases,
respectively. For each heating component, individual
heating profiles are sampled first as a function of rain
intensity (i.e., at 0–20, 80–100, 180–200, 380–400 and
480–500 mm day21) for a given stratiform amount (i.e.,
0%–5%, the most convective) and then as a function ofstratiform fraction (i.e., 0%–5%, 20%–25%, 45%–50%,
70%–75%, and 95%–100%) for a given rain intensity(i.e., 140–160 mm day21, approximately the strongest
common rain rate among the different stratiform bins).
The heating profiles were first summed over the individual GCE model subdomains (i.e., 64 continuous gridswith 1-km spacing) and then normalized by the rain areaand binned according to the conditional rain rates andstratiform fraction in each subdomain. This approach assumes that all of the LH in each subdomain is associatedwith the rain area in that subdomain (i.e., LH not in therain area but still in the subdomain is still included in the
average for the rain area). This assumption is also made forthe eddy heating but not the radiation, which is also summed over the entire grid box but normalized by the total
grid area. Binning is still the same as for the LH. Notable
patterns include the following: 1) the magnitude of LH
increases with increasing surface rain intensity (Figs. 5aand 6a); 2) the level of maximum heating increases withincreasing rain intensity (Figs. 5a and 6a); 3) the depth ofheating increases with increasing rain intensity so that lightrain is associated with shallow convection and heavy rainwith deep convection (Figs. 5a and 6a); 4) both eddy andradiative heating are much smaller than LH but may benonnegligible for light surface rain rates (i.e., less than
100 mm day21, Figs. 5b,c,e,f and 6b,c,e,f); and 5) the levelof maximum heating increases with increasing stratiform
fraction (Figs. 5d and 6d). There are some differences
between the land and ocean profiles, namely a double
heating maxima in the continental convective profiles forweak rain rates (Fig. 6a), a higher level of maximum
heating over land (Figs. 5a and 6a), and stronger eddy
heating over land (Figs. 5b and 6b). The latter is due tohaving stronger convective vertical velocities over land.
These GCE model-simulated heating profiles, which arein many ways in good agreement with observed convective

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FIG. 5. Mean vertical profiles of (top) latent, (middle) eddy, and (bottom) radiative heating rates for various
conditional rain intensity and stratiform fraction bins from the GCE-based oceanic LUT.

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FIG. 6. As in Fig. 5, but for the continental LUT.

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TAO ET AL.

and stratiform heating structures (Johnson 1984; Houze
1982, 1997), constitute the new CSH algorithm’s LUT.

4. A new CSH algorithm: Details, evaluation,
and application
The CSHv1 algorithm (Tao et al. 1993a) uses surface
precipitation rates, amount of stratiform rain, and an
LUT of rain-normalized convective and stratiform diabatic heating profiles (i.e., Q1) representing various
types of cloud systems of differing geographic origin thatwere obtained from GCE model simulations and budget
calculations. The CSHv1 LUT consists of 20 pairs ofheating profiles: 16 oceanic and 4 continental cases. For
most applications, those 20 pairs are composited into
just two convective/stratiform pairs, representing general ocean and land conditions. A single additional pairis used to represent shallow heating. The new CSH algorithm (hereafter referred to as CSHv2) also uses surface precipitation rates and stratiform rain fraction, butthere are several notable differences. The key difference
is in the new LUT and how it is accessed. First, there aremany more heating profiles (approximately 700 total)in the new LUT because of their being separated into
detailed intensity and stratiform bins. And second, theprofiles are distributed and thus accessed according toconditional rain rates. Together these lead to several
potential advantages regarding heating structure. Obviously, having many more profiles in the LUT allows forthe possibility of having many more heating structures.
For example, rather than just having shallow or deep
heating profiles, the new LUT allows the depth of heating
to vary considerably7 (e.g., Fig. 5a). Using conditionalrain rates is what allows those structures to be better
differentiated. For example, given a stratiform fraction
and an average rain rate over a region (i.e., a 0.58 3 0.58
area), knowing that that average rain rate is due to a small
area of intense rain (e.g., a single intense convective cell)rather than a larger area of weak rain (e.g., a broader fieldof weaker convective cells) allows the algorithm to selecta more representative heating structure. In CSHv1, these
two rain areas would have been treated the same.
There are also additional refinements in CSHv2. In
addition to the LUTs based on grids with rain, an additional set of LUTs is constructed in a like manner but
using grids that do not contain rain themselves but are
adjacent to grids with rain. Heating in these model subdomains is summed over the entire subdomain as before
but then normalized by the average rain area from thesurrounding grids and binned according to the average
7
Mean echo top heights from the PR and from the model correlate nicely over almost the entire range of LUT bins (not shown).

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conditional rain rate from the surrounding grids. This
allows for heating to be retrieved in areas that are nonraining but that are adjacent to raining areas. Typicallythe LH in these near rain areas is on the order of orslightly stronger than the eddy term within the rainy
areas or about 1–2 orders of magnitude less than the LH
in the raining areas. LH profiles next to stratiform areas
have weak heating aloft and weak cooling at lower levels(similar to classic stratiform heating profiles but weaker),whereas profiles next to convective areas have weakcooling aloft and weak heating at low levels. The eddy
term in the near-rain areas is weaker but on the sameorder as that in the rainy areas. Radiation, which is averaged over the entire subdomain area as it was for the
rainy LUTs, is of the same order of magnitude as theradiation in the rainy areas. Finally, mean latent, eddy,
and radiative heating/cooling profiles are constructedfrom all of the remaining grids (i.e., those which neither
have rain nor are adjacent to rain). The LH and eddy
heating in these profiles are quite small, but the radiation is comparable to that for the rain and near-rain
areas and is thus the dominant term for this region.
Next, the new CSH algorithm is evaluated using a selfconsistency approach and then applied to a 10-yr TRMM
dataset and compared against the CSHv1 algorithm.

a. Consistency check
The first step in evaluating the new CSHv2 algorithm
is to perform a consistency check with CRM data sincethose data (e.g., the heating profiles and the surface raincharacteristics) are internally self consistent. Surface
rain data (i.e., conditional and average rain rates and theassociated stratiform fraction) were extracted from thelong-term SCSMEX simulation every hour for eachmodel subdomain (i.e., 64 km) and supplied to the CSHv2
algorithm, which was then used to reconstruct the heating
profiles. The retrieved heating profiles from the algorithm
can then be compared against those from the CRM, which
can be regarded as the ‘‘truth.’’ Both sets of profiles canalso be compared to those derived from the diagnostic
sounding budget, which was used to force the model.
These types of comparisons against observations andCRM simulations have been a standard way to performconsistency checks on algorithms in the past (Tao et al.
1990, 1993a, 2000; Olson et al. 1999, 2006; Shige et al.
2004, 2007, 2008, 2009).
Figure 7 shows the time series of domain-average total
heating profiles (i.e., Q1) from the GCE model simulation, the CSHv2 reconstructed heating profiles using themodel surface rain data, and the sounding-based diagnostic heating budget for the SCSMEX case. The CSHv2
heating was reconstructed for all three types of subdomains: rainy, near rain, and away from rain. The results

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FIG. 7. (top) Modeled, (middle) retrieved, and (bottom) observed time–height cross sections of domain-average Q1
for SCSMEX NESA.

show that the temporal variation of the CSHv2 heating
agrees well with that from the GCE simulation and thesounding budget. Both the model and the retrievals havefiner-scale time variations than the budget because they
are every hour as opposed to every 6 h. One notabledifference is that the retrieved heating structure shows
light heating above the 10-km level at all times. This is an
artifact of spurious radiative heating in the model simulation being averaged into the CSHv2 ‘‘away fromrain’’ radiative heating LUT profile. The strong heating
and cooling evident in the upper troposphere of the GCE
simulation are mainly caused by radiative processes.
Forty-four-day-averaged heating profiles from themodel simulation, the CSHv2 reconstructions, and thesounding budget are shown in Fig. 8. These profiles are
simply the time averages of the profiles shown in Fig. 7.
The time-averaged CSHv2 reconstructed heating profile
agrees very well with the model. The level of maximum

heating is about 7 km for both the model and the CSHv2
algorithm, which is in good agreement with the sounding
budget. Both the simulated and reconstructed heating
profiles also have a distinct cooling near 4 km, which isdue to the melting processes. This is because the eddy
heat flux convergence compensates for this cooling.
Both the GCE and CSHv2 average profiles are stronger
than that from the sounding budget. This is primarily
due to the fact that the model did not simulate the strong
cooling in the middle and lower troposphere between
active convective events evident in the budget (Fig. 7).

b. Application
The top two panels of Fig. 9 show the 10-yr mean Q1 at
two different altitudes, 1 and 7 km, over the global
tropics obtained from the new CSHv2 algorithm using
the essentially daily gridded PR rainfall product from
3G68. The concept of the new and old CSH algorithms is

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TAO ET AL.

FIG. 8. Observed (thick solid), modeled (thin solid), and retrieved (thick dashed) mean vertical profiles of Q1 over SCSMEXNESA.

the same. The main difference between the new and old
CSH algorithms is the LUT and how it is accessed.
However, another useful feature of the new version isthat all of the major heating components are now retrieved separately. Thus, for example, to facilitate comparisons with CSHv1, the total heating shown in thissection using the 10 yr of PR data include all of thecomponents in grids where it is raining, the LH and eddy
components in the near-rain grids (which are a new feature and not something that was intentionally omitted in
CSHv1), and none of the components in the ‘‘away fromrain’’ grids. As expected from the design of the CSH algorithm, the horizontal distribution of the estimated Q1
structure is similar to the surface rainfall pattern (lower
panel in Fig. 9). For example, there are well-defined
ITCZs across the Pacific, Atlantic, and eastern Indian
Ocean, a well-defined South Pacific convergence zone
(SPCZ) in the south-central Pacific Ocean, and midlatitude storm tracks over and downwind of the continents. At the lowest levels in CSHv2, oceanic rain is
associated with robust heating, while cooling is prevalent for continental rainfall (Fig. 9, middle panel). At
upper levels, heating is intense and stronger over continents than over oceans (Fig. 9, top panel).
To contrast the new version of the CSH algorithm,
CSHv2, with the old, CSHv1, cross sections of 10-yr

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mean zonal average heating were constructed from eachalgorithm using the same daily gridded PR dataset (notethat additional PR echo top height information was used
for the CSHv1 algorithm to screen for shallow convection but was not used for CSHv2). The results for CSHv2
and CSHv1 are shown in the top and middle panels of
Fig. 10, respectively. Clearly, both versions show twoheating maxima. Both of these maxima occur at thesame locations and are in response to the surface rainfall
associated with the ITCZ (at ;58N) in the Northern
Hemisphere and the SPCZ in the Southern Hemisphere(;2.58S). The heating is stronger in the Northern Hemisphere because the surface rainfall is larger in the Northern
Hemisphere. This difference has implications for thelarge-scale circulation, which responds to the heating
gradient between the Northern and Southern Hemispheres. Although both versions of the CSH algorithm
depict the same basic pattern, the overall CSHv2 heating is noticeably stronger, especially in the lower troposphere near the equator. Also, the level of maximum
heating is shifted slightly lower in the new version, fromapproximately 7 km in CSHv1 down to about 6 km in
CSHv2.
Figure 10 (bottom panel) shows the mean 10-yr average heating profiles over the global tropics and subtropics (i.e., between 378N and 378S) for the old and newversions of the CSH algorithm. The overall shapes are
not that dissimilar. Although the level of maximum
heating appears to be at a higher level (based on thecurvature) in CSHv1 because of its broad heating maximum aloft (the result of compositing a larger variety ofcases), the actual level of peak heating near 7 km is thesame for both versions. Heating above 8 km is nearly
identical, but between 1 and 8 km the CSHv2 heating
profile is significantly stronger by nearly a constantamount. This equates to a larger increase in heating interms of percentage between 1 and 4 km. The averageheating over land and ocean is also shown for each algorithm. From these profiles, it is clear that most of thedifference comes from land. The oceanic profiles differ
by a much smaller degree and mainly below about 4 km
where the CSHv2 profile is stronger. There is very little
variation in the heating between land and ocean for
CSHv1. For CSHv2, average heating is much stronger
over land between 2 and 8 km in altitude, while in thelowest levels there is strong average cooling over land
but none over oceans. The stronger mid- to upper-level
heating over the land is engrained in the LUT (Figs. 6a,c
versus Figs. 5a,c) and is likely the consequence of stronger vertical velocities and a greater amount of ice overland. The strong low-level cooling over land is consistent
with it having a drier environment and hence more lowlevel evaporation.

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FIG. 9. (top), (middle) Ten-year (1998–2007) mean cloud heating rates over the global tropics
at (top) 7 and (middle) 1 km AGL obtained from the new CSH algorithm using (bottom)
gridded instantaneous TRMM PR rain rates.

Lin and Johnson (1996) compared the mean Q1 fromthe TOGA COARE Marshall Islands region (Yanai
et al. 1973) with the GATE region (Thompson et al.
1979). Their results showed that the level of maximum
heating was about 6–6.5 km in altitude for the western
Pacific (i.e., the TOGA COARE Marshall Islands region) but only about 4 km for the tropical Atlantic (i.e.,
the GATE region). The lower maximum heating level
for the GATE region may be due to the lower SSTs inthe eastern Atlantic (Thompson et al. 1979). Greco et al.
(1994) calculated Q1 profiles over South America froma sounding network. Their results indicated that the
distribution of heating was quite similar to that obtained
from studies of West African squall lines (Chong andHauser 1990), where peak heating also occurred between 500 and 550 hPa (about 5–6 km). The new CSH
algorithm’s retrieved level of the maximum heating isabout 6 km over land and 7 km over ocean, which is in
general agreement with these diagnostic studies. However, the level of the maximum heating has been foundto be higher (about 7.5 km) during the monsoon over
the South China Sea (SCSMEX NESA; Johnson andCiesielski 2002) and for convective systems over SouthAmerica [Large-Scale Biosphere–Atmosphere (LBA);
Halverson et al. 2002]. Regional analyses of the new
CSH products, including comparisons with diagnostic
studies and with other heating products [i.e., products
derived from other heating algorithms, such as SLH and1 APRIL 2010

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the trained radiometer algorithm (TRAIN)], are stillneeded.

5. Summary and future work
The relationship between conditional surface rainfall
intensity and stratiform fraction over the global tropics
and subtropics was examined using both gridded (0.58 30.58) instantaneous TRMM PR observations and longterm (i.e., multiweek) Goddard Cumulus Ensemble(GCE) model simulations sampled over subdomains
similar in size to the PR grids. The similarity of thesubsequent land and ocean distributions between thesatellite observations and model simulations was used tojustify the formulation of a new convective–stratiform
heating algorithm, CSHv2. LUTs for the new algorithm
were obtained by distributing heating/cooling profiles
from the model subdomains into the same conditionalrain intensity and stratiform rain percentage bins used
to construct the surface rainfall distributions. Separate
LUTs were constructed for each of the three main heating/cooling components: latent, eddy, and radiative. A similar
set of secondary LUTs was created in a like manner fornear-rain areas using the mean conditional rain rates
and stratiform fractions from neighboring grids. After
conducting a self-consistency check using model data,
the performance of the new CSH algorithm was presented by comparing its results against those from theprevious version of the CSH algorithm, CSHv1, using
10 yr of gridded instantaneous TRMM PR data. The major highlights are as follows:
Conditional instantaneous surface rain-rate distributions as a function of intensity and stratiform fraction
obtained from the model for both land and ocean are
similar in many ways to those obtained from PR observations. For example, light rain rates (less than
100 mm day21) tend to dominate the distributions
and more so over ocean and at high stratiform fractions. Peak probabilities shift to higher intensities
for the most convective portions of the distributions.
Also, maximum intensities in the tails of the distributions and hence the overall widths of the distributions
increase monotonically with increasing convective
fraction for both the model and the PR over bothland and ocean.
d Despite the overall similarity, there are some notabledifferences between the surface rain distributions fromthe PR and the model. The agreement in the predominance of light rain rates holds true for both moderate
and high stratiform fractions for oceanic conditions but
only for high stratiform conditions for land. The model
distributions tend to have more moderate rain rates atmoderate to high convective fractions, especially overdFIG. 10. (top), (middle) Latitude–height cross sections of 10-yr
mean zonal cloud heating from the (top) new and (middle) old
CSH algorithm; (bottom) 10-yr mean global cloud heating profiles,
as well as those for land and ocean, using the new (black) and old(gray) CSH algorithm.

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land. Also, because the minimum detectable returnfor the PR is 17 dBZ, which is equivalent to about
0.4 mm h21 (or 9.6 mm day21) of rain, the highest
probabilities for the model fall into the very lowest rain
intensity bin, whereas for the PR the highest probabilities fall into slightly more intense bins. Finally, forhigh stratiform fractions, extreme values are stronger
in the PR while the converse is true at high convective
fractions.
d Of the five cases to which the GCE model was applied,
two fell within TRMM satellite coverage. The GCE
model-simulated stratiform rain percentage was foundto be in excellent agreement with the PR estimates forboth the SCSMEX (1998) and ARM (2002) cases;
however, the GCE simulated far more rain than the
PR observed for the ARM 2002 case. This is likely due
to sampling as the GCE simulated rainfall amount isin good agreement with estimates from the sounding
budget, from which forcing was used to drive themodel.
d LUTs containing the latent, eddy, and radiative heating/cooling profiles for the new CSH algorithm were constructed by compositing the associated model-simulated
heating profiles into the same bins used to delineate
the surface rain distributions. There were several notable patterns: 1) both the magnitude of LH and thelevel of maximum heating increase with increasing
rain intensity; 2) the depth of heating increases withincreasing rain intensity so that light rain is associatedwith shallow convection and heavy rain with deep
convection, allowing the depth of heating to vary
without prior knowledge of the echo top heights;
3) eddy and radiative heating are much smaller than
LH but may be nonnegligible for light surface rain
rates (i.e., less than 100 mm day21); and 4) the levelof maximum heating increases with increasing stratiform fraction. Differences between the land and ocean
profiles include a double heating maxima in the continental convective profiles for weak rain rates, a higher
level of maximum heating over land, and stronger eddy
heating over land.
d Following a successful consistency check of the new
CSH algorithm using GCE model data, 10 yr of gridded‘‘daily’’ PR surface rainfall data (i.e., 3G68) were used
to derive cloud heating over the global tropics andsubtropics with both the new and old versions of the
CSH algorithm, CSHv2 and CSHv1, respectively. The
overall geographic patterns are quite similar because
they are both tied to the same surface rainfall pattern.
Mean heating profiles over the global tropics revealthat despite the broad heating maximum aloft for
CSHv1, the actual level of peak heating is near 7 km
for both versions. Mean heating above 8 km is nearly

VOLUME 23

identical, but between 1 and 8 km the CSHv2 heating
profile is significantly stronger by nearly a constantamount. This equates to a larger increase in heatingin terms of percentage between 1 and 4 km and shifts
the emphasis on heating to lower levels in CSHv2. It
is clear from the land and oceanic components thatmost of the difference comes from land. The oceanic
profiles differ by a much smaller degree and mainly
below about 4 km, where the CSHv2 profile has stronger low-level heating. While there is little variationin the mean heating over land and ocean for CSHv1,
for CSHv2 average heating is much stronger overland between 2 and 8 km in altitude, while in thelowest levels there is strong average cooling over land
but not over oceans. These differences are engrainedin the LUTs.
The 2D version of the GCE model was used to provide the heating profiles for the new CSH algorithm’s
LUTs. It is well known that the results from 2D and 3D
CRM simulations can differ not only in cloud dynamics
but also in microphysics (e.g., Tao and Soong 1986;
Johnson et al. 2002; Zeng et al. 2008). More convective
cores with stronger vertical velocities exist in a 3D CRM.
As a result, the upper tropospheric cloud ice content ishigher in a 3D CRM (Zeng et al. 2008). Also, because
perturbations in a 2D model are constrained to a verticalplane, there can be more fluctuations in a 2D CRM. The
relationship between conditional surface rainfall intensity, its stratiform amount, and the associated heating
profiles needs to be examined in 3D.
Finally, only a limited number of CRM-simulatedcases were used in this study. Observations from additional field experiments [e.g., the Tropical Warm Pool–International Cloud Experiment (TWP-ICE), the North
American Monsoon Experiment (NAME), and the African Monsoon Multidisciplinary Analysis (AMMA)] anda future GPM ground validation (GV) site will be needed
to provide new types of initial conditions to the GCE
model to expand the number of cases and environmentsin the LUT. In addition, large-scale analyses from theNASA Goddard Modern Era Retrospective Analysis
for Research and Applications (MERRA) could also be
used to provide initial conditions and forcing for CRM
simulations of environments not sampled by field campaigns. Figure 11 shows some preliminary results using
MERRA forcing to drive the GCE model. The fact thatthe simulation forced by MERRA generally agrees wellwith that forced by the sounding budget from the field
campaign indicates that the GCE1MERRA approachhas the potential to provide reasonably good-quality
simulations to the CSH algorithm for a variety of locations and conditions, including those regions with large

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FIG. 11. Eight-day domain average time series of surface rainfall for SCSMEX. The black line is the observed
3-hourly time series from 0600 UTC 18 May to 0600 UTC 26 May 1998. The dark gray line is the 3-hourly time series
from the GCE simulation driven by the SCSMEX sounding-based observed large-scale tendencies. The light grayline is same as the dark gray line except that the GCE was driven by tendencies from MERRA output. The twosimulations generally agree well with each other and show the viability of using GCE1MERRA to obtain quality
simulations for undersampled environments.

surface rainfall, such as the Indian Ocean, SPCZ, SouthAmerica, and Africa.
Acknowledgments. This research was supported by
the NASA Headquarters Atmospheric Dynamics andThermodynamics Program and the NASA Precipitation
Measuring Mission (PMM). The authors are grateful to
Dr. R. Kakar at NASA headquarters for his support ofthis research. We also thank two anonymous reviewers
for their constructive comments and suggestions that improved this paper significantly. Acknowledgment is also
made to the NASA Goddard Space Flight Center andNASA Ames computing centers for the computational
resources used in this research.
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