1 MARCH 2021

MASUNAGA ET AL.

1685

Transient Aggregation of Convection: Observed Behavior and Underlying Processes
HIROHIKO MASUNAGA,a CHRISTOPHER E. HOLLOWAY,b HIRONARI KANAMORI,a SANDRINE BONY,cb
AND THORWALD H. M. STEINa

Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japanb
Department of Meteorology, University of Reading, Reading, United Kingdomc
LMD/IPSL, CNRS, Sorbonne Universities, University Pierre and Marie Curie, Paris, France(Manuscript received 12 December 2019, in final form 30 September 2020)
ABSTRACT: Convective self-aggregation is among the most striking features emerging from radiative–convective
equilibrium simulations, but its relevance to convective disturbances observed in the real atmosphere remains under debate. This work seeks the observational signals of convective aggregation intrinsic to the life cycle of cloud clusters. To thisend, composite time series of the Simple Convective Aggregation Index (SCAI), a metric of aggregation, and other variables from satellite measurements are constructed around the temporal maxima of precipitation. All the parameters analyzed are large-scale means over 108 3 108 domains. The composite evolution for heavy precipitation regimes shows thatcloud clusters are gathered into fewer members during a period of 612 h as precipitation picks up. The high-cloud cover per
cluster expands as the number of clusters drops, suggesting a transient occurrence of convective aggregation. The sign of thetransient aggregation is less evident or entirely absent in light precipitation regimes. An energy budget analysis is performedin search of the physical processes underlying the transient aggregation. The column moist static energy (MSE) accumulates
before the precipitation peak and dissipates after, accounted for primarily by the horizontal MSE advection. The domainaveraged column radiative cooling is greater in a more aggregated composite than in a less aggregated one, although the roleof radiative–convective feedback behind this remains unclear.
KEYWORDS: Tropics; Convection; Convective clouds; Satellite observations

1. Introduction
Convective self-aggregation is a form of spontaneous
symmetry breaking that is known to occur under particularconditions in an idealized atmosphere under radiative–
convective equilibrium (RCE). Unlike traditional convective organization such as the formation of mesoscaleconvective systems (Houze 2004, and references therein), selfaggregation involves a whole set of thermodynamic processes involved in the expanding clear-sky environment aswell as the areas of convection being increasingly localized
over time. While pioneering work reporting such phenomena
underscored the roles of moisture for the localization of
convection (Held et al. 1993; Tompkins and Craig 1998;
Tompkins 2001), Bretherton et al. (2005), who first used theterm ‘‘convective self-aggregation’’ in the literature, analyzed their RCE simulations in light of the atmospheric energy budget and found radiative feedbacks to be particularly
important in addition to the moisture feedback for convective self-aggregation. It was confirmed in subsequent studies
that the radiative contrast across the clear and cloudy skies
promotes self-aggregation through, for instance, a muted
longwave cooling by high clouds (Stephens et al. 2008) andan enhanced lower-atmospheric cooling by low clouds in

Denotes content that is immediately available upon publication as open access.
Corresponding author: Hirohiko Masunaga, masunaga@
nagoya-u.jp

dry areas (Muller and Held 2012). Otherwise the physicalprocesses crucial for convective self-aggregation are notfully understood. The occurrence or absence of selfaggregation can be sensitive to numerical model setups
such as the domain size and grid resolution (Muller andHeld 2012; Jeevanjee and Romps 2013). Wing andEmanuel (2014) found that self-aggregation does not occur
over ocean surfaces colder than 300 K, while signs of convective self-aggregation are evident for a broader range of
SST in other studies (Coppin and Bony 2015; Holloway and
Woolnough 2016; Wing and Cronin 2016) [a thorough review on the sensitivity to SST is provided by Wing (2019)].
Aspects of self-aggregation learned from idealized simulations are confirmed also in numerical runs with realistic
configurations, with a potentially similar magnitude sensitivity to cloud radiative interactions when accounting foreffects of boundary conditions on the limited-area realistic
runs (Holloway 2017). Theoretical models have been developed to explain convective self-aggregation in terms ofan instability intrinsic to moisture–convection interactions(Craig and Mack 2013) or inherent in the interplay of radiative cooling with tropospheric water vapor (Emanuelet al. 2014) and the production of available potential energy primarily in the boundary layer (Yang 2018). A morecomprehensive review is found in Wing et al. (2017) andWing (2019).
Signs of convective aggregation have been sought in observations to test its relevance to the real atmosphere [see review
by Holloway et al. (2017)]. The atmosphere tends to be drier
and less cloudy, and thus more efficient in longwave radiative
cooling in a more aggregated state (Tobin et al. 2012, 2013),

DOI: 10.1175/JCLI-D-19-0933.1
Ó 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).
Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1686

JOURNAL OF CLIMATEVOLUME 34

FIG. 1. Composite time series of (a) precipitation, (b) SST, (c) CWV, and (d) standard deviation of CWV within a
108 3 108 domain. Composite curves separated by different P0 regimes are plotted in different colors as indicated in
the legend in (b). Time 0 refers to the hour when precipitation reaches a local maximum.

where a contraction of cloud cover is pronounced in anvil
clouds, typically associated with deep cumulus towers (Steinet al. 2017). These studies present evidence that some key
processes essential for simulated convective aggregation are
at work in nature, whereas other aspects of self-aggregation
specific to idealized model setups may not be directly comparable to observations. The aggregation time scale isamong the latter, because it takes 15–100 days in RCE simulations for self-aggregation to develop from a perfectly
disaggregated initial condition, which does not exist in nature(Holloway et al. 2017). In the real atmosphere, known tropical disturbances with a range of different lifetimes could be
potential candidates for the real-world realization of convective
aggregation, including tropical cyclones (e.g., Bretherton et al.
2005; Nolan et al. 2007; Khairoutdinov and Emanuel 2013)
and the MJO (Arnold and Randall 2015; Khairoutdinov andEmanuel 2018). More short-lived systems such as cloud clusters,
having a life cycle from subdaily to a few occurrences daily(Chen et al. 1996), have the tendency to be gregarious (Mapes
1993). It has not been explored in depth, however, to what extent
such a short-term convective variability could be understood in
the context of self-aggregation.
This paper analyzes satellite infrared measurements insearch of the possible signals of convective aggregation (anddisaggregation) in association with the life cycle of tropicalcloud clusters. In the sections that follow, the term ‘‘selfaggregation’’ is reserved for the aforementioned physicalphenomena explored in the literature, while temporal changes
in the morphological characteristics of observed cloud clusters
are described merely by aggregation or disaggregation. As
such, the terms self-aggregation and aggregation have different
nuances: the former refers to specific physical processes known
from the literature and the latter is used for a description ofobserved features. Different metrics to quantify the degree of
aggregation have been proposed such as the simple convective
aggregation index (SCAI) (Tobin et al. 2012), the organizationindex or Iorg (Tompkins and Semie 2017), the convective organization potential (COP) (White et al. 2018), and the morphological index of convective aggregation (MICA) (Kadoya
and Masunaga 2018). The mutual consistency in performance
among these indices has only very recently begun to be assessed (Pscheidt et al. 2019; Xu et al. 2019). We adopt SCAI inthis study, as SCAI is the oldest of this kind and often regarded
as the ‘‘standard’’ for a newer index to be compared against(White et al. 2018; Kadoya and Masunaga 2018). The physicalnature of observed aggregation effects is studied from reanalysisbased energy budget considerations to seek the underlying
physical processes as known for conventional self-aggregation
in idealized simulations.
This article is structured as follows. Following a brief description of the datasets in section 2, possible signatures ofshort-range aggregation are sought in satellite observations(section 3) and an energy-budget analysis is performed insearch of the key processes behind the observed signatures

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1687

MASUNAGA ET AL.

FIG. 2. As in Fig. 1, but for (a) SCAI, (b) the number of clusters, (c) normalized D0, (d) convective area fraction,(e) the area fraction of the largest cluster, and (f) convective area fraction divided by the number of clusters.

(section 4). The findings are summarized and discussed in
section 5.

2. Data
The input satellite observations for identifying cloud clusters
are global imagery at a 4-km resolution taken from the NOAA
Climate Prediction Center (CPC) merged IR dataset (Janowiak
et al. 2001). Cloud clusters are identified by a contiguous areaof satellite pixels with window-channel IR brightness temperatures colder than 240 K. We use 4-connectivity: this is what
Tobin et al. (2012) used, and they found that results were notsensitive to using 8-connectivity instead (I. Tobin 2020, personal communication). Each 108 3 108 domain, at each 3hourly snapshot, is treated as if it were an independent scene.
Cloud clusters that touch any domain boundary are counted

the same as clusters that do not touch a boundary, and there is
no attempt to connect clusters from one scene to another. For
more details about the SCAI data (and related data), see section 2 of Stein et al. (2017), in which the same SCAI dataset was
analyzed.
Convective area fraction Ac is defined as the fractional area
coverage of all cloud clusters together within a 108 3 108 domain.
SCAI, originally devised by Tobin et al. (2012), is defined as
SCAI 5

Nc D 03 1000,
Nmax L(1)

where the first factor on the rhs is the number of cloud clusters(Nc) normalized by a prescribed constant (Nmax) to scale themagnitude of Nc, and the second is the geometrical mean ofthe distance between each pair of the cluster centroids (D0),

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1688

JOURNAL OF CLIMATEVOLUME 34

FIG. 3. Composite time series of SCAI stratified by different ranges of underlying SST at t 5 0 (SST0) as indicated byeach panel.

normalized by the domain size (L). As such, SCAI would decrease as cloud clusters are merged into fewer clusters (i.e.,
smaller Nc) that are more clumped together (i.e., smaller D0)
and therefore may be considered as an inverse measure of thedegree of convective aggregation; that is, SCAI decreases asconvection becomes more aggregated. In this work, SCAI iscomputed for every 108 3 108 domain (hence L 5 108) withneighboring boxes overlapping each other by 58, and Nmax ischosen to be the largest possible value of Nc or half the total
pixel number within each box. SCAI is by design insensitive tosome key aspects of convective aggregation that other proposed
metrics explicitly rely on. The properties accounted for by otherindices but not by SCAI include the area of cloud clusters in
COP (White et al. 2018), randomness in the probability distribution of intercloud distance in Iorg (Tompkins and Semie 2017),
and the spatial extent of cloud-free regions in MICA (Kadoya
and Masunaga 2018). We nonetheless adopt SCAI in this study,
taking advantage of its simplicity and hence of the ease ofinterpretation.
A variety of atmospheric and surface parameters, all averaged horizontally over the same 108 3 108 domains as done for
SCAI unless otherwise noted, are analyzed together with SCAI
as outlined below. Three-hourly surface precipitation is obtained from the TRMM 3B42 product (Huffman et al. 2007).
The SST data are from the 0.258 TMI/AMSRE ‘‘fusion’’ (optimally interpolated) daily data (and the same value is repeatedat each 3-h time during each day). This uses TMI microwavebased data (Wentz 2000), and since 2002 these data have been

blended with AMSR-E microwave data using the optimal interpolation technique of Reynolds and Smith (1994). Column
water vapor (CWV) is obtained from the ERA-Interim(ERAI) data (Dee et al. 2011). The ERAI datasets are also
employed to provide a set of the parameters ingested into
energy-budget analysis, that is, air temperature, vapor mixing
ratio, geopotential height, horizontal and vertical winds, radiative heating rate, and surface heat fluxes. GridSat IR images(Knapp et al. 2011) are used for presenting sequential snapshots of cloud clusters in case studies.
All oceanic domains, from which any grid box partiallycovered with land is excluded, bound between 208S and 208N
are included in the analysis for the 3.5-yr period from July 2006
to December 2009.

3. Temporal evolution
a. Overview of composite time series
The evolution of the atmospheric and surface states is firststudied in terms of time series composited around a local peakin the Eulerian temporal sequence of precipitation. The local
maxima of 3-hourly precipitation, averaged over a 108 3 108
domain, are identified within a search window of 612 h in order to filter out short-term noise. The results were found insensitive to the window width when it is varied from 66 to
624 h (not shown). The composite samples are broken down
into seven precipitation regimes of P0 , 10, 10–15, 15–20,
20–25, 25–30, 30–35, and .35 mm day21, where P0 denotes theUnauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1689

MASUNAGA ET AL.

FIG. 4. The diurnal cycle of (a) SCAI, (b) the number of clusters, (c) normalized D0, and (d) convective area fraction
for different precipitation regimes.

domain-mean precipitation at the hour of the local precipitation maximum. The size of composite samples is summarized inappendix A. SCAI is meant to measure the degree of aggregation within each precipitation regime, making distinctions
whether a given amount of precipitation is produced by heavily
clustered clouds (i.e., more aggregated systems) or highly
scattering convection (less aggregated). SCAI is not intended
to be compared across different precipitation regimes.
Composite time series constructed in this simple Eulerian
approach are potentially contaminated with spurious variability
as convective disturbances enter and leave the study domain.
Given that a typical migration speed of tropical cloud clusters isabout 10 m s21 (e.g., Nakazawa 1988), it takes roughly one day
for convective disturbances to travel across a 108 3 108 domain.
Precipitation and cloud variability substantially longer than
1 day are likely affected by the appearance and disappearance ofthe disturbances through the domain boundaries, while more
quickly varying signals, which are of main interest in this work as
will become clear below, are explained mainly by the variability
intrinsic of convective systems.
The composite time series of precipitation, SST, and CWV
are shown for different precipitation regimes in Fig. 1.
Precipitation has a striking peak at t 5 0 by construction, with
its half-width at half maximum being roughly 12 h. SST is nearly
constant over time except for a subtle decrease after t 5 0 for large
P0 values. CWV has a maximum at t 5 0 but the variability around it
is much less sharp than found for precipitation, as may be expectedfrom the known nonlinear relationships between P and CWV(Bretherton et al. 2004; Peters and Neelin 2006). The standard

deviation of CWV within a 108 3 108 domain has a modest enhancement similar to CWV itself, but a smaller P0 is associatedwith a larger magnitude of the intradomain standard deviation of
CWV. This may be because a modest precipitation peak is typicallylinked to a dry environment (Fig. 1c) and hence would not occur
without an appreciable CWV variability with highly concentrated
moist spots protecting precipitating clouds. The maximum of the
CWV variability slightly lags the precipitation peak (t 5 0). A possible explanation for this is that the stratiform component of organized cloud systems, having a tighter correlation with the ambientmoisture than the convective component (Ahmed and Schumacher2015), develops in a later stage of the convective life cycle.
Figure 2 presents SCAI and the related parameters. SCAI
has a maximum slightly delayed (by 6–12 h) behind precipitation. Diurnal modulation is also evident, as discussed later. For
the largest values of P0, SCAI temporarily reduces, showing
signs of increased aggregation, while precipitation rapidly picks
up during ;12 h prior to time 0 and then increases back again
until t 5 12 h. A decline of SCAI after its maximum for t . 0 h
may result from the dissipation and/or disappearance of the
disturbances through the observed domain boundaries as argued
above, but the one before the peak is not intuitively obvious.
Because SCAI is constituted of Nc and D0 as shown by (1), thesetwo parameters are assessed individually in Figs. 2b and 2c. It isfound that Nc primarily accounts for the variability of SCAI
while the role of D0 is secondary, confirming the findings ofTobin et al. (2012). Convective area fraction, Ac, increases overtime to its peak at t 5 0 with no trace of a temporary minimum as
seen for SCAI (Fig. 2d). The evolution of Ac is accounted for by

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1690

JOURNAL OF CLIMATEVOLUME 34

FIG. 5. (a)–(e) Plan views of infrared brightness temperature at selected hours of 212, 26, 0, 6, and 12 h, respectively, around 1500 UTC
11 Jun 2008, at which the largest P0 of 107 mm day21 is observed for the more-aggregated (0.6 , SCAI0 , 0.9) category. (f) The time seriesof precipitation averaged over a 108 3 108 domain indicated by the black rectangle in (a)–(e). The three-point running mean of the original
3-hourly time series is shown in red. (g) As in (f), but for SCAI.

the spreading of high clouds around the time of peak convective
activity, but the behavior of SCAI requires another explanation.
The dip of SCAI around t 5 0 for the heaviest precipitation
regime is so shallow that it may not be interpreted with confidence
as a proxy of aggregation without more supporting evidence. To aid
in understanding this behavior of SCAI, Fig. 2e shows the cloud
cover occupied by the largest cluster, which approaches a level very
close to the total cloud fraction Ac at t 5 0 (Fig. 2d). The high cloud
cover therefore consists predominantly of a few largest clusters at
the time of peak precipitation. In addition, the temporal change inthe size distribution function of cloud clusters is evaluated in termsof the mean size of a cluster, that is, Ac divided by Nc. This parameter represents the ratio of the first moment of the cluster size
distribution function to its zeroth moment:ð
n0 sf (s) ds
Ac
,
(2)
5 ð
Nc
n0 f (s) ds
where s refers to the fractional area of clusters relative to the 108 3
108 domain area, and f(s) is the normalized size distribution function
with n0 being its scaling factor. Note that Ac/Nc varies only with theshape of the distribution function and is independent of n0. Figure 2f
shows that Ac/Nc rises to the maximum at t 5 0 and then drops
during a spell of 612 h, resembling the behavior of the cloud coveroccupied by the largest cluster. It is implied, given that Ac/Nc would
increase if f(s) shifts toward large sizes, that small cloud clusters gather
into a few larger clusters as precipitation intensifies. This result appears
to be in support of the hypothesis that a transient aggregation process isin progress as suggested by the behavior of SCAI.

When the composite SCAI is stratified by SST at t 5 0 or
SST0 (Fig. 3), the major features found in Fig. 2 above are allpresent for SST0 . 298C. The SCAI dip at t 5 0 and diurnal
undulations become less clear as SST decreases and disappear
for SST0 values below 278C.
The SCAI value at t 5 0, or hereafter SCAI0, is used to break
down the composite evolution of SCAI for the purpose of highlighting differences in convective events with and without a noticeable sign of aggregation. Four SCAI ranges are chosen: SCAI0 . 1.5,
1.2 # SCAI0 # 1.5, 0.9 # SCAI0 # 1.2, and 0.6 # SCAI0 # 0.9, withthe samples with SCAI0 # 0.6 discarded. This choice of SCAI ranges
preferentially samples warm ocean surfaces because SCAI generally
exceeds 0.6 for SSTs higher than 288C (Figs. 3a,b) while SCAI often
falls below 0.6 for lower SSTs (Figs. 3c,d). Cold SSTs do not accompany the temporary aggregation (or the SCAI dip) are thus notof interest in the analysis that follows. The two contrasting cases of
SCAI0 . 1.5 and 0.6 , SCAI0 # 0.9 are defined as less-aggregatedand more-aggregated cases, respectively, for the energy budget
analysis presented in section 4.

b. Effects of diurnal cycle
A 24-h oscillation is clearly visible in the composite evolution of SCAI (Fig. 2), suggesting a possible influence of diurnal
forcing. Figures 4a and 4b show that SCAI and the number ofclusters have an intrinsic diurnal cycle with an afternoon peakas discovered also by Doyle (2018) and Pscheidt et al. (2019).
Its relevance to the diurnal cycle of precipitation is unclear,
given that oceanic rainfall typically has an early-morning
peak (e.g., Gray and Jacobson 1977). The amplitude of thediurnal cycle, largest for the lowest value of P0, diminishes as

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1691

MASUNAGA ET AL.

FIG. 6. As in Fig. 5, but for the second largest P0 of 103 mm day21 (0900 UTC 4 Jun 2009).

P0 increases. A possible reason is that heavily precipitating
clouds are likely linked to the synoptic-scale dynamics beyond
the control of the diurnal cycle, making a contrast to weak
precipitation more susceptible to the local diurnal forcing.
Diurnal variability is not pronounced for D0 (Fig. 4c) and Ac(Fig. 4d), except for a slight reduction of Ac during 18–24 h. The
day–night contrast in cloud-top temperature could potentiallygive rise to an artificial diurnal undulation in Ac because a fixed

infrared threshold of 240 K is applied uniformly over local time
to define cloud clusters. The overall stability of Ac found in
Fig. 4d, however, suggests that this effect does not introduce
any discernible diurnal bias.
Figure 4a suggests that diurnal cycle has little influence on
SCAI for heavily precipitating systems. The transient aggregation within 612 h around a striking precipitation peak isthus unlikely controlled by the diurnal forcing. When the

FIG. 7. As in Fig. 5, but for the third largest P0 of 101 mm day21 (0900 UTC 7 Jun 2008).

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1692

JOURNAL OF CLIMATEVOLUME 34

FIG. 8. Composite time series of the CMSE budget terms for the more-aggregated case (0.6 , SCAI0 , 0.9):(a) the Eulerian MSE tendency, (b) latent heat flux (solid) and sensible heat flux (dashed), (c) horizontal MSE
advection, (d) radiative heating rate, (e) vertical MSE advection, and (f) the budget residual.

composite SCAI is broken down by different local time att 5 0 to further confirm this, SCAI, although having a distinct
diurnal cycle that varies in phase among different local times,
agree in that SCAI has a minimum near t 5 0 and hence thesign of the transient aggregation persists regardless of local
time (see appendix B).

c. Case study
Are the temporary aggregation and the subsequent disaggregation visually recognized in individual convective events? A casestudy is conducted with three events having the first, second, andthird largest values of P0 among the samples with 0.6 , SCAI0 ,0.9. In the first event (Fig. 5), infrared imagery shows that two major
cloud clusters at 212 h (Fig. 5a) are merged into a larger cluster 6 hlater (Fig. 5b) and then reach very cold cloud tops over a large area
(Fig. 5c) before breaking up into smaller clusters with slightly
warmer cloud tops (Figs. 5d,e). This observation from visual inspection may be qualitatively interpreted as a momentary aggregation toward 26 h, around which SCAI hits the minimum (Fig. 5g)
despite the fact that precipitation then picks up (Fig. 5f). The second
event is relatively stable over time in terms of SCAI (Fig. 6g),
dominated by a single cloud cluster that is already in an aggregatedstate at 212 h (Fig. 6a), which is slowly dissolved into multiple
clusters by 12 h (Fig. 6e). A systematic evolution of SCAI is unclear
within 612 h in this case although, given that SCAI stays as low as;0.3–0.6, this particular case as a whole might be viewed as aprolonged period of an aggregated state. The last event (Fig. 7)
exhibits a merger of multiple clusters into colder, larger, and fewer

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1693

MASUNAGA ET AL.

FIG. 9. A 3-hourly histogram of the precipitation peaks of P0 .
35 mm day21 as a function of local time for the more-aggregatedcase (0.6 , SCAI0 , 0.9; in black) and less-aggregated case (SCAI0. 1.5; in red).

clusters until 0 h (Fig. 7c), followed by a separation of large cold
clusters into smaller, warmer clusters, similarly to the first event.
Note that cloud clusters begin to disperse out of the domain at t 5
12 h and as a result SCAI, closely related to the number of clusters,
decreases to near zero at t ’ 30 h. This case raises a caveat that a
reduction of SCAI should not be interpreted as a sign of aggregation when precipitation is virtually absent, in which case diminishing
SCAI merely signifies the disappearance of clouds from the observed domain. In summary, at least two of the three events show ahint of aggregation as precipitation intensifies toward the peak, as
may be expected from the composite ensemble. Aggregation isvisible in the infrared imagery of individual events, but (at least forthese cases and this methodology) it is far more modest and transient than a long-lasting aggregation process as seen in idealized
simulations.

4. Energy budget analysis
a. Temporal evolution
It was found in the current observations that a sign of transient convective aggregation is present around the peak ofheavy rainfall, although it is far more short-lived and subtle inmagnitude than that seen in previous idealized numericalstudies. Is the transient aggregation an entirely different entity
from the well-known self-aggregation phenomena, or do theyshare any mechanisms at the process level? A useful strategy to
pursue such potential similarities in the underlying physics is tocompare the individual components of the moist static energy(MSE) budget in light of the processes known to be crucial forthe self-aggregation such as moisture, radiation, and surface
heat fluxes (see section 1). To this end, the MSE budget
equation integrated over height,h›t hi 5 2hv  =hi 2 hv ›p hi 1 LE 1 S 1 hQR i 1 «RA ,(3)

is analyzed, where angle brackets designate the vertical integral from the bottom to the top of the atmosphere, v ishorizontal wind, h is MSE, L is the specific latent heat of vaporization, E is the surface evaporation flux, S is the surface
sensible heat flux, QR is the radiative heating rate, and «RAdenotes the budget residual due to the reanalysis errors.
The 108 3 108 domain mean of each term in (3) is first presented in the composite time series as shown in the previous
section. The evolution for the more-aggregated composite(0.6 , SCAI0 , 0.9) is shown in Fig. 8. The composite timeseries of the column MSE (CMSE) tendency (Fig. 8a)undergoes a salient diurnal modulation, and otherwise thetendency mostly stays positive before the precipitation peakbut is negative after the peak. The diurnal modulation is attributed to the solar cycle in the column radiative heating(Fig. 8d), which is not entirely averaged out in the composite
statistics because of the inhomogeneous diurnal variability
intrinsic to the precipitation-peak samples (Fig. 9). The dynamical terms such as the horizontal and vertical MSE advection, on the contrary, have little trace of the 24-h cycle. The
diurnal component of the MSE tendency is largely accounted
for by the day–night radiative contrast, while the slowly varying component is almost exclusively attributed to the dynamical processes. The temporal asymmetry as found in the CMSE
tendency is primarily brought about by the horizontal MSE
advection (Fig. 8c) and, to a lesser extent, by unknown sourcesin the residual term (Fig. 8f). The horizontal MSE advection isoverall negative except during limited hours prior to the precipitation peak for P0 . 35 mm day21, where the horizontal
advection imports MSE. The horizontal MSE advection begins
to enhance much earlier than precipitation (which sharply rises
to the peak; Fig. 1a), indicating that a horizontal moisturegradient develops before convection develops. The vertical
MSE advection stays always negative and reaches the minimum slightly after the precipitation peak (Fig. 8e), as expectedfrom the invigoration of deep convection exporting MSE. The
surface turbulent fluxes (Fig. 8b) are invariant over time andinsensitive to P0.
The less-aggregated composite is very similar to the moreaggregated case as illustrated above, except that the horizontal
MSE advection enhances only modestly and never exceeds
zero in the more-aggregated case even at its maximum(not shown).

b. Internal variability
Next examined is the horizontal variability of the MSE
budget parameters. The budget terms, computed on the
0.758 3 0.758 ERAI grid, are ordered by the magnitude of thecolumn MSE within an encompassing large-scale (108 3 108)
domain. This procedure is repeated for all large-scale domains and averaged into the composite statistics sorted by
the column MSE rank, following a convention of numerical
work (Bretherton et al. 2005; Muller and Held 2012; Wing
and Emanuel 2014; Muller and Bony 2015; Holloway and
Woolnough 2016). Wing and Emanuel (2014) demonstrated
the utility of variance-based MSE budget analysis for diagnosing the processes essential for convective aggregation, but
this approach is not explored here because high-resolution
data necessary to compute such variance are unavailable
from the ERAI data.

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1694

JOURNAL OF CLIMATEVOLUME 34

FIG. 10. The CMSE budget terms at selected hours, as indicated in the legend in (d), from the more-aggregated(0.6 , SCAI0 , 0.9) composite time series for P0 . 35 mm day21: (a) the Eulerian MSE tendency, (b) latent heat
flux (solid) and sensible heat flux (dashed), (c) horizontal MSE advection, (d) radiative heating rate, (e) vertical
MSE advection, and (f) the budget residual. The abscissa is the rank of column MSE ordered from the lowest to thehighest.

Figure 10 presents the MSE budget breakdown for selected
hours from the more aggregated (0.6 , SCAI0 , 0.9) composite time series. The CMSE tendency at t 5 0 (black curve in
Fig. 10a) is negative for the lower half while positive for theupper half. Care must be taken, however, because the budget
residual (Fig. 10f) implies a similar systematic bias of comparable magnitude and hence the CMSE tendency may be affected by reanalysis errors to a certain degree. The horizontal
advection (Fig. 10c) is relatively homogeneous across the domain. The vertical advection (Fig. 10e) exports CMSE as seen
earlier but sharply turns to positive in very moist columns. The
latent heat flux (Fig. 10b) stays above 100 W m22 with a slightdecreases as CMSE increases. The sensible heat flux is minimal
across all CMSE ranks. The radiative cooling becomes weaker(or approaches zero) with increasing MSE, likely because
of increasing water vapor and high cloud cover from dry tomoist columns. It is reminded that some of these features may
be affected by systematic reanalysis errors as found in theresidual bias.
The less-aggregated case is subtracted from the moreaggregated case next (Fig. 11) in order to focus on the difference between the two cases. It is also anticipated that «RA will
be canceled out in the difference plots, assuming that the reanalysis errors are not correlated with the degree of convective
aggregation. Figure 11 shows that, although the difference isoverall small in magnitude (note that the vertical range spans
6100 W m22 here and 6300 W m22 in Fig. 10), the moreaggregated and less-aggregated composites are not entirely
identical. The more-aggregated case is more efficient in column radiative cooling by more than 30 W m22 at t 5 0. The
CMSE tendency difference is overall attributable to the horizontal advection difference except for t 5 0 and t 5 218 h, at

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1695

MASUNAGA ET AL.

FIG. 11. As in Fig. 10, but for the difference between the more-aggregated case (0.6 , SCAI0 , 0.9) minus theless-aggregated (SCAI0 . 1.5). Thick solid lines are the five-point running mean applied to the original curves (thindashed). Only three time slices at 612 and 0 h are shown for visual clarity.

which time a positive difference in the horizontal advection islargely offset by a negative difference in QR and hence the
CMSE tendency difference stays near zero. A closer examination reveals that the CMSE tendency difference at t 5 0(black) has a slight positive gradient extending from almost thelowest MSE rank to the highest. This gradient, accounted forby the vertical advection difference, implies that the columns
with low CMSEs continue to lose further CMSE while thehigh-CMSE columns maintain or even gain more CMSE. Suchan upgradient transport of CMSE works somewhat more efficiently in more-aggregated events than in less-aggregatedevents, although the difference is so subtle that this remains
speculative without further evidence. The difference in «RA
suffers little systematic bias, so the more-aggregated versus
less-aggregated differences turn out to be less subject to thereanalysis errors than each individual composite.

5. Discussion and summary
In this paper, possible signs of convective aggregation are
explored in satellite observations and reanalysis datasets. The
time scales of present interest are a few days or shorter insteadof 15–100 days as seen in RCE simulations in order to seek theaggregation signatures intrinsic to the life cycle of organized
convective systems. The composite time series of various
parameters, all averaged over 108 3 108 domains, are built
around a local maximum of precipitation (P0) as a statisticalrepresentative of the convective life cycle. The composite
samples are stratified by seven precipitation regimes fromthe lightest (5 , P0 # 10 mm day21) to the heaviest (P0 .
35 mm day21) categories.
The composite evolution exhibits a momentary decline of
SCAI as precipitation picks up and the high-cloud cover

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1696

JOURNAL OF CLIMATEVOLUME 34

TABLE A1. The number of samples (at t 5 0) stratified by precipitation. The unit is mm day21 for precipitation.

FIG. 12. The 108 3 108 mean (a) v and (b) MSE as a function of
the MSE rank from the more aggregated (0.6 , SCAI0 , 0.9)
composite at t 5 0 for P0 . 35 mm day21. The height of the maximum ascent and the minimum MSE is traced in gray in (a) and (b),respectively.

expands to their peak. This decrease of SCAI accompanies a
modest shift in the histogram of cloud clusters so that small
cloud clusters are merged into fewer and larger clusters,suggesting a transient occurrence of convective aggregation.
The duration time of this aggregation effect is 1 day or shorter,and the degree to which aggregation proceeds, as visually
recognized from a case study, is rather limited. The sign of thetransient aggregation in the composite evolution of SCAI issalient in the heaviest precipitation regime, but becomes
fainter as P0 decreases.
The time scale of the observed transient aggregation process
is substantially smaller than the known time scales of 15–
100 days from idealized simulations (Wing et al. 2017). The
discrepancy in time scale, however, may not necessarily imply
that the short-term aggregation in the current observations is
entirely irrelevant to what we have learned from past numerical simulations. The key feedback processes crucial for aggregation as identified in idealized simulations are at work inmore realistic simulations as well (Holloway 2017), while theaggregation time scales in RCE simulations initiated with ahomogeneous field have little direct relevance to the realworld (Holloway et al. 2017). The real atmosphere neverexperiences a uniform, disaggregated state to start with, and a
108 3 108 domain in nature is exposed constantly to external
synoptic-scale disturbances, potentially destroying an environment favorable for the continuous development of aggregation. On the other hand, this transient aggregation may

Precipitation

No. of peaks

35 , P
30 , P # 35
25 , P # 30
20 , P # 25
15 , P # 20
10 , P # 15
5 , P # 10

6217
4505
7423
12 14519 34831 93056 247possibly be relevant to the gregarious nature of tropical cloudclusters as found in satellite imagery by Mapes (1993), who
proposed a theory that the gravity wave propagation triggeredby initial convection generates a thermodynamic state favorable for subsequent convection in close vicinity. The time scaleof this mechanism is several hours, comparable to the aggregation time found in this work.
The transient form of convective aggregation is detectable
only over warm oceans (SST . 288C), which appears to confirm
some existing numerical studies (Wing and Emanuel 2014)
although the sensitivity to SST is still in dispute (Coppin andBony 2015; Wing and Cronin 2016; Holloway and Woolnough2016). SST tends to be higher for a larger P0 but somewhat
decreases with time as precipitation decays after its peak, ascribable to multiple possibilities including the high-cloudshielding of insolation (Wall et al. 2018) and the enhanced
surface heat flux following a spell of active convection (Younget al. 1995). This also resembles the evolution of convective
aggregation in a coupled model where convection chases
after a warmer ocean until it finds itself over the warmest spot
and eventually dies out (Coppin and Bony 2017).
Diurnal modulation is evident in the temporal evolution of
SCAI because the SCAI itself has a diurnal variation and thecomposite samples are not entirely homogeneously distributed
over local time. The diurnal peak of SCAI lies in the afternoon,nearly half a day out of phase from the diurnal cycle of precipitation for unknown reasons over tropical oceans. Precipitationand SCAI, on the contrary, are nearly in phase over tropicalcontinents, both having a distinct afternoon peak (Doyle 2018).
It is noted that the diurnal cycle of cold cloud fraction varies
with the infrared threshold, where the local time of the peakmoves forward from around noon to 0600 or earlier as thethreshold is lowered from 235 to 215 K (Janowiak et al. 1994).
The afternoon maximum of SCAI therefore may be peculiar
to a relatively warm threshold of 240 K as currently chosen,
and a colder threshold could make the diurnal peak shift closer
to that of precipitation. In any case, the transient aggregation is
not merely an aliasing effect of the diurnal cycle, given that thetemporal minimum of SCAI around t 5 0 persists regardless of
local time when the composite time series are subsampled bydifferent local hours.
There is no evidence indicating that the latent and sensible
heat fluxes make any significant contribution to the transient
aggregation, given that the more-aggregated (0.3 , SCAI0 #0.6) and less-aggregated (SCAI0 . 1.5) composites are nearly

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

1697

MASUNAGA ET AL.

TABLE A2. The number of samples (at t 5 0) stratified by precipitation and SST. The unit is mm day21 for P and 8C for SST.
Precipitation

29 , SST

28 , SST # 29

27 , SST # 28

26 , SST # 27

35 , P
30 , P # 35
25 , P # 30
20 , P # 25
15 , P # 20
10 , P # 15
5 , P # 10

2479
1602
2327
3472
4735
6833
9713

1828
1471
2458
3925
6006
9458
15 381

718
693
1333
2421
4311
7494
13 520

348
237
465
930
1887
3848
8249

identical in the surface fluxes (Fig. 11b). This is consistent withprevious idealized studies showing that, while surface fluxes canbe important for initiation of self-aggregation, they are not important for its maintenance (Holloway and Woolnough 2016).
The diurnal cycle of radiative cooling is similar in magnitude
but not identical in phase between the more-aggregated
and the less-aggregated composites. As a result, the moreaggregated case has a radiative cooling that is more than
30 W m22 stronger at t 5 0 than the less-aggregated case. It
follows that the large-scale atmosphere including a developing
convective system may experience a distinct radiative cooling
during the transient aggregation. It is unclear, however, towhat extent this enhanced radiative cooling corroborates theconvective-radiative feedback important for convective selfaggregation in idealized numerical simulations (Wing et al.
2017, and references therein). The difference in QR between
the more- and less-aggregated composites has little systematic
dependence on the column MSE (Fig. 11). A potential radiative feedback implied by the QR dependence on CMSE for the
more-aggregated composite (Fig. 10d) is hence not discernibly
stronger than for the less-aggregated case. The lack of evidence
for any distinct effect of QR on the aggregation may be understood in the context of the scale dependence of the aggregation processes. Beucler and Cronin (2019) and Beucler
et al. (2019) showed that the longwave effects favor a growthof large-scale aggregation with horizontal wavelengths of;1000 km or larger, which exceeds the typical size of cloudclusters studied in the current analysis. Shortwave radiation, on
the other hand, has the effect of shrinking the aggregation tosmaller scales (500–2000 km) (Beucler and Cronin 2019). This
has a possible link to the diurnal maximum of disaggregation atafternoon hours (Fig. 4a).
The horizontal MSE advection is overall negative, suggestingthat the domain of interest may be incessantly exposed to an intrusion of relatively dry ambient air. This hypothesis is notunrealistic, given that the composite time series are constructedaround a precipitation maximum and hence the domain of interest is likely moister than the surroundings. The horizontal MSE
advection exhibits a positive anomaly hours before the peak
precipitation and a negative anomaly after with their amplitude
more pronounced for more intense precipitation. This pair ofanomalies with opposite signs implies the development of a horizontal moisture gradient prior to the intensification of convection
and the dissipation of the moisture gradient as the convection diesout. The positive anomaly prior to the rainfall peak is a primary
driver of the enhanced CMSE tendency, especially for the moreaggregated case. It is suggested that the horizontal advection has
the potential to help the moist air further moisten with the possibility to boost a new convective burst. This effect, if it exists, may
be related to the moisture-memory feedback as often discussed inattempt to interpret convective self-aggregation in numericalsimulations (Held et al. 1993; Tompkins 2001; Muller and Bony2015). The importance of the advection term in the CMSE budget
is in line with Bretherton and Khairoutdinov (2015), who showedthat the advection accounts for the rapid (,4 days) growth of
MSE at the earliest stage of aggregation, although at odds with
Beucler et al. (2019), who found that the advection damps theMSE variance at all spatial scales.
The vertical MSE advection sharply rises to above zero forcolumns with the largest MSEs. The reason for this is illustrated in Fig. 12a, where the vertical structure of v transitions
abruptly from a top-heavy profile to a bottom-heavy one ataround the 150th rank (out of the ;170 columns in total). Thisfeature in theory activates an upgradient transport of CMSE,
an element known as critical for aggregation (Bretherton et al.
2005; Muller and Held 2012; Muller and Bony 2015), since abottom-heavy updraft imports lower-tropospheric MSE morethan it exports MSE at higher levels and hence enhances
CMSE. One should bear in mind that v profiles from reanalysis
data may be sensitive to the parameterization uncertainties,

TABLE A3. The number of samples (at t 5 0) stratified by precipitation and SCAI. The unit is mm day21 for precipitation.
Precipitation

1.5 , SCAI

1.2 , SCAI # 1.5

0.9 , SCAI # 1.2

0.6 , SCAI # 0.9

35 , P
30 , P # 35
25 , P # 30
20 , P # 25
15 , P # 20
10 , P # 15
5 , P # 10

810
683
1022
1442
1663
1899
1491

782
552
869
1188
1539
1797
1642

1185
861
1277
1950
2697
3265
3394

1519
1036
1616
2679
4151
6042
6997

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1698

JOURNAL OF CLIMATEVOLUME 34

FIG. B1. As in Fig. 2, but broken down by local time at t 5 0 into four 12-h windows (with 6-h overlaps). All curves
are conditioned by P0 . 35 mm day21.

and the robustness of this result has yet to be confirmed. The
minimum in the vertical MSE profiles is somewhat low in altitude for the lowest-CMSE columns, while it stays invariant
across the highest-CMSE columns (Fig. 12b). The suddentransition in the vertical MSE advection for the moistest columns is therefore solely ascribed to the aforementioned
change in the vertical structure of v.
The transience of the aggregation processes in the observations may be partly due to limitations of the present analysis
strategy. The composite time series by design represent theEulerian evolution within a 108 3 108 domain. This practicallylimits the time scale of interest because convective disturbances rarely stay at the same location over an extended periodof time beyond ;1 day. The utility of the Lagrangian analysis
would be worth pursuing in future work to overcome the current technical limitations, although a Lagrangian analysis
with a cloud tracking algorithm has its own technical challenges
including how to deal with the merging and splitting of cloudclusters. The Eulerian and Lagrangian approaches each havestrengths and drawbacks that are complementary by nature.
Slowly evolving convective aggregation, if it exists in nature,should be sought in a significantly larger domain than we currently analyzed. It is noted, on the other hand, that past numerical work found convective self-aggregation to occur in acomputational domain with a size comparable to or evensmaller than a 108 3 108 square. Signs of the transient aggregation might emerge in numerical simulations as well when thelong-term variability is filtered out, although this has so far notreceived much attention to in the literature.
Acknowledgments. We thank three anonymous reviewers
for their comments, which helped us enrich the discussion andimprove the presentation. H. Masunaga is supported by Japan
Society for the Promotion of Science (JSPS) Grants-in-Aid for
Scientific Research (KAKENHI) 19H01966. The GridSat data
were obtained from NOAA (www.ncdc.noaa.gov/gridsat/) andthe ERAI data were provided by ECMWF (apps.ecmwf.int/
datasets/). The combined dataset including SCAI and its ancillaryparameters was created using funding from U.K. NERC Grant
NE/I021012/1 and is available through the NERC Centre forEnvironmental Data Archival (CEDA) (catalogue.ceda.ac.uk).

APPENDIX A
Sample Size in the Composite Statistics
Tables A1–A3 provide the size of composite samples. The
sample size declines with increasing precipitation, except for
the P . 35 mm day21 category owing to its broader bin size
than other P classes. Higher SSTs are preferred by heavy
precipitation while moderate SSTs are most sampled for lower
precipitation rates (Table A2). Lower SCAIs have a larger
sample size particularly for light precipitation (Table A3).

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1 MARCH 2021

MASUNAGA ET AL.

APPENDIX B
Composite Time Series Stratified by Local TimeTo quantify the effects of diurnal variation on the composite
evolution SCAI, Fig. B1 presents the breakdown by different
local times at t 5 0 for P0 . 35 mm day21. Local time is sampled
at 0, 6, 12, and 18 h with a half-day window, allowing 6-hoverlaps to maximize the sample size for statistical robustness.
SCAI and the number of clusters have a distinct diurnal cyclethat varies in phase among different local times. All curves,
nevertheless, agree in that SCAI has a minimum near t 5 0 andhence the sign of the transient aggregation persists regardlessof local time. The diurnal undulation is somewhat magnified inamplitude for the night and morning curves (1800–0500 and
0000–1100 LT) immediately after t 5 0. Diurnal modulation isminimal in D0 and Ac as expected from the results above.
REFERENCES
Ahmed, F., and C. Schumacher, 2015: Convective and stratiform components of the precipitation–moisture relationship. Geophys. Res. Lett., 42, 10 453–10 462, https://doi.org/
10.1002/2015GL066957.
Arnold, N. P., and D. A. Randall, 2015: Global-scale convective
aggregation: Implications for the Madden–Julian Oscillation.
J. Adv. Model. Earth Syst., 7, 1499–1518, https://doi.org/
10.1002/2015MS000498.
Beucler, T., and T. Cronin, 2019: A budget for the size of convective self-aggregation. Quart. J. Roy. Meteor. Soc., 145, 947–
966, https://doi.org/10.1002/qj.3468.
——, T. H. Abbott, T. W. Cronin, and M. S. Pritchard, 2019: Comparing
convective self-aggregation in idealized models to observed moist
static energy variability near the equator. Geophys. Res. Lett., 46,
10 589–10 598, https://doi.org/10.1029/2019GL084130.
Bretherton, C. S., and M. F. Khairoutdinov, 2015: Convective selfaggregation feedbacks in near-global cloud-resolving simulations of an aquaplanet. J. Adv. Model. Earth Syst., 7, 1765–
1787, https://doi.org/10.1002/2015MS000499.
——, M. E. Peters, and L. E. Back, 2004: Relationships between
water vapor path and precipitation over the tropical oceans.
J. Climate, 17, 1517–1528, https://doi.org/10.1175/15200442(2004)017,1517:RBWVPA.2.0.CO;2.
——, P. N. Blossey, and M. Khairoutdinov, 2005: An energybalance analysis of deep convective self-aggregation above
uniform SST. J. Atmos. Sci., 62, 4273–4292, https://doi.org/
10.1175/JAS3614.1.
Chen, S. S., R. A. Houze Jr., and B. E. Mapes, 1996: Multiscale variability of deep convection in relation to large-scale circulation in
TOGA COARE. J. Atmos. Sci., 53, 1380–1409, https://doi.org/
10.1175/1520-0469(1996)053,1380:MVODCI.2.0.CO;2.
Coppin, D., and S. Bony, 2015: Physical mechanisms controllingthe initiation of convective self-aggregation in a general circulation model. J. Adv. Model. Earth Syst., 7, 2060–2078,
https://doi.org/10.1002/2015MS000571.
——, and ——, 2017: Internal variability in a coupled general circulation
model in radiative-convective equilibrium. Geophys. Res. Lett., 44,5142–5149, https://doi.org/10.1002/2017GL073658.
Craig, G. C., and J. M. Mack, 2013: A coarsening model for selforganization of tropical convection. J. Geophys. Res. Atmos.,
118, 8761–8769, https://doi.org/10.1002/jgrd.50674.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis:
Configuration and performance of the data assimilation

1699

system. Quart. J. Roy. Meteor. Soc., 137, 553–597, https://doi.org/10.1002/qj.828.
Doyle, A., 2018: Spatio-temporal development of convective aggregation in the tropics. M.S. thesis, Dept. of Meteorology,
University of Reading, 32 pp.
Emanuel, K., A. A. Wing, and E. M. Vincent, 2014: Radiativeconvective instability. J. Adv. Model. Earth Syst., 6, 75–90,
https://doi.org/10.1002/2013MS000270.
Gray, W. M., and R. W. Jacobson Jr., 1977: Diurnal variation of deep
cumulus convection. Mon. Wea. Rev., 105, 1171–1188, https://doi.org/10.1175/1520-0493(1977)105,1171:DVODCC.2.0.CO;2.
Held, I. M., R. S. Hemler, and V. Ramaswamy, 1993: Radiativeconvective equilibrium with explicit two-dimensional moist
convection. J. Atmos. Sci., 50, 3909–3927, https://doi.org/
10.1175/1520-0469(1993)050,3909:RCEWET.2.0.CO;2.
Holloway, C. E., 2017: Convective aggregation in realistic
convective-scale simulation. J. Adv. Model. Earth Syst., 9,1450–1472, https://doi.org/10.1002/2017MS000980.
——, and S. J. Woolnough, 2016: The sensitivity of convective
aggregation to diabatic processes in idealized radiativeconvective equilibrium simulations. J. Adv. Model. Earth
Syst., 8, 166–195, https://doi.org/10.1002/2015MS000511.
——, A. A. Wing, S. Bony, C. Muller, H. Masunaga, T. S. L’Ecuyer,
D. D. Turner, and P. Zuidema, 2017: Observing convective
aggregation. Surv. Geophys., 38, 1199–1236, https://doi.org/
10.1007/s10712-017-9419-1.
Houze, R. A., Jr., 2004: Mesoscale convective systems. Rev.
Geophys., 42, RG4003, https://doi.org/10.1029/2004RG000150.
Huffman, G. J., and Coauthors, 2007: The TRMM Multisatellite
Precipitation Analysis: Quasi-global, multi-year, combinedsensor precipitation estimates at fine scale. J. Hydrometeor., 8,
38–55, https://doi.org/10.1175/JHM560.1.
Janowiak, J. E., P. A. Arkin, and M. Morrissey, 1994: An examinationof the diurnal cycle in oceanic tropical rainfall using satellite andin situ data. Mon. Wea. Rev., 122, 2296–2311, https://doi.org/
10.1175/1520-0493(1994)122,2296:AEOTDC.2.0.CO;2.
——, R. A. Joyce, and Y. Yarosh, 2001: A real-time global halfhourly pixel-resolution infrared dataset and its applications.
Bull. Amer. Meteor. Soc., 82, 205–218, https://doi.org/10.1175/
1520-0477(2001)082,0205:ARTGHH.2.3.CO;2.
Jeevanjee, N., and D. M. Romps, 2013: Convective selfaggregation, cold pools, and domain size. Geophys. Res.
Lett., 40, 994–998, https://doi.org/10.1002/grl.50204.
Kadoya, T., and H. Masunaga, 2018: New observational metrics ofconvective self-aggregation: Methodology and a case study.
J. Meteor. Soc. Japan, 96, 535–548, https://doi.org/10.2151/
jmsj.2018-054.
Khairoutdinov, M., and K. Emanuel, 2013: Rotating radiativeconvective equilibrium simulated by a cloud-resolving model.
J. Adv. Model. Earth Syst., 5, 816–825, https://doi.org/10.1002/
2013MS000253.
——, and ——, 2018: Intraseasonal variability in a cloud-permittingnear-global equatorial aquaplanet model. J. Atmos. Sci., 75,
4337–4355, https://doi.org/10.1175/JAS-D-18-0152.1.
Knapp, K. R., and Coauthors, 2011: Globally gridded satellite
observations for climate studies. Bull. Amer. Meteor. Soc., 92,
893–907, https://doi.org/10.1175/2011BAMS3039.1.
Mapes, B. E., 1993: Gregarious tropical convection. J. Atmos. Sci.,
50, 2026–2037, https://doi.org/10.1175/1520-0469(1993)050,2026:
GTC.2.0.CO;2.
Muller, C. J., and I. M. Held, 2012: Detailed investigation of the selfaggregation of convection in cloud-resolving simulations. J. Atmos.
Sci., 69, 2551–2565, https://doi.org/10.1175/JAS-D-11-0257.1.

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC

1700

JOURNAL OF CLIMATE——, and S. Bony, 2015: What favors convective aggregation andwhy? Geophys. Res. Lett., 42, 5626–5634, https://doi.org/
10.1002/2015GL064260.
Nakazawa, T., 1988: Tropical super clusters within intraseasonalvariations over the western Pacific. J. Meteor. Soc. Japan, 66,
823–839, https://doi.org/10.2151/jmsj1965.66.6_823.
Nolan, D. S., E. D. Rappin, and K. A. Emanuel, 2007: Tropical
cyclogenesis sensitivity to environmental parameters inradiative-convective equilibrium. Quart. J. Roy. Meteor. Soc.,
133, 2085–2107, https://doi.org/10.1002/qj.170.
Peters, O., and J. D. Neelin, 2006: Critical phenomena in atmospheric precipitation. Nat. Phys., 2, 393–396, https://doi.org/
10.1038/nphys314.
Pscheidt, I., F. Senf, R. Heinze, H. Deneke, S. Trömel, andC. Hohenegger, 2019: How organized is deep convection overGermany? Quart. J. Roy. Meteor. Soc., 145, 2366–2384, https://doi.org/10.1002/qj.3552.
Reynolds, R. W., and T. M. Smith, 1994: Improved global sea
surface temperature analyses using optimum interpolation.
J. Climate, 7, 929–948, https://doi.org/10.1175/1520-0442(1994)
007,0929:IGSSTA.2.0.CO;2.
Stein, T. H. M., C. E. Holloway, S. Bony, and I. Tobin, 2017:
Observed relationships between cloud vertical structure andconvective aggregation over tropical ocean. J. Climate, 30,
2187–2207, https://doi.org/10.1175/JCLI-D-16-0125.1.
Stephens, G. L., S. van den Heever, and L. Pakula, 2008: Radiativeconvective feedbacks in idealized states of radiative-convective
equilibrium. J. Atmos. Sci., 65, 3899–3916, https://doi.org/10.1175/
2008JAS2524.1.
Tobin, I., S. Bony, and R. Roca, 2012: Observational evidence forrelationships between the degree of aggregation of deep convection, water vapor, surface fluxes, and radiation. J. Climate,25, 6885–6904, https://doi.org/10.1175/JCLI-D-11-00258.1.
——, ——, C. E. Holloway, J.-Y. Grandpeix, G. Sèze, D. Coppin, S. J.
Woolnough, and R. Roca, 2013: Does convective aggregation need
to be represented in cumulus parameterizations? J. Adv. Model.
Earth Syst., 5, 692–703, https://doi.org/10.1002/jame.20047.
Tompkins, A. M., 2001: Organization of tropical convection in
low vertical wind shears: The role of water vapor. J. Atmos.
Sci., 58, 529–545, https://doi.org/10.1175/1520-0469(2001)
058,0529:OOTCIL.2.0.CO;2.
——, and G. C. Craig, 1998: Radiative-convective equilibrium in a threedimensional cloud-ensemble model. Quart. J. Roy. Meteor. Soc.,
124, 2073–2097, https://doi.org/10.1002/qj.49712455013.

VOLUME 34——, and A. Semie, 2017: Organization of tropical convection in
low vertical wind shears: Role of updraft entrainment. J. Adv.
Model. Earth Syst., 9, 1046–1068, https://doi.org/10.1002/
2016MS000802.
Wall, C. J., D. L. Hartmann, M. M. Thieman, W. L. Smith Jr., and
P. Minnis, 2018: The life cycle of anvil clouds and the top-ofatmosphere radiation balance over the tropical west Pacific.
J. Climate, 31, 10 059–10 080, https://doi.org/10.1175/JCLI-D18-0154.1.
Wentz, F. J., 2000: Satellite measurements of sea surface temperature through clouds. Science, 288, 847–850, https://doi.org/
10.1126/science.288.5467.847.
White, B. A., A. M. Buchanan, C. E. Birch, P. Stier, and K. J.
Pearson, 2018: Quantifying the effects of horizontal grid
length and parameterized convection on the degree of convective organization using a metric of the potential for convective interaction. J. Atmos. Sci., 75, 425–450, https://doi.org/
10.1175/JAS-D-16-0307.1.
Wing, A. A., 2019: Self-aggregation of deep convection and its
implications for climate. Curr. Climate Change Rep., 5, 1–11,
https://doi.org/10.1007/s40641-019-00120-3.
——, and K. A. Emanuel, 2014: Physical mechanisms controlling
self-aggregation of convection in idealized numerical modeling simulations. J. Adv. Model. Earth Syst., 6, 59–74, https://doi.org/10.1002/2013MS000269.
——, and T. W. Cronin, 2016: Self-aggregation of convection inlong channel geometry. Quart. J. Roy. Meteor. Soc., 142, 1–15,
https://doi.org/10.1002/qj.2628.
——, K. Emanuel, C. E. Holloway, and C. Muller, 2017:
Convective self-aggregation in numerical simulations: A review. Surv. Geophys., 38, 1173–1197, https://doi.org/10.1007/
s10712-017-9408-4.
Xu, K.-M., Y. Hu, and T. Wong, 2019: Convective aggregation andindices examined from CERES cloud object data. J. Geophys.
Res. Atmos., 124, 13 604–13 624, https://doi.org/10.1029/
2019JD030816.
Yang, D., 2018: Boundary layer diabatic processes, the virtual effect, and convective self-aggregation. J. Adv. Model. Earth
Syst., 10, 2163–2176, https://doi.org/10.1029/2017MS001261.
Young, G. S., S. M. Perugini, and C. W. Fairall, 1995: Convective
wakes in the equatorial western Pacific during TOGA. Mon. Wea.
Rev., 123, 110–123, https://doi.org/10.1175/1520-0493(1995)123,0110:
CWITEW.2.0.CO;2.

Unauthenticated | Downloaded 02/03/21 12:02 AM UTC