RETRIEVAL OF LATENT HEATINGFROM TRMM MEASUREMENTS
BY W.-K. TAO, E. A. SMITH, R. F. ADLER, Z. S. HADDAD, A. Y. HOU, T. IGUCHI, R. K AKAR,
T. N. KRISHNAMURTI, C. D. KUMMEROW, S. L ANG, R. MENEGHINI, K. NAKAMURA, T. NAKAZAWA,
K. OKAMOTO, W. S. OLSON, S. SATOH, S. SHIGE, J. SIMPSON, Y. TAKAYABU,
G. J. TRIPOLI, AND S. YANG

TRMM-based latent heating products—not long ago considered out of our technological reach—are beginning to contribute to global modeling, but the necessary retrieval
algorithms produce varying results and will require further research.

P

recipitation, in driving the global hydrologicalcycle, strongly influences the behavior of the
Earth’s weather and climate systems and iscentral to their variability. Two-thirds of the global
rainfall occurs over the Tropics,1 which leads to its
profound effect on the general circulation of theatmosphere. This is because its energetic equivalent,latent heating (LH), is the tropical convective heat1

engine’s primary fuel source as originally emphasizedby Riehl and Malkus (1958). At low latitudes, LH
stemming from extended bands of rainfall modulates
large-scale zonal and meridional circulations andtheir consequent mass overturnings (e.g., Hartmann
et al. 1984; Hack and Schubert 1990). Also, LH is theprincipal energy source in the creation, growth, vertical structure, and propagation of long-lived tropical

The Tropics are liberally taken as the area bounded by the 25°N–25°S latitude zone.

AFFILIATIONS : TAO, S MITH , A DLER , HOU, M ENEGHINI , AND

SIMPSON —Laboratory for Atmospheres, NASA Goddard Space
Flight Center, Greenbelt, Maryland; HADDAD —NASA Jet Propulsion
Laboratory–California Institute of Technology, Pasadena, California; IGUCHI AND SATOH —National Institute of Information andCommunications Technology, Tokyo, Japan; K AKAR—NASA
Headquarters, Washington, DC; KRISHNAMURTI —Department ofMeteorology, The Florida State University, Tallahassee, Florida;
KUMMEROW —Department of Atmospheric Science, Colorado State
University, Fort Collins, Colorado; L ANG —Science Systems andApplications, Inc., Greenbelt, Maryland; NAKAMURA—Hydrospheric
Atmospheric Research Center, Nagoya University, Nagoya, Japan;
NAKAZAWA—Japan Meteorological Agency, Meteorological ResearchInstitute, Tsukuba, Japan; OKAMOTO AND S HIGE —Department of
Aerospace Engineering, Osaka Prefecture University, Sakai, Osaka,

AMERICAN METEOROLOGICAL SOCIETY

Japan; OLSON —UMBC Joint Center for Earth Systems Technology,
Baltimore, Maryland; TAKAYABU —Center for Climate System
Research, University of Tokyo, Tokyo, Japan; TRIPOLI —Department
of Atmospheric and Oceanic Sciences, University of Wisconsin—
Madison, Madison, Wisconsin; YANG —School of Computational
Sciences, George Mason University, Fairfax, Virginia
CORRESPONDING AUTHOR : Dr. Wei-Kuo Tao, NASA Goddard
Space Flight Center, Code 613.1, Greenbelt, MD 20771
E-mail: tao@agnes.gsfc.nasa.gov
The abstract for this article can be found in this issue, following the tableof contents.
DOI:10.1175/BAMS-87-11-1555
In final form 26 May 2006
©2006 American Meteorological Society

NOVEMBER 2006

| 1555

(1998–2002), mapped atthree vertical levels (2, 5,
and 8 km), along with theassociated averaged surface
rain-rate map (this diagram is discussed in detailin “Temporal and spatial
averages”).
The TRMM satellite is
the centerpiece of a joint
rainfall mission between
the American and Japanesespace agencies, the National
Aeronautics and Space Administration (NASA) and theJapan Aerospace Exploration
Agency [(JAXA); formerly
the National Space Development Agency of Japan(NASDA)], providing thefirst high-quality rainfall
a nd space–t i me st r uctures of LH over the global
Tropics and subtropics (seeSimpson et al. 1996). The
TRMM observatory waslaunched in November 1997,
in a 350-km orbit inclined
35° to the Earth’s equatorial plane (in August 2001,
the orbit was boosted to~400 km to preserve fuelby reducing atmosphericdrag). The main rain instruFIG. 1. (upper three panels) Five-year mean Q1 heating rates at 8, 5, and 2
ments are JAXA’s Ku-band
km AGL (upper 3 panels) along with (bottom) surface rain rates over global
Precipitation Radar (PR)Tropics determined by GSFC CSH algorithm applied to 1998–2002 PR meaand NASA’s nine-channel
surements acquired from the TRMM satellite.
TRMM Microwave Imager(TMI).
waves (e.g., Puri 1987; Lau and Chan 1988). Moreover,Studies of latent heat estimation from satellites
the distinct vertical distribution properties of convec- date back to the first spaceborne passive microwave
tive and stratiform LH profiles help influence climatic (PMW) rain radiometer [see, e.g., a study by Adler andoutcomes via their tight control on large-scale circula- Rodgers (1977) concerning total column LH withintions (Lau and Peng 1987; Nakazawa 1988; Sui and tropical cyclones]. Latent heating is that portion of
Lau 1988; Emanuel et al. 1994; Yanai et al. 2000; Sumi diabatic heating that is either released or absorbed
and Nakazawa 2002; Schumacher et al. 2004).
within the atmosphere as a result of the phase changes
The purpose of this paper is to describe how LH of water (i.e., from gas to liquid, liquid to solid, gas toprofiles are being derived from satellite precipita- solid, and their reverse processes). The related terms
tion rate retrievals, focusing on those being made are condensation–evaporation, freezing–melting, andwith Tropical Rainfall Measuring Mission (TRMM) deposition–sublimation. Latent heating is dominatedsatellite measurements. As an example, Fig. 1 by phase changes between water vapor and small
provides an illustration of averaged patterns of LH liquid or frozen cloud-sized particles. These prodetermined from five years of TRMM measurements cesses are not directly detectable with current remote1556 |NOVEMBER 2006

sensing or in situ instruments, which explains why
the retrieval schemes to be discussed depend heavily
on some type of cloud-resolving model (CRM).
CRMs require detailed physical parameterizations,particularly for a) radiative transfer, b) surface
radiation, heat, moisture, and momentum fluxes,c) boundary layer heat, moisture, and momentum
turbulent transport, and d) cloud microphysics.
These specialized physics are needed for simulating
dynamical interactions of individual clouds andcloud ensembles within the large-scale environment.
The studies of Soong and Tao (1980, 1984) were someof the first to use CRMs for understanding interactions between clouds and their environment. Early
CRMs credibly reproduced the statistical propertiesof clouds as noted by Lipps and Hemler (1986), Taoand Soong (1986), and Tao et al. (1987), and later
were corroborated by Krueger (1988) in a detailed
study and by others in specialized applications(e.g., Tripoli and Cotton 1989a,b). Since the TRMM
launch, and in anticipation of the future Global
Precipitation Measurement (GPM) Mission (Smithet al. 2006), modern CRMs are used to simulate
phase changes of water and mass transfers of water
species in support of LH retrieval, notably the Goddard Cumulus Ensemble (GCE) model (Tao andSoong 1986; Tao and Simpson 1993; Tao 2003; Taoet al. 2003), the University of Wisconsin (UW) Nonhydrostatic Modeling System (NMS; Tripoli 1992a,b,
Tripoli and Smith 2006, manuscript submitted toMon. Wea. Rev.), and the fifth-generation Pennsylvania State University (PSU)–National Center for
Atmospheric Research (NCAR) Mesoscale Model(MM5) (Dudhia 1993).
Under the Boussinesq approximation, the thermodynamic (or temperature) budget can be explicitly
calculated from CRMs as

where the primes indicate deviations from the largescale environment mainly due to small-scale cloud
processes. The variable θ is potential temperature, ρ− isair density, π− = (p/P00) R/cp is nondimensional pressure(where p and p00 are dimensional and reference pressures with p00 taken as 1000 hPa), and cp and R represent the specific heat at constant pressure and gas
constant of dry air, respectively. The variables Lv, Lf ,and Ls are the latent heats of condensation, freezing,and sublimation, respectively, while the variables (c, e,
f, m, d, s) denote rates for 1) the condensation of cloud
droplets, 2) evaporation of cloud droplets and rain
AMERICAN METEOROLOGICAL SOCIETY

drops, 3) freezing of water droplets and raindrops,4) melting of ice crystals, snowflakes, graupel, andhail, 5) deposition of ice crystals, and 6) sublimationof all ice hydrometeors, respectively.
The term (1/cp) [Lv (e – e) + Lf (f – m) + Ls (d – s)]is the LH due to microphysical phase changes. As
defined in Yanai et al. (1973), Q1 is the apparent heatsource, while QR is the radiative heating rate associated with radiative transfer processes. The first two
terms on the right-hand side of Eq. (1) are the verticaland horizontal eddy heat flux convergence

where the horizontal diffusion term is neglected when
Eq. (1) is spatially averaged over a large area suitable
for large-scale diagnostic analysis.

FIG . 2. Height–length cross sections of GCE CRMgenerated LH (°C day–1) consisting of sum of heating bycondensation, freezing, and deposition, and cooling by
evaporation, melting, and sublimation, associated with(top) midlatitude continental (PRE-STORM) squall lineand (bottom) tropical oceanic (TOGA COARE) MCS.
[Simulations are discussed in Tao et al. (1993a, 1995,
1996), Wang et al. (1996), and Lang et al. (2003).]
NOVEMBER 2006

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Figure 2 illustrates the instantaneous LH structures associated with both a midlatitude and a tropical mesoscale convective system (MCS) simulatedby the GCE CRM in a two-dimensional framework.
The cases were drawn from two field campaigns,
the midlatitude continental Preliminary Regional
Experiment for Storm-Scale Operational andResearch Meteorology (PRE-STORM) and tropical oceanic Tropical Ocean Global Atmosphere
Coupled Ocean–Atmosphere Response Experiment(TOGA COAR E). 2 Ev ident in t he f ig ure a re1) condensation heating in the lower to middle
troposphere of the convective leading edge of thecloud systems, 2) deposition heating in the upperparts of the convective and stratiform regions,3) cooling at low levels in the stratiform regions
stemming from evaporation of rain, 4) coolingfrom melting of precipitation particles in a narrowlayer near the freezing level, and 5) cooling fromsublimation adjacent to depositional heating in thestratiform regions.
The alternating heating–cooling pattern at upper
levels is caused by gravity wave dispersion induced
by deep convection. This is more significant for the
midlatitude case because the associated convective
updrafts are stronger. Also, cooling within the stratiform region is larger and deeper for midlatitudes dueto the generally drier environments. Finally, the levelseparating the heating and cooling layers within thestratiform regions (i.e., the melting level) is different for the two systems. The simulated squall line
structures are generally consistent with observed
squall lines (e.g., Biggerstaff and Houze 1991; andJorgensen et al. 1997).
Using a residual approach, Q1 can be derived
indirectly over a spatial domain by measuring profilesof temperature, pressure, and the three-dimensional
wind vector from a suitably spaced circumscribing network of radiosondes. This “diagnostic heatbudget” methodology was first described by Yanai
et al. (1973) and has been extensively studied by others(e.g., Nitta 1977; Houze 1982, 1989, 1997; Johnson
1984). It can be expressed by

2(2)
There is an accompanying equation for the apparent
moisture sink or drying (Q2) similar to Eq. (2), except−that θ and Q1 are replaced by water vapor specifichumidity (q−) and negative Q2, respectively.
Latent heating estimates from satellite precipitation rate profiles can be assessed from Q1 budgets
determined in CRM simulations, from regional- andlarge-scale prediction models, and from global climate
reanalysis products (Nigam et al. 2000). Because current
LH retrieval schemes are all tied to CRMs, a more independent approach for validating TRMM LH estimatesis to use the radiosonde-based diagnostic heat budget
approach discussed above. For purposes of this study, Q1
budgets diagnosed from sounding observations taken
during three TRMM field campaigns [South China
Sea Monsoon Experiment (SCSMEX), TRMM Large
Scale Biosphere–Atmosphere Experiment in Amazonia(LBA), and the Kwajalein Experiment (KWAJEX)] andother past and current field campaigns [Global Atmospheric Research Programme (GARP) Atlantic Tropical
Experiment (GATE), PRE-STORM, TOGA COARE,
and the Department of Energy’s (DOE’s) Atmospheric
Radiation Measurement (ARM) Program]3 are used as
the principal validation datasets.
In “Descriptions of latent heating algorithms,”
a set of five LH algorithms developed for TRMM
applications are described; “Heating structures estimated from individual algorithms” presents highlights from various applications of the algorithms;“Global modeling applications” describes how LH
products are currently being used in conjunction
with global weather and climate models; and finally“Final remarks and recommended future research”
offers discussion and remarks intended to stimulate
further research.
DESCRIPTIONS OF LATENT HEATINGALGORITHMS. In this section, brief descriptions
are provided for five different LH algorithms designed

PRE-STORM Central took place in Kansas and Oklahoma during May–June 1985 (Cunning 1986). TOGA COARE took placeover the Pacific Ocean warm pool from November 1992 to February 1993 (Webster and Lukas 1992; Nakazawa 1995).
3SCSMEX took place over the South China Sea during May–June 1998 (Lau et al. 2000); LBA took place in Rondonia, Brazil,
during January–February 1999 (Halverson et al. 2002; Petersen et al. 2002); KWAJEX took place in the vicinity of Kwajalein
Atoll, Marshall Islands, during July–September 1999 (Yuter et al. 2005); GATE took place over the eastern tropical Atlantic
Ocean during June–September 1974 (GATE International Scientific and Management Group 1974; Houze and Betts 1981);
and the DOE ARM Program supports experiments in Oklahoma at DOE ARM’s Southern Great Plains (SGP) Cloud andRadiation Test Bed (CART) site (Stokes and Schwartz 1994).

1558 |NOVEMBER 2006

for applications with satellite-generated precipitation
rate profile inputs, with attention given to TRMM
products. They are referred to as the 1) Goddard

Convective–Stratiform Heating (CSH) algorithm,
2) Goddard Profiling Heating (GPROF Heating)algorithm, 3) Hydrometeor Heating (HH) algorithm,

TABLE 1. Summary of CSH, GPROF Heating, HH, PRH, and SLH algorithms, in which key references, essential algorithm input parameters, past case studies, and relevant space–time resolutions of heating calculations are provided. Wherever + symbols precede citations in the “References” column, corresponding+ symbols in other columns denote associated information vis à vis those citations. In the “Alg” column,“RECON” indicates reconstruction algorithm (i.e., heating is calculated by using model-generated parameters of surface rain rate and convective/stratiform fractions as input to the CSH heating algorithm),“COMB” indicates combined PR–TMI algorithm, and SSM/I indicates Special Sensor Microwave Imager,
which is a PMW radiometer used on Defense Military Satellite Program (DMSP) satellites. In the “Resolution” column, inst indicates instantaneous, hr indicates 1 hr, dy indicates 1 day, and mo indicates 1 month.
Alg

References

CSH(RECON:
SSM/I

CSH(RECON:PR)

GPROF(SSM/I;TMI)

Tao et al. (1993b)+ Tao et al. (2000)+ Tao et al. (2001)+ This study+ Olson et al. (1999)+ Olson et al. (2006)+ Yang et al. (2006)+ This study

Input parameters• Surface rain rate and convective/
stratiform fractions

Cases

Resolution• GATE (1974)
200–300 km; dy• PRE-STORM (1985)• Tropical Cyclone Thelma 1987

+ Surface rain rate and convective/+ TOGA COARE (1992–93)
stratiform fractions+ Various tropical regimes+ CSH, GPROF Heating, and HH(February 1998)
algorithm outputs+ Global Tropics (December+ Surface rain rate and convective strati1997–November 2000)
form fractions• Lookup table linking CRM-generatedhydrometeor density/Q1 – QR profiles
and radiative transfer equation (RTE)model-generated PMW TBs+ 500 km; 3–6 hr+ 110 km; dy+ 55 km; mo+ Hurricane Andrew (1992)+ Tropical MCSs (1992)+ TOGA COARE (1992–93)+ Squall line

+ 25 km; inst
+ 25 km; inst
+ 500 km; dy+ 28 km; inst

• GATE (1974)• EMEX (1987)+ 15 km; inst
+ 15 km; inst
+ 15–50 km; inst
+ 275 km; mo+ 5 km; inst

• Surface rain rate for all precipitation
categories• Hydrometeor density profiles (cloud/
HH

Tao et al. (1990, 1993b)(RECON) Simpson and Tao (1993)

HH(SSM/I;
PR; TMI;COMB)

rain/ice crystal/snow/aggregate/
graupel)• PRE-STORM (1985)• Terminal velocities of rain/snow/
aggregate/graupel hydrometeors+ Tropical Cyclones Thermal+ Smith et al. (1992, 1994a)
1987/Hugo 1989
+ Smith et al. (1994a, 1994b)+ TOGA COARE (1992–93)+ Yang and Smith (1999a, 2000) • Frozen and/or liquid rain-rate profile (s)+ TOGA COARE (1992–93)+ Yang and Smith (1996b)+ Global Tropics (1992)+ This study+ Hurricane Bonnie 1998

5–100 km; inst

• Surface rain rates for all precipitation
categories
PRH
(PR)

Satoh and Noda (2001)
This study• Terminal velocities of rainhydrometeors• Squall line in Oklahoma

5–100 km; inst

• TOGA COARE (1992–93)

5–100 km; inst

• Cloud vertical velocities• Precipitation top height (PTH)• Bright band and cloud-base heights• Surface rain rates for all precipitation

Takayabu (2002)
Shige et al. (2004)(RECON)
This study
SLH

categories• Convective/stratiform/anvil
classification• PTH• Rain rate at and height of melting level

AMERICAN METEOROLOGICAL SOCIETYNOVEMBER 2006

| 15594) Precipitation Radar Heating (PRH) algorithm,
and 5) Spectral Latent Heating (SLH) algorithm. The
CSH, GPROF, and SLH algorithms require the fullcomplement of cloud model data generated by a CRM.
Table 1 summarizes algorithm features, including
principal authorship, key algorithm inputs, identification of satellite datasets to which the algorithms
have been applied, and the notational space–timeresolutions associated with the algorithms. As an aid
to understanding these algorithms and interpreting
their results, a compilation of their “general” strengths
and weaknesses is provided in Table 2, while full ex-

planations are provided in Tao et al. (2006, manuscript
submitted to Mon. Wea. Rev.).
A preliminary comparison between earlier versionsof three of the algorithms (CSH, GPROF Heating, andHH) was performed with February 1998 TRMM data
by Tao et al. (2001). An important finding was theoverall equivalence in the horizontal distributions oflatent heat release produced by the three schemes andthe close relationships of these distributions to surface
rainfall. They all were able to identify areas of major
convective activity, including well-defined sectorsof the intertropical convergence zone (ITCZ) within

TABLE 2. General strengths and weaknesses of CSH, GPROF Heating, HH, PRH, and SLHl algorithms.
Algorithm

CSH

GPROF
Heating

General strengths

General weaknesses• CRM-based and robust algorithm with long history.
• Adaptable to any TRMM level-2 algorithm (PR, TMI,

• Restricted to convective/stratiform categories and• CRM based in which diagnosed Q1 – QR profiles consistent• Hydrometeor density and Q1 – QR profiles have different

sensitive to errors in corresponding cover fractions.
COMB).
• Imperfections and incompleteness in CRM-generated
heating profiles defined in lookup table lead to systematic• Adheres to convective/stratiform heating variational
errors in retrieved profiles.
characteristics based on diagnostic budget studies.
• Extensive simulation and Q1 validation studies involving field • Zero surface rainfall leads to zero heating profiles aloft.
campaign datasets from GATE, EMEX, PRE-STORM, TOGACOARE, SCSMEX, TRMM LBA, KWAJEX, and DOE ARM
programs.
with associated retrieved hydrometeor density profiles.
• Random errors in retrieved Q1 – QR profiles well defined
because of Bayesian framework.
• Q1 – QR profiles retrievable instantaneously at TMI beamscale (~14 km) or at space–time-averaged scales.

temporal scales.

• Errors in CRM/RTE model database simulations lead tosystematic errors in retrieved Q1 – QR profiles.

• Underrepresentation of CRM/RTE model-simulatedhydrometeor density profiles linked to Q1 – QR profiles indatabase leads to Q1 – QR representativeness errors.

• Physically based and direct microphysics approach with long • Sensitive to noise in retrieved precipitation profiles, i.e.,
history.

noise in hydrometeor density or rain-rate profiles passed
on to LH profiles.
algorithm (PR, TMI, COMB).
• Greater uncertainties generated from errors informulation of hydrometeor terminal velocities, more so at• LH profile vertical structure closely related to vertical rainrate gradients, accurate precipitation mass flux inputs result upper levels.
in small systematic errors.
• Lesser uncertainties generated without knowledge ofcloud-scale vertical motion, must be assumed zero if• LH profiles retrievable instantaneously at either PR or TMI
unknown.
beam scales (~5 or ~14 km, respectively) or at space–timeaveraged scales.

• Adaptable to any TRMM level-2 precipitation profile
HH• Produces distinct LH profiles for various types of organized • Sensitive to estimated vertical velocities and hydrometeor

PRH

SLH

precipitation systems (e.g., squall lines, tropical cyclones,
MCSs).
• Differentiated cloud vertical velocities provided forconvective, stratiform, and deep anvil precipitation
categories.
• LH profiles retrievable at instantaneous scale from PR.

density (or rain rate) profiles, especially for mixed phase.

• Uses idealized thermodynamic assumptions, and may
produce cooling near cloud top and in upper part of cloud.

• Limited sampling due to PR’s narrow swath width.

• Differentiates heating structures between shallow• Restricted to convective/shallow stratiform/anvil stratus

convective and deep
• Produces heating profiles for decaying anvil stage even withzero surface rain rate.
• Heating profiles retrievable at instantaneous scale from PR.

categories and sensitive to errors in corresponding cover
fractions.
• Imperfections and incompleteness in CRM-generated
heating profiles defined in lookup table lead to systematic
errors in retrieved heating profiles.

• Limited sampling due to PR’s narrow swath width.

1560 |NOVEMBER 2006

the central and east Pacific, and along the southern
Pacific convergence zone (SPCZ). The only significant differences between the algorithms pertained
to the derived altitudes of maximum heating. In allcases, the CSH estimates exhibited one heating level
maximum with the level varying between different
geographic locations—features in general agreementwith diagnostic budget studies.
A broader heating maximum, often with twoembedded peaks, was obtained with the GPROF
and HH algorithms. This type of vertical heating
structure resulted from these two algorithms
averaging sets of individual LH profile solutions
drawn from mixes of retrieved convective andstratiform precipitation rate profiles. In essence,the distinct LH structures, associated with the twounderlying precipitation modes and controlled byfundamental differences in the two mode’s characteristic precipitating ice profiles, combine under an
averaging operator to produce a sharp and distinct
minimum and an additional secondary maximum
in the lower atmospheric layers.
While such structures are not normally foundin diagnostic calculations, they are a realistic interpretation by the GPROF and HH algorithmsof what are potentially f lawed precipitating ice
profiles produced by the precipitation rate retrieval
algorithms preceding the application of the LH
algorithms. Because all five of the algorithms arestill undergoing development and improvement,
and because comprehensive comparisons of thecurrent versions of the algorithms with independent diagnostic estimates have yet to be performed,
the general strengths and weaknesses can only beassessed in relative terms.
In such circumstances, the effects of differing
physical assumptions on the various algorithms’
diagnosed LH properties deserve careful attention.
It is emphasized that the HH and PRH algorithms
are similarly constrained by hydrometeor conservation under a steady-state assumption, but withdifferent formulations for LH generation. The otherthree algorithms are directly CRM based, differing
insofar as the cloud-type classification scheme, thelookup table indexing strategy, and the details of the
precalculated lookup table heating profile entries. The
CSH, SLH, and GPROF algorithms are designed toretrieve both LH and Q1 – QR because these schemes
use cloud information directly generated by the CRM
simulations, which exactly correspond to terms
included in Eq. (1). In essence, the CRMs provide
cloud database lookup tables consisting of both LH and
Q1 – QR. Alternatively, the HH and PRH algorithms are
AMERICAN METEOROLOGICAL SOCIETY

designed to estimate just the LH term because theseschemes are tied directly to the vertically distributed
structure of precipitation rate profiles, which may or
may not have been generated by a precipitation ratealgorithm utilizing a CRM for guidance.
HEATING STRUCTURES ESTIMATE D
FROM INDIVIDUAL ALGORITHMS. Application of the TRMM LH algorithms is being conducted
over a range of space and time scales, from an orderof 10 to 500 km spatially, and from instantaneous tomonthly temporally. Although there is no preferredscale for calculating LH, there are a variety of current
applications using LH products, with further researchunderway, to determine the optimal scales at which
LH retrievals can be considered reliable.4
Instantaneous latent heating structure. Several of the
TRMM LH algorithms determine instantaneous
precipitation rates and heating profiles at satellite
footprint resolution. The rationale for operating thealgorithms at the highest possible resolution is thatsystematic errors in averages of high-resolution estimates of heating are generally less than the systematic
error of a single heating estimate made at the scale of
the average (i.e., the LH derivations represent nonlinear transforms of pixel-level precipitation rates).
Therefore, even though instantaneous footprint-scaleestimates may contain undesirable errors, spatial
averaging and/or filtering can reduce random effects
to acceptable levels, while ensuring that smoothed
products contain a minimum of systematic error.
Figure 3 illustrates instantaneous, high-resolution (~4 km) rain rates and LH structures in an
intense Atlantic tropical cyclone (Hurricane Bonnie)
retrieved by the HH algorithm, based on the verticalderivative of rain mass f lux from the combined
PR–TMI algorithm. The structure of the hurricane
eye and the convective rain spiral bands are properly captured. Precipitation mass appears at highaltitudes in the presence of deep convection, suchas around 200 km along the satellite’s nadir track(seen in the middle panel). Widespread weaker rain
rates are found between convective cells. In the weakrain areas, rain rates are mostly concentrated in the
4

A comprehensive intercomparison and validation project
involving five heating algorithms is now underway. It is
examining multiple cases from full resolution to large scale,including validation with diagnostic calculations obtained
from three NASA field experiment datasets, SCSMEX,
TRMM LBA, and KWAJEX, plus two datasets from DOE’s
ARM CART program.
NOVEMBER 2006

| 1561gorithms to produce complete LH
profiles with PR-based precipitation
information.)
Figure 4 presents results fromthe GPROF Heating algorithm fora squall line in the tropical North
Atlantic Ocean. The different panels include estimates of instantaneous surface rain rate, convective
rain rate (rain mass assigned toconvective category), and verticalcross sections spatially averaged
to 28 km of the total precipitation
mass content, along with Q1 – QR .
The heaviest rains are seen along
the convective leading edge ofthe system, while generally lower
precipitation rate intensities areobserved in the trailing stratiform
areas to the north and west of theleading edge. The transect A–B isFIG. 3. (top) Plan view of near-surface rain rates for Hurricane Bonnie (22 Aug 1998) retrieved from combined algorithm [i.e., TRMM
nearly perpendicular to the leading
PR–TMI rain-rate algorithm described by Haddad et al. (1997) andedge, traversing both the convective
Smith et al. (1997)]; (middle) vertical cross section of rain-rateand stratiform regions. The leadingprofiles along satellite nadir track; (bottom) vertical cross sectionedge convection is characterized byof LH profiles from HH algorithm along satellite nadir track. In all
relatively high precipitation mass
three panels, distances across (top) or along satellite nadir trackcontents, exceeding 1 g m –3 nearare given in km.
the surface. Horizontally collocatedwith the maximum precipitation
middle to lower troposphere where stratiform condi- mass contents are maximum estimated heatingtions are prevalent. Deep LH is associated with the rates, exceeding 9°C h–1 between 5- and 8-km altistrongest convective cells (lower panel of figure). tude. Stratiform rains (horizontal coordinates less
Peaks of maximum LH vary with different condi- than 120 km) are associated with maximum precipitions. For example, one peak is located at 3–5 km at tation mass contents at midlevels. The decrease of
180 km along nadir track, while another is at 3–4 km precipitation mass contents in the lower troposphereat 200 km along satellite track. Altitudes of the LH is due to the evaporation of rain, where cooling rates
maxima are generally at or below 5 km. Evaporative of ~ –1°C h–1 are estimated. The overall heating
cooling occurs in the lower troposphere in the strati- structures are similar to those in Fig. 2, except thatform regions.
the fine features simulated by the GCE CRM are
Overall, the general structure of LH based on the not diagnosed due to the coarser resolution of the
HH algorithm is heuristically correct for a hurricane, GPROF Heating algorithm’s TMI radiance input.
although the level of maximum heating is lower thanFigure 5a shows instantaneous LH profiles rethat found from other studies of tropical cyclones. trieved by both the PRH and SLH algorithms, spaThis is because the current version of the combined tially averaged to 50-km resolution, associated with
PR–TMI algorithm (as well as the PR algorithm) does 1) a Pacific tropical cyclone (Typhoon Jelawat) in
not produce precipitation by any but the largest frozen its developing stage (upper diagram), and 2) a MCS
hydrometeors. By including the effect of all precipitat- over the tropical ocean northwest of Australia (lower
ing ice hydrometeors, the level of maximum heating diagram). The PR-estimated rain rates used as input
would be elevated. (An experimental version of the for these two algorithms are also shown. Overall, for
combined algorithm now includes a frozen precipita- the tropical cyclone case, there are several similarities
tion mode to account for all deposition–sublimation between the PRH and SLH algorithm profiles. For
and freezing–melting processes above and below example, both indicate strong heating on both sides
the melting level, enabling HH- and PRH-type al- of the eye. In addition, both algorithms exhibit strong
1562 |NOVEMBER 2006

heating in a narrow shaft in the lower troposphere to and LH profiles peak at middle levels (~6 km). This
the right of the eye. Away from the eyewall region, agrees well with the midtropospheric heating maxithe heating patterns are similar to those observed mum found for the Australian Monsoon Experimentand simulated by CRMs in the stratiform regions of (AMEX) convective systems (Frank and McBride
MCSs (e.g., Houze 1982, 1997; Tao et al. 1993b, 2000; 1989). The estimated LH profile has a distinct coolingand Lang et al. 2003).
feature (relative minimum of heating) near 4 km due
As expected, there are noteworthy differences to melting processes. Conversely, the Q1 – QR profile
between the two sets of heating profiles. First, PRH does not indicate cooling near 4 km because the eddy
heating is confined to the same altitude range as that heat flux convergence compensates for the cooling dueof the rainfall profiles, while SLH retrieves heating to melting. As in the tropical cyclone case, PRH yields
well above the rain. This is evident in larger heating stronger cooling in the lower troposphere while SLH
amplitudes at higher altitudes in the horizontal mean heating features are smoother.
profiles in Fig. 5a (two right-hand panels of upper
Figure 5b shows the LH structure of a midlatitude
diagram). Second, the SLH level of maximum heating squall line retrieved using only the PRH algorithm.
is lower than that of PRH. Third, the cooling region The PR-observed radar reflectivities and estimatedretrieved using PRH in the lower troposphere is stron- rain rates used as algorithm inputs are also shown.
ger than that from SLH. Fourth, PRH also produces The radar reflectivity pattern is similar to that of an
low-level cooling in its convective region. Fifth, the observed PRE-STORM squall line (Rutledge et al.
SLH heating structure has smoother features because 1988). Strong heating (> 10°C h–1) is associated withit uses a lookup table based on averaged CRM-gener- large rain rates (> 50 mm h–1) at the leading edge of
ated profiles. On a final note, the general structure the squall system. There is weak heating aloft andof the SLH-generated Q1 – QR and LH profiles are cooling below in the trailing stratiform region. Thesesimilar, except that the Q1 – QR profile has a larger features are similar to those simulated by CRMs [e.g.,
maximum at a higher altitude (upper-right-hand Fig. 1b from Lang et al. (2003)], those observed (e.g.,panel of upper diagram).
The SLH and PRH LH analyses associated with an offshore
Australian MCS are illustrated in
the lower diagram of Fig. 5a. Again,
the PR-estimated rain rates thatare used as algorithm input are
shown in the diagram. Strong heating (> 10°C h–1) is associated withlarge rain rates (> 50 mm h–1) in theconvective region of the squall system. There is weak heating aloft andcooling below in the trailing stratiform region. Both averaged Q1 – QR
and LH profiles peak at middle levels (about 6 km, according to theupper-right-hand panel of the lower
diagram). For this case, the SLHretrieved level of maximum heating
is higher than that of the tropical
cyclone case. This is because the convective system is in its mature stage
while the tropical cyclone system isFIG. 4. (top left) Surface and (top right) convective rain rates for squall
in its developing stage. That explains
line in North Atlantic Ocean (7 Apr 1998) retrieved from GPROF
why the magnitudes of stratiform
algorithm [i.e., TMI rain-rate algorithm described by Kummerow etheating and cooling for the MCS caseal. (1996, 2001) and Olson et al. (1999, 2006)]. (bottom) Height–length
exceed those of the tropical cyclone.
cross section (~28 km horizontal resolution) of total precipitation
As is evident in the upper-right-handwater content (color shading in g m –3) and Q1 – QR diabatic heating(contours in °C h –1) from GPROF Heating algorithm.
panel, both the averaged Q1 – QR
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Johnson and Hamilton
1988), and those retrievedby the GPROF Heating
algorithm (Fig. 4). The LH
profile shown in the righthand panel is also similar
to both CRM and observational results.
As Figs. 3, 4, and 5a,b
illustrate, regardless of differences in spatial resolution, the instantaneous
LH profiles retrieved by
the four different algorithms that qualitatively
agree with one another fora) tropical cyclones (HH,
PRH, and SLH), b) squall
l i nes (GPROF Heat i ng
and PRH), and c) tropical oceanic MCSs (PRHand SLH). Quantitatively,
there are differences. Someare caused by the different
resolutions and filtering
techniques employed by
the different algorithms,
a nd some by d i f ferent
algorithm inputs. Other
differences stem from thevarying physical assumptions used by the different
algorithms. As one example drawn from the above
analyses, PRH consistently
produces LH profiles withstronger cooling in thelower troposphere.

FIG. 5a. (top five) LH analysis for tropical Pacific Typhoon Jelawat in developing
stage (2 Aug 2000). Arrows indicate location of eye and (bottom five) identical analysis for tropical, oceanic MCS over northwest Australia (16 Feb
1998). (left) For each set of diagrams height–scan cross sections of PR-basedrain-rate profiles (mm h –1), along with SLH- and PRH-generated LH profiles(°C h –1), are shown respectively. [TRMM PR rain-rate algorithm is describedby Iguchi et al. (2000) and Meneghini et al. (2000).] (right) area mean verticalprofiles of both SLH-generated Q1 – QR (red) and LH (black) and PRH-generated LH (black) in °C h –1, respectively.

Te m p o r a l a n d s p a t i a laverages. The upper threepanels of Fig. 1 illustrate
the 5-yr mean apparent
heating at three different
altitudes (2, 5, and 8 km)
over the global Tropics
from the CSH algorithm based upon the PR monthly
rainfall product. The Q1 profiles are calculated byaveraging two normalized convective and stratiform kernel heating profiles (scaled according to
PR-retrieved surface rain rates and weighted by theconvective/stratiform fractions) at a grid scale of
0.5° for either oceanic or continental locations. The
1564 |NOVEMBER 2006

normalized convective/stratiform kernel profiles are
created by averaging all 16 (4) oceanic (continental) base profiles in the CSH algorithm’s complete
library of 20 heating profile pairs, which are distributed regionally and according to storm type.
As expected from the design of the CSH algorithm,
the horizontal distribution of the estimated Q1

that this stems from higher
moisture contents at lower
levels inhibiting evaporative cooling by raindrops
in the relatively moister
regions.
Figure 6 illustrates the
Q1 structures associatedwith two climate events:a) an El Niño episode from
December 1997 throughFebr u a r y 1998 , a ndb) a La Niña episode from
December 1998 throughFebruary 1999. The diagrams in the two left-handpa nel s show ret r ie ved
heating anomalies for thetwo events (relative to a
3-yr mean commencing
in December 1997). The
FIG. 5b. Latent heating analysis for midlatitude Oklahoma squall line (10 May
greatest anomalies appear
1999). (left) Height–scan cross sections of TRMM PR radar reflectivity profiles
over the equatorial Pacific,(ZE in dBZ), PR-retrieved rain-rate profiles (mm h –1), and PRH-generated
LH profiles (°C h –1), all along satellite nadir track. (right) Area mean verticalwest Pacific, and Indian
profile of PRH-generated LH in °C h –1.
Oceans. The regional Q1
anomaly patterns over the
Maritime Continent, North
structure is similar to the pattern of surface rainfall America, and Africa are nearly invariant between the(lower panel of Fig. 1), especially at the middle and two phases. Average Q1 profiles over the Tropics forupper levels. For example, well-defined ITCZs in these two episodes and their deviations from the 3-yr
the east and central Pacific and Atlantic Oceans, a mean are shown in the right-hand panel. The level ofwell-defined SPCZ in the central southern Pacific maximum heating is ~7 km. Variations in the level
Ocean, and broad areas of precipitation events spread and magnitude of maximum heating are small. This
over the continental regions are all evident. Also, is because global tropical rainfall accumulations forthe strong LH release in the middle and upper tro- El Niño and La Nina are nearly identical as observed
posphere (5°C day–1 and greater) is associated with by the PR. However, there are differing cold andheavier surface precipitation. Heating in the upper warm anomalies associated with the two phases due
troposphere over the Pacific and Indian Oceans to the fact that the PR observes a higher percentage ofcovers a much broader area than the heating over stratiform precipitation during the El Niño episode,
Africa, South America, and the Atlantic. The large- leading to the generally stronger low-level cooling.
scale heating distributions (i.e., differential latentheating) between continents and oceans and within GLOBAL MODELING APPLICATIONS.
continents and oceans by themselves are capable Whereas assimilation of TRMM rainfall data hasof altering the ambient horizontal gradients in the proven to be an effective technique for improving
temperature fields that then can feed back to the predictive skill in global weather prediction models
general circulation.
(e.g., Bauer et al. 2002; Hou et al. 2000a,b, 2001,
An interesting feature observed in Fig. 1 is the rela- 2004; Krishnamurti et al. 2000a,b, 2001; Marecal
tively weaker heating at the 2-km level (< 1.5°C day–1), et al. 2002), the use of explicit LH information forin comparison to the mid- and upper-tropospheric initialization and/or assimilation in global models
levels, throughout the regions exhibiting the strongest is a research topic that is just beginning to emerge.
rain rates. Whereas this may be simply convective Various recent TRMM studies are now reachingheating and stratiform cooling in the lower tropo- beyond the pioneering research in diabatic initialsphere compensating for one another, it is also possible ization and assimilation of latent heat information
AMERICAN METEOROLOGICAL SOCIETYNOVEMBER 2006

| 1565

FIG. 6. TRMM PR-based Q1 heating anomalies at 8 km AGL for (top left) El Niño episode during DJF 1997/98
and (bottom left) La Niña episode during DJF 1998/99 generated from CSH algorithm. (right) Average 3-yr
(1997–99), 3-month El Niño episode, and 3-month La Niña episode heating and heating anomaly profile pairs
over entire Tropics are shown in black, red, and blue, respectively. [Note: 3-yr profile is indistinguishable from
3-month La Niña profile.]

originally published by Wang and Warner (1988),
Puri and Miller (1990), and Raymond et al. (1995).
Two global models from The Florida State University(FSU) and the NASA Goddard Space Flight Center(GSFC) are currently using TRMM-based LH datasets to improve cumulus parameterization schemes
while at the same time addressing physical shortcomings with the schemes.
At this stage it appears that the direct use of satellite
diabatic heating profile information for atmosphericmodeling is best accomplished using physical initialization. For example, T. N. Krishnamurti and hiscolleagues at FSU, using the Krishnamurti et al. (1991)
global spectral model as the host, have developed a
new experimental cumulus parameterization scheme(ECPS). Past model analysis datasets are used to relate
Q1 – QR to TRMM-retrieved LH. Tests are now being
conducted with the ECPS in conjunction with a Q1/Q2
estimation scheme to produce vertical distributions ofheating and moistening for a cumulus environment.
Figure 7 shows test results of ECPS that improve a
precipitation forecast over a 72-h period relative to acontrol run without ECPS. The comparison between
the ECPS run (lower panel) and the GPCP satellite ob1566 |NOVEMBER 2006

servations at verification time (upper panel) are muchcloser in agreement than is shown by the control
forecast (middle panel). The control run produces
far too much equatorial rain and generally too little
precipitation at the middle latitudes and over tropical
Africa in comparison to the ECPS run. Also, the ECPS
run produces a more realistic ITCZ (i.e., a system of
MCSs and squall lines rather than the widespreadrain). This confirms that explicit assimilation ofsatellite-retrieved LH profiles can produce a positive
impact on a forecast. This is significant because itis the vertical distribution of diabatic heating that
represents the important forcing on atmosphericcirculation, not surface rainfall. However, additional
studies will be needed to quantify how much predictive improvement can be obtained on a regular basis
in moving from surface rainfall assimilation (and/or
PMW Tb assimilation) to LH assimilation.
Research is also taking place at GSFC to develop
variational techniques to assimilate TMI-derived
convective and stratiform LH rates within the generalframework of parameter estimation, using disposable
parameters in the relevant moist physics scheme as
the control variables. The focus here is to explore

the feasibility of improving global climate analyses
and weather forecasts through the assimilation ofsatellite-retrieved LH profiles that are radiatively
compatible with multichannel PMW radiometerradiances. Such optimization of physical parameterizations in the context of data assimilation provides
valuable information for diagnosing both model andparameterization deficiencies.
There is a final important application also
involving NWP modeling, in which satellite-retrieved
LH profiles represent a valuable data resource. As thenumber of NWP models subjected to initialization by
retrieved LH profiles increases, substantitive improvements in forecasts via “superensemble” techniques are
expected to take place. The superensemble approachis a powerful tool for improving the robustness of
weather and climate forecasts, as has been emphasized in studies from the FSU modeling group (i.e.,
Krishnamurti et al. 2001). The goal of superensemble
forecasting is to reduce overall uncertainties while
better estimating errors
associated with the various models, their physicalparameterizations, and theingested datasets.
FINAL REMARKS AND
RECOMMENDED FUTURE RESEARCH.
Three of the TRMM LH
a lgor it h ms (i.e., C SH,GPROF Heating, and SLH)
use CRM-simulated clouddatasets involving precalculated heating profiles.
Given the concern withsystematic errors arisingf rom too few avai lable
CRM simulations, creating“gaps” in the algorithmsupporting databases, thenumber of heating profiles
associated with different
types of clouds and convective systems occurring
at a variety of geographic
locations and throughout
the seasonal cycle needs to
be increased. Observations
from additional field experi ments w i l l a lso beneeded to prov ide new
types of initial conditions

for CRMs, as well as validation of the CRM-simulated
LH calculations. Heating profiles obtained fromnumerical model simulations and large-scale model
reanalyses should also be compared with those from
CRMs and the associated retrieval algorithms.
Such comparisons will identify the key physicalprocesses leading to similarities and differences
produced by the CRMs and the retrieval algorithms.
Data from field campaigns that provide extensive,high-quality in situ microphysical observations,
including TRMM LBA and KWAJEX, will be mostuseful in validating and improving CRM-generated
microphysics. Marzano et al. (1999), Panegrossi et al.
(1998), and Fiorino and Smith (2006) have alreadyaddressed critical issues concerning how realistic
microphysical representations can be used to improve
precipitation retrieval algorithms, an essential step inbetter estimating LH.
It is important that diagnostically based heating profiles obtained from TRMM field campaign

FIG. 7. (top) GPCP precipitation for 8 Feb 1998 representing blend of satellite
retrievals and rain gauge observations, (middle) FSU GSM day-2 forecast
from ECPS experiment, and (bottom) FSU GSM day-2 forecast from control
experiment. [From Rajendran et al. (2004).]

AMERICAN METEOROLOGICAL SOCIETYNOVEMBER 2006

| 1567

data, as well as from other field campaigns suchas those conducted by the DOE ARM program,be compared to corresponding heating profiles
from the LH algorithms. This would include diagnostic analyses based on the use of Doppler radarmeasurements to infer horizontal wind divergenceand vertical motion, which are directly related todiabatic heating (e.g., Mapes and Lin 2005), anddual-Doppler measurements that explicitly provide the horizontal wind field [e.g., see the DOE
ARM–related paper by Clothiaux et al. (2000)].
These analyses will help quantify errors within thecurrent LH algorithms, plus provide insight for
overall algorithm improvements.
As a follow-up to this study, a comprehensive
intercomparison between the different LH algorithms
applied to various common TRMM datasets has
been initiated. This effort will be consistent withpast intercomparisons efforts involving precipitation
retrieval algorithms (e.g., Ebert and Manton 1998;
Smith et al. 1998; Adler et al. 2001) and the radiative transfer models underpinning these algorithms(e.g., Smith et al. 2002). Here the emphasis has beenon understanding the strengths and weaknessesof different methods and underlying assumptions,an indispensable process for guiding generational
upgrades in algorithm philosophy and design.
The new LH algorithm intercomparison study will
focus on the major heat budget terms

Global analyses will be used to identify and compare
the large-scale circulation patterns for important
retrieval periods and for key periods of earlier field
campaigns, including the GATE and TOGA COARE
tropical ocean campaigns. These will be useful
because extending what is learned from local field
campaign observations to other parts of the Tropics
where campaigns have yet to be conducted invites theuse of LH “similarity” assumptions. Identification of
optimal spatial scales and suitable filtering schemes
for the reduction of noise in the instantaneous,
high-resolution retrievals are other issues that needattention.
Standard LH products from TRMM will represent
a valuable new source of data to the research community, products that a decade ago were consideredbeyond reach. These data products will enable compelling new investigations into the complexities ofstorm life cycles, diabatic heating controls and feedbacks related to mesosynoptic circulations, and, mostimportantly, the influence of diabatic heating on the
Earth’s general circulation and climate.
1568 |NOVEMBER 2006

ACKNOWLEDGMENTS. The authors extend theirappreciation to Professors Robert Houze of the University of Washington, Richard Johnson of Colorado State
University, Michio Yanai of the University of California,
Los Angeles, and Edward Zipser of the University of Utah,
whose willingness over the years to discuss their ideas
concerning atmospheric latent heating has had a profoundinfluence on various ideas central to this paper. The authors
wish to thank to Dr. Kwo-Sen Kuo of the NASA Goddard
Space Flight Center for preparing Fig. 1, and to Mr. Ken’ichi
Ito of the Remote Technology Center of Japan for preparing
Figs. 5a–b. The authors also thank Dr. G. Huffman and two
anonymous reviewers for their constructive comments thatwere used to improve the paper. This research has been
supported by an assortment of TRMM Science Team grants
under the auspices of both the National Aeronautics andSpace Administration (NASA) and the Japan Aerospace
Exploration Agency (JAXA).

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