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Spectral Retrieval of Latent Heating Profiles from TRMM PR Data. Part II:
Algorithm Improvement and Heating Estimates over Tropical Ocean Regions
SHOICHI SHIGE
Department of Aerospace Engineering, Osaka Prefecture University, Osaka, Japan

YUKARI N. TAKAYABU
Center for Climate System Research, University of Tokyo, and Institute of Observational Research for Global Change, Japan Agency
for Marine–Earth Science and Technology, Kanagawa, Japan

WEI-KUO TAO
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland

CHUNG-LIN SHIE
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, and Goddard Earth Sciences and Technology Center,
University of Maryland, Baltimore County, Baltimore, Maryland(Manuscript received 21 December 2005, in final form 17 October 2006)
ABSTRACTThe spectral latent heating (SLH) algorithm was developed for the Tropical Rainfall Measuring Mission(TRMM) precipitation radar (PR) in Part I of this study. The method uses PR information [precipitationtop height (PTH), precipitation rates at the surface and melting level, and rain type] to select heating
profiles from lookup tables. Heating-profile lookup tables for the three rain types—convective, shallow
stratiform, and anvil rain (deep stratiform with a melting level)—were derived from numerical simulationsof tropical cloud systems from the Tropical Ocean and Global Atmosphere Coupled Ocean–AtmosphereResponse Experiment (TOGA COARE) utilizing a cloud-resolving model (CRM). To assess its global
application to TRMM PR data, the universality of the lookup tables from the TOGA COARE simulations
is examined in this paper. Heating profiles are reconstructed from CRM-simulated parameters (i.e., PTH,
precipitation rates at the surface and melting level, and rain type) and are compared with the true CRMsimulated heating profiles, which are computed directly by the model thermodynamic equation. CRMsimulated data from the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE),
South China Sea Monsoon Experiment (SCSMEX), and Kwajalein Experiment (KWAJEX) are used as aconsistency check. The consistency check reveals discrepancies between the SLH-reconstructed and Goddard Cumulus Ensemble (GCE)-simulated heating above the melting level in the convective region and at
the melting level in the stratiform region that are attributable to the TOGA COARE table. Discrepancies
in the convective region are due to differences in the vertical distribution of deep convective heating due
to the relative importance of liquid and ice water processes, which varies from case to case. Discrepancies
in the stratiform region are due to differences in the level separating upper-level heating and lower-level
cooling. Based on these results, improvements were made to the SLH algorithm. Convective heating
retrieval is now separated into upper-level heating due to ice processes and lower-level heating due to liquidwater processes. In the stratiform region, the heating profile is shifted up or down by matching the melting
level in the TOGA COARE lookup table with the observed one. Consistency checks indicate the revised
SLH algorithm performs much better for both the convective and stratiform components than does theoriginal one. The revised SLH algorithm was applied to PR data, and the results were compared withheating profiles derived diagnostically from SCSMEX sounding data. Key features of the vertical profiles
agree well—in particular, the level of maximum heating. The revised SLH algorithm was also applied to PRdata for February 1998 and February 1999. The results are compared with heating profiles derived by theconvective–stratiform heating (CSH) algorithm. Because observed information on precipitation depth isused in addition to precipitation type and intensity, differences between shallow and deep convection are
more distinct in the SLH algorithm in comparison with the CSH algorithm.

Corresponding author address: Dr. Shoichi Shige, Department of Aerospace Engineering, Osaka Prefecture University, 1-1 Gakuencho, Sakai, Osaka 599-8531, Japan.
E-mail: shige@aero.osakafu-u.ac.jp
DOI: 10.1175/JAM2510.1© 2007 American Meteorological Society

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1. Introduction
The Tropical Rainfall Measuring Mission (TRMM;
Simpson et al. 1988, 1996; Kummerow et al. 2000), a
joint Japanese–U.S. cooperative earth probe satellite,
was successfully launched in 1997 to advance understanding of the global energy and water cycle. The
TRMM satellite has been in operation for more than 9
years, providing the distribution of rainfall throughout
the Tropics using microwave observations from the precipitation radar (PR) and the TRMM Microwave Imager (TMI). Estimating vertical profiles of latent heating released by precipitating cloud systems is one of the
key objectives of TRMM, together with accurately
measuring the horizontal distribution of tropical rainfall [see a review by Tao et al. (2006)].
The PR is the first spaceborne precipitation radarand can provide height information based upon thetime delay of the precipitation-backscattered return
power. This allows for vertical profiles of precipitation
to be obtained directly over the global Tropics (Kozu etal. 2001; Okamoto 2003). The classification between
convective and stratiform regions of mesoscale convective systems (MCS) became more straightforward utilizing observed precipitation profiles (Awaka et al.
1998). The accuracy of this classification is very important for estimating latent heating because differences indiabatic heating profiles exist between convective andstratiform regions of MCSs (Houze 1982; Johnson andYoung 1983). For convective regions of MCSs, theheating profile has warming at all levels with a maximum at midlevels, whereas in stratiform regions there
is a warming peak in the upper troposphere and a cooling peak at low levels. The resulting MCS heating profile is positive at all levels but with a maximum value inthe upper troposphere (top-heavy profile). Hartmann
et al. (1984) demonstrated with a simple linear global
model that the top-heavy heat source produces aWalker circulation, which is in much better agreementwith observations than those that are produced with amore conventional heat source having a maximum
value in the middle troposphere. Recently, Schumacher
et al. (2004) showed that the horizontal variation of thevertical distribution of heating, controlled by the horizontal variation of stratiform rain fraction [as obtained
from TRMM PR data by Schumacher and Houze(2003a)], is also very important in simulating the largescale tropical circulation correctly.
Tao et al. (2001) used TRMM precipitation information to estimate the four-dimensional latent heating
structure over the global Tropics for one month (February 1998). Three different latent heating algorithms,
the hydrometeor heating (HH; Yang and Smith

1099

1999a,b, 2000), the convective–stratiform heating(CSH; Tao et al. 1993, 2000), and the Goddard profiling(GPROF) heating (Olson et al. 1999) algorithms wereused, and their results were intercompared. The HH
and GPROF algorithms are microwave radiometerbased for the TMI. Only one of the three algorithms,
the CSH algorithm, can use PR products as input, as
well as TMI products. This is because the CSH algorithm utilizes only the surface rain rate and an estimateof the fractions of rainfall produced by convective andstratiform processes. Recently, Magagi and Barros(2004) also proposed a simple algorithm to estimate
latent heating from a combination of radiosonde andTRMM PR data.
The concept of spectral approach originates from
Austin and Houze (1973) and Houze (1973) in which
precipitation-top height (PTH) observed by surfacebased radar data were utilized in estimating the verticalmass transports (proportional to latent heating) by cumulus-scale convection as a function of storm-top
height. This spectral approach was extended by Houze
and Leary (1976), Leary and Houze (1980), Houze etal. (1980), and Cheng and Houze (1980). Takayabu(2002) used a similar concept and obtained a spectral
expression of precipitation profiles to examine convective and stratiform rain characteristics as a function of
PTH over the equatorial area (10°N–10°S) observed by
the TRMM PR. In her study, nadir data from PR 2A25,
version 5, (Iguchi et al. 2000) for the period of 1998–99
were utilized, and convective and stratiform precipitation were separated based on the TRMM PR version-5
2A23 convective–stratiform separation algorithm. Precipitation profiles with a 0.3 mm h⫺1 precipitation-top
threshold were accumulated and stratified according to
PTHs. The threshold of 0.3 mm h⫺1 corresponds to 17.2
dBZ (stratiform) and 15.5 dBZ (convective) above the
0°C height and 17.0 dBZ (stratiform) and 14.2 dBZ(convective) just below the 0°C height in typical initial
Ze–R relations used in the PR 2A25 version-5 algorithm(Iguchi et al. 2000), where Ze is the effective radar reflectivity factor and R is the rainfall rate. Convective
rain profiles show near monotonic change with cumulative frequency. Stratiform rain profiles consist of twogroups. One group consists of shallow stratiform rain
profiles, which are very weak and increase downward.
The other group consists of anvil rain profiles, characterized by maximum intensity around the melting level,much less intensity above, and a downward decrease
below as indicated in traditional radar observations(e.g., Leary and Houze 1979). Schumacher and Houze(2003b) recently suggested that because the shallow,
isolated echoes represent warm-rain processes, theyshould be classified as convective. After the suggestion

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of Schumacher and Houze (2003b), the spectral plots of
Takayabu (2002, her Fig. 1) were revised by reclassifying shallow, isolated rain (rain type 15 in product 2A23)
as convective (Shige et al. 2004, their Fig. 2).
Based on the results of the spectral precipitation statistics of Takayabu (2002), the spectral latent heating(SLH) algorithm was developed for the TRMM PR in
Shige et al. 2004, hereinafter Part I). The method uses
PR information (i.e., PTH, precipitation rates at thesurface and melting level, and rain type) to select theheating profiles in lookup tables. Heating profile
lookup tables for the three rain types—convective,
shallow stratiform, and anvil rain (deep stratiform witha melting level)—were derived with numerical simulations of tropical cloud systems in TOGA COARE(Webster and Lukas 1992) utilizing a cloud-resolving
model (CRM). For convective and shallow stratiform
regions, the lookup table is based on the PTH. Considering the sensitivity of the PR, we used a threshold of
0.3 mm h⫺1 to determine the PTH. Properties of theconvective and shallow stratiform heating profiles shownear monotonic change with PTH, suggesting the distribution of latent heating is a strong function of PTH.
On the other hand, the PR cannot observe the PTH
accurately enough for the anvil regions because of its
insensitivity to the small ice-phase hydrometeors(Heymsfield et al. 2000). Thus, for the anvil region, thelookup table refers to the precipitation rate at the melting level Pm instead of PTH. The utilization of PTH and
Pm provides two distinct advantages for the SLH algorithm. First, the differences in heating profiles between
the shallow convective stage and the deep convective
stage can be realistically retrieved. Second, heating profiles in the decaying stage with no surface rain can also
be retrieved. Preliminary applications of the SLH algorithm using TRMM PR data have been done. Tao et al.
(2006) presented latent heating structure for a tropical
Pacific Ocean typhoon and a tropical, oceanic MCS
estimated by the SLH algorithm. Morita et al. (2006)
examined latent heating structure of the Madden–
Julian oscillation (MJO; Madden and Julian 1994) using
the SLH estimates. On the other hand, Grecu and Olson (2006) used a procedure similar to the SLH algorithm to assign a heating profile physically consistent
with each precipitation profile derived from the combined TRMM PR–TMI algorithm.
For global applications of the SLH algorithm using
TRMM PR data, it is necessary to examine the universality of the lookup table. If the relationship between
the precipitation profiles and associated latent heating
profiles changes between regions, the lookup table
would lead to large errors. In this study, lookup tablesfrom TOGA COARE, the Global Atmospheric Re-

VOLUME 46

search Program Atlantic Tropical Experiment (GATE;
Houze and Betts 1981), the 1998 South China Sea Monsoon Experiment (SCSMEX; Lau et al. 2000), and the1999 Kwajalein Atoll field experiment (KWAJEX;Yuter et al. 2005) simulations are compared to examine
their universality. The SLH algorithm is applied to PR
data, and the results are compared with heating profiles
derived diagnostically from SCSMEX sounding data
(Johnson and Ciesielski 2002). It is also applied to PRdata for February 1998 and February 1999 and compared with heating profiles derived by the CSH algorithm (Tao et al. 1993, 2000) using PR data.

2. Approach
Figure 1 shows the procedure for refining and validating the SLH algorithm. Because of the scarcity of
reliable validation data and difficulties associated withthe collocation of validation data and satellite measurements, a consistency check of the SLH algorithm isperformed using CRM-simulated precipitation profiles
as a proxy for the PR data. Algorithm-reconstructedheating profiles are derived from CRM-simulated precipitation profiles and compared with CRM-simulatedtrue heating profiles, which are computed directly fromthe model thermodynamic equation. The consistency
check is a useful and necessary precondition for theapplication of the algorithm to actual TRMM PR data.
In addition to TOGA COARE simulations, GATE,SCSMEX, and KWAJEX simulations produced with a
CRM are used as part of the consistency check in thisstudy. Locations of sounding arrays deployed during
TOGA COARE, GATE, SCSMEX, and KWAJEX
are shown in Fig. 2. Only precipitation over ocean isconsidered in the current investigation. In this paper,
the SLH algorithm is applied to PR data, and the results
are compared with heating profiles derived diagnostically from SCSMEX sounding data (Johnson andCiesielski 2002).

a. CRM simulations
The CRM used in this study is the two-dimensionalversion of the Goddard Cumulus Ensemble (GCE)model and is primarily documented in Tao and Simpson (1993). Recent improvements were presented in
Tao (2003) and Tao et al. (2003a).
The model includes solar and infrared radiativetransfer processes, and explicit cloud–radiation interactive processes (Tao et al. 1996). Simulations presented
in this study employ a parameterized Kessler-type twocategory liquid water scheme (cloud water and rain)
and a three-category ice-phase scheme (cloud ice, snow,
and graupel) by Rutledge and Hobbs (1984). Subgridscale (turbulent) processes in the GCE model are pa-

JULY 2007

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FIG. 1. Diagram showing the procedure for refining and validating the SLH algorithm. Letters denote convective
and stratiform classification (C/S), PTH, the precipitation rate at the lowest observable level Ps, and the precipitation rate at the melting level Pm. The “?” means to compare and examine the heating profiles reconstructed fromthe SLH algorithm with the heating profiles from model simulations. This consistency check is a necessary precondition for the application of the algorithm to actual TRMM PR data.

rameterized using a scheme based on Klemp and Wilhelmson (1978) and Soong and Ogura (1980). The effects of both dry and moist processes on the generationof subgrid scale kinetic energy have been incorporated
in the model. The model domain is 1024 km in the x
direction (horizontal) and 22.4 km in the z direction(vertical). The horizontal resolution is 1000 m. The vertical resolution varies from 100 m at the lower boundary to 1000 m at the top of the domain. The time stepis 12 s.
In this study, tropical convective systems in TOGACOARE, GATE, SCSMEX, and KWAJEX are simulated with an approach, so-called cloud ensemble modeling. In this approach, many clouds of different sizes invarious stages of their life cycles can be present at any
model simulation time. Observed large-scale advective
tendencies of temperature, moisture, and horizontal
momentum are used as the main large-scale forcingsthat govern the GCE model in a semiprognostic manner (Soong and Ogura 1980). These are applied uniformly over the model domain with the assumption thatthe model domain is considerably smaller than thelarge-scale disturbance. Large-scale advective tendencies for temperature T and specific humidity q are defined as冉 冊⭸T⭸Tobs ␣obs⫹
⫽ ⫺vobs · ⵱Tobs ⫺ ␻obs
␻
and
⭸t LS
⭸p
Cp obs
共1兲

冉 冊

⭸q
⭸qobs
⫽ ⫺vobs · ⵱qobs ⫺ ␻obs
⭸t LS
⭸p

共2兲

and were derived from sounding networks deployedduring TOGA COARE, GATE, SCSMEX, andKWAJEX. Here, v is the horizontal wind vector, ␻ isthe vertical pressure velocity, ␣ is the specific volume,
and Cp is the heat capacity at constant pressure.
Because accurate calculations of the large-scale horizontal momentum forcing terms are difficult to obtainfrom observations in the Tropics (Soong and Tao 1984),
the terms are instead replaced by a nudging term:

冉 冊⭸v
v ⫺ vobs
⫽⫺
,
⭸t LS
␶

共3兲

where v is the model domain averaged horizontal velocity, vobs is the observed large-scale horizontal vector
over the sounding networks, and ␶ is the specified adjustment time scale of 6 h. This method constrains thedomain-averaged horizontal velocities to follow the ob-

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FIG. 2. Locations of sounding arrays deployed during TOGA COARE, GATE, SCSMEX, andKWAJEX.

served values, and thereby provides a simple means incontrolling the cloud system dynamics by the largescale momentum and shear. Cyclic lateral boundary
conditions are incorporated to ensure that there is no
additional heat and moisture forcing inside the domain
other than the imposed large-scale forcing.
The TOGA COARE simulations in this study are
not the same as in Part I. An ice-water saturation adjustment scheme following Tao et al. (1989), which is a
modified version of the water-phase-only saturation adjustment that does not require iterative computations(Soong and Ogura 1973), was used in Part I. The simulations in this study were made with a new saturation
technique (Tao et al. 2003a), which allows the temperature to change after the water phase before the ice
phase is treated. Although the overall cloud system
structure and character are not sensitive to the different
saturation schemes, the biggest differences between thetwo methods occur at about 9 km (⫺25°C). The alternating heating and cooling pattern at about 9 km seen
in Part I (see Fig. 3e of Part I) is removed in the simulations using the new saturation technique.
The accuracy of the convective–stratiform separation
affects the inference of the vertical distribution of heating. The TRMM PR rain-type classifications, in whichbrightband identification is very important, cannot bedirectly applied to GCE outputs (Awaka et al. 1996).
The microphysical schemes utilized in CRMs (e.g., Linet al. 1983; Rutledge and Hobbs 1984) typically do notcontain an explicit description of the partially melted
precipitation particles that lead to a bright band of enhanced radar reflectivity. Thus, the GCE convective
and stratiform separation method (Lang et al. 2003) isused with some modifications done in Part I to maintainthe consistency with the TRMM PR rain-type classification.

b. Latent heating
In diagnostic studies (Yanai et al. 1973; Yanai andJohnson 1993), it is customary to define the apparent

heat source Q1 of a large-scale system by averaging
horizontally the thermodynamic equation as
Q1 ⫽ ␲

冉冊⭸␪⭸␪
⫹ v · ⵱␪ ⫹ w
,
⭸t
⭸z

共4兲

where ␪ is the potential temperature, ␲ ⫽ ( p/P00)R/Cp isthe nondimensional pressure, P00 is the reference pressure (1000 hPa), Cp is the specific heat of dry air atconstant pressure, and R is the gas constant for dry air.
Here, Q1 can be directly related to the contributionsof cloud effects, which can be explicitly estimated by
CRMs as冉

Q1 ⫽ ␲ ⫺冊

1 ⭸␳ w⬘␪⬘¯⫹Q .
⫺ v⬘ · ⵱␪⬘ ⫹ D␪ ⫹ LH
R
␳ ⭸z
共5兲

The overbars denote horizontal averages, the primes
indicate deviations from the horizontal averages, ␳ isthe air density, QR is the cooling/heating rate associatedwith radiative processes, and D␪ is the subgrid-scale(smaller than the cloud scale) diffusion that is usuallysmall relative to other terms above the boundary layer(Soong and Tao 1980). The term LH is the net latentheating due to the phase change of water:
LH ⫽

Lf
Ls
L␷
共c ⫺ e兲 ⫹共 f ⫺ m兲 ⫹共d ⫺ s兲.
Cp
Cp
Cp

共6兲

Here, L␷ , Lf , and Ls are the latent heats of vaporization, fusion and sublimation, respectively. Variables c,
e, f, m, d, and s stand for the rates of condensation,
evaporation, freezing of raindrops, melting of snow andgraupel, deposition of ice particles, and sublimation ofice particles, respectively. These processes are not directly detectable with remote sensing (or for that matter, with in situ measurements). Thus, latent heating
retrieval schemes depend heavily on the use of CRM.
The first term on the right-hand side of Eq. (5) is thevertical eddy heat flux convergence from upward anddownward cloud motions. The second term is the hori-JULY 2007

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1103

FIG. 3. Eight-day average profiles of (a) the GCE-simulated LH and (b) Q1R without and (c) with horizontal eddy
heat flux for the total (solid), convective (dashed), and stratiform (dotted) regions for the TOGA COARE (19–26
Dec 1992) case.

zontal eddy heat flux convergence. Traditionally, thehorizontal eddy heat flux convergence is neglected
when Eq. (5) is spatially averaged over an area suitablefor diagnostic analysis. The justification for this omission has been that the net lateral transports across theboundaries of a fixed area by cumulus convection are
negligible relative to the horizontal transports by thelarge-scale motion (Arakawa and Schubert 1974). Figures 3a–c show GCE-simulated average profiles of LH
and of Q1 ⫺ QR (hereinafter Q1R) without and withhorizontal eddy heat flux for the 19–26 December 1992
period, respectively. The vertical eddy heat flux convergence compensates for the distinct LH cooling due
to the melting for the total region (Sui et al. 1994; Shieet al. 2003). Neglecting the horizontal eddy heat flux
convergence is appropriate for Q1R for the total region
because differences between profiles of Q1R without
and with horizontal eddy heat flux are negligible. However, there are the differences between profiles of Q1R
without and with horizontal eddy heat flux in the convective and stratiform regions. Largest differences occur around the melting level (4 km). This is because
both the vertical eddy heat flux convergence and thehorizontal eddy heat flux convergence compensate forthe distinct heating and cooling in the convective andstratiform regions.
The precipitation falling at a given time is not related
to latent heating that is occurring at the same time but
rather to the accumulated latent heating that led up to
the precipitation over a finite time period. Therefore,
LH and Q1R should be basically integrated over thetime periods encompassing the life cycles of cloud processes producing the precipitation. However, it is extremely difficult to tabulate, for example, the effect ofindividual mesoscale systems. Instead, we depend hereon the statistics. In the CRM simulation, as well as in
the real world, cloud systems develop and decay. Although instantaneous matching between a certain rainfall profile and a heating profile is an ill conceived concept, statistical tabulation still could be done, if the life
cycle of cloud systems are realistically reproduced in
the CRM. For example, a shallow convective rain profile may be at a developing stage of a mesoscale systemwith a certain probability A, or it may be just an isolated convection with a probability of 1 ⫺ A. The latentheating associated with the two cases should be different. However, if the CRM reproduce the statistics ofrain systems well enough, CRM-based tables can statistically represent an average heating profile for a certain rain profile. Besides, we accumulate LH and Q1R
over a period of 5 min for each data sampling, sinceaccumulation over long periods are inadequate forgrowing convective cells (Shige and Satomura 2000,
their Fig. 4a) and moving convective systems. Additional sensitivity tests with periods of 1 and 2 min do
not alter the overall results of our study. Hereinafter
heating (LH and Q1R) accumulated over a period of 5
min for each data sampling is represented as instantaneous heating.
Apparent heat source Q1 is more important than LH
as a dynamical quantity. Yanai et al. (2000) have shownthat during TOGA COARE the generation of available
potential energy, wherein positive Q1 anomalies coincide with the warm amplitude, maintains the perturbation kinetic energy of the MJO (Madden and Julian
1994). On the other hand, positive (negative) isentropic
potential vorticity can be generated where Q1 increases(decreases) with height (Holton 2004, p. 110). Braun

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FIG. 4. Eight-day averaged profiles of Q1Rp reconstructed by the original SLH algorithm(SLH1) with the COARE lookup table (thick solid line) and Q1R simulated by the GCE
model (dotted line) for the (a) TOGA COARE (19–26 Dec 1992) case, (b) GATE (1–8 Sep
1974) case, (c) SCSMEX (2–9 Jun 1998), and (d) KWAJEX (6–13 Sep 1999), respectively. Leftpanels are for the convective regions, center panels for the stratiform regions, and the rightpanels are for the total regions. Thin solid lines indicate differences between the SLH1reconstructed and the GCE-simulated profiles.

and Houze (1996) discussed the production of potential
vorticity anomalies from the Q1 associated with a midlatitude squall line. Although the PR footprint scale (4km) estimates of Q1R are less meaningful because Q1R
is a large-scale variable, the SLH algorithm aims toestimate Q1R for each precipitation profile. Over thetropical oceans, heat released by condensation within
deep cumulus convection provides the major heatsource (e.g., Yanai and Tomita 1998). However, otherprocesses can be a major source of heat over local areas. For example, in spring over the Tibetan Plateau,sensible heating from the surface is a major component

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TABLE 1. Domain averaged surface rainfall amounts and stratiform percentage from the GCE model for the COARE, GATE,SCSMEX, and KWAJEX episodes used in the consistency check. Rainfall estimated by sounding network is also shown.

TOGA COARE (19–26 Dec 1992)
GATE (1–8 Sep 1974)SCSMEX (2–9 Jun 1998)
KWAJEX (6–13 Sep 1999)

GCE rainfall (mm day⫺1)

GCE stratiform (%)

Sounding rainfall (mm day⫺1)

20.26
11.80
17.35
9.17

43
35
35
46

19.91
10.97
22.76
8.66

of the heat source (Luo and Yanai 1984; Yanai andTomita 1998). In such a situation, the SLH algorithm
cannot estimate Q1R because it estimates Q1R mainly
due to precipitation processes. Hereinafter, Q1R estimated by the SLH algorithm is represented as Q1Rp tobring attention to this point.
The SLH algorithm is severely limited by the inherent sensitivity of the PR. For latent heating, thequantity required is actually cloud top, but the PR candetect only precipitation-sized particles. For convective
clouds, cloud-top and radar-echo top may often correlate well. The consistency check of the SLH algorithm
showed that the transition from the shallow convective
stage to the deep convective stage of a quasi-2-day oscillation (Takayabu et al. 1996) can be retrieved very
well (Part I, their Fig. 15). This may be because during
the growing phase of a congestus cloud, cloud-top andradar-echo top may correlate well (Kingsmill and
Wakimoto 1991). On the other hand, during the decaying phase of a cumulonimbus cloud, the two tops may
differ significantly, leading to storm-height underestimation. The problem of storm-height underestimationis revisited in section 4a, when we evaluate the algorithm against radiosonde. The limited PR sensitivity
also results in the failure to detect very weak precipitating systems and small convective cells (Heymsfield etal. 2000). Contributions to the distribution of heatingfrom very weak precipitating systems or small convective cells, though smaller, are not negligible. Therefore,
measurements from other sensors will have to be integrated to obtain a more complete estimation of latentheating profiles. Nevertheless, the latent heating profiles in the Tropics from the SLH algorithm using the
TRMM PR data is felt to make a contribution to better
understand global climate.

3. Algorithm improvementsa. Consistency check of the original algorithm
In addition to an 8-day period from TOGA COARE(19–26 December 1992) as shown in Part I, three 8-day
periods from GATE (1–8 September 1974), SCSMEX(2–9 June 1998), and KWAJEX (6–13 September 1999)

are used for a consistency check of the original SLH
algorithm (hereinafter SLH1), as shown in Fig. 4. For
each period, heating profiles were also reconstructedusing the simulated parameters (i.e., PTH, convective/
stratiform characteristics, Ps, and Pm) as input. The algorithm-reconstructed heating profiles from the GCEsimulated precipitation profiles are compared with
GCE-simulated true heating profiles for the convective,
stratiform, and total regions. Domain-averaged surface
rainfall amounts and stratiform percentage from the
GCE model for the COARE, GATE, SCSMEX, andKWAJEX periods used in the consistency check areshown in Table 1. The importance of the fraction ofstratiform rainfall on the total heating profile shape has
been shown by Johnson (1984) and has been taken into
account by the CSH algorithm. Figure 4 and Table 1,
however, indicate that a higher percentage of stratiform
rain does not always imply a maximum heating rate ata higher altitude. A higher-level heating maximum isfound in the SCSMEX case with a stratiform percentage of 35% than in the GATE (KWAJEX) case with35% (46%). This is because the total heating profile
shape is affected not only by the fraction of stratiform
rainfall but also the shape of the convective heating
profile.
Observed (determined from sounding networks)
rainfall is also shown in Table 1 for comparison. The
rainfall amount simulated by the GCE model and estimated by sounding is in good agreement with eachother for COARE and KWAJEX cases. The model
overestimates the rainfall by 8% for the GATE caseand underestimates 24% for the SCSMEX case, respectively, relative to that diagnosed from sounding. All ofthese cases are forced by a prescribed large-scale advective forcing determined from soundings. The radiation and surface fluxes can be influenced by clouds
simulated by the models and may cause the rainfall
differences between the model and the sounding estimates. The model physics may be another reason forthis discrepancy. Accurate and consistent large-scale
advective tendencies in temperature and water vapor
are also needed for CRM simulations. Tao et al. (2000)
found that the large-scale advective terms for tempera-

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ture and water vapor are not always consistent. For
example, large-scale forcing could indicate strong drying (which would produce cooling in the model throughevaporation) but could not contain large-scale advective heating to compensate. This discrepancy in forcing
would cause differences between the observed andmodeled rainfall.
The SLH1 algorithm with the COARE lookup tableproduces excellent agreement between the SLHreconstructed and GCE-simulated heating profiles for
TOGA COARE (Fig. 4a) as shown in Part I. However,the SLH1-reconstructed convective heating above thefreezing level is slightly stronger than was simulated by
the GCE. This is because the simulated data used forthe construction of the lookup tables includes the two
subperiods with 9-day durations (9–17 February 1993,
and 18–26 February 1993) in which convective heating
was stronger above the freezing level than in the 19–26
December 1992 period. This is consistent with the result of DeMott and Rutledge (1998a,b), who reported
that convection in cruise 3 (29 January–25 February1993) had greater liquid and ice water masses above thefreezing level than cruise 2 (21 December 1992–19
January 1993) using radar data.
For the GATE case, the TOGA COARE lookup
table results in less agreement between the SLHreconstructed and GCE-simulated heating profiles forthe convective and stratiform regions (Fig. 4b). The
SLH1-reconstructed heating at z ⫽ 4–6 km is stronger
than the GCE-simulated for the convective heating
profiles, and while the SLH1 algorithm produces cooling at z ⫽ 4–6 km, the GCE model simulates heating forthe stratiform heating profiles. The reconstructed total
heating is in good agreement with the simulated profile.
Compensating errors at z ⫽ 4–6 km from each component (convective and stratiform) is the reason for thisgood agreement.
The TOGA COARE lookup table produces better
agreement between reconstructed and simulated heating profiles for the SCSMEX convective region than for
the GATE convective region (Fig. 4c). The SLH1reconstructed convective heating profile decreases
more rapidly with height above the freezing level thanthe GCE-simulated one does. However, the reconstructed total heating is in poorer agreement with themodel for SCSMEX than for GATE. The level of maximum heating in the reconstructed total heating profile
is about 5 km, while in the simulated total heating profile it is about 7 km. This is because the SLH1 algorithm
reconstructs cooling at z ⫽ 4–6 km whereas the GCE
model simulates heating in the stratiform profiles andthe error for each component does not compensate.
The SLH1-reconstructed total heating profile at z ⫽VOLUME 46

4–6 km is weaker than was simulated by the GCE
model for KWAJEX (Fig. 4d). Relatively large discrepancies between the reconstructed and GCE-simulated
heating profiles are found in the stratiform regions
where the SLH1 algorithm reconstructs cooling at z ⫽4–5 km and the GCE model produces heating. Thus,
the algorithm needs to be improved in the stratiform
region.
In general, the disagreement between the reconstructed and GCE-simulated heating profiles is smaller
for the convective region than for the stratiform region.
The convective lookup table of the SLH1 algorithm
prepares spectral vertical profiles of latent heating forvarious PTHs, leading better agreement for the convective region than for the stratiform region. However, as
pointed out by Houze (1989), the heating profile shapefor convection within a given PTH may vary, leading asmall but nonnegligible disagreement in convective
heating profiles.

b. Comparisons of lookup tables
Figures 5a–d show lookup tables for convective rain
produced from TOGA COARE, GATE, SCSMEX,
and KWAJEX simulations. The GCE-simulated precipitation profiles with a 0.3 mm h⫺1 precipitation-top
threshold and corresponding heating profiles are accumulated and averaged for each PTH with model gridintervals. Two periods from SCSMEX (18–26 May and
2–11 June 1998), two from GATE (1–8 and 9–18 September 1974), and four from KWAJEX (7–11 August,
17–20 August, 29 August–5 September and 6–12 September 1999) are used to increase the number ofsample profiles.
The similarity in the lookup tables from case to caseis evident. Features of the convective heating profiles
show near-monotonic changes with PTH. The shallow
convective heating profiles (PTH ⬍ 6 km) are characterized by cooling aloft due to an excess of evaporation
over condensation, such as in trade wind cumulus(Nitta and Esbensen 1974). Another interesting featureis that the convective heating profiles for the highest
PTH are also characterized by cooling aloft. Thisfeature is consistent with the strong cooling above
mesoscale convective systems observed by Johnson and
Kriete (1982) and Lin and Johnson (1996b). Because
the population of deep convection is small in the
GATE (KWAJEX) simulations, the confidence level inthe mean heating profiles with PTH higher than 15 km(14 km) from GATE (KWAJEX) is low.
On the other hand, there exist variations in verticalstructure (e.g., the level of maximum Q1Rp heating) fora given PTH. These account for the differences be-

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1107

FIG. 5. Ensemble-mean GCE-simulated Q1Rp profiles plotted as a function of PTH from the convective regions of the (a) COARE, (b) GATE, (c) SCSMEX, and (d) KWAJEX cases. Contours indicate
confidence intervals for a mean at the 95% level using the Student’s t test. The contour interval (CI) is
2.0 K h⫺1.

tween the SLH1-reconstructed convective heating profiles and GCE-simulated ones seen in Fig. 4. Figure 6
shows GCE-simulated Q1Rp and precipitation profiles
with selected PTHs of 3.1, 5.9, 8.2, and 11 km from theconvective regions of the COARE, GATE, SCSMEX,
and KWAJEX cases. Note that the Q1Rp profiles andprecipitation profiles are normalized by the nearsurface rain rate. Heating top height is determined by
the PTH, and the heating depth for a given PTH does
not vary from location to location. The vertical structure (e.g., maximum heating level) of the shallow convective heating profiles (PTH ⫽ 3.1 km) does not varyfrom location to location. However, the differences inconvective heating profile shape among the cases increase with PTH. TOGA COARE convection has
stronger heating above the melting level with a higherlevel maximum than GATE convection does, but isweaker with a lower-level maximum than SCSMEX
convection. Similarly, the differences in corresponding
precipitation profile shape among cases also increases
with PTH. TOGA COARE convection has stronger
precipitation intensity above the melting level than
GATE convection, but weaker intensity than SCSMEX
convection. KWAJEX convection shows somewhat
anomalous features. Although convection in KWAJEX
has a lower maximum heating level than in COARE,

heating above the melting level in KWAJEX convection is comparable to that of COARE convection. Correspondingly, KWAJEX convection has somewhat
stronger precipitation intensity above the freezing level
than COARE convection does. This accounts for thesmall difference between the SLH1-reconstructed convective heating and that simulated by the GCE for the
KWAJEX period. Though KWAJEX convection issomewhat anomalous, the same systematic variabilityof heating and precipitation profiles due to the relative
importance of liquid water and ice processes is foundabove the melting level. Convective cells with enhanced
liquid water processes have latent heating and precipitation concentrated below the freezing level, whereas
convective cells with significant ice processes provide
stronger latent heating and more precipitation above
the freezing level. Thus, the precipitation profiles may
be indicative of the convective heating profile shape.
Petersen and Rutledge (2001) showed a large systematic variability in precipitation vertical structure between tropical locations above the freezing level using
the TRMM PR and Lightning Imaging Sensor (LIS)
observations. They found slightly stronger convection
over the South China Sea (i.e., SCSMEX) relative toisolated oceanic regimes (i.e., COARE, GATE, andKWAJEX) while convection over the western Pacific1108

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FIG. 6. Ensemble-mean GCE-simulated Q1Rp profiles plotted as a function of PTH from the convective regionsof the (a) COARE, (b) GATE, (c) SCSMEX, and (d) KWAJEX cases. Contours indicate confidence intervals fora mean at the 95% level using Student’s t test. The CI is 2.0 K h⫺1.

warm pool (i.e., COARE and KWAJEX) was slightly
more intense than that sampled over other oceans (i.e.,GATE). Thus, the aforementioned differences between
COARE, GATE, SCSMEX, and KWAJEX convectionin the GCE results may be consistent with their results.
Figures 7a–d show lookup tables for anvil (deepstratiform with a melting level) rain produced from the
COARE, GATE, SCSMEX, and KWAJEX simulations. The similarity in the anvil heating profiles among
the various lookup tables for each case is readily apparent, although there are differences in the level separating upper-level heating and lower-level cooling,which is tied to the 0°C level. These results agree wellwith observations of stratiform heating profiles summarized in Houze (1989), who concluded that stratiform
heating profiles are not substantially different from one
location to the next.

c. Revised procedure for heating retrieval
To retrieve convective heating profiles, the SLH algorithm selects a heating profile corresponding to the

PTH in the convective heating profile lookup table(Fig. 5a). In the original procedure (Fig. 8a), the entirelevel heating amplitude is determined by
Q共z兲 ⫽

Q̃共z兲
P̃s

Ps,

共7兲

where Ps is the precipitation rate at the lowest observable level and tildes denote the variables in the lookup
table.
Comparisons of convective lookup tables suggested
that the variability in heating profiles above the freezing level should be taken into account for convective
heating retrieval. Hence, the upper-level heating amplitude due to ice processes and the lower-level heating
amplitude due to liquid water processes are determined
separately in the revised procedure for convective heating retrieval (Fig. 8b). Braun and Houze (1995) showed
the peak heating rate by freezing within the convective
region occurs immediately above the freezing level.
Based on sensitivity tests, the level separating upperlevel heating from lower-level heating is determined toJULY 2007

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1109

FIG. 7. Lookup tables for the stratiform region produced from the (a) COARE, (b) GATE, (c)SCSMEX, and (d) KWAJEX simulations.

be 1 km above the melting level. In the revised procedure for convective heating retrieval, the upper-level
heating due to ice processes is determined by
Q共z兲 high ⫽Q̃high共z兲
P̃f

Pf ,

共8兲

where Pf is the precipitation rate at the level separating
upper-level heating from lower-level heating. Likewise,
the lower-level heating due to liquid water processes isdetermined by
Q共z兲low ⫽Q̃low共z兲
P̃s

Ps.

共9兲

This revised procedure is only applied to convective
rain with PTHs that are 3 km higher than the levelseparating upper-level heating from lower-level heating. The original procedure shown in Fig. 8a is applied
to the remaining convective rain.
For stratiform regions, the heating profile is shiftedby matching the melting level of the COARE lookup
table with the observed melting level. Although, inprinciple one can use the melting levels grid by gridfrom the CRM simulations (or PR observations), consistency checks indicate the SLH algorithm performs

much poorer (not shown) when the melting levels gridby grid are used. Thus, the climatological melting levels
are used here.

d. Consistency check of the revised algorithm
Again, the four periods from TOGA COARE (19–26 December 1992), GATE (1–8 September 1974),
SCSMEX (2–9 June 1998), and KWAJEX (6–13 September 1999) are used for the consistency check of therevised SLH algorithm (hereinafter SLH2) as shown in
Fig. 9.
For the COARE period, the SLH2-reconstructedheating profiles for the convective, stratiform, and total
regions are almost identical to those reconstructed by
the SLH1 algorithm. Actually, the SLH2-reconstructedheating profile for the stratiform region is exactly thesame as the SLH1-reconstructed one because adjustment of the melting level is not needed. The SLH2
algorithm produces slightly weaker convective heating
at z ⫽ 5–6.5 km than the SLH1 algorithm does and is inbetter agreement with the GCE model.
Although the total heating profile reconstructed by
the SLH2 algorithm is almost identical to that reconstructed by the SLH1 algorithm for GATE, the error ineach component is reduced. For the convective region,
the SLH2 algorithm produces weaker heating above

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FIG. 8. Diagram showing the procedure for deriving latent heating profiles using the SLH
algorithm.

z ⫽ 5 km than the SLH1 algorithm does and is in muchbetter agreement with the GCE model. For the stratiform region, the discrepancy in the level separating upper-level heating from lower-level cooling as reconstructed by the SLH2 algorithm and simulated by the
GCE model is reduced.
For SCSMEX, the SLH2 algorithm produces stronger convective heating above z ⫽ 5 km than the SLH1
algorithm does, different from the COARE and GATE
periods, and in very good agreement with the GCE
model. For the stratiform region, the discrepancy in thelevel separating upper-level heating from lower-level
cooling as reconstructed by the SLH2 algorithm andsimulated by the GCE model is reduced such that very
good agreement is obtained between the two heating
profiles. As a result of the improvements in the convective and stratiform estimates, the total heating profile reconstructed by the SLH2 algorithm is in very
good agreement with that simulated by the GCE
model. The level of maximum heating reconstructed by
SLH2 agrees with the GCE-simulated one.
For KWAJEX, the better agreement between the
total heating profile reconstructed by the SLH2 algorithm and that simulated by the GCE model is explained by the fact that the discrepancy between thelevel separating upper-level heating from lower-level
cooling as reconstructed by the SLH2 algorithm andsimulated by the GCE model is reduced in the stratiform region. Still, the SLH2 algorithm produces slightly
weaker convective heating at z ⫽ 5–6 km than the

SLH1 algorithm does in better agreement with the
GCE model.

e. Error estimation
As mentioned in Part I, lookup tables are constructed based on the assumption that heating profiles
correspond statistically to precipitation profiles or precipitation parameters (i.e., PTH, Pm). However, the instantaneous grid cell relationship between precipitation
profiles and heating profiles is somewhat ambiguous.
Part I performed a preliminary evaluation of the horizontally averaged estimates and found that horizontal
averaging over ⬃50 km width was required to reduce
random errors in the SLH-reconstructed heating profiles to acceptable levels.
Following Part I, a preliminary evaluation of thehorizontally averaged estimates for the COARE,GATE, SCSMEX, and KWAJEX periods used in theconsistency check is performed. Heating profiles werereconstructed grid by grid for each 8-day period using
the simulated parameters as input. Then, the differences between the reconstructed heating profiles andthe simulated ones were examined statistically to see
the errors in the instantaneous grid cell estimates using
the table method. Larger root-mean-square (rms) errors were found for COARE and SCSMEX than withGATE and KWAJEX. This is because there werelarger surface rainfall amounts and thus were larger
heating associated with COARE and SCSMEX thanwith GATE and KWAJEX (Table 1). For COARE andJULY 2007

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1111

FIG. 9. Same as Fig. 4, but reconstructed with the revised SLH algorithm (SLH2) using the
TOGA COARE lookup table and simulated by the GCE model. Thin solid line indicatesdifferences between SLH2 and the GCE.

SCSMEX, horizontal averaging reduces the rms error.
Averaging over ⬃30 km in width reduces the rms toabout 1 K2 h⫺2. From these results, averaging over ⬃30
km in width is recommended so as to use the SLH
algorithm estimates quantitatively. The large rms errors
at about 9-km height seen in Part I (see their Fig. 12)
are not found in the COARE case (Fig. 10a). This isbecause the alternating heating and cooling pattern at
about 9 km seen in Part I (see their Fig. 3e) is gone in

the new saturation technique (Tao et al. 2003a) used inthis paper.

4. PR applications
In this section, the revised SLH algorithm is applied
to precipitation profiles from version 6 of the TRMM
PR 2A25 dataset, which is instantaneous and at footprint-scale (i.e., a level-2 product). Brightband height1112

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FIG. 10. The rms error in the horizontal averaged profiles between the SLH algorithm-reconstructed
Q1Rp and the GCE-simulated Q1R for the (a) TOGA COARE, (b) GATE, (c) SCSMEX, and (d)KWAJEX cases.

estimates from version 6 of TRMM PR 3A25, gridded
5° spatial resolution monthly composite of instantaneous and footprint-scale data (PR 2A25), are also
used as the melting levels.

caused by the fact the SLH-retrieved Q1Rp does notinclude QR which is included in the sounding-derived
Q1. Tao et al. (2003b, 2004) reported that net radiation(cooling) accounts for about 20% or more of the net

a. Comparison of Q1 profiles over the SCSMEXNESA region
The accuracy of the SLH-retrieved heating can beevaluated by comparing with a rawinsonde-based
analysis of diabatic heating for the SCSMEX Northern
Enhanced Sounding Array (NESA) derived by
Johnson and Ciesielski (2002). Magagi and Barros(2004) and Grecu and Olson (2006) also compared theirresults with heating estimates over the SCSMEXNESA derived by Johnson and Ciesielski (2002). Figure 11 shows a comparison between SLH-retrieved
Q1Rp from version 6 of the TRMM PR datasets andsounding-based Q1 during the campaign’s most convectively active period (15 May–20 June 1998). Mapes etal. (2003) suggested that averages of about 30 days reduce sampling errors in the rainfall-rate estimate(proportional to integrated Q1 or Q2) to 10% for the
SCSMEX NESA. There is good agreement in several
key features of the vertical profiles, particularly thelevel of maximum heating. The SLH-retrieved Q1Rp
heating magnitudes are somewhat greater than thesounding-derived magnitudes. This difference is mainly

FIG. 11. Heating from diagnostic calculations (Johnson andCiesielski 2002) and the SLH2 algorithm using version 6 of the
TRMM PR datasets for SCSMEX (15 May–20 Jun 1998).

JULY 2007

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FIG. 12. Contribution to total rain rate as a function of thesurface rain intensity estimated by TMI 2A12, version 6, over the
PR swath (⬃215 km) and over the full TMI swath (⬃760 km).

condensation for the SCSMEX cloud systems simulatedby the GCE model. The vertical profile of QR simulatedby the GCE model for the SCSMEX periods (18–26
May 1998 and 2–11 June 1998) is shown on the left sideof the figure. This QR component is added to the SLHretrieved Q1Rp estimates. The level of maximum heating of Q1Rp ⫹ QR and its magnitude are in very good
agreement with the sounding-derived Q1.
Figure 11 shows that in the lower troposphere, theQ1Rp ⫹ QR heating magnitudes are somewhat greaterthan the sounding-derived magnitudes, because the
SLH-estimated convective Q1Rp ⫹ QR heating magnitudes are larger than the SLH-estimated stratiform
Q1Rp ⫹ QR cooling magnitudes. Heating estimates fromPR data are subject to sampling errors attributable to
the PR’s narrow swath width, leading to a discrepancy
with the sounding estimates. Grecu and Olson (2006)
showed that the rawinsonde surface precipitation estimates are better correlated with the TMI surface precipitation estimates than with the TRMM PR surface
precipitation estimates. Although all of the estimates
are affected by sampling errors, the TRMM PR surface
precipitation estimates are probably subject to the largest sampling errors despite being the most accurate at
the footprint instantaneous level, leading to a discrepancy with the other estimates. Sampling errors affectnot only the precipitation estimates but also heating
estimates, and therefore it is expected that for periods
when sampling errors in the precipitation estimates arelarge heating estimates will also be subject to large sampling errors (Grecu and Olson 2006, their Fig. 9). Figure 12 presents a histogram of surface rain rates estimated by the TMI (i.e., 2A12, version 6) over the PR

1113

swath (⬃215 km) and over the full TMI swath (⬃760km). The occurrence of moderate-to-heavy rain rates(ⱖ5 mm h⫺1) is more for the PR swath than for the
TMI swath. These moderate-to-heavy rain pixels areclassified mostly as convective rain. The heating estimates are sensitive to the estimated fraction of stratiform rainfall from the PR data. Thus, sampling errors
may account for the overestimation of Q1Rp ⫹ QR heating in the lower troposphere.
It is also evident from Fig. 11 that the Q1Rp ⫹ QR
heating magnitudes are smaller than the soundingderived magnitudes above 9 km. Magagi and Barros(2004) also showed differences in the upper limit between their heating estimates and the sounding-derived
Q1 over the SCSMEX NESA together with in the lower
limit. The radiative cooling of the upper tropospheremust be balanced by deep convection. Because thesaturation mixing ration is low in the upper troposphere, deep convection heats the upper tropospherelargely by eddy heat-flux convergence (Mapes 2001).
As mentioned before, the SLH algorithm is severely
limited by the inherent sensitivity of the PR that can
detect only precipitation-sized particles. During thegrowing phase of a congestus cloud, cloud-top, and radar-echo top may correlate well during the growing
phase of a congestus cloud (Kingsmill and Wakimoto
1991). However, during the decaying phase of a cumulonimbus cloud and in stratiform regions, the two tops
may differ significantly, leading to underestimate ofheating in the upper troposphere. Therefore, measurements from other sensors [e.g., Visible and Infrared
Scanner (VIRS)] will have to be integrated to obtain amore complete estimation of latent heating profiles, but
it is beyond the scope of this study.

b. Comparison with the CSH algorithm
Tao et al. (2001) represented the first attempt at using version-5 TRMM rainfall products to estimate thelatent heating structure over the global Tropics for
February 1998, corresponding to the warm phase (ElNiño) of the 1997/1998 El Niño–Southern Oscillation(ENSO). Three different latent heating algorithms—
the HH algorithm, the convective–stratiform heating
CSH algorithm, and the GPROF heating algorithm—
were used, and their results were compared. Only oneof the three algorithms, the CSH algorithm, can use PR
products as input (CSH can also use the TMI products).
The CSH algorithm has been developed based on theassumption that the shape of the overall MCS heating
profile is determined by the relative amounts of convective and mesoscale heating, which are proportional
to the relative amounts of convective and stratiform
precipitation:

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FIG. 13. Monthly mean rainfall (mm day⫺1) derived from PR 2A25, version 6, for (a) February 1998 and (b)February 1999. The heating profiles will be compared and examined for the various geographic locations identified
by the boxes.

Q共z兲 ⫽ PconvQ共z兲conv ⫹ PstraQ共z兲stra.

共10兲Here, Pconv and Pstra are observed surface precipitation rates in the convective and stratiform regions, andQ(z)conv and Q(z)stra are model-generated convective
and stratiform heating profiles, normalized by the convective and stratiform rainfall. An appropriate selection of latent heating profiles from the lookup table isvery important for the CSH algorithm (Tao et al. 2000).
Schumacher et al. (2004) demonstrated the horizontal
variation in the heating profile across the Tropics calculated from TRMM PR observations using a method
similar to the CSH algorithm, except they used simpler,assumed profiles. In addition, they input their heating
profiles into an idealized climate model to determine
the response of the large-scale circulation to the heating
patterns. The SLH algorithm performance is comparedwith the CSH algorithm using version 6 of the TRMM
PR products for February 1998 and February 1999, corresponding to the warm and cold phase (La Niña), respectively.
Figures 13a,b show the monthly mean surface rainfall(mm day⫺1) for February 1998 and February 1999, re-spectively. Heating structures over the six oceanic regions (western Pacific, central Pacific, east Pacific,
South Pacific, Indian Ocean, and Atlantic Ocean)shown in Fig. 13 will be examined and compared. Threeregions (central Pacific, east Pacific, and South Pacific)
are completely the same as those examined by Tao etal. (2001). Because only precipitation over oceans is
considered in the current investigation, smaller areas
over oceans are selected than those in Tao et al. (2001)
for the Indian and Atlantic Oceans. On the other hand,for western Pacific, larger areas are selected than thosein Tao et al. (2001) in order to improve sampling. Table
2 shows the PR-derived rainfall and its stratiform percentage for the six different geographic areas. The
monthly surface rainfall and its stratiform percentage
for February 1999 are larger than those for February
1998 over the western Pacific and Atlantic Oceans. On
the other hand, the monthly surface rainfall and its
stratiform percentage for February 1998 are larger thanthose for February 1999 over the central and east Pacific, and the Indian Ocean. The surface rainfall over all
six geographic areas for February 1998 derived fromthe PR version-6 (V6) data is larger than that derived

JULY 2007

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SHIGE ET AL.

TABLE 2. PR version-6-algorithm-derived rainfall and stratiform percentage for February 1998 and February 1999 for the various
geographic areas. Figures in parentheses indicate PR version-6-algorithm-derived rainfall and stratiform percentage for the same areas
examined by Tao et al. (2001) for western Pacific Ocean (TOGA COARE Intensive Flux Array), Indian Ocean, and Atlantic Ocean.
Feb 1998⫺1

Western PacificCentral Pacific
East PacificSouth PacificIndian Ocean
Atlantic Ocean

Feb 1999⫺1

Rainfall (mm day )Stratiform (%)

Rainfall (mm day )Stratiform (%)

5.67 (4.68)
9.78
5.44
2.16
4.99 (3.94)
1.29 (1.21)

45 (45)57
47
52
46 (45)25 (28)

8.75
3.38
1.16
4.70
2.51
2.02

51
38
30
55
33
31

from the PR version-5 (V5) data used in Tao et al.
(2001; see their Table 2). Shige et al. (2006) recently
investigated the consistency between TMI-observedbrightness temperatures at 10 GHz and those simulated
from PR 2A25 V5 and V6 rain profiles for ITCZ rainsystems during the warm phase of the 1997/98 ENSO
using a radiative transfer model. They showed thatsimulated brightness temperatures from PR 2A25 V6
are higher than those from PR 2A25 V5 and exhibit
better agreement with the observed brightness temperatures, especially for higher values (associated withheavy rainfall). This is explained by the inclusion of
attenuation corrections for water vapor and cloud liquid water, and more relative weight to the surface reference technique estimate of the path-integrated attenuation in V6 than in V5.
Figures 14 and 15 show the monthly mean convective, stratiform and total heating profiles derived fromthe SLH algorithm for six locations over the tropicaloceans for February of 1998 and February of 1999, respectively. Also the CSH algorithm estimates using PR
rainfall information are shown for comparison. Because
the CSH algorithm estimates Q1 due to precipitation
processes, Q1 estimated by the CSH algorithm is denoted as Q 1p . It should be noted that the SLHestimated heating does not include QR, while the CSH
estimated heating does.
The SLH- and CSH-estimated mean latent heating
profiles over the western Pacific for February 1998 andFebruary 1999 are in good agreement with each other(Figs. 14a and 15a). For February 1998, however, a secondary maximum at low levels (⬃2 km) is found in the
SLH-estimated total heating profile, while the CSH algorithm-estimated heating profiles only show one maximum heating level. This low-level maximum in the
SLH-estimated total heating profile comes from theSLH-estimated convective heating profile with a lowlevel maximum, reflecting the abundance of shallow
convection. Diagnostic budget studies over west Pacificregions (Reed and Recker 1971; Nitta 1972; Yanai et al.

1973; Lin and Johnson 1996a) indicate a single heating
maximum at 7–8 km altitude. The SLH-estimated mean
heating profile for February 1999 resembles those determined from the diagnostic budget studies as well as
the CSH algorithm. Furthermore, the SLH-estimatedconvective heating profile for February 1999 indicates asingle heating peak at 4.5 km, similar to the result fromJohnson (1984) who partitioned the total heating profile of Yanai et al. (1973) into convective and mesoscale
component. On the other hand, the SLH-estimatedmean heating profile with the low-level maximum for
February 1998 does not resemble those determinedfrom the diagnostic budget studies. It should be notedthat diagnostic budget studies over the western Pacificdo not contain periods corresponding to the warm
phases of ENSO, except for two months out of theperiod from March to July of 1958 in Nitta (1972). Deep
convection over the western Pacific is suppressed during the warm phase of ENSO (February 1998) relative
to the cold phase (February 1999) because of lower sea
surface temperatures. Tradelike regimes with abundant
shallow cumulus (Johnson and Lin 1997) are expected
to be more frequent during the warm phase of ENSO
(February 1998) than during the cold phase (February1999). Thus, the difference in the SLH-estimated mean
heating profile between February 1998 and February
1999 may be reasonable.
Total heating profiles over the central and eastern
Pacific for February 1998 and over the south Pacific for
February 1999 from the SLH algorithm also have secondary maxima at low-levels (⬃2 km), while those estimated by the CSH algorithm have a single heating
maximum at 7 km altitude. Although both the SLH andCSH algorithms estimate shallow heating over the eastern Pacific for February 1999, the SLH-estimated heating peak is much sharper than the CSH-estimated one.
Because it uses observed information not only on precipitation type and intensity but also on precipitation
depth, the SLH algorithm estimate between shallow
and deep convection are more distinct than the CSH

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FIG. 14. Monthly (February 1998) mean total, convective and stratiform heating profiles derived from the SLH2 algorithm for various
locations. Total Q1Rp profiles derived from the SLH algorithm are also shown. The geographic areas are the (a) western Pacific, (b)central Pacific, (c) east Pacific, (d) South Pacific, (e) Indian Ocean, and (f) Atlantic Ocean. Note that the abscissa scales are the same
except in (f).

algorithm (see Part I). Zhang et al. (2004) recently presented observational evidence of a shallow meridional
circulation cell in the eastern tropical Pacific. The top of
the shallow meridional circulation cell was found to be
immediately above the atmospheric boundary layer,
which may be consistent with the SLH-estimated shallow heating profile over the eastern Pacific for February 1999.
Schumacher and Houze (2003a) showed dramaticdifferences in PR stratiform rain fraction and precipitation between the 1998 El Niño event and the 1999 La
Niña event. Based on the results of Schumacher andHouze (2003a), Schumacher et al. (2004) demonstrated
that the response of the tropical circulation to latentheating during the 1998 El Niño is extremely sensitive
to the magnitude and horizontal variability of the stratiform rain fraction across the Pacific. Figures 14a–c and

15a–c indicate that the 1998 El Niño event and the 1999
La Niña event exhibit dramatic differences in the shapeof convective heating profile, together with those in theamplitude of stratiform heating profile. Schumacher etal. (2004) did take into account the effect of shallow aswell as deep convection, but they did not fully take into
account the variation of height of the profile from region to region. By utilizing the information about precipitation profiles, the SLH algorithm retrieves differences in the shape of convective heating profile between the eastern Pacific and the western Pacific during
the cold phase. The differences in the shape of convective heating profiles across the Pacific could have an
important effect on the tropical circulation. It is possible that the radar echoes observed by PR are shallower over the eastern Pacific in comparison with thoseover the western Pacific during the 1999 La Niña event,JULY 2007

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1117

FIG. 15. Same as Fig. 14, but for February 1999.

but the cloud top are still high. Figures 16a,b show themonthly mean outgoing longwave radiation (OLR)
from National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites (Liebmann andSmith 1996) for February 1998 and February 1999, respectively. The east–west gradient in the monthly mean
OLR is more pronounced during the cold phase than
the warm phase. The OLR values in the eastern Pacific
are much higher than those in the western Pacific, supporting the notion that the convection is shallower inthe eastern Pacific relative to the western Pacific during
the cold phase.
A larger difference exists between the SLH- andCSH-estimated mean heating profiles over the South
Pacific for February 1998. There is a distinct double
peak in the SLH-estimated heating, while the CSHestimated heating profile shows a minimum near 4 km
but not very pronounced. The SLH-estimated heating
profile is very similar to the vertical distribution ofheating during the undisturbed Barbados Oceanographic and Meteorological Experiment (BOMEX) period in the trade wind belts (Nitta and Esbensen 1974)
and that during episodic trade wind regimes over thewestern Pacific (Johnson and Lin 1997).
The SLH- and CSH-estimated mean latent heating
profiles over the Indian Ocean for February 1998 are ingood agreement with each other. On the other hand,
there are differences between the two estimates overthe Indian Ocean for February 1999. The SLH-estimated mean latent heating profile has a midlevel maximum, while the CSH-estimated mean latent heating
profile has a lower-level maximum. Similar differences
can be found over the Atlantic Ocean for February 1998
and February 1999. These SLH-estimated heating profiles resemble the mean heating profile with a midlevel
maximum that was determined from a diagnostic budget study during GATE (Thompson et al. 1979) andsimulated by the GCE model (see Figs. 4b or 9b).

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FIG. 16. Monthly mean OLR (W m⫺2) for (a) February 1998 and (b) February 1999. The heating profiles arecompared and examined for the various geographic locations identified by the boxes.

In general, the SLH-estimated heating magnitudes at
7–8 km are somewhat larger than the CSH-estimatedvalues, even if the two estimates are qualitatively ingood agreement with each other. This is caused by two
reasons. First, the SLH-estimated heating does not include QR, while the CSH estimated heating does. Second, as shown in Part I (see their Fig. 15d), the SLH
algorithm can retrieve heating profiles in the decaying
stage with no surface rain from the precipitation rate at
the melting level in the stratiform region, while theCSH algorithm estimates no heating profiles from theno-surface rain [see Eq. (10)].

c. Variability of heating profile
The average profiles shown in Figs. 14 and 15 may
not be very representative, because there is great spatial and temporal variability in rainfall over a larger
region such as those selected in Figs. 13 and 16. To
provide actual variability of latent heating profile
shapes, we used contoured-frequency-by-altitude diagrams (CFADs; Yuter and Houze 1995).
Many of the negative values in the low to middle
troposphere in Figs. 17a–e and Figs. 18a,b,d are associ-ated with evaporation and melting in the stratiform region, suggesting great variability in stratiform rain fraction over the regions. The distinct peak in the frequency of heating at levels below 3 km with weak (ⱕ2⌲ day⫺1) heating is also evident for all six geographic
areas for both February 1998 and February 1999 in the
CFADs (Figs. 17 and 18), corresponding to a heating
peak at 2 km seen in the mean convective heating profiles (Figs. 14 and 15). It is inferred from the convective
heating-profile lookup table (Fig. 5a) that shallow convection with PTHs lower than 4 km (shallow cumulus)
accounts for this distinct peak. Capping of cloud growthby the trade wind stable layer (2 km), with some overshooting, leads to large populations of shallow cumulus.
Although a lower-level heating peak cannot be seenin the mean convective heating profile over the western
Pacific for February 1999 (Fig. 15a), it remains true that
the CFAD (Fig. 18a) indicates a distinct population ofheating at levels below 2 km. Johnson and Lin (1997)
showed that, in association with the MJO, the western
Pacific warm pool lower troposphere periodically develops tradelike characteristics with abundant shallow
cumulus. The CFAD (Fig. 18a) indicates another dis-JULY 2007

SHIGE ET AL.

1119

FIG. 17. CFADs of monthly (February 1998) total Q1Rp profiles at 0.5° resolution derived from the SLH2 algorithm for various
locations. The geographic areas are the (a) western Pacific, (b) central Pacific, (c) east Pacific, (d) South Pacific, (e) Indian Ocean, and(f) Atlantic Ocean. The bin size is 0.5 K. CFAD contour interval: 1% for values ⬍4% and 4% above. Values ⬎20% are shaded.

tinct population of lower-level heating, extending up to⬃4 km with stronger heating (⬃3.5 K day⫺1). It is inferred from the convective heating-profile lookup table(Fig. 5a) that convection with PTHs between 4 and 8
km (cumulus congestus) accounts for the latter one.
The relative abundance of cumulus congestus can be
attributed to a single heating peak at 4.5 km in themean convective heating profile over the western Pacific for February 1999 (Fig. 15a). This is consistent withthe result from Johnson et al. (1999) who indicate thatcumulus congestus with tops between 4.5 and 9.5 km
are the most abundant of all precipitating clouds in
TOGA COARE based on cumulus echo-top statistics
from 5-cm radar aboard the R/V Vickers. They showedthat large populations of cumulus congestus correspondto the stable layer near the melting level (Johnson et al.
1996; Zuidema 1998).

5. Summary and future work
In this study, the universality of the lookup tableproduced from TOGA COARE simulations used in the

SLH algorithm (Shige et al. 2004) was examined for its
global application to TRMM PR data. Heating profiles
were reconstructed from CRM-simulated parameters(i.e., PTH, precipitation rate at the melting level, rain
rate, and type) with the TOGA COARE table and thencompared with CRM-simulated true heating profiles,
which were computed directly from the model thermodynamic equation. GATE, SCSMEX, and KWAJEX
periods were used for the consistency check.
The consistency check indicates that the COARE
table produces discrepancies between the SLH-reconstructed and GCE-simulated heating above the melting
level in the convective region and at the melting level inthe stratiform region. Comparisons of the TOGACOARE lookup table with those from GATE,SCSMEX, and KWAJEX simulations show that thediscrepancies in the convective region are explained bydifferences in the vertical distribution of deeper convective heating due to the relative importance of liquidwater and ice processes that varies from case to case.
On the other hand, the discrepancies in the stratiform
region are explained by differences in the level sepa-

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FIG. 18. Same as Fig. 17, but for February 1999.

rating upper-level heating and lower-level cooling near
the melting level.
Based on these results, algorithm improvements havebeen made to the SLH algorithm. In the revised procedure for convective heating retrieval, the upper-level
heating amplitude due to ice processes and lower-level
heating amplitude due to liquid water processes are
determined separately. For stratiform regions, the heating profile is shifted up or down by matching the melting level of the TOGA COARE lookup table with theobserved one. A consistency check indicates that therevised SLH algorithm performs better for each component (convective and stratiform) than the originalone.
The revised SLH algorithm was applied to PR data
and the results were compared with heating profiles
derived diagnostically from SCSMEX sounding data
(Johnson and Ciesielski 2002). There is a good agreement in the key features of the vertical profiles, particularly the level of maximum heating. The SLHretrieved Q 1Rp heating magnitudes are somewhat
greater than the sounding-derived magnitudes. This iscaused by the fact the SLH-retrieved Q1Rp does notinclude the QR implied by the sounding-derived Q1.
Adding GCE-simulated QR to Q1Rp provides better
agreement. It was also shown that the heating estimatesfrom PR data are subject to sampling errors attributable to the PR’s narrow swath width (⬃215 km), leading to a discrepancy with the sounding estimates.
The revised SLH algorithm was also applied to PRdata for February 1998 and February 1999, and theresults were compared with heating profiles derived by
the CSH algorithm (Tao et al. 1993, 2000) using PR
data. Because it uses observed information not only on
precipitation type and intensity but also on precipitation depth, the SLH algorithm estimates between shallow and deep convection are more distinct than the
CSH algorithm (see Part I). The SLH- and CSH-estimated mean latent heating profiles over the western
Pacific for February 1998 and February 1999 are ingood agreement with each other. For February 1998,
however, a secondary maximum at low levels (⬃2 km)
is found in the SLH-estimated total heating profile,
while the CSH algorithm-estimated heating profiles
only have one maximum heating level. This low-level
maximum in the SLH-estimated total heating profileJULY 2007

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comes from the SLH-estimated convective heating profile with a low-level maximum, reflecting the abundance of shallow convection. Deep convection over thewestern Pacific is suppressed during the warm phase of
ENSO (February 1998) relative to the cold phase (February 1999) because of lower sea surface temperatures.
Thus, the difference in the SLH-estimated mean heating profile between February 1998 and February 1999
may be reasonable. Total heating profiles over the central and eastern Pacific for February 1998 and over theSouth Pacific for February 1999 from the SLH algorithm also have secondary maxima at low levels (⬃2km), while those estimated by the CSH algorithm havea single heating maximum at 7 km altitude. Althoughboth the SLH and CSH algorithms estimate shallow
heating over the eastern Pacific for February 1999, theSLH-estimated heating peak is much sharper than the
CSH-estimated one. The tops of shallow meridional circulation cells were found to be immediately above theatmospheric boundary in the eastern tropical Pacific(Zhang et al. 2004), which may be consistent with the
SLH-estimated shallow heating profiles over the eastern Pacific for February 1999. The SLH- and CSHestimated mean latent heating profiles over the Indian
Ocean for February 1998 are in good agreement witheach other. On the other hand, there are differences
between the two estimates over the Indian Ocean for
February 1999. The SLH-estimated mean latent heating profile has a midlevel maximum, while the CSHestimated mean latent heating profile has a lower-level
maximum. Similar differences can be found over the
Atlantic Ocean for February 1998 and February 1999.
These SLH-estimated heating profiles resemble themean heating profile with a midlevel maximum thatwas determined from a diagnostic budget study during
GATE (Thompson et al. 1979) and simulated by the
GCE model.
Only precipitation over oceans was considered in thecurrent investigation. To preserve the simplicity andtransparency, we use the lookup table produced fromCOARE simulations as the oceanic lookup table. On
the other hand, significant differences in precipitation
features between ocean and land have been shown by
TRMM observations (e.g., Nesbitt et al. 2000; Petersen
and Rutledge 2001; Takayabu 2002; Schumacher andHouze 2003a,b). Continental locations exhibit marked
variability in precipitation structure both regionally andseasonally, thus possibly we need to vary the lookup
table regionally and seasonally. This study will be extended to simulations of other field experiments [e.g.,
Global Energy and Water Cycle Experiment Asian
Monsoon Experiment (GAME) in the Indochina Peninsula (Yasunari 1994) and Atmospheric Radiation

Measurement Program (ARM) in the southern U.S.
Great Plains (Ackerman and Stokes 2003)] to produce
lookup tables for precipitation over land. The results
will be reported in a publication in the near future.
Acknowledgments. This study is supported by the Japan Aerospace Exploration Agency/Earth Observation
Research Center (JAXA/EORC) TRMM project. The
first author is grateful to Mr. K. Ito and Mr. A. Numataof the Remote Sensing Technology Center (RESTEC)
of Japan and Dr. T. Kubota of Japan Science and Technology Agency (JST) for helpful computing assistanceand to Mr. H. Sasaki of Osaka Prefecture University
for preparing the TRMM data. He is also supported by
the fund of JST Corporation–Core Research for Evolution Science and Technology (CREST). Yukari N.
Takayabu expresses her hearty gratitude to the lateProf. Tsuyoshi Nitta for motivating her to develop thelatent heating algorithm utilizing TRMM PR data.
W.-K. Tao and C.-L. Shie are mainly supported by theNASA headquarters Atmospheric Dynamics and Thermodynamics Program and the NASA TRMM. They
thank Dr. R. Kakar at NASA headquarters for his support. The authors also thank Mr. S. Lang of NASA/
GSFC for proofreading the manuscripts. The TRMM
products were provided by JAXA. The CSH estimates
were obtained from the NASA Goddard Earth Sciences (GES) Data and Information Services Center(DISC) Web site. The OLR dataset was obtained fromthe NOAA Climate Diagnostics Center Web site. The
Grid Analysis and Display System (GrADS) package
was utilized for the figures.
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