Surv Geophys (2017) 38:1257–1282
https://doi.org/10.1007/s10712-017-9429-z

Implications of Warm Rain in Shallow Cumulus
and Congestus Clouds for Large-Scale Circulations
Louise Nuijens1 • Kerry Emanuel2 • Hirohiko Masunaga3 •Tristan L’Ecuyer4

Received: 15 February 2017 / Accepted: 18 September 2017 / Published online: 27 September 2017Ó The Author(s) 2017. This article is an open access publication

Abstract Space-borne observations reveal that 20–40% of marine convective clouds
below the freezing level produce rain. In this paper we speculate what the prevalence ofwarm rain might imply for convection and large-scale circulations over tropical oceans.
We present results using a two-column radiative–convective model of hydrostatic, nonlinear flow on a non-rotating sphere, with parameterized convection and radiation, andreview ongoing efforts in high-resolution modeling and observations of warm rain. The
model experiments investigate the response of convection and circulation to sea surface
temperature (SST) gradients between the columns and to changes in a parameter that
controls the conversion of cloud condensate to rain. Convection over the cold oceancollapses to a shallow mode with tops near 850 hPa, but a congestus mode with tops near
600 hPa can develop at small SST differences when warm rain formation is more efficient.
Here, interactive radiation and the response of the circulation are crucial: along withcongestus a deeper moist layer develops, which leads to less low-level radiative cooling, asmaller buoyancy gradient between the columns, and therefore a weaker circulation andless subsidence over the cold ocean. The congestus mode is accompanied with more
surface precipitation in the subsiding column and less surface precipitation in the deep
convecting column. For the shallow mode over colder oceans, circulations also weakenwith more efficient warm rain formation, but only marginally. Here, more warm rain
reduces convective tops and the boundary layer depth—similar to Large-Eddy Simulation(LES) studies—which reduces the integrated buoyancy gradient. Elucidating the impact ofwarm rain can benefit from large-domain high-resolution simulations and observations.
Parameterizations of warm rain may be constrained through collocated cloud and rain
profiling from ground, and concurrent changes in convection and rain in subsiding and& Louise Nuijens
louise.nuijens@tudelft.nl
1

Delft University of Technology, 2628 CN Delft, Netherlands

2

Massachusetts Institute of Technology, Cambridge, MA 02139, USA

3

Nagoya University, Nagoya 464-8601, Japan

4

University of Wisconsin-Madison, Madison, WI 53706, USA

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convecting branches of circulations may be revealed from a collocation of space-borne
sensors, including the Global Precipitation Measurement (GPM) and upcoming Aeolus
missions.
Keywords Warm rain  Shallow cumulus  Congestus  Circulations  Climate

1 Introduction
Before observations demonstrated that clouds with tops below the freezing level are raining(Byers and Hall 1955; Battan and Braham 1956), scientists believed that ice nuclei arenecessary to produce rain. Inspired by those observations, scientists soon discovered theimportance of coalescence processes for warm rain formation. Coalescence processes also
helped explain why clouds over oceans with a similar depth as clouds over land rain moreeasily. Namely, oceans are deprived of aerosol, except for sea salt and sulfate. Hence, there
are relatively few cloud condensation nuclei over oceans, so that cloud droplets are relatively
large, and auto-conversion and accretion processes are very efficient (Kubar et al. 2009).
In the subtropics and tropics, the freezing level is located between 4 and 5 km, andraining clouds include subtropical stratocumulus over cold eastern ocean boundaries;
shallow cumulus clouds that are more widespread throughout the subtropics and tropics;
and congestus clouds, which tend to be confined to warmer oceans. According to the WMO
cloud atlas, congestus is not a cloud type on its own, but a species of cumulus with tops
between 2 km and the freezing level (although in the literature congestus is often used todenote cumuli with tops up to 8 km). Although both shallow cumulus and congestus
produce drizzle and rain alike, a point we return to below, the distinction is useful, because
congestus appears more sensitive to changing large-scale states (Nuijens et al. 2014).
The CloudSat cloud profiling radar (CPR), which is currently the only sensor capable ofdelineating warm cloud, drizzle and rain, has demonstrated that oceans are covered by
10–50% of warm clouds (Fig. 1a). Of these warm clouds, between 20 and 40% contain
Raining Fraction (0. 082)

0.5

0.40

0.4

0.32

0.2

0.24
0.16
0.08

0.1

d

Fraction with Precip (0. 192)

0.00

Drizzling Fraction (0. 110)

0.40

0.40

0.32

0.32

0.24
0.16

Fraction

b

0.0

0.24
0.16

0.08

0.08

0.00

0.00

Fraction

0.3

FractioncWarm Cloud Fraction (0. 172)FractionaFig. 1 Global warm rain occurrence observed by CloudSat during 2007–2010. Warm clouds are as thosewith tops [273 K. Drizzle is defined as having a ‘‘near-surface’’ (the lowest detectable range bin in
CloudSat observations) reflectivity Z greater than -7.5 dBZ, while rain is defined as Z [ 0 dBZ. The rain
and drizzle fractions represent the fraction of warm clouds that contain rain or drizzle, respectively.
CloudSat data are processed using the 2C-PRECIP-COLUMN and 2C-RAIN-PROFILE algorithms
described in Haynes et al. (2009) and Lebsock and L’Ecuyer (2011), respectively

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precipitation (Fig. 1b). Somewhat lower fractions are found near ocean boundaries andhigher fractions in the Eastern Pacific, but overall most regions have clouds with a precipitating fraction of at least 5–10%. Figure 1c, d further separates precipitation in drizzle
and rain, which shows that drizzle is widespread and concentrated over eastern ocean
boundaries, whereas rain is concentrated in the downstream trades and near the Intertropical convergence zone (ITCZ), e.g., just north of the Equator in the Pacific and Atlantic
oceans, or just south of the Equator in the Indian ocean.
One might not be impressed by those numbers. But those who live on islands have longappreciated the occasional passing of warm rain showers, which on windward sides of hilly
islands make for lush vegetation, even during the ‘‘dry’’ season when deep convection
abates.
Measurements from the precipitation radar (PR) deployed during the Tropical Rainfall
Measuring Mission (TRMM, 1997–2015) first emphasized the prevalence of warm rainover global oceans and their potential impact on large-scale heating rates (Short andNakamura 2000; Schumacher and Houze 2003; Takayabu et al. 2010). But the TRMM PR
has a minimum detection threshold of about 0.4–0:5 mm h1 and therefore misses about
9% of accumulated rain and up to 50% of the occurrence of light rain compared to
CloudSat (Berg et al. 2009). Global precipitation estimates from passive microwave sensors also lack a sensitivity to light rain, especially when rain covers only small areas, whichis the case for isolated cumulus showers (Burdanowitz et al. 2015). The most widely used
Global Precipitation Climatology Project (GPCP) product has long been used to derive
surface latent heat fluxes to construct the global mean energy budget, and a lack of warm
rain might explain why observed heat fluxes at the ocean surface have not matchedobserved ocean heating rates. By increasing global precipitation rates by about 16% basedon CloudSat data, equivalent to increasing the latent heat flux by 12 W m2 , the global
mean surface energy budget can be closed (Stephens et al. 2012). But warm rain isprobably not the only reason for residuals in the surface energy budget. Largest residuals
are found in regions where shallow cumuli dominate but alternate with deeper convection(Kato et al. 2016), but these residuals are larger than warm rain can account for. One
hypothesis is that retrieval errors are caused by greater variability in deeper convection
along with shallow convection, which warrants a better understanding of the coupling
between different types of convection.
Warm rain may also alter the radiation budget by influencing the microphysical andmesoscale structure of clouds, which satellite images, corroborated by in-situ measurements and high-resolution modeling, have demonstrated. Numerous cells of seemingly
cloud-free air (pockets of open cells, POCs) surrounded by walls of drizzle can beembedded into an otherwise homogeneous stratocumulus cloud deck (Stevens et al. 2005;
Wood et al. 2008). In these cells cloud droplets have been scavenged by drizzle drops,
leading to very low cloud droplet number concentrations. Observations have also
demonstrated that fields of shallow cumuli accompanied by significant rain are organized
into arc-shaped formations (Snodgrass et al. 2009; Zuidema et al. 2012). These are representative for the presence of cold pools, which are produced by the evaporation of rain
and convective downdrafts, similar to the cold pools that accompany deep convection(Tompkins 2001).
When rain evaporates, it no longer produces a net (latent) heating, and it redistributes
moisture in the atmosphere. The relative fraction of rain that evaporates or reaches thesurface is thus important for large-scale heat and moisture budgets. Herbert Riehl derived
the first heat budget of the trades and argued that each layer of the lower atmosphere would

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precipitate (and heat) just as much as would be required to balance the loss of heat fromradiation. Hence, from the profile of radiative cooling, one could predict the profile of therain flux and thus the profile of the moisture flux (Riehl et al. 1951).
But, since Riehl’s study, not much research has focused on large-scale controls andimpacts of warm rain. More attention has been given to microphysical aspects of warm
rain, including the role of aerosols in the onset of warm rain. For instance, aerosol andcloud condensation nuclei (CCN) concentrations control the height at which rain-sized
drops first start to form. Figure 2, adopted from Lonitz et al. (2015), shows how radarreflectivity, which measures the sixth moment of the drop-size distribution, increases withheight above cloud base for different CCN concentrations. The gray lines illustrate theoretical behavior, assuming a gamma distribution of the drop-size distribution, and the blacklines illustrate the behavior of a 1D kinematic bin microphysics model (Seifert and Stevens
2010). According to the CloudSat definition, a reflectivity larger than -7 dBZ corresponds
to drizzle, which implies that for a CCN concentration of 100 cm3 drizzle forms whenclouds reach 1.7 km. Indeed, the percentage of clouds that develop a maximum reflectivity
larger than -7 dBZ (drizzle) or 0 dBZ (rain) increases substantially for cloud tops beyond
1.5 km (Fig. 2b): 20% of clouds contain drizzle, and 20% contain rain. For cloud tops
beyond 2 km, most clouds already contain rain (82%).
Warm rain is thus an integral part of shallow convection, which may influence climate
in ways that are not yet well measured or modeled on a global scale. Do we understandhow the presence of warm rain changes the character of warm clouds and the large-scale
circulations in which these clouds are embedded? And what regulates variations in thedepth of the convection?
To formulate ideas about the interaction between convection, warm rain and circulations, a conceptual model can be helpful and bypass some of the complexities of global

b

35

10
0

300

a

Lonitz et al 2015

Fig. 2 On the left: the increase in radar reflectivity, a measure of the sixth moment of the rain-drop-size
distribution, with height in developing (not-raining) clouds as simulated with a kinematic 1D bin model ofmicrophysics (black lines) and from theory assuming a gamma distribution for the rain-drop-size
distribution (gray lines). The figure is adopted from an earlier version in Lonitz et al. (2015). On the right:
distributions of the maximum radar reflectivity found anywhere in individual cloud entities with a cloud base\ 800 m, as observed at the Barbados Cloud Observatory during 3 years. The distributions in black are forthree cloud top height (CTH) categories, and percentages indicate the total number of clouds (in %) whichhave a maximum reflectivity  -7 dBZ/  0 dBZ. The distributions in light gray are for maximum
reflectivities below cloud base only123

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models. In this paper we use a two-column radiative–convective equilibrium (RCE) model
to do so, and Sect. 2 introduces the model and presents first results. Even with such asimplified framework, the interaction between circulation and convection appears intricate,but we will speculate on a few mechanisms that can be tested in further studies or evaluated in models with explicit convection or observations. In Sect. 3 we will discuss
ongoing efforts in fine-scale modeling of convection (Large-Eddy Simulations), spaceborne and ground-based observations, and we summarize our thoughts in Sect. 4.

2 Warm Rain in Large-Scale Circulations
The prevalence of warm rain demands a better understanding of what warm rain implies
for the structure of the lower atmosphere and the energy budget of subtropical and tropicaloceans. Because regions with warm clouds are connected to regions with cold clouds
through large-scale circulations, the influence of warm rain may also be felt remotely.
A number of studies have hinted that shallow convection can have far-reaching effects.
For instance, in an idealized model of tropical climate shallow convection is responsible
for the ventilation of boundary layer humidity, which affects the width and the intensity of
the intertropical convergence zone (Neggers et al. 2007). Shallow convective mixing is
also an attractive tuning factor in numerical weather prediction and global models, because
it can substantially influence global distributions of liquid water, cloudiness and theradiation budget (Bechtold et al. 2014; Mauritsen et al. 2012). Even the climate sensitivityof a global model appears to be strongly regulated by local mixing by shallow convection
and large-scale shallow overturning circulations (Sherwood et al. 2014). An important
process underlying these far-reaching effects is the radiative cooling of the cloud-topped
boundary layer. Stronger cloud-radiative effects in the subsiding branch of Walker circulations have been shown to narrow the area of deep convection in the upward branch(Bretherton and Sobel 2002; Peters and Bretherton 2005). Cloud-radiative effects also help
aggregate deep convection in cloud-resolving and large eddy simulation (LES) models inradiative-convective equilibrium (RCE) (Muller and Held 2012; Wing and Emanuel 2014;
Hohenegger and Stevens 2016).
Observations also show hints that differences in the characteristics of rain are accompanied by differences in the circulation. When shallow overturning circulations in thetropical Eastern Pacific are stronger, the Eastern Pacific is characterized by more large
clusters of rain, whereas weaker shallow circulations are accompanied with a larger
fraction of smaller isolated raining cells (Chen and Liu 2015). Such findings suggest thatimportant feedbacks between regions of warm and cold cloud may exist, which include not
only the vertical structure of moisture and cloud, but also rain.
Ideally global climate models (GCMs) would provide us insight into such feedbacks.
But GCMs already disagree on the shallow convection that precedes warm rain (Sherwood
et al. 2014) and their complexity makes it challenging to isolate processes. Instead, we aim
for a more simplified setting following a series of studies that have used idealized two-box
or four-box equilibrium models to study the sensitivity of tropical climate. Notably,
Pierrehumbert (1995) demonstrated that the interaction between dry subsiding regions andmoist convecting regions is an important determinant of tropical climate. His study andthat of others (Miller 1997; Larson et al. 1999) also emphasize the strong sensitivity oftropical circulations to water vapor, cloudiness and radiative cooling in the subsiding
region. Other factors that are important for circulation strength are the relative area

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occupied by subsiding versus convecting areas (Pierrehumbert 1995; Bellon and Le Treut
2003), e.g., the relative size of the two boxes, and the sea surface temperature (SST)
gradients as set by surface winds and ocean transport (Sun and Liu 1996; Clement andSeager 1999).
In our first exploration of the sensitivity of circulations to warm rain, we use an extensionof a one-dimensional (single-column) RCE model, which numerically solves the hydrostatic
equations of motion for non-rotating, nonlinear flow in two side-by-side columns. Rather
than assuming convection in the subsiding column is limited to the boundary layer, as in mostof the two-column model studies just mentioned, the depth of convection is calculated
interactively by the convection scheme. Furthermore, radiation is interactive and a cloud
scheme is used. A version of this model for linear flow was first used by Nilsson and Emanuel(1999), which demonstrated that a positive feedback between the circulation, clear-sky water
vapor and radiation can destabilize radiative–convective equilibrium and attain a new
equilibrium with a thermally direct circulation between the columns. In our simplified setup
we prescribe SST gradients, and the two columns are of equal size. The latter is a shortcomingof the model setup that we are aware of. The model also uses parameterized physics and thus
carries similar uncertainties as the physics used in GCMs. Nevertheless, the simplified
geometry of the model allows us to get a first insight into mechanisms that may be relevant towarm rain in circulations, which we hope are further tested in future studies. The next section
describes the model and its setup in more detail.

2.1 A Two-Column RCE Model
The model’s columns are oriented in a x, z plane, and the following equations for temperature T, specific humidity qv and the vorticity g are solved by time integration:
oT
oT
oT ax
o2 T
¼ c 2 þ FSH þ FR þ FQ1
þu
þx
þ
ot
ox
op cp
ox

ð1Þ

oqv
oqv
oqv
o2 qv
þu
þx
¼ c 2 þ FLH þ FQ2
ot
ox
op
ox

ð2Þ

og
og
ov
oa
o2 g omðog=opÞ oFcu
þu þf¼
þc 2 þ
þ
ot
ox
op
ox
ox
op
op

ð3Þ

whereby the vorticity g of the flow is defined as:
ou ox

op ox

ð4Þ

T Rd ð1  qv þ qv =Þ
p

ð5Þ

g¼
and the specific volume a as:a¼

Here, Rd is the gas constant for dry air and  is the ratio of the molecular mass of water
vapor and of dry air. Furthermore, u is the zonal wind; x is the vertical velocity in pressure
coordinates; cp is the specific heat capacity of dry air; FSH and FLH are the sensible andlatent heat fluxes at the surface; FR is the net radiative heating tendency; FQ1 and FQ2 are
the heat source and moisture source/sink due to convection and condensation; f is the
Coriolis parameter; c represents the inverse of a damping timescale s; Fcu is the tendency of123

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initial RCE
15kmz

SST = 30 C

SST = 30 C
x

(1A)

(2A)

ql threshold = 1.4 g/kg

15km

ql threshold = 1.4 g/kg

15km

BL top

3km

BL top

1km

ΔSST = 1 K

(1B)

2km
1km

ΔSST = 1.75 K(2B)

ql threshold = 1.1 g/kg

15km

ql threshold = 1.1 g/kg

15km

5km
2km
1km

ΔSST = 1 K

1km

ΔSST = 1.75 K

Fig. 3 A sketch of the two-column overturning circulation with deep convection in both columns in theinitial RCE state (top). Below two scenarios are sketched whereby deep convection has developed over thewarm ocean and shallow convection over the cold ocean. 1A and 1B correspond to a SST difference of 1 K
between the columns, and 2A and 2B to a SST difference of 1.75 K. In experiment (A) the condensate
threshold for rain formation is 1:4 g kg1 and in experiment (B) the threshold is 1:1 g kg1 . The horizontal
dashed lines denote convective tops over the cold ocean. The arrows denote the large-scale vertical velocity
in each column and the zonal flow at the column boundary

the zonal wind due to convective momentum transport; and omðog=opÞ
represents theopmomentum flux divergence in the boundary layer, whereby m is a shear viscosity.
The nonlinear flow is thus forced by zonal gradients in a, and a is inversely proportional
to the virtual temperature predicted by Eqs. (1) and (2). The Coriolis acceleration is put tozero; hence, the circulation may be considered a mock-Walker circulation. A simple
Fickian damping of the flow takes place in the model interior through diffusion at atimescale s. Furthermore, the momentum flux divergence linearly decreases from a maximum damping near the surface to zero damping above the depth of the boundary layer.

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Fig. 4 Sensitivity of convection and precipitation in a Walker-like circulation to the conversion of liquid to crain. The circulation occurs between two columns with different sea surface temperatures (SST), with anincreasing SST difference on the x-axis (DSST). On the y-axis are shown: (a) convective tops, (b) surface
precipitation rate, (c) column water vapor, (d) equivalent potential temperature (he ) of the well-mixed layer,(e) surface wind speed at the column boundary, (f) surface latent heat flux, (g) integral of radiative coolingrate from the surface up to 500 hPa, (h) integral of the virtual temperature gradient (DTv =L) between thecolumns from the surface up to the convective top in the cold column (L is the width of one column). Bothblack lines are for the column over the colder ocean, with dashed lines for a condensate-to-rain threshold of
1:4 g kg1 , and solid lines for a threshold of 1:1 g kg1 (more efficient warm rain formation). The gray lines
are for the column over the warm ocean instead

Momentum is also damped through convective momentum transport. At the surface, alinearized surface drag formula is used as the boundary condition for the horizontal flow,
and a free-slip condition is applied at the model top.
The two columns are of equal size and 1500 km wide. A vertical grid of 100 pressurelevels is used, with a resolution of about 125 m that becomes finer above 100 hPa. The
model integration is performed using a time step of 1 min and continued until equilibrium
is reached, usually after 100 days.
Parameterizations are used for the absorption and emission of radiation (Morcrette1991), for convection and precipitation (Emanuel and Zivkovic-Rothman 1999) and forcloudiness (Bony and Emanuel 2001), which is an extension to the clear-sky-only calculations in Nilsson and Emanuel (1999). The Emanuel convection scheme is based on
buoyancy sorting principles, which allows a spectrum of mixtures to ascend or descend totheir level of neutral buoyancy. Notably, the scheme does not distinguish between shallow
and deep convection and has the ability (in the past deemed a disability) to produce lightrain in the absence of deep convection. A simple buoyancy closure determines the massflux at cloud base, e.g., the mass flux is adjusted to maintain sub-cloud layer air neutrally
buoyant when displaced beyond the top of the sub-cloud layer. Surface fluxes are calculated using standard bulk formulae.
We carry out experiments in which we alter the efficiency of rain formation. The
convection scheme has a straightforward way of dealing with (warm) rain formation: allcondensate in excess of a temperature-dependent threshold is turned to rain. This
assumption is based on the idea that the efficiency of coalescence increases with theamount of condensate and thus the presence of large drops. The threshold is constant up to
the freezing level and decreases beyond this level in light of the Bergeron–Findeisen
process. Rain and its associated heat are added to a single hydrostatic unsaturated
downdraft, and rain evaporates as a function of the temperature and humidity of theenvironment and the downdraft (Emanuel 1991).
Given the models’ physics and lack of a separate boundary layer scheme, our experiments exclude stratocumulus clouds, but we acknowledge that also these shallow clouds
produce a significant amount of warm rain that may be relevant to circulating equilibria in
the tropical atmosphere (Sect. 1).

2.2 Circulating Equilibria in the Two-Column System
A sketch of the two-column system is shown in Fig. 3. The columns are first run into RCE
at a uniform prescribed sea surface temperature (SST) of 30  C (top panel). No circulation
exists when both columns have an identical RCE state (top panel). Consequently, the SST
in one of the columns is lowered with increments of 0.25 K up to an SST difference(DSST) of 2 K. Alternatively, we can increase the SST in one of the columns from a colder

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cold column

warm column

b

c

d

e

f

g

h

u

a

RCE state. This gives qualitatively the same results, but some hysteresis is present, becauseof differences in the initial moisture structure.
The black dashed lines in Fig. 4a show how the tops of convection over the cold oceancollapse with DSST for a condensate-to-rain threshold of 1:4 g kg1 , with blue-huedmarkers for the largest DSST. Here, convective tops are defined as the maximum level ofpositive convective mass flux. For all DSST convection over the warm ocean remains deep
with tops up to 150 hPa (the gray dashed lines). Evidently, a DSST = 0.5 K is enough to

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collapse convective tops to roughly 600 hPa (about 4 km), and a DSST = 0.75 K collapses
convection to roughly 800 hPa (about 2 km). Even the shallowest modes produce precipitation with surface rates just below 1 mm day1 .
Because convection collapses, the atmosphere above the tops of convection experiences
a net (radiative) cooling. This results in a temperature difference with the other column,
which triggers a circulation: subsidence develops over the cold ocean (xcold [ 0) andrising motion over the warm ocean (xwarm \0). Near the tropopause the flow is directedfrom the warm to the cold column (u [ 0) and near the surface from the cold to the warm
column (u\0), as illustrated in Fig. 3-1A, 2A (middle panels) for a SST difference (DSST)
of 1, respectively, 1.75 K. A new circulating equilibrium develops in which radiative
cooling above the cloud layer over the cold ocean is now balanced by subsidence warming
instead of convective heating. Over the warm ocean the mean rising motion introduces
extra cooling next to radiative cooling, both of which are balanced by deep convective
heating.
Nonlinear behavior at low DSST, such as in the surface precipitation rates, are caused
by a reverse in the circulation. For DSST  0.5 K convection over the cold ocean has not
yet collapsed, and a weak oscillatory circulation can develop. Furthermore, the convection
scheme favors detrainment near mid-levels, which can produce large cloud fractions thatsignificantly lower radiative cooling in the lower troposphere, and also reverse thecirculation.
The profiles of x and u over the cold ocean show how divergence and near-surface windspeeds increase with DSST (Fig. 5), but saturate as DSST [ 1.5 K, and even weaken again
at very large DSST ¼ 5 K. The strength of the circulation may be understood through asimplified form of the equation for the flow’s vorticity (Eq. 3). For non-rotating flow andignoring horizontal advection, damping, surface friction and convective momentum
transport, we may write:
og oa o
og
ð6Þ
¼ þ
m
ot ox op op
The first term on the right-hand side measures the buoyancy gradient between the columns
and tends to increase the vorticity. The second term is the momentum flux divergence inthe boundary layer. This shear stress tends to decrease the vorticity, but may be assumed tovanish at the top of the convective layer. Hence, if we integrate from the surface ps up to

Fig. 5 Vertical profiles of the vertical velocity x, the horizontal wind speed u, the relative humidity RH, theheating tendency due to radiation Qr and the cloud fraction, for circulations at DSST between 0.25 and 2 K.
Colors correspond to those used in Fig. 4. All profiles are for the column over the colder ocean surface andfor the higher threshold of condensate-to-rain conversion (1:4 g kg1 )123

Surv Geophys (2017) 38:1257–1282

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the top of the boundary layer ph and rearrange the stress term to the left-hand side, we canwrite:
 
Z ph
og
oa
dp
¼
ms
ð7Þ
op s
ps ox
 
The term og
op s on the left-hand side represents a measure of the strength of the circulation.
Equation (7) thus shows how the circulation is not only a function of DSST, but of
buoyancy differences over the entire boundary layer h. Those buoyancy differences arestrongly regulated by the radiative cooling (Qr ) over the cold ocean, which changes as thefree troposphere dries with increasing DSST, which is best seen from the RH profiles inFig. 5. Qr tends to peak where temperature and moisture gradients and cloudiness are large,
for instance at the inversion and at the mixed layer top (950 hPa). The maximum in Qr
increases as the inversion lowers. Larger cloudiness below the inversion can do so, butalone the interaction of long wave radiation with the clear-sky humidity profile would be
sufficient (for example, see Stevens et al. 2017 in this same book collection). Large
increases in DSST further dry the convective layer, leading to less liquid water andcloudiness, and therefore less radiative cooling and a weaker circulation (black dashedlines, Fig. 5).
In these experiments condensate is turned into rain at a threshold of 1:4 g kg1 . For
liquid water lapse rates at these temperatures, a threshold of 1:4 g kg1 is exceeded after
about 600 m. A lower threshold of 1:1 g kg1 is exceeded after about 450 m, which is asmall difference, but one which has a relatively large impact on the character of convection
and the circulation at intermediate DSSTs (the black solid lines in Fig. 4). Convection stillcollapses, but is more stepwise, with convective tops preferably located near 600 hPa at
DSSTs = 1 K, indicative of congestus clouds. Although convective tops are higher andcolumn water vapor increases (Fig. 4c), surface precipitation rates remain near or below
1 mm day1 (Fig. 4b).
Also in nature surface precipitation rates slowly increase with column water vapor
values between 20 and 60 mm and only pick up beyond a critical value (Holloway and
Neelin 2009). One idea that could explain the slow increase in surface precipitation is thatin order for precipitation and latent heating to increase, the atmosphere would need to coolmore or warm less. Less warming could result from weaker subsidence as congestus
develops. However, subsidence warming is still largely balanced by Qr , and Qr itself
decreases as congestus deepens the moist layer.
In the next two sections, some more details of the changes in circulation for the shallow
cumulus mode at DSST = 1.75 K (Fig. 3-2A, B) and the congestus mode at DSST = 1 K(Fig. 3-1A, B) are discussed.

2.3 Shallow Cumulus
At large DSST (  1.5 K) the cold ocean column develops shallow cumulus with tops up
to 850 hPa and surface precipitation rates \1 mm day1 , suggestive of light rain or
drizzle. For this shallow mode, experiments with a condensate threshold of 1.4 and
1:1 g kg1 are notably similar. However, when looking closely a few interesting differences
can be seen, further illustrated with vertical profiles of the difference in potential temperature between low and high condensate thresholds (Dh), and profiles of specifichumidity, radiative cooling, convective heating and the vertical velocity (Fig. 6). The

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dashed and solid lines refer to experiments with ql thresholds of 1:4 g kg1 ; respectively,
1:1 g kg1 .
Convection is slightly shallower when rain formation is more efficient (ql ¼ 1:1 g kg1 ),and the surface precipitation rate is marginally smaller (Fig. 4b). The vertical humidity
profile shows that the boundary layer is also a little shallower with a moister sub-cloud andcloud layer (hhe iML in Fig. 4d, q in Fig. 6). Accordingly, the surface evaporation is lower(Fig. 4f). The evaporation of cloud condensate takes place in a somewhat thinner andstronger inversion layer, with a stronger peak in cooling. As we will discuss later, in
Sect. 3, these results are consistent with LES studies, which show that rain regulates
inversion height by removing condensate that would otherwise deepen the boundary layer.
Because of shallower convection, the integrated buoyancy difference between the twocolumns is smaller (Fig. 4h). Without any change in the viscosity, this implies a weakercirculation (Eq. 7). The maximum xcold at h is smaller, along with smaller xcold throughout
the rest of the troposphere. Less subsidence drying leads to a slightly moister free troposphere, consistent with somewhat lower radiative cooling rates.
For the congestus mode the change in the circulation with warm rain efficiency can be
explained in a similar manner, as we will see next. However, in that regime convective tops

cold column

warm column

Fig. 6 For the circulations in Fig. 4 at DSST ¼ 1 and 1.75 K we show vertical profiles of the difference inpotential temperature between the two experiments Dh ¼ hql¼1:1  hql¼1:4 , specific humidity q, the heating
tendency due to convection Qc , the heating tendency due to radiation Qr and the vertical velocity x. Blackand gray lines are for the cold, respectively, and warm column, and solid and dashed lines are for the low,respectively, and high threshold on liquid water for conversion to rain

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increase with more efficient rain formation and are accompanied by larger changes incirculation and convection over the warm ocean.

2.4 Congestus
For DSST between 0.75 and 1.5 K convection is more sensitive to the change in condensate-to-rain threshold. More efficient rain formation (ql ¼ 1:1 g kg1 ) gives rise to
deeper convection and larger surface precipitation rates (Fig. 4). When more condensate isturned to rain, at a lower altitude, updraft buoyancy increases. For DSST = 1 K a marginalincrease in convective heating Qc can be seen between cloud base (950 hPa) and 850 hPa
with more efficient rain formation (Fig. 6). The level where convective heating turns into
cooling has shifted upward, and most of the detrainment and evaporative cooling takes
place at cloud tops near 650 hPa. At this level, where cooling is pronounced, subsidence
peaks.
Again, the change in condensate-to-rain threshold is small, yet important in thisscheme where convection is modeled based on buoyancy sorting principles. Each mixtureof air ascends or descends to its level of neutral buoyancy, which might involve several
episodes of mixing, especially when precipitation changes the amount of condensate
during ascent/descent. Dealing with multiple mixing episodes is bypassed in the current
scheme by insisting that mixed air detrains at levels where its liquid water potential
temperature is equal to that of the environment (Emanuel 1991). This is illustrated inFig. 7, which shows the liquid water potential temperature (or liquid water static energyhw ) of a lifted parcel (hw;p , dashed lines) and that of the environment (hw ¼ h, solid lines)
before mixing. hw;p is conserved and equal to the dry static energy h of the sub-cloud layer
when there is no precipitation and no mixing. But upon precipitation hw increases. In thiscase, the lower condensate-to-rain threshold of 1:1 g kg1 has almost shifted the liquidwater static energy of lifted parcels at DSST = 1 K to that of lifted parcels at
DSST = 0.5 K. Indeed, these two experiments have almost similar congestus tops
(Fig. 4a). In other words, the SST is crucial at setting convective tops, but the precipitation
efficiency may allow convection over colder SSTs to reach a similar depth as convection
over warmer SSTs.

ΔSST = 0.5K
ΔSST = 1K

Fig. 7 The liquid water static energy of the environment hw (solid lines), and of a lifted parcel hw;p before
mixing (dashed lines), as calculated in the convection scheme. Two sets of lines are shown, which both
represent the column over the colder ocean: one for the experiment with DSST ¼ 1 K and a threshold of
1:1 g kg1 (green) and one for the experiment with DSST ¼ 0:5 K and a threshold of 1:4 g kg1 (brown).
The arrows indicate the levels at which the parcel would detrain upon mixing in this scheme. Increasing hw;pimplies that air will not descend as far before detraining

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Along with these changes, the thermodynamic structure over the cold ocean, the circulation, and the character of convection over the warm ocean change. For instance, at athreshold of 1:1 g kg1 the mixed layer has a larger equivalent potential temperature (he , inFig. 4d). The larger mixed layer he can be explained by less low-level radiative cooling, adecrease in subsidence drying and more precipitation. For the congestus modes, the larger
mixed layer he is accompanied by larger column water vapor (Fig. 4c), which is also
evident from the deeper moist layer in the vertical profiles in Fig. 6. Similar to the shallow
cumulus mode, the circulation decreases in strength at a lower condensate-to-rain
threshold. Whereas for the shallow mode the reduction in h helps explain the weakercirculation (Eq. 7), in the congestus regime the reduced humidity gradient (followed by thetemperature gradient) is responsible for a smaller buoyancy gradient and a weaker circulation (Fig. 4h).
One may question if the response to warm rain efficiency is the same if there were nointeraction between the two columns, i.e., when the circulation is fixed and there is nofeedback of subsidence to latent heating. LES studies of shallow convection generally
impose a fixed subsidence rate and therefore constrain the depth of convection a priori. If
we fix the profile of xcold (using the profile of the experiment with a threshold of
1:4 g kg1 ) and run a single-column experiment with a lower threshold of 1:1 g kg1
convection is shallower instead of deeper (green lines in Fig. 8). To balance the fixedmoderate subsidence warming while having larger latent heating in the cloud layer, themodel has to find a new equilibrium with larger radiative cooling in the cloud layer. This
layer will be shallower, with a stronger inversion and a drier overlying free troposphere. In
this case, the response is similar to that of the shallow mode and similar to LES studies
discussed in Sect. 3.1.
The circulation is thus critical to the impact of warm rain in the subsiding column. It
leads to small changes in deep convection over the warm ocean. As convection over thecold ocean precipitates more, convection over the warm ocean precipitates less (Fig. 4b).
Less precipitation is consistent with a weaker circulation and less cooling from mean
vertical ascent over the warm ocean. There is also less cloud-base mass flux, moredetrainment and larger cloud fractions near 400 hPa (Fig. 8j, k), which leads to lessradiative cooling at low and mid-levels (Fig. 8n).
An intricate interaction between convection, rain microphysics, radiation and the circulation is thus responsible for congestus modes in the two-column model. In the next
section, we turn our focus to reviewing some ongoing efforts in fine-scale modeling of
convection and space-borne observations, which may be used to address ideas suggestedby the two-column model. What limits the congestus modes at mid-levels specifically is
discussed in more detail in an upcoming manuscript (Nuijens and Emanuel, in preparation), along with a longer discussion on the influence of model resolution, domain size andthe momentum of the flow.

3 From a Conceptual Model to Nature
The two-column model suggests that changes in the depth of convection and warm rain in
subsiding regions may be accompanied by changes in convection in ascending regions. The
model also suggests that small-scale processes such as mixing and warm rain formation,
followed by feedbacks through the circulation, have a noticeable impact on the character ofconvection and the circulation. But in our setup we have made a number of simplifications,123Surv Geophys (2017) 38:1257–1282

a

1271

b

u

c

i

d

j

e

k

f

l

g

h

m

n

Fig. 8 Vertical profiles of circulation, convection and thermodynamic structure for the experiment withDSST ¼ 1 K, which develops congestus with more efficient rain formation. Solid and dashed black lines
correspond to condensate-to-rain thresholds of 1.1 and 1:4 g kg1 (same as in the bottom panel of Fig. 6).
Green lines show an experiment with a threshold of 1:1 g kg1 but fixed xcold and near-surface u and fixedmoisture convergence. The latter are taken from the experiment with a 1:4 g kg1 threshold. Shown are: (toppanel) the vertical velocity and moisture convergence, and (middle and bottom panels) the potential
temperature lapse rate s, relative humidity, the saturated mass flux Msat , both upward and downward
components, the unsaturated mass flux driven by precipitation falling outside of the cloud Munsat , convective
heating Qc and radiative cooling Qr

most importantly that the columns are of equal size. As suggested by Pierrehumbert (1995)
and Bellon and Le Treut (2003), an important follow-up to this study would be to change
the relative size of the columns, or even adding columns. Our findings also cruciallydepend on the parameterized convection and cloudiness. Hence, our findings should beinterpreted as ideas, which need further testing with models that explicitly simulate
convection.
For instance, cloud-resolving models (CRMs) that are run on very large domains, evenspanning ocean basins, may be forced with a surface temperature gradient to study thesensitivity of circulations to convection (Bretherton et al. 2006). In another approach,

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CRMs on two domains may be used to simulate convection explicitly, and the two domains
can be coupled through a circulation derived from the weak-temperature gradientapproximation (Daleu et al. 2012).
Because shallow convection and cloudiness occur on scales smaller than conventional
CRM grids, Large-Eddy simulations (LESs) may be preferred to investigate warm rain
implications. So far LESs have been run on domains too small for circulations to develop,
and too small for convection to organize itself into moist clusters surrounded by dry
regions—a process that may crucially impact climate (Pierrehumbert 1995; Mauritsen
et al. 2012). Nevertheless, LES studies have given some insight into the influence of warm
rain on the thermodynamic structure of the lower atmosphere. We shall discuss these in thenext section and draw out similarities with the two-column model results. Furthermore, we
discuss how ground-based or airborne observations may help constrain warm rain formation, which remains uncertain even in LES.

3.1 Large-Eddy Simulations
Large-Eddy simulation has long been a tool to study turbulent flows including the cloudy
boundary layer on limited horizontal domains (20  20  4 km3 ) at fine grids(100  100  40 m3 ). LES is also increasingly used to simulate deeper convection (up to
10–12 km) on horizontal domains of 50  50 km2 and larger and with global-scale simulations underway. Microphysics in LES are typically parameterized using either a bulk
scheme, which prognoses one or two moments of the drop-size distribution (only the total
mass of rain, or the mass and number of rain drops), or a bin scheme, which uses a
discretized version of the drop-size distribution and attempts to model the full evolution of
the droplet spectrum. For the bulk schemes, the total cloud mass is inferred from anequilibrium assumption and the cloud droplet number is specified. Hence, these schemes
implicitly assume an aerosol or cloud condensation nuclei concentration. By varying thecloud droplet number concentration, the sensitivity to warm rain formation has beenstudied.
Such sensitivity studies have demonstrated that at larger cloud droplet number concentrations shallow cumuli get deeper before they rain (Stevens and Seifert 2008; Seifert
et al. 2015). Therefore, larger cloud droplet number concentrations produce less rainfall
initially. But the response of clouds and the boundary layer will mitigate this initial effect.
Namely, the removal of liquid water via rain reduces evaporative cooling and mixing nearcloud tops and thus the entrainment of warm free tropospheric air into the boundary layer
and the deepening of convection and the boundary layer. Therefore, after a long enough([30 h) simulation time, differences in cloud and rain statistics for different cloud droplet
number (aerosol) concentrations are small (Xue and Feingold 2006).
The regulation of inversion height by warm rain has been noted in early bulk theories ofshallow cumulus convection and also matters for the sensitivity of shallow cumuli to global
warming scenarios. Larger SSTs and less large-scale subsidence under global warming
lead to a deepening of shallow cumuli. This increases the entrainment of dry air into theboundary layer, which dries the cumulus layer drier and reduces cloud fraction. But rainfall
puts a notable limit to such deepening, so that changes in cloudiness with global warming
are overall small (Blossey et al. 2013; Bretherton et al. 2013; Vogel et al. 2016).
In the two-column model, the response of the shallow mode to more efficient warm rain
(Fig. 6, top panels), as well as the response of the congestus mode under fixed subsidence(Fig. 8, green lines), is similar to these LES studies. But in LES the subsidence rate is123Surv Geophys (2017) 38:1257–1282

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0.0

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CF [%]

3.0

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20

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1
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300

310

θ [K]

320

e

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d

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height [km]

b

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CTL
CTL.2K.ω6
DRY

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a

6

generally fixed. Our two-column model experiments suggest that changes in subsidencewith (latent) heating can change the response to rain at SSTs that are favorable forcongestus.
A recent study using LES demonstrates processes that are important in the transition
from a shallow to a congestus regime, and we may use these to loosely evaluate changes inatmospheric structure produced by the two-column model. Vogel et al. (2016) and Vogel
and Nuijens (in preparation) use a constant exponential profile of subsidence, prescribed
SSTs and interactive radiation, for a model domain of 51:2  51:2  10 km3 with a resolution of 50 m in the horizontal and 10 m in the vertical. To reproduce many of thedifferences in cloud and boundary layer structure that are observed during months withpredominantly shallow or deeper convection (congestus), an increase in SST and decreasein subsidence (at a reference scale height) are sufficient.
A 2K increase in SST and 1:5 mm s1 decrease in x lead to a deepening of convection
from 2 to 7 km, a quadrupling of surface precipitation and a 15% decrease in cloud cover.
The cloud and boundary layer structure of these control (CTL) and CTL.2K.x6 simulations
is shown in Fig. 9 and reveals that as congestus develops, moisture and temperature aremuch better mixed in the vertical, and the inversion is weaker. Because the inversion is
weaker, less cloudiness develops near the inversion.
Critical to reproducing the character of convection and cloudiness in the two regimes is
the role of interactive radiation, which can both stabilize and destabilize convection (Vogel
and Nuijens, in preparation). For instance, interactive radiation is crucial for stabilizing
convection and developing the stratiform outflow layers near the inversion for the CTL
simulation. Sometimes interactive radiation also leads to a response one might not expect.
For instance, when the free troposphere is drier, convection gets deeper and rains more.
This is illustrated with the DRY simulation in Fig. 9, which has 1 g kg1 less water vapor
in the free troposphere. This enhances the radiative cooling in the moist convective layer
and inversion layer, which boosts the buoyancy of cloudy updrafts that reach those layers.
As congestus develops and moisture is mixed over a deeper layer, radiative cooling within
the cloud and sub-cloud layer and its maximum value decrease (Fig. 9e). Because of the
deeper moist layer, the surface latent heat flux also decreases (Fig. 10). Both factors—lessdestabilization from radiative cooling and a lower surface latent heat flux—could imply
that convection self-limits itself. However, in these simulations there is no feedback

0

10

20

30

40

50
−2

R flux [Wm ]

60

−4.5

−3.5

−2.5

−1.5

−1

Q R [Kd ]Fig. 9 Domain-averaged profiles of cloud fraction, specific humidity, potential temperature, precipitation
flux and radiative cooling from LES. The CTL (orange) and DRY (gray) simulations differ only in theirinitial profile of specific humidity in the free troposphere, whereby the CTL run is about 1 g kg1 morehumid. The CTL.2K.x6 (blue) simulations has a 2K larger SST and a 1:5 mm s1 reduction in the prescribed
x profile compared to the CTL simulation

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CTL.2K.ω6
DRY

400

600

Surv Geophys (2017) 38:1257–1282

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LHF [Wm −2]

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0

Fig. 10 Time series of the surface latent heat flux, the inversion height, the surface precipitation rate andtotal cloud cover for the CTL (orange), DRY (gray) and CTL.2K.x6 (blue) simulations shown in Fig. 9through the circulation such as in the two-column model, where the reduced cooling leads
to a weakening of subsidence.
Average surface rain rates for the congestus clouds in LES are between 20 and
40 W m2 (Fig. 10). But the simulated rainfall is very intermittent, which is caused by thelimited number of deeper clusters and cold pools that this domain size can support. The
profile of the rain flux also shows that a fraction of rain evaporates in the lower cloud andsub-cloud layer (Fig. 9d). The evaporation of rain triggers downdrafts which pull down
cooler air that can spread out in the sub-cloud layer like a density current (cold pools).
Such cold pools have been long known to exist for deep convection (see also Zuidema
et al. in this collection). Within cold pools convection is suppressed, but at the downwind(colliding) boundaries of cold pools new convection can be triggered. This leads to arcshaped cloud formations with clear skies in between as seen from satellite imagery (Snodgrass et al. 2009; Zuidema et al. 2012), and which the LES reproduces. The cold pools
from shallow cumuli and congestus are mostly dry in their center, similar to deep convection, because rain rates are sufficiently strong to bring down relatively dry air fromhigher altitudes. This is different from the cold pools observed in open cell stratocumulus
decks, which tend to be moist instead. At what rain rates either dry or moist cold pools
develops and for which fraction of rain falling through unsaturated air are still open
questions. And even in LES rain microphysics still carry a considerable uncertainty(VanZanten et al. 2011; Seifert and Heus 2013; Li et al. 2015). LES development would
thus greatly benefit from progress made in deriving vertical profiles of rain and cloud fromground-based remote sensing networks, which we discuss next.

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3.2 Observations
Relationships Between Cloud and Rain Estimates of how much condensate is turned intorain would help validate microphysical models used in LES, which in turn could help
inform models of rain for large-scale models, such as the simple condensate-to-rain
threshold used in the convection scheme in the two-column model. Useful first steps would
be estimating how much water is removed via rain. Surface measurements of rainfall overa larger area (such as from a weather radar), alongside measurements of surface evaporation (from buoys or ships), and measurements of advection (from sounding arrays) could
provide such estimates. For instance, during the Rain in Cumulus over the Ocean (RICO)
field campaign surface precipitation rates comprised about a fifth of the surface evaporation rate (Nuijens et al. 2009). The upcoming EUREC4 A field study (see Bony et al. 2017
in this collection) will provide the measurements needed for such a study.
But surface precipitation rates alone do not reveal at what levels rain has evaporated, or
how much rain has fallen through clouds or clear sky. Those differences are important forunderstanding how moisture is distributed vertically or how convective downdrafts form.
This requires better estimates of the vertical profile of the rain flux alongside that of cloud
condensate. But an inherent problem is that the profile of cloud condensate and rain cannot
be measured simultaneously with a single radar wavelength. Existing methods use avertically pointing cloud radar (typically 36 GHz or Ka band) to measure the sixth momentof the drop-size distribution, which may be turned into a profile of cloud liquid water byusing the liquid water path obtained from a microwave radiometer, and by making
assumptions on the drop-size distribution. Through synergy of instruments at dedicatedfield sites (such as the CloudNet network in Europe or the US Department of Energy’s
Atmospheric Radiation Measurement (ARM) sites), refined algorithms have been developed to do so. Such data sets seem ripe for further exploration, but are not without
challenges. As drizzle or rain-sized drops develop the drop-size distribution changes, andassumptions underlying these algorithms need to be adjusted. Furthermore, when rain rates
are sufficiently high the (cloud) radar beam will become attenuated, and the microwave
radiometer has to be shut down. Hence, to estimate the profile of rain that develops instatistically similar clouds, a radar with a smaller frequency (larger wavelength), whichsuffers less from attenuation, has to be employed at a nearby location, where it has asimilar radar footprint. To accurately estimate rain evaporation, the radar should be almost
as sensitive as the cloud radar, and hence, a K or Ku band radar would be ideal. Unfortunately, this would exclude deep convection whose rain rates can be so high that even a K
or Ku band radar signal will be attenuated.
Globally, the CloudSat Cloud Profiling Radar (CPR) can be used to relate measured
cloud top heights to surface precipitation rates. But also this is not straightforward. A
94 GHz W band radar suffers from significant attenuation as rain intensity increases, andsurface backscatter remains an issue. A recently Bayesian Monte Carlo algorithm uses a
cloud-resolving model database to link observed vertical and integrated measurements ofliquid clouds to latent heating structures and precipitation rates at the surface (Nelson et al.
2016). A histogram of surface rain rates of each CloudSat CPR profile, stratified by cloud
top heights (Fig. 11), shows that clouds with tops beyond 1.6 km produce rain that reaches
the surface (similar to what we infer from Fig. 2). Clouds with tops beyond 2 km clearly
produce even higher rain rates, but beyond 3 km, the increase in rain rates is overall small,with the exception of very high rain rates, yet these are very rare.

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Fig. 11 Histogram of near-surface rain rates stratified by cloud top heights over tropical oceans as
generated with the algorithm of Nelson et al. (2016) using CloudSat CPR data

The successor of the TRMM mission, the Global Precipitation Measurement (GPM)
mission, has launched a dual-frequency precipitation radar (DPR) in 2014. This radar has a
Ka and a Ku band, which suffer less from attenuation than CloudSat’s W band. The DPR flies
in a non-Sun synchronous orbit with an inclination angle of 65 , allowing it to measureextratropical clouds and the Arctic and Antarctic circles, which TRMM did not sample.
Along with a microwave imager, the DPR will measure the vertical structure of precipitation
intensities. By combining these measurements with traditional radiometers that alreadyonboard satellites, the GPM mission promises to provide three-hourly rain estimates almost
globally (Hou et al. 2013). This will allow studies on relationships between rain and thelarge-scale flow that can be done on much shorter timescales than has been possible so far.
Temporal Relationships One idea suggested by the two-column model experiments isthat periods with shallow cumuli and drizzle occur in a different circulation than periods
with congestus and rain. Data from the Barbados Cloud Observatory, currently the only
remote sensing platform in the tropics, have already demonstrated that congestus and rainvary predominantly on timescales of days to weeks (Nuijens et al. 2014), which suggeststhat their occurrence is favored during certain large-scale states.
Linking clouds to circulations has been mostly done by long-term averaging of satellite
observations over geographical regions or dynamical regimes. But to study variability on
daily to synoptic timescales a different approach is needed, because most (polar orbiting)satellites sample a given location too infrequently (one exception being the new GPM
mission with its three-hourly precipitation rates globally). One approach is to project
different polar orbiting satellites onto a composite time axis centered on a rain event, astrategy that has been used in Masunaga (2013) and Masunaga and L’Ecuyer (2014). The
result is a statistical time series on hourly and daily timescales, which precedes and follows
those rain events. To illustrate this approach, we can use the areal rain coverage data from
TRMM over the subtropical Pacific as a proxy for congestus. This is an area with considerable warm rain (Fig. 1). Because TRMM’s minimum detection threshold is 17 dBZ,

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much larger than values observed for cloud tops up to 2 km (see also Fig. 2), TRMM likely
does not observe drizzle, but only the more intense warm rain showers from congestus. We
assume that congestus has an areal rain coverage less than 25%, and use all those events tocreate the time series in Fig. 12, which shows the evolution of profiles of cloud cover(measured by CloudSat’s CPR), dry static energy and humidity, and the moisture budget.

a Cloud Cover (-)

b DSE (kJ/kg)

c q (g/kg)

d Moisture Budget:

Fig. 12 Top panel (a) shows a composite time series of CloudSat cloud fraction anomalies from thebackground state for congestus rain events over the subtropical Pacific at 0 h. Similar composites for the
profile of water vapor mixing ratio (g kg1 ) and dry static energy DSE (kJ kg1 are shown in panels (b) and(c). The bottom panel (d) shows the composite moisture budget, including the surface evaporation rate (solid
green), the surface evaporation (red dotted) and the vertically integrated moisture convergence (in shading,with convergence in light red and divergence in blue)

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Figure 12a shows that after the rain event, cloudiness in the lower troposphere is larger for
up to 12 h. The surface precipitation rate increases only little at the time of the rain event,which suggests that other precipitating clouds are always nearby (Fig. 12d). We also
observe that the surface evaporation is rather invariant, which suggests it does not play amajor role in controlling rain, unless its heterogeneity is not captured by the measurements.
Between two days before and after the rain event a cool anomaly in the lower and midtroposphere is present (Fig. 12b). This cooling can destabilize the atmosphere and promote
convection. Furthermore, during and following rain events the lower troposphere moistens,
especially up to about 3 km (700 hPa) (Fig. 12c). Radiative cooling might explain the coolinganomalies, because these anomalies (even those in the upper atmosphere 72–36 h preceding therain event) roughly correspond to the moist anomalies. But without knowing the winds and thus
advection, we cannot draw any conclusions yet. This approach should therefore be repeated withadditional satellite data, where the zonal wind profiles measured by the upcoming ADM Aeolus
mission are particularly interesting. We may also use GPM data, which is more sensitive to lightrain, and use cloud top heights instead of rain coverage as proxies for convection.

4 Concluding Thoughts
During the last decade, the cloud radar deployed aboard CloudSat has demonstrated thatwarm rain over oceans is ubiquitous. Recognizing its importance for shallow convection
and low-level cloudiness, parameterizations of warm rain formation have been included inhigh-resolution models, such as LES. LES studies have demonstrated that warm rain cansignificantly alter the character of shallow convection, such as the depth of clouds, theirorganization and low-level cloudiness. In turn, shallow convection has been shown to
impact large-scale circulations and climate. At least, the radiative driving from low-levelcloud has been shown to strengthen large-scale circulations, and differences in low-levelcloudiness among GCMs result in different predictions of climate sensitivity. Therefore, inthis paper we question how warm rain itself—a process that may alter the character ofshallow convection on larger scales—matters for circulations and climate.
We presented new experiments with an idealized two-column model to speculate on theinfluence of warm rain on tropical circulations. This model solves for two-dimensional
non-rotating flow between two columns on a fairly fine vertical grid (125 m) and uses
parameterized convection, cloudiness and radiation. Naturally, these parameterizations
carry uncertainties, alike those used in GCMs. But the simpler dynamics in the two-column
framework allow us to gain some insight into mechanisms involving warm rain, which may
serve as a starting point for future studies using models with explicit convection. A circulation with deep convection in one column and subsidence in the other column is forced
by prescribing the DSST between the columns. The circulation and depth of convection in
the subsiding column as a function of DSST are found to depend on an intricate interaction
between convection, warm rain, the circulation and radiation. The most interesting findings
with respect to the sensitivity to warm rain can be summarized as follows:1.

2.

At large DSST efficient warm rain formation lowers shallow cumulus tops and theinversion height over the cold ocean. This leads to a small reduction in the integrated
buoyancy gradient between subsiding and ascending columns (Fig. 3-2A, B).
At smaller DSST efficient warm rain formation raises shallow cumulus tops, leading tocongestus clouds. These congestus clouds are accompanied with deeper moist

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3.

4.

1279

boundary layers and a reduction in the integrated buoyancy gradient between thecolumns (Fig. 3-1A, B).
Efficient warm rain formation can thus weaken the circulation across a range of DSST
(but especially at smaller DSST). Surface precipitation rates over the cold ocean
consequently increase, while surface precipitation and cloud-base mass fluxes over thewarm ocean decrease.
Congestus clouds can develop because of the extra latent heating with more efficientwarm rain, which raises parcel buoyancy. But the weakening of the circulation(weaker subsidence) is important for maintaining the congestus mode. Here, the strong
reduction of low-level radiative cooling in response to low-level moistening bycongestus is crucial.

We may thus postulate that warm rain formation has a negative feedback on the strength ofcirculations by regulating the depth and thermal structure of the lower troposphere. In otherwords, raining or deeper shallow cumuli in regions with subsidence may also weaken
circulations, besides strengthening them through radiative cooling. An interesting observation in that regard is that periods with stronger near-surface winds are accompanied withdeeper cloud layers and significant rain showers (Nuijens et al. 2009, 2015). This could
suggest that, as circulations strengthen, convection in the subsiding branches responds bydeepening and raining more, which can slow down the circulation.
Because the convection scheme we use is based on the premise that microphysicalprocesses are important for the humidity structure of the atmosphere, a sensitivity to warm
rain formation may not be a surprise. Given the uncertainty associated with any convection
scheme, the above results should be considered speculative and merely a basis for further
testing with models and observations.
An important step forward in improving warm rain processes in models is to use
existing ground-based remote sensing. For instance, collocated vertical profiles of cloudand rain from ground-based radar can be exploited to constrain how much cloud condensate detrains and moistens the atmosphere, compared to how much condensate reaches
the surface via precipitation. Even in LES such processes remain uncertain. Furthermore,deriving large-scale winds through the use of sounding arrays, combined with intensive
vertical profiling of cloud, rain and the thermal structure of the atmosphere, can shed lighton relationships between convection and the large-scale flow. These measurements areplanned for the EUREC4 A field campaign (see Bony et al. 2017 in this collection). Finally,
to test ideas suggested by the two-column model framework, satellite remote sensing, inparticular the new GPM and Aeolus missions, can be used. Namely, these may identify
whether long-term variations in circulation strength are linked to variations in rain in
subsiding and ascending branches.
Acknowledgements This paper arises from the International Space Science Institute (ISSI) workshop on
Shallow clouds and water vapor, circulation and climate sensitivity. The first author wishes to express a
special thanks to Reimar Luest and the Max Kade Foundation for the opportunity to spend a year at MIT.
Thanks go to Ethan Nelson, Raphaela Vogel, Katrin Lonitz and Vivek Sant for their help in creating figures,and to Cathy Hohenegger, Chris Bretherton and Robert Pincus for insightful discussions. Lastly, we thankthree reviewers for providing insightful feedback.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate if changes were made.

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References
Battan LJ, Braham RR (1956) A study of convective precipitation based on cloud and radar observations.
J Meteorol 13(6):587–591
Bechtold P, Sandu I, Klocke D, Semane N, Ahlgrimm M, Beljaars A, Forbes R, Rodwell M (2014) The roleof shallow convection in ECMWFs Integrated Forecasting System. Ecmwf technicalmemoranda,
ECMWF
Bellon G, Le Treut HL (2003) Large-scale and evaporation-wind feedbacks in a box model of the tropicalclimate. Geophys Res Lett 30(22):2145. doi:10.1029/2003GL017895
Berg W, L’Ecuyer T, Haynes JM (2009) The distribution of rainfall over oceans from spaceborne radars.
J Appl Meteorol Climatol 49(3):535–543
Blossey PN, Bretherton CS, Zhang M, Cheng A, Endo S, Heus T, Liu Y, Lock AP, de Roode SR, Xu KM(2013) Marine low cloud sensitivity to an idealized climate change: the CGILS LES intercomparison.
J Adv Model Earth Syst 5(2):234–258
Bony S, Emanuel KA (2001) A parameterization of the cloudiness associated with cumulus convection;
evaluation using TOGA COARE data. J Atmos Sci 58:3158–3183
Bony S, Stevens B, Ament F, Bigorre S, Chazette P, Crewell S, Delanoë J, Emanuel K, Farrell D, Flamant
C, Gross S, Hirsch L, Karstensen J, Mayer B, Nuijens L, Ruppert JH Jr., Sandu I, Siebesma P, SpeichS, Szczap F, Totems J, Vogel R, Wendisch M, Wirth M (2017) EUREC4A: A field campaign toelucidate the couplings between clouds, convection and circulation. Surv Geophys. doi:10.1007/
s10712-017-9428-0
Bretherton CS, Sobel AH (2002) A simple model of a convectively coupled walker circulation using the
weak temperature gradient approximation. J Clim 15(20):2907–2920
Bretherton CS, Blossey PN, Peters ME (2006) Interpretation of simple and cloud-resolving simulations ofmoist convection radiation interaction with a Mock–Walker circulation. Theor Comput Fluid Dyn20(5):421–442
Bretherton CS, Blossey PN, Jones CR (2013) Mechanisms of marine low cloud sensitivity to idealized
climate perturbations: a single-LES exploration extending the CGILS cases. J Adv Model Earth Syst
5(2):316–337
Burdanowitz J, Nuijens L, Stevens B, Klepp C (2015) Evaluating light rain from satellite- and ground-based
remote sensing data over the subtropical North Atlantic. J Appl Meteorol Climatol 54(3):556–572
Byers HR, Hall RK (1955) A census of cumulus height versus precipitation in the vicinity of Puerto Ricoduring the Winter and Spring of 1953–1954. J Meteorol 12(2):176–178
Chen B, Liu C (2015) Warm organized rain systems over the tropical Eastern Pacific. J Clim
29(9):3403–3422
Clement A, Seager R (1999) Climate and the tropical oceans. J Clim 12(12):3383–3401. doi:10.1175/15200442(1999)012\3383:CATTO[2.0.CO;2
Daleu CL, Woolnough SJ, Plant RS (2012) Cloud-resolving model simulations with one- and two-way
couplings via the weak temperature gradient approximation. J Atmos Sci 69(12):3683–3699. doi:10.
1175/JAS-D-12-058.1
Emanuel KA (1991) A scheme for representing cumulus convection in large-scale models. J Atmos Sci
48(21):2313–2329
Emanuel KA, Zivkovic-Rothman M (1999) Development and evaluation of a convection scheme for use in
climate models. J Atmos Sci 56:1766–1782
Haynes JM, L’Ecuyer TS, Stephens GL, Miller SD, Mitrescu C, Wood NB, Tanelli S (2009) Rainfall
retrieval over the ocean with spaceborne W-band radar. J Geophys Res Atmos 114(D8):n/a–n/a
Hohenegger C, Stevens B (2016) Coupled radiative convective equilibrium simulations with explicit andparameterized convection. J Adv Model Earth Syst 8(3):1468–1482
Holloway CE, Neelin JD (2009) Moisture vertical structure, column water vapor, and tropical deep convection. J Atmos Sci 66(6):1665–1683
Hou AY, Kakar RK, Neeck S, Azarbarzin AA, Kummerow CD, Kojima M, Oki R, Nakamura K, Iguchi T(2013) The global precipitation measurement mission. Bull Am Meteorol Soc 95(5):701–722
Kato S, Xu KM, Wong T, Loeb NG, Rose FG, Trenberth KE, Thorsen TJ (2016) Investigation of theresidual in column-integrated atmospheric energy balance using cloud objects. J Clim
29(20):7435–7452
Kubar TL, Hartmann DL, Wood R (2009) Understanding the importance of microphysics and macrophysics
for warm rain in marine low clouds. Part I: satellite observations. J Atmos Sci 66(10):2953–2972
Larson K, Hartmann DL, Klein SA (1999) The role of clouds, water vapor, circulation, and boundary layer
structure in the sensitivity of the tropical climate. J Clim 12(8 PART 1):2359–2374. doi:10.1175/15200442(1999)012\2359:TROCWV[2.0.CO;2123

Surv Geophys (2017) 38:1257–1282

1281

Lebsock MD, L’Ecuyer TS (2011) The retrieval of warm rain from CloudSat. J Geophys Res Atmos. doi:10.
1029/2010JD015415
Li Z, Zuidema P, Zhu P, Morrison H (2015) The sensitivity of simulated shallow cumulus convection andcold pools to microphysics. J Atmos Sci 72(9):3340–3355
Lonitz K, Stevens B, Nuijens L, Sant V, Hirsch L, Seifert A (2015) The signature of aerosols and meteorology in long-term cloud radar observations of trade wind cumuli. J Atmos Sci 72(12):4643–4659
Masunaga H (2013) A satellite study of tropical moist convection and environmental variability: a moistureand thermal budget analysis. J Atmos Sci 70(8):2443–2466
Masunaga H, L’Ecuyer TS (2014) A mechanism of tropical convection inferred from observed variability inthe moist static energy budget. J Atmos Sci 71(10):3747–3766
Mauritsen T, Stevens B, Roeckner E, Crueger T, Esch M, Giorgetta M, Haak H, Jungclaus J, Klocke D,
Matei D, Mikolajewicz U, Notz D, Pincus R, Schmidt H, Tomassini L (2012) Tuning the climate of a
global model. J Adv Model Earth Syst. doi:10.1029/2012MS000154
Miller RL (1997) Tropical thermostats and low cloud cover. J Clim 10(3):409–440. doi:10.1175/15200442(1997)010\0409:TTALCC[2.0.CO;2
Morcrette JJ (1991) Radiation and cloud radiative properties in the European Centre for medium range
weather forecasts forecasting system. J Geophys Res Atmos 96(D5):9121–9132
Muller CJ, Held IM (2012) Detailed investigation of the self-aggregation of convection in cloud-resolving
simulations. J Atmos Sci 69(8):2551–2565
Neggers RAJ, Neelin JD, Stevens B (2007) Impact mechanisms of shallow cumulus convection on tropicalclimate dynamics. J Clim 20(11):2623–2642
Nelson EL, L’Ecuyer TS, Saleeby SM, Berg W, Herbener SR, van den Heever SC (2016) Toward analgorithm for estimating latent heat release in warm rain systems. J Atmos Ocean Technol
33(6):1309–1329
Nilsson J, Emanuel K (1999) Equilibrium atmospheres of a two-column radiative–convective model. Q J R
Meteorol Soc 125:2239–2264
Nuijens L, Stevens B, Siebesma aP (2009) The environment of precipitating shallow cumulus convection.
J Atmos Sci 66(7):1962–1979
Nuijens L, Serikov I, Hirsch L, Lonitz K, Stevens B (2014) The distribution and variability of low-levelcloud in the North-Atlantic trades. QJRMS 140:2364–2374
Nuijens L, Medeiros B, Sandu I, Ahlgrimm M (2015) Observed and modeled patterns of covariability
between low-level cloudiness and the structure of the trade-wind layer. J Adv Model Earth Syst
7(4):1741–1764
Peters ME, Bretherton CS (2005) A simplified model of the Walker circulation with an interactive ocean
mixed layer and cloud-radiative feedbacks. J Clim 18(20):4216–4234
Pierrehumbert RT (1995) Thermostats, radiator fins, and the local runaway greenhouse. J Atmos Sci
52(10):1784–1806. doi:10.1175/1520-0469(1995)052\1784:TRFATL[2.0.CO;2Riehl H, Yeh TC, Malkus JS, la Seur NE (1951) The north-east trade of the Pacific Ocean. Q J R Meteorol
Soc 77(334):598–626
Schumacher C, Houze Ra (2003) Stratiform rain in the tropics as seen by the TRMM precipitation radar.
J Clim 16(11):1739–1756
Seifert A, Heus T (2013) Large-eddy simulation of organized precipitating trade wind cumulus clouds.
Atmos Chem Phys 13(11):5631–5645
Seifert A, Stevens B (2010) Microphysical scaling relations in a kinematic model of isolated shallow
cumulus clouds. J Atmos Sci 67(5):1575–1590
Seifert A, Heus T, Pincus R, Stevens B (2015) Large-eddy simulation of the transient and near-equilibrium
behavior of precipitating shallow convection. JAdv Model Earth Syst 7(4):1918–1937
Sherwood SC, Bony S, Dufresne JL (2014) Spread in model climate sensitivity traced to atmospheric
convective mixing. Nature 505(7481):37–42
Short DA, Nakamura K (2000) TRMM radar observations of shallow precipitation over the Tropical Oceans.
J Clim 13(23):4107–4124
Snodgrass ER, Di Girolamo L, Rauber RM (2009) Precipitation characteristics of trade wind clouds duringrico derived from radar, satellite, and aircraft measurements. J Appl Meteorol Climatol 48(3):464–483
Stephens GL, Li J, Wild M, Clayson CA, Loeb N, Kato S, L’Ecuyer T, Stackhouse PW, Lebsock M,
Andrews T (2012) An update on Earth’s energy balance in light of the latest global observations.
Nature Geosci 5(10):691–696
Stevens B, Seifert A (2008) Understanding macrophysical outcomes of microphysical choices in simulationsof shallow cumulus convection. J Meteorol Soc Jpn Ser II 86A:143–162
Stevens B, Vali G, Comstock K, Wood R, Zanten MCV, Austin PH, Bretherton CS, Lenschow DH (2005)
Pockets of open cells and drizzle in marine stratocumulus. Bull Am Meteorol Soc 86(1):51–57

123

1282

Surv Geophys (2017) 38:1257–1282

Stevens B, Brogniez H, Kiemle C, Lacour J-L, Crevoisier C, Kiliani J (2017) Structure and dynamical
influence of water vapor in the lower tropical troposphere. Surv Geophys. doi:10.1007/s10712-0179420-8
Sun DZ, Liu Z (1996) Dynamic ocean–atmosphere coupling: a thermostat for the tropics. Science272(5265):1148–1150
Takayabu YN, Shige S, Tao WK, Hirota N (2010) Shallow and deep latent heating modes over Tropical
Oceans observed with TRMM PR spectral latent heating data. J Clim 23(8):2030–2046
Tompkins AM (2001) Organization of tropical convection in low vertical wind shears: the role of cold pools.
J Atmos Sci 58(13):1650–1672
VanZanten MC, Stevens B, Nuijens L, Siebesma AP, Ackerman AS, Burnet F, Cheng A, Couvreux F, Jiang
H, Khairoutdinov M, Kogan Y, Lewellen DC, Mechem D, Nakamura K, Noda A, Shipway BJ,
Slawinska J, Wang S, Wyszogrodzki A (2011) Controls on precipitation and cloudiness in simulationsof trade-wind cumulus as observed during RICO. J Adv Model Earth Syst 3(2):M06,001
Vogel R, Nuijens L, Stevens B (2016) The role of precipitation and spatial organization in the response of
trade-wind clouds to warming. J Adv Model Earth Syst 8(2):843–862
Wing AA, Emanuel KA (2014) Physical mechanisms controlling self-aggregation of convection in idealized
numerical modeling simulations. J Adv Model Earth Syst 6(1):59–74
Wood R, Comstock KK, Bretherton CS, Cornish C, Tomlinson J, Collins DR, Fairall C (2008) Open cellular
structure in marine stratocumulus sheets. J Geophys Res Atmos. doi:10.1029/2007JD009371
Xue H, Feingold G (2006) Large-eddy simulations of trade wind cumuli: investigation of aerosol indirect
effects. J Atmos Sci 63(6):1605–1622
Zuidema P, Li Z, Hill RJ, Bariteau L, Rilling B, Fairall C, Brewer WA, Albrecht B, Hare J (2012) On tradewind cumulus cold pools. J Atmos Sci 69(1):258–280

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