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JOURNAL OF CLIMATEVOLUME 23

Estimates of Tropical Diabatic Heating Profiles: Commonalities and Uncertainties
SAMSON HAGOS,*,1 CHIDONG ZHANG,* WEI-KUO TAO,# STEVE LANG,#YUKARI N. TAKAYABU,@ SHOICHI SHIGE,&,** MASAKI KATSUMATA,11
BILL OLSON,# AND TRISTAN L’ECUYER##* Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida# NASA Goddard Space Flight Center, Greenbelt, Maryland@ Center for Climate System Research, University of Tokyo, Tokyo, Japan& Department of Aerospace Engineering, Osaka Prefecture University, Osaka, Japan
11 JAMSTEC/RIGC, Yokosuka, Japan## Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado(Manuscript received 9 January 2009, in final form 4 August 2009)
ABSTRACTThis study aims to evaluate the consistency and discrepancies in estimates of diabatic heating profiles
associated with precipitation based on satellite observations and microphysics and those derived from thethermodynamics of the large-scale environment. It presents a survey of diabatic heating profile estimates fromfour Tropical Rainfall Measuring Mission (TRMM) products, four global reanalyses, and in situ sounding
measurements from eight field campaigns at various tropical locations. Common in most of the estimates are
the following: (i) bottom-heavy profiles, ubiquitous over the oceans, are associated with relatively low rain
rates, while top-heavy profiles are generally associated with high rain rates; (ii) temporal variability of latentheating profiles is dominated by two modes, a deep mode with a peak in the upper troposphere and a shallow
mode with a low-level peak; and (iii) the structure of the deep modes is almost the same in different estimatesand different regions in the tropics. The primary uncertainty is in the amount of shallow heating over thetropical oceans, which differs substantially among the estimates.

1. Introduction
To the first order, the atmospheric general circulation
redistributes energy and balances the horizontal andvertical gradients of diabatic heating. Since the earth’s
atmosphere is primarily heated from the surface, convective processes are required to maintain the troposphere close to neutral stratification. On the large scale,the heating gradient between the tropics and extratropics is balanced by the poleward transport of the heatof the general circulation. However, the heat fluxes from

1 Current affiliation: Pacific Northwest National Laboratory,
Richland, Washington.
** Current affiliation: Graduate School of Science, Kyoto University, Kyoto, Japan.

Corresponding author address: Samson Hagos, Pacific Northwest
National Laboratory, P.O. Box 999, MSIN: K9-24, Richland, WA
99352.
E-mail: samson.hagos@pnl.gov
DOI: 10.1175/2009JCLI3025.1
Ó 2010 American Meteorological Society

the surface to the atmosphere are influenced by the ambient surface winds as well as temperature and moisture
distributions. Hence, the three-dimensional structure of
the diabatic heating is closely related to the atmosphericcirculation because it not only drives the circulation, butalso receives feedback from it.
This is particularly true for the diabatic heating associated with tropical precipitation, which on the one handis a result of instability due to the accumulation of
convective-scale moist static energy near the surface and,on the other, drives circulation. In fact, this heating accounts for three-fourth of the total heat energy available
in the earth’s atmosphere and two-thirds of this rainfall
occurs in the tropics (Tao et al. 2006). The interaction of
diabatic heating and the circulation is further complicated by the fact that the vertical structure of the heating
is related to the microphysical processes within convective systems. As pointed out by Houze (1982) andJohnson and Young (1983), there is a remarkable difference in the heating profiles between convective and stratiform regions of mesoscale convective systems (MCSs).

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They found that in convective regions of MCSs, theheating profile has positive heating throughout the troposphere with a maximum in the midtroposphere, while,in stratiform regions, there is an upper-level heating andcooling below the melting level. Hartmann et al. (1984)
showed that the pattern of the large-scale circulation issensitive to the vertical structure of the diabatic heating.
In their linear modeling study, the inclusion of the topheavy heating profile associated with mature cloud clusters elevates the circulation response, resulting in a better
agreement of the simulated Walker circulation with theobservations than a conventional middle-heavy profilethat is often associated with young deep convection.
Another modeling study by Schumacher et al. (2004)
also suggests significant sensitivity of the circulation tovariations in the stratiform–convective heating fraction
across the tropical Pacific.
In addition to their influence on the structure of largescale circulation, diabatic heating profiles and their variability play an important role in the organization ofmesoscale convective systems through the generationof vorticity. For example, the midtropospheric positive
vertical gradient of heating in stratiform regions favors
the generation of positive potential vorticity anomalies(Zhang and Fritsch 1987; Raymond and Jiang 1990),
which are believed to contribute to a longer life span for
precipitation systems and to heavy rainfall. Furthermore, the vertical structure of the heating in concert withtemperature anomalies contribute to the generation ofavailable potential energy, thereby influencing the energetics of disturbances (Wang 2006).
For the last 10 yr, global tropical precipitation has
been observed at high resolution by instruments aboard
the Tropical Rainfall Measuring Mission (TRMM) satellite (Kummerow et al. 2000). One of these instruments
is the TRMM Precipitation Radar (PR), which resolves
the vertical structure of precipitation and enables theidentification of convective and stratiform precipitation
based on the reflectivity and echo-top height of the
precipitating clouds. The other is the TRMM Microwave Imager (TMI) that enables the measurement of
rainfall characteristics over a wider areal swath. Thus,
for the first time, estimation of the three-dimensional
structure of diabatic heating associated with precipitationand its temporal variability over the entire tropics became
possible.
Several ways of utilizing the TRMM data to calculate
diabatic heating profiles have been proposed and implemented. Tao et al. (2001) presented an intercomparisonof profiles from three diabatic heating algorithms, thehydrometeor heating (HH; Yang and Smith 1999a,b),
convective–stratiform heating (CSH; Tao et al. 1993),
and the Goddard Profiler heating (GPROF; Olson et al.

5431999) for February of 1998. Based on the results of thespectral precipitation statistics of Takayabu (2002),
Shige et al. (2004, 2007, 2008) also developed the spectral latent heating (SLH) algorithm and data. Grecu
et al. (2009) developed a similar technique to utilize
TMI data to remedy the undersampling associated with
the narrow swath of the PR using a training algorithm(TRAIN). Yet another estimate from TRMM is basedon the precipitation radar heating (PRH) algorithm by
Kodama et al. (2009). Even though these algorithms
differ in their details and they continue to be improved,
the basic approach remains to involve an examinationof the vertical structure of the precipitation and an assignment of the appropriate heating or vertical velocity
profiles.
While the microphysical basis for the above-describedheating estimates is justified, errors in the categorizationof precipitation systems as well as the structure of theassigned profiles can easily introduce significant uncertainties in the final products. The accuracy and usefulness of an estimate of the heating profiles are ultimately
hinged on their consistency with the circulation. Specifically, the heating estimates based on the microphysics, and those based on the large-scale circulation andthermodynamics, need to show some degree of agreement not only in terms of averages over a certain region
and/or time but also in terms of their spatial and temporal variabilities. In practice, however, estimates ofheating from the circulation present a different set ofchallenges. For example, the common approach of calculating diabatic heating using a residual diagnosis of
the thermodynamic budget depends on the estimate ofdivergence or vertical velocity, which are prone to errors
associated with low resolution. In the case of diabatic
heating from reanalysis products, the estimate is further
complicated by parameterization of moist processes in
the assimilation schemes.
Because of the various potential sources of uncertainties, a comparison of diabatic heating estimates
based on independent data sources, assumptions, andmethods would enable us to test the validity of the assumptions and methods, to build confidence in the elements of the estimates that are consistent with eachother, and to draw cautionary attention to those thatdiffer substantially. With this general purpose in mind,
this study aims to(i) present the mean and variability characteristics inestimates of heating profiles over various tropicalregions based on the observations by the TRMM
satellite, global reanalyses, and sounding data; and(ii) identify primary interproduct differences and similarities in the profiles and quantify their uncertainties.

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2. Data and method
a. TRMM products
Four available heating estimates derived from TRMM
(CSH, SLH, PRH, and TRAIN) are included in thisstudy. In the CSH algorithm (Tao et al. 1993, 2000), thediabatic heating is determined by the surface rainfall
rate and its stratiform fraction, which are obtained fromthe PR. The CSH algorithm uses a lookup table (LUT)
of rain-normalized heating profiles associated with various types of cloud systems in different geographic locations (see Figs. 3 and 4 in Tao et al. 2001) that havebeen averaged into three convective and stratiform rain
types: oceanic, continental, and shallow. The profiles are
generated by cloud-resolving model (CRM) simulations
that have been validated against sounding observations
in limited tropical regions. The depth of the heating
varies depending on the PR echo-top height and its
magnitude is determined according to the PR surface
precipitation amount The SLH algorithm (Shige et al.
2004, 2007, 2008) follows generally the same strategy of
the CSH algorithm except a CRM was used to generate
the predetermined vertical profiles of the latent heatingthat vary continuously with the PR echo-top height, instead of only a limited number of heating profiles in the
LUT as in the CSH algorithm. The PRH algorithm(Kodama et al. 2009) estimates the latent heating fromthe growth–evaporation of raindrops during their vertical displacement. It utilizes the vertical gradient ofprecipitating water with respect to the motion of precipitating particles. An observed increase in precipitation water amount with respect to the direction of the
motion of the precipitating particles is regarded as theresult of the condensation and deposition. A decrease,on the other hand, is regarded as the result of theevaporation of the precipitating particles. In a manner
similar to that of SLH, the TRAIN algorithm utilizes the
PR data and a cloud-resolving model. However, in thisalgorithm heating profiles along with coincident TMI
brightness temperature observations are assembled intoa large database. Then, if TMI provides a set of brightness temperatures at a given location, the large databasecan be queried to find brightness temperatures that areconsistent. The surface rain rates, stratiform rain rates,
precipitation profiles, and the profiles in the databasethat are associated with consistent brightness temperatures are composited using a Bayesian method to findthe ‘‘expected values’’ of these parameters, given the
TMI observations. This algorithm for estimating heating
is referred to as TRAIN because the TMI method isessentially trained to find a best estimate of Q1–QR,
where Q1 is the total diabatic heating and QR is theradiative heating. To calculate Q1, the radiative heating

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estimated from the atmospheric radiative heating climatology derived from an approach known as the Hydrologic Cycle and Earth’s Radiation Budget (HERB)
algorithm (L’Ecuyer and Stephens 2003, 2007) is added
to the Q1–QR.
All the estimates depend on lookup tables: baseheating profiles in CSH, SLH, and TRAIN, and verticalmotion profiles in PRH. CSH and SLH are daily on
a 0.58 3 0.58 horizontal grid and at 19 height levels;
TRAIN provides the orbital data on 29 height levels.
The PRH data are in pentad format on a 2.58 3 2.58 gridat 41 height levels. All of these data cover 1 January
1998–31 December 2007.

b. In situ soundings
The apparent heating sources (Q1) calculated fromin situ soundings from eight field campaigns at various
tropical locations are included in this study. These are
the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE),
the Global Atmospheric Research Program Atlantic
Tropical Experiment (GATE), the Kwajelin Experiment(KWAJEX), the Tropical Warm Pool International
Cloud Experiment (TWP-ICE), the South China Sea
Monsoon Experiment’s Northern and Southern Enhanced Arrays (SCSMEX-N and SCSMEX-S), the LargeScale Biosphere–Atmosphere Experiment in Amazonia(LBA), and the Mirai Indian Ocean Cruise for the Studyof the MJO-Convection Onset (MISMO). The locations
and durations, as well as references of these field campaigns, are listed in Table 1. In calculating Q1, verticalvelocity is first derived from the horizontal wind andpressure by vertical integration of the divergence; then,
the three-dimensional wind, pressure, and temperatureare substituted into the energy conservation equation(Yanai et al. 1973). The spatial coverage areas andtemporal resolutions, as well as the lengths of the datasets, vary substantially among these datasets. For all thefield campaigns, the Q1 data are available every 6 h at
a fixed location, except for GATE. In GATE the average of the 3-hourly gridded data from the inner hexagon
is averaged into 6-hourly data for consistency. The Q1values estimated from sounding observations are usuallytaken as the ground truth for calibration and validationof satellite products. They, therefore, are included in thisstudy in spite of their very limited coverage in time andspace. A more detailed diagnostics of sounding Q1 using
similar methods as in this study is given by Zhang and
Hagos (2009).

c. Reanalysis products
Estimates of diabatic heating associated with precipitation from four global reanalyses are also included

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TABLE 1. Locations, durations, and references of soundings data.

Experiment

Location

PeriodReference

TOGA COAREGATEKWAJEXTWP-ICESCSMEX (-N and -S)
LBA
MISMO

Equatorial western PacificTropical Atlantic
Marshall Islands
Darwin, Australia
South China Sea
Amazonia
Equatorial Indian Ocean

1 Nov 1992–28 Feb 1993
26 June–19 Sep 1974
24 Jul–15 Sep 1999
21 Jan–12 Feb 2006
5–25 May and 5–22 Jun 1998
1 Nov 1998–28 Feb 1999
24 Oct–25 Nov 2006

Webster and Lukas (1992)
Houze and Betts (1981)
Yuter et al. (2005)
May et al. (2008)
Lau et al. (2000)
Silva Dias et al. (2002)
Yoneyama et al. (2008)

in this study: the National Centers for Environmental
Prediction–Department of Energy (NCEP–DOE) reanalysis (NCEPII; Kanamitsu et al. 2002), the Japanese
25-yr reanalysis (JRA25; Onogi et al. 2007), the 40-yr
European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al.
2005); and the Modern Era Retrospective Analysis for
Research and Applications (MERRA) from the National Aeronautics and Space Administration (NASA)
Global Modeling and Assimilation Office (Bosilovich
et al. 2006). NCEP and JRA25 are 6-hourly data; ERA-40
and MERRA are daily. To overlap with the TRMM
data, all of the reanalysis products used in this study startfrom 1 January 1998. The lengths of the time periods,
however, vary depending on the data availability: 10 yr
for NCEPII and JRA25, 4 yr for ERA-40, and 6 yr for
MERRA.
For all of the reanalyses, the diabatic heating associated with precipitation is estimated from the threedimensional wind, temperature, and precipitation fields.
This estimate of the heating from the reanalysis products
involved a two-step process. First, total diabatic heating
Q1 is calculated as the residual of the thermodynamic
equation on pressure surfaces [Eq. (1)] in a manner
similar to that presented by Nigam et al. (2000):
Q1 5



Cp T ›u
›u
›u
›u
1u
1y
1v
,
›t
›x
›y
›p
u

(1)

where u and y are the zonal and meridional wind components; u 5 T( ps /p)R/Cp is the potential temperature,with T being the temperature; p is the pressure and ps
the surface pressure; Cp is the specific heat capacity ofdry air; and R is the specific gas constant of dry air. Here,Q1 is calculated using central finite differencing at thehorizontal grids at the 17 pressure levels. To reduce error due to irregular pressure level spacing, ›u/›p is replaced by ›u/p› ln( p) in the finite differencing.
The second step is to estimate the diabatic heating
associated with precipitation. That is calculated by conditioning the total diabatic heating (Q1) by the presenceof precipitation. In other words, the diabatic heating

associated with precipitation is equal to the total diabatic heating if the precipitation is greater than zero andis zero otherwise. This is because the heating profiles in
the TRMM products are available only in regions with
precipitation (and hence dominantly latent heating);
this conditioning would eliminate the effects of diabatic
heating in grid points where precipitation is absent(where sensible heat fluxes and radiative cooling dominate). One has to keep in mind that even this is nota perfect comparison, because even though the conditioning by precipitation in the TRMM products is at thesatellite footprint level, those for the reanalyses are attheir own resolutions. Therefore, the diabatic heating
estimates from the reanalyses are likely to be contaminated by diabatic heating not necessarily associated with
precipitation.
It is important to note that the vertical velocity andassociated divergent circulation are influenced by theparticular convection parameterization in the reanalyses.
Furthermore, in the calculation of diabatic heating using
the soundings, vertical velocity is calculated by the vertical integration of divergence. Because divergent wind
generally composes only a small fraction of the total
wind, calculation of the vertical velocity using only divergence can result in significant errors in diabatic
heating. To address this problem, Sardeshmukh (1993)
proposed a method of calculating the vertical velocity inwhich both conservations of energy and vorticity requirements are satisfied. For consistency with the sounding estimates, results with diabatic heating estimated asa residual of the energy budget in the reanalyses arepresented in this study. Since the primary focus of thisstudy is on the structure of the heating profiles over thetropics, not the actual magnitude (which depends on
estimates of total rainfall, which are more sensitive tocumulus parameterizations in the reanalysis products),
the profiles presented in this study are all normalized(divided by the norm, which is the square root of the sumof the squared heating at the 17 levels.) for propercomparison. However, the magnitudes of the heatingfrom all the products are briefly discussed at the end of
the next section.

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impact on the normalized profiles of the total heating.
For brevity, however all the variables will be referred toas diabatic heating.

3. Resultsa. Mean profiles over global tropics profiles andregional variability

FIG. 1. Comparison of diabatic heating from the standard outputof the MERRA reanalysis and that estimated from the associateddynamical fields according to the method discussed in the text: (a)Q1 and (b) normalized Q1.

To provide insight into the nature of the uncertainty
associated with the above-discussed approach of estimating diabatic heating conditioned by precipitation
using the analysis data, an estimate from the MERRA
reanalysis is compared to its standard total diabatic
heating output, which is also conditioned by precipitation. Figure 1a shows a comparison of the diabatic
heating over the Atlantic (Q1) from the standard model
output and that calculated from the dynamical fields,
both conditioned by precipitation. The estimate is quite
close to the standard output not only in magnitude but
also in the levels of the peaks (600 and 900 hPa). The
normalized profiles of the estimated and standard output latent heating results, on the other hand, are fairly
close (Fig. 1b).
For proper comparisons, the 6-hourly reanalysis heating data are averaged onto daily data and the TRMM
products are regridded on to the reanalyses (2.58 3 2.58)
horizontal grids. They are also interpolated onto 17
reanalysis pressure levels. In comparing diabatic heating
profiles from the soundings with those from the TRMM
and reanalysis products, one should bear in mind thatthe estimates from the TRMM and reanalysis products
are either purely latent heating (SLH and PRH) or
diabatic heating only when there is precipitation (CSH,
TRAIN, NCEPII, JRA25, ERA-40, and MERRA),
while those from the soundings are purely total diabatic
heating. But diabatic heating profiles from the soundings
include clear-sky points, which presumably do not contribute much to the total heating and hence have little

In this section, the global and regional mean profiles
from the eight products (four reanalyses and fourTRMM), as well as the soundings, are compared. The
tropical domain is divided into nine regions based on
TRMM (3B42) gridded 10-yr mean rainfall results (Fig. 2).
They represent regions of continents (Africa and SouthAmerica), monsoons (Asian monsoon), warm pools(West Pacific), the ITCZ (central, east Pacific, and Atlantic), the SPCZ (South Pacific), and the Indian Ocean.
Table 2 shows their latitudes and longitudes. These regions together define the global tropics for the rest of
this article.
Tropical mean profiles and spatial variability are compared first. Figure 3 shows the spatially and temporally
averaged profiles (solid lines) and 61 standard deviation(dashed lines) calculated using the normalized profiles
at every grid point in all regions. The differences among
the estimates are striking. CSH is dominated by a topheavy mean profile with little low-level heating, while
the SLH mean profile has two peaks: one in the upper
troposphere (400 hPa) and another in the lower troposphere (850 hPa). The PRH profile shows one sharp
maximum near the melting level, while TRAIN has two
peaks: one at 400 hPa and another at about 750 hPa.
Somewhat more subtle differences exist among thereanalyses products. ERA-40 has its peak near the
500-hPa level with a hint of a low-level peak near 850 hPa.
NCEPII is bottom heavy, with a peak near 700 hPa.
MERRA has a middle-level heating peak near 600 hPa
and secondary low-level heating near 900 hPa. JRA25
has a peak at 400 hPa and a secondary peak at about
900 hPa. The profile from the average of all of thesoundings combined end to end tends to be relatively
top heavy compared to those of the reanalysis estimates.
This might be due to the fact that unlike the otherproducts, which are climatological averages, the in situ
measurements are often performed over regions andperiods where deep intense heating is frequent. The
main point here is that a secondary lower-troposphericheating peak exists in most estimates, even though its
exact pressure level and relative magnitude in comparison to the primary upper–middle-tropospheric peakdiffer among the estimates.
The mean profile in each region and each estimate
is shown in Fig. 4. As noted above, the nature of the

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HAGOS ET AL.

FIG. 2. The 10-yr mean precipitation from TRMM (3B42) (mm day21). The boxes indicate thedomains of analysis (listed in Table 2). The locations of the soundings are marked by an X.

differences and similarities among the mean profiles
shows little regional variability. The major differencesamong the products can be generalized to most of theregions. The primary peak of NCEPII is at relatively
lower levels (600–700 hPa). In MERRA, the low-levelpeak is closer to the surface (900 hPa). PRH has a particularly sharp peak at 500 hPa. CSH has a peak near
400 hPa (highest of all the products) and no secondary
low-level peak. SLH, in agreement with the reanalysis
estimates, has more low-level heating than the other
TRMM estimates. The TRAIN profile over the oceans
often lies between CSH and SLH. Overall, with the
exception of MERRA, which has unusually bottomheavy heating in the central Pacific, the reanalysis estimates appear to be in better agreement with each otherthan do the TRMM estimates. This suggests that the
influences of the input observations on the data assimilation procedures dominate those from differences parameterization schemes.
Based on mesoscale cloud dynamics, it is known that
there are several categories of precipitation systems, eachwith a characteristic heating profile (e.g., Schumacher
et al. 2007). Even though identifying these profiles in theestimates based on satellites, sounding observations,and global reanalyses is impractical, given their spatial
and temporal resolutions, the roots of the differences in
the mean profiles can be explored by asking the following questions:
What kind of individual instantaneous profiles constitute the regional and temporal mean profiles?
d Do interproduct differences come from the structuresof these individual profiles or from their combinations(relative amounts)?

viously in terms of physical processes, compositions ofthese mean profiles have to be analyzed. For example,
an individual type of heating profiles that occurs infrequently with large amplitudes should be distinguishedfrom those that occur frequently with small amplitudes.
Both may contribute similarly to the mean but they
represent different physical processes. Therefore, froma statistical point of view, a physical agreement among
heating profiles requires consistency in their higher-ordermoments or probability distribution functions (PDFs), as
well as in their mean structures. For this purpose, we
examine the heating profiles as functions of precipitation rate. Since the magnitude of the precipitation spansa wide range, it is convenient to consider its probability
distribution in log scale. The range of precipitation rate
between 1022 and 102 mm day21 is partitioned into
60 bins to construct the PDF. The mean heating profile
within each bin is normalized and plotted in Fig. 5 for the
Atlantic region.
All TRMM and reanalysis estimates, except PRH,
show their heating peaks becoming elevated as the precipitation rate increases. The only estimate that produces
stratiform cooling in the lower troposphere at highprecipitation rate is TRMM PRH. The relationships
between the profiles and the precipitation rate areconsistent between CSH and SLH, with shallow heating
at low precipitation rate, except at a very low precipitation rate where the CSH heating is elevated. The

dThese questions are the subject of the next subsection.

b. Relationship of latent heating profiles with
precipitation rate
To aid in the interpretation of the agreements anddiscrepancies among the mean profiles discussed pre-TABLE 2. Definition of domains.
RegionLat

Lon

AfricaIndian Ocean
South Asia
West PacificSouth PacificCentral Pacific
East PacificSouth America
Atlantic Ocean

108S–108N
108S–108N
108–208N
08–228N
208S–08
08–158N
08–158N
158–58S
08–108N

108–308E
508–1108E
608–1108E
1108–1708E
1308E–1608W
1708E–1308W
1308–808W
808–458W
458W–08

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FIG. 3. (a)–(h) Normalized mean heating profiles averaged over the entire tropics (all the boxes in Fig. 2) and (i) the mean profile of the
diabatic heating from all the soundings.

deep heating in CSH is deeper than in SLH and thereanalyses. The gradual transition of the SLH profile
from shallow to deep as the precipitation rate increases
is in better agreement with the reanalyses than other

TRMM estimates. This relationship between the latentheating profile and the precipitation intensity is in agreement with the results of Short and Nakamura (2000) thatshow a correlation of 0.71 between PR echo-top height1 FEBRUARY 2010

HAGOS ET AL.

549

FIG. 4. Normalized mean profiles of heating, averaged over the respective regions in Fig. 3.

and conditional rain rate over the Atlantic and eastern
Pacific Oceans. In PRH, the relationship between the
precipitation rate and the heating profiles is very different. Top-heavy profiles dominate throughout the precipitation rate range, and they are even more elevatedat the low-precipitation tail. As with CSH and SLH,TRAIN has upper-level heating and low-level cooling at
higher precipitation rate limits and some shallow heating

at low precipitation rates, but unlike in those products,
heating is essentially absent at very low precipitation
rates (,1 mm day21).
A similar diagnostic process is performed over Africa(Fig. 6). There is no low-level heating peak in any of thethree TRMM estimates (TRAIN has no estimate ofheating over land). At the low precipitation rate tails, theTRMM estimates have elevated heating and low-level

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FIG. 5. (a)–(h) Normalized heating profiles as functions of (top panels of two panels) PDFs and (bottom panels) precipitation intensity of
precipitation over the Atlantic.

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FIG. 6. As in Fig. 5, but over Africa.

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cooling. In the reanalysis estimates, there is an abrupt
transition in the profile of the diabatic heating with sensible heat fluxes and radiative cooling dominating below
about 1 mm day21 and elevated latent heating at higher
precipitation rates, because shallow latent heating isessentially absent there.
In summary, in the mean, these estimates differ fromeach other mainly in where their heating peaks are andwhether they have just a single peak or double peaks.
With respect to precipitation intensity, the profiles of
SLH are well within the uncertainties of the reanalyses
at the high precipitation limit, while CSH is more top
heavy. Because observed information on precipitation
depth is used in addition to precipitation type and intensity, the amount of shallow heating is greater in SLH
than CSH (Shige et al. 2007). PRH has a characteristic
sharp midtropospheric peak and in general TRAIN
profiles lie in between CSH and SLH. The differences in
the oceanic low-level heating among the TRMM products are, however, in the amount and structure of theshallow latent heating, which is most abundant in SLH,
small in CSH and TRAIN, and essentially absent in
PRH. On the other hand, while all the reanalyses have
low-level heating peak near the surface, the magnitudeand height vary.

c. Temporal variability
Because of the differences in the methodologies andthe stochastic nature of precipitation and diabatic heating, one cannot expect to gain much insight from directcomparison of instantaneous heating. However, sincethese estimates should represent the same physical processes, they may share similar temporal characteristics,
such as the primary modes of variability. One way ofcomparing their temporal variabilities is the use of empirical orthogonal functions (EOFs). However, thevertical structure of physically meaningful modes should
not be constrained a priori. For example, there is no
physical reason for stratiform and convective heating
profiles to be spatially orthogonal. In this study, varimax
rotated EOF (REOF) analysis (Kaiser 1958; Wilks 2006)
is performed at every grid point in all eight of the
TRMM and reanalysis datasets using their respective
daily time series (5 times daily for PRH) as well as thesoundings. This method maximizes the simplicity (thesum of the variances of squared eigenvectors) so thatphysical interpretation of the modes might be possible.
The eigenvectors are normalized such that the REOFs
are not orthogonal in space (see Mestas-Nuñez 2000).
Temporally, however, the principal components are kept
uncorrelated. The rotation is applied on the EOF modes
that satisfy the North et al. (1982) conditionpﬃﬃﬃﬃﬃﬃﬃﬃﬃfor the
separability of the modes, [li /(li  li11 )] , 2/M, where

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li is the eigenvalue of the ith mode and M is the sample
size.
Figure 7 shows the first and second REOF modes for
the TRMM estimates. The dashed lines represent therange of spatial variability, that is, the tropical average
61 standard deviation calculated using every grid point
where the REOF analysis is performed. The relatively
small standard deviation, in comparison to the profile ofthe mode itself, shows that the structures of the twomodes have little variability in space. Note also that thetwo modes explain much of the variance (99% for CSH,
97% for SLH, 74% for PRH, and 96% TRAIN). For all
four products, the first mode peaks at about 400 hPa(deep mode hereafter) and the second mode peaks at
about 700 hPa (shallow mode). There are small amountsof low-level cooling in the deep mode of CSH and PRH,
suggesting contributions from stratiform precipitation.
In SLH the shallow mode explains a larger fraction of
the variance than the others, in agreement with its relatively strong low-level peak.
The first two modes account for much of the variancein the reanalyses as well (Fig. 8). Both deep and shallow
modes maintain the same sign throughout the troposphere. In NCEPII, where the mean profile is generally
bottom heavy (Fig. 3), its shallow mode is the first mode
and its deep mode is the second.
Figure 9 further compares all estimates in terms of
their mean profiles and respective deep and shallow
modes. Note the contrast among the mean profiles on
the one hand and the agreement among their respective
shallow and deep modes on the other. The differencesamong the mean profiles (Figs. 9a and 9e) are larger thanthose among the deep modes (Figs. 9b and 9f) as well as
the shallow modes (Figs. 9c and 9g). The agreement
among the modes is also shown in Fig. 9d for the soundings. This is also true for TRMM and reanalysis products(Fig. 9h). But there are discrepancies. The deep modesof CSH and PRH are outliers in their lack of heating at
low levels. The peak of the deep heating of PRH andCSH (at 300 hPa) is higher than that of the sounding
average (near 400 hPa). For the shallow modes, PRH
has a peak near 600 hPa and JRA25 at 850 hPa, while
those of the other estimates as well as the soundings are
at 700 hPa. The main point is that the bimodal variability of the latent (diabatic) heating is shared by all theestimates and the modes of variability in the estimatesshow better agreement than the mean profiles.
If the differences among the modes of variability ofthe estimates are in fact very similar, as shown in Fig. 9,then how do the regional differences among the profiles
arise? To address this question, the variances explainedby the deep and shallow modes are considered. Table 3
shows the variance explained by the first two modes of

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HAGOS ET AL.

FIG. 7. The mean profile, and the (left) deep and (right) shallow modes ofthe variability averaged throughout the tropical domain for the TRMM
products. The dashed lines indicate their respective spatial variabilities(61 std dev).

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FIG. 8. The (left) deep and (right) shallow modes of the variability averaged
throughout the tropical domain for the reanalyses. The dashed lines indicate
their respective spatial variabilities (61 std dev).

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FIG. 9. (a) Mean profile, and the (b) deep and (c) shallow modes, as well as (d) the average ofthe deep and shallow modes and their standard deviation from the soundings. (e)–(h) As in(a)–(d), but for the reanalyses and TRMM products.

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JOURNAL OF CLIMATETABLE 3. The variance explained by the deep and shallow
modes for soundings.
Sounding

Var1

Var2

TOGA COAREGATEKWAJEXTWP-ICESCSMEX-NSCSMEX-S
LBA
MISMO
All combined

84
81
82
89
88
89
49
86
81

11
12
15
6
8
10
35
9
12

the variability in the soundings. The smaller the percentage of the variance explained by the shallow mode, themore top heavy a sounding is (TWP-ICE, SCSMEX-N)and vice versa (GATE). When the REOF analysis isperformed on all the soundings combined, the deep
mode explains about 81% of the variance and the shallow mode explains only 12% of the variance. This isconsistent with the fact that most of the soundings have
top-heavy profiles (Fig. 9a). Similarly, the regional differences in the variance of the TRMM and reanalyses
estimates are shown in Table 4. With the exception of
PRH, all estimates show that the first two modes explain
more than 80% of the variance in all the tropical regions.
Overall, the variance explained by the deep mode islarger over the western and southern Pacific and smaller
over the eastern and central Pacific. The top-heavy profiles of TRAIN and CSH are manifested in the large
variance explained by their deep mode throughout thetropics. The fractional variance explained by the deep
mode of TRAIN is the largest among all the estimates.
Even though the purpose of the study is to evaluate
the uncertainties and commonalities in latent heatingproducts, one has to keep in mind that there are alsosignificant differences in the magnitudes of the diabatic
heating from these products. The total variance obtained
from EOF analysis provides a convenient proxy forheating activity. Table 5 shows the total variance averaged over each region in the global tropics. Among theVOLUME 23

TRMM products, SLH has the largest heating and PRH
the lowest (likely because the 5-day averaging reduces
the variance, the use of variance as a proxy breaks downin this case). CSH and TRAIN have comparable magnitudes of heating.

4. Summary and discussion
The vertical structures of the diabatic heating profiles
have been compared among their estimates from threesources: TRMM satellite retrievals, global reanalyses,
and in situ sounding data. Similarities shared by most or
all of them provide a certain confidence in our ability toestimate certain features of the heating profiles and theirapplications. Discrepancies among them, however, callfor their further improvement and caution us to use theircurrent versions with care.
In the TRMM products considered in this study (CSH,
SLH, PRH, and TRAIN), diabatic heating is estimatedfrom the precipitation rate and its vertical structure as
observed by the TRMM Precipitation Radar. However,these products differ in their utilizations of the observed
data and retrieval algorithms. While in the reanalyses(ERA-40, NCEPII, and JRA25), the total diabatic
heating is calculated as a residual of the thermodynamic
budget and then conditioned by the presence of precipitation. This study also includes diabatic heating estimates from eight field campaigns at various tropicallocations over the last 35 yr (TOGA COARE, GATE,KWAJEX, SCSMEX-N and -S, TWP-ICE, LBA, andMISMO). In these soundings, the diabatic heating (Q1)
is also calculated as a residual of the energy budget.
The general characteristics agreed upon by most or allof the estimates include the following:Over the oceans, profiles have two peaks—one in the
midtroposphere (500–400 hPa) and the other in thelower troposphere (900–700 hPa). The upper peak is
associated with an intense precipitation rate and thelower peak with low precipitation intensity.
d The temporal variability of latent heating is dominated by the first two rotated EOF modes: a deepd

TABLE 4. Percentages of the variance explained by deep (shallow) modes.
Region/product

ERA-40NCEPII

MERRA

JRA25

CSH

SLH

PRH

TRAIN

AfricaIndian Ocean
Asian monsoon
Western PacificSouthern PacificCentral PacificEastern PacificSouth America
Atlantic

66 (23)71 (16)63 (21)65 (21)66 (19)26 (54)51 (37)22 (60)68 (24)56 (28)26 (65)46 (45)86 (5)
50 (38)10 (74)18 (70)15 (73)6 (85)48 (28)61 (19)76 (9)
58 (23)66 (15)48 (24)72 (10)74 (12)68 (19)N/A
76 (8)
72 (13)83 (5)
79 (6)
66 (14)65 (16)55 (21)74 (9)

77 (22)78 (22)78 (22)81 (19)79 (21)83 (17)79 (20)76 (23)74 (25)86 (12)58 (39)48 (49)63 (33)67 (30)68 (27)76 (22)73 (24)60 (37)42 (32)47 (25)49 (27)54 (20)60 (18)53 (23)43 (33)50 (21)55 (25)

N/A
85 (12)
N/A
86 (11)84 (13)78 (17)82 (15)
N/A
86 (12)

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HAGOS ET AL.
TABLE 5. Total variance by region (K2 day22).

Region/product

ERA-40NCEPII

MERRA

JRA25

CSH

SLH

PRH

TRAIN

AfricaIndian Ocean
Asian monsoon
Western PacificSouthern PacificCentral PacificEastern PacificSouth America
Atlantic

80.0
157.5
85.0
143.5
149.9
83.8
158.4
124.5
188.1

31.8
84.6
77.0
70.4
62.8
59.1
72.4
55.6
82.7

25.4
28.5
42.9
28.0
20.9
17.17
40.0
50.2
50.6

33.0
88.3
97.6
128.3
108.9
72.7
84.9
51.5
102.8

51.33
94.7
70.9
122.3
96.3
86.9
91.5
58.6
98.7

789
342.9
327.0
345.0
289.33
202.9
294.4
531.8
374.3

15.6
14.2
21.1
22.3
12.0
13.1
7.4
13.0
8.0

N/A
156.6
N/A
201.1
157.6
110.5
175.2
N/A
166.5

mode with a peak between 500 and 400 hPa and ashallow mode with a peak between 850 and 700 hPa.
Combined, these two modes explain between 74%
and 99% of the total variance, respectively.
d Differences among the estimates are significantly
smaller in their respective leading modes than in theirmean profiles.
The main discrepancies are as follow:
The mean profiles differ in where their heating peaksare (mid- to upper versus lower troposphere) andwhether they have a single peak or double peaks.
d Differences among the TRMM estimates are in general larger than those among the reanalysis estimates.
SLH, in agreement with the reanalysis estimates, hasmore low-level heating than do the other TRMM estimates. There is a unique sharp midlevel peak in
PRH, and CSH has a relatively top-heavy profile.
d Differences among the shallow REOF modes arelarger (due mainly to the singular structures of JRA25
and PRH) than those among the deep modes.
dAmong others, the most intriguing finding in thisstudy is perhaps the ubiquity of the two REOF leading
modes in all of the heating estimates. Considering that
all three types of estimates rely on almost independent
data sources (satellite remote sensing, data assimilationof large-scale dynamical variables, and sounding observations) and different methods (cloud microphysics plus
CRM versus heat budget), one cannot help but believethat the similarities in the two REOF leading modesof all the estimates carry the same physical implications.
In a separate study (Zhang and Hagos 2009), we argue
that the two leading modes suggest the existence of two
distinct populations of precipitation systems: warm rainwith latent heating peaks in the lower troposphere (below the melting level) and cold rain with latent heatingpeaks in the upper troposphere (above the melting
level). If this is the case, then the large discrepancies
among the heating estimates compared in this study atlower precipitation ranges and for the shallow modes

indicate that the key to producing accurate heating
structures in both models and remote sensing observations is to get the amount of warm rain right.
In this study, the regional and temporal variabilities of
the heating profiles and their relationships with the precipitation rate are used to compare the different products.
While the results from this study provide some guidance
to applications of these products, one has to keep inmind that this evaluation is neither complete nor final.
The techniques of diabatic heating retrieval from thesatellite measurements as well as its estimation fromlarge-scale dynamics, continue to be refined, and advances
will be reported upon in the future. Another aspect of theevaluation of the uncertainties in the heating estimates
pertains to their implications to our understanding of thelarge-scale circulation and climate. The relationship ofthese uncertainties to those of other important variables
in tropical dynamics has to be quantitatively assessed.
Those issues will be investigated in a separate study.
Acknowledgments. We express our sincere gratitude
to the editor and anonymous reviewers, as well as Paul
Ciesielski, Steve Esbensen, Richard Johnson, Yasu-Masa
Kodama, Steve Kruger, Wen-wen Tung, Xiaoqing Wu,
Xiping Zeng, and Minghua Zhang, who provided orhelped us acquire the various sounding datasets. This
study was support by the NASA TRMM/GPM project.

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