Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE
10.1002/2016JD024753
Key Points:• A new strategy is proposed to analyze
convective and large-scale mass
ﬂuxes from satellite data
• The systematic evolution of the mass
ﬂuxes is captured in association withconvective development• The ﬁndings have the potential toserve as an observational basis toassess GCM parameterizations

Correspondence to:
H. Masunaga,
masunaga@nagoya-u.jp

Citation:
Masunaga, H., and Z. J. Luo (2016),
Convective and large-scale mass
ﬂux proﬁles over tropical oceans
determined from synergistic analysis
of a suite of satellite observations,J. Geophys. Res. Atmos., 121,
doi:10.1002/2016JD024753.

Received 22 FEB 2016
Accepted 16 JUN 2016
Accepted article online 24 JUN 2016

Convective and large-scale mass ﬂux proﬁles over tropicaloceans determined from synergistic analysis
of a suite of satellite observations
Hirohiko Masunaga1 and Zhengzhao Johnny Luo2
1 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan, 2 Department of Earth andAtmospheric Sciences and NOAA-CREST Institute, City University of New York, City College, New York, New York, USA

Abstract A new, satellite-based methodology is developed to evaluate convective mass ﬂux andlarge-scale total mass ﬂux. To derive the convective mass ﬂux, candidate proﬁles of in-cloud vertical velocity
are ﬁrst constructed with a simple plume model under the constraint of ambient sounding and thennarrowed down to the solution that matches satellite-derived cloud top buoyancy. Meanwhile, thelarge-scale total mass ﬂux is provided separately from satellite soundings by a method developed
previously. All satellite snapshots are sorted into a composite time series that delineates the evolution of avigorous and organized convective system. Principal ﬁndings are the following. First, convective mass ﬂux
is modulated primarily by convective cloud cover, with the intensity of individual convection being lessvariable over time. Second, convective mass ﬂux dominates the total mass ﬂux only during the early hoursof the convective evolution; as convective system matures, a residual mass ﬂux builds up in the mass ﬂux
balance that is reminiscent of stratiform dynamics. The method developed in this study is expected to be of
unique utility for future observational diagnosis of tropical convective dynamics and for evaluation of global
climate model cumulus parameterizations in a global sense.
1. Introduction
Moist convection has been long known to be a critical element of the tropical atmospheric circulations. It
remains an elusive problem, however, to thoroughly formulate the convective processes in light of large-scale
dynamics, despite of a series of achievements since early monumental work, for instance, by Yanai et al.
[1973] and Arakawa and Schubert [1974]. It is noted that “large scale” refers here to a horizontal scale ofO(100) km, comparable to the typical grid size of traditional climate models. A challenge remains partly, if
not largely, because global observations to verify theories and numerical models are not readily available.
Although eﬀorts have been made over decades to observe convective and ambient air mass ﬂuxes by various
means including aircraft wind measurements [LeMone and Zipser, 1980] and more recently by wind proﬁlers[e.g., May and Rajopathyaya, 1999; Kumar et al., 2015], the spatial and temporal sampling is often so limited
that it is diﬃcult to physically interpret those measurements in a robust large-scale context to generalize
the ﬁndings. Long-term, global observations from satellites could oﬀer a solution to the sampling problem.
However, no satellite instrument currently in orbit is designed for the purpose of measuring vertical velocity
at any spatial scale. A new approach is explored in this study to work out this diﬃculty, by combining andextending two satellite-based analysis methods recently developed by the authors so that both large-scaleand convective-scale mass ﬂuxes are estimated over the globe.

©2016. The Authors.
This is an open access article under theterms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use anddistribution in any medium, provided
the original work is properly cited, theuse is non-commercial and no
modiﬁcations or adaptations are made.

MASUNAGA AND LUO

The ﬁrst method was developed to target convective plumes sampled by CloudSat and other A-Train measurements. It produces estimates of cloud top buoyancy [Luo et al., 2010] and cloud top vertical velocity [Luoet al., 2014] at convective scale on the order of 1 km (O(1 km)). These two estimates, in particular the cloud
top buoyancy, are adopted in the current study to derive convective mass ﬂuxes (section 2.2). The second
method of interest was proposed by Masunaga and L’Ecuyer [2014], where large-scale (O(100 km)) verticalmotion is quantiﬁed from a thermodynamic budget analysis applied to infrared soundings and other satellite measurements. These two independent techniques in tandem provide a unique opportunity to study
jointly the convective mass ﬂux and total large-scale mass ﬂux, the latter of which formally includes downdraft mass ﬂux as well. These two mass ﬂux estimates from the present techniques are, although subject totheir own uncertainties, by design free of any external assumption prescribing the physical linkage between
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Table 1. Summary of Satellite Data Analyzed in This Work
Platforms

Instruments

Description

Footprint Size

Target Parameters

TRMM

PR

Ku-band radar

4.3 km at nadir

Convective occurrence for the composite base point

Aqua

AIRS

Hyperspectral IR sounder

13.5 km at nadir

Air temperature and water vapor proﬁlesAqua

AMSR-E

Microwave radiometer

74 km × 43 km to 6 km × 4 km

SST, CWV, and surface precipitation

Aqua

MODIS

Vis/IR imager

1 km at nadir

Cloud top temperature
Cloud top height, cumulus occurrence, and QR

CloudSatCPR

W band radar

1.7 km × 1.3 km

CALIPSOCALIOP

Lidar

100 m

Cloud top height

QuikSCAT

SeaWinds

Microwave scatterometer

37 km × 25 km

Wind at 10 m height

convective clouds and their environment. In general circulation models (GCMs), the total large-scale mass ﬂux
is explicitly simulated in a prognostic manner, whereas the convective mass ﬂux is treated implicitly in cumulus
parameterization. Findings from our study will thus serve as an important observational basis against which
GCM cumulus parameterization, or more generally the interaction between convection and large-scale environment, may be vigorously evaluated. This article, as the ﬁrst of a series of papers to follow, is intended toreport the proposed methodology and some preliminary results applied to observations over tropical oceans,leaving in-depth analysis and speciﬁc applications for future work.
A summary of the input satellite data and a review of the methods from those previous papers are presented in
section 2. A simple plume model is described in section 3.1 to construct the in-cloud vertical velocity proﬁlesthat are matched with cloud top buoyancy and vertical velocity estimates (section 3.2). The analysis resultsfor 2 years (2008–2009) are presented in section 4, followed by discussions and summary in section 5. A brief
error analysis is provided in Appendix A.

2. Satellite Data, Derived Parameters, and Composite Method
This section is devoted to a brief summary of the data and method from previous studies employed as an
input to the present analysis. Further technical details are found in the cited references.
2.1. Data Summary
The satellite instruments used in this study are summarized in Table 1. The Tropical Rainfall Measuring Mission(TRMM) Precipitation Radar (PR) oﬀers a reliable measure of precipitation (or rain-cell) occurrence and is usedas the “anchor” of statistical time series before and after convection is developed (to be detailed in section 2.4).
The Atmospheric Infrared Sounder and Advanced Microwave Sounder Unit (AIRS/AMSU, hereafter AIRS collectively) Level-2 product provides the vertical proﬁles of temperature and humidity at a vertical resolution ofroughly 1 km [Susskind et al., 2003, 2011]. Column water vapor (CWV) and sea surface temperature (SST) are
obtained from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) data sets
produced by the Remote Sensing Systems [Wentz and Meissner, 2000]. AMSR-E is employed also for surface
precipitation estimates with the Goddard Proﬁling (GPROF) 2010 data [Kummerow et al., 2011]. Ocean surface
wind estimates are taken from the Quick Scatterometer (QuikSCAT) SeaWinds Level-3 daily gridded data set[Perry, 2001]. The CloudSat Cloud Proﬁling Radar (CPR) and the Cloud-Aerosol Lidar and Infrared Pathﬁnder
Satellite Observation (CALIPSO) Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) are utilized for
determining the cloud top height of convective clouds, while cloud top temperature is estimated from theModerate Resolution Imaging Spectroradiometer (MODIS). The footprint size varies on an instantaneous basis
from sensor to sensor, but the inconsistency in spatial resolution is alleviated when the estimates are averaged
over a large-scale (100 km radius) domain in the present analysis.
Pressure levels are ﬁxed at 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa in accordance with
the AIRS product design. Additional two levels below 925 hPa are introduced to represent the surface andcloud base, the latter of which is given by the lifting condensation level determined with the near-surface
temperature and humidity estimates from the AIRS observations.
2.2. Cloud Top Buoyancy and Vertical Velocity
Cloud top buoyancy of convective clouds is derived based on the normalized temperature diﬀerence between
the cloud top and the ambient air at the same height [Luo et al., 2010; Takahashi and Luo, 2012; Wang et al.,2014]. Cloud top temperature is evaluated with IR measurements from MODIS, with an IR emissivity correction
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applied making use of simultaneous observations from the CALIPSO and CloudSat satellites. CloudSat radar
echoes are used also for determining cloud top height and ensuring that a detected convective core continuously extends up from the cloud base located near the surface. It is noted that the cases where near-surface
echoes disappear due to heavy attenuation by precipitation are assumed to be associated with vigorous convection and are retained in the samples. The ambient temperature is adopted from the collocated European
Centre for Medium-Range Weather Forecast (ECMWF) operational analysis. A key observational requirement
for buoyancy estimation is simultaneous and independent measurements of cloud top height (CloudSat) andcloud top temperature (MODIS), as well as information on ambient temperature proﬁle (ECMWF).
Shallow convection is, in general, diﬃcult to capture with a suﬃcient level of conﬁdence in the present
methodology, so cloud top buoyancy and vertical velocity estimates are unavailable where cloud top is lower
than 3 km. This criterion imposes a major restriction on sampling completeness, given the prevalence ofshallow cumuli over tropical oceans [Johnson et al., 1999; Short and Nakamura, 2000]. The current analysis
tentatively deals with shallow cumuli in a simpliﬁed approach as described later in section 4, leaving a more
realistic treatment for follow-up work in the future. It is hence stressed that the primary interests of the present
work are conﬁned to deep convection and congestus.
Buoyancy is in theory aﬀected by in-cloud and ambient humidity (through the virtual temperature eﬀect)
and the condensate loading in addition to the temperature diﬀerence (see (12) in section 3.1). The eﬀects ofhumidity and condensate are not considered in the current measure of cloud top buoyancy in order to avoid
unnecessary complication. This is deemed to be justiﬁable since we focus mainly on deep convection andcongestus where cloud top temperatures are low enough such that the vapor and condensate mixing ratios
are generally very small.
Luo et al. [2014] demonstrated that convective cloud top vertical velocity can be evaluated by exploiting asmall overpass time diﬀerence between the two IR sensors belonging to the A-Train constellation, namely, theAqua MODIS and the CALIPSO Imaging Infrared Radiometer (IIR). Basically, an actively developing convective
plume will grow colder with time, and its cloud top vertical velocity is proportional to the change rate of cloud
top temperature with time. By measuring the time-diﬀerenced cloud top temperature, together with knowledge of the lapse rate, one can estimate the convective cloud top vertical velocity. We have used both cloud
top vertical velocity and cloud top buoyancy in our analysis and found the results were virtually the same.
Although cloud top vertical velocity may appear as a more natural choice for deriving the whole in-cloud proﬁle of vertical velocity than using cloud top buoyancy, the observational requirements are far more restrictive
for the former. Hence, there are signiﬁcantly more data points for buoyancy than for vertical velocity, leading
to a less noisy analysis result. This paper, therefore, presents only the buoyancy-based analysis.
2.3. Large-Scale Vertical Motion
The vertical proﬁles of humidity and temperature observed from the AIRS serve as a primary input into themoisture and thermal budget analysis that is employed for evaluating large-scale vertical p velocity, 𝜔, orequivalently the total large-scale mean mass ﬂux, M0 , multiplied by gravitational acceleration.
The moisture and thermal budget equations integrated vertically over the troposphere serve as diagnostic
formulae to evaluate moisture convergence and dry static energy (DSE) convergence, given the other terms
all constrained observationally𝜕− ⟨∇ ⋅ qv⟩ = ⟨q⟩ − E + P
(1)
𝜕t
and
− ⟨∇ ⋅ sv⟩ =𝜕⟨s⟩ − S − Lv P − ⟨QR ⟩,𝜕t(2)where ⟨· · ·⟩ denotes the vertical integral over the troposphere, q the vapor mixing ratio, s the DSE, v the horizontal wind, E the evaporative ﬂux, P the surface precipitation, S the sensible heat ﬂux, Lv the speciﬁc latent
heat of vaporization, and QR the radiative heating rate. The overbar designates horizontal averaging over alarge-scale domain with the radius of 100 km.
The moisture and DSE convergence integrated vertically may be viewed as lower and upper troposphereweighted convergence, respectively, because moisture has higher concentration in the lower troposphere
while DSE has greater value in the upper troposphere. Vertical velocity, or the vertical integral of horizontal
convergence, may be therefore obtained in each lower and upper troposphere exploiting (1) and (2),MASUNAGA AND LUOMASS FLUX ESTIMATES FROM SATELLITES

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respectively, together. This idea is further extended so that a complete vertical proﬁle of 𝜔 is obtained when
the degree of freedom is reduced to a tractable level through vertical mode decomposition into the ﬁrst andsecond baroclinic modes and the shallow mode combined with a time-invariant background state of 𝜔. The
equations to yield the three 𝜔 modes consist of
∑

⟨

i

∑

𝜕𝜔
q i
𝜕p

⟨
s

i

𝜕𝜔i
𝜕p

⟩
≈ −⟨∇ ⋅ qv⟩,

(3)

≈ −⟨∇ ⋅ sv⟩,

(4)⟩

where the subscript i represents each vertical mode, and∑𝜔i,CB = ⟨∇ ⋅ qv⟩SC ,(5)iwhere 𝜔 at cloud base (CB) is quantiﬁed from the subcloud layer (SC) convergence determined with QuikSCAT
winds. The right-hand side of equations (3) and (4) are as given by equations (1) and (2). The sum of all thethree modes, 𝜔i , yields 𝜔 and serves as the total large-scale mass ﬂux discussed in section (4). More details inmethodology are provided by Masunaga and L’Ecuyer [2014].
2.4. Integration Into Composite Time Series
Cloud top buoyancy (and cloud top vertical velocity) and large-scale 𝜔 retrievals are applied individually to
instantaneous measurements over global tropical oceans. Convective cloud structure is substantially diﬀerent
over land from over ocean [Liu et al., 2007], so aspects of the current ﬁndings apply only to oceanic convective systems. Limiting the analysis to oceans mitigates the diurnal sampling bias in Sun-synchronous satellite
measurements owing to the weakness of diurnal variation in oceanic precipitation [e.g., Imaoka and Spencer,
2000]. The observations are time stamped according to the temporal diﬀerence with respect to the time when
the TRMM PR detects rain cells some hours before or after at the same location and are then averaged overthe surrounding 100 km radius domain for each hour to constitute a composite time sequence around thetime of rain cell occurrence (Masunaga [2012], see the schematic in Figure 1). Note that this circular domain
is comparable in area to a 177 km × 177 km box if applied to a square ﬁeld.
The number of A-Train buoyancy samples ranges from about 3000 to 6000 for each hourly bin in composite
space, as shown later in section 4 and Figure 6c. The AIRS samples for large-scale 𝜔 consist of roughly
30,000–300,000 each hour, for which the minimum corresponds to the hours of peak convection because
infrared sounding is unavailable for totally cloudy skies. The composite time series shown in this work
are hence constructed with a reasonably large body of statistics. The robustness of the composite statistics, including the potential errors due to the migration of convective disturbances, has been assessed in
Masunaga [2015].
The TRMM detection of rain cells is deﬁned when the PR ﬁnds precipitation echoes beyond the noise levelacross a few vertically consecutive bins within a column, ﬂagged as the “rain certain” in the TRMM data product. In the present analysis, this procedure is carried out only when the TRMM PR ﬁnds the rain cell coverage
exceed 50% of the 100 km radius domain. As such, the resulting time series is considered as a statistical representation of the variability over time in association with the development and dissipation of highly organized
convective systems (see Figure 2 of Masunaga [2013]). The present compositing procedure has another advantage that the composite 100 km domain contains a large number of CloudSat/CALIPSO samples as noted
above, although those samples, conﬁned spatially to a narrow vertical scan, cover only a fraction of the domain
on an instantaneous basis.
The QuikSCAT satellite had the Sun-synchronous orbit of ∼6:00 local time, ﬂying behind the A-Train satellites
by roughly 4.5 h. This temporal oﬀset could potentially introduce some bias when the QuikSCAT and A-Train
measurements are combined into the composite time series. The bias would be, however, small because thediurnal cycle of tropical disturbances is modest as mentioned above, with the magnitude being not larger
than 30% in surface divergence over tropical oceans [Deser, 1994]. This magnitude should be further reduced
when the opposite diurnal phases are averaged between ascending and descending orbits.
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Figure 1. Flowchart of the analysis procedures. Solid arrows indicate the analysis ﬂow and dashed arrows represent the primary input parameters and thesatellites that provide these parameters. The schematic on the right shows the current composite technique where many pairs of TRMM and A-Train snapshots
are averaged into statistical time series. Here the A-Train snapshots consist of the parameters as shown in each ﬂowchart box except for the “plume model,” while
the TRMM is employed to seek the occurrence of rain cells that may be prior or subsequent to each A-Train snapshot (see section 2.4 for details).

2.5. Analysis Period and Area
The analysis period spans 2 years from 1 January 2008 to 31 December 2009 for cloud top buoyancy estimates(section 2.2). The large-scale vertical motion (section 2.3) is constructed with a longer period from 1 December
2002 to 30 November 2009 to ensure the statistical robustness in the composite time series (section 2.4). The
diﬀerence in the temporal length is not essential since the composite statistics are known to be insensitive tothe choice of the analysis period [Masunaga, 2015].
The target region is global tropical oceans between 15∘ S and 15∘ N with land masses all excluded. Tropicalclouds, in particular organized convective systems, are known to be distributed nonuniformly over tropical oceans [e.g., Mohr and Zipser, 1996]. However, our previous results (e.g., Figure 12 of Masunaga [2013])
show that the overall features of the sampled convective systems, conditioned on the 50+% coverage as
deﬁned above, are insensitive to the regionality such as the east versus west Paciﬁc. The statistics are in eﬀect
representative of convective active regions in general. It follows that individual systems selected by the common criteria exhibit certain universal characteristics beyond the climatological diﬀerences in their large-scale
environment.

3. In-cloud Vertical Velocity Proﬁles
Buoyancy or vertical velocity estimates from radar and IR measurements are available only at cloud tops, while
the full in-cloud structure of updraft velocity is required for our science goal. A new strategy is developedin this work to reconstruct the in-cloud vertical velocity proﬁles with the aid of a steady state single-column
plume model described in section 3.1. Entrainment rate, a key uncertainty in the model, is varied so that a
broad range of solutions are allowed to exist for a given environmental sounding. A Bayesian procedure is thenapplied to narrow down the candidate proﬁles to the solution that best matches the cloud top buoyancy orvertical velocity estimates derived from observations (section 3.2). A ﬂowchart is shown in Figure 1 to outline
the whole procedures in the present work.
The plume model developed here is by design meant to represent updraft in cumulus convection without convective downdraft and mesoscale dynamics considered. This deﬁnition is consistent with the cloud
top buoyancy and vertical velocity estimation from satellites, where the samples are conservatively chosen to focus on rapidly growing convective cores [Luo et al., 2010, 2014], which belong, together with the
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surrounding stratiform clouds, to the organized system identiﬁed by the TRMM during hours around zero. The
present analysis, however, formally includes the downdrafts as well in terms of the residual in the large-scalemass ﬂux balance as discussed later in section 5.
3.1. Single-Column Plume Model
The entrainment and detrainment rates, 𝜖 and 𝛿 , are deﬁned conventionally as
1 𝜕(𝜌wc )= 𝜖 − 𝛿,
𝜌wc 𝜕z(6)where w is vertical velocity, 𝜌 is the mass density of air, and the subscript c indicates in-cloud properties. The
entrainment and detrainment rates may be separated into dynamic and turbulent components [Houghton
and Cramer, 1951],
𝜖 = 𝜖dyn + 𝜖tur ,𝛿 = 𝛿dyn + 𝛿tur ,(7)

where the dynamic components are determined so as to satisfy the mass conservation [Asai and Kasahara,
1967]
[
]
[
]
𝜕(𝜌wc )
𝜕(𝜌wc )1 𝜕(𝜌wc )1 𝜕(𝜌wc )H, 𝛿dyn = −H −,𝜖dyn =(8)𝜌wc 𝜕z𝜕z𝜌wc 𝜕z𝜕zwhere H is the Heaviside function. The turbulent components are by deﬁnition canceled out at each height inthe continuity equation (i.e., 𝜖tur = 𝛿tur ) while not eliminated in the other conservation equations described
below.
The conservation of an arbitrary parameter 𝜑 may be written as∑𝜕(𝜌wc 𝜑c )= 𝜌wc (𝜖𝜑a − 𝛿𝜑c ) + 𝜌
F𝜑,i ,𝜕zi(9)where the subscript a designates the ambient environment and F𝜑,i accounts for the source and sink terms asneeded. Equations (6) and (9) are combined into𝜕𝜑c1 ∑= −𝜖(𝜑c − 𝜑a ) +F .
𝜕z
wc i 𝜑,i(10)Note that the detrainment terms, although not explicitly apparent in (10), remain in the formulation as
originally deﬁned. The equation of motion is derived as
1 𝜕wc= aB B − 𝜖wc2 − cD wc2 ,
2 𝜕z
2

(11)

where 𝜑 has been replaced by wc2 . Here the in-cloud buoyancy, B, is characterized by(
B = gaB

Tv,c − Tv,aTv,a)− qw ,(12)

where g is the gravitational acceleration and Tv is virtual temperature. The portion of the buoyancy production
usable for vertical acceleration, aB , is set to be 1/6 [Gregory, 2001]. The third term in the right-hand side of (11),aimed to account for a drag force owing to pressure perturbation from the hydrostatic state [e.g., Simpson
and Wiggert, 1969], is highly uncertain and hence not explicitly speciﬁed here. Instead, uncertainties in cD areformally combined into those in 𝜖tur . As such, 𝜖tur is the controlling parameter in this work to be chosen froma range of possibilities and then constrained by observations.
In-cloud moist static energy (MSE), hc , ishc = cp Tc + gz + Lv qv,c ,(13)where cp is the speciﬁc heat capacity under constant pressure, and z is altitude. The conservation equation (10)is applied to the MSE budget with the freezing eﬀect included (i.e., 𝜑c = hc − Li qi and 𝜑a = ha ),𝜕(hc − Li qi )= −𝜖(hc − Li qi − ha ),𝜕z

MASUNAGA AND LUOMASS FLUX ESTIMATES FROM SATELLITES

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where Li is the speciﬁc latent heat of fusion and qi is the ice mixing ratio. The ice mixing ratio is determined
diagnostically as
q i = fi q w ,where fi =1 − tanh[(Tc − T0,i )∕dTi ]2(15)

where T0,i and dTi are chosen to be −20∘ C and 7∘ C, respectively, so that fi smoothly transitions from zero tounity as temperature decreases from 0∘ C to −40∘ C. In-cloud temperature Tc is obtained from hc , assumingthat the in-cloud air is saturated at all heights and qv,c is approximated by saturation vapor mixing ratio withrespect to liquid water, q∗v (Tc ). It has been conﬁrmed that the buoyancy proﬁles remain similar when q∗v (Tc ) is
replaced by the saturation vapor pressure with respect to ice at cold temperatures.
Replacing 𝜑c with qw in (10) leads to the equation for the condensate mixing ratio,𝜕qw
1= −𝜖qw +(q̇
− q̇ auto ),𝜕z
wc cond(16)

where q̇ cond is the condensation rate and q̇ auto is the autoconversion rate. The ambient temperature and vapor
proﬁles are known parameters taken from AIRS/AMSU soundings, same as those ingested for 𝜔 estimates(section 2.3). The condensation rate is diagnosed from the vapor budget equation, obtained by substituting
vapor mixing ratio qv for 𝜑 in (10),[q̇ cond = −wc

𝜕qv,c
𝜕z

]
+ 𝜖(qv,c − qv,a ) .

(17)

Here again qv,c is replaced by saturation vapor mixing ratio q∗v (Tc ). The autoconversion rate is estimated usinga primitive form of the Kessler formula [Kessler, 1969],q̇ auto =1(q − qw,crit )H(qw − qw,crit ),𝜏auto w(18)

where 𝜏auto = 103 s and qw,crit = 10−3 kg kg−1 . Precipitating particles are assumed to immediately fall outof the ascending air, and their thermodynamic eﬀects such as reevaporation and melting are not taken into
account. The reader is reminded that the current plume model is designed to target convective updraft only.
Equations (11), (14), and (16) are integrated over height from cloud base to the level at which wc reaches zero.
Each vertical layer from the ambient soundings (see section 2.1) is divided into ﬁve sublayers for use by thenumerical integration. The boundary condition for (14) and (16) is rather obvious: hc is as observed from thesatellite sounding, and qw is zero immediately below cloud base. On the other hand, wc at cloud base is notknown from the observations and is assumed here to be twice as large as the subcloud layer vertical velocity
scale, w∗ (for further details, see Grant [2001] and Gregory [2001]). In this study, an approximate formula of w∗
is adopted as
(
(
)1∕3
)
gzCB ′ ′ 1∕3
gzCB
w∗ ≡
w 𝜃v0
≈
S
,
(19)
𝜃v,SC
cp TSC
where TSC and 𝜃v,SC are the temperature and virtual potential temperature averaged over the subcloud layer,′zCB is the cloud base height, w′ 𝜃v0
is the surface turbulent ﬂux of virtual potential temperature, and S is surface
sensible heat ﬂux. The sensible heat ﬂux is evaluated using a bulk formula as employed by Masunaga [2013].
Typical values of w∗ estimated from the present satellite soundings are 0.6–0.7 m s−1 , which fall within therange studied by Grant [2001].
Figure 2 shows the plume model solutions for a range of 𝜖tur varied from 0 to 0.4 km−1 . The ambient soundings to force this run are taken from the composite time series at 24 h prior to the time of peak convection,
but the results are qualitatively insensitive to the choice of timing. The normalized temperature diﬀerence,(Tc − Ta )∕Ta , is presented as a proxy of buoyancy in Figure 2a, since this is the parameter to compare withcloud top observations in the Bayesian procedure described next (section 3.2). As expected, a change tothe entrainment rate leads to a great diﬀerence in the depth of clouds from shallow cumulus topped near
700 hPa to overshooting deep convection reaching beyond 150 hPa. The resulting variation in the maximum
updraft velocity spans a broad range from less than 3 m s−1 (shallow cumulus) to 14 m s−1 (deep convection)(Figure 2b). Shallow cumuli with even lower cloud tops are outside the present target and are not attempted
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Figure 2. The plume model solutions of (a) (Tc − Ta )∕Ta and (b) wc (m s−1 ). Colors indicate diﬀerent turbulent
entrainment rates, 𝜖tur , changing by an increment of 0.01 km−1 from 0 up to 0.1 km−1 , followed by 0.12, 0.15, 0.2, 0.3,
and 0.4 km−1 (from red to purple in the increasing order). The ambient soundings are taken from the composite timeseries at t = −24 h. Cloud base is labeled as “CB” on the pressure coordinate.

to simulate with the current model. The enhanced buoyancy above 400 hPa (Figure 2a) is brought by an additional heating owing to the freezing of cloud water, resulting in continuing acceleration of plumes as seen in
the wc proﬁles (Figure 2b). Vertical velocity then rapidly declines with height as buoyancy sharply drops to alarge negative near the top of overshooting deep convection. The general characteristics of the wc proﬁlessimulated for deep convection is consistent with Doppler radar measurements by Heymsﬁeld et al. [2010] inthat wc increases with height until it reaches the upper tropospheric peak exceeding 10 m s−1 .

CB

CB

Figure 3. The plume model solutions of (a) the entrainment rate (km−1 ), 𝜖 , and (b) the detrainment rate, 𝛿 (km−1 ). Colors
indicate diﬀerent turbulent entrainment rates, 𝜖tur , changing by an increment of 0.01 km−1 from 0 up to 0.1 km−1 ,followed by 0.12, 0.15, 0.2, 0.3, and 0.4 km−1 (from red to purple in the increasing order). The ambient soundings aretaken from the composite time series at t = −24 h. Cloud base is labeled as “CB” on the pressure coordinate.

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Table 2. Sensitivity Experiment Design for the Plume Model
Model Assumptions

Lower End

ControlaB

0.1

1/6 (0.166· · ·)Higher End
0.2

dTi

5K

7K

10 K

qw,crit1 × 10−4 kg kg−1

1 × 10−3 kg kg−1

5 × 10−3 kg kg−1

𝜏auto

5 × 102 s

1 × 103 s

5 × 103 s

The corresponding proﬁles of the entrainment and detrainment rates are shown in Figure 3. The overall vertical structure of 𝜖 is dominated by 𝜖dyn rather than 𝜖tur , the latter of which is assigned with a range of possible
values constant over height. The entrainment rate is greatest immediately above cloud base, where the accelerating updraft eﬃciently sucks in the ambient air. The detrainment rate, with a somewhat larger spread
depending on 𝛿tur , has a striking spike near cloud tops generated by an abrupt deceleration of updraft. Modest
peaks at 400–500 hPa arise from the combination of a buoyancy loss by the condensate loading and the following recovery of buoyancy due to freezing. This midtropospheric detrainment peak is a factor responsible
for the formation of cumulus congestus clouds prevailing over tropical oceans [Johnson et al., 1999]. The ideathat the eﬀect of freezing on buoyancy could reinvigorate the updraft so the convective cloud eventuallyreaches the tropopause has been supported by later studies [e.g., Zipser, 2003] and will be worth revisiting in
the future by recent satellite observations.
The simulated proﬁles presented above depend also on various model assumptions other than 𝜖tur . A set ofsensitivity experiments are, therefore, conducted for assessing uncertainties in the assumptions. Each of aB ,dTi , qw,crit , and 𝜏auto is perturbed one after another with all the other assumptions ﬁxed at the control value.
It is diﬃcult to determine the realistic range of assumptions with conﬁdence, so the lower and higher ends
are chosen somewhat arbitrarily within roughly an order of magnitude as listed in Table 2. The results arepresented in Figures 4 and 5. In all cases, the vertical proﬁles remain qualitatively similar in that wc increases
with height toward a single maximum, followed by a steep decline immediately above. A large spread in wc
arises for moderate entrainment rates (green shade) in Figure 5 because in these cases a subtle change tothe assumptions could result in distinct consequences of either a buoyancy loss due to condensation loading(congestus) or a reinvigoration of updraft by freezing (deeper convection). Nevertheless, the spread due toany perturbation assumption (as represented by the breadth of the curves) is relatively small compared tothe diﬀerences associated with varying 𝜖tur values, spanning across diﬀerent curves from congestus to deep
convection. It may be therefore concluded that 𝜖tur is the parameter responsible for yielding broad solutions
from shallow cumulus to deep convection, while uncertainties in other assumptions per se are not so large as
to entirely modify the depth of convection.
3.2. Synthesis of Satellite and Model Estimates
A set of the wc proﬁles presented in the previous section (Figure 2b) constitutes a database to be searched forthe optimal solution. The proﬁle consistent with a given cloud top buoyancy (or cloud top vertical velocity)
estimate is selected from the candidate solutions in a Bayesian manner [e.g., Lorenc, 1986]. The expectationof vertical velocity structure, ŵ c , isŵ c (z) ≡∑p(𝜖tur,i |zT , ΔTT )wc,i (z) =∑ip(𝜖tur,i )p(zT , ΔTT |𝜖tur,i )wc,i (z),

(20)

i

where 𝜖tur,i indicates the ith member of 𝜖tur (see the caption of Figure 2 for speciﬁc numbers), wc,i is the corresponding vertical velocity proﬁle from the plume model, p(𝜖tur,i ) is the priori probability distribution of 𝜖tur,i ,p(𝜖tur,i |zT , ΔT) is the posteriori probability function for a given pair of observations of cloud top height, zT , andthe normalized temperature diﬀerence at the cloud top height, ΔT ≡ (Tc − Ta )∕Ta , and p(zT , ΔTT |𝜖tur,i ) is theconditional probability of zT and ΔT for given ith plume model proﬁle. The conditional probability distribution
may be written as][s0,i(zT − zi (s))2 (ΔTT − ΔTc,i (s))21ds,p(zT , ΔTT |𝜖tur,i ) ∝
exp −
−
2
s0,i − sCB ∫sCB
2𝜎z2
2𝜎ΔT

(21)

where 𝜎z and 𝜎ΔT are the measurement errors associated with zT and ΔT , respectively. It is assumed in thiswork that 𝜎z =1 km and 𝜎ΔT ≈ 𝜎T ∕Ta where 𝜎T = 1 K. The sensitivity to the choice of 𝜎z and 𝜎ΔT will be tested
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Figure 4. A sensitivity experiment of the plume model of (a and c) (Tc −Ta )∕Ta and (b and d) wc (m s−1 ) varying (a and b)
aB and (c and d) dTi with all other assumptions ﬁxed. Only every third proﬁle (i.e., 𝜖tur =0, 0.03, 0.06, 0.09, 0.15, and0.4 km−1 ) for visual clarity. The resultant range of simulated proﬁles is color shaded around the control proﬁle drawn inblack. The ambient soundings are taken from the composite time series at t = −24 h. Cloud base is labeled as “CB” on
the pressure coordinate.

in Appendix A. The integral is performed along the plume model trajectory, s, in the ΔT -z plane as drawn in
Figure 2a from cloud base, sCB , to the level at which wc vanishes, s0,i . The priori probability distribution p(𝜖tur,i )is initially assumed to be constant and is then updated by repeating the Bayesian procedure until the solution
converges.
Mean convective intensity, ŵ c , and convective mass ﬂux, Mc , are each computed from ŵ c asŵ c =1 ∑ŵ ,Aw ∈A c(22)

1 ∑𝜌ŵ c ,
A0 ∈A

(23)

w

Mc =

w

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Figure 5. A sensitivity experiment of the plume model of (a and c) (Tc − Ta )∕Ta and (b and d) wc (m s−1 ) varying(a and b) qw,crit and (c and d) 𝜏auto with all other assumptions ﬁxed. Only every third proﬁle (i.e., 𝜖tur =0, 0.03, 0.06, 0.09,
0.15, and 0.4 km−1 ) for visual clarity. The resultant range of simulated proﬁles is color shaded around the control proﬁledrawn in black. The ambient soundings are taken from the composite time series at t = −24 h. Cloud base is labeled as“CB” on the pressure coordinate.

where the area A0 designates the portion of the large-scale domain that is sampled by CloudSat granules, and
Aw denotes its subset constituted only of the footprints with nonzero buoyancy estimates, that is, the footprints where CloudSat detects deep convection and congestus. In (22) ŵ c is averaged conditionally whereconvection is observed so that it provides a measure of convective intensity, while Mc in (23) is the unconditional mean over the whole large-scale domain, thus representing the convective mass ﬂux as often used in
GCM cumulus parameterizations.

4. The Composite Time Series of Vertical Velocity and Mass Flux
The analysis results from the algorithm outlined in section 3.2 are presented in this section. Potential errors
associated with Mc are discussed later in Appendix A.
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Figure 6. The composite time series of (a) vertical velocity ŵ c (m s−1 ), (b) convective mass ﬂux Mc (10−2 kg m−2 s−1 ),and (c) the number of hourly samples of all CloudSat footprints (black dotted, labeled on left), those with buoyancy
estimates (blue solid, labeled on right), and shallow cumuli (green dashed, labeled on right). Cloud base is labeled as“CB” on the pressure coordinate. Altitudes lower than 3 km are hatched in (a) and (b) to mask out the heights wherecloud top buoyancy estimates are unavailable.

Figure 6a shows the composite time series of ŵ c , implying the persistence of deep convection with the verticalvelocity peak at 200–300 hPa. The near invariance of ŵ c is not surprising, since the atmosphere stays humid
and marginally unstable most of the time given that the statistics are constructed around the occurrence oforganized convection over tropical oceans. Convection therefore has the potential to develop deep wheneverit occurs, whereas the frequency of occurrence may be largely modulated by the large-scale dynamics asshown later. A closer examination, however, reveals a subtle but systematic variation in ŵ c . The atmosphere
undergoes a gradual lower tropospheric moistening (destabilization) toward the time of convection and asubsequent near-surface cooling (stabilization) [Masunaga, 2012], which is probably responsible for a slightintensiﬁcation during negative hours and a sudden weakening of ŵ c at t ∼ 0. It is noted that the persistenceof deep convection could be somewhat exaggerated because less developed convection concealed beneathan overlapping high cloud would be diﬃcult to sample from infrared measurements.
It is reminded that samples of convective clouds are absent when cloud top height does not reach beyond
3 km. It is attempted here to ﬁll in the eﬀects of shallow cumuli by a simplistic approach where the ŵ c
proﬁle is prescribed with the most heavily entraining plume model simulation, plotted in darkest blue in
Figure 2. This choice of the least-developed cumulus proﬁle is intended to provide a conservative estimateof shallow convective updraft. The result emerges as a weak enhancement of ŵ c below 3 km (hatched in
Figure 6a), somewhat strengthening as the ambient atmosphere moistens toward time zero. Shallow cumulus
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is nevertheless weak in the variability of ŵ c as one might expect from its ubiquitous nature over tropical oceans[e.g., Short and Nakamura, 2000] and is hence unlikely to introduce signiﬁcant error in the ŵ c variability.
Convective mass ﬂux (Figure 6b) has a bottom-heavy proﬁle compared to ŵ c as a result of the upward decreasing 𝜌. Another feature contrasting with ŵ c is that Mc experiences a drastic enhancement during the hours ofactive convection. Convective mass ﬂux reaches as large as 2–3 ×10−2 kg m−2 s−1 at times when convection ismost intense (t ∼ −3 h), while an order of magnitude smaller during the hours away from the peak (hereafter
called the background). This enhancement occurs in parallel with the sample size of convective clouds (solid
curve in Figure 6c), which primarily reﬂects the frequency of convective occurrence since CloudSat overpasses
are overall homogeneously sampled (∼4–5×105 ) along the composite time axis (dotted curve in Figure 6c).
The number of convective cloud samples with buoyancy estimates spans the range from around 1000 in the
background up to ∼3000 at the peak convection, or from 0.2–0.25% to 0.6–0.75% when translated into theconvective cloud cover, 𝜎c . Note that these values correspond to the coverage of convective cores that are
selected by some rather strict criteria on radar echo characteristics, as described in [Luo et al., 2010]; convective cores usually cover only a very tiny fraction of the whole convective cloud system. Equation (23) may be
rewritten as Mc ∼ 𝜎c 𝜌ŵ c when ŵ c is relatively constant throughout the evolution as is actually the case, sothat Mc evolves roughly in proportional to 𝜎c . Kumar et al. [2015] also concluded based on their wind-proﬁler
and radar measurements that the cumulus cloud cover, rather than vertical velocity, chieﬂy contributes to thevariability of the domain-mean mass ﬂux.
The third (green dashed) curve in Figure 6c provides a rough measure of shallow cumulus occurrence as
2km
4km
deﬁned by NCu− NCu, where NCu is the sample size of the cumulus (Cu) category at the indicated height
4km
from the CloudSat CLDCLASS product [Wang and Sassen, 2001]. The subtraction by NCu
is meant to avoid
congestus clouds already included in the buoyancy samples. The small sample size and weak updraft resultin a barely visible contribution of shallow cumuli to convective mass ﬂux (hatched in Figure 6b). Note that
the CloudSat radar is insensitive to clouds whose droplets are too small to detect, and the shallow cumulus
mass ﬂux may be underestimated. This limitation is to be mitigated in future work using additional satellite
instruments capable to detect thin low clouds such as CALIOP together with improved cloud-model setupsthat better characterize shallow cumuli.
Convective mass ﬂux is next compared against an independent measurement of 𝜔 as described in section 2.3.
The total large-scale mass ﬂux, M0 , is proportional to 𝜔 under the hydrostatic assumption and is broken down
into three components;
M0 ≡𝜔
= Mc + MR + M∗ ,
g

(24)

𝜕sa
Q
= R,
𝜕p
g

(25)

where MR is the radiatively forced subsidence,MR

where sa is DSE of the ambient air and QR is the radiative cooling rate adopted from the CloudSat
2B-FLXHR-LIDAR product. The last term, M∗ , is the residual mass ﬂux unaccounted for by the other terms inthe mass balance equation (24).
Figures 7a–7c show each mass ﬂux component at diﬀerent pressure levels of 200, 300, and 400 hPa. Convective mass ﬂux delineates coherent evolutionary tracks across all the levels. The evolution of M0 begins witha weak ascent comparable to Mc but then rapidly grows to a striking updraft around time zero to a degree
that Mc alone is far from able to account for. This discrepancy in the peak amplitude gives rise to a substantial
magnitude of the residual ﬂux M∗ , which at its maximum momentarily exceeds Mc at 400 hPa while staying
relatively minor at 200 hPa. During the whole period, MR is negligible and has little impact on the mass ﬂux
balance.
The vertical structure of M0 and M∗ is presented in Figures 7d and 7e. As seen above, the most conspicuous
feature in M∗ is the upper tropospheric updraft peak around the hours of intense convection. Figure 7e showsthat M∗ is also characterized by a lower tropospheric downdraft persistent throughout the entire time series.
The downdraft arises either when the total domain-mean ascent is short of the convective updraft or when M0
is negative in the ﬁrst place. It is noted that the M∗ downdraft occurs mostly at heights below 3 km (hatched),
where the Mc updraft is likely to be underestimated because shallow cumuli are not fully considered in this
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Total
Convective
Radiative
Residual

CB

CB

Figure 7. The composite time series of convective mass ﬂux Mc , total mass ﬂux M0 , radiatively forced mass ﬂux MR , andresidual mass ﬂux M∗ at (a) 400 hPa, (b) 300 hPa, and (c) 200 hPa. The complete vertical structure of (d) total mass ﬂux
M0 and (e) residual mass ﬂux M∗ . The mass ﬂux unit is 10−2 kg m−2 s−1 .

study. The M∗ downdraft is hence probably underestimated as well because (24) needs to be satisﬁed for agiven estimate of M0 . Physical implications of the residual mass ﬂux will be discussed in the next section.

5. Discussion and Conclusions
In this work, a new methodology is explored to derive the convective and total mass ﬂuxes from avariety of satellite measurements. Convective-scale vertical velocity is proﬁled using cloud top (>3 km)
buoyancy (or cloud top vertical velocity) estimates with the aid of a single-column plume model, whilelarge-scale vertical motion is evaluated from a thermodynamic consideration applied to satellite soundings.
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Both the convective- and large-scale vertical velocities are composited together into statistical time series
constructed in association with the development and dissipation of organized convective systems.
In-cloud vertical velocity proﬁles are found to be peaked in the upper troposphere regardless of the evolutionary stage of convective development. It follows that deep convection in the relatively quiescent spells
builds up, once it occurs, as vigorously (or even somewhat more intensively) as during organized systems. It is
the frequency of convective occurrence rather than the individual cloud properties that modulates the convective mass ﬂux as convective systems develop and dissipate, consistent with a recent study by Kumar et al.
[2015] that used collocated wind-proﬁler and precipitation radar measurements. These ﬁndings are in harmony with existing observational work of the Madden-Julian Oscillation despite the vast diﬀerence in timescale, showing that deep convection prevails throughout although convection better structures itself into anorganized system with extensive stratiform clouds during the mature phase than in the dry phase [Morita
et al., 2006; Tromeur and Rossow, 2010].
When the convective and total mass ﬂuxes, Mc and M0 , are compared, the mass balance relationship requires
a residual mass ﬂux, M∗ , that exhibits a signiﬁcant updraft peak in the upper troposphere at the time of peak
convection and a persistent lower tropospheric downdraft. The residual ﬂux arises for several possible reasons.
One possibility is retrieval bias since the measurements of Mc and M0 are derived in quite diﬀerent manners
and, therefore, would have independent sources of uncertainty that are hardly canceled out. An error analysis
provided in Appendix A, however, suggests that the current estimate of Mc lies close to the higher end within
the range of uncertainty examined, so that the residual ﬂux is unlikely ascribed entirely to retrieval bias.
There are multiple lines of circumstantial evidence suggesting that M∗ indeed embodies an actual physicalentity, primarily ascribable to stratiform updraft and downdraft. First, Mc closely tracks M0 before convection
begins to be invigorated and organized, leaving M∗ stays near zero. This is as expected in that isolated convection is exclusively responsible for convective mass ﬂux in the absence of organized convective systems. The
high similarity between Mc and M0 except when convection is organized probably serves as indirect evidence
that our estimations of Mc and M0 , although obtained through entirely independent and separate channels,
are rather unbiased. Second, the observed pair of upper tropospheric updraft and lower tropospheric downdraft in M∗ is a known signature of stratiform dynamics (Zipser [1977] and Houze [1982], among others). Lastly,
the known fact that stratiform updraft is most active during the mature and dissipating phases of organized
convective systems conforms with the evolution of M∗ , which rapidly grows near time zero and subsequently
fades away over time. Indeed, this temporal pattern of M∗ qualitatively traces the variability of the second
baroclinic (or stratiform) mode of large-scale vertical motion (Figure 5a of Masunaga and L’Ecuyer [2014]).
The algorithm requires technical reﬁnements with particular focus on major outstanding issues including thecrude assumptions on the plume model and shallow cumuli and the exclusion of continental convection. With
this caveat, the current methodology is expected to open new pathways for a further understanding of tropical atmospheric dynamics. In particular, the present analysis of convective mass ﬂux and total large-scale mass
ﬂux could be of unique utility for the observational diagnosis and evaluation of cumulus parameterizations
in a global sense.

Appendix A: Error Analysis of Convective Mass Flux
A brief error analysis is provided in this section to demonstrate uncertainties in the composite time series ofMc . The sources of errors examined here are the prescribed assumptions in the plume model as investigated in
section 3.1 and the measurement errors (𝜎z and 𝜎T ) assumed for the Bayesian estimation (section 3.2). Other
uncertainties related to cloud top buoyancy (section 2.2), large-scale mean vertical motion (section 2.3), andthe composite satellite soundings (section 2.4) are discussed elsewhere [Luo et al., 2010; Masunaga, 2012,2013, 2015] and are not repeated here.
Figure A1 summarizes the error analysis results at three pressure levels. The assumptions being tested are
aB , qw,crit , and 𝜏auto from the plume model assumptions and 𝜎z and 𝜎T from the Bayesian estimation. Notethat dTi is not included because its uncertainty has little impact on the plume model solutions (Figures 4c
and 4d). The sensitivity to the model assumptions is largest near the time of convective peak (t ≈ 0) at
all heights, with the magnitude decreasing with increasing height. Among the parameters examined, qw,critand 𝜏auto have the greatest contributions at 300 and 400 hPa. The amplitude of the 𝜎z and 𝜎T uncertainties
remains small, although recognizable at 200 hPa. The control run stays close to the high end of the error range
throughout the evolution particularly at 300 and 400 hPa. It follows that Mc is more likely overestimated than
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Acknowledgments
The authors are grateful to Bill Rossow
and Kenta Suzuki for their comments
on earlier versions of the manuscript.
The AIRS/AMSU product was provided
by Goddard Earth Sciences (GES) Dataand Information Services Center (DISC)(http://disc.sci.gsfc.nasa.gov) and the
TRMM PR (2A25) data set by the Japan
Aerospace Exploration Agency (JAXA)(https://www.gportal.jaxa.jp/gp/top.html).
The data sets also crucial, although
not explicitly presented, in thecurrent analysis are the GPROF
2010 precipitation productfrom Colorado State University(http://rain.atmos.colostate.edu/
RAINMAP), the AMSR-E SST and
CWV product by Remote Sensing
Systems (http://www.remss.com),
the CloudSat data sets by the
CloudSat Data Processing Center(http://www.cloudsat.cira.colostate.edu),
and QuikSCAT data from theNASA Jet Propulsion Laboratory(https://podaac.jpl.nasa.gov/QuikSCAT).
H.M. is supported by the Japan Society
for the Promotion of Science (JSPS)
Grant-in-Aid (KAKENHI) for Challenging
Exploratory Research (26610150). Z. J. L.
would like to acknowledge funding
support by NASA grant NNX12AC13G
and support from JPL CloudSat andRadar Science and Engineering group.

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Figure A1. The composite time series of convective mass ﬂux, Mc , for a range of model assumptions and measurement
errors at (a) 400 hPa, (b) 300 hPa, and (c) 200 hPa. The mass ﬂux unit is 10−2 kg m−2 s−1 . The range of uncertainties isshaded in orange for aB , blue for qw,crit , green for 𝜏auto , and red for the measurement error (𝜎z and 𝜎T ). The lower andupper ends of each model assumption are as indicated in Table 2. The measurement error range is bounded by (𝜎z , 𝜎T )= (1.5 km, 1 K) and (0.5 km, 2 K). The control run, identical to the blue solid curve in Figures 7a–7c, is plotted in black.

underestimated in the present analysis, suggesting that the residual mass ﬂux, M∗ , from the control run isplausibly a conservative estimate for given M0 .
The drag of precipitation is not included and is diﬃcult to quantify for uncertainty in the present model where
precipitation immediately falls out and is not tracked down further. The absence of precipitation drag would
lead to an overestimation of buoyancy and hence an underestimation of the residual mass ﬂux. The upper
tropospheric updraft in M∗ thus could be even larger, while the lower tropospheric downdraft might havebeen somewhat exaggerated.
The error magnitude is minimal in the background state away from the hours of vigorous convection. It is
implied that the earlier conclusion that Mc solely accounts for M0 before convection is invigorated remains
robust regardless of prescribed assumptions.

References
Arakawa, A., and W. H. Schubert (1974), Interaction of a cumulus cloud ensemble with the large-scale environment. Part I., J. Atmos. Sci., 31,
674–701.
Asai, T., and A. Kasahara (1967), A theoretical study of the compensating downward motions associated with cumulus clouds, J. Atmos. Sci.,
24, 487–496.
Deser, C. (1994), Daily surface wind variations over the equatorial Paciﬁc Ocean, J. Geophys. Res., 99, 23,071–23,078.
Grant, A. L. M. (2001), Cloud-base ﬂuxes in the cumulus-capped boundary layer, Q. J. R. Meteorol. Soc., 127, 407–421.
Gregory, D. (2001), Estimation of entrainment rate in simple models of convective clouds, Q. J. R. Meteorol. Soc., 127, 53–72.
Heymsﬁeld, G. M., L. Tian, A. J. Heymsﬁeld, L. Li, and S. Guimond (2010), Characteristics of deep tropical and subtropical convection fromnadir-viewing high-altitude airborne Doppler radar, J. Atmos. Sci., 67, 285–308.
Houghton, H. G., and H. E. Cramer (1951), A theory of entrainment in convective currents, J. Meteorol., 8, 95–102.
Houze, R. A. J. (1982), Cloud clusters and large-scale vertical motions in the tropics, J. Meteorol. Soc. Jpn., 60, 396–410.

MASS FLUX ESTIMATES FROM SATELLITES

16

Journal of Geophysical Research: Atmospheres

10.1002/2016JD024753

Imaoka, K., and R. W. Spencer (2000), Diurnal variation of precipitation over the tropical oceans observed by TRMM/TMI combined with
SSM/I, J. Clim., 13, 4149–4158.
Johnson, R. H., T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski, and W. H. Schubert (1999), Trimodal characteristics of tropical convection,
J. Clim., 12, 2397–2418.
Kessler, E. (1969), On the Distribution and Continuity of Water Substance in Atmospheric Circulations, Am. Meteorol. Soc., pp. 1–84, Boston.
Kumar, V. V., C. Jakob, A. Protat, C. R. Williams, and P. T. May (2015), Mass-ﬂux characteristics of tropical cumulus clouds from wind proﬁler
observations at Darwin, Australia, J. Atmos. Sci., 72, 1837–1855, doi:10.1175/JAS-D-14-0259.1.
Kummerow, C. D., S. Ringerud, J. Crook, D. Randel, and W. Berg (2011), An observationally generated a-priori database for microwave rainfall
retrievals, 28, 113–130.
LeMone, M. A., and E. J. Zipser (1980), Cumulusnimbus vertical velocity events in GATE. Part I: Diameter, intensity and mass ﬂux,
J. Atmos. Sci., 37, 2444–2457.
Liu, C., E. J. Zipser, and S. W. Nesbitt (2007), Global distribution of tropical deep convection: Diﬀerent perspectives from TRMM infrared andradar data, J. Clim., 20, 489–503.
Lorenc, A. C. (1986), Analysis methods for numerical weather prediction, Q. J. R. Meteorol. Soc., 112, 1177–1194.
Luo, Z. J., G. Y. Liu, and G. L. Stephens (2010), Use of A-Train data to estimate convective buoyancy and entrainment rate, Geophys. Res. Lett.,
37, L09804, doi:10.1029/2010GL042904.
Luo, Z. J., J. Jeyaratnam, S. Iwasaki, H. Takahashi, and R. Anderson (2014), Convective vertical velocity and cloud internal vertical structure:
An A-Train perspective, Geophys. Res. Lett., 41, 723–729, doi:10.1002/2013GL058922.
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.
Masunaga, H. (2013), A satellite study of tropical moist convection and environmental variability: A moisture and thermal budget analysis,
J. Atmos. Sci., 70, 2443–2466.
Masunaga, H. (2015), Assessment of a satellite-based atmospheric budget analysis method using CINDY2011/DYNAMO/AMIE and TOGACOARE sounding array data, J. Meteorol. Soc. Jpn, 93A, 21–40.
Masunaga, H., and T. S. L’Ecuyer (2014), A mechanism of tropical convection inferred from observed variability in the moist static energy
budget, J. Atmos. Sci., 71, 3747–3766.
May, P. T., and D. K. Rajopathyaya (1999), Vertical velocity characteristics of deep convection over Darwin, Australia, Mon. Weather Rev., 127,
1056–1071.
Mohr, K. I., and E. J. Zipser (1996), Deﬁning mesoscale convective systems by their 85 GHz ice-scattering signatures, Bull. Am. Meteorol. Soc.,
77, 1179–1189.
Morita, J., Y. N. Takayabu, S. Shige, and Y. Kodama (2006), Analysis of rainfall characteristics of the Madden-Julian Oscillation using TRMM
satellite data, Dyn. Atmos. Oceans, 42, 107–126.
Perry, K. L. (2001), SeaWinds on QuikSCAT level 3 daily, gridded ocean wind vectors (JPL SeaWinds project) version 1.1, JPL document
D-20335, Jet Propulsion Laboratory. [Available at ftp://podaac.jpl.nasa.gov/OceanWinds/quikscat/L3/jpl/v2/docs/qscat_L3.pdf.]
Short, D. A., and K. Nakamura (2000), TRMM radar observations of shallow precipitation over the tropical oceans, J. Clim., 13, 4107–4124.
Simpson, J., and V. Wiggert (1969), Models of precipitating cumulus towers, Mon. Weather Rev., 97, 471–489.
Susskind, J., C. D. Barnet, and J. M. Blaisdell (2003), Retrieval of atmospheric and surface parameters from AIRS/AMSU/HSB data in thepresence of clouds, IEEE Trans. Geosci. Remote Sens., 41, 390–409.
Susskind, J., 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.
Takahashi, H., and Z. J. Luo (2012), Where is the level of neutral buoyancy for deep convection?, Geophys. Res. Lett., 39, L15809,
doi:10.1029/2012GL052638.
Tromeur, E., and W. B. Rossow (2010), Interaction of tropical deep convection with the large-scale circulation in the MJO, J. Clim., 23,
1837–1853.
Wang, C., Z. J. Luo, X. Cheng, X. Zeng, W.-K. Tao, and X. Huang (2014), A physically based algorithm for non-blackbody correction ofcloud-top temperature and application to convection study, J. Appl. Meteorol. Climatol., 53, 1844–1857.
Wang, Z., and K. Sassen (2001), Cloud type and macrophysical property retrieval using multiple remote sensors, J. Appl. Meteorol., 40,
1665–1682.
Wentz, F. J., and T. Meissner (2000), AMSR Ocean Algorithm, Algorithm Theoretical Basis Document, Remote Sensing Systems, Santa Rosa,
Calif. [Available at http://www.ssmi.com/.]
Yanai, M., S. Esbensen, and J.-H. Chu (1973), Determination of bulk properties of tropical cloud clusters from large scale heat and moisturebudgets, J. Atmos. Sci., 30, 611–627.
Zipser, E. J. (1977), Mesoscale and convective-scale downdrafts as distinct components of squall-line structure, Mon. Weather Rev., 105,
1568–1589.
Zipser, E. J. (2003), Some views on “Hot Towers” after 50 years of tropical ﬁeld programs and two years of TRMM data, in Cloud Systems,
Hurricanes, and the Tropical Rainfall Measuring Mission (TRMM), Meteor. Monogr., vol. 29, pp. 49–58, Am. Meteorol. Soc.

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