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Observed Self-Similarity of Precipitation Regimes over the Tropical Oceans
GREGORY S. ELSAESSER, CHRISTIAN D. KUMMEROW, AND TRISTAN S. L’ECUYER
Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

YUKARI N. TAKAYABU
Center for Climate System Research, University of Tokyo, Kashiwa, Chiba, and Institute of Observational Research
for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Kanagawa, JapanSHOICHI SHIGE*
Department of Aerospace Engineering, Osaka Prefecture University, Osaka, Japan(Manuscript received 6 July 2009, in final form 3 December 2009)
ABSTRACTA K-means clustering algorithm was used to classify Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) scenes within 18 square patches over the tropical (158S–158N) oceans. Three cluster
centroids or ‘‘regimes’’ that minimize the Euclidean distance metric in a five-dimensional space of standardized variables were sought [convective surface rainfall rate; ratio of convective rain to total rain; andfractions of convective echo profiles with tops in three fixed height ranges (,5, 5–9, and .9 km)]. Independent cluster computations in adjacent ocean basins return very similar clusters in terms of PR echo-top
distributions, rainfall, and diabatic heating profiles. The clusters consist of shallow convection (SHAL cluster), with a unimodal distribution of PR echo tops and composite diabatic heating rates of ;2 K day21 below
3 km; midlevel convection (MID-LEV cluster), with a bimodal distribution of PR echo tops and ;5 K day21
heating up to about 7 km; and deeper convection (DEEP cluster), with a multimodal distribution of PR echo
tops and .20 K day21 heating from 5 to 10 km. Each contributes roughly 20%–40% in terms of total tropicalrainfall, but with MID-LEV clusters especially enhanced in the Indian and Atlantic sectors, SHAL relatively
enhanced in the central and east Pacific, and DEEP most prominent in the western Pacific. While the clusters
themselves are quite similar in rainfall and heating, specific cloud types defined according to the PR echo top
and surface rainfall rate are less similar and exhibit systematic differences from one cluster to another, implying that the degree to which precipitation structures are similar decreases when one considers individual
precipitating clouds as repeating tropical structures instead of larger-scale cluster ensembles themselves.

1. Introduction
A variety of precipitating clouds, categorized by their
vertical extent and rainfall characteristics, have been
observed over the tropical oceans (e.g., Warren et al.
1985; Masunaga and Kummerow 2006). Even though the* Current affiliation: Division of Earth and Planetary Sciences,
Graduate School of Science, Kyoto University, KitashirakawaOiwake-cho, Sakyo-ku, Kyoto, Japan.

Corresponding author address: Gregory Elsaesser, Department
of Atmospheric Science, Colorado State University, Fort Collins,
CO 80523-1371.
E-mail: elsaesser@atmos.colostate.edu
DOI: 10.1175/2010JCLI3330.1
Ó 2010 American Meteorological Society

distribution of precipitating clouds is continuous in nature, a number of studies have consistently shown that
dominant ones emerge from the spectrum: three convective types, consisting of shallow cumuli, congestus
cumuli, and deep precipitating cumulonimbi (Johnson
et al. 1999), and a nonconvective stratiform type, considered to be, in large, a by-product of deep convective
activity in the tropics (Houze 1997). Given a particularbasin, the longer-term temporal mean state of precipitating convection can be thought of as comprising the
average prevalence of each convective and the attendant
stratiform precipitating cloud type. Over the past few
decades, satellite and in situ studies have sought todocument both the mean characteristics of precipitating
convection across the tropics, as well as the differences

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that exist from one basin to another. Consistently, anumber of observational studies have shown that thestatistical average heating rate, rainfall rate, cloud fraction,
cloud type, and spatial extent of rainfall systems is nothomogeneous across the tropical oceans (e.g., Houze andBetts 1981; Berg et al. 2002; Masunaga and Kummerow
2006; Zuidema and Mapes 2008).
Despite the documented dissimilarities in the mean
precipitation states, uncertainty remains regarding theextent to which a particular precipitation regime (containing a particular distribution of precipitating clouds)
occurring in one geographic basin resembles the same
regime type occurring in another basin. Specifically, it remains unclear whether or not the proportions of each cloudtype (shallow precipitating cumulus, congestus, and deep
convective) are approximately constant given the presenceof a particular precipitation regime, to what extent precipitation regimes are mixed in terms of cloud types, andhow similar particular precipitating cloud types are fromone basin and one precipitation regime to another.
There is continued motivation, then, to determine
whether or not precipitation regimes can be describedfrom an instantaneous perspective with universal descriptors versus describing precipitation from a longer
temporal mean perspective. This study explores thenature of precipitation regimes through considerationof the ensemble of precipitating clouds (beyond themost prevalent cloud type) belonging to a precipitation
regime, with further investigation into how consistenteach regime’s spectral cloud ensemble is as a functionof a tropical ocean basin. Precipitation regimes are objectively identified and characterized using a commonclustering framework applied separately and independently to adjacent geographic basins spanning the entire
tropics, with the intention of diagnosing the extent towhich regimes are similar. It is assumed a priori that
regimes contain a mixture of precipitating cloud types
and, therefore, individual precipitating clouds are notisolated so as to avoid compositing similar precipitating
clouds from different regimes. The role of each cloudtype within the precipitation regimes, in terms of theircontribution to regime diabatic heating, is also investigated using new satellite-based products.
Results are presented that support a stronger idea ofprecipitation regime self-similarity by considering a regime comprising an ensemble of precipitating clouds asa whole, rather than considering precipitating clouds
independent of the precipitation regime in which they
are developing. These precipitation regimes in their entirety may better serve as repeatable, recurring ‘‘building
blocks’’ of the mean state of tropical precipitation insteadof considering individual precipitating clouds as thebuilding blocks themselves.

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2. Data sources
The primary data products used are derived from instruments onboard the Tropical Rainfall Measuring
Mission (TRMM) satellite. The period of study consistsof 24 months from June 2006 to May 2008. Both TRMM
Precipitation Radar (PR) attenuation-corrected radarreflectivity (ZE) profiles (surface to 20 km) and surface
rainfall rates at the PR native spatial resolution (approximately 5 km) are used and are provided in thestandard TRMM PR 2A25 product (hereafter the 2A25
product; Iguchi et al. 2000). For each PR pixel classified
as convective, the precipitation-top height (PTH) corresponding to the observed precipitating cloud is computed. The PTH is the altitude of the highest radar echo
above the earth’s surface with a reflectivity of at least
17 dBZ (further details in Short and Nakamura 2000). A
new dataset is created, with a 18 horizontal resolution
centered on nadir PR pixels for all TRMM orbits, where
each sample now comprises all PTHs associated with thespectrum of precipitating convective clouds that arepresent in the 18 grid. The decision is made to consider
the distribution of PTHs within a 18 grid for the following three primary reasons: 1) the root-mean-square(RMS) error variances in the ancillary diabatic heatingproducts decrease as the spatial averaging widths increase; 2) the desire to capture the statistical distributionof cloud PTHs present at some instantaneous time ina larger-scale regime requires the consideration of larger
box widths; and 3) the nature of the PR scan geometry
leads to an undersampling of shallow cloud PTHs for
pixels significantly off-nadir, and, therefore, a coarserthan-18 resolution leads to PTH distributions that arebiased with respect to the number of shallow precipitating clouds that are present. The average rainfall rate foreach type of precipitating convective cloud, the average
stratiform rainfall rate, diabatic heating, and the numberof nonconvective and nonraining pixels are also stored foreach 18 sample.
The apparent heat source (Q1; Yanai et al. 1973) is the
diabatic heating associated with unresolved cloud processes occurring in a rainfall regime. Here, Q1 can be
written as
Q1 5

›
›
›
s 1 $  (sV) 1 s v 5 QR 1 LH 
s9v9,
›t
›p
›p
(1)

where the total change in the dry static energy (s 5
cpT 1 gz), horizontally averaged over a specified domain
size (as indicated by the overbar), is given by the sum of
three horizontally averaged diabatic heating components: the radiative heating rate (QR), the latent heating
rate resulting from phase changes of water (LH), and the2688

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FIG. 1. (left) The distribution of rainfall as a function of convective cloud PTH for basins
spanning the tropical oceans. Distributions are normalized to account for differences in total
rainfall in each basin (see text for further description). (right) The average Q1 profile for eachbasin is illustrated.

heating resulting from vertical eddy heat flux (s9v9) convergence (the primes indicate a departure from a horizontalmean). A term incorporating the effects of horizontal
eddy heat fluxes is assumed to be small, and has not been
derived. The spectral latent heating algorithm product(SLH product; Shige et al. 2004, 2007) is used for quantification of the latter two components of the right-handside of Eq. (1). These combined components are mathematically equivalent to Q1 2 QR (occasionally referred
to as Q12R). Heating profiles are available for each
TRMM PR pixel at the PR native resolution. The SLH
algorithm takes into account the vertical extent of theconvection and is therefore able to differentiate shallower heating structures from deeper heating structures
corresponding to various vertically extended precipitating clouds. It is important to note that the SLH algorithm estimates heating resulting from precipitation
processes only, as discussed in Shige et al. (2007). The
Q12R is averaged to the same 18 grids described above,and the heating profile represents the composite effectof the various precipitating clouds that are present in a
rainfall regime. Horizontal averaging also has the effectof reducing the RMS error variance associated with theheating estimates (Shige et al. 2007).
The Hydrologic Cycle and Earth Radiation Budget(HERB) algorithm produces radiative heating profiles(QR) at 0.258 horizontal resolution and 1-km verticalresolution (L’Ecuyer and Stephens 2003, 2007; L’Ecuyer
and McGarragh 2010). The algorithm utilizes cloud andprecipitation information in conjunction with atmosphericwater vapor, temperature profiles, and surface variables
derived using sensors onboard the TRMM satellite, andincorporates a radiative transfer model that simulatesvertical profiles of longwave (LW) and shortwave (SW)radiative fluxes. Heating rates are then derived using

radiative flux divergences, and these estimates are averaged to 18 [these represent the first term on the right-handside of Eq. (1)]. Only data from June 2006–December
2007 are used in this study because the satellite data fromJanuary 2008 onward are not yet processed. The verticalprofiles of QR are smoothed using a 3-km boxcar-averaging
window because the nominal 1-km vertical resolution of
the product is likely coarser due to the sole use of passive
remote sensing techniques for determining cloud boundaries in the algorithm (L’Ecuyer and McGarragh 2010).

3. Precipitation regime identification andself-similarity
Figure 1 shows the temporal mean state of precipitationand the associated Q1 for five adjacent geographic regions
spanning the tropics for the time period under study.
These five regions extend meridionally from 158S to 158N
over the tropical oceans and are labeled according to theocean basin they predominantly encompass [see Fig. 4;
Indian (INDI), west Pacific (WPAC), central Pacific(CPAC), east Pacific (EPAC) and Atlantic (ATLA)].
Zonally, INDI extends from 308–1008E, WPAC from1008–1708E, CPAC from 1708–2208E, EPAC from 2208–
2908E, and ATLA from 2908–3608E longitude. It is fromthis background mean precipitation state that prevalentprecipitation clusters or ‘‘regimes’’ are extracted.
The left panel of Fig. 1 shows the normalized rainfall
histograms as a function of cloud PTH. Histograms havebeen normalized as in Berg et al. (2002, their Fig. 8), suchthat the maximum rainfall value is equal to 1 and the area
under the rainfall curve is the same for each basin. In
the average sense, because the total accumulated rainfall is quite different for each basin, normalizing in thismanner allows for the easier comparison of rainfall

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histograms and allows one to determine which cloudtypes play the largest role in rainfall accumulation foreach basin. Upon inspection of Fig. 1, it becomes clearthat rainfall distributions for various tropical basins areneither simply scaled by a constant nor are they unimodal. There is a distinct shift in the types of precipitating
clouds that produce most of the rainfall as one traverses
geographic basins in the tropics. Because the majorityof the rain falls from deeper clouds in the Indian andwest Pacific basins (left panel of Fig. 1), one would expectthat Q1, on average, is larger in magnitude at higher altitudes compared to the other basins, a result that is seenin the right panel of Fig. 1. Like the rainfall histograms,
Q1 profiles are not unimodal either, with peak heatingnear 2 and 6–8 km. These results are consistent with thestudies summarized in section 1 noting differences inrainfall and heating across the tropics, as well as the differences in the numbers of various precipitating cloudtypes across the tropical oceans.
The focus now turns toward determining if dominantprecipitation clusters can be extracted from the meanstate. Precipitation clusters are identified through the useof a simple K-means clustering algorithm (Anderberg
1973). A number of recent studies (Jakob and Tselioudis
2003; Boccippio et al. 2004; Jakob et al. 2005; Rossow
et al. 2005; Zhang et al. 2007; Caine et al. 2009) used thissame technique to identify cloud and precipitation regimes, and the results show the usefulness of the technique. A cluster is assumed to always contain a spectrumof precipitation clouds. To capture the ensemble, the Kmeans algorithm is applied to five variables in each 18 gridbox: the number of clouds with PTHs less than 5 km, thenumber of clouds with PTHs from 5 to 9 km, the numberof clouds with PTHs greater than 9 km, the convective
rainfall rate averaged over all pixels identified as convective, and the ratio of the average convective rainfall
rate to the average rainfall rate (defined as the averageover all of the raining pixels). The first three variables arenormalized by the number of convective precipitation
pixels in the grid box. All five variables are standardized,
and the K-means algorithm is then applied to all 18 grid
samples for each ocean basin (independently) across thetropics. The algorithm seeks to find the centers of naturalclusters present in a dataset. One begins by specifying
both the number of clusters and the initial data centers(termed centroids, and they are chosen at random). The
technique involves assigning each 18-grid (a data point)
membership to a particular cluster based on a minimum
Euclidean distance measure. The distance is defined as
the sum of the squared differences between each centroid
variable and the same variable corresponding to the data
point. After evaluating the entire dataset, centroids arerecomputed by computing the new mean of each variable

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for all data points belonging to a particular cluster. The
algorithm proceeds in an iterative manner, and when thecentroid of the current iteration is the same as that ofthe previous iteration (decided based on the sum of thesquared differences in the centroid variables from one
iteration to the next), the specified convergence criterion
is met and a solution is found.

a. Regime cloud-top distributions and rainfall
Three precipitation clusters emerge in each basin; together, they explain approximately 60% of the variationin the five clustering variables across the tropical oceans,a magnitude that is consistent for each geographic basin.
The percent of explained variance increases much lessrapidly upon the consideration of additional clusters;
therefore, the a priori choice of the three clusters is considered reasonable. Over 100 iterations of the clustering
algorithm were executed for each ocean basin, using arandom assignment for first-guess centroids each time.
The precipitation clusters were found to be largely invariant to the initial centroid assignment, providing aheuristic measure of the robustness of the results.
Figure 2 shows the relative frequency of occurrence(RFO) distributions for clouds of given PTHs for the threeclusters. While a cluster is classified based on the predominant, most vertically extended precipitating cloud, eachcluster consistently contains a spectrum of precipitating
clouds. The shallow (SHAL) precipitation cluster in the
top panel of Fig. 2 is largely unimodal, and contains precipitating clouds with PTHs peaking in the 2–3-km altitude
range, with very few clouds having PTHs extending beyond 5 km. The cluster in the middle panel of Fig. 2 isconsistently bimodal in all basins, with a peak in cloud
PTHs near 3 km, and a prevalence of precipitating clouds
with PTHs extending from 5.5 to 9 km. This is classified asa congestus precipitation (MID-LEV) cluster and is sochosen based on the definition of precipitating congestus
clouds provided by Johnson et al. (1999)—namely, thatcongestus clouds are classified as such if their cloud tops
range from 5 to 9 km. The final precipitation cluster (classified as DEEP) consists of a shallow cloud PTH
peak near 3 km, and a broad second PTH peak extending in height up to 16 km, implying the existence of numerous congestus and progressively deeper precipitating
clouds. It should be noted that the distributions of precipitating clouds in Fig. 2 are fairly insensitive to thecurrent choice of PTH bin limits used for the first threeclustering variables described in the previous section. For
each cluster, the convective rain fractions can be determined by summing all of the RFO values for eachconvective cloud type (identified based on the cloud’s
PTH) shown in Fig. 2. These fractions are show in Table 1.

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TABLE 1. Rainfall and heating characteristics of precipitation
clusters.

Convective rain fraction (%)
Rain fraction (%)
Average surface rainfall (mm h21)
% of surface rainfall classified
as stratiform
hQ1 2 QRi (K day21)
hQRi (K day21)

FIG. 2. The distributions of PTH for the precipitating cloud
ensembles that characterize the SHAL, MID-LEV, and DEEP
precipitation clusters for all tropical ocean basins. The RFO iscomputed by dividing the number of clouds with a given PTH by
the number of pixels within each grid box.

SHAL

MID-LEV

DEEP

2.7
4.5
2.1
30

7.1
17.8
14.2
40

9.9
43.8
53.9
50

0.4
21.2

3.1
20.8

12.7
20.3

While it has been discussed that the number of precipitating clouds stratified by cloud PTH varies acrossthe tropics, the distributions of precipitating clouds areapproximately constant within each cluster, independent of the basin under study (Fig. 2). Additionally, the
MID-LEV and DEEP clusters are similar in distribution
and are multimodal for all basins, with one mode consisting of prevalent warm-rain clouds topping out below
the mean freezing level in the tropics, in close proximity to deeper precipitating clouds. The average rainfall
fractions (defined as the total number of raining pixels
divided by the total number of pixels in a grid box) are
shown in Table 1. The variations of both the convective
and total rainfall fractions with respect to the cluster
average magnitudes are on the order of 5%, further
implying that the ratio of stratiform-to-convective rain
fraction is approximately the same for each cluster as afunction of ocean basin, as well.
The distribution of convective rainfall parsed by PTH
for each cluster and each geographic basin is shown in
Fig. 3. The data analysis illustrated here is exactly thesame as that illustrated in the left panel of Fig. 1, except
the focus is shifted to a comparison of separate precipitation clusters for each geographic basin, and not thegeographic basin in its entirety (irrespective of precipitation cluster present). Whereas the rainfall distributions are quite different in the mean sense (Fig. 1), thedistributions track each other quite closely within eachcluster, and the dominant peaks for convective rainfall
production are quite similar for each basin given thepresence of a particular cluster. These peaks are around
2–3 km for the SHAL cluster, 6–7 km for the MID-LEV
cluster, and 8–9 km for the DEEP cluster. The shallower
precipitating clouds (associated with PTHs extending
from 3 to 4 km) that contribute to the bimodality in the
PTH distribution in the MID-LEV and DEEP clusters
also contribute to the bimodal rainfall histograms as
well, although the peaks are less pronounced.
In the time mean sense, the average surface rainfall
rate for 18 grids in each geographic basin varies, on average, by approximately 30% with respect to the tropical
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18 grids, so nonraining grids are included as well). If nonraining grids are neglected, the average difference decreases to approximately 16%, so a significant percentageof the average variation arises from notable differences in
the number of nonraining scenes that exist in each basin.
When stratifying by cluster, however, the rainfall-ratedifferences are typically under 5% for all basins withrespect to the cluster mean. The cluster average surface
rainfall rates are provided in Table 1.
For all grid boxes covering the tropical oceans, thevarious cluster contributions to total accumulated rainfall are shown in the top three panels of Fig. 4. The
SHAL cluster contributes 20%–25% of the total rainfall
in both the INDI and WPAC regions, and as one approaches the date line and continues eastward, the
SHAL cluster progressively contributes more toward
the net accumulated rainfall. In the EPAC basin, the
SHAL cluster contributes almost as much rainfall as the
MID-LEV cluster, and more than the DEEP cluster.
MID-LEV and DEEP clusters are observed everywhere
throughout the tropics, including outside of the intertropical convergence zone (ITCZ) regions, and, notsurprisingly, contribute significantly to the total rainfall
in each geographic basin.

b. Regime diabatic heating

FIG. 3. As in the top panel of Fig. 1, but the rainfall distributions
are now stratified by a precipitation cluster observed in each geographic basin.

The Q12R profiles for the three clusters are shown in
Fig. 5. Qualitatively, the profiles are quite similar foreach basin, and as the intensity of convection increases,
corresponding to a transition from SHAL to MID-LEV
to DEEP clusters, the peak and magnitude of Q12R increases. The convective (stratiform) Q12R is the mean of
the convective (stratiform) Q12R profiles corresponding
to each convective (stratiform) precipitating cloud present in the cluster. As the strength of the convection increases, corresponding to stronger and deeper convective
clouds, the anvil production of rainfall increases, and sodoes the stratiform signature of Q12R. The stratiform
signature is an order of magnitude smaller in the SHAL
cluster compared to the DEEP cluster. Because of thefact that stratiform rainfall production in the tropics is
considered primarily to be the result of convective activity (when considering a large enough spatial scale), a
sole stratiform rainfall cluster is not observed in thisstudy. Therefore, the issue could arise where stratiform
rainfall is significant outside of our identified clusters, farremoved from convective towers. The right panel of Fig. 5
shows that the Q12R profiles associated with the residual stratiform rainfall for each geographic basin is quite
small. The column-averaged (defined from the ocean surface to approximately 18 km) Q12R magnitudes for the
residual (or unclassified) locations are approximately
0.03 K day21. This is more than an order of magnitude

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FIG. 4. (from top to bottom) The percent contribution to the total accumulated rainfall by each precipitation
cluster as a function of ocean location; and, considering the five large geographic basins in their entirety, the percent
contribution to the total rainfall by each cluster.

smaller than the average SHAL cluster column-averaged
stratiform and convective Q12R combined. Consideringthat these samples make up less than 10% of the numberof raining samples, the contribution to total rainfall and
Q12R is minimal.
The total Q12R for each cluster and each basin isshown in Fig. 6, and is mathematically equivalent tothe addition of the convective and stratiform components in each precipitation cluster. The column-averaged
total Q12R magnitudes for the clusters are provided inTable 1. Regarding the profile characteristics, the SHAL
cluster Q12R peaks near 2 km (Fig. 6, center panel), andthe total Q12R profiles in the MID-LEV and DEEP clusters peak much higher in the atmosphere (6–8 km for theDEEP cluster). These peaks are both consistent in magnitude and altitude across all tropical ocean basins.
The radiative heating (QR) profiles for all clusters andbasins are shown in the left panel of Fig. 6. Because the
HERB QR algorithm uses additional, independent satellite observations for the cloud field characteristics andgeometry, investigating the QR profiles for each cluster

and for all basins can provide additional insight into thesimilarity of precipitation clusters. As the precipitation
cluster becomes deeper, the cooling below about 11 km
decreases in magnitude, likely resulting from the effectof increasing cloud cover at all altitudes leading to adecrease in the radiative flux divergences. Near thesurface, as the intensity of the cluster increases (from
SHAL to DEEP), QR rapidly approaches 0 K day21,
presumably because of an increasing peak in total cloud
cover in the lowest levels of the atmosphere (which istypical of more convectively active regimes), and theassociated increasing downward-directed LW flux. The
opposite trend occurs above 11 km, where radiative
cooling increases as the cluster becomes deeper, likely
resulting from the increasing cloud and anvil coveragein the 10–15-km range and the associated LW cooling tospace that occurs in the vicinity of higher cloud tops.
Increased cooling in the DEEP cluster aloft could also
be due to increased upper-tropospheric water vapor
associated with detraining deep convection leading
to increased LW emission. The column-averaged QR

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FIG. 5. The composite (left) convective and (middle) stratiform Q1 2 QR profiles for each of the precipitation clusters and eachgeographic basin, and (right) the residual Q1 2 QR profiles that remain unclassified for each basin. The SHAL (dashed), MID-LEV(dotted), and DEEP (solid) clusters are denoted in the left and middle panels.

magnitudes are shown in Table 1. These QR magnitudes
are quite different from each other, suggesting significant
differences in the cloud fields from one cluster to another.
However, the average differences of these magnitudes
with respect to the cluster-stratified QR magnitudes areon the order of 5% for all basins. This implies that given
the presence of a particular precipitation cluster, thecloud fields across the tropical geographic basins are
fairly similar.
Given the QR and Q12R components of diabatic heating, the apparent heat source Q1 can now be quantified
for each cluster and basin (Fig. 6). In heavily precipitatingclusters Q12R is much larger in magnitude than QR (resulting from the effects of latent heating), and therefore
QR serves to only slightly shift (negative direction) the
Q12R profiles for the MID-LEV and DEEP clusters; incontrast, QR has a larger impact in the weakly convecting
SHAL clusters because Q12R is comparable in magni-

tude. In these commonly observed SHAL clusters, Q1
shows cooling throughout the troposphere above 2–3 km,
and warming below resulting from the action of precipitating shallow cumulus clouds.
Provided with the relative frequency of occurrence ofeach cluster as a function of geographic basin, one can
now assess the contribution each cluster makes toward
the statistical basin-averaged Q1 profiles (bottom panel ofFig. 1). The 2-km peak in Q1, which is evident in all basins, is largely the result of the unimodal SHAL clusters
being present in most tropical oceanic locations. Specifically, 80% of the magnitude of this peak can be attributed
to the SHAL clusters (top panel of Fig. 7), which isa consistent result seen from one basin to the next. The
next peak in Q1, centered near 8 km, is contributed toheavily and almost equally by all clusters. The warming by convection in the MID-LEV and DEEP clusters
contributes positively to this peak, while radiative cooling

FIG. 6. The (left) QR, (middle) Q1 2 QR, and (right) Q1 profiles for each of the precipitation clusters and basins are shown. The clusters areindicated according to line style as in Fig. 5.

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in the SHAL clusters contributes negatively and decrease
the magnitude of this peak. Because deeper clusters areless prevalent in the eastern Pacific and Atlantic Oceans,the Q1 magnitude at this altitude is closer to 0 K day21(Fig. 1) because radiative cooling from the SHAL clusters
overwhelms the heating by the less prevalent deeper
convective clusters.

c. Cloud-type contributions to cluster Q1 profiles

FIG. 7. The percent contribution to the average Q1 by eachprecipitation cluster (as a function of altitude) for each ocean basin.

While a precipitation cluster is characterized according to the most prominent, vertically extended cloud
type, other precipitating cloud types consistently coexist
in the deeper clusters. There are three prominent peaks
in convective cloud PTHs that are clearly seen in thebottom two panels of Fig. 2: the first peak extends from0 to 5 km, the second from 5 to 9 km, and the third(mostly a DEEP feature) encompasses the deeper convective clouds with precipitation tops extending from 9
to 20 km. These three broad peaks are likely the resultof often-observed precipitating convective clouds andcan loosely be classified as precipitating shallow, congestus, and deep clouds, consistent with the definition
provided by Johnson et al. (1999) and others. Because
clusters have been shown to consist of well-defined
cloud ensembles, independent of the basin under study,
it is worthwhile to proceed with an investigation of therole each cloud type plays in terms of net heating observed in a cluster.
In the top-left panel of Fig. 8, the average MID-LEV
cluster Q1 profile is reconstructed by sequentially adding
in progressively shallower precipitating convective clouds
and associated Q12R profiles to the combined average
stratiform Q12R and QR profiles that are representativeof the cluster. In the top-right panel of Fig. 8, the relative
importance (in terms of the percent of contribution)of the particular cloud types (stratiform, shallow, congestus, and deep convective) to the MID-LEV Q1 profileis shown. The uppermost part of the Q1 profile in the
MID-LEV cluster (above 7 km) is mostly reproduced by
the stratiform component of Q12R (see the 90% contribution by the Strat 1 QR profile in the top-right panel ofFig. 8). The lower half of Q1 (lower than 7 km) is nearly
reproduced upon the addition of the congestus cloud
Q12R (40%–80% of peak is the result of heating by theseclouds). Adding in the shallow convective cloud Q12R
allows for a broadening of the lower portion of the profile(1–2 K day21), as indicated by comparing the dashed andsolid lines in the top-left panel of Fig. 8. Heating by
shallow convection is responsible for 20% of the Q1
magnitude near the surface (the solid line in the top-rightpanel), with significant cooling resulting from evaporation of precipitation and radiative cooling as indicated by
the Strat 1 QR profile. Shallow, congestus, and stratiform

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FIG. 8. The reconstruction of the average (top left) MID-LEV and (bottom left) DEEP Q1
profiles, computed by successively adding the average convective Q1 2 QR profiles (associatedwith three specified subsets of convective cloud ensembles) to the combined stratiform Q1 2 QR
and average QR profile characterizing the cluster. The three convective ensembles consist of
clouds with PTHs ranging from 9 to 20 km (dotted), 5 to 20 km (dashed), and 1 to 20 km (solid).
The contribution by cloud-type ensemble (stratiform and the three convective ensembles) tothe average Q1 profile characterizing the (top right) MID-LEV and (bottom right) DEEPclusters.

cloud types all contribute to significant but varying degrees (as a function of height) to the net MID-LEV cluster
Q1, and do so in a consistent manner for each ocean basin.
Considering now the DEEP cluster, and proceeding as
before, successively shallower Q12R profiles are added
to the DEEP cluster combined stratiform Q12R and QR
profiles toward reconstruction of the cluster average Q1.
It is evident that the positive lower portion of Q1 emerges
after the congestus Q12R is taken into consideration[the congestus clouds contribute 40%–60% toward thenet heating, which is slightly larger than the contribution by deeper (9–20-km PTHs) clouds]. The role of theshallower convective clouds (consisting of PTHs from0 to 5 km) is not as significant in the DEEP cluster as in
the MID-LEV one (seen by comparing dashed to solidline in bottom-left panel), contributing only slightly tothe magnitude of the Q1 profile from 1 to 4 km. The

uppermost portion of DEEP Q1 (above 7 km) is largely
reproduced upon consideration of the deep convective
precipitating cloud (PTHs from 9 to 20 km) and thestratiform component of heating.

4. Dissimilarity in precipitating cloud types
An attempt has been made to show that precipitation
clusters are similar in appearance, with nearly indistinguishable cloud ensembles, rainfall distributions, andheating profiles. It is worth discussing whether or not
the idea of self-similarity can be extended to specificprecipitating cloud types. For instance, does a precipitating congestus cloud observed in one precipitation cluster
look similar to that in another cluster in terms of surface rainfall rate and vertical profile of radar reflectivity? While deep convective clouds produce a significant

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FIG. 9. (top left) The average convective Q1 2 QR profiles for convective clouds having PTHs of 3 km for each precipitation cluster[SHAL (dashed), MID-LEV (dotted), and DEEP (solid) clusters]. (top middle) As at top left, but for the PR ZE profiles. (top right) For
each precipitation cluster (line style denotes the cluster), the percent difference in ZE as a function of height given a convective cloud witha 3-km PTH and the same surface rainfall rate (averaged over all basins). The bottom three panels are constructed as in the top two panels,
but for the precipitating clouds having PTHs of 6 km.

amount of rainfall and latent heating, shallow and congestus cloud types (defined as earlier according to their
PTH distributions), resulting from their significant RFO
over the tropical oceans, contribute roughly 38% and
47% of the observed total convective rainfall, respectively. Because these clouds are particularly importantin terms of rainfall in the tropics, the idea of cloud-typesimilarity is discussed through consideration of particular precipitating clouds within the broad shallow andcongestus classifications.
Consider two particular precipitating cloud types withinthese categories that have PTHs of 3 and 6 km. The cloudwith a 3-km PTH can be considered a shallow, warmraining cloud, while the 6-km precipitating cloud most
likely extends beyond the tropical freezing level and may
contain ice near the cloud top. Stratified by precipitation
cluster, the average surface rainfall rate for a cloud witha 3-km PTH (at TRMM PR instantaneous resolution)is 2.1, 1.5, and 1.4 mm h21 for SHAL, MID-LEV, andDEEP clusters, respectively. As the cluster becomesdeeper, the strength of the 3-km precipitating clouds decrease in terms of surface rainfall rate, which is somewhat
surprising, but is nonetheless consistent for all basins.
Figure 9 depicts the Q12R and radar reflectivity profiles
for the 3-km clouds in the top three panels. One would
expect that the Q12R from these 3-km cloud types should
decrease, consistent with the surface rainfall-rate trends,
which is indeed what is observed. It must be noted that
Q12R can be considered a larger-scale variable dependent on the precipitating cloud system as a whole, so
further interpretation of the Q12R profiles would be
more speculative. The top-middle panel of Fig. 9 shows
the corresponding 2A25 product radar reflectivity profiles for the 3-km precipitating clouds. Consistent withthe rainfall rates, as the precipitation regime grows deeper,
the radar reflectivity profiles weaken for these cloud types.
The Q12R and radar reflectivity profiles for the clouds
with 6-km PTHs are shown in the bottom three panels of
Fig. 9. For a precipitating cloud with a 6-km PTH, theaverage surface rainfall rate is 7.5, 8.2, and 10.7 mm h21

15 MAY 2010

ELSAESSER ET AL.

for SHAL, MID-LEV, and DEEP clusters, respectively.
Unlike the trend for clouds with 3-km PTHs, the rainfall
rate, Q12R, and radar reflectivity values increase as theclusters transition from SHAL to DEEP (bottom-left andbottom-center panels of Fig. 9). This is also qualitatively
consistent from one geographic basin to the next.
If one becomes more stringent in the definition of a
precipitating cloud type, such that it is now defined byboth a particular vertical thickness and surface rainfall
rate, then further investigation into the differences in
the profiles of radar reflectivity as a function of height
for the three clusters can be made. The results are averaged over all basins, and the average percent difference in radar reflectivity relative to the mean radarreflectivity profile is shown for precipitating clouds defined according to PTH and surface rainfall rate. The
results can be seen in the far-right two panels of Fig. 9.
Robust differences emerge, and for the 3-km clouds,
given the same surface rainfall rate, there is a 14% difference in radar reflectivity at 2 km between precipitating clouds developing in the SHAL cluster versus theDEEP cluster. For the 6-km clouds, given the same surface rainfall rates once again, there is an 18% difference
in radar reflectivity at 3.5 km between precipitating clouds
developing in the SHAL cluster compared to those developing in the MID-LEV cluster.
It is evident that the differences between these average surface rainfall rates, Q12R, and radar reflectivity
are large and highly dependent on the precipitation regime in which the cloud is developing. However, the rainfall rates are similar with respect to the tropical averagesurface rainfall rate for these clouds when one stratifies
by precipitation cluster (less than a 7% difference fromthe cluster average). These results provide motivation
for the study of precipitating clouds within the context ofthe precipitation regime in which they are developing, as
opposed to considering precipitating clouds with thesame vertical extent and/or rainfall characteristics as selfsimilar entities, independent of the precipitation regime.

5. Conclusions
A wealth of knowledge exists on the nature of tropicalprecipitation, both in the temporal mean sense and alsowith respect to the prevalence of precipitating clouds as
one traverses the various ocean basins in the tropics. In
this study, an analysis geared toward extracting precipitation regimes from the mean tropical state is performed, but is done so independently for adjacent ocean
regions with the purpose of determining how similarvarious precipitation regimes are across the tropics. The
framework has the advantage of not requiring, for example, the specification of how many deep precipitating

2697

clouds must exist in a regime for it to be declared ‘‘deep’’or what percentage of stratiform/convective cloud types
must exist in a given area for a particular type of regime
to be defined. Three similar precipitation clusters emerge
such that a particular cluster occurring in one basin isnearly indistinguishable from the same cluster identified
in another basin. Clusters are quantitatively similar interms of the ensembles of cloud types, the distributions ofrainfall, and the distributions of heating resulting fromthe spectrum of precipitating clouds that are present.
Precipitating shallow and congestus clouds are in close
proximity to each other, as well as in close proximity to
deep convective clouds in deeper precipitation clusters.
Because a cluster contains a distribution of cloud entities
that are not self-similar (despite having the same verticalextent and rainfall), studies that focus on a particular
cloud type and its associated ambient thermodynamic
characteristics may inadvertently mix regimes by, forexample, extracting shallow clouds from a deeper convection regime and shallow clouds from a weakly convecting regime and compositing the profiles and theircorresponding environmental characteristics together.
Within the deeper precipitation clusters, the distributions of PTHs are consistently bimodal. It is shownthat particular ensembles of cloud types play significant
roles in the composite structure of the heating profiles.
These results are both robust and consistent from one
tropical ocean basin to the next. Additionally, theseresults indicate that it may be necessary to consider theentire spectrum of precipitating that are clouds present
in a particular regime in order to capture the heating
profile (largely driven by the latent heating term), beyond a rainfall scaling of a generalized latent heating
function that depends largely on the amount of stratiform and convective rainfall present.
It is an important result that similar precipitation
clusters emerge, particularly because equatorial atmospheric wave activity frequency and large-scale dynamics vary as a function of the tropical oceanic basin.
Considering that convectively coupled equatorial waves
are more prevalent in some basins than others, and that
the Madden–Julian oscillation (MJO) primarily influences the Indian and west Pacific Ocean basins, the result of cluster similarity in terms of the distributions ofPTH, rainfall, and heating is a significant one, implyingthat precipitation clusters do not change regardless of thetype of equatorial disturbance; rather, they are simply
modulated in terms of frequency of occurrence by the
disturbance.
Continued interpretation of these clusters, as well as
their placement within the ‘‘extended building block’’
hypothesis recently proposed by Mapes et al. (2006),
which describes a self-similar progression of precipitating

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convection from shallow to deeper structures despite
being modulated by different large-scale tropical waves,requires the incorporation of additional datasets describing the thermodynamic and dynamic states of theatmosphere. Furthermore, reconciling the remaining
cluster differences that exist from one basin to anothermay require consideration of the idea that some precipitation regimes may be either terminal (i.e., they havereached their peak intensity) or transient (i.e., intensifying and growing toward a deep convective state), as
discussed in Luo et al. (2009). It is possible that the same
distribution of precipitating clouds could exist in either
case, but there is good reason to expect that the heating
and rainfall may be different between the two cases,
which could provide some insight into why precipitating
clouds have similar characteristics with respect to thecluster in which they are developing, but not with respect
to the same cloud types developing in another cluster.
Acknowledgments. This work has been supported by
the National Science Foundation Science and Technology
Center for Multiscale Modeling of Atmospheric Processes(CMMAP), managed by the Colorado State University
under Cooperative Agreement ATM-0425247. It was also
partially supported by NASA Grant NNX07AD75G.
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