OCTOBER 2014

MASUNAGA AND L’ECUYER

3747

A Mechanism of Tropical Convection Inferred from Observed
Variability in the Moist Static Energy Budget
HIROHIKO MASUNAGA
Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan

TRISTAN S. L’ECUYER
Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin(Manuscript received 23 January 2014, in final form 16 June 2014)
ABSTRACT
Temporal variability in the moist static energy (MSE) budget is studied with measurements from a combination of different satellites including the Tropical Rainfall Measuring Mission (TRMM) and A-Train platforms. A composite time series before and after the development of moist convection is obtained from theobservations to delineate the evolution of MSE and moisture convergences and, in their combination, grossmoist stability (GMS). A new algorithm is then applied to estimate large-scale vertical motion from energy
budget constraints through vertical-mode decomposition into first and second baroclinic modes and a background shallow mode. The findings are indicative of a possible mechanism of tropical convection. A gradualdestabilization is brought about by the MSE convergence intrinsic to the positive second baroclinic mode
(congestus mode) that increasingly counteracts a weak MSE divergence in the background state. GMS is driven
to nearly zero as the first baroclinic mode begins to intensify, accelerating the growth of vigorous large-scale
updrafts and deep convection. As the convective burst peaks, the positive second mode switches to the negativemode (stratiform mode) and introduces an abrupt rise in MSE divergence that likely discourages further
maintenance of deep convection. The first mode quickly dissipates and GMS increases away from zero,
eventually returning to the background shallow-mode state. A notable caveat to this scenario is that GMS serves
as a more reliable metric when defined with a radiative heating rate included to offset MSE convergence.

1. Introduction
Moist processes are crucial for the maintenance oftropical large-scale circulation that, in turn, conditions the
local environment to be favorable or unfavorable formoist convection. A wide spectrum of ideas from simple
conceptual theory to sophisticated cumulus parameterizations have been proposed to deal with those two-way
processes central to tropical dynamics. As a simplest approach to this problem, Neelin and Held (1987) devised
a way to reduce the intrinsic complexity to a tractablelevel by invoking the concept of gross moist stability1

1
The term ‘‘gross moist stability’’ itself was first coined by Heldand Hoskins (1985).

Corresponding author address: Hirohiko Masunaga, Hydrospheric Atmospheric Research Center, Nagoya University, Furocho,
Chikusa-ku, Nagoya 464-8601, Japan.
E-mail: masunaga@hyarc.nagoya-u.ac.jp
DOI: 10.1175/JAS-D-14-0015.1
Ó 2014 American Meteorological Society(GMS). GMS in its original form is equivalent to thevertically integrated horizontal divergence of moist static
energy (MSE) divided by lower-tropospheric convergence. Variants of GMS have since been utilized extensively for different theoretical applications (e.g., Neelin
and Yu 1994; Neelin and Zeng 2000; Sobel and Gildor
2003; Sobel and Neelin 2006; Raymond and Fuchs 2007,2009; Sugiyama 2009a,b; Raymond et al. 2009).
Whereas GMS was originally intended as a positive
constant prescribed to seek steady-state solutions, GMS
is in theory applicable to time-dependent solutions.
Raymond (2000) explored this direction and discussed
the possibility of GMS being negative, in which case thesystem is subject to a positive feedback where an importof MSE would lead to heavier precipitation and thus
further strengthen the MSE convergence (or conversely
an MSE export would make a dry column even drier). A
negative GMS was confirmed to take place during times
when a self-sustaining growth of convection and largescale vertical motion occurs in cloud-resolving model

3748

JOURNAL OF THE ATMOSPHERIC SCIENCES

simulations (Bretherton et al. 2005; Sessions et al. 2010).
GMS is thus not an externally specifiable constant but
a variable internal to the system itself (Kuang 2011). The
temporal evolution of GMS as convection grows anddecays, however, has yet to be verified against observational evidence.
In contrast to the widespread interests in theoreticaland modeling studies, GMS has not received as muchattention in observational work with a few notable exceptions based on reanalysis datasets (Yu et al. 1998;
Back and Bretherton 2006; Peters et al. 2008). Theseauthors, aware of the potential limitations in reanalysis
data, compared multiple datasets from different sources
and found tolerable but consistent disagreements
among them. GMS is in the first place aimed at ‘‘summarizing our ignorance of the details of the convective
and large-scale transients’’ (Neelin and Held 1987),
which involve the processes that may be controlled by(or even built into) parameterized physics in the reanalysis data production. Genuine observations of GMS,
on the other hand, are technically challenging. Satellite
observations provide uniform soundings of the global
atmosphere beyond the reach of ground networks, but
no currently operational satellite sensor is capable ofmeasuring the complete vertical profile of divergencefrom which GMS is calculated.
Meanwhile, Masunaga (2013) demonstrated that thevertically integrated moisture convergence and dry
static energy (DSE) convergence could be estimatedfrom satellite observations alone with the help of waterand thermal budget constraints. This strategy is further
extended in the present paper to yield a full verticalstructure of large-scale mean divergence (and thus vertical velocity). A unique aspect of the current approachis that it avoids using the momentum equations to derive
atmospheric vertical motion, relying instead largely on
thermodynamic consideration. This offers a huge advantage for satellite data analyses, given that satellite
remote sensing provides limited access to wind measurements but is a rich source of the thermodynamic
variables such as air temperature, humidity, and precipitation (or vertically integrated condensational
heating). The new approach proposed here opens apathway to generating observationally based estimatesof GMS fully independent of model parameterizations.
This direction is also explored by Handlos and Back(2014), who developed a semiempirical approach toevaluating large-scale vertical motion by combining
various satellite-based data products with reanalysis
data.
The main objectives of this work are to provide anobservational diagnosis of GMS with particular focus on
its evolution over time and to discuss a plausible

VOLUME 71

mechanism of tropical convection as inferred from theobservations. Following sections 2 and 3, which outline
the data and method, analysis results are presented in
section 4. A mechanism of tropical convection is discussed in light of the current findings in section 5, andconcluding remarks are given in section 6.

2. Data
The data ingested into the analysis are summarized inthis section. The Aqua Atmospheric Infrared Sounderand Advanced Microwave Sounder Unit (AIRS/
AMSU, hereafter AIRS collectively) provide a cloudcleared air temperature and water vapor mixing ratio in
the level-2 AIRX2RET, version 5, dataset (Susskind
et al. 2003, 2011). The Aqua Advanced Microwave
Scanning Radiometer for Earth Observing System(AMSR-E) is employed for column water vapor (CWV)
and sea surface temperature (SST) via the Remote
Sensing Systems (RSS; Wentz and Meissner 2000), as
well as for precipitation retrieved by the Goddard Profiling (GPROF) 2010 algorithm (Kummerow et al. 2001,2011). The CloudSat Cloud Profiling Radar (CPR) 2BCLDCLASS (Wang and Sassen 2001), 2B-FLXHRlidar (L’Ecuyer et al. 2008; Henderson et al. 2013), and
2C-PRECIP-COLUMN (Haynes et al. 2009) products
are used for cloud properties, the radiative heating rate,
and precipitation-type identification, respectively. Nearsurface wind vectors are obtained from the Quick
Scatterometer (QuikSCAT) SeaWinds level-3 daily
gridded data (Perry 2001). The Aqua and CloudSat
satellites, both participating in the A-Train instrument
constellation, have overpasses around 0130 and 1330
local time (LT). The QuikSCAT satellite had been flying
around 0600 and 1800 LT until it ceased to operate in
November 2009. Diurnal variations are expected to bestatistically smeared out when averaged between theascending and descending paths, with the exception ofshortwave heating, which, being sampled at 1330 LT,
overestimates the true daytime-mean solar radiation(section 5b). These sun-synchronous satellite observations are analyzed in combination with precipitating
clouds detected by the Tropical Rainfall Measuring
Mission (TRMM) Precipitation Radar (PR) level-2
products (TRMM PR Team 2005). TRMM is in a precessing orbit with a 47-day repeat cycle so the local timeof TRMM observations changes from one orbit to another.
We adopt 13 pressure levels for this analysis (925, 850,
700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa), in
addition to levels at the surface and cloud base that areallowed to vary temporally and spatially. Cloud-basepressure pCB is defined as the lifting condensation level

OCTOBER 2014

3749

MASUNAGA AND L’ECUYER(LCL) determined from observations, and surface pressure is interpolated to AIRS footprints internally in the
AIRS operational algorithm. The analysis covers theglobal tropical oceans (158S–158N) with continents andislands excluded. The analysis period spans 7 years from
1 December 2002 to 30 November 2009 with the exception of CloudSat data, which are only available beginning on 1 July 2006.

the layer below cloud base is referred to as the subcloudlayer (SC). Moisture and DSE convergences are required for the vertical velocity estimates described laterand the algorithm flow is briefly reviewed.
The moisture and thermal budget equations are›q›q
1 v  $q 1 v 5 e 2 c,
›t
›p
›s
›s
1 v  $s 1 v 5 L(c 2 e) 1 QR ,›t›p

3. Methoda. Composite time series
The temporal evolution is constructed with a large
number of sporadic satellite observations that arecomposited into a statistically continuous time series.
The methodology is thoroughly described elsewhere(Masunaga 2012, 2013) and is not repeated here in great
detail. A short summary of the analysis procedure may
be outlined as follows. CloudSat, AIRS, and QuikSCAT
measurements collected over a length of time are sorted
in terms of the lead or lag time relative to the moment
when TRMM detects precipitating clouds. Since theprecessing TRMM orbit intersects other satellite overpasses at irregular time intervals, the overpass timedifference drifts over time. The large collection of satellite measurements analyzed is eventually distributed
continuously along the composite time axis and, when
averaged in each hourly time bin, yields a statisticalrepresentation of the atmospheric variability prior andsubsequent to the occurrence of moist convection.
The large-scale mean thermodynamic field is constructed from the cloud-cleared AIRS retrievals oftemperature and humidity in combination with a semianalytical estimate of the in-cloud sounding (Masunaga2013). In the previous work, the composite analysis was
separated into three cloud types—isolated cumulus
clouds, moderately developed clouds, and highly organized systems—depending on the population density of
TRMM-detected precipitation. We have tested thepresent method with these three types and found little
qualitative difference, so in this paper only highly organized systems, defined when TRMM precipitation
coverage exceeds 50% at time 0, are analyzed to avoid
redundancy.

b. Free-tropospheric convergence of moisture and dry
static energy
Following the method of Masunaga (2013), themoisture and DSE convergences integrated over thefree troposphere (FT) are evaluated based on moistureand thermal budget considerations. Here, FT is definedas the whole tropospheric layer above cloud base, while(1)

These relations may be written in the flux form:›q›qv
1 $  qv 1
5 e 2 c,
›t
›p
›s
›sv
1 $  sv 1
5 L(c 2 e) 1 QR ,
›t
›p

(2)

where v is the horizontal velocity vector, v is the verticalp velocity, e is the reevaporation rate per unit mass, c isthe condensation rate per unit mass, L is the specificlatent heat of liquid water, and QR is the radiative
heating rate per unit mass. Vertically integrating andhorizontally averaging (2) with the horizontal convergence term split into the SC and FT, one obtains
2h$  qviFT 5

Dp›
hqi 1 $  [q( ps )v10 ] SC 2 E 1 Ps
›t
g

(3)

and
2h$  sviFT 5

Dp›
hsi 1 $  [s( ps )v10 ] SC 2 S›tg
2 LPs 2 hQR i ,(4)where DpSC is the SC thickness, ps is the surface pressure, v10 is near-surface wind at 10 m above sea surface,and angle brackets denote vertical integrals:hi[ðpspTPh    iFT [

ðp

CB

pTP

⋯

dp
,
g

⋯

dp
,
g

where the tropopause pressure pTP is fixed at 100 hPa.
The overbar indicates horizontal averaging over a circular large-scale domain with a radius of 100 km.
Each term on the right-hand sides of (3) and (4) is
directly constrained by observations: the storage term isderived from a central difference to the composite timeseries, surface latent and sensible heat fluxes are obtained from the bulk formulas of Large et al. (1994), andsurface precipitation and the radiative heating rate are

3750

JOURNAL OF THE ATMOSPHERIC SCIENCES

adopted from the AMSR-E and CloudSat data products,
respectively. The SC convergence of moisture and DSE
is computed with the AIRS sounding and scatterometerwind under the assumption that SC is well mixed overheight dynamically and thermodynamically at all times.
This assumption assures that q, s, and v10 are each vertically homogeneous below cloud base, allowing the integral over SC to be expressed by near-surface variables
alone, as found on the right-hand sides of (3) and (4). In
general, q and s are known to be nearly vertically constantover tropical oceans (Johnson et al. 2001, and references
therein). The SC wind is also relatively well mixed fromthe surface up to cloud base or roughly 500 m in height(Brümmer et al. 1974), although wind speeds averaged
over the atmospheric boundary layer might be larger than
jv10j by 10%–20% (Stevens et al. 2002). In this work, noattempt is made to reconcile the difference between v10
and the SC-mean wind since the discrepancy is generally
small and there is no robust method to precisely offset thepotential bias.
Uncertainties in the budget measurements are withina standard error of 1 W m22 and a bias of approximately
35 W m22 or less [see the appendix in Masunaga (2013)].
These values are small compared to the magnitude ofmoisture and DSE convergences during active convection
and unlikely to introduce significant errors into the verticalvelocity estimates described next. Along with the errors in
the individual parameters listed above, other uncertainties
may arise from limitations to the analysis methodology.
An obvious limitation is that any vertical motion unaccounted for by a superposition of the three modes inconsideration might not be properly reproduced. One
might raise another concern that it has yet to be investigated further: how well the statistical time series averaged from sporadic snapshots over time represents theevolution of ‘‘real’’ convective systems. Such questions
will be addressed in future work by reevaluating the results
and methodology in light of in situ sounding array data.

c. Large-scale mean vertical velocity
Atmospheric water vapor rapidly decreases upward,
while DSE increases with height toward the tropopause
and beyond. The vertically integrated moisture convergence thus may be considered to mainly represent thelower-tropospheric convergence field, in contrast to
DSE, which is more sensitive to the upper-tropospheric
convergence. It follows that moisture and DSE convergence combined would provide a loose but useful observational constraint on the vertical structure of FT
horizontal convergence (and hence of vertical velocity).
To formulate this into a practical algorithm, the verticalprofile of p velocity is expanded into a finite series of
nondimensional basis functions fk( p) as

VOLUME 71

FIG. 1. Base functions of vertical velocity: first baroclinic mode(solid), second baroclinic mode (dotted), and shallow mode (dashed).

v( p, t) 5 vbg0 ( p) 1 å Vk (t)fk (p) ,kwhere vbg0( p) is the time-independent background pvelocity and Vk(t) is the expansion coefficient associatedwith the kth vertical mode. It is hereafter assumed thatthe temporal variability of v is accounted for by threebasis functions consisting of first and second baroclinic
modes, denoted by fbc1 and fbc2, respectively, anda shallow mode fshl so thatv( p, t) 5 vbg0 ( p) 1 Vbc1 (t)fbc1 ( p)1 Vbc2 (t) fbc2 (p) 1 Vshl (t) fshl ( p) .

(5)

The two baroclinic modes are each prescribed simply bya sinusoidal basis function bounded between the surface
and tropopause:
p 2 pTP,fbc1 ( p) 5 2sin p
ps 2 pTP
p 2 pTP,(6)
fbc2 ( p) 5 2sin 2p
ps 2 pTP
The shallow-mode basis function is determined from thebackground v field as explained later in section 3c(2).
The three basis functions are drawn in Fig. 1.
The first baroclinic mode is often referred to as a deep
convective mode and the second baroclinic mode with its
sign flipped, or the negative second mode, is calleda stratiform mode, based on the fact that the adiabatic
heating structure associated with each vertical mode resembles the diabatic heating profile of the corresponding
cloud type (Mapes 2000; Wu et al. 2000; Majda andShefter 2001). In addition, the second baroclinic modewith low-level updraft (hereafter the positive second

OCTOBER 2014

3751

MASUNAGA AND L’ECUYER

mode) may be dynamically linked with congestus heating
and is called a congestus mode (Khouider and Majda 2006;
Kuang 2008b). The shallow mode is meant to account for
heating confined to the lower troposphere that arises fromshallow cumuli (Wu 2003; Waite and Khouider 2009). The
three basis functions are expected as a whole to describe
the large-scale dynamics within the context of a full spectrum of tropical convective clouds (Johnson et al. 1999).
The method for deriving the temporal evolution of
Vbc1, Vbc2, and Vshl is described in section 3c(1), followed by section 3c(2), where the ancillary algorithm
used to obtain vbg0 and fshl is outlined.

and






›f
›f
›f
Vbc1 s bc1
1 Vbc2 s bc2
1 Vshl s shl
›p FT
›p FT
›p FT
+
*
›vbg0
5 2h$  sviFT 1 hv  $siFT 2 s
.
›p
(10)
FT
The convergence term on the right-hand side is as givenby (3) and (4). At this point, vbg0 is also considered to be
known. Another equation to solve is the boundary
condition at cloud base,vbg0 ( pCB ) 1 V bc1 fbc1 ( pCB ) 1 V bc2 fbc2 ( pCB )1) VERTICAL VELOCITY AND HORIZONTAL

1 Vshl fshl ( pCB ) 5 v( pCB ) ,CONVERGENCE PROFILES

In this study, unlike an authentic approach based on thevertical spectral transformation of basic equations (e.g.,
Fulton and Schubert 1985), time series of the vertical velocity modes are diagnosed from the observed constraint
on large-scale mean moisture and DSE convergences:›v
5 2q$  v 5 2[$  qv 2 $  (q 0 v 0 )]1[v  $q 2 v 0 $q 0 ],›p›v
5 2s$  v 5 2[$  sv 2 $  (s 0 v 0 )] 1 [v  $s 2 v 0 $s 0 ].
s
›p
(7)

(11)

whose right-hand side is determined by the continuity
equation integrated over the SC:ðpCBv( pCB ) 5 2$  v dp 5 $  v10 D pSC .

(12)

ps

q

The horizontal eddy terms above are negligibly small
when the fluctuations in horizontal wind have no appreciable correlation with those in moisture and DSE
and their horizontal gradient, an assumption valid forthe spatial scales of present interest (;100 km) overtropical oceans (e.g., Yanai et al. 1973). Equation (7) isthus reduced to›v’ 2$  qv 1 v  $q,›p›vs’ 2$  sv 1 v  $s ,
›p

q

(8)

It is noted that the vertical eddy transport of moisture and
DSE is significant during active convection and explicitly
included in the present formulation, as will be discussed in
section 5c. For the moment, we focus on the vertical-mode
decomposition of the large-scale mean field. Substituting
the ›v/›p term in (8) with the expanded series [(5)] andintegrating vertically over the FT, one finds






›fbc1
›fbc2
›fshl
1 Vbc2 q
1 Vshl q
Vbc1 q
›p FT
›p FT
›p FT
*
+
›vbg0
5 2h$  qviFT 1 hv  $qiFT 2 q
›p
FT

(9)

As discussed earlier, horizontal wind is assumed to bevertically homogeneous within the SC.
We now have a closed system of three linear equations[(9)–(11)] that yield the three mode coefficients: Vbc1,
Vbc2, and Vshl. The horizontal advection term in (9) and(10), however, has yet to be determined. This is resolved
by an iterative procedure outlined as follows.
(i) First, a slightly simplified version of (9)–(11) issolved with the horizontal advection term omitted. A solution is sought from one time step to thenext until the whole time series of Vbc1, Vbc2, andVshl are obtained. These solutions are derived
individually for each 25-km-wide ring with increasing radii (0–25, 25–50, 50–75 km, etc.) thatas a whole constitutes a circular large-scale domain that is then averaged over the entire domainas[][1pR2

ðR[    ]2pr dr

0

r 5R

’

1 i
å [    ]i21/2 (r 2i 2 r 2i21 ) ,R2 i51

where R (5100 km) is the large-scale-domain radius and ri and ri21 refer to the outer and inner radiiof the (i 2 1/2)th ring. Subdividing the large-scaledomain in this way facilitates computing horizontal
advection.
(ii) The vertical gradient of the p velocity is written interms of the radial wind u as

3752

JOURNAL OF THE ATMOSPHERIC SCIENCES›v(r, p)1 ›ru(r, p)
5 2$  v(r, p) 5 2
,
›p
r
›r

*
(13)

where r denotes the radial coordinate originating at
the composite base point. Azimuthal wind does notappear in (13) because the azimuthal derivative term
is integrated out by large-scale averaging. Equation(13) leads to the following formulation of radial wind:ð 
1 r ›v(r0 , p) 0 0r dru(r, p) 5 2
r 0›p

r 0 5r 
1 i
›v
02
’2 å
(r0 2 2 ri21).
2r i51 ›p i21/2 i(14)The large-scale mean horizontal advection can be
now computed asr 5R 
›q 1 idq’ 2 å u(r 2 2 r 2i21 ),›r R i51
dr i21/2 i
r 5R 
›s
1 i
dsv  $s 5 u ’ 2 å u(r 2 2 r 2i21 ) ,›r R i51
dr i21/2 iv  $q 5 u(15)
where u is given by (14) and d/dr designates the
upwind finite difference over r.
(iii) The time series of Vbc1, Vbc2, and Vshl are updatedwith the complete forms of (9) and (10) andincluding the advection term in (15).
(iv) The procedure from the first three steps is repeateduntil the solution converges. Convergence requires
only six iterations, at most, since horizontal advection
stays much smaller than horizontal convergence in thecurrent applications. A brief discussion on the smallness of the horizontal advection is given in section 6.

2) BACKGROUND VERTICAL VELOCITY AND
SHALLOW MODE

The three modes introduced above are augmented by
the large-scale-mean time-invariant background field
vbg0 to fully explain the observations. This constantbackground and the shallow mode, denoted collectively
by the background shallow mode vbgs , are determinedfrom the quiescent state devoid of active convection.
The quiescent state is defined as the temporal averageover the first and last 12-h sequences out of a 672-h
composite time series. During this stage, the precipitation stays constantly low at 0.2 mm h21 (Masunaga2013). The strategy for obtaining vbgs parallels the procedure for finding the mode coefficients but uses a reduced version of (9)–(11):

q0
*
s0

›vbgs

+

›p
›vbgs
›p

VOLUME 71

5 2h$  q0 v0 iFT ,(16)

5 2h$  s0 v0 iFT ,

(17)

FT

+
FT

and
vbgs ( pCB ) 5 v0 ( pCB ) ,(18)

where the two baroclinic modes and horizontal advection have been omitted since they are safely neglected in
the absence of vigorous convection. The subscript 0 denotes the quiescent state.
A full vertical profile of vbgs is derived with an additional requirement that vbgs be as close as possible to thesubsidence rate required to cancel radiative cooling vrad .
The vertical structure of vrad is computed directly fromthe observed DSE and radiative heating profiles:
vrad

›s0
5 QR,0 .
›p(19)

The background shallow mode is determined by minimizingpTPå [vbgs ( p) 2 vrad ( p)]2

(20)

p5ps

under the constraints of (16)–(18). This procedure is
performed by following the Lagrangian multipliermethod, which provides 16 equations (13 levels 1 3
constraints) to find 16 unknowns that include vbgs given
at all pressure levels.
Figure 2 shows that vbgs is found to be bimodal, consisting of a primary peak around 400–500 hPa anda weaker one at cloud base. The upper peak is consistent
with midtropospheric large-scale ascent typical of tropical climate (e.g., Nitta 1972; Yanai et al. 1973;
Thompson et al. 1979; Houze 1982; Lin and Johnson
1996), while the lower peak is presumably associatedwith shallow cumuli prevailing across tropical oceans aswell (Yanai et al. 1976). In the current formulation, theupper peak is considered to be vbg0 and the lower one isthought of as the shallow mode. The shallow mode isdetached from the constant background so it is allowed
to vary with time. The shallow updraft vshl is separated
from vbg0 in a simple manner such that(vshl ( p) 5

0
forvbgs (p) 2 vrad ( p) for

p , 850 hPa
p $ 850 hPa

OCTOBER 2014

3753

MASUNAGA AND L’ECUYER

Rather, (20) represents the assumption that the background sounding is as close as possible to the radiatively
driven subsidence under the condition that the budget
equations [see (16)–(18)] be satisfied exactly.

4. Results
In this section, the evolution of the MSE budget parameters is presented and examined within the context
of vertical-mode decomposition.

a. MSE budget and GMS
Vertically integrating and horizontally averaging (2)leads to an equation for quantifying the large-scalemean moisture convergence:
2h$  qvi 5

FIG. 2. Subsidence rate balanced against radiative cooling(dashed), and background shallow mode p velocity (solid), as wellas its breakdown into its time-invariant component (filled circle),and shallow mode (shaded).

(
vbg0 ( p) 5

vbgs ( p) for

p , 850 hPa

vrad ( p) for

p $ 850 hPa(see Fig. 2). Note that vbg0 1 vshl 5 vbgs for all pressurelevels. The shallow-mode basis function is defined bynormalizing vshl asfshl ( p) 5

vshl ( p).
vshl ( pCB )(21)

The shallow and background modes as defined here
are not orthogonal to the two baroclinic modes introduced earlier. The lack of orthogonality does not violate mathematical self-consistency in the current
method, which only involves the observationally constrained algebraic equations without invoking any
spectral transformation. By design, the backgroundshallow mode explains the whole budget residual unaccounted for by the first two baroclinic modes and,hence, in theory absorbs the contributions from all of thehigher-order modes. It is also noted that the minimization operation [(20)] should not be confused as the solution is obtained through a least squares fit to thebudget constraint and thus is exact only to that extent.

(22)

The right-hand side contains known observables only
[see discussion in section 3c(1)] and is used as a diagnostic measure of moisture convergence integrated
over the whole troposphere. Similarly, the MSE conservation equation serves as a formula for estimating
MSE convergence:
2h$  hvi 5

and›hqi 2 E 1 Ps .
›t›hhi 2 LE 2 S 2 hQR i ,
›t

(23)

where h [ s 1 Lq is MSE.
Figure 3 delineates the composite time series ofmoisture and MSE convergences estimated with (22)and (23). The time of the precipitation occurrence detected by the TRMM PR defines time 0 in the composite
time series. Moisture convergence is enhanced during
periods of active convection, largely counteracted by
precipitation with minimal contributions from surface
evaporation and moisture storage (Fig. 3a). It is notedthat the magnitude of moisture convergence depends on
the intensity of the associated convection and would
weaken to a level only slightly greater than local evaporation when composited with respect to isolated cumuli(Masunaga 2013). MSE convergence (solid curve in
Fig. 3b) begins slightly negative and gradually approaches zero before abruptly dropping at the time ofpeak convection and then slowly increasing toward zeroagain. The weak MSE divergence at the initial (orbackground) stage is balanced by the surface latent heat
supply (dashed) and the radiative cooling (dotted–
dashed). Sensible heat flux (dotted) is negligible
throughout. The MSE storage term (shaded) exhibitsa systematic increase over time with the exception ofa sudden drop in the middle, closely paralleling the
temporal evolution of the MSE divergence.

3754

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 71

FIG. 3. Composite time series of moisture and MSE budget parameters. (a) Moisture convergence (blue solid), surface precipitation (green dashed), evaporation (red dotted), andmoisture storage (shaded), all scaled by L into the energy unit (W m22). (b) MSE convergence(blue solid), evaporation (green dashed), sensible heat (red dotted), radiative heating (brown
dotted–dashed), and MSE storage (shaded; W m22). (c) Raw (shaded) and smoothed (solid)
normalized GMS (no units). A 66-h running mean is applied to the smoothing of GMS.

These estimates of moisture and MSE convergences
make it possible to explicitly evaluate a slightly modified
version of the ‘‘normalized GMS’’ proposed by Raymond
et al. (2007):
h$  hvi.
GMS [ 2
Lh$  qvi

(24)

The time series of GMS (Fig. 3c) suffers a statisticalfluctuation that arises when the denominator (moisture
convergence) diminishes to within the noise levelaround zero. With the noises smoothed out by 66-h
running mean, GMS is found to gradually decrease fromabout 1 and nearly vanishes at 224 h. After remaining
close to zero until 26 h, GMS slowly climbs back toa level on the order of unity but somewhat higher thanits initial value. Typical values of the normalized GMS in
the literature range between 0.1 and 0.6 (Raymond et al.
2009; Sugiyama 2009a), roughly comparable to thepresent estimate when averaged over time. Figure 3
suggests, however, that GMS should have a systematic
temporal evolution associated with convective growthand decay. Physical processes relevant to the GMS
variability and underlying dynamics will be explored in
section 5.

b. Vertical motion and mode decomposition
Figure 4 shows the vertical structure of large-scalemean p velocity [the sum of all modes constructed
through (5)] and horizontal convergence obtained asa by-product. A strong updraft sharply develops within
12 h of time 0 and gives rise to a midtropospheric maximum around 500 hPa before quickly dissipating. The
structural evolution of horizontal convergence is characterized by a deepening of the lower-tropospheric
convergence prior to convection, followed by an
abrupt SC, divergence likely due to convective downdraft. A coupling of lower-tropospheric convergenceand upper-tropospheric divergence is evident at thepeak time of convection, a feature known to accompany
organized convective systems (Mapes and Houze 1995).
The breakdown into individual v-mode coefficients ispresented in Fig. 5a. The first baroclinic mode rapidly
grows to a prominent peak and then dies out quickly,
closely in line with the moisture convergence and precipitation (Fig. 3a). The first mode largely dominates theother modes in amplitude (note that Vbc1 is rescaled aslabeled along the right axis) and is almost solely responsible for establishing the midtropospheric updraft
maximum seen in Fig. 4a. The second baroclinic mode

OCTOBER 2014

MASUNAGA AND L’ECUYER

3755

FIG. 4. (left) Composite time series of (a) the large-scale mean vertical velocity anomaly and (b) the horizontal
convergence anomaly. The anomaly is defined against (right) the background (the first and last 12-h sequences
averaged together).

initially emerges as the positive mode and gradually
evolves until around 26 h, when Vbc2 suddenly becomes negative. The negative second mode then slowly
declines and eventually disappears. The shallow mode
stays nearly constant aside from a ‘‘dip’’ shortly after
the time of peak convection, when Vshl momentarily
hits zero.

The evolution of precipitating-cloud occurrence is presented in Fig. 5b for comparison with the vertical-mode
coefficients. Each of the cloud types shown here (i.e.,
shallow, convective, and stratiform) is derived from theprecipitation-type flag from the CloudSat 2C-PRECIPCOLUMN product. Congestus clouds are likely represented by the shallow category but may be partially

FIG. 5. Composite time series of the vertical modes and precipitating cloud occurrences.
(a) Vertical velocity mode coefficients for the first baroclinic mode (blue solid; labeled on theright axis), second baroclinic mode (green dashed), and shallow mode (red dotted).
(b) CloudSat precipitation occurrence for the three cloud types of convective (blue solid),
stratiform (green dashed; labeled on the right axis), and shallow/congestus (brown dotted).

3756

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 71

FIG. 6. Composite time series of (a) moisture convergence, (b) MSE convergence, and(c) GMS, each broken down into the first baroclinic mode (blue solid), second baroclinic mode
(green dashed), and background shallow mode (red dotted). The total is shaded.

classified as convective when the cloud top develops
relatively deeply. The population of shallow/congestus
clouds gradually increases over time until they give way
to stratiform clouds around 26 h. This behavior appears
to support the expectation that the first and second
halves of the second baroclinic mode are associated withcongestus and stratiform clouds, respectively. Convective clouds, on the other hand, bear similarity to the firstbaroclinic mode. The convective curve reaches a peakjust 1–2 h before time 0 in accordance with the first mode
peak, followed a few hours later by the stratiform peak.
Convective clouds have smaller areal coverage thanstratiform clouds by almost an order of magnitude, although convective clouds are known to predominate in
rainfall, and thus in condensational heating, once vigorous deep convective cores develop.

5. Mechanics of GMS variability
a. Mode decomposition of GMS and a mechanism of
tropical convection
Once the vertical mode coefficients are obtained,moisture convergence can be similarly decomposed into

individual modes as expanded in (9). Figure 6a showsthat the first baroclinic mode alone nearly describes the
moisture convergence as one might expect from its
predominance over other modes (Fig. 5a). In contrast,
the evolution of MSE convergence arises from a moreeven competition among the three modes (Fig. 6b). A
weak MSE divergence in the background state is morestrongly counteracted by a growing MSE convergence
brought on by the positive second mode (congestusmode) as time proceeds. The second mode then becomes
sufficiently strong to totally cancel out the backgroundshallow mode, resulting in zero MSE convergence prior
to the peak convection, as observed in Fig. 3b. The positive second mode suddenly switches to the negativemode at 26 h, which introduces a sudden onset of MSE
divergence that now enhances (rather than competing
against) the diverging background. The first mode also
momentarily strengthens the MSE divergence but remains minimal through the rest of the period. The MSE
divergence gradually weakens as the second mode tapers off after the convection ceases.
The contrast among the different patterns of behavior
specific to each mode is best illustrated in GMS (Fig. 6c).
Different GMS modes are defined here simply as theOCTOBER 2014

MASUNAGA AND L’ECUYER

3757

FIG. 7. Composite time series of large-scale mean vertical MSE advection (K day21) for the(a) first baroclinic mode, (b) second baroclinic mode, and (c) background shallow mode.

ratio of the MSE and moisture convergences that are
individually computed, and hence the decomposedmodes do not sum to the original GMS. GMS stays
positive for the background shallow mode, while thesecond baroclinic mode is consistently negative in GMS.
The first baroclinic mode virtually vanishes throughout.
The constant nature of GMS for the two baroclinic
modes arises from a near cancellation of timedependent mode coefficients between the numerator
and denominator in (24).
Reasons why the different GMS modes are diverse insign and magnitude can be understood as follows. MSE
convergence is mathematically equivalent to the vertically integrated vertical advection of MSE:
+
*
+
*
›v
›h
52 v
.
(25)
h
›p
›p
In the mean tropical sounding, MSE decreases withheight, reaching a midtropospheric minimum and thenincreases with height aloft; that is, ›h/›p is positive in thelower troposphere and negative in the upper troposphere. Given this feature common to all vertical modes,
the nature of MSE convergence depends on the shape ofthe v profile in (25). The first baroclinic mode, for whichv , 0 at all pressure levels, yields a vertical MSE

advection that changes sign from positive to negativewith large-scale upward motion through the middle
troposphere (Fig. 7a). Vertical MSE advection, although very large at individual levels, is canceled out toa large extent when integrated vertically and therefore
the contribution of the first mode to MSE convergence is
unexpectedly small (Fig. 6b) despite its dominant sharein large-scale dynamics (Fig. 5a). Recalling as well thatthe first mode gives rise to robust moisture convergence(Fig. 6a), one finds that the first mode has the effect ofstrongly reducing GMS.
For the second baroclinic mode, v has opposite signs
between the lower and upper halves of the troposphere.
It follows that vertical MSE gradient and v each change
sign at the same height and would in tandem makevertical MSE advection entirely positive or negative
throughout the troposphere. Figure 7b confirms thissimple deduction, with the exception of a thin layer at
600 hPa where the MSE minimum and the second-mode
node have a slight difference in altitude. The positive
second mode results in MSE import and the negativemode leads to MSE export at almost all heights, explaining the abrupt change in MSE convergence at 26 hwhen the second mode changes sign (Fig. 6b). A similartransition occurs simultaneously in moisture convergence (Fig. 6a), so GMS stays negative at all times for3758

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 71

FIG. 8. Composite time series of the vertical profile of cloud radiative effect (W m22) constructed with (a) ascending or afternoon (1330 LT) paths and (b) descending or midnight (0130
LT) paths.

the second mode. This is the origin of the unique importance of the second baroclinic mode in the mechanism of tropical convection, as discussed later.
The upper-troposphere-peaked vbg0 profile (Fig. 2)
makes MSE divergent (Fig. 7c), although MSE is imported to a lesser extent by the lower-tropospherepeaked vshl . These two competing processes explaina weak MSE divergence in the background shallowmode.
A modest moisture import is persistently driven by theshallow mode except during a short period immediately
after the convective peak. The shallow mode is temporarily shut off during this period, which may likely beascribed to a downdraft of dry, cold air. The transient
cutoff in moisture convergence is responsible for the
spike in the background shallow-mode GMS (Fig. 6c).
The findings thus far may be summarized into a working hypothesis for a mechanism of tropical convection.
GMS slowly diminishes from a positive value on theorder of unity to zero prior to convection, primarily due
to a weakening of MSE divergence. The reduction of
GMS is ultimately attributable to the growth of thecongestus mode, which in theory has a negative GMS if
acting alone. GMS, however, stays tightly bound to zero.
This may be explained by the fact that a reduction of
GMS allows the convection to deepen and helps the firstbaroclinic mode, having zero GMS, to dominate. In
other words, a deep updraft acts against the onset ofMSE convergence because it activates an uppertropospheric MSE export that closely cancels out thelower-tropospheric MSE import. Nevertheless, GMS
staying near zero finally gives rise to a vigorous convective burst accompanying a drastic amplification of
the first mode. The convective burst, however, is notsustained for long as it is followed by a rapid buildup of
MSE divergence coinciding with a transition of thecongestus mode into the stratiform mode. The restoration of MSE divergence brings GMS back to a positive
value and puts an end to the period of enhanced largescale updraft driven by active convection.
There remain two MSE budget terms (i.e., radiative
heating and convective eddy transport) that have yet to
be examined. They are each investigated in the remainder of this section.

b. Effects of radiative heating on the MSE budget
The composite diagrams presented so far are constructed from all satellite orbits with no distinction in thelocal time of observation. The ascending and descending
orbital swaths are individually analyzed in this section sothat afternoon (1330 LT) and midnight (0130 LT) observations are separated to depict the diurnal contrast inradiative heating. The afternoon observations of shortwave radiation qualitatively reflect daytime-mean climatology but exaggerate its magnitude as noted in
section 2. Note that the entire calculations including vradin (19) are redone individually with the morning or afternoon path.
Figure 8 shows the vertical profile of the cloud radiative effect (CRE) defined as[Y[Y
2 Fclr) 2 (Fall
2 Fall
),CRE 5 (Fclr

where Fclr and Fall are the net (shortwave plus longwave)
radiative fluxes for clear and all skies, respectively, andarrows indicate upwelling ([) and downwelling (Y)fluxes. Note that the CloudSat radiative flux product isderived from broadband radiative transfer calculations

OCTOBER 2014

MASUNAGA AND L’ECUYER

3759

FIG. 9. As Fig. 8, but for the radiative heating rate (K day21).

applied to the observed cloud properties, making a synthetic ‘‘clear sky’’ estimate readily available by eliminating clouds internally in the radiative transfer model(Henderson et al. 2013). A sharp minimum occurs at thetime of convection and falls deeper as altitude decreases
in the afternoon CRE (Fig. 8a). This striking featurearises from the cloud shielding incoming shortwave radiation as well as an elevated greenhouse effect due tocirrus and cirrostratus clouds detrained from penetrating convection. The longwave effect is solely observed in
CRE at midnight (Fig. 8b), where a broad uppertropospheric maximum develops during active convection as expected.
The vertical distribution of the net radiative heating
rate QR is plotted in Fig. 9. In the afternoon, radiative
heating is marked by elevated shortwave cloud absorption during active convection in the upper troposphere(Fig. 9a). Longwave cooling at the tops of melting-layer
clouds, frequently observed over tropical oceans (Mapes
and Zuidema 1996; Yasunaga et al. 2006), are likely
responsible for the sharp discontinuity at a height of
4–5 km. The midnight composite (Fig. 9b) shows that thegreenhouse effect is mildly modulated by convective
activity in the lower and midtroposphere while at upper
levels, in contrast, a cloud-top cooling develops immediately after time 0.
This temporal evolution remains visible but is not asprominent in the total tropospheric cooling hQRi (Fig. 10),
since the upper-tropospheric contribution is diluted tosome extent by the density-weighted vertical integral.
More evident is the diurnal contrast that arises between
the afternoon heating slightly below 100 W m22 (Fig. 10a)and the midnight cooling at 2200 W m22 (Fig. 10b). A
caveat is that any day-long temporal sequence in reality
must involve a diurnal cycle superimposed while thecomposite time series in this work by design lacks it. The
current compositing technique is unrealistic in this regard and care must be taken not to overinterpret theresults.
Another notable feature of Fig. 10 is that MSE convergence (dotted) no longer vanishes but stays negative(afternoon) or positive (midnight) prior to active convection. It is instead the sum of MSE and radiative
heating (solid) that consistently approaches zero in allcases. The working hypothesis argued in section 5a remains valid but must be revised to note that MSE
convergence is augmented by radiative heating. Accordingly, GMS is modified with a radiative cooling rate
added to the numerator,h$  hvi 2 hQR i,
GMS(updated) 5 2
Lh$  qvi

(26)

which is conceptually equivalent to the ‘‘effective
GMS’’ introduced by Su and Neelin (2002) andBretherton and Sobel (2002). Figure 11 shows two
versions of GMS (smoothed over time for visual clarity) that are obtained with or without radiative heating
included in the numerator. The time axis ends at 24 hbecause the sample-size reduction from separating day
and night increases the statistical noise in the denominator of GMS to an intolerable level for t . 24 h.
The large dispersion between the afternoon and midnight composites inherent in the original definition of
GMS given by (24) (Fig. 11a) is substantially reduced
when the numerator is updated to include radiative
heating via (26) (Fig. 11b). GMS is confirmed to offer
a more universal reference to the mechanism of tropical convection when radiative effects are explicitly
taken into account.

3760

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 71

FIG. 10. Vertically integrated MSE convergence (black dotted), radiative heating (brown
dotted–dashed), their sum (blue solid), and MSE storage (color shaded) for (a) ascending or
afternoon (1330 LT) paths only, (b) descending or midnight (0130 LT) paths only, and (c) all
satellite paths.

c. Vertical eddy transport of MSE
It has been seen that the combination of verticallyintegrated MSE convergence and radiative heatingnearly vanishes preceding the growth of convection.
This may be physically interpreted to mean that a coordinated growth of convection and large-scale updraft

is promoted when the diabatic heating source reaches
a level sufficient for the ascent to work against largescale adiabatic cooling. This argument, however, is incomplete in that only the vertically integrated MSE
budget has been examined so far. An additional mechanism is needed to internally transport the latent heating

FIG. 11. Composite time series of GMS smoothed temporally by a 66-h running mean.
(a) Original definition from (24) and (b) updated definition in (26) with radiative heating included in the numerator. Hours beyond 124 h are omitted.

OCTOBER 2014

MASUNAGA AND L’ECUYER

3761

FIG. 12. Composite time series of (a) large-scale mean vertical MSE advection (K day21),(b) vertical eddy MSE transport (K day21), and (c) total MSE transport plus QR (K day21).

from low-level moisture to the upper troposphere, where
an upward-increasing MSE hampers vertical motion fromoccurring spontaneously. The solution to this problem
has been known since the pioneering work of Riehl and
Malkus (1958), who found that towering convective
clouds are a key ingredient in the vertical redistribution of
MSE. The thermodynamic impact of condensational
heating was later formulated in terms of eddy energetics
by Manabe and Smagorinsky (1967), Nitta (1970) and in
subsequent energy budget studies (e.g., Yanai et al. 1973).
This section is devoted to a brief investigation of verticaleddy transport as a bulk measure of the convective effects
on the MSE budget, aimed at confirming that the current
analysis is in line with the literature.
Averaging (1) horizontally, one finds the large-scalemean MSE budget equation
›h
›h
›h0
1 v  $h 1 v 5 QR 2 v0 ,
›t
›p
›p

(27)

where the last term refers to the vertical eddy transportof MSE. The eddy advection term v0 ›h0 /›p is interchangeable with the flux-form expression of the vertical eddy transport ›h0 v0 /›p when horizontal eddy flux
is negligible. All terms in (27) except the last one are
known at every height from the present analysis so far,so this equation can be used to evaluate the verticalprofile of eddy MSE transport as a residual of the otherterms.
A striking contrast is evident between large-scalemean vertical MSE advection (Fig. 12a) and its eddy
counterpart (Fig. 12b). Large-scale mean vertical advection, or the third term on the left-hand side of (27), is
positive in the lower troposphere and negative in theupper troposphere, primarily in response to the firstbaroclinic mode (Fig. 7a). The vertical eddy advectionof MSE, on the other hand, consists of an uppertropospheric positive and a lower-level negative component. The positive eddy advection aloft is presumed tooriginate from convective plumes through which highMSE air in the subcloud layer is lifted moist adiabatically to the level where it is detrained. At the same time,a mesoscale downdraft in a mature convective systemdraws down midtropospheric low-MSE air and is speculated to account for the negative eddy advection in thelower troposphere. The competing effects of large-scale
dynamics and convective eddies, with the radiative
heating profile taken into account, largely cancel eachother but leave behind a faint residual (Fig. 12c). Equation(27) indicates that the storage and horizontal advection
terms make up this residual, with the former dominating the latter since MSE is horizontally homogeneous

3762

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 71

modest values of moisture convergence and MSE divergence. The trajectory of the observed temporal
evolution follows an oval-like path, as schematicallydrawn in Fig. 13, and can be explained in terms of three
distinct stages.
Stage I (t , 26 h)—The background MSE divergenceis gradually offset toward zero by the MSE convergence brought about by the positive second baroclinic
mode (congestus mode). The congestus mode consistsof modest lower-tropospheric ascent associated withcongestus clouds and upper-level subsidence, which
together import both moisture and MSE. Recallingthat the background vertical motion consists of a weak
upper-tropospheric updraft, one could attribute theupper-level subsidence in the second mode to a gradual weakening of the background ascent during periods devoid of vigorous disturbances. GMS is driven
close to zero, a critical line for an unstable growth ofmoist convection to occur. The first baroclinic modeand deep convection begin to intensify.
d Stage II (26 , t , 0 h)—The growth of vigorous largescale updrafts accelerates sharply in concert witha burst of deep convection. This involves the development of the first baroclinic mode, in whicha low-level MSE import is now totally (or evenexcessively) compensated by an upper-level MSE
export. A negative GMS thus does not occur but
GMS remains zero during this stage. At the sametime, the positive second mode switches to the negative mode (stratiform mode), presumably concurrent
with the onset of a lower-tropospheric downdraft
characteristic of the development of stratiform rain
in mature convective systems. The onset of thestratiform mode introduces an abrupt rise in MSE
divergence and now makes the thermodynamic environment less favorable for convection development.
d Stage III (t . 0 h)—The first mode and deep convection rapidly dissipate. The stratiform mode also
weakens but more slowly. At this stage, MSE isdiverging while moisture is converging once themomentary low-level downdraft ceases, which together leads to a positive GMS. GMS increases awayfrom zero and is restored to beyond the initial level as
the background shallow mode alone is being left
behind.
dFIG. 13. Schematic summary. Trajectories are projected onto theplane of moisture convergence (abscissa) and MSE convergenceplus radiative heating (ordinate).

over the spatial scale of interest. A temporary lowertropospheric negative around time 0 in Fig. 12c suggeststhat the drying due to convective downdraft overcompensates the moistening by large-scale ascent at theconvective peak. This possibly has the effect of hindering the convective system from intensifying further.

6. Conclusions and discussion
Observations from multiple satellite platforms arecoordinated to perform a composite analysis of thetemporal variability associated with convective development within the context of the MSE budget. The
analysis is designed to yield a statistically continuous
time series of the atmospheric state prior and subsequent to the occurrence of convection by compositing
pairs of satellite measurements with respect to the observational lag or lead time between them. Observational thermodynamic constraints are then exploited toevaluate large-scale vertical motion through verticalmode decomposition.
A schematic summary of the results is presented inFig. 13, where the temporal variability in the MSE
budget is illustrated in terms of moisture convergence(abscissa) and MSE convergence plus radiative heating(ordinate). GMS is defined on this plane as the inclination of the vector pointed from the origin to a given
point, with its sign indicated in each quadrant of the
figure. GMS is therefore close to zero near the abscissa
and increases in absolute value moving toward theordinate.
The first baroclinic mode spans a long distance boundto the abscissa, while the second mode stays on a shortslanted path, which moves back and forth between thequadrants of negative GMS. The background shallow
mode barely deviates from the background state having

These three stages are reminiscent of a recent schoolof thought for convectively coupled equatorial waves
where the first and second baroclinic modes alternatewith each other in line with the progression wherecongestus clouds gradually grow deeper and finally give
way to stratiform clouds (e.g., Khouider and Majda
2006; Peters and Bretherton 2006; Kuang 2008a,b).

OCTOBER 2014

MASUNAGA AND L’ECUYER

Similar mechanics are shown to be at work withina general meteorological context beyond wave dynamics. Among the family of tropical waves ranging overa wide spectrum of frequencies, the 2-day waves are ofparticular interest because they are similar in time scale
to the variability found in this study. The 2-day wave
dynamics is known to be explained in terms of the firsttwo or three baroclinic modes developing one after another (Haertel and Kiladis 2004; Haertel et al. 2008) ina manner parallel with the findings of this work. It is
unclear whether the 2-day waves have a dominant influence on the fundamental nature of tropical convectionor, conversely, whether some intrinsic time scale inherent
in the convective effects on large-scale dynamics controls
the scale selection in favor of the 2-day mode, or possibly
the resemblance may be little more than coincidence.
The destabilizing mechanism is explained primarily by
the MSE import intrinsic to the congestus mode in thepresent picture, resembling the ‘‘discharge–recharge’’
scenario discussed by Peters and Bretherton (2006). This
involves large-scale dynamics only and does not necessitate an FT moistening through congestus cloudsor ‘‘preconditioning’’ (e.g., Waite and Khouider 2010;
Hohenegger and Stevens 2013).
One of the intriguing findings above is that GMS isanchored tightly to zero without going negative during
the convective intensification. A negative GMS, with
MSE and moisture both converging, is not observed, as
theorized by Raymond et al. (2009) and simulated by
Sessions et al. (2010), but instead zero GMS appears tobe sufficient to drive an accelerating growth of largescale updrafts. A key element that keeps GMS frombecoming negative is the quick development of the firstmode that efficiently exports high MSE in the upper
troposphere. A dry-gets-drier case of negative GMS isalso worth attention (Bretherton et al. 2005; Sessions
et al. 2010) but is outside the scope of the present
analysis. Our compositing technique is built around thetime of convection and, by design, excludes a prolonged
absence of precipitation.
GMS provides a more reliable metric when radiative
heating is included in its definition [‘‘effective GMS’’;see (26)]. This conclusion is drawn from the fact that
MSE convergence plus radiative heating rate rather
than MSE convergence alone follows a consistent evolutionary track in comparisons between the afternoon
and midnight composite diagrams. Nocturnal convection accompanies a larger (even a positive) MSE convergence than does afternoon convection so as to work
against a greater radiative cooling due to the absence ofshortwave absorption. This supports the arguments of
Randall et al. (1991), who found that a diurnal cycle inlarge-scale vertical motion over the ocean arises in their3763

model because the cloud absorption of solar radiation
somewhat stabilizes the upper troposphere during thedaytime.
The climatology of vertical velocity profiles and,accordingly, of the GMS characteristics changes fromone region to another across tropical oceans (Backand Bretherton 2006). Regional variability in freetropospheric convergence from the present dataset wasstudied previously and was found to be rather small(Masunaga 2013). The temporal evolution of the MSE
budget parameters and GMS are also qualitatively insensitive to the choice of region when broken down
geographically, although the background level of MSE
divergence is somewhat lower in the eastern Pacificwhere large-scale vertical motion climatologically does
not reach as high as in the rest of the tropics (not shown).
Clear regionality is absent in the temporal variability
presumably because the composite time series is constructed around the occurrence of organized convective
systems. Even though the vertical velocity profiles are
climatologically bottom heavy in the tropical eastern
Pacific, occasional intrusions of disturbances there may
temporarily destabilize the troposphere through its entire depth. Such cases may be preferentially sampled in
the current composite analysis, leading to a potential
underrepresentation of the regional climatology.
The results could depend also on the horizontal scaleof interest. Horizontal MSE advection (v  $h) was
found to be minimal throughout, leaving the MSEtransport due to wind divergence (h$  v), which isequivalent to the vertical MSE advection when integrated over the troposphere, to be responsible for
MSE import or export. This is because the horizontal
moisture field, as an ensemble of many convective
events, is nearly uniform within the 100-km-radius domain currently analyzed. Note that this scale is comparable in size to a single grid box typical of climate models
and global assimilation models and is chosen to bebarely large enough to encompass a mature mesoscaleconvective system (Houze 2004) so it represents largescale dynamics but yet retains a close physical relevanceto the convective processes at work inside. Horizontal
moisture gradients can be larger while convergencegenerally weakens as the horizontal scale increases, andas a result horizontal MSE advection would be comparable to or may even overwhelm the vertical advection
over a sufficiently large domain. This is indeed what isobserved in reanalysis datasets (Back and Bretherton2006) and climate models (Maloney 2009), where thehorizontal scale of interest should be at least a few times
as large as the grid resolution. This scale dependence
could raise a terminological ambiguity in the definitionof ‘‘large scale’’ and should be addressed elsewhere.

3764

JOURNAL OF THE ATMOSPHERIC SCIENCES

Acknowledgments. The authors thank Johnny Luo andYu Xie for their comments on an early version of thiswork. The TRMM PR (2A25) dataset was provided by
the Japan Aerospace Exploration Agency (JAXA); theGPROF 2010 precipitation product by Colorado State
University (rain.atmos.colostate.edu/RAINMAP10); the
AMSR-E CWV and SST product by Remote Sensing
Systems (www.remss.com); the CloudSat 2B-CLDCLASS,
2B-FLXHR-LIDAR, and 2C-PRECIP-COLUMN datasets by the CloudSat Data Processing Center (www.
cloudsat.cira.colostate.edu); QuikSCAT SeaWinds ocean
wind vector data by the Physical Oceanography Distributed Active Archive Center (PO.DAAC) at the NASA
Jet Propulsion Laboratory (podaac.jpl.nasa.gov); and the
AIRS/AMSU product by the Goddard Earth Sciences(GES) Data and Information Services Center (DISC;
disc.sci.gsfc.nasa.gov). This work is supported by theJapan Society for the Promotion of Science (JSPS)
Grant-in-Aid for Young Scientists (23740351) and for
Challenging Exploratory Research (26610150).
REFERENCES
Back, L. E., and C. S. Bretherton, 2006: Geographic variability
in the export of moist static energy and vertical motion
profiles in the tropical Pacific. Geophys. Res. Lett., 33,
L17810, doi:10.1029/2006GL026672.
Bretherton, C. S., and A. H. Sobel, 2002: A simple model of a convectively coupled Walker circulation using the weak temperature gradient approximation. J. Climate, 15, 2907–2920,
doi:10.1175/1520-0442(2002)015,2907:ASMOAC.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, doi:10.1175/
JAS3614.1.
Brümmer, B., E. Augstein, and H. Riehl, 1974: On the low-level
wind structure in the Atlantic trade. Quart. J. Roy. Meteor.
Soc., 100, 109–121, doi:10.1002/qj.49710042310.
Fulton, S. R., and W. H. Schubert, 1985: Vertical normal
mode transforms: Theory and application. Mon. Wea.
Rev., 113, 647–658, doi:10.1175/1520-0493(1985)113,0647:
VNMTTA.2.0.CO;2.
Haertel, P. T., and G. N. Kiladis, 2004: Dynamics of 2-day equatorial waves. J. Atmos. Sci., 61, 2707–2721, doi:10.1175/
JAS3352.1.
——, ——, A. Denno, and T. M. Rickenbach, 2008: Verticalmode decompositions of 2-day waves and the Madden–
Julian oscillation. J. Atmos. Sci., 65, 813–833, doi:10.1175/
2007JAS2314.1.
Handlos, Z. J., and L. E. Back, 2014: Estimating vertical motion
profile shape within tropical weather states over the oceans.
J. Climate, doi:10.1175/JCLI-D-13-00602.1, in press.
Haynes, J. M., T. S. L’Ecuyer, G. L. Stephens, S. D. Miller,
C. Mitrescu, N. B. Wood, and S. Tanelli, 2009: Rainfall retrieval over the ocean with spaceborne W-band radar.
J. Geophys. Res., 114, D00A22, doi:10.1029/2008JD009973.
Held, I. M., and B. J. Hoskins, 1985: Large-scale eddies and the generalcirculation of the troposphere. Advances in Geophysics, Vol. 28,
Academic Press, 3–31, doi:10.1016/S0065-2687(08)60218-6.

VOLUME 71

Henderson, D. S., T. S. L’Ecuyer, G. Stephens, P. Partain, and
M. Sekiguchi, 2013: A multisensor perspective on the radiative
impacts of clouds and aerosols. J. Appl. Meteor. Climatol., 52,
853–871, doi:10.1175/JAMC-D-12-025.1.
Hohenegger, C., and B. Stevens, 2013: Preconditioning deep convection with cumulus congestus. J. Atmos. Sci., 70, 448–464,
doi:10.1175/JAS-D-12-089.1.
Houze, R. A., Jr., 1982: Cloud clusters and large-scale verticalmotions in the tropics. J. Meteor. Soc. Japan, 60, 396–410.
——, 2004: Mesoscale convective systems. Rev. Geophys., 42,
RG4003, doi:10.1029/2004RG000150.
Johnson, R. H., T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski,
and W. H. Schubert, 1999: Trimodal characteristics oftropical convection. J. Climate, 12, 2397–2418, doi:10.1175/
1520-0442(1999)012,2397:TCOTC.2.0.CO;2.
——, P. E. Ciesielski, and J. A. Cotturone, 2001: Multiscalevariability of the atmospheric mixed layer over the western
Pacific warm pool. J. Atmos. Sci., 58, 2729–2750, doi:10.1175/
1520-0469(2001)058,2729:MVOTAM.2.0.CO;2.
Khouider, B., and A. J. Majda, 2006: A simple multicloud parameterization for convectively coupled tropical waves. Part I:
Linear analysis. J. Atmos. Sci., 63, 1308–1323, doi:10.1175/
JAS3677.1.
Kuang, Z., 2008a: A moisture-stratiform instability for convectively coupled waves. J. Atmos. Sci., 65, 834–854,
doi:10.1175/2007JAS2444.1.
——, 2008b: Modeling the interaction between cumulus convection
and linear gravity waves using a limited-domain cloud systemresolving model. J. Atmos. Sci., 65, 576–591, doi:10.1175/
2007JAS2399.1.
——, 2011: The wavelength dependence of the gross moist stability
and the scale selection in the instability of column-integrated
moist static energy. J. Atmos. Sci., 68, 61–74, doi:10.1175/
2010JAS3591.1.
Kummerow, C. D., and Coauthors, 2001: The evolution of
the Goddard Profiling Algorithm (GPROF) for rainfall
estimation from passive microwave sensors. J. Appl.
Meteor., 40, 1801–1820, doi:10.1175/1520-0450(2001)040,1801:
TEOTGP.2.0.CO;2.
——, S. Ringerud, J. Crook, D. Randel, and W. Berg, 2011: An
observationally generated a priori database for microwave
rainfall retrievals. J. Atmos. Oceanic Technol., 28, 113–130,
doi:10.1175/2010JTECHA1468.1.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic
vertical mixing: A review and a model with a nonlocal
boundary layer parameterization. Rev. Geophys., 32, 363–403,
doi:10.1029/94RG01872.
L’Ecuyer, T. S., N. B. Wood, T. Haladay, G. L. Stephens, andP. W. Stackhouse Jr., 2008: Impact of clouds on atmosphericheating based on the R04 CloudSat fluxes and heating rates
data set. J. Geophys. Res., 113, D00A15, doi:10.1029/
2008JD009951.
Lin, X., and R. H. Johnson, 1996: Kinematic and thermodynamic
characteristics of the flow over the western Pacific warm pool
during TOGA COARE. J. Atmos. Sci., 53, 695–715, doi:10.1175/
1520-0469(1996)053,0695:KATCOT.2.0.CO;2.
Majda, A. J., and M. G. Shefter, 2001: Models for stratiform
instability and convectively coupled waves. J. Atmos.
Sci., 58, 1567–1584, doi:10.1175/1520-0469(2001)058,1567:
MFSIAC.2.0.CO;2.
Maloney, E. D., 2009: The moist static energy budget of a composite tropical intraseasonal oscillation in a climate model.
J. Climate, 22, 711–729, doi:10.1175/2008JCLI2542.1.

OCTOBER 2014

MASUNAGA AND L’ECUYER

Manabe, S., and J. Smagorinsky, 1967: Simulated climatology ofa general circulation model with a hydrological cycle II. Analysis of the tropical atmosphere. Mon. Wea. Rev., 95, 155–169,
doi:10.1175/1520-0493(1967)095,0155:SCOAGC.2.3.CO;2.
Mapes, B. E., 2000: Convective inhibition, subgrid-scale triggering energy, and stratiform instability in a toy tropicalwave model. J. Atmos. Sci., 57, 1515–1535, doi:10.1175/
1520-0469(2000)057,1515:CISSTE.2.0.CO;2.
——, and R. A. Houze Jr., 1995: Diabatic divergence profiles
in western Pacific mesoscale convective systems. J. Atmos.
Sci., 52, 1807–1828, doi:10.1175/1520-0469(1995)052,1807:
DDPIWP.2.0.CO;2.
——, and P. Zuidema, 1996: Radiative-dynamical consequences of dry
tongues in the tropical troposphere. J. Atmos. Sci., 53, 620–638,
doi:10.1175/1520-0469(1996)053,0620:RDCODT.2.0.CO;2.
Masunaga, H., 2012: A satellite study of the atmospheric forcing
and response to moist convection over tropical and subtropical oceans. J. Atmos. Sci., 69, 150–167, doi:10.1175/
JAS-D-11-016.1.
——, 2013: A satellite study of tropical moist convection and environmental variability: A moisture and thermal budget analysis.
J. Atmos. Sci., 70, 2443–2466, doi:10.1175/JAS-D-12-0273.1.
Neelin, J. D., and I. M. Held, 1987: Modeling tropical convergence based on the moist static energy budget. Mon. Wea.
Rev., 115, 3–12, doi:10.1175/1520-0493(1987)115,0003:
MTCBOT.2.0.CO;2.
——, and J.-Y. Yu, 1994: Modes of tropical variability under convective adjustment and the Madden–Julian oscillation. Part I:
Analytical theory. J. Atmos. Sci., 51, 1876–1894, doi:10.1175/
1520-0469(1994)051,1876:MOTVUC.2.0.CO;2.
——, and N. Zeng, 2000: A quasi-equilibrium tropical circulation
model—Formulation. J. Atmos. Sci., 57, 1741–1766,
doi:10.1175/1520-0469(2000)057,1741:AQETCM.2.0.CO;2.
Nitta, T., 1970: A study of generation and conversion of eddy
available potential energy in the tropics. J. Meteor. Soc. Japan,
48, 524–528.
——, 1972: Energy budget of heat disturbances over the MarshallIslands during the years of 1956 and 1958. J. Meteor. Soc.
Japan, 50, 71–84.
Perry, K. L., 2001: SeaWinds on QuikSCAT level 3 daily, gridded
ocean wind vectors (JPL SeaWinds project) version 1.1. JPL
Doc. D-20335, Jet Propulsion Laboratory, 39 pp. [Available
online at http://podaac.jpl.nasa.gov.]
Peters, M. E., and C. S. Bretherton, 2006: Structure of tropicalvariability from a vertical mode perspective. Theor. Comput.
Fluid Dyn., 20, 501–524, doi:10.1007/s00162-006-0034-x.
——, Z. Kuang, and C. C. Walker, 2008: Analysis of atmosphericenergy transport in ERA-40 and implications for simple
models of the mean tropical circulation. J. Climate, 21, 5229–
5241, doi:10.1175/2008JCLI2073.1.
Randall, D. A., Harshvardhan, and D. A. Dazlich, 1991: Diurnal
variability of the hydrologic cycle in a general circulation model.
J. Atmos. Sci., 48, 40–62, doi:10.1175/1520-0469(1991)048,0040:
DVOTHC.2.0.CO;2.
Raymond, D. J., 2000: Thermodynamic control on tropical rainfall.
Quart. J. Roy. Meteor. Soc., 126, 889–898, doi:10.1002/
qj.49712656406.
 Fuchs, 2007: Convectively coupled gravity and mois——, and Z.
ture modes in a simple atmospheric model. Tellus, 59A, 627–
640, doi:10.1111/j.1600-0870.2007.00268.x.
——, and ——, 2009: Moisture modes and the Madden–Julian
oscillation. J. Climate, 22, 3031–3046, doi:10.1175/
2008JCLI2739.1.

3765

 Fuchs, 2007: A theory for the spinup of——, S. L. Sessions, and Z.
tropical depressions. Quart. J. Roy. Meteor. Soc., 133, 1743–
1754, doi:10.1002/qj.125.
 Fuchs, 2009: The mechanics of gross——, ——, A. H. Sobel, and Z.
moist stability. J. Adv. Model. Earth Syst., 1, 9, doi:10.3894/
JAMES.2009.1.9.
Riehl, H., and J. S. Malkus, 1958: On the heat balance in theequatorial trough zone. Geophysica, 6, 503–538.
Sessions, S. L., S. Sugaya, D. J. Raymond, and A. H. Sobel, 2010:
Multiple equilibria in a cloud-resolving model using the weaktemperature gradient approximation. J. Geophys. Res., 115,
D12110, doi:10.1029/2009JD013376.
Sobel, A. H., and H. Gildor, 2003: A simple time-dependent
model of SST hot spots. J. Climate, 16, 3978–3992, doi:10.1175/
1520-0442(2003)016,3978:ASTMOS.2.0.CO;2.
——, and J. D. Neelin, 2006: The boundary layer contribution tointertropical convergence zones in the quasi-equilibrium
tropical circulation model framework. Theor. Comput. Fluid
Dyn., 20, 323–350, doi:10.1007/s00162-006-0033-y.
Stevens, B., J. Duan, M. M. J. C. McWilliams, and J. D. Neelin,
2002: Entrainment, Rayleigh friction, and boundary layer
winds over the tropical Pacific. J. Climate, 15, 30–44,
doi:10.1175/1520-0442(2002)015,0030:ERFABL.2.0.CO;2.
Su, H., and J. D. Neelin, 2002: Teleconnection mechanisms fortropical Pacific descent anomalies during El Niño. J. Atmos.
Sci., 59, 2694–2712, doi:10.1175/1520-0469(2002)059,2694:
TMFTPD.2.0.CO;2.
Sugiyama, M., 2009a: The moisture mode in the quasi-equilibrium
tropical circulation model. Part I: Analysis based on the weaktemperature gradient approximation. J. Atmos. Sci., 66, 1507–
1523, doi:10.1175/2008JAS2690.1.
——, 2009b: The moisture mode in the quasi-equilibrium tropicalcirculation model. Part II: Nonlinear behavior on an equatorial b plane. J. Atmos. Sci., 66, 1525–1542, doi:10.1175/
2008JAS2691.1.
Susskind, J., C. D. Barnet, and J. M. Blaisdell, 2003: Retrieval of
atmospheric and surface parameters from AIRS/AMSU/HSB
data in the presence of clouds. IEEE Trans. Geosci. Remote
Sens., 41, 390–409, doi:10.1109/TGRS.2002.808236.
——, J. M. Blaisdell, L. Iredell, and F. Keita, 2011: Improved
temperature sounding and quality control methodology using
AIRS/AMSU data: The AIRS Science Team version 5 retrieval algorithm. IEEE Trans. Geosci. Remote Sens., 49, 883–
907, doi:10.1109/TGRS.2010.2070508.
Thompson, R. M., S. W. Payne, E. E. Recker, and R. J. Reed, 1979:
Structure and properties of synoptic-scale wave disturbancesin the intertropical convergence zone of the eastern Atlantic.
J. Atmos. Sci., 36, 53–72, doi:10.1175/1520-0469(1979)036,0053:
SAPOSS.2.0.CO;2.
TRMM PR Team, 2005: Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar algorithm. Instruction
manual for version 6. Japan Aerospace Exploration Agency
and National Aeronautics and Space Administration,
175 pp. [Available online at http://www.eorc.jaxa.jp/TRMM/
index_e.htm.]
Waite, M. L., and B. Khouider, 2009: Boundary layer dynamics
in a simple model for convectively coupled gravity waves.
J. Atmos. Sci., 66, 2780–2795, doi:10.1175/2009JAS2871.1.
——, and ——, 2010: The deepening of tropical convection bycongestus preconditioning. J. Atmos. Sci., 67, 2601–2615,
doi:10.1175/2010JAS3357.1.
Wang, Z., and K. Sassen, 2001: Cloud type and macrophysicalproperty retrieval using multiple remote sensors. J. Appl.

3766

JOURNAL OF THE ATMOSPHERIC SCIENCES

Meteor., 40, 1665–1682, doi:10.1175/1520-0450(2001)040,1665:
CTAMPR.2.0.CO;2.
Wentz, F. J., and T. Meissner, 2000: AMSR ocean algorithm. Algorithm Theoretical Basis Doc., Remote Sensing Systems,
59 pp. [Available online at http://www.ssmi.com/.]
Wu, Z., 2003: A shallow CISK, deep equilibrium mechanism for theinteraction between large-scale convection and large-scale
circulations in the tropics. J. Atmos. Sci., 60, 377–392,
doi:10.1175/1520-0469(2003)060,0377:ASCDEM.2.0.CO;2.
——, E. S. Sarachik, and D. S. Battisti, 2000: Vertical structureof convective heating and the three-dimensional structure of
the forced circulation on an equatorial beta plane. J. Atmos.
Sci., 57, 2169–2187, doi:10.1175/1520-0469(2000)057,2169:
VSOCHA.2.0.CO;2.

VOLUME 71

Yanai, M., S. Esbensen, and J.-H. Chu, 1973: Determination of
bulk properties of tropical cloud clusters from large-scale heatand moisture budgets. J. Atmos. Sci., 30, 611–627, doi:10.1175/
1520-0469(1973)030,0611:DOBPOT.2.0.CO;2.
——, J.-H. Chu, T. E. Stark, and T. Nitta, 1976: Response ofdeep and shallow tropical maritime cumuli to large-scale
processes. J. Atmos. Sci., 33, 976–991, doi:10.1175/
1520-0469(1976)033,0976:RODAST.2.0.CO;2.
Yasunaga, K., and Coauthors, 2006: Melting layer cloud observed
during R/V Mirai cruise MR01-K05. J. Atmos. Sci., 63, 3020–
3032, doi:10.1175/JAS3779.1.
Yu, J.-Y., C. Chou, and J. D. Neelin, 1998: Estimating the gross moist
stability of the tropical atmosphere. J. Atmos. Sci., 55, 1354–1372,
doi:10.1175/1520-0469(1998)055,1354:ETGMSO.2.0.CO;2.