VOLUME 77

JOURNAL OF THE ATMOSPHERIC SCIENCESAPRIL 2020

A Mechanism for the Maintenance of Sharp Tropical Margins
HIROHIKO MASUNAGA
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, JapanBRIAN E. MAPES
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida(Manuscript received 4 June 2019, in final form 15 January 2020)
ABSTRACTThe moist deep tropics are typically separated from the drier subtropics by a sharp horizontal gradient ofmoisture. The physical nature of this tropical margin is investigated by using A-Train satellite observations toreconstruct its composite mean quasi-meridional thermodynamic structure and processes. The margin isdefined here as the most poleward position of a specified column water vapor (CWV) threshold along asatellite track. Multiple CWV thresholds are selected from 35 to 60 mm, bracketing the global tropics histogram minimum value of 48 mm. For all margin thresholds, CWV increases equatorward from the subtropics
and eventually asymptotically approaches 48 mm far on the tropical side, apparently as a coincidence ofcomposite averaging since values of 48 mm are infrequent as noted above. For all margin thresholds, precipitation peaks on the tropical side and then asymptotically approaches equatorward a value of 85 W m22,
equal to the evaporation asymptote. For the 48-mm threshold, total diabatic forcing of the air column (radiative
heating plus surface latent and sensible heat fluxes) changes sign from positive on the tropical side to negativein the subtropics, with the main contrast in radiative heating, owing principally to the longwave effect of highclouds. An analytic two-vertical-mode model of equatorward-flowing air columns is fitted from the observations to elucidate the processes in a Lagrangian column transition. The model captures key features of thecomposite, and suggests that a key process in the abrupt moistening at the margin is bottom-heavy ascent
growing upward beneath the deep subtropical subsidence.

1. Introduction
Early modern theories of the Hadley circulation(Schneider and Lindzen 1977; Schneider 1977; Heldand Hou 1980) were built largely around dry dynamics,
with moist processes viewed as secondary or implicit.
In the typical cartoon, deep convection is sketched in
the ascending branch, with shallow cumuli at the bottom of the descending branch. This schematic view issilent about water vapor. While precipitation needs toprevail in the tropics to balance column moisture
convergence implied by the mean ascent, this waterbudget balance alone does not give a quantitative estimate of how moist the balanced state must be.
Denotes content that is immediately available upon publication as open access.
Corresponding author: Hirohiko Masunaga, masunaga@
nagoya-u.jp

Recent water vapor observations offer a new basis fordefining the meteorological boundary of the tropics: amoisture threshold. Mapes et al. (2018) found that thehistogram of instantaneous column water vapor (CWV)
estimated from satellite microwave measurements isbimodal, with a moist and a dry peak straddling a shallow dip around 48 mm. Sequences of maps show that the
48-mm contour delineates the sharp but meanderingand sinuous margin of a synoptic-scale moist regime,
bounding the occurrence of the much spottier mesoscaleprecipitating cloud systems, which are shaped in turn by
all their local triggering mechanisms. Mapes et al. (2018)
also showed that a column of air passing through thismargin from subtropics to tropics (the usual case,since planetary flow is convergent into the tropics inthe moisture-bearing lower half of the troposphere)
exhibits a momentary enhancement of its Lagrangianmoistening rate, that is, a rapid moistening within the aircolumn as it enters the tropics across the margin. This
surge of column moistening rate near 48 mm explains

DOI: 10.1175/JAS-D-19-0154.1
Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).

1181

1182

JOURNAL OF THE ATMOSPHERIC SCIENCES

the relative rarity of that value (the minimum in the
CWV histogram), and indicates that some systematicmechanism maintains the sharpness of the margin evenas horizontal advection restlessly changes its shape andlocation. We speculate that this maintenance mechanism involves moist convection, but depends on subtle
vertical structure issues, and may be an unexploited
constraint on parameterization, since climate models get
it wrong in diverse ways (Fig. 6 of Mapes et al. 2018).
How does the sharp 48-mm margin bounding the deep
tropics fit with climate notions based on monthly andlonger averages? Broadly speaking, high CWV occurs
over warm sea surface temperature (SST), and indeed
on average the 48-mm definition even agrees quantitatively with the 27.58C SST (Fig. 3 of Mapes et al. 2018)
definition of the convecting deep tropics in older literature about monthly means (Graham and Barnett 1987).
Although a near-Clausius–Clapeyron relationship holds
between CWV and SST in a statistical sense (Stephens1990), oceanic heat capacity prevents SST from keeping
up closely with the rapidly deforming envelope of humid
air columns on a daily basis. Precipitation is even more
patchy and sporadic than water vapor, so rainfall iscorrelated with SST only in gross averages (Inoue 1990;
Kanemaru and Masunaga 2013) compared to its tighter
coupling with CWV (e.g., Bretherton et al. 2004; Petersand Neelin 2006; Holloway and Neelin 2009).
The moist regime of Mapes et al. (2018) thus should
be viewed as a synoptic-scale ‘‘dynamic tropics’’ interacting actively with day-to-day weather, which on
average feels its oceanic boundary condition and hews
to the static tropical margin envisioned by theoriesof the geographically bound Hadley circulation andmean climate.
This paper, a follow-on study of Mapes et al. (2018), is
aimed at understanding why the tropical margin ispreferentially found around a CWV of 48 mm, and exploring the mean physical processes that may govern theenhanced moistening rate as air crosses the margin into
the tropics. To this end, satellite measurements from asuite of the A-Train instruments (see section 2) are firstcomposited to analyze the thermodynamic properties of
the atmosphere and estimates of thermodynamic budget
terms across the margin (section 3). Then, these observations are interpreted physically in light of a simple
conceptual model (section 4) and the whole findings are
summarized in section 5.

2. Satellite and ancillary data
This section summarizes the data products analyzed
in this work. The CALIPSO and CloudSat satellites fly
closely together in a 0130 and 1330 LT sun-synchronous

VOLUME 77

orbit as a member of the A-Train constellation.
The W-band radar carried by the CloudSat satellite
provide detailed measurements of the in-cloud structure, complemented by the CALIPSO lidar observations of thin clouds including those left undetectedby the CloudSat. The vertical profiles of cloud coverand radiative heating rate QR are obtained from the
2B-GEOPROF-lidar Release 4 (R04) dataset (Maceet al. 2009) and 2B-FLXHR-lidar R04 product (L’Ecuyer
et al. 2008; Henderson et al. 2013), respectively. The latest
release (R05) of the CloudSat data distribution is not yet
available for the combined radar-lidar products above at
the time of this writing. The AMSR-E instrument aboard
the Aqua satellite, belonging also to the A-Train,provides CWV, precipitation, SST, and sea surface
wind at the 10-m height (u10) in the Remote Sensing
Systems (REMSS) version 7 daily products. Surface
latent-heat flux is estimated with the bulk equation(Large et al. 1994) forced by the CWV, SST, and u10
from AMSR-E, where near-surface vapor mixing ratio
is derived empirically with CWV and SST using a regression equation constructed from TAO buoy arraydata (see appendix of Masunaga and L’Ecuyer 2010).
Temperature and water vapor soundings are collectedfrom the Aqua AIRS AMSU level-2 (AIRS2RET) version 6 product (Kahn et al. 2014), with any data otherthan flagged as ‘‘best’’ masked out to assure the qualityof estimates.
The present analysis is applied to CloudSat–CALIPSO
orbits and the matched AMSR-E and AIRS nadir observations over global tropical oceans (258S and 258N)
for 4.5 years from 1 July 2006 to 31 December 2010.
This duration covers a major portion of the period of
CloudSat operation in its full capacity from its launch in2006 to the spacecraft battery failure in 2011 that later
forced the satellite operation into the daylight-onlymode. No satellite sensor capable of measuring wind
was available during the study period, so horizontal wind
is obtained from the ECMWF interim reanalysis (ERAInterim, hereafter ERAI) data (Dee et al. 2011) and isinterpolated in space and time to CloudSat–CALIPSO
overpasses.

3. Composite meridional structurea. Compositing method
In Mapes et al. (2018), the mean properties of atmospheric structure across the margin were studied
in a composite quasi-meridional plane constructed withan ensemble of A-Train satellite down-track measurements averaged together. This approach is adopted in
the present paper with some minor updates. The tropicalmargin is simply defined as the most poleward latitude

APRIL 2020

MASUNAGA AND MAPES

where a CloudSat–CALIPSO track intersects with the
CWV threshold of 48 mm. All the measurements arethen composited as a function of down-track distancemeasured relative to that margin.
The search for the margin begins at the latitude of 258
in each hemisphere and proceeds toward the equator.
Some moisture features associated with midlatitude
winter storms (‘‘atmospheric rivers’’ and associatedconcepts) may be excluded in this way. While thesouthward search in the Northern Hemisphere ends atthe equator if CWV never reaches the threshold, thenorthward search from south continues up to 58N. Thisirregular treatment allows us to detect the southern edgeof the ITCZ even when it stays to the north of theequator as is typically the case in the east Pacific and theAtlantic.
The composite cloud structure, presented in Fig. 1a,illustrates a rich low- and high-level cloud cover, as well
as a subtler but distinct midlevel peak (Riley and Mapes
2009), equatorward of the margin (negative distancevalues), contrasting with suppressed free-troposphericcloudiness on its poleward side except for slightly enhanced cloud cover near the tropopause extending
beyond the margin.
The associated ERAI-analyzed cross-margin windis depicted in Fig. 1b. Since y * , the horizontal windprojected onto CloudSat–CALIPSO tracks, is approximately meridional (the polar orbits are primarily
north–south in low latitudes), the pattern may be described as equatorward wind below 700 hPa and mid- toupper-tropospheric poleward wind, as expected for the
Hadley cell, with a slight midlevel wiggle fundamental
to the tropics (e.g., Fig. 4 of Mapes 2001). Most of the
moisture (contoured in Fig. 1b) is concentrated in thelower troposphere, so the horizontal transport of moisture in the composite plane is equatorward (inflowing) on
the subtropical side of the margin (positive distances).
The CWV threshold of 48 mm is adopted from Mapes
et al. (2018) based only on its distribution minimum inglobally pooled CWV data. Rescaling by mean temperature or saturation value (Kuo et al. 2018, 2020)
makes clear that 48 mm is not a magic number for precipitation impacts, but rather a climate- and regiondependent one. For simplicity we prefer to retain theobservational purity of CWV rather than bring in ancillary data to construct a rescaled moisture metric. We
have examined all our results as a function of ocean
basin and present only robust results in this paper. Far
beyond that slight basin dependence, however, we also
explore very different thresholds below, as an illustration of the conditional sampling effects on the composites. In doing so, another arguably special property ofvalues near 48 mm emerges.

1183

FIG. 1. (a) The vertical structure of cloud cover compositedaround the 48-mm threshold (shaded and contours). The contour
interval is 0.05. (b) The vertical structure of y* (horizontal windprojected onto CloudSat–CALIPSO tracks, shaded) and vapor
mixing ratio (contoured every 2 g kg21) composited around the
48-mm threshold.

b. CWV, precipitation, and diabatic forcing
CWV monotonically increases equatorward fromevery threshold used as the composite basis (Fig. 2a),essentially by construction as the threshold-crossing
algorithm feels for gradients. Even for high thresholds,
precipitation stays weak or virtually absent poleward of
the 48-mm value (Fig. 2b). On the equatorward side, all
CWV curves gradually asymptotically approach nearly
48 mm, a result that is not at all by construction. Itshows a potential hazard of composite averaging, since
48 mm is specifically a PDF minimum (rare value), not acommon value in the deep tropics.
Precipitation is always enhanced on the equatorward
side of distance zero, even for thresholds of 35 or 40 mm
for which the equatorward-side values are well under
45 mm. These may be forced cases, when cool-core
midlatitude synoptic eddies intruded into the lower
subtropics. Thresholds of 60 mm reveal heavy rain andvery sharp gradients, and undoubtedly include tropical
cyclones and other intense small-scale weather systems.
For precipitation too, an asymptote is approached deep
into the tropical side of the composite: a relatively
modest value of 80–90 W m22, which is near radiative–
convective equilibrium levels for the global tropics orwhole globe. Again, it must be remembered that this is1184

JOURNAL OF THE ATMOSPHERIC SCIENCES

FIG. 2. (a) CWV (mm) and (b) precipitation in (W m22) composited around various CWV thresholds from 35 to 60 mm in different colors as indicated in the legend in (b). The standard
composite plot with the threshold of 48 mm is shown in black.

an average over many situations, including cold tongues
on the equatorial side of moist intertropical convergencezones that can be narrower than 1000 km at some longitudes and times. Still, this figure suggests that the
moistest air and heaviest precipitation may tend to befound at the periphery of tropical moist air masses, notquite randomly within them as suggested by Allen and
Mapes (2017).
In summary, for all thresholds used as a composite
key, CWV and precipitation appear to asymptoticallyapproach universal values of 48 mm and ;85 W m22,
respectively, in the deep tropics. Is this a coincidence ofconditional sampling and averaging, or something more
physically determined? The extreme closeness of thelines at the left-hand edge of Fig. 2 makes the latter seemplausible. To further explore possible physical reasonsfor these numbers, based on modern diabatic views oftropical circulations as opposed to the geographicallyconstrained Hadley cells, the atmospheric energy balance is analyzed in this composite space (Fig. 3).

VOLUME 77

Total diabatic heating of an air column (Fig. 3a) isdefined as the sum of surface latent heat flux (LHF;
Fig. 3b), column radiative heating (Figs. 3c,d), and surface sensible heat flux (fixed at 10 W m22 for simplicity).
Here the 48-mm threshold is indeed special: the composite curves of total diabatic heating differs in character between lower and higher groups of the CWV
threshold. For the lowest CWV threshold (35 mm), theatmosphere loses net thermal energy across almost an
entire section of the composite space, and even for
45 mm the value is negative inside the humid side of themargin. High threshold values are associated with net
heating peaked around distance zero and extending wellinto the dry side. Suppressed longwave cooling as wellas increased shortwave heating, making a qualitative
distinction to the low-threshold composites, are themajor terms governing the spatial structure of the highthreshold result. These radiative effects are brought
about primarily by cirrus clouds as visually evident in
Fig. 1 and to a minor extent by water vapor itself(Masunaga and Bony 2018). LHF shows much lessstructure, aside from providing distinctive enhancements on the dry side of the lowest thresholds.
For an intermediate CWV threshold of 48 or 50 mm,
total diabatic forcing vanishes very nearly at distancezero, being positive toward the equator and negative
toward the pole. This adds a thermodynamic budget
dimension to the histogram-based assertion that the
48-mm CWV value of Mapes et al. (2018) traces out ameaningful regime boundary.
The deep tropical mean LHF (near 21000 km in allcomposites), and the standard (48 mm) composite of
LHF averaged over distances ,0, is found to be about
86 W m22, very close to the asymptotic value of tropicalprecipitation seen above. On average, precipitation far
on the tropical side of the margin is almost exactly balanced against evaporation in these atmospheric water
budget data.

c. Linking budgets to vertical motion
The diabatic forcing terms as presented in Fig. 3
are instrumental in characterizing moist tropical atmospheric dynamics (Neelin and Held 1987). In this subsection, observations of terms in the CWV and column
moist static energy (CMSE) budget are transformed into
the two coefficients of a two vertical mode truncationof a diabatic vertical velocity vd, for use in the analytic
model of the next section. This vd is defined to maintain
constant temperature by balancing physically heating
and cooling processes through (it is assumed) verticaladvection of the composite mean vertical gradients.
This derived vd could be viewed as an independent
estimate of actual atmospheric vertical motion, which isAPRIL 2020

MASUNAGA AND MAPES

1185

FIG. 3. (a) Total diabatic forcing, (b) surface latent-heat flux, (c) column longwave heating, and (d) column
shortwave heating (W m22) composited around various CWV thresholds from 35 to 60 mm in different colors as
indicated in the legend in (b). The standard composite plot with the threshold of 48 mm is shown in black.

weakly constrained on these scales in reanalyses. However,since the basis set of modes utilized is nonunique, andadvection of composite gradients by composite v is acrude treatment of vertical transport, it is better to regard this more abstractly as a two-parameter truncation,reflecting thermodynamic considerations alone.
In the real zonal mean Hadley cell, denoted by square
brackets, [v] satisfies mass continuity with [y], which ispurely divergent, while [u] is purely rotational. Thus [y]and [v] are strongly constrained by the angular momentum budget on [u], and low-level [y] flowing into thetropics is confined to the near-surface layer upon which
zonal surface stress acts. While our composite is only
over ocean, and has a meandering latitudinal center
point, it has aspects of a zonal mean, and composited
ERAI v does exhibit such sharply bottom-intensified
vertical structure (Fig. 4) for both 48- and 60-mm
thresholds, satisfying mass continuity with the surfaceintensified composite y seen in Fig. 1b.
Nevertheless, the qualitative tilted shape of our twomode vd profiles (estimated as detailed below) remains
meaningful. Because of the very different vertical gradients of moisture (monotonic) and moist static energy(MSE; reversing with height), the two components ofvertical motion–the strength of a deep-layer mean, and a

vertical dipole governing top-heaviness versus bottomheaviness of the profile–span a space relevant to true
profiles of v. These mean gradients are so robust that thesimplifying assumptions below (products of composite
variables; neglect of eddies) are merely quantitative
errors, not qualitative.
Our estimation of a two-mode vd flows from verticallyintegrated conservation laws under a steady-state assumption appropriate for time averages, neglecting
eddy correlations for simplicity. For specific humidity
q (i.e., ›t [ 0),hvd ›p qi 5 2hv  $qi 1 E 2 P ,(1)while for dry static energy s,
hvd ›p si 5 2hv  $si 1 S 1 hQR i 1 LP.

(2)Here the overbar denotes the composite averages
displayed above (omitted in equations hereafter for
simplicity), and hi represents vertical integral over thewhole mass of the atmosphere. Variables E and P denote surface evaporation and precipitation, S is surface
sensible heat flux, L is the latent heat of vaporization,
QR is net radiative heating rate, and other variables and1186

JOURNAL OF THE ATMOSPHERIC SCIENCES

FIG. 4. The composite vertical profile of ERAI v (hPa h21) for(a) the 48- and (b) the 60-mm thresholds, contoured with an interval of 0.25 hPa h21 in solid lines where positive and dashedwhere negative.

symbols are in standard notation. Eddy correlations
between velocity and thermodynamic variables are neglected in the use of ‘‘apparent advection’’ (Yanai et al.
1973), with averaging applied before multiplication,
an approximation that is arguably more modest than
the ambiguities around vertical basis functions as
explained below.
Equation (1) diagnoses vertical moisture advection on
the lhs from the rhs terms, which are all known inthe composite space from satellite measurements and
ERAI-based horizontal wind as illustrated in Figs. 1–4.
Figure 5 shows different terms in the moistureand energy budgets. Horizontal moisture advection
induces a modest drying tendency as the result of thearid subtropical air transported toward the tropicalmargin, but swiftly tapers off on its tropical side (or at
negative distances). Vertical moisture advection, derived from (1), also tends to dry the subtropical atmosphere, while moistening the tropical air. This picture isconfirmed by vertical dry static energy (DSE) advection(Fig. 5b), in which the adiabatic effects of mean vertical

VOLUME 77

FIG. 5. (a) Moisture budget components (W m22) in the composite space: vertically integrated horizontal moisture advection(light blue), vertically integrated vertical moisture advection (red),precipitation (dark blue), and evaporation (green). (b) Thermalenergy budget components (W m22) in the composite space: vertically integrated horizontal DSE advection (light blue), verticallyintegrated vertical DSE advection (red), vertically integrated radiative heating (purple), and precipitation (dark blue). The sign isflipped as necessary so each term has the tendency to increase(decrease) moisture/DSE where positive (negative).

motion balance radiative cooling in the subtropics andconvective heating in the tropics.
A two-mode truncation of vd, following Masunaga
and L’Ecuyer (2014), transforms the rhs terms into an
estimate of v profiles that satisfy the budget equations.
We decompose v into first and second modes,^ 1 (p) 1 V2 v
^ 2 (p) ,vd (p) 5 V1 v

(3)

where v
^ i (p) denotes the normalized basis function for
the ith mode and Vi defines the amplitude of each corresponding mode. The vertical advection of moisture
and DSE is hence written asv1 ›p qi 1 V2 h^v2 ›p qi
hvd ›p qi 5 V1 h^
and

(4)

APRIL 2020

MASUNAGA AND MAPES

1187

FIG. 6. The composite vertical profile of vd (hPa h21) decomposed into the first baroclinic mode (a),(b) and thesecond baroclinic mode (c),(d) in color shade for two CWV thresholds of (a),(c) 48 and (b),(d) 60 mm. In each panel
the sum of the two vertical modes is contoured with an interval of 0.25 hPa h21 in solid lines where positive anddashed where negative.

hvd ›p si 5 V1 h^v1 ›p si 1 V2 h^v2 ›p si .

(5)Equations (4) and (5) constitute a closed system toyield V1 and V2 with all other variables being known: thecomposite profiles of q and s are obtained from AIRS
soundings, the vertical advection terms on the lhs are
diagnosed from (1) and (2), and the basis functions,v^ i , are adopted from previous work (Masunaga andSumi 2017).
Those basis functions or vertical modes were computed as the leading (fastest-propagating) dynamical
modes of linearized internal wave equations for a realistic tropical static stability profile, in the manner proposed originally by Fulton and Schubert (1985). Such
fastest-propagating internal waves are important insmall-scale tropical dynamics, because they optimallyradiate away the intense quantities of latent heat released in spatially concentrated mesoscale convective
systems (e.g., Mapes and Houze 1995). However, theytake no account of planetary-scale angular momentum
constraints that shape the Hadley cell as discussed
above, and thus are not expected to recover the true
profiles of [y] and [v] in the almost-zonal-mean composite of Figs. 1b and 4. Future work could invoke otherbasis functions, such as empirical maximum covariancemodes (EOFs) of v, or the v profiles derived fromleading modes of y. Since the goal here is merely toestablish a two-mode truncation for diagnostic modelingbelow, errors in the exact vertical spatial structure aresecondary, as long as the modes project differently onto
the distinct background gradients of s and q.
With the basis functions established, complete verticalprofiles of vd can be reconstructed from V1 and V2 with(3). This reconstruction procedure is repeated over eachatmospheric column from the far subtropics to deepest
in the tropics, and displayed in Fig. 6. As expectedfrom the arguments earlier, subsidence (solid contours)
dominates to the subtropical side of the margin andweak ascent (dashed contours) prevails to its tropicalside. Like the precipitation seen in Fig. 2, diagnosed
ascent becomes more intense and sharper as the CWV
threshold is increased from 48 mm (Figs. 6a,c) to 60 mm(Figs. 6b,d).
Comparing to the ERAI results in Fig. 4, our modebased, purely thermodynamically deduced tropical ascent is weaker while subtropical subsidence is stronger
for the 48-mm threshold (Figs. 6a,c). When composited
against the 60-mm threshold (Figs. 6b,d), the budgetderived v exhibits a confined, intense updraft corresponding to the sharp precipitation peak, while such
sharpness is absent in the ERAI tropical ascent. This
discrepancy may show the challenges of reanalysis

1188

JOURNAL OF THE ATMOSPHERIC SCIENCES

models for vertical velocity at fine scales, given thatascent in the tropical (nonrotating) atmosphere is theoretically expected to be tightly constrained by precipitation. There is a lot of interproduct spread in different
reanalysis tropical v profiles, which often differ evenqualitatively (Back and Bretherton 2006; Zhang et al.
2008; Handlos and Back 2014; Huaman and Schumacher2018). Specifically, Huaman and Takahashi (2016)
found that the ERAI tends to exaggerate the bottomheaviness in the v profile, consistent with the discrepancy in the present comparison. Might model moist
physics schemes systematically lack some mechanisms
near sharp margins in the CWV field (a state variable
that does tend to be well analyzed), potentially making
the present observations a usefully discriminating input
to model development?
Another remarkable feature of the 48-mm vd composite in Fig. 6 is the meridional gradient of the secondmode vd to the poleward side of the margin, resulting
in a continuous structural transformation from abottom-heavy subsidence in the far subtropics into a
top-heavy one near the tropical margin. A similar
structural transformation is discernible also in the ERAIv profile (Fig. 4a). This gradient over the y . 0 subdomain in the diagnosed vd profile is rooted in the ydependence of s, q, and the column-mean terms on therhs of (1) and (2), but in vertically nonlocal ways that are
not quite easy to attribute.
The matrix inversion behind these v estimates propagates the information content and errors intrinsic to the
input observations into the diagnosed results in a waythat is not quite intuitively obvious, and depends on
the specifics of the basis functions used. Despite allthese concerns with its literal accuracy in detail, thepoint of this diagnostic exercise is really to provide aframework for an interpretive analytic model in thenext section, and this two-mode truncation suffices forthat purpose.

4. A toy Lagrangian model
The satellite data analysis in the previous section suggests that CWV and precipitation are most enhancednear the tropical margin, where an atmospheric moistureand energy-budget imbalance is seen, asymptoticallyapproaching equilibrium deeper in the composite
tropics. To facilitate a physical interpretation of theseresults, we develop a simple Lagrangian model thatenvisions a lower-tropospheric air mass traveling fromthe subtropics into the tropics. Prognostic variables include CWV and CMSE while diagnostic parameters
including precipitation and vertical moisture advection
are fitted empirically from the results above. This model

VOLUME 77

is designed to mimic the composite satellite measurements as shown in Figs. 1–6, when the time dimension in
the model is mapped to a quasi-meridional spatial axis.
The theoretical formulation is described first, followedby an analysis of model results.

a. Basic equations
The present model is built upon column integrated
prognostic equations for moisture,2

Dt hqi 5 2 å hvi ›p qi 1 E 2 P ,

(6)

i51

and MSE (h),2

Dt hhi 5 2 å hvi ›p hi 1 LE 1 S 1 hQR i ,

(7)

i51

where Dt [ ›t 1 vhor  $ denotes an effective horizontally Lagrangian derivative for the column-mean quantities, and vertical motion has been expanded into two^ i , as done earlierinternal-wave vertical modes, vi 5 Vi v
in section 3c. Neglecting changes and advection of hTi,(7) can be rewritten in terms of q as
2

LDt hqi 5 L å g i hvi ›p qi 1 LE 1 S 1 hQR i ,

(8)

i51

where vertical MSE advection has been substitutedby vertical moisture advection using symbol g for a ratio that is a version of the normalized gross moist
stability (GMS) (Neelin and Held 1987; Raymond andSessions 2007),hvi ›p hi,
gi 5 2
Lhvi ›p qi(9)defined separately for each vertical mode. The diabatic
forcing terms and GMS are assumed to be functions onlyof CWV as described later in section 4b.
Two empirical closures are introduced to constrain
two remaining unknowns, hv1›pqi and hv2›pqi. The
first closure hinges on the relative contribution of thevertical monopole and dipole modes in vertical MSE
advection; or in other words on a top-heaviness ofthe v profile:
gi hvi ›p qi,
ji 5 2(10)

å gi hvi ›p qi

i51

where j1 1 j2 5 1 by construction. To demonstrate how
j2 varies from the subtropics to the tropics, vertical

APRIL 2020

1189

MASUNAGA AND MAPES

FIG. 7. (a) The composite trajectories of g 2hv2›pqi (ordinate) and åi51 g i hvi ›p qi (abscissa) for different CWV
thresholds. Arrows indicate the equatorward direction along the trajectories. Dashed and dotted lines represent j2 5 0.6
and 0.7 for reference. (b) A schematic model of j2 implied from the observations. CWV0 refers to the CWV threshold.
2

moisture advection in the composite space is mapped on
the plane of its second-mode component (ordinate) andthe total advection (abscissa) in Fig. 7a, where the ratioof the y component to the x component of a given point
provides j2. The trajectories are rooted initially (i.e., on
their subtropical end) in the lower-right quadrant andproceed into the upper-right quadrant before making a
sharp turn toward the origin. With the exception of
the highest CWV threshold, all the composite trajectories are eventually (or to the tropical end) collapsed
asymptotically into a slope of ;0.6–0.7. This behavior may be translated in terms of j2 as schematicallyillustrated in Fig. 7b, showing that j2 increases equatorward until saturated at a certain level designatedby j2,‘ ’ 0.6 or 0.7.
The second closure is the precipitation inefficiency of
Masunaga and Sumi (2017) hi, defined as the fraction of
the column moistening owing to the ith vertical modethat does not instantly precipitate out. The originalform of hi is generalized for the present model by
including a background precipitation Pbg, the precipitation rate that is produced irrespective of large-scale
updraft,2

P 5 2 å (1 2 hi )hvi ›p qi 1 Pbg .

Precipitation does not occur in association with acolumn advective drying, so hi must be precisely
unity for hvi›pqi . 0. Otherwise it is known that hi ismodestly variable from around 0.1 to slightly below
0 for the first mode and varies between 1 and ;0.8 forthe second mode (see Masunaga and Sumi 2017). In
other words, the first-mode column moistening is almost entirely converted into precipitation, while thesecond-mode dynamics is by far less efficient in rainfall production.
Equations (6), (8), (10), and (11) are combined into
the diagnostic equation of vertical moisture advection
for each vertical mode,
" 
 #21
2
ji
hi
,
j
Lhvi ›p qi 5 2 (LPbg 1 S 1 hQR i) å 1 1
gi
gi i
i51
(12)
and the prognostic equation of moisture,


21



h
h
h
h
,
LDt hqi 5 L(E 2 Pbg ) 1 1 (1 2 j2 ) 1 2 j2 (LE 1 S 1 hQR i) 1 1 1 (1 2 j2 ) 1 2 j2
g1
g2
g1
g2
where j1 has been eliminated with j1 5 1 2 j2.

b. Model assumptions
To complete a prognostic model of moisture, each parameter in the rhs of (13) is prescribed as a function of hqi.

(11)

i51

(13)

The diabatic forcing terms (E, S, and hQRi) are modeled
so they mimic the observations presented in Fig. 3.
Surface latent-heat flux varies only to a minor extent in
an unsystematic manner with CWV in Fig. 3b and thus is
set to a constant at the tropical mean of 85 W m22.

1190

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 77

which vanishes when hqi 5 47.9 mm, hereafter denotedby hqieq, confirming the argument earlier that a CWVof about 48 mm provides the energy budget neutrality.
An exponential fit is also successfully applied to the firstmode GMS (Fig. 8b) as
g 1 5 7:55 exp(26:10 3 1022 hqi).

(16)

The decrease of g 1 toward zero with increasing CWV is
expected from the fact that a low-level import of MSE
almost suffices for moist tropical soundings, while far
from sufficient in the dry subtropical air, to offset theupper-level MSE export associated with deep ascent.
The observations indicate that g2 is practically independent of CWV and is safely set to a constant at 20.75.
A set of the CWV thresholds defining the composite
base points for Figs. 1–6 are emulated in model runs byswitching a ‘‘subtropics regime’’ to a ‘‘tropics regime’’at a specified CWV value, hereafter denoted by CWV0,in every 5 mm from 35 to 60 mm. The regime transition iscontrolled by j2 and Pbg. The schematic illustration in
Fig. 7 is adopted to prescribe j2,"#
8
CWV 2 CWV0>>
< j2,‘ 1 1
for
Dq
j2 5
>
>
:
j2,‘
for

CWV , CWV0CWV $ CWV0 ,(17)

FIG. 8. The composite trajectories mapped on (a) the hQRi–CWV
plane and (b) the g i–CWV plane for different CWV thresholds.
The exponential fit to hQRi and g1 as a function of CWV is depicted
as a solid curve (see text for fitted coefficients). The reference tog 2 is a horizontal line at 20.75.

Surface sensible-heat flux is fixed at 10 W m22 for thesame reason. Column radiative heating, in contrast, isthe primary driver of total diabatic forcing, tightly related to CWV mainly through the cirrus radiative effects. Figure 8a shows the observed relationship of hQRi
with CWV constructed from the composite satellite
measurements. The observations imply a surprisingly
close coupling between the two parameters, tightly lined
up along an exponential curve. The exponential fit to thedata is found to be
hQR i 5 2:32 exp(6:19 3 1022 hqi) 2 140,(14)

for hQRi in the units of watts per square meter and hqi
in kilograms per square meter (or equivalently millimeters). Total diabatic forcing is thereby formulated as
LE 1 S 1 hQR i 5 2:32 exp(6:19 3 1022 hqi) 2 45 ,(15)

where Dq is chosen to be 20 mm. In the subtropics regime(CWV , CWV0), j2 is designed to increase with t according to (17), exploiting the observational fact thatCWV persistently rises toward distance zero on its
poleward side (Fig. 2) and thus CWV is expected to be
monotonically related to t. The background precipitation, Pbg, is assumed to obey a step function,
(
Pbg 5

0

for

CWV , CWV0E

for

CWV $ CWV0 .

(18)

This is a simplistic realization of the observation thatprecipitation is absent in the subtropics, and asymptotically approaches an equilibrium against evaporation in
the deep tropics (Fig. 2).
Table 1 summarizes the parameter settings as described above in the top row (control) as well as three
additional runs performed to test the sensitivity to somemajor uncertainties in the model assumptions. The default settings for the control run are h1 5 0.1, h2 5 1, andj2,‘ ’ 0.6. The h208 run is identical to the control run
except that h2 is set to 0.8 instead of 1. In the h100 run, h1
is reduced from 0.1 to 0. The selected values for h1 andh2 in these two experiments roughly bound the plausible

APRIL 2020

1191

MASUNAGA AND MAPES

TABLE 1. Parameter settings for the conceptual model. A pair of numbers are provided for hi (i 5 1 and 2) to indicate the cases ofhvi›pqi , 0 and hvi›pqi . 0 in this order.
Run

LE (W m22)

S (W m22)

hQRi (W m22)

g1

g2

h1

h2

j2,‘

Controlh2 5 0.8
h1 5 0.0
j2 5 0.7

85
85
85
85

10
10
10
10

(14)
(14)
(14)
(14)

(16)
(16)
(16)
(16)

20.75
20.75
20.75
20.75

(0.1, 1)
(0.1, 1)
(0.0, 1)
(0.1, 1)

(1, 1)(0.8, 1)
(1, 1)(1, 1)

0.6
0.6
0.6
0.7

range of each parameter that accounts for observations(Masunaga and Sumi 2017). In the fourth run (j07), j2,‘
is slightly changed from 0.6 to 0.7 in (17) in order to test
the sensitivity to j2.

c. Model runs
1) SIMULATED RESULTS OF THE CONTROL RUN
Equation (13) is integrated over time to simulate theLagrangian evolution of hqi, as a simple prognostic
model for interpreting the observed meridional variation of CWV as mentioned in the beginning of section 4.
The initial condition of CWV is CWV0 2 Dq so thatj2 5 0 at t 5 0. Figures 9a and 9b presents the control
simulations of CWV and precipitation, where the time

axis is reversed in direction and all curves are shifted intime so that CWV equals CWV0 at t 5 0 (with a minimal
offset for visual clarity). The simulations are hencecomparable with the observations in Figs. 9c and 9d for ahypothetical Lagrangian air mass moving equatorward
at a constant speed, assuming that the quasi-north–south
track of the A-Train satellites may be considered asa steady-state representation of such air masses in thecomposite space. CWV increases monotonically withtime until reaching CWV0 and then tend to converge,
successfully capturing the overall characteristics of theobservations. Differences are also evident, however,particularly in the latter stage of the simulated evolution(t . 0), where CWV converges too slowly for low valuesof CWV0 and somewhat too rapidly for the higher

FIG. 9. Control model simulations of (a) CWV and (b) precipitation for different values of CWV0 as indicated in
the legend in (b). Time proceeds from right to left and is defined to be zero when CWV reaches CWV0. Different
curves are slightly offset in time to avoid visually overlapping together at t 5 0. The observations of (c) CWV and(d) precipitation are shown for comparison, copied from Fig. 2 with the 48-mm composite omitted.

1192

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 77

values. The simulations qualitatively reproduce a sharp
rise and a subsequent decay of precipitation as found in
the observations.
For tracking down the sources of Lagrangian moistening or drying during the evolution, a scale analysis isperformed with (13) to measure the moistening timescale t q:Lihqi 1 h’L(E 2 Pbg ) 1 ðD 2 1Þ(LE 1 S 1 hQR i) ,
tq D
(19)

where
D 511

FIG. 10. The moistening rates in the control simulations: t21
q,E (solid)
and t21q,Q (dashed).

h1
h(1 2 j2 ) 1 2 j2 .
g1
g2

Equation (19) implies that the temporal change of CWV
is brought about by two factors: an evaporation excess
over the background precipitation (the first term on
the right), and an energy imbalance (the second term).
The moistening rate owing to each component may be
estimated by
t 21
q,E ’

E 2 Pbg
hqiD(20)

for the evaporative moistening and
t21
q,Q ’

ðD 2 1Þ(LE 1 S 1 hQR i)
hqiLD

(21)

for the energy imbalance. Figure 10 indicates that t 21
q,E21
exceeds t 21
q,Q for t , 0 but otherwise t q,Q alone accounts
for the moistening with t 21
q,E totally vanishing. It follows
that an air mass is primarily moistened by surface
evaporation as it travels toward the equator during theearlier stage of the evolution, while in the latter stage
moisture in the air mass is adjusted so the energy imbalance diminishes, either enhanced or reduced depending on the sign of the imposed imbalance. It isnoted that the sharp cutoff of t 21
q,E in the latter stage
results from the simplification that a finite Pbg is introduced abruptly at t 5 0 and thereafter to precisely cancel out evaporation. In reality Pbg increases
smoothly and the evaporative moistening remains tocontribute to a certain degree after time 0. A more
realistic formulation of Pbg would thus accelerate themoistening or decelerate the drying for t . 0, presumably rectifying the awkwardness in the way CWV
converges as seen in Fig. 9a. To aid an intuitive interpretation of this awkwardness, (13) can be approximated with the second term on the rhs expandedaround the energy equilibrium,

LDt hqi ’i1hL(E 2 Pbg ) 1 c1,eq ðD 2 1Þ(hqi 2 hqieq ) ,D(22)

where c1,eq is the linear coefficient in the Taylor series of(15). The formal solution of (22) in the absence of theevaporative moistening (i.e., E 2 Pbg 5 0) offers aphysical basis for the exponential damping of CWV tothe equilibrium value hqieq or 47.9 mm as shown earlier.
An evaporative moistening present in the course of thedamping would act as an external source of moisture,
hampering the decay to some degree.
The model provides the vertical mode decomposition of vertical moisture advection by (12). Figure 11
presents the first- and second-mode components ofsimulated vertical moisture advection (Figs. 11a,b)
and their observational counterparts (Figs. 11c,d).
The first-mode advection in the model implies a persistent column drying for t , 0 and a following sharpenhancement of column moistening when CWV0 isgreater than 50 mm, in remarkable agreement with theobservations. The second-mode advection has a positive spike just before time 0 with a larger magnitude
for a lower value of CWV0. A similar moistening peakis confirmed in the observed second-mode advection.
On the other hand, a sudden drying after time 0 apparent in the simulations for CWV0 $ 50 mm is virtually missing in the observations (comparing Fig. 11b
and Fig. 11d). This excessive drying in the modelis responsible for the aforementioned artifact thatCWV is damped too fast when CWV0 exceeds theequilibrium value.

2) LAGRANGIAN MOISTENING SIMULATED WITH
DIFFERENT RUNSThe first-mode dynamics is a main driver of precipitation and the second mode is inefficient in producing

APRIL 2020

1193

MASUNAGA AND MAPES

FIG. 11. As in Fig. 9, but for vertical moisture advection: (a) simulated first-mode advection, (b) simulated secondmode advection, (c) observed first-mode advection, and (d) observed second-mode advection.

rainfall under the current model setups (i.e., h1 ; 0 and
h2 ; 1). The salient enhancement of the first-mode
column moistening therefore accounts for the burst of
precipitation seen in Fig. 9b. Vertical moisture advection tapers off eventually to zero (Fig. 11), explaining
why precipitation decays to Pbg. The moisture accumulated by the second-mode dynamics, on the contrary, isdesigned not to instantly precipitate out and hence
to be left behind in the Lagrangian moisture storage.
Figure 12 depicts the evolution of the Dthqi term fromdifferent runs. Qualitative aspects of the evolution resemble the second-mode component of vertical moisture advection as expected, whereas the peak amplitudevaries from one simulation to another. The control run(Fig. 11a) produces a pair of relatively modest peaks
straddling t 5 0, positive (moistening) for t , 0 and
negative (drying) for t . 0. The drying peak is sharpened if h1 is decreased from 0.1 to 0 (Fig. 11c). The
moistening peak appears to be insensitive to the choiceof h1 and h2 within a plausible range, but is substantially magnified when j2 is increased slightly from
0.6 to 0.7 (Fig. 11d).
This sharp moistening sensitive to j2 can be understood by examining the behavior of the prognostic
moisture equation [(13)] as a function of j2. The denominator of the rhs,

D 511

h1
h
(1 2 j2 ) 1 2 j2 ,
g1
g2

(23)

decreases as j2 increases, or as a bottom-heavy subsidence transforms into a top-heavy one, since g1 . 0 and
g2 , 0. For typical values of h1 5 h2 5 1, g 1 5 0.5, andg2 5 20.75, D decreases from 1 to 2/3 with a subtle
increase of j2 from 0.6 to 0.7, and would fall to zero for
j2 5 0.9. A modest change to j2 would therefore havethe potential to rapidly accelerate the Lagrangianmoistening. Equation (23) is rewritten using (9) and(11) toD 5

hv›p si 2 (P 2 Pbg )hv›p hi.

(24)

In the close vicinity of and to the subtropical side of themargin, P 2 Pbg ; 0 (i.e., precipitation is hardly fueled
dynamically by vertical moisture advection) and hence
D ’hv›p sihv›p hi.

(25)

Equation (25) admits a specific shape of the v profilethat would optimize the vertical gradient weights in the
numerator and denominator, just like the normalized

1194

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 77

FIG. 12. Simulated Lagrangian moistening, Dthqi for different model runs: (a) control, (b) h2 5 0.8, (c) h1 5 0.0, and(d) j2 5 0.7. See Table 1 for details of the model setups.

GMS given in (9). The condition of accelerated moistening, D / 0, is met when the mass integral of vertical
DSE advection vanishes, exclusive of the trivial casev 5 0 at all altitudes. This condition occurs where thesubtropical subsidence (hv›psi , 0) transitions to thetropical ascent (hv›psi . 0), driven by an increasing
contribution of the second-mode shallow updraft. The
observations shows that hv›psi indeed intersects the xintercept near the margin (Fig. 5b). Apart from themathematical singularity caused by a zero denominator,
the sharp spike in hDtqi presumably offers a qualitativeinterpretation of the observed Lagrangian moistening
at the tropical margin.

5. Summary and discussion
This work explores physical processes near the sharp
CWV margin observed to encompass the moist tropics
as documented in Mapes et al. (2018), which showeda true minimum of the global tropics CWV PDF neara value of 48 mm. Near that value, an enhanced
Lagrangian column moistening process is observed,
meaning that air columns spend little time at that value,
which is what makes its observed frequency of occurrence rare. These relationships are seen in instantaneous data, but the margin moves with time, requiringa moving composite strategy to localize and quantify the
key mechanisms and processes. The ultimate goal of thiswork is to understand why such rapid moistening tends
to occur around the margin.
Observations and retrievals from the A-Train satellite
instruments including CloudSat, CALIPSO, and AIRS
were analyzed to examine how thermodynamic properties of the atmosphere and energy and water fluxes
vary systematically from the subtropical to the tropicalside of CWV-threshold defined margins. Millions ofindividual satellite measurements were averaged into
the mean along-track structure of the atmospherearound the margin, defined as the most poleward position of a specified CWV threshold. Six values of the
CWV threshold were chosen from 35 to 60 mm tocompare with the reference value of 48 mm (the global
pdf minimum) from Mapes et al. (2018). The resulting
composite observations in the quasi-meridional plane
paint out, in a climatological sense, the evolving
properties of a lower-tropospheric air mass travelingalong the equatorward branch of the Hadley circulation. As a theoretical framework to physically interpret these observations, a two-vertical-mode model
closed by q and h budgets is developed to prognose theLagrangian history of moisture within such a traveling
air mass.

APRIL 2020

MASUNAGA AND MAPES

1195

FIG. 13. The globally mapped number count of a specified CWV threshold for CWV 5 (top) 48 and (bottom)
60 mm. The grid resolution is adjusted to 18 3 18.

The observed CWV is found to increase equatorwardin the subtropics, but eventually converges to 48 mm in
the deep tropics irrespectively of the CWV thresholds.
Precipitation intensifies to a peak on the tropical side of
the margin and then asymptotically approaches equatorward a value of 85 W m22, almost equal to evaporation.
When the CWV threshold for conditional sampling is
set higher, a sharper and higher peak emerges as thecomposite samples rarer and more intense weather situations. An important implication from these results isthat the most abundant moisture and precipitation arefound not necessarily deepest in the tropics as one might
intuitively expect, but instead near margins.
The toy two-mode Lagrangian mathematical model
reproduces these key aspects of the observations. In themodel, a burst of convection occurs once the air masspasses beyond the margin into the tropics, invigorated
by the positivity of diabatic forcing with the aid of anear-zero first-mode GMS. At the same time, however,that enhanced precipitation removes moisture out of theatmosphere, a negatively feedback effect on precipitation through the CWV dependence of radiative heating.
Far downstream (deep in the tropics), CWV and precipitation asymptotically approach the balanced climate
state. The CWV value for the energy balance neutrality,
estimated to be ;48 mm, hence serves as the asymptotic
value of CWV deepest in the tropics, as well as a CWV
minimum in the observed frequency (a rare value). Notethat the 48-mm threshold holds only for the global statistics and should be adjusted to the local neutrality criteria when applied regionally. This may partly explain the

known regional dependence of the CWV–precipitation
relationship (Bretherton et al. 2004; Kuo et al. 2018).
The behavior described above may be glimpsed ininstantaneous satellite images (Fig. 2 in Mapes et al.
2018), but is absent in climatological CWV or rainfall
maps because the tropical margins incessantly move andare blurred by Eulerian averaging, leaving behind only
slowly varying signals such as the loose connection between convection and the underlying SST (e.g., Gadgil
et al. 1984). Figure 13 (top) shows that the 48-mm
threshold is found broadly across the tropical and subtropical oceans, except 1) within the Indo-Pacific warm
pool (partly because only the most poleward margins arechosen for the CWV threshold along each satellite
track), and 2) over cold oceans such as the southeast
Pacific and the southern Atlantic. The 60-mm threshold(Fig. 13 bottom), on the other hand, occurs well within
the tropical convergence zones, so the composite segments for high threshold values would be tightly drawn
around this pattern. It follows that the sharp enhancement of CWV and precipitation near the 60-mm intersection (Fig. 2) mostly occurs deep in the tropics,
relaxing swiftly toward the equilibrium (Fig. 2) as does
the atmospheric energy imbalance or forcing (Fig. 3).
The climatologically moist, rainy tropics of the unconditional mean is hardly static, but rather results from theincessant interplay of budget imbalances and adjustments in mesoscale convective events.
Mapes et al. (2018) found a band of localized column
moistening extending along the CWV 5 48-mm contour, and showed some satellite cloud-field snapshots.

1196

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 77

FIG. 14. Schematic summary of the observations and model interpretations. CWVeq denotes the value giving the energy budget neutrality, corresponding ;48 mm for the present
tropical climate.

The current model predicts a marked moistening on thesubtropical side of the margin in response to increasing
j2, or as the bottom-heavy subsidence in the far subtropics gives way to a bottom-heavy ascent near themargin. The Lagrangian moistening rate from the model
diverges to infinity in the limit of hv›psi/hv›phi / 0,that is, when a lower-tropospheric ascent grows tolargely offset the upper-tropospheric subsidence in thevertical integral of v›ps.
The present findings are schematically summarized inFig. 14. Outstanding questions include how this picture
would be modified from region to region. Of particularinterest is the east Pacific, where the narrowness of the
ITCZ will certainly affect the interpretation of spatial
lags of 21000 km for instance. To inquire whether
these results (and the model to mimic them) are delicately process dependent, we can look for consilience or
discrepancies in AGCMs and global cloud-resolving
models. Two of the three randomly selected climate
models studied by Mapes et al. (2018) fail to reproduce
the bimodality in the CWV histogram, in diverse ways,
suggesting that climate models may lack or miscalibrate
the processes essential for the maintenance of sharp
margins. Further understanding of those processes may
therefore be incisive for diagnosing and ultimately improving the performance of moist process parameterizations in atmosphere models.
Acknowledgments. This work is supported by Japan
Society for the Promotion of Science (JSPS) Grants-in-Aid

for Scientific Research (KAKENHI) 15KK0157 and
19H01966, as well as by NASA NEWS Program Grant
NNX15AD11G and by the National Science Foundation
under Grant 1639722.
Data availability statement: The CloudSat–CALIPSO
data products were provided by the CloudSat Data
Processing Center (http://www.cloudsat.cira.colostate.edu);
the AMSR-E products by Remote Sensing Systems(http://www.remss.com); the AIRS/AMSU product by
the Goddard Earth Sciences (GES) Data and Information
Services Center (DISC; https://disc.sci.gsfc.nasa.gov);
and the ERAI data by ECMWF (https://apps.ecmwf.int/
datasets/).
REFERENCES
Allen, T. L., and B. E. Mapes, 2017: The late spring Caribbean
rain-belt: Climatology and dynamics. Int. J. Climatol., 37,
4981–4993, https://doi.org/10.1002/joc.5136.
Back, L. E., and C. S. Bretherton, 2006: Geographic variability inthe export of moist static energy and vertical motion profiles inthe tropical Pacific. Geophys. Res. Lett., 33, L17810, https://doi.org/10.1029/2006GL026672.
Bretherton, C. S., M. E. Peters, and L. E. Back, 2004: Relationships
between water vapor path and precipitation over the tropicaloceans. J. Climate, 17, 1517–1528, https://doi.org/10.1175/
1520-0442(2004)017,1517:RBWVPA.2.0.CO;2.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis:
Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, https://doi.org/
10.1002/qj.828.
Fulton, S. R., and W. H. Schubert, 1985: Vertical normal modetransforms: Theory and application. Mon. Wea. Rev., 113,APRIL 2020

MASUNAGA AND MAPES

647–658, https://doi.org/10.1175/1520-0493(1985)113,0647:
VNMTTA.2.0.CO;2.
Gadgil, S., P. V. Joseph, and N. V. Joshi, 1984: Ocean–atmosphere
coupling over monsoon regions. Nature, 312, 141–143, https://doi.org/10.1038/312141a0.
Graham, N. E., and T. P. Barnett, 1987: Sea surface temperature, surface wind divergence, and convection over tropical oceans. Science, 238, 657–659, https://doi.org/10.1126/
science.238.4827.657.
Handlos, Z. J., and L. E. Back, 2014: Estimating vertical motion
profile shape within tropical weather states over theoceans. J. Climate, 27, 7667–7686, https://doi.org/10.1175/
JCLI-D-13-00602.1.
Held, I. M., and A. Y. Hou, 1980: Nonlinear axially symmetriccirculations in a nearly inviscid atmosphere. J. Atmos. Sci.,
37, 515–533, https://doi.org/10.1175/1520-0469(1980)037,0515:
NASCIA.2.0.CO;2.
Henderson, D. S., T. S. L’Ecuyer, G. Stephens, P. Partain, and
M. Sekiguchi, 2013: A multisensor perspective on the radiative
impacts of clouds and aerosols. J. Appl. Meteor. Climatol., 52,
853–871, https://doi.org/10.1175/JAMC-D-12-025.1.
Holloway, C. E., and J. D. Neelin, 2009: Moisture vertical structure,column water vapor, and tropical deep convection. J. Atmos.
Sci., 66, 1665–1683, https://doi.org/10.1175/2008JAS2806.1.
Huaman, L., and K. Takahashi, 2016: The vertical structure of theeastern Pacific ITCZs and associated circulation using the
TRMM Precipitation Radar and in situ data. Geophys. Res.
Lett., 43, 8230–8239, https://doi.org/10.1002/2016GL068835.
——, and C. Schumacher, 2018: Assessing the vertical latentheating structure of the east Pacific ITCZ using the CloudSat
CPR and TRMM PR. J. Climate, 31, 2563–2577, https://doi.org/10.1175/JCLI-D-17-0590.1.
Inoue, T., 1990: The relationship of sea-surface temperature
and water-vapor amount to convection over the western
tropical Pacific revealed from split window measurements.
J. Meteor. Soc. Japan, 68, 589–606, https://doi.org/10.2151/
jmsj1965.68.5_589.
Kahn, B. H., and Coauthors, 2014: The Atmospheric InfraredSounder version 6 cloud products. Atmos. Chem. Phys., 14,
399–426, https://doi.org/10.5194/acp-14-399-2014.
Kanemaru, K., and H. Masunaga, 2013: A satellite study of therelationship between sea surface temperature and column
water vapor over tropical and subtropical oceans. J. Climate,26, 4204–4218, https://doi.org/10.1175/JCLI-D-12-00307.1.
Kuo, Y.-H., K. A. Schiro, and J. D. Neelin, 2018: Convective
transition statistics over tropical oceans for climate model
diagnostics: Observational baseline. J. Atmos. Sci., 75, 1553–
1570, https://doi.org/10.1175/JAS-D-17-0287.1.
——, and Coauthors, 2020: Convective transition statistics overtropical oceans for climate model diagnostics: GCM evaluation. J. Atmos. Sci., 77, 379–403, https://doi.org/10.1175/
JAS-D-19-0132.1.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic
vertical mixing: A review and a model with a nonlocal
boundary layer parameterization. Rev. Geophys., 32, 363–403,
https://doi.org/10.1029/94RG01872.
L’Ecuyer, T. S., N. B. Wood, T. Haladay, G. L. Stephens, and P. W.
Stackhouse Jr., 2008: Impact of clouds on atmospheric heatingbased on the R04 CloudSat fluxes and heating rates data
set. J. Geophys. Res., 113, D00A15, https://doi.org/10.1029/
2008JD009951.

1197

Mace, G. G., Q. Zhang, M. Vaughan, R. Marchand, G. Stephens,
C. Trepte, and D. Winker, 2009: A description of hydrometeor layer occurrence statistics derived from the first year of
merged Cloudsat and CALIPSO data. J. Geophys. Res., 114,
D00A26, https://doi.org/10.1029/2007JD009755.
Mapes, B. E., 2001: Water’s two height scales: The moist adiabat
and the radiative troposphere. Quart. J. Roy. Meteor. Soc.,
127, 2353–2366, https://doi.org/10.1002/qj.49712757708.
——, and R. A. Houze Jr., 1995: Diabatic divergence profiles
in western Pacific mesoscale convective systems. J. Atmos.
Sci., 52, 1807–1828, https://doi.org/10.1175/1520-0469(1995)
052,1807:DDPIWP.2.0.CO;2.
——, E.-S. Chung, W. M. Hannah, H. Masunaga, A. J. Wimmers,
and C. S. Velden, 2018: The meandering margin of the meteorological moist tropics. Geophys. Res. Lett., 45, 1177–1184,
https://doi.org/10.1002/2017GL076440.
Masunaga, H., and T. S. L’Ecuyer, 2010: The southeast Pacificwarm band and double ITCZ. J. Climate, 23, 1189–1208,
https://doi.org/10.1175/2009JCLI3124.1.
——, and ——, 2014: A mechanism of tropical convection inferred from observed variability in the moist static energy
budget. J. Atmos. Sci., 71, 3747–3766, https://doi.org/10.1175/
JAS-D-14-0015.1.
——, and Y. Sumi, 2017: A toy model of tropical convection with amoisture storage closure. J. Adv. Model. Earth Syst., 9, 647–
667, https://doi.org/10.1002/2016MS000855.
——, and S. Bony, 2018: Radiative invigoration of tropical convection by preceding cirrus clouds. J. Atmos. Sci., 75, 1327–
1342, https://doi.org/10.1175/JAS-D-17-0355.1.
Neelin, J. D., and I. M. Held, 1987: Modeling tropical convergencebased on the moist static energy budget. Mon. Wea. Rev.,
115, 3–12, https://doi.org/10.1175/1520-0493(1987)115,0003:
MTCBOT.2.0.CO;2.
Peters, O., and J. D. Neelin, 2006: Critical phenomena in atmospheric precipitation. Nat. Phys., 2, 393–396, https://doi.org/
10.1038/nphys314.
Raymond, D. J., and S. L. Sessions, 2007: Evolution of convection
during tropical cyclogenesis. Geophys. Res. Lett., 34, L06811,
https://doi.org/10.1029/2006GL028607.
Riley, E. M., and B. E. Mapes, 2009: Unexpected peak near 2158C
in Cloudsat echo top climatology. Geophys. Res. Lett., 36,
L09819, https://doi.org/10.1029/2009GL037558.
Schneider, E. K., 1977: Axially symmetric steady-state models of thebasic state for instability and climate studies. Part II: Nonlinear
calculations. J. Atmos. Sci., 34, 280–296, https://doi.org/10.1175/
1520-0469(1977)034,0280:ASSSMO.2.0.CO;2.
——, and R. S. Lindzen, 1977: Axially symmetric steady-state modelsof the basic state for instability and climate studies. Part I:
Linearized calculations. J. Atmos. Sci., 34, 263–279, https://doi.org/10.1175/1520-0469(1977)034,0263:ASSSMO.2.0.CO;2.
Stephens, G. L., 1990: On the relationship between water vapor
over the oceans and sea surface temperature. J. Climate,
3, 634–645, https://doi.org/10.1175/1520-0442(1990)003,0634:
OTRBWV.2.0.CO;2.
Yanai, M., S. Esbensen, and J.-H. Chu, 1973: Determination of bulk
properties of tropical cloud clusters from large-scale heat andmoisture budgets. J. Atmos. Sci., 30, 611–627, https://doi.org/
10.1175/1520-0469(1973)030,0611:DOBPOT.2.0.CO;2.
Zhang, C., D. S. Nolan, C. D. Thorncroft, and H. Nguyen, 2008:
Shallow meridional circulations in the tropical atmosphere.
J. Climate, 21, 3453–3470, https://doi.org/10.1175/2007JCLI1870.1.