convective and large-scale mass ux pro les over tropical oceans...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1002/,

Convective and large-scale mass flux profiles over tropical

oceans determined from synergistic analysis of a suite of satellite

observations

Hirohiko Masunaga1 and Zhengzhao Johnny Luo2

Abstract. A new, satellite-based methodology is developed to evaluate convective massflux and large-scale total mass flux. To derive the convective mass flux, candidate pro-files of in-cloud vertical velocity are first constructed with a simple plume model underthe constraint of ambient sounding and then narrowed down to the solution that matchessatellite-derived cloud-top buoyancy. Meanwhile, the large-scale total mass flux is pro-vided separately from satellite soundings by a method developed previously. All satel-lite snapshots are sorted into a composite time series that delineates the evolution of avigorous and organized convective system. Principal findings are the following. First, con-vective mass flux is modulated primarily by convective cloud cover, with the intensityof individual convection being less variable over time. Second, convective mass flux dom-inates the total mass flux only during the early hours of the convective evolution; as con-vective system matures, a residual mass flux builds up in the mass flux balance that isreminiscent of stratiform dynamics. The method developed in this study is expected tobe of unique utility for future observational diagnosis of tropical convective dynamics andfor evaluation of global climate model cumulus parameterizations in a global sense.

1. Introduction

Moist convection has been long known to be a critical ele-ment of the tropical atmospheric circulations. It remains anelusive problem, however, to thoroughly formulate the con-vective processes in light of large-scale dynamics, despite ofa series of achievements since early monumental work, forinstance, by Yanai et al. [1973] and Arakawa and Schubert[1974]. It is noted that “large scale” refers here to a horizon-tal scale of O(100) km, comparable to the typical grid sizeof traditional climate models. A challenge remains partly,if not largely, because global observations to verify theoriesand numerical models are not readily available. Although ef-forts have been made over decades to observe convective andambient air mass fluxes by various means including aircraftwind measurements [LeMone and Zipser , 1980] and more re-cently by wind profilers [e.g., May and Rajopathyaya, 1999;Kumar et al., 2015], the spatial and temporal sampling is of-ten so limited that it is difficult to physically interpret thosemeasurements in a robust large-scale context to generalizethe findings. Long-term, global observations from satellitescould offer a solution to the sampling problem. However,no satellite instrument currently in orbit is designed for thepurpose of measuring vertical velocity at any spatial scale.A new approach is explored in this study to work out thisdifficulty, by combining and extending two satellite-basedanalysis methods recently developed by the authors so thatboth large-scale and convective-scale mass fluxes are esti-mated over the globe.

The first method was developed to target convectiveplumes sampled by CloudSat and other A-Train measure-ments. It produces estimates of cloud-top buoyancy Luo

1Institute for Space-Earth Environmental Research,Nagoya University, Nagoya, Japan

2Department of Earth and Atmospheric Sciences andNOAA-CREST Institute, City University of New York, CityCollege, New York, New York, USA

Copyright 2016 by the American Geophysical Union.0148-0227/16/$9.00

et al. [2010] and cloud-top vertical velocity [Luo et al.,2014] at convective scale on the order of 1 km (O(1 km)).These two estimates, in particular the cloud-top buoyancy,is adopted in the current study to derive convective massfluxes (Section 2.2). The second method of interest was pro-posed by Masunaga and L’Ecuyer [2014], where large-scale(O(100 km)) vertical motion is quantified from a thermo-dynamic budget analysis applied to infrared soundings andother satellite measurements. These two independent tech-niques in tandem provide a unique opportunity to studyjointly the convective mass flux and total large-scale massflux, the latter of which formally includes downdraft massflux as well. These two mass-flux estimates from the presenttechniques are, although subject to their own uncertainties,by design free of any external assumption prescribing thephysical linkage between convective clouds and their envi-ronment. In general circulation models (GCMs), the totallarge-scale mass flux is explicitly simulated in a prognosticmanner, whereas the convective mass flux is treated implic-itly in cumulus parameterization. Findings from our studywill thus serve as an important observational basis againstwhich GCM cumulus parameterization, or more generallythe interaction between convection and large-scale environ-ment, may be vigorously evaluated. This article, as the firstof a series of papers to follow, is intended to report the pro-posed methodology and some preliminary results applied toobservations over tropical oceans, leaving in-depth analysisand specific applications for future work.

A summary of the input satellite data and a review ofthe methods from those previous papers are presented insection 2. A simple plume model is described in section3.1 to construct the in-cloud vertical velocity profiles thatare matched with cloud-top buoyancy and vertical velocityestimates (section 3.2). The analysis results for two years(2008-2009) are presented in section 4, followed by discus-sions and summary in section 5. A brief error analysis isprovided in Appendix.

2. Satellite Data, Derived Parameters, andComposite Method

1

X - 2 MASUNAGA AND LUO: MASS FLUX ESTIMATES FROM SATELLITES

Table 1. Summary of Satellite Data Analyzed in This Work

Platforms Instruments Description Footprint Size Target ParametersTRMM PR Ku-band radar 4.3 km at nadir Convective occurrence for

the composite base pointAqua AIRS Hyper-spectral

IR sounder13.5 km at nadir Air temperature and water

vapor profilesAqua AMSR-E Microwave

radiometer74 km × 43 kmto 6 km × 4 km

SST, CWV, and surfaceprecipitation

Aqua MODIS Vis/IR imager 1 km at nadir Cloud top temperatureCloudSat CPR W-band radar 1.7 km × 1.3 km Cloud-top height, cumulus

occurrence, and QR

CALIPSO CALIOP Lidar 100 m Cloud-top heightQuikSCAT SeaWinds Microwave scat-

terometer37 km × 25 km Wind at 10-m height

This section is devoted to a brief summary of the dataand method from previous studies employed as an input tothe present analysis. Further technical details are found inthe cited references.

2.1. Data summary

The satellite instruments used in this study are summa-rized in Table 1. The Tropical Rainfall Measuring Mission(TRMM) Precipitation Radar (PR) offers a reliable mea-sure of precipitation (or rain-cell) occurrence and is used asthe “anchor” of statistical time series before and after con-vection is developed (to be detailed in section 2.4). TheAtmospheric Infrared Sounder and Advanced MicrowaveSounder Unit (AIRS/AMSU, hereafter AIRS collectively)Level-2 product provides the vertical profiles of tempera-ture and humidity at a vertical resolution of roughly 1 km[Susskind et al., 2003, 2011]. Column water vapor (CWV)and sea surface temperature (SST) are obtained from theAdvanced Microwave Scanning Radiometer for Earth Ob-serving System (AMSR-E) datasets produced by the Re-mote Sensing Systems (RSS) [Wentz and Meissner , 2000].AMSR-E is employed also for surface precipitation estimateswith the Goddard Profiling (GPROF) 2010 data [Kum-merow et al., 2011]. Ocean-surface wind estimates are takenfrom the Quick Scatterometer (QuikSCAT) SeaWinds Level-3 daily gridded dataset [Perry , 2001]. The CloudSat CloudProfiling Radar (CPR) and Cloud-Aerosol Lidar and In-frared Pathfinder Satellite Observation (CALIPSO) Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) areutilized for determining the cloud top height of convectiveclouds, while cloud top temperature is estimated from theModerate-Resolution Imaging Spectroradiometer (MODIS).The footprint size varies on an instantaneous basis from sen-sor to sensor, but the inconsistency in spatial resolution isalleviated 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 AIRSproduct design. Additional two levels below 925 hPa are in-troduced to represent the surface and cloud base, the latterof which is given by the lifting condensation level (LCL) de-termined with the near-surface temperature and humidityestimates from the AIRS observations.

2.2. Cloud-top buoyancy and vertical velocity

Cloud-top buoyancy of convective clouds is derived basedon the normalized temperature difference between the cloudtop 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 fromMODIS, with an IR emissivity correction applied makinguse of simultaneous observations from the CALIPSO andCloudSat satellites. CloudSat radar echoes are used also fordetermining cloud-top height and ensuring that a detectedconvective core continuously extends up from the cloud base

located near the surface. It is noted that the cases wherenear-surface echoes disappear due to heavy attenuation byprecipitation are assumed to be associated with vigorousconvection and are retained in the samples. The ambienttemperature is adopted from the collocated European Cen-tre for Medium-Range Weather Forecast (ECMWF) opera-tional analysis. A key observational requirement for buoy-ancy estimation is simultaneous and independent measure-ments of cloud-top height (CloudSat) and cloud-top temper-ature (MODIS), as well as information on ambient temper-ature profile (ECMWF).

Shallow convection is in general difficult to capture with asufficient level of confidence in the present methodology, socloud-top buoyancy and vertical velocity estimates are un-available where cloud top is lower than 3 km. This criterionimposes a major restriction on sampling completeness, giventhe prevalence of shallow cumuli over tropical oceans [John-son et al., 1999; Short and Nakamura, 2000]. The currentanalysis tentatively deals with shallow cumuli in a simplifiedapproach as described later in section 4, leaving a more real-istic treatment for follow-up work in the future. It is hencestressed that the primary interests of the present work areconfined to deep convection and congestus.

Buoyancy is in theory affected by in-cloud and ambienthumidity (through the virtual temperature effect) and thecondensate loading in addition to the temperature difference[see (12) in section 3.1]. The effects of humidity and conden-sate are not considered in the current measure of cloud-topbuoyancy in order to avoid unnecessary complication. Thisis deemed to be justifiable since we focus mainly on deepconvection and congestus where cloud top temperatures arelow enough such that the vapor and condensate mixing ra-tios are generally very small.

Luo et al. [2014] demonstrated that convective cloud-top vertical velocity can be evaluated by exploiting a smalloverpass-time difference between the two IR sensors belong-ing to the A-Train constellation, namely, the Aqua MODISand the CALIPSO Imaging Infrared Radiometer (IIR). Ba-sically, an actively developing convective plume will growcolder with time and its cloud-top vertical velocity is pro-portional to the change rate of cloud-top temperature withtime. By measuring the time-differenced cloud-top temper-ature, together with knowledge of the lapse rate, one canestimate the convective cloud-top vertical velocity. We haveused both cloud-top vertical velocity and cloud-top buoy-ancy in our analysis and found the results were virtually thesame. Although cloud-top vertical velocity may appear as amore natural choice for deriving the whole in-cloud profile ofvertical velocity than using cloud-top buoyancy, the obser-vational requirements are far more restrictive for the former.Hence, there are significantly more data points for buoyancythan for vertical velocity, leading to a less noisy analysis re-sult. This paper therefore presents only the buoyancy-basedanalysis.

2.3. Large-scale vertical motion

MASUNAGA AND LUO: MASS FLUX ESTIMATES FROM SATELLITES X - 3

Table 2. Sensitivity Experiment Design for the Plume Model

Model Assumptions Lower End Control Higher EndaB 0.1 1/6 (0.166· · ·) 0.2dTi 5 K 7 K 10 K

qw,crit 1× 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 vertical profiles of humidity and temperature ob-served from the AIRS serve as a primary input into themoisture and thermal budget analysis that is employed forevaluating large-scale vertical p-velocity, ω, or equivalentlythe total large-scale mean mass flux, M0, multiplied by grav-itational acceleration.

The moisture and thermal budget equations integratedvertically over the troposphere serve as diagnostic formu-lae to evaluate moisture convergence and dry static energy(DSE) convergence given the other terms all constrained ob-servationally:

−⟨∇ · qv⟩ = ∂

∂t⟨q⟩ − E + P (1)

and

−⟨∇ · sv⟩ = ∂

∂t⟨s⟩ − S − LvP − ⟨QR⟩, (2)

where ⟨· · ·⟩ denotes the vertical integral over the tropo-sphere, q the vapor mixing ratio, s the DSE, v the horizontalwind, E the evaporative flux, P the surface precipitation, Sthe sensible heat flux, Lv the specific latent heat of vapor-ization, and QR the radiative heating rate. The overbar des-ignates horizontal averaging over a large-scale domain withthe radius of 100 km.

The moisture and DSE convergence integrated verticallymay be viewed as lower- and upper-troposphere weightedconvergence, respectively, because moisture has higher con-centration in the lower troposphere while DSE has greatervalue in the upper troposphere. Vertical velocity, or thevertical integral of horizontal convergence, may be thereforeobtained in each lower and upper troposphere exploiting (1)and (2), respectively, together. This idea is further extendedso that a complete vertical profile of ω is obtained when thedegree of freedom is reduced to a tractable level through ver-tical mode decomposition into the first and second baroclinicmodes and the shallow mode combined with a time-invariantbackground state of ω. The equations to yield the three ωmodes consist of∑

i

⟨q∂ωi

∂p

⟩≈ −⟨∇ · qv⟩, (3)

∑i

⟨s∂ωi

∂p

⟩≈ −⟨∇ · sv⟩, (4)

where the subscript i represents each vertical mode, and∑i

ωi,CB = ⟨∇ · qv⟩SC, (5)

where ω at cloud base (CB) is quantified from the sub-cloudlayer (SC) convergence determined with QuikSCAT winds.The RHS of equations (3) and (4) are as given by equations(1) and (2). The sum of all the three modes, ωi, yields ωand serves as the total large-scale mass flux discussed in 4.More details in methodology are provided by Masunaga andL’Ecuyer [2014].

2.4. Integration into composite time series

Cloud-top buoyancy (and cloud-top vertical velocity) andlarge-scale ω retrievals are applied individually to instanta-neous measurements over global tropical oceans. Convective

cloud structure is substantially different over land from overocean [Liu et al., 2007], so aspects of the current findings ap-ply only to oceanic convective systems. Limiting the anal-ysis to oceans mitigates the diurnal sampling bias in sun-synchronous satellite measurements owing to the weaknessof diurnal variation in oceanic precipitation [e.g., Imaokaand Spencer , 2000]. The observations are time-stamped ac-cording to the temporal difference with respect to the timewhen the TRMM PR detects rain cells some hours before orafter at the same location, and are then averaged over thesurrounding 100-km radius domain for each hour to consti-tute a composite time sequence around the time of rain-celloccurrence [Masunaga, 2012, see the schematic in Fig. 1].Note that this circular domain is comparable in area to a177 km × 177 km box if applied to a square field.

The number of A-Train buoyancy samples ranges fromabout 3000 to 6000 for each hourly bin in composite space,as shown later in section 4 and Figure 6c. The AIRS sam-ples for large-scale ω consist of roughly 30,000-300,000 eachhour, for which the minimum corresponds to the hours ofpeak convection because infrared sounding is unavailable fortotally cloudy skies. The composite time series shown in thiswork are hence constructed with a reasonably large body ofstatistics. The robustness of the composite statistics, includ-ing the potential errors due to the migration of convectivedisturbances, has been assessed in Masunaga [2015].

The TRMM detection of rain cells is defined when thePR finds precipitation echoes beyond the noise level acrossa few vertically consecutive bins within a column, flaggedas the “rain certain” in the TRMM data product. In thepresent analysis, this procedure is carried out only when theTRMM PR finds the rain-cell coverage exceed 50 % of the100-km radius domain. As such, the resulting time series isconsidered as a statistical representation of the variabilityover time in association with the development and dissipa-tion of highly organized convective systems (see Figure 2of Masunaga [2013]). The present compositing procedurehas another advantage that the composite 100-km domaincontains a large number of CloudSat/CALIPSO samples asnoted above although those samples, confined spatially to anarrow vertical scan, cover only a fraction of the domain onan instantaneous basis.

The QuikSCAT satellite had the sun-synchronous orbitof ∼6:00 local time, flying behind the A-Train satellites byroughly 4.5 hours. This temporal offset could potentiallyintroduce some bias when the QuikSCAT and A-Train mea-surements are combined into the composite time series. Thebias would be however small because the diurnal cycle oftropical disturbances is modest as mentioned above, withthe magnitude being not larger than 30 % in surface diver-gence over tropical oceans [Deser , 1994]. This magnitudeshould be further reduced when the opposite diurnal phasesare averaged between ascending and descending orbits.

2.5. Analysis period and area

The analysis period spans 2 years from January 1, 2008 toDecember 31, 2009 for cloud-top buoyancy estimates (sec-tion 2.2). The large-scale vertical motion (section 2.3) isconstructed with a longer period from December 1, 2002to November 30, 2009 to ensure the statistical robustnessin the composite time series (section 2.4). The differencein the temporal length is not essential since the composite


Cloud-top buoyancy

(and/or Cloud-top

vertical velocity)

(section 2.2)

Plume model

(section 3.1)

Total large-scale

mass flux profile

(section 2.3)

In-cloud vertical

velocity profile

(section 3.2)

Convective

mass flux profile

(section 3.2) Residual

mass flux profile

(section 4)

CloudSat

Cloud-top height

Cloud-top temperature Air temperature, vapor,

and surface wind etc.

CALIPSO

Aqua QuikSCAT

Cumulus occurrenceRadiative cooling Day i

Day j

Day k

0 1:37 AM/PM 24 (LT)

......

Dti

Dt

Dt

j

k

Composite time

Dti

Dtk

Dtj

t=0

Instantaneous observations

TRMM

TRMM

TRMM

A-Train

TRMM

A-Train

A-Train

A-Train A-Train

TRMM compositing procedure (seection 2.4)

Figure 1. Flowchart of the analysis procedures. Solid arrows indicate the analysis flow and dashedarrows represent the primary input parameters and the satellites that provide these parameters. Theschematic on the right shows the current composite technique where many pairs of TRMM and A-Trainsnapshots are averaged into statistical time series. Here the A-Train snapshots consist of the parametersas shown in each flowchart box except for the “Plume model”, while the TRMM is employed to seek theoccurrence of rain cells that may be prior or subsequent to each A-Train snapshot (see section 2.4 fordetails).

statistics are known to be insensitive to the choice of theanalysis period [Masunaga, 2015].

The target region is global tropical oceans between 15◦S-15◦N with landmasses all excluded. Tropical clouds, in par-ticular organized convective systems, are known to be dis-tributed non-uniformly over tropical oceans [e.g., Mohr andZipser , 1996]. However, our previous results (e.g., Figure12 of Masunaga [2013]) show that the overall features of thesampled convective systems, conditioned on the 50+ % cov-erage as defined above, are insensitive to the regionality suchas the east versus west Pacific. The statistics are in effectrepresentative of convective active regions in general. It fol-lows that individual systems selected by the common criteriaexhibit certain universal characteristics beyond the climato-logical differences in their large-scale environment.

3. In-cloud Vertical Velocity Profiles

Buoyancy or vertical velocity estimates from radar and IRmeasurements are available only at cloud tops, while the fullin-cloud structure of updraft velocity is required for our sci-ence goal. A new strategy is developed in this work to recon-struct the in-cloud vertical velocity profiles with the aid ofa steady-state single-column plume model described in sec-tion 3.1. Entrainment rate, a key uncertainty in the model,is varied so that a broad range of solutions are allowed toexist for a given environmental sounding. A Bayesian proce-dure is then applied to narrow down the candidate profilesto the solution that best matches the cloud-top buoyancy orvertical velocity estimates derived from observations (sec-tion 3.2). A flowchart is shown in Figure 1 to outline thewhole procedures in the present work.

The plume model developed here is by design meant torepresent updraft in cumulus convection without convectivedowndraft and mesoscale dynamics considered. This defini-tion is consistent with the cloud-top buoyancy and verticalvelocity estimation from satellites, where the samples are

conservatively chosen to focus on rapidly growing convectivecores [Luo et al., 2010, 2014], which belong, together withthe surrounding stratiform clouds, to the organized systemidentified by the TRMM during hours around zero. Thepresent analysis, however, formally includes the downdraftsas well in terms of the residual in the large-scale mass-fluxbalance as discussed later in section 5.

3.1. Single-column plume model

The entrainment and detrainment rates, ϵ and δ, are de-fined conventionally as

1

ρwc

∂(ρwc)

∂z= ϵ− δ. (6)

where w is vertical velocity, ρ is the mass density of air, andthe subscript c indicates in-cloud properties. The entrain-ment and detrainment rates may be separated into dynamicand turbulent components [Houghton and Cramer , 1951],

ϵ = ϵdyn + ϵtur, δ = δdyn + δtur, (7)

where the dynamic components are determined so as to sat-isfy the mass conservation [Asai and Kasahara, 1967],

ϵdyn =1

ρwc

∂(ρwc)

∂zH

[∂(ρwc)

∂z

],

δdyn = − 1

ρwc

∂(ρwc)

∂zH

[−∂(ρwc)

∂z

], (8)

where H is the Heaviside function. The turbulent compo-nents are by definition cancelled out at each height in thecontinuity equation (i.e., ϵtur = δtur) while not eliminatedin the other conservation equations described below.


CB CB

Figure 2. The plume-model solutions of (a) (Tc − Ta)/Ta and (b) wc (m s−1). Colors indicate differentturbulent entrainment rates, ϵtur, changing by an increment of 0.01 km−1 from 0 up to 0.1 km−1, followedby 0.12, 0.15, 0.2, 0.3, and 0.4 km−1 (from red to purple in the increasing order). The ambient soundingsare taken from the composite time series at t = −24 h. Cloud base is labeled as “CB” on the pressurecoordinate.

CB CB

Figure 3. The plume-model solutions of (a) the entrainment rate (km−1), ϵ, and (b) the detrainmentrate, δ (km−1). Colors indicate different turbulent entrainment rates, ϵtur, changing by an increment of0.01 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 inthe increasing order). The ambient soundings are taken from the composite time series at t = −24 h.Cloud base is labeled as “CB” on the pressure coordinate.

The conservation of an arbitrary parameter φ may be

written as

∂(ρwcφc)

∂z= ρwc(ϵφa − δφc) + ρ

∑i

Fφ,i, (9)

where the subscript a designates the ambient environment

and Fφ,i accounts for the source and sink terms as needed.

Equations (6) and (9) are combined into

∂φc

∂z= −ϵ(φc − φa) +

1

wc

∑i

Fφ,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

2

∂w2c

∂z= aBB − ϵw2

c − cDw2c , (11)

where φ has been replaced by w2c . Here the in-cloud buoy-

ancy, B, is characterized by

B = gaB

(Tv,c − Tv,a

Tv,a− qw

), (12)

where g is the gravitational acceleration and Tv is virtualtemperature. The portion of the buoyancy production us-able for vertical acceleration, aB , is set to be 1/6 [Gregory ,2001]. The third term in the right-hand side of (11), aimedto account for a drag force owing to pressure perturba-tion from the hydrostatic state [e.g., Simpson and Wiggert ,1969], is highly uncertain and hence not explicitly specifiedhere. Instead, uncertainties in cD are formally combinedinto those in ϵtur. As such, ϵtur is the controlling parameterin this work to be chosen from a range of possibilities andthen constrained by observations.

In-cloud moist static energy (MSE), hc, is

hc = cpTc + gz + Lvqv,c, (13)

where cp is the specific heat capacity under constant pres-sure, and z is altitude. The conservation equation (10) isapplied to the MSE budget with the freezing effect included(i.e., φc = hc − Liqi and φa = ha),

∂(hc − Liqi)

∂z= −ϵ(hc − Liqi − ha), (14)

where Li is the specific latent heat of fusion and qi is the icemixing ratio. The ice mixing ratio is determined diagnosti-cally as

qi = fiqw, where fi =1− tanh[(Tc − T0,i)/dTi]

2(15)

where T0,i and dTi are chosen to be −20◦C and 7◦C, respec-tively, so that fi smoothly transitions from zero to unity astemperature decreases from 0◦C to −40◦C. In-cloud tem-perature Tc is obtained from hc, assuming that the in-cloudair is saturated at all heights and qv,c is approximated bysaturation vapor mixing ratio with respect to liquid water,q∗v(Tc). It has been confirmed that the buoyancy profiles re-main similar when q∗v(Tc) is replaced by the saturation vaporpressure with respect to ice at cold temperatures.

Replacing φc with qw in (10) leads to the equation for thecondensate mixing ratio,

∂qw∂z

= −ϵqw +1

wc(qcond − qauto), (16)

where qcond is the condensation rate and qauto is the auto-conversion rate. The ambient temperature and vapor pro-files are known parameters taken from AIRS/AMSU sound-ings, same as those ingested for ω estimates (section 2.3).The condensation rate is diagnosed from the vapor budgetequation, obtained by substituting vapor mixing ratio qv forφ in (10),

qcond = −wc

[∂qv,c∂z

+ ϵ(qv,c − qv,a)]. (17)

Here again qv,c is replaced by saturation vapor mixing ra-tio q∗v(Tc). The auto-conversion rate is estimated using aprimitive form of the Kessler formula [Kessler , 1969],

qauto =1

τauto(qw − qw,crit)H(qw − qw,crit), (18)

where τauto = 103 s and qw,crit = 10−3 kg kg−1. Precipitat-ing particles are assumed to immediately fall out of the as-cending air and their thermodynamic effects such as reevap-oration and melting are not taken into account. The readeris reminded that the current plume-model is designed totarget convective updraft only.

Equations (11), (14), and (16) are integrated over heightfrom cloud base to the level at which wc reaches zero. Eachvertical layer from the ambient soundings (see section 2.1)is divided into 5 sub-layers for use by the numerical inte-gration. The boundary condition for (14) and (16) is ratherobvious: hc is as observed from the satellite sounding and qwis zero immediately below cloud base. On the other hand,wc at cloud base is not known from the observations and isassumed here to be twice as large as the sub-cloud layer ver-tical velocity scale, w∗ [for further details, see Grant , 2001;Gregory , 2001]. In this study, an approximate formula of w∗is adopted as

w∗ ≡(gzCB

θv,SCw′θ′v0

)1/3

≈(

gzCB

cpTSCS

)1/3

, (19)

where TSC and θv,SC are the temperature and virtual po-tential temperature averaged over the sub-cloud layer, zCB

is the cloud-base height, w′θ′v0 is the surface turbulent fluxof virtual potential temperature, and S is surface sensibleheat flux. The sensible heat flux is evaluated using a bulkformula as employed by Masunaga [2013]. Typical values ofw∗ estimated from the present satellite soundings are 0.6-0.7m s−1, which fall within the range studied by Grant [2001].

Figure 2 shows the plume-model solutions for a range ofϵtur varied from 0 to 0.4 km−1. The ambient soundings toforce this run are taken from the composite time series at 24hours prior to the time of peak convection, but the resultsare qualitatively insensitive to the choice of timing. The nor-malized temperature difference, (Tc − Ta)/Ta, is presentedas a proxy of buoyancy in Fig. 2a, since this is the parameterto compare with cloud-top observations in the Bayesian pro-cedure described next (section 3.2). As expected, a changeto the entrainment rate leads to a great difference in thedepth of clouds from shallow cumulus topped near 700 hPato overshooting deep convection reaching beyond 150 hPa.The resulting variation in the maximum updraft velocityspans a broad range from less than 3 m s−1 (shallow cu-mulus) to 14 m s−1 (deep convection) (Fig. 2b). Shallowcumuli with even lower cloud tops are outside the presenttarget and are not attempted to simulate with the currentmodel. The enhanced buoyancy above 400 hPa (Fig. 2a)is brought by an additional heating owing to the freezing ofcloud water, resulting in continuing acceleration of plumesas seen in the wc profiles (Fig. 2b). Vertical velocity thenrapidly declines with height as buoyancy sharply drops to alarge negative near the top of overshooting deep convection.The general characteristics of the wc profiles simulated fordeep convection is consistent with Doppler-radar measure-ments by Heymsfield et al. [2010] in that wc increases withheight until it reaches the upper tropospheric peak exceed-ing 10 m s−1.

The corresponding profiles of the entrainment and de-trainment rates are shown in Figure 3. The overall verticalstructure of ϵ is dominated by ϵdyn rather than ϵtur, thelatter of which is assigned with a range of possible valuesconstant over height. The entrainment rate is greatest im-mediately above cloud base, where the accelerating updraftefficiently sucks in the ambient air. The detrainment rate,with a somewhat larger spread depending on δtur, has astriking spike near cloud tops generated by an abrupt de-celeration of updraft. Modest peaks at 400-500 hPa arise


CB CB

CB CB

Figure 4. A sensitivity experiment of the plume model of (Tc − Ta)/Ta (a and c) and wc (m s−1) (band d) varying aB (a and b) and dTi (c and d) 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 simulatedprofiles is color-shaded around the control profile drawn in black. The ambient soundings are taken fromthe composite time series at t = −24 h. Cloud base is labeled as “CB” on the pressure coordinate.

from the combination of a buoyancy loss by the condensateloading and the following recovery of buoyancy due to freez-ing. This mid-tropospheric detrainment peak is a factorresponsible for the formation of cumulus congestus cloudsprevailing over tropical oceans [Johnson et al., 1999]. Theidea that the effect of freezing on buoyancy could reinvigo-rate the updraft so the convective cloud eventually reachesthe tropopause has been supported by later studies [e.g.,Zipser , 2003] and will be worth revisiting in the future byrecent satellite observations.

The simulated profiles presented above depend also onvarious model assumptions other than ϵtur. A set of sen-sitivity experiments are therefore conducted for assessinguncertainties in the assumptions. Each of aB , dTi, qw,crit,and τauto are perturbed one after another with all the otherassumptions fixed at the control value. It is difficult to de-termine the realistic range of assumptions with confidence,so the lower and higher ends are chosen somewhat arbitrar-

ily within roughly an order of magnitude as listed in Table 2.The results are presented in Figures 4 and 5. In all cases, thevertical profiles remain qualitatively similar in that wc in-creases with height toward a single maximum, followed by asteep decline immediately above. A large spread in wc arisesfor moderate entrainment rates (green shade) in Figure 5 be-cause in these cases a subtle change to the assumptions couldresult in distinct consequences of either a buoyancy loss dueto condensation loading (congestus) or a reinvigoration ofupdraft by freezing (deeper convection). Nevertheless, thespread due to any perturbation assumption (as representedby the breadth of the curves) is relatively small compared tothe differences associated with varying ϵtur values, spanningacross different curves from congestus to deep convection.It may be therefore concluded that ϵtur is the parameter re-sponsible for yielding broad solutions from shallow cumulusto deep convection, while uncertainties in other assumptions


CB CB

CB CB

Figure 5. A sensitivity experiment of the plume model of (Tc−Ta)/Ta (a and c) and wc (m s−1) (b andd) varying qw,crit (a and b) and τauto (c and d) 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 simulatedprofiles is color-shaded around the control profile drawn in black. The ambient soundings are taken fromthe composite time series at t = −24 h. Cloud base is labeled as “CB” on the pressure coordinate.

per se are not so large as to entirely modify the depth of con-vection.

3.2. Synthesis of Satellite and Model Estimates

A set of the wc profiles presented in the previous sec-tion (Fig. 2b) constitute a database to be searched for theoptimal solution. The profile consistent with a given cloud-top buoyancy (or cloud-top vertical velocity) estimate is se-lected from the candidate solutions in a Bayesian manner[e.g., Lorenc, 1986]. The expectation of vertical velocitystructure, wc, is

wc(z) ≡∑i

p(ϵtur,i|zT ,∆TT )wc,i(z) =

∑i

p(ϵtur,i)p(zT ,∆TT |ϵtur,i)wc,i(z), (20)

where ϵtur,i indicates the i-th member of ϵtur (see the cap-tion of Fig. 2 for specific numbers), wc,i is the correspondingvertical velocity profile from the plume model, p(ϵtur,i) is thepriori probability distribution of ϵtur,i, p(ϵtur,i|zT ,∆T ) is theposteriori probability function for a given pair of observa-tions of cloud-top height, zT , and the normalized tempera-ture difference at the cloud-top height, ∆T ≡ (Tc − Ta)/Ta,and p(zT ,∆TT |ϵtur,i) is the conditional probability of zTand ∆T for given i-th plume-model profile. The conditionalprobability distribution may be written as

p(zT ,∆TT |ϵtur,i) ∝1

s0,i − sCB×

∫ s0,i

sCB

exp

[− (zT − zi(s))

2

2σ2z

− (∆TT −∆Tc,i(s))2

2σ2∆T

]ds,(21)


CB

CB

Figure 6. The composite time series of (a) vertical velocity wc (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, labeledon 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 kmare hatched in (a) and (b) to mask out the heights where cloud-top buoyancy estimates are unavailable.

where σz and σ∆T is the measurement error associated withzT and ∆T , respectively. It is assumed in this work thatσz =1 km and σ∆T ≈ σT /Ta where σT = 1 K. The sen-sitivity to the choice of σz and σ∆T will be tested in Ap-pendix. The integral is performed along the plume-modeltrajectory, s, in the ∆T -z plane as drawn in Fig. 2a fromcloud base, sCB, to the level at which wc vanishes, s0,i. Thepriori probability distribution p(ϵtur,i) is initially assumed tobe constant and is then updated by repeating the Bayesianprocedure until the solution converges.

Mean convective intensity, wc, and convective mass flux,Mc, are each computed from wc as

wc =1

Aw

∑∈Aw

wc, (22)

Mc =1

A0

∑∈Aw

ρwc, (23)

where the area A0 designates the portion of the large-scaledomain that is sampled by CloudSat granules, and Aw

denotes its subset constituted only of the footprints withnon-zero buoyancy estimates, that is, the footprints whereCloudSat detects deep convection and congestus. In (22)wc is averaged conditionally where convection is observedso that it provides a measure of convective intensity, whileMc in (23) is the unconditional mean over the whole large-

scale domain, thus representing the convective mass flux asoften used in GCM cumulus parameterizations.

4. The Composite Time Series of VerticalVelocity and Mass Flux

The analysis results from the algorithm outlined in sec-tion 3.2 are presented in this section. Potential errors asso-ciated with Mc are discussed later in Appendix.

Figure 6a shows the composite time series of wc, implyingthe persistence of deep convection with the vertical velocitypeak at 200-300 hPa. The near invariance of wc is not sur-prising, since the atmosphere stays humid and marginallyunstable most of the time given that the statistics are con-structed around the occurrence of organized convection overtropical oceans. Convection therefore has the potential todevelop deep whenever it occurs, whereas the frequency ofoccurrence may be largely modulated by the large-scale dy-namics as shown later. A closer examination, however, re-veals a subtle but systematic variation in wc. The atmo-sphere undergoes a gradual lower-tropospheric moistening(destabilization) toward the time of convection and a subse-quent near-surface cooling (stabilization) [Masunaga, 2012],which is probably responsible for a slight intensification dur-ing negative hours and a sudden weakening of wc at t ∼ 0.It is noted that the persistence of deep convection couldbe somewhat exaggerated because less developed convection


concealed beneath an overlapping high cloud would be dif-ficult to sample from infrared measurements.

It is reminded that samples of convective clouds are ab-sent when cloud-top height does not reach beyond 3 km. Itis attempted here to fill in the effects of shallow cumuli by asimplistic approach where the wc profile is prescribed withthe most heavily entraining plume-model simulation, plottedin darkest blue in Fig. 2. This choice of the least-developedcumulus profile is intended to provide a conservative esti-mate of shallow convective updraft. The result emerges asa weak enhancement of wc below 3 km (hatched in Fig. 6a),somewhat strengthening as the ambient atmosphere moist-ens toward time zero. Shallow cumulus is nevertheless weakin the variability of wc as one might expect from its ubiqui-tous nature over tropical oceans [e.g., Short and Nakamura,2000], and is hence unlikely to introduce significant error inthe wc variability.

Convective mass flux (Fig. 6b) has a bottom-heavy profilecompared to wc as a result of the upward-decreasing ρ. An-other feature contrasting with wc is that Mc experiences adrastic enhancement during the hours of active convection.Convective mass flux reaches as large as 2-3 ×10−2 kg m−2

s−1 at times when convection is most intense (t ∼ −3 h),while an order-of-magnitude smaller during the hours awayfrom the peak (hereafter called the background). This en-hancement occurs in parallel with the sample size of convec-tive clouds (solid curve in Fig. 6c), which primarily reflectsthe frequency of convective occurrence since CloudSat over-passes are overall homogeneously sampled (∼4-5×105) alongthe composite time axis (dotted curve in Fig. 6c). The num-ber of convective cloud samples with buoyancy estimatesspans 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 the convective cloud cover, σc.Note that these values correspond to the coverage of con-vective cores that are selected by some rather strict criteriaon radar echo characteristics, as described in [Luo et al.,2010]; convective cores usually cover only a very tiny frac-tion of the whole convective cloud system. Equation (23)may be rewritten as Mc ∼ σcρwc when wc is relatively con-stant 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 radarmeasurements that the cumulus cloud cover, rather thanvertical velocity, chiefly contributes to the variability of thedomain-mean mass flux.

The third (green dashed) curve in Fig. 6c provides arough measure of shallow cumulus occurrence as defined byN2km

Cu − N4kmCu , where NCu is the sample size of the cumu-

lus (Cu) category at the indicated height from the CloudSatCLDCLASS product [Wang and Sassen, 2001]. The sub-traction by N4km

Cu is meant to avoid congestus clouds alreadyincluded in the buoyancy samples. The small sample sizeand weak updraft result in a barely visible contribution ofshallow cumuli to convective mass flux (hatched in Fig. 6b).Note that the CloudSat radar is insensitive to clouds whosedroplets are too small to detect and the shallow-cumulusmass flux may be underestimated. This limitation is to bemitigated in future work using additional satellite instru-ments capable to detect thin low clouds such as CALIOPtogether with improved cloud-model setups that better char-acterize shallow cumuli.

Convective mass flux is next compared against an inde-pendent measurement of ω as described in section 2.3. Thetotal large-scale mass flux, M0, is proportional to ω underthe hydrostatic assumption and is broken down into threecomponents;

M0 ≡ ω

g= Mc +MR +M∗, (24)

where MR is the radiatively forced subsidence,

MR∂sa∂p

=QR

g, (25)

where sa is DSE of the ambient air and QR is the radiativecooling rate adopted from the CloudSat 2B-FLXHR-LIDARproduct. The last term, M∗, is the residual mass flux unac-counted for by the other terms in the mass balance equation(24).

Figure 7a-c shows each mass flux component at differ-ent pressure levels of 200, 300, and 400 hPa. Convectivemass flux delineates coherent evolutionary tracks across allthe levels. The evolution of M0 begins with a weak ascentcomparable to Mc, but then rapidly grows to a striking up-draft around time zero to a degree that Mc alone is far fromable to account for. This discrepancy in the peak amplitudegives rise to a substantial magnitude of the residual flux M∗,which at its maximum momentarily exceeds Mc at 400 hPawhile staying relatively minor at 200 hPa. During the wholeperiod, MR is negligible and has little impact on the massflux balance.

The vertical structure of M0 and M∗ is presented in Fig.7d,e. As seen above, the most conspicuous feature in M∗ isthe upper tropospheric updraft peak around the hours of in-tense convection. Figure 7e shows that M∗ is also character-ized by a lower-tropospheric downdraft persistent through-out the entire time series. The downdraft arises either whenthe total domain-mean ascent is short of the convective up-draft or when M0 is negative in the first place. It is notedthat the M∗ downdraft occurs mostly at heights below 3 km(hatched), where the Mc updraft is likely to be underesti-mated because shallow cumuli are not fully considered inthis study. The M∗ downdraft is hence probably underesti-mated as well because (24) needs to be satisfied for a givenestimate of M0. Physical implications of the residual massflux will be discussed in the next section.

5. Discussion and Conclusions

In this work, a new methodology is explored to derive theconvective and total mass fluxes from a variety of satellitemeasurements. Convective-scale vertical velocity is profiledusing cloud-top (> 3 km) buoyancy (or cloud-top verticalvelocity) estimates with the aid of a single-column plumemodel, while large-scale vertical motion is evaluated from athermodynamic consideration applied to satellite soundings.Both the convective- and large-scale vertical velocities arecomposited together into statistical time series constructedin association with the development and dissipation of or-ganized convective systems.

In-cloud vertical velocity profiles are found to be peakedin the upper troposphere regardlessly of the evolutionarystage of convective development. It follows that deep con-vection in the relatively quiescent spells builds up, once itoccurs, as vigorously (or even somewhat more intensively)as during organized systems. It is the frequency of convec-tive occurrence rather than the individual cloud propertiesthat modulates the convective mass flux as convective sys-tems develop and dissipate, consistent with a recent studyby Kumar et al. [2015] that used collocated wind-profilerand precipitation radar measurements. These findings arein harmony with existing observational work of the Madden-Julian Oscillation (MJO) despite the vast difference in timescale, showing that deep convection prevails throughout al-though convection better structures itself into an organizedsystem with extensive stratiform clouds during the maturephase than in the dry phase [Morita et al., 2006; Tromeurand Rossow , 2010].


CB

CB

Total

Convective

Residual

Radiative

Figure 7. (a)-(c) The composite time series of convective mass flux Mc, total mass flux M0, radiatively

forced mass flux MR, and residual mass flux M∗, at (a) 400 hPa, (b) 300 hPa, and (c) 200 hPa. (d)-(e)

The complete vertical structure of (d) total mass flux M0, and (e) residual mass flux M∗. The mass fluxunit is 10−2 kg m−2 s−1.

When the convective and total mass fluxes, Mc and M0,are compared, the mass balance relationship requires a resid-ual mass flux, M∗, that exhibits a significant updraft peakin the upper troposphere at the time of peak convectionand a persistent lower-tropospheric downdraft. The resid-ual flux arises for several possible reasons. One possibilityis retrieval bias since the measurements of Mc and M0 arederived in quite different manners and therefore would haveindependent sources of uncertainty that are hardly cancelledout. An error analysis provided in Appendix, however, sug-

gests that the current estimate of Mc lies close to the higherend within the range of uncertainty examined, so that theresidual flux is unlikely ascribed entirely to retrieval bias.

There are multiple lines of circumstantial evidence sug-gesting that M∗ indeed embodies an actual physical entity,primarily ascribable to stratiform updraft and downdraft.First, Mc closely tracks M0 before convection begins to beinvigorated and organized, leaving M∗ stay near zero. Thisis as expected in that isolated convection is exclusively re-sponsible for convective mass flux in the absence of orga-


Figure 8. The composite time series of convective mass flux, Mc, for a range of model assumptionsand measurement errors at (a) 400 hPa (b) 300 hPa, and (c) 200 hPa. The mass flux unit is 10−2 kgm−2 s−1. The range of uncertainties is shaded in orange for aB , blue for qw,crit, green for τauto, andred for the measurement error (σz and σT ). The lower and upper ends of each model assumption are asindicated in Table 2. The measurement error range is bounded by (σz, σT ) = (1.5 km, 1 K) and (0.5km, 2 K). The control run, identical to the blue solid curve in Figure 7a-c, is plotted in black.

nized convective systems. The high similarity between Mc

and M0 except when convection is organized probably servesas indirect evidence that our estimations of Mc and M0,although obtained through entirely independent and sepa-rate channels, are rather unbiased. Second, the observedpair of upper-tropospheric updraft and lower-troposphericdowndraft in M∗ is a known signature of stratiform dy-namics [Zipser , 1977; Houze, 1982, among others]. Lastly,the known fact that stratiform updraft is most active dur-ing the mature and dissipating phases of organized con-vective systems conforms with the evolution of M∗, whichrapidly grows near time zero and subsequently fades awayover time. Indeed, this temporal pattern of M∗ qualitativelytraces the variability of the second baroclinic (or stratiform)mode of large-scale vertical motion (Fig. 5a ofMasunaga andL’Ecuyer [2014]).

The algorithm requires technical refinements with partic-ular focus on major outstanding issues including the crudeassumptions on the plume model and shallow cumuli andthe exclusion of continental convection. With this caveat,the current methodology is expected to open new pathwaysfor a further understanding of tropical atmospheric dynam-ics. In particular, the present analysis of convective massflux and total large-scale mass flux could be of unique util-ity for the observational diagnosis and evaluation of cumulusparameterizations in a global sense.

Acknowledgments. The authors are grateful to Bill Rossowand Kenta Suzuki for their comments on earlier versions of themanuscript. The AIRS/AMSU product was provided by God-dard Earth Sciences (GES) Data and Information Services Cen-ter (DISC) (disc.sci.gsfc.nasa.gov) and the TRMM PR (2A25)dataset by the Japan Aerospace Exploration Agency (JAXA).The datasets also crucial, although not explicitly presented, inthe current analysis are the GPROF 2010 precipitation productfrom Colorado State University, the AMSR-E SST and CWVproduct by Remote Sensing Systems, the CloudSat datasets bythe CloudSat Data Processing Center, and QuikSCAT data fromthe NASA Jet Propulsion Laboratory. HM is supported by theJapan Society for the Promotion of Science (JSPS) Grant-in-Aid(KAKENHI) for Challenging Exploratory Research (26610150).JZL would like to acknowledge funding support by NASA grantNNX12AC13G and support from JPL CloudSat and Radar Sci-ence and Engineering group.

Appendix A: Error Analysis of ConvectiveMass Flux

A brief error analysis is provided in this section to demon-strate uncertainties in the composite time series of Mc. Thesources of errors examined here are the prescribed assump-tions in the plume model as investigated in section 3.1and the measurement errors (σz and σT ) assumed for theBayesian estimation (section 3.2). Other uncertainties re-lated to cloud-top buoyancy (section 2.2), large-scale mean


vertical motion (section 2.3), and the composite satellitesoundings (section 2.4) are discussed elsewhere [Luo et al.,2010; Masunaga, 2012, 2013, 2015] and are not repeatedhere.

Figure 8 summarizes the error analysis results at threepressure levels. The assumptions being tested are aB , qw,crit,and τauto from the plume-model assumptions and σz andσT from the Bayesian estimation. Note that dTi is notincluded because its uncertainty has little impact on theplume-model solutions (Figure 4c-d). The sensitivity to themodel assumptions is largest near the time of convectivepeak (t ≈ 0) at all heights, with the magnitude decreasingwith increasing height. Among the parameters examined,qw,crit, and τauto have the greatest contributions at 300 and400 hPa. The amplitude of the σz and σT uncertainties re-mains small, although recognizable at 200 hPa. The controlrun stays close to the high end of the error range through-out the evolution particularly at 300 and 400 hPa. It followsthat Mc is more likely overestimated than underestimatedin the present analysis, suggesting that the residual massflux, M∗, from the control run is plausibly a conservativeestimate for given M0.

The drag of precipitation is not included and is difficultto quantify for uncertainty in the present model where pre-cipitation immediately falls out and is not tracked downfurther. The absence of precipitation drag would lead to anoverestimation of buoyancy and hence an underestimationof the residual mass flux. The upper-tropospheric updraft inM∗ thus could be even larger, while the lower-troposphericdowndraft might have been somewhat exaggerated.

The error magnitude is minimal in the background stateaway from the hours of vigorous convection. It is impliedthat the earlier conclusion that Mc solely accounts for M0

before convection is invigorated remains robust regardless ofprescribed assumptions.

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Corresponding author: Hirohiko Masunaga, Institute forSpace-Earth Environmental Research, Nagoya University, Nagoya464-8601, Japan ([email protected])

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