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MJO Signals in Latent Heating: Results from TRMM Retrievals
CHIDONG ZHANG,* JIAN LING,* SAMSON HAGOS,*,1 WEI-KUO TAO,# STEVE LANG,#YUKARI N. TAKAYABU,@ SHOICHI SHIGE,& MASAKI KATSUMATA,** WILLIAM S. OLSON,11
AND TRISTAN L’ECUYER##* RSMAS, University of Miami, Miami, Florida#
GSFC, NASA, Greenbelt, Maryland@
Center for Climate System Research, University of Tokyo, Tokyo, Japan&
Graduate School of Science, Kyoto University, Kyoto, Japan** RIGC, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan
11
JCET, University of Maryland, Baltimore County, Baltimore, Maryland##
Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado(Manuscript received 4 December 2009, in final form 9 June 2010)
ABSTRACT
Four Tropical Rainfall Measuring Mission (TRMM) datasets of latent heating were diagnosed for signals in
the Madden–Julian oscillation (MJO). In all four datasets, vertical structures of latent heating are dominatedby two components—one deep with its peak above the melting level and one shallow with its peak below.
Profiles of the two components are nearly ubiquitous in longitude, allowing a separation of the vertical andzonal/temporal variations when the latitudinal dependence is not considered. All four datasets exhibit robust
MJO spectral signals in the deep component as eastward propagating spectral peaks centered at a period of
50 days and zonal wavenumber 1, well distinguished from lower- and higher-frequency power and muchstronger than the corresponding westward power. The shallow component shows similar but slightly lessrobust MJO spectral peaks. MJO signals were further extracted from a combination of bandpass (30–90 day)filtered deep and shallow components. Largest amplitudes of both deep and shallow components of the MJO
are confined to the Indian and western Pacific Oceans. There is a local minimum in the deep components over
the Maritime Continent. The shallow components of the MJO differ substantially among the four TRMM
datasets in their detailed zonal distributions in the Eastern Hemisphere. In composites of the heating evolution through the life cycle of the MJO, the shallow components lead the deep ones in some datasets and at
certain longitudes. In many respects, the four TRMM datasets agree well in their deep components, but not intheir shallow components and in the phase relations between the deep and shallow components. These results
indicate that caution must be exercised in applications of these latent heating data.

1. Introduction
The Madden–Julian oscillation (MJO; Madden andJulian 1971, 1972) is commonly viewed as driven by
convection–circulation coupling or interaction. Such aperception comes mainly from observed coherence between winds and convective signals, such as outgoing
longwave radiation (OLR) and precipitation [see Madden
1

Current affiliation: Pacific Northwest National Laboratory,
Richland, Washington.
Corresponding author address: Chidong Zhang, RSMAS/MPO,
University of Miami, 4600 Rickenbacker Causeway, Miami, FL
33149.
E-mail: czhang@rsmas.miami.edu
DOI: 10.1175/2010JAS3398.1
Ó 2010 American Meteorological Society

and Julian (1994), Lau and Waliser (2005), and Zhang(2005) for summaries of MJO observations]. This perception has been a basis for the development of simple
models for understanding certain aspects of MJO dynamics. It has often been assumed, explicitly or otherwise, that diabatic heating associated with the MJO takes
a simple profile with its peak in the midtroposphere andbecomes zero at the surface and tropopause. The corresponding atmospheric circulation is of the first baroclinic structure, with winds of the opposite directions in
the lower and upper troposphere. Under this assumption, the atmosphere is often treated as a single level (orlayer) in the study of the MJO [see summaries of theoretical studies on the MJO by Wang (2005), Zhang (2005),
and Raymond and Fuchs (2009)].

NOVEMBER 2010

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This simple conventional approach of representing the
diabatic heating profile of the MJO has, however, beenchallenged. Since the very early stage of MJO research,efforts have been made to explain the slow eastward
propagating speed (;5 m s21) of the MJO in observations in contrast to the unrealistically fast speeds ofintraseasonal oscillations in numerical simulations bysimple as well as complex numerical models. For example, Chang (1977) showed that the phase speed of theequatorial Kelvin wave is reduced when friction is explicitly included in the linear wave theory (Matsuno 1966).
According to such linear theory of the equatorial waves,the phase speed c of the Kelvin wave is directly related
to the equivalent depth h as c 5 (gh)1/2. It was pointed
out that if tropical diabatic heating, mainly convective
latent heating, had its peak in the lower troposphere,
rather than the mid- or upper troposphere, the verticalscales of the perturbations, measured by the equivalent
depth, would be reduced, and so would the phase speedof the MJO (Chang and Lim 1988; Sui and Lau 1989).
This idea was not further pursued, largely because tropical convective latent heating has long been perceived
as dominated by heating related to deep convective andstratiform precipitation from mature mesoscale convective systems with its peak in the upper troposphere (Houze1997).
The recent development of theoretical understanding of tropical convectively related perturbations has
considered the MJO a ‘‘moisture mode’’ (Raymond andFuchs 2009). Such a moisture mode would become unstable and grow when the gross moist stability (GMS;
Neelin and Held 1987) is negative. Low-level mass flux
and moisture convergence associated with shallow diabatic heating can effectively yield negative GMS (Sobel
2007; Raymond et al. 2009). It has also been suggested
that low-level heating is more efficient in inducing largescale moisture convergence in the boundary layer andlower troposphere as the main energy supply for the
MJO (Wu 2003). These ideas have roused new interestin shallow heating associated with the MJO.
Conditions that lead to negative GMS indeed exist in
the tropical region with prominent MJO signals. Field
observations during the Tropical Ocean–Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE, November 1992–February 1993;
Webster and Lukas 1992) indicated that, in addition to
deep convection, the western Pacific warm pool is full of
shallow precipitating convection that would supply theatmosphere with heating in the lower troposphere (e.g.,
Johnson et al. 1999), resulting in negative GMS (López
Carrillo and Raymond 2005). Observations have suggested that shallow precipitating clouds might become
more prominent during the transition from convectively

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inactive to active phases of the MJO (e.g., Kikuchi and
Takayabu 2004). This and the trailing stratiform-like
upper-level heating west of the convection center yielda westward tilt of diabatic heating profiles associatedwith the eastward propagating MJO. This has beenshown in some observational studies (Lin et al. 2004;
Kiladis et al. 2005). Other studies, however, failed todetect without ambiguity this tilt in latent or diabatic
heating based on satellite observations, global reanalysis
products, and sounding observations (Morita et al. 2006;
Jiang et al. 2009; Katsumata et al. 2009).
Modeling studies also produced inconsistent resultsin this regard. Some numerical simulations that exhibit
certain observed features of the MJO produced shallow
heating immediately preceding deep heating (Zhang and
Mu 2005; Benedict and Randall 2007), whereas others
did not (Masunaga et al. 2008; Maloney 2009). In somenumerical models, shallow heating appears to play anessential role in MJO simulations (Li et al. 2009; Zhang
and Song 2009). In others, top-heavy, stratiform-like heating is critical to reproduction of the MJO (Fu and Wang2009). Nonetheless, the uncertainties in observations, numerical simulations, and theoretical studies (Khouider andMajda 2006, 2008) have emphasized the importance ofthe shallow to deep structural evolution of latent heatingin the MJO. Further investigations on issues related to thevertical structure and evolution of latent heating areneeded to advance our understanding of MJO dynamics.
This serves as the main motivation of this study.
MJO signals in latent heating and their structural
evolution estimated from satellite observations are explored in this study. A common practice of diagnosing
MJO signals is making a composite using an MJO index
based on dynamical and thermodynamical variables (e.g.,wind and OLR). This method would help demonstrate
the vertical structure of latent heating associated withknown MJO dynamical and thermodynamical fields (Linet al. 2004; Morita et al. 2006; Lau and Wu 2010). In thisstudy, we pose an alternative question: What would thevertical structure of latent heating associated with the
MJO be without any reference to its dynamical andthermodynamical fields? If latent heating is truly an essential component of the MJO, then its MJO signals
should be identifiable independently of other fields. Efforts of seeking coherence between latent heating andother MJO measures (e.g., wind and OLR) are justifiable
only if MJO signals in latent heating can be independently detected. If we fail to identify MJO signals in
latent heating without the help of other dynamical andthermodynamical variables, we have to ponder why. This
would lead to questions regarding the physical meaning of
its coherence with other variables and our current perception of its role in the MJO.

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Empirical orthogonal function (EOF) analysis is commonly used to define the MJO. This method, however,usually fails to identify without ambiguity MJO signals
in precipitation (or OLR) alone without reference towind. A single EOF mode represents a stationary pattern. Propagating signals are represented by a pair of
EOF modes with their phase in quadrature, with theireigenvalues very close to each other but separated fromtheir neighboring modes according to a given criterion(e.g., North et al. 1982). The EOF analysis applied totropical precipitation (or OLR) often yields a single
leading mode well separated from the second mode,
which may or may not be separated from the third mode.
Such leading EOF modes represent an intraseasonal stationary oscillation in tropical precipitation (or OLR) overland or over warm water, which can be comparable toor stronger than the eastward propagating component
that defines the MJO. The zonal propagating MJO signals in precipitation (or OLR) can be better detectedby combining either one with a dynamical variable (e.g.,zonal wind) in a multivariate EOF analysis (e.g., Wheeler
and Hendon 2004) or by using different versions of EOF
that filter out the stationary component, such as extended EOF (Weare and Nasstrom 1982), complex EOF(Maloney et al. 2008), or Hilbert singular value decomposition (HSVD; Zhang and Hendon 1997). None ofthese methods has been applied to latent heating on the
global scale. Whether MJO signals in latent heating canbe independently and objectively identified has yet to be
determined.
In this study, we will present diagnostics of MJO signals in latent heating based on satellite observationsof the Tropical Rainfall Measuring Mission (TRMM;
Kummerow et al. 2000). We focus on two topics: (i) thevertical structure and its evolution in latent heating associated with the MJO detected independently of otherdynamical and thermodynamical fields and (ii) the similarities and discrepancies of the MJO signals in latentheating based on four TRMM retrieval algorithms. Special attention is paid to the evolution of vertical structure of latent heating during the life cycle of the MJO,
which may help address the controversial issue of therelative importance of shallow versus deep heating to
the MJO discussed earlier. The comparison among four
TRMM retrievals will demonstrate the utility and uncertainty of these satellite remote sensing products. Toward the end of this study, we will relax the constraint anduse an independent MJO index to construct the latentheating field associated with the MJO.
The reliability of TRMM retrievals of latent heating
profiles is a subject under debate. As with all satellite
remote sensing products, there are assumptions and simplifications made in the processes of retrieving latent

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heating profiles. TRMM retrievals offer an alternative
source of information of the latent heating field thatprovides much better coverage in time and space thanwhat is available from field observations, and they are
not affected by the notorious cumulus parameterization
problems plaguing numerical models that produce global
reanalysis data. Most of them, however, are not immune
from problems in parameterization of cloud microphysics
because (with one exception) they use look-up tables
generated by cloud-system-resolving models (CSRMs)
validated against field observations. In general, the latentheating retrievals based on TRMM satellite remote sensing data are no less ‘‘observational’’ than global reanalyses. Both are proxies for observations and their fidelity
in representing reality must not be taken for granted.
This study has no intention of providing a comprehensive comparison among the TRMM latent heating
datasets, which was done by Tao et al. (2006), or between
the TRMM data and observations, which was done by
Hagos et al. (2010). Our discussions will be limited to the
topic of interest: the MJO. We will focus on the verticaland zonal structures of the MJO signals in latent heating and ignore their meridional dependence. Whether
and how the vertical structure of latent heating may varyas the MJO migrates seasonally in latitude (Zhang andDong 2004) or propagates northward during the summer
Asian monsoon season (Waliser 2006) should be discussed in separate studies.
Latent heating data derived from four TRMM retrievals are introduced in section 2a. An unconventional
method was applied to extract MJO signals in latentheating, which is described in sections 2b–e. Results arepresented in section 3 in terms of spectra, variance, andvertical, zonal, and temporal variability. A summary anddiscussion are given in section 4.

2. Data and method
a. Latent heating
Four latent heating estimates derived from TRMM
observations (Table 1) were used in this study: spectral latent heating (SLH), convective–stratiform heating(CSH), precipitation radar heating (PRH), and thetrained radiometer algorithm (TRN). These datasets provide different quantities: latent heating (LH), total diabatic
heating Q1, and latent heating equivalence (Q1 2 QR,
where QR is radiative heating). The main difference between LH and Q1 2 QR is the flux of vertical eddy transport of sensible heat (Yanai et al. 1973), which is small,
except at the melting level and near the tropopause(Mapes 2001; Shie et al. 2003). In this study, we did not
distinguish LH from Q1 2 QR. In this sense, all four
TRMM datasets provide LH, while two (CSH and TRN)NOVEMBER 2010

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ZHANG ET AL.
TABLE 1. TRMM heating data.

Datasets

SLH

CSH

VariableQ1 2 QR, LH
Temporal resolution
Daily
Horizontal resolution
0.58 3 0.58
Vertical levels
19
Algorithm input
PR (2A25): rain type,data
surface and meltinglevel rain rates, PTH

Lookup table

Main strength

Main weakness

Q1, LH
Daily
0.58 3 0.58
19
PR 1 TMI (3G68): rain
type, surface rain rate,
stratiform rain fraction,rain location (land vsocean), PTH[rain type, PTH, melting[rain type, surface rain rate,level rain rate] / LH(z)stratiform rain fraction,rain location, PTH] /LH(z)Larger sample sizes thanNonzero heating for anvil
rain with zero surface
PR-only estimate
rain
Depend on CSRMDepend on CSRMgenerated lookup tables;
generated lookup tables;
zero LH in regions withlimited PR samplingzero surface rain

Known biases

Underestimated heating inupper troposphere

References

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

PRH

TRN

LH
Pentadal
2.58 3 2.58
41
PR (2A25): rain type,surface rain rate,
rainwater profiles,
bright brand height

Q1, Q1 2 QR (’LH)
Orbital0.58 3 0.58
29
PR (2A25): rain type,surface rain rate,
PTH; TMI: radiance—Independent of CSRMs[TMI radiance] /LH(z)Larger sample sizes thanPR-only estimate

Uncertainty in vertical
Depend on CSRMvelocity profiles;
generated lookup
limited PR sampling;tables; no data overassuming steady-state
land; zero LH inand vertically 1D
regions with zerosurface rain
UnderestimatedUnderestimated
Overestimated shallow(overestimated) heating(overestimated) LH
convective heating;above (below) 9 km
above (below)
accounting of
melting levelboundary-layer
sensible heating
Tao et al. (1993, 2000, 2010) Kodama et al. (2009)
Grecu and Olson (2006);
Grecu et al. (2009)

provide Q1. For direct comparisons, we used LH fromall four datasets and will make a comment in section 4 onresults based on Q1.
In the SLH algorithm (Shige et al. 2004, 2007, 2008,2009), a lookup table (LUT) generated by a CSRM
includes vertical profiles of latent heating that vary
continuously with precipitation top height (PTH) and
precipitation rates at the surface for convective and shallow stratiform rain and with the melting-level rain rate
for anvil (deep stratiform) rain. TRMM Precipitation
Radar (PR) information of the PTH, precipitation rates,
and rain types is used to select vertical profiles of latentheating from the LUT.
Data from a new CSH algorithm (Tao et al. 2010) wasused in this study, which is an updated version of theprevious one (Tao et al. 1993, 2000). Based on PR information of surface rain rates and stratiform rain fraction, it also uses an LUT generated by a CSRM to selectvertical profiles of latent heating for convective andstratiform rain over the ocean and land, respectively,
and for shallow rain.
The PRH algorithm (Kodama et al. 2009) estimateslatent heating from the growth/evaporation of raindrops
during their vertical displacement based on the verticalgradient of the precipitating water with respect to the
motion of the precipitating particles. Condensation anddeposition (evaporation) are regarded as the cause ofobserved increases (decreases) in precipitation wateramount with respect to the direction of the motion of
the precipitating particles. This algorithm does not use
information from any numerical model.
In the TRN algorithm (Grecu and Olson 2006; Grecu
et al. 2009), PR-based latent heating profiles, coincident
TRMM Microwave Imager (TMI) brightness temperature observations, and a CSRM-generated LUT are used
to assemble a large database, which is queried to findbrightness temperatures consistent with TMI-observed
values at a given location. Latent heating profiles, among
other parameters, in the database associated with theconsistent brightness temperatures are composited using a Bayesian method to find their corresponding‘‘expected values.’’ Total diabatic heating was estimatedby combining latent heating with an ancillary atmosphericradiative heating climatology derived on an identical vertical and horizontal grid from an approach known as theHydrologic Cycle and Earth’s Radiation Budget (HERB)
algorithm (L’Ecuyer and Stephens 2003, 2007). TRN data
are available only over the oceans.

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A common known problem of PR-based latent heat
retrievals is the inherent sensitivity of the PR that can
detect only precipitation-sized particles. This leads to anunderestimate of the contribution of nonprecipitating
shallow clouds, which should have low-level total heating (e.g., Nitta and Esbensen 1974; Johnson and Lin 1997).
An LUT sensitively depends on the CSRM that generates it (e.g., Shige et al. 2009).
Table 1 lists major differences in the four algorithms
and their known strengths, weaknesses, and biases. A
detailed comparison among them and with other TRMM
latent heating datasets was made by Tao et al. (2006).
Morita et al. (2006) examined statistical structures oflatent heating associated with the MJO using an earlyversion of SLH. Jiang et al. (2009) compared TRN andan early version of CSH to two global data assimilation
products for MJO events in boreal winter of 1998/99.
Lau and Wu (2010) used multiyear data of TRMM, including an early version of CSH latent heating, to examine the evolution of cloud structure and associatedlatent heating through the life cycle of the MJO over thewestern Pacific. Hagos et al. (2010) compared the four
TRMM datasets to diabatic heating estimated fromsounding observations and global reanalysis products inseveral tropical regions. The present study focuses on
statistical signals of the MJO from the four TRMM latent heating datasets and their longitudinal and temporal variability.
All four datasets cover 10 years (1 January 1998–
31 December 2007). The daily data of CSH and SLH andorbital data of TRN were made into pentadal time series. All data were interpolated onto common 2.58 3 2.58
grids and 17 height levels (0.5 and 1–16 km). Latitudinalvariability was ignored by taking averages over 158S–158N.
Zonal mean profiles and variability (mean 1 1 standard
deviation) of the resulting four TRMM heating datasets
are obviously different (Fig. 1, left panels). The mean
profiles (solid lines) of SLH and CSH show unique
double peaks, one above and one below the melting
level (;5.5 km). The double-peak structure is subtle inthe mean of TRN and hardly discernable in PRH. The
mean profiles of the four TRMM latent heating datasets differ more in the lower than the upper troposphere.
This is the first sign of potential large uncertainties inretrievals of latent heating due to shallow convection that
produces warm rain and low-level heating.

b. Separation of variables
Two general steps were taken to diagnose the data.
The first separated the vertical dependence of heating
profiles from their zonal and temporal dependence. The
second isolated MJO signals in the vertically independent
components of the heating field. Each step involved an

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FIG. 1. (left) Zonal means (solid) and means 1 1 std dev(dashed). (right) Zonal mean eigenvectors of the first (fRdg, solid)
and second (fRsg, dashed) REOF modes.

analysis of EOF or the like that produced two leading
modes of its own. To avoid confusion in terminology,
these two steps are described in detail.
First, as mentioned earlier, with the latitudinal variability within the tropics ignored for simplicity, a threedimensional heating field Q(x, z, t) was generated byaveraging over 158S–158N, where x is longitude, z isheight, and t is time. The latitudinal mean did not completely remove equatorially asymmetric signals such as
those in the eastern Pacific, as will be seen later. The timemean Q(x, z) was then removed to create its anomalies
Q*(x, z, t). At each given longitude x0, Q*(x0, z, t) was
subject to a rotated EOF (REOF) analysis. We used raw
VARIMAX REOF in this study. The results cannot becompletely reproduced by normal VARIMAX REOF
(Kaiser 1958). In normal REOF, heating at each level
carries an equal weight in rotation. But heating at the

NOVEMBER 2010
TABLE 2. Definitions of symbols.
SymbolDefinition

Y
Y*
Y9
fYg
Yd
Ys
YMJO
Y^

Time mean of Y
Deviation of Y from its time mean
Intraseasonally filtered Y
Zonal mean of Y
First REOF model (deep component) of Y
Second REOF model (shallow component) of Y
MJO in Y
Composite of Y
Amplitude of H
Principal components (PCs) of HSVD
Latent heating
PCs of REOF
Eigenvectors of REOF
Eigenvectors of HSVD
Variance of Y

AH
H
Q
P
R
X
sY

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lowest and highest levels is near zero (Fig. 1), whichshould not be weighted equally as heating at levels withlarge amplitudes. Raw VARIMAX REOF is thus more
appropriate for this study.
With few exceptions, each REOF analysis yielded twoleading components. The first is deep, with its peakabove the melting level (see details below), denoted
Qd(x0, z, t) 5 Rd(x0, z)Pd(x0, t), where Rd(x0, z) is its
eigenvector and Pd(x0, t) its time series or principal component (PC). The second component is shallow, with its
peak below the melting level, denoted Qs(x0, z, t) 5
Rs(x0, z)Ps(x0, t). A list of symbols used in this study
is given in Table 2. At all longitudes, total heating
can be approximated by these first two leading REOF
components:

Q(x, z, t) 5 Q(x, z) 1 Q*(x, z, t)’ Q(x, z) 1 Qd (x, z, t) 1 Qs (x, z, t).

(1)

The approximation of Q*(x, z, t) in terms of the first two
leading REOF components can be written as Q*(x, z, t) ’R(x, z)P(x, t), with R 5 [Rd(x, z), Rs(x, z)] being theireigenvector matrix and P 5 [Pd(x, t), Ps(x, t)]T their
PC matrix. The right panels in Fig. 1 show the verticalstructures of these two components for the four TRMM
datasets. Despite the distinct mean profiles of the four
TRMM latent heating datasets (e.g., with or without
double peaks), their zonally averaged first REOF components are all deep (with peaks above the melting
level) and second modes are all shallow (peaks below
the melting level). There are discernable discrepancies
in the two leading REOF components of the four latent
heat datasets: the amplitude of the deep component is
not close to zero in the lower troposphere only in PRH;
the deep components exhibit two peaks only in SLH and
CSH; the amplitudes of the shallow components are notclose to zero above the melting level only in CSH and
PRH; and the peak level of the shallow component is thelowest in CSH among the four, possibly due to a uniquerain type (warm rain) in its retrieval algorithm, andhighest in PRH, possibly because of reduced sampling of
low-level heating by its treatment of surface clutter of PR
signals. The deep versus shallow structures in the leading
REOF components are, however, the same for all four
datasets. They exist also in diabatic heating derived fromin situ sounding observations and global reanalysis products (Hagos et al. 2010).

FIG. 2. Eigenvector of Rd(x, z) (REOF 1, left) and Rs(x, z) (REOF 2, right).

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Another interesting feature of the two leading REOF
components is that their vertical structure is nearlyubiquitous in longitude (Fig. 2). There are a few exceptions. The zonal variation of the deep component of CSH
is more obvious than the other three. The slightly elevatedpeak level of the shallow component of TRN over the
Maritime Continent might be related to its samplingissues (no data over land). Nevertheless, zonal ubiquity
roughly exists for the deep components and, to a lesser
degree, the shallow components. The spatial ubiquity ofthe deep and shallow components also exists in total
diabatic heating derived from sounding observations
and global reanalysis products (Zhang and Hagos 2009;
Hagos et al. 2010). The reason for this ubiquity is unclear, given the large spatial variability in tropical precipitation composition, such as the convective–stratiform
rain rate ratio (Schumacher and Houze 2003). It may berelated to the two distinct rain formation processes(liquid versus ice) or the two large-scale stability regimes
separated by the minimum equivalent potential temperature in the midtroposphere. In any case, this ubiquity
leads to a convenient simplification of our diagnostic
procedure.
Figure 3 shows that because R(x, z) does not varymuch zonally (i.e., zonal ubiquity), the variance ofR(x, z)P(x, t) is very close to that of fRg(z)P(x, t), that is,sRP ’ sfRgP, where fg represents zonal mean. Thisvalidates an approach of replacing R(x, z) with fRg(z)in representing the heating anomalies, Q*(x, z, t) ’fRg(z)P(x, t). When the vertical dependence of the threedimensional field Q* is separable from its zonal andtemporal dependence this way, the conventional approach of extracting MJO signals from variables ata single level (e.g., precipitation, zonal winds at 850 or
200 hPa) can be directly applied to P(x, t). We adapted
this approach of separation of variables and extracted
MJO signals in Q* from P(x, t). The variability in thevertical structure in Q* was recovered later by combining
the MJO signals in P(x, t) with the vertical componentfRg(z), which will be described next in more detail.

c. MJO identification
To isolate MJO signals, the PC [i.e., P(x, t)] was subjected to an intraseasonal (30–90 day) bandpass filtering, which yielded its intraseasonal anomaly P9. This
bandpass filtering is justified by the intraseasonal peaks
shown in the time–space spectra (section 3a). We applied an EOF analysis to extract MJO signals from theintraseasonal anomalies of latent heating P9. No pair of
EOF modes could, however, be identified for Pd and Ps
individually, or their combination P9 for any of the four
TRMM datasets. Only the first EOF mode is outstanding or separated from the neighboring mode, suggesting

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FIG. 3. Zonal and temporal variance of Q (solid line), reconstructed heating using the two leading REOF modes R(x, z)P(x, t)(sRP, dashed), and reconstructed heating using the two leading
REOF modes with zonally averaged eigenvectors fRg(z)P(x, t)(sfRgP, circles).

that a stationary component in latent heating in Pd,
Ps, and P9 dominates any propagating component. The
EOF method thus fails to objectively identify and isolate
MJO signals in latent heating for the reason discussed in
section 1.
We then applied an HSVD method. It is an SVD
analysis of a field and its Hilbert transform. In contrast
to EOF, for which a single mode defines a stationary
oscillation, HSVD modes appear only in pairs; each pair
represents propagating oscillations, such as the MJO(Zhang and Hendon 1997), if they satisfy a separation
criterion. No stationary oscillation exists in individual
HSVD modes. Unless one insists that stationary oscillations are part of the MJO, this exclusive identificationof propagating signals by HSVD might be its most obvious advantage over EOF as a method of extracting the
MJO. Based on the HSVD method, the first pair ofleading modes separated from the rest was identified forboth Pd and Ps individually and for their combination P9from all four TRMM datasets, confirming the existenceof MJO signals in all these variables. Under the assumption that deep (Pd) and shallow (Ps) heating shouldbe treated not as independent but as closely related
variables in the context of the MJO, P9, rather than Pd
and Ps separately, was diagnosed in this study to extract
MJO signals (section 3b).

d. MJO reconstruction
The two leading HSVD modes in pair for P9 weretaken to represent the MJO in the equatorial domain(longitude):NOVEMBER 2010

ZHANG ET AL.

$
MJO

P

(x, t) 5 X(x)H(t) 5"
5

Xd1(x) Xd2 (x)%$Xs1(x) Xs2 (x)#Xd1 (x)H1 (t) 1 Xd2 (x)H2 (t)Xs1 (x)H1 (t) 1 Xs2 (x)H2 (t)%(x, t)PMJO
d,5(x, t)PMJOs

H1 (t)%

H2 (t)

$

MJO

Q

3495

where Xkn(x) represents the HSVD eigenvectors andHn(t) its PCs, with k 5 d, s being the index of the deepand shallow REOF components and n 5 1, 2 the index
for the first two (first pair) HSVD modes. The verticalstructure of the MJO can be recovered by combining
PMJO with fRg:

(2)

"
#
   (x, t)PMJO
d(x, z, t) 5 fRg(z)P(x, t) 5 [ Rd (z) Rs (z)] MJO
Ps (x, t)
 
 
MJO
MJO
5 Rd (z)Pd (x, t) 1 Rs (z)Ps (x, t)  
5 Rd (z)[Xd1 (x)H1(t) 1 Xd2 (x)H2(t)] 1 Rs (z)[Xs1 (x)H1(t) 1 Xs2 (x)H2(t)]MJO

5 QMJO(x, z, t) 1 QMJO
(x, z, t),
d
s

(3)

where QMJO
(x, z, t) and QsMJO(x, z, t) represent MJO
dsignals in latent heating associated with the deep andshallow components, Qd and Qs, respectively.

H2(t) to define MJO phases. To reduce uncertainties due
to small amplitudes of H1(t) and H2(t), defined as AH(t) 5[H1(t)2 1 H2(t)2]1/2, composites were made only whenAH(t) . AH0, where AH0 is a threshold. The Real-TimeMultivariate MJO (RMM) index of Wheeler and Hendon(2004) was also used (section 3d).

e. MJO composite
Composites (indicated by a caret) can be made foreach of the MJO phases (m 5 1, 2, . . .) using reconstructed heating of the deep component,^ MJO (x, z, m) 5Qd 
^ MJO (x, m),åQMJO(x, z, t) 5 Rd (z)P
d
d
t2m
(4a)

the shallow component,^ MJO (x, z, m) 5Qs 
^ MJO (x, m),åQMJO(x, z, t) 5 Rs (z)P
s
s
t2m
(4b)

or their combination,^ MJO (x, z, m) 5 Q^ MJO (x, z, m) 1 Q^ MJO (x, z, m). (4c)Qdsds
Without the deep and shallow decomposition, composites can be made using total heating Q,^ MJO (x, z, m) 5Qtotal

å Q(x, z, t),

(4d)

t2m

or its intraseasonal anomalies,^ MJO (x, z, m) 5Qintra

å Q9(x, z, t).

(4e)

t2m

MJO phases can be defined using any MJO index. In thisstudy, we first used the HSVD time series H1(t) and3. Results
Before applying any diagnostic tool, we first demonstrate that MJO signals can be seen in the latent heating data of TRMM without any statistical manipulation.
Figure 4 shows time–longitude diagrams of verticallyaveraged latent heating in the tropics (158S–158N) for an
arbitrarily chosen period. Eastward propagation of concentrated heating at a speed of roughly 5 m s21 (black
straight lines) can be seen over the Indian and western
Pacific Oceans and sometimes farther eastward withsmaller amplitudes. This is no surprise. The spatial distribution and temporal variability of vertically averaged
latent heating must match those of surface precipitation.
MJO signals can be seen in precipitation without any
statistical assistance (Zhang 2005). The most obvious
differences among the four datasets are in their amplitudes. This results partially from different surface precipitation estimates (PR based for SLH, CSH, and PRH
versus TMI based for TRN) used to determine the amplitudes of latent heating, and partially from details in
the latent heating algorithms (e.g., underestimation of
convective heating in the lower troposphere by PRH).
Despite these discrepancies, the visible MJO signals in
unfiltered latent heating data of TRMM assure that theresults shown in the rest of this section are not statisticalartifacts.

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FIG. 4. Time–longitude diagrams of vertically averaged tropical (158S–158N) Q (K day21) for an arbitrary period.
The black straight lines mark eastward propagation of 5 m s21.

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FIG. 5. Time–space spectra of Pd(x, t) (REOF PC1). Amplitudes are scaled for best visual effects.

a. Spectrum
The MJO is such a prominent intraseasonal phenomenon that without any filtering its signal can be easily
identified from total time–space spectra of zonal wind andprecipitation (or OLR) as eastward spectral peaks thatare well distinguished from lower- and higher-frequency
power and much stronger than their westward counterparts (Zhang 2005). This is the case for TRMM latentheating datasets as well. Figures 5 and 6 show time–
space spectra of the PCs of the deep and shallow components of heating anomalies [i.e., Pd(x, t) and Ps(x, t)]without any filtering except smoothing of the contours.
For the deep component (Fig. 5), all four TRMM datasets exhibit robust MJO spectral peaks centered at an
eastward (positive) period of 50 days and zonal wavenumber 1, as seen in precipitation. The MJO spectral
signals for the shallow component (Fig. 6) are less prominent. There is stronger westward intraseasonal power in
SLH and TRN. The eastward intraseasonal powerin PRH is weak but still discernable. Nevertheless, similar to the deep component, the spectral peaks of theshallow component are all centered near 50 days andzonal wavenumber 1. These spectra unambiguously indicate the existence of MJO signals in the deep andshallow components of the TRMM latent heating datasets and therefore justify the application of intraseasonalfiltering to further isolate the MJO signals as described in
section 2c.
There are spectral peaks at higher frequencies (period ’ 23 days) at zonal wavenumbers 2–4 for the shallow components, which are particularly strong in SLH
and PRH. They also exist in the spectrum for the deep
component of CSH. They have comparable amplitudes
at the positive and negative frequencies, implying a possible stationary nature. These spectral peaks are likely to
be unphysical, caused by the aliasing of the diurnal cycle
onto the 23-day repeat cycle of TRMM’s precessing orbit (Negri et al. 2002). Their existence, however, does
not affect the diagnosis of the MJO. They are not included in the intraseasonally band-passed (30–90 days)
anomalous time series used in the rest of the study. In
fact, similar results were obtained from 20–90-day bandpass filtered time series.

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FIG. 6. As in Fig. 5, but for Ps(x, t) (REOF PC2).

b. HSVD modes
As described in section 2c, MJO signals were extracted from total intraseasonal heating using an HSVD
analysis applied to the deep and shallow components
combined. The first two HSVD modes are well separated from their neighboring modes according to theNorth et al. (1982) criterion. Their zonal scale (zonal
wavenumber 1–2) matches well that of the known MJO
scales, and their fractional variances are 74% (SLH),
73% (CSH), 76% (PRH), and 79% (TRN), respectively. These two modes together are taken to represent
the MJO.
The third and fourth HSVD modes are also well
separated from their neighboring higher modes. Their
fractional variance is at most 12%. Their zonal scales(zonal wavenumber 4) are smaller than those of the firsttwo modes and the MJO. Reconstructed heating basedon the third and fourth modes propagate eastward in
SLH and CSH, but westward in PRH and TRN. These
two modes are not included in the MJO representationof this study. The physical interpretations for the thirdand fourth HSVD modes, if they are not artifacts, should
be reported in a separate study.
For all four TRMM datasets, correlation between thePCs of the first two HSVD leading modes reaches
maximum at a lag of about 2–3 pentads (not shown).
This indicates a period of 40–60 days, consistent with the
known MJO time scales and the spectra in Figs. 5 and 6.
The eigenvectors of the two leading HSVD modes [seeEq. (2)] are shown in Fig. 7. In all four TRMM datasets,
the eigenvectors for the deep component (Xd1 and Xd2)
have significant amplitudes only over the Indian andwestern Pacific Oceans and the phases of the first andsecond HSVD modes are in quadrature with each other(Fig. 7, left panels). These are typical features in the eigenvectors of the leading modes for the MJO that canalso be derived from other variables (e.g., Wheeler andHendon 2004). The eigenvectors for the shallow component (Xs1 and Xs2) show less consistent structuresand phase relationships across the four TRMM datasets (Fig. 7, right panels). Their quadrature phase relations are less obvious in some datasets (e.g., PRH)
than others (e.g., CSH and TRN). This is another example

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FIG. 7. Eigenvectors of the first (n 5 1, solid) and second (n 5 2,
dashed) HSVD modes of the (left) Xdn and (right) Xsn. Amplitudes
are scaled for better comparison of the phases.

that the retrievals of heating due to shallow convection
and warm rain by the four TRMM algorithms are not incomplete agreement.

c. Variance
Zonal distributions of variance in the deep and shallow components of unfiltered latent heating are shownin Fig. 8, which was calculated using their REOF PCs(Pd and Ps). The variability in the deep components is
at least an order of magnitude greater than the shallow
components. Whereas the vertical structures of the deepand shallow components of latent heating exhibit zonal
ubiquity, as seen in Fig. 2, the amplitudes of their temporal fluctuations vary substantially in longitude. Three
convective centers over the Indian Ocean–Maritime
Continent–western Pacific, South America, and Africa
are clearly seen in both deep and shallow componentsof latent heating. Three local minima are over the western Indian, eastern Pacific, and eastern Atlantic Oceans,
all characterized with relatively low sea surface temperature (SST). This zonal distribution is expected from thatof mean precipitation. The almost identical zonal distributions of the variance in the deep and shallow components, different amplitudes notwithstanding, suggest thatthey are both modulated by the same factors: zonal distributions of the land–sea contrast and SST.
Zonal distributions of variance in the deep and shallow components of MJO latent heating (e.g., PdMJO and) are shown in Fig. 9. As for the total heating, thePMJOsvariability of the deep components is an order of magnitude greater than the shallow components. For all four
TRMM datasets, the strongest MJO heating, including

FIG. 8. Variance (K2 day22) of Pd (solid) and Ps (dashed). The
amplitudes of the shallow components are amplified 10 times (20for SLH).

both its deep and shallow components, is confined to theIndian and western/central Pacific Oceans. There is an
obvious local minimum in the deep components over
the Maritime Continent in all four datasets. The exact
longitude of this minimum varies only slightly. The
strength of MJO latent heating is comparable over theeastern Indian and western Pacific Oceans. The Maritime Continent minimum is a unique feature of the MJO,
also seen in its precipitation (Waliser et al. 2009). No suchminimum over the Maritime Continent in the varianceof total latent heating can be clearly identified (Fig. 8).
MJO heating in other equatorial regions is much weaker,
despite strong total latent heating there, especially overtropical South America and Africa (Fig. 8). Robust MJO
signals in wind and OLR along the intertropical convergence zone (ITCZ) have been detected over the eastern
Pacific (Maloney and Esbensen 2003), but these signals
are very local and relatively weak in the global MJO
derived from the HSVD analysis. They are visible, however, as a secondary peak over the eastern Pacific in thevariance of the deep component of total intraseasonallatent heating (P9d, not shown) and in the composite of
total heating (section 3d).
Among the four TRMM datasets, the zonal distributions of the deep components of MJO latent heating

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FIG. 9. As in Fig. 8, but for PdMJO (solid) and PsMJO (dashed). The
amplitudes of the shallow components are amplified 20 times.

agree well. In contrast, distributions of the shallow components of MJO latent heating differ substantially, except for relatively large variability over eastern Indian
and western Pacific Oceans. The peaks of their varianceare located at different longitudes, with a single peak for
SLH and TRN and double peaks for CSH and PRH.
Figures 8 and 9 together imply, again, that uncertainties
in the shallow components of the four TRMM datasetsare larger than those in the deep components.

d. Composite
Reconstructed heating profiles of both deep and shallow components exhibit a systematic eastward propagation, as expected from their spectra (Figs. 5 and 6), fromthe Indian to central Pacific Oceans. Their phase relationships can be examined through composites of the^ MJO (x, m) for^ MJO (x; m) and P
REOF PCs, namely Pds
MJO phases (m 5 1, . . . , 8), based on Eqs. (4a) and (4b).
These composites are shown in Fig. 10. MJO phases
were defined using the HSVD PCs (H1 and H2) ina similar way as using the RMM index in Wheeler andHendon (2004). The amplitude threshold for the composite AH0 (section 2d) was set to 1.5 standard deviations of AH. For each dataset, H1 and H2 are unique.
No effort was made to define the phase based on thelongitudes of the maxima or minima of the composites.
The continuous eastward propagation in both deepand shallow components of all TRMM datasets starts

VOLUME 67

over the Indian Ocean with amplitudes maintained
through the western Pacific. As seen before, outside theIndian and western Pacific Ocean region, the deep components are very weak, but the shallow components
exhibit visible variability over the eastern Pacific andAtlantic Oceans.
The relative phases of the shallow and deep components vary substantially among the four latent heating
datasets. In three of them (SLH, CSH, and PRH), theshallow and deep components are almost completely outof phase over the Indian and western Pacific Oceans.
One may get an impression that the shallow components
lead (to the east of) the deep components. But this phaserelationship is not nearly as clear as that observed for
the MJO events during TOGA COARE and reconstructed using a multiyear global reanalysis time series(Lin et al. 2004; Kiladis et al. 2005), in which shallow
heating immediately precedes (or is located east of)deep heating. This can be clearly seen only in TRN(Fig. 10d).
The phase relationship between the deep and shallow
components can be further examined through composites at a given longitude following a different approach.
First, ‘‘major’’ MJO events, defined as those with AH
greater than the standard deviation for at least 30 consecutive days, were selected. Those events were thenmade into composites over 50 days centered at the dayof the heating peak at a given longitude reference point.
Figures 11 and 12 show such composites at 908 and
1508E, respectively. They are very similar. The shallow
components (contours) lead the deep ones (colors, left
panels) by 15–20 days in all datasets but TRN, in which
the lead is about 5 days. The maximum shallow cooling
5 days behind the deep heating maximum in SLH, CSH,
and PRH may imply trailing stratiform precipitation. In
the deep and shallow combined MJO heating field^ MJO in Eq. (4c), right panels of Figs. 11 and 12], there[Qds
is a sign of low-level heating preceding the main heating
centers of the MJO but no visible indication of trailingstratiform-like upper-level heating following the main
deep heating maxima. The level of the low-level heating
varies among the datasets. It is the highest in PRH andlowest in CSH, as seen earlier. The subtle phase change
related to low-level heating is more visible following thezero contours than following the amplitude (colors),
mainly because the shallow component is much weaker
than the deep one.
The composites in Figs. 10–12 are all based on the
TRMM latent heating data alone. The purpose of thishas been stated in section 1, which is to determine the
MJO signals in latent heating independent of other variables. One might be concerned about information degeneration in such practice: the definition of the MJO andNOVEMBER 2010

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FIG. 10. Composite PdMJO (solid) and PsMJO (dashed) as functions of longitude and MJO phases (indicated in theupper right corners) defined by H1 and H2. Each curve was scaled by its standard deviation for a better visual effect ofphase relationships.

the quantity made into the MJO composite are the same.
Next, we relaxed our constraint in two ways: we used
an independent MJO index, the RMM of Wheeler andHendon (2004), to define the MJO phases and we used
intraseasonal anomalous time series of the deep andshallow components combined (Q9d 1 Q9s) instead of theleading modes from the HSVD analysis. The only remaining constraint in the composites is the REOF decomposition of the deep and shallow components. The
results are given in Fig. 13. The eastward propagation

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FIG. 11. Composite latent heating profiles (K day21) as functions of time at 908E for (left) the deep (colors) andshallow (contour interval 5 0.05 K day21) components and (right) deep and shallow components combined. Zeros
are marked by white contours.

and the deep heating structures of the four datasets agree
well with each other in general. Interestingly, the local
minimum over the Maritime Continent seen in the variance of the deep components (Fig. 9) is manifested here
as a temporary weakening of the deep heating peak inphase 4. There are secondary deep heating peaks overthe eastern Pacific, likely related to the MJO activity

there (Maloney and Esbensen 2003), which propagate
into the Atlantic. This eastern Pacific MJO coexists with
the MJO over the western Pacific and the two propagate
eastward simultaneously in a semi-synchronized fashionin phases 6, 7, 8, and 1. The eastern Pacific MJO is thus
distinguished from the western Pacific MJO but may betriggered by the latter (Small et al. 2010).

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3503

FIG. 12. As in Fig. 11, but at 1508E.

Shallow heating preceding deep heating seen fromthe previous composites is also shown in Fig. 13. Again,
it is easier to see by following the zero contours than thecolors (amplitude) because of the weak shallow components. This structural evolution is more visible in SLH
and TRN than the other two and exists only over the
Indian and western Pacific Oceans. There is no such
structural evolution over the eastern Pacific Ocean eventhough eastward propagating signals representing the
MJO are evident there.

4. Summary and discussion
Motivated by the potential importance of structural
evolution of latent heating to MJO dynamics (section 1),
we examined and compared MJO signals in four latent

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FIG. 13. Composites of intraseasonal anomalous latent heating (K day21) with the deep and shallow components
combined as functions of longitude and MJO phases (indicated in the upper right corners) defined by the RMM index(Wheeler and Hendon 2004). Zeros are marked by white contours.

heating datasets derived from TRMM observations.
Similarities in these datasets may lend us confidence intheir credibility. Their discrepancies, due to differencesin their algorithms, point to the uncertainties and needfor improvement in the datasets and the caution thatmust be exercised in their applications.

The gross vertical structure of latent heating in thetropics (averaged between 158S and 158N) and its variability can be well represented by the eigenvectors of
the two leading REOF components, one deep with its
peak above the melting level and one shallow with its
peak below (Fig. 1). The eigenvectors of the two leadingNOVEMBER 2010

ZHANG ET AL.

REOF components are nearly ubiquitous in longitude(Fig. 2). Almost all zonal and temporal variability intropical latent heating resides in the principal components (PCs) (Fig. 3). This allows a separation of variables that decomposes the latent heating field in thetropics into two independent parts: its vertical structures
represented by the deep and shallow components, andits longitudinal and temporal variability represented by
the PCs. Latent heating associated with the MJO can be
diagnosed by first extracting MJO signals from its zonal
and temporal variability and then recovering its verticalstructures using the REOF eigenvectors (i.e., the deepand shallow components).
Following this approach, we have focused on the structural variability in latent heating of the MJO in longitude and time. The main results are as follows:
1) There are clear spectral signals of the MJO in both
deep and shallow components of latent heating. The
intraseasonal (50 days), planetary-scale (zonal wavenumber 1), and eastward moving spectral peaks arewell distinct from spectral power at lower and higher
frequencies. The spectral signal of the MJO is much
more robust (much stronger than the corresponding
westward power) in the deep component than theshallow one (Figs. 5 and 6). MJO signals in deep andshallow components of latent heating were successfully extracted from their intraseasonal anomalies by
an HSVD analysis.
2) The strongest MJO signals in both deep and shallow
components of latent heating are confined to theIndian and western Pacific Oceans. Deep components
exhibit an obvious local minimum over the Maritime Continent. Detailed zonal distributions of the
MJO shallow components of the four TRMM datasets, however, disagree substantially (Fig. 9).
3) There are signs of the shallow component immediately leading (to the east of) the deep component.
However, this is obvious only in certain datasets at
certain longitudes (Figs. 10 and 13).
4) MJO signals propagating from the eastern Pacific to
the Atlantic coexist in synchronization with thoseover the western Pacific (Fig. 13).
These results lead to several implications. The strong
evidence of MJO signals in latent heating provides justification for using it in combination with other variables
to seek their coherence in the context of the MJO (e.g.,Morita et al. 2006; Lau and Wu 2010). The synchronizedcoexistence of the western and eastern Pacific MJO
during a half of the life cycle of the global MJO may
explain the extension of the MJO spectral peak fromzonal wavenumber 1 to 2 (Fig. 5) and also suggests that3505

the former may act to trigger the latter. The consistentbehaviors of the MJO signal in the deep component inall four latent heating datasets, compatible with the expectation based on known MJO signatures in precipitation, suggest the reliability of these datasets in detecting
latent heating due to deep convective cloud systems. In
contrast, the disagreements among the four datasets inthe shallow components in general (their mean verticalprofiles in Figs. 1 and 2), in their zonal distributions (Fig. 8),
and in their MJO signals (the eigenvectors in Fig. 7 andthe variance distributions in Fig. 9) indicate that thechallenge of retrieving latent heating by shallow, warmrain cloud systems has yet to be met.
The previously reported vertical tilt in MJO latentheating (Lin et al. 2004; Kiladis et al. 2005) is not confirmed without ambiguity in this study. Such tilt consistsof two features: shallow heating preceding (to the eastof) main deep heating in the MJO convection center,and trailing stratiform-like heating in the upper troposphere behind (to the west of) the MJO convection center. Shallow heating leading deep heating can indeed befound but only in some TRMM datasets and at certain
longitudes. No trailing stratiform-like heating behind(west of) the main heating center of the MJO is detected in this study. There are several possible explanations for this. First, the westward tilt was previously
reported in total diabatic heating. Radiative heating could
contribute significantly to the total diabatic heating when
the precipitation rate is low and latent heating is relatively weak during the transition period from convectively inactive to active phases of the MJO. If so, latentheating alone may not yield the tilt. Two TRMM datasets (CSH and TRN) provide both latent heating andtotal diabatic heating. We applied the same diagnosis
to their total diabatic heating and the results are notvisibly distinguishable from those of latent heating.
MJO signals from the radiative heating component QR
cannot be diagnosed using the same approach. It does
not have any zonally ubiquitous deep or shallow components.
Second, the westward tilt in latent heating may occur
only to a subset of MJO events, which happened to include those observed by the TOGA COARE data usedin the previous reports (Lin et al. 2004; Kiladis et al.
2005). This possibility is implied by recent case studies
using two TRMM latent heating datasets (TRN and an
earlier version of CSH), two data assimilation products
over a season with multiple MJO events (Jiang et al.
2009), and in situ sounding observations from the Indian
Ocean for a particular MJO event (Katsumata et al.
2009). These studies did not find any obvious shallow
leading deep heating in latent or total diabatic heating
profiles during individual MJO events. If this is the case,

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we should not expect a strong signal of the tilt in ourcomposites.
Third, as discussed before, deficiencies in retrieving
shallow heating from TRMM observations may makethem unsuitable for detecting the structural evolution
through the life cycle of the MJO. Other TRMM observations have, however, shown clearly that shallow
convection tends to lead deep convection in the MJO
life cycle (Kikuchi and Takayabu 2004; Masunaga et al.
2005; Lau and Wu 2010). This strongly suggests a systematic structural change in the latent heating field thatis consistent with the westward tilt. More careful comparisons between TRMM retrievals of latent heating andother measures of convective cloud properties may yielduseful information on this.
Finally, the decomposition into the deep and shallow
components may not be adequate to fully resolve thestructural evolution in latent heating. Higher modes may
be needed to represent stratiform-like heating in theupper troposphere. When the same REOF decomposition of deep and shallow heating was applied to total
diabatic heating profiles based on sounding observations,a shallow–deep stratiform heating structural sequence
was clearly resolved, but not specifically for the MJO(Zhang and Hagos 2009).
To further address some of these issues, we are currently examining the latent heating structure and evolution associated with the MJO using a different approach:comparing latent and total diabatic heating fields (nodeep versus shallow decomposition) from TRMM andglobal reanalysis products, scrutinizing latent heating
structures in individual MJO events in detail during
and outside the TOGA COARE period, and combining latent heating with other variables deemed important to MJO dynamics. Results will be reported
separately.
This article demonstrates the utility and uncertaintyof TRMM latent heating retrievals in the study of the
MJO and calls for further scrutiny of the issue regarding
the structural evolution of latent heating through the life
cycle of the MJO. In our view, whether shallow heating immediately preceding MJO convection centers andstratiform-like heating immediately following them areessential features of the MJO and whether they playindispensible roles in MJO dynamics remain as open
questions.

Acknowledgments. The authors thank David Raymondand two anonymous reviewers for their constructive
comments, which helped improve the presentation ofthis study. This study was supported by NASA Grant
NNX07AD41G.

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