Surv Geophys (2017) 38:1199–1236
https://doi.org/10.1007/s10712-017-9419-1

Observing Convective Aggregation
Christopher E. Holloway1 • Allison A. Wing2,3 •Sandrine Bony4 • Caroline Muller5 • Hirohiko Masunaga6 •Tristan S. L’Ecuyer7 • David D. Turner8 • Paquita Zuidema9

Received: 23 November 2016 / Accepted: 14 June 2017 / Published online: 28 June 2017 The Author(s) 2017. This article is an open access publication

Abstract Convective self-aggregation, the spontaneous organization of initially scatteredconvection into isolated convective clusters despite spatially homogeneous boundary
conditions and forcing, was first recognized and studied in idealized numerical simulations.
While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to lookspecifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We
acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and meanstate extremes, but we argue that these differences vary greatly across the diverse range of& Christopher E. Holloway
c.e.holloway@reading.ac.uk
1

Department of Meteorology, University of Reading, Reading RG6 6BB, UK

2

Lamont-Doherty Earth Observatory, Columbia University, PO Box 1000, 61 Route 9W, Palisades,
NY 10964-1000, USA

3

Department of Earth, Ocean and Atmospheric Science, Florida State University,
Mail Code 4520, PO Box 3064520, Tallahassee, FL 32306-4520, USA

4

Sorbonne University, LMD/IPSL, CNRS, Univ Paris 06, mailbox 99, 4 Place Jussieu,
75252 Paris cedex 05, France

5

LMD/IPSL, CNRS, École Normale Supérieure, Paris Sciences Et Lettres, 24 rue Lhomond,
75230 Paris cedex 05, France

6

Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-ku,
Nagoya 464-8601, Japan

7

Department of Atmospheric and Oceanic Sciences, University of Wisconsin-Madison, 1225 West
Dayton Street, Madison, WI 53706, USA

8

NOAA/Earth System Research Laboratory, Global Systems Division, 325 Broadway, Boulder,
CO 80305-3337, USA

9

Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker
Causeway, Miami, FL 33149, USA

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model simulations in the literature and that these comparisons are already offering
important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry
has too broad distribution of humidity and is too dry in the driest regions when comparedwith radiosonde records from Nauru, while an elongated channel simulation has realistic
representations of atmospheric humidity and its variability. We discuss recent work
increasing our understanding of how organized convection and climate change mayinteract, and how model discrepancies related to this question are prompting interest inobservational comparisons. We also propose possible future directions for observational
work related to convective aggregation, including novel satellite approaches and a groundbased observational network.
Keywords Self-aggregation  Tropical convection  Convective organization  Climate
sensitivity  Cloud feedback

1 Introduction
From the very first studies describing convective self-aggregation (e.g., Held et al. 1993;
Tompkins 2001; Bretherton et al. 2005), the spontaneous clustering of convection, cloud,and moisture in idealized numerical simulations of radiative–convective equilibrium(RCE) despite homogeneous initial conditions, boundary conditions, and forcing (cf. Wing
et al. 2017), there has been a recurring question: Is this ‘‘real’’? In other words, is theintriguing clumping behavior representative of actual convective organization in nature, oris it just a model artifact? And, to the extent that the behavior is relevant for understanding
real atmospheric convection, what does it tell us about the role of convective organization
in weather and climate?
Here we argue that this behavior in models does appear to be relevant to real-world
convection and climate. Certainly, the study of convective self-aggregation is leading to
exciting new insights into processes that allow convection to interact with its environment
in models. There are encouraging signs that these processes may operate in nature too, as
we discuss below. There are also some aspects of self-aggregation in models that conflictwith observations, and many aspects that need more observational study.
This paper is organized as follows. In the remainder of this section, we motivate thestudy of aggregation as a means of understanding real-world climate and review theliterature on observations of organized convection and convective aggregation. Section 2
presents a fairly brief review of processes important for self-aggregation and the maintenance of aggregated convection in idealized simulations, with a focus on aspects of theseprocesses that could be targeted in observational studies. We then discuss observational
pathways toward assessing the relevance of the idealized framework for real-world
applications, including some new results comparing humidity profiles from radiosondes
with humidity profiles from idealized self-aggregation, in Sect. 3. Section 4 provides
observational perspectives on the possible interaction between convective aggregation andclimate change, while Sect. 5 proposes novel approaches to observing convective aggregation, including ideas for new satellite studies and ground-based networks; this is followed by our conclusions.

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Fig. 1 A visible satellite image showing an active Madden–Julian Oscillation (MJO) event on 8 April 2009
and convection organized over a wide range of scales. Image taken from the NERC Satellite Receiving
Station, Dundee University, Scotland http://www.sat.dundee.ac.uk/

1.1 Importance of Aggregation
Convective clouds exhibit a very large diversity of spatial organization, ranging fromspatially random distributions to coherent structures such as mesoscale cloud clusters,
cloud streets, and squall lines up to cloud envelopes of planetary scale (Fig. 1). For many
decades, studies of convective organization have been developed by mesoscale meteorologists and weather forecasters, motivated by the wish to understand why convection
would organize in one form rather than another, and by the evidence that the organizationof convection matters for the prediction of severe weather. Over the last decade, however,
the ability to study the organization of convection with models running at increasingly fineresolution over increasingly large domains has led to new perspectives and to a new line ofquestioning: Does it make any difference for climate whether convection organizes in one
form or another?
It has long been recognized that convective organization influences the diabatic heating
profile of the atmosphere and thus affects the mean large-scale atmospheric circulation(e.g., Hartmann et al. 1984). More recent numerical studies show that the clumping of
convection can occur spontaneously even in the absence of external drivers such as
inhomogeneous surface boundary conditions or equatorial wave dynamics (e.g., Held et al.
1993; Bretherton et al. 2005; Muller and Held 2012; Wing and Emanuel 2014) and that thisbehavior, referred to as convective self-aggregation, may be considered as a fundamental
instability of radiative–convective equilibrium (Emanuel et al. 2014). Could tropicalphenomena such as tropical cyclones or Madden–Julian Oscillation (MJO) events represent
manifestations of this self-aggregation behavior at different spatial scales (Khairoutdinov

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and Emanuel 2010, 2013; Arnold and Randall 2015)? Answering this question would
provide new opportunities to understand and to predict these phenomena through completely novel approaches.
Numerical studies of convective aggregation also show that the clumping of convection
is associated with changes in the large-scale state, including a drying of the atmosphere, ashrinking of upper-tropospheric clouds, and an enhanced ability of the atmosphere to lose
heat to space (e.g., Wing and Emanuel 2014; Wing and Cronin 2016; Holloway and
Woolnough 2016; Bony et al. 2016). Self-aggregation in numerical models also exhibits
some temperature dependence (Khairoutdinov and Emanuel 2010; Wing and Emanuel2014; Emanuel et al. 2014; Coppin and Bony 2015; Wing and Cronin 2016). The combination of these different findings implies that changes in convective organization could
occur under climate change, potentially affecting the water vapor and cloud feedbacks.
These numerical results shed new light on the role that convective aggregation might playin climate (Mapes 2016): Could a sensitivity of convective aggregation to temperature
modulate climate sensitivity and hydrological sensitivity (Khairoutdinov and Emanuel2010; Mauritsen and Stevens 2015; Bony et al. 2015)? In a warmer climate, could it play arole in the intensification of the MJO (Arnold and Randall 2015; Arnold et al. 2015) or in
the narrowing of tropical rain belts (Bony et al. 2016)?
Many of these exciting scientific questions primarily stem from numerical investigations. However, numerous studies (e.g., Stephens et al. 2008; Muller and Bony 2015; Wing
and Cronin 2016; Holloway and Woolnough 2016; Silvers et al. 2016; Tompkins andSemie 2017) demonstrate that the behavior of convective aggregation in models can besensitive to aspects of the experimental setup (such as the size of the domain) and/or to themodels themselves (e.g., horizontal resolution, the representation of diabatic processes or
the parameterization of subgrid-scale mixing).
To move forward, we must therefore expand our study of the aggregation of convection
using observations. We must probe links between processes in idealized self-aggregationand observed convective organization and also confront differences between idealized
frameworks and the real world. We first present a review of relevant literature below
before addressing these topics in the following sections.

1.2 Literature Review: Observational Studies of Convective Organization
There is a rich history of observational work on convective clustering and organization,much of which details the climatology and life cycles of these systems. The primary sourceof data for this observational work is infrared and visible images from geostationary
satellites, dating back to at least Arkin (1979) and encompassing Velasco and Fritsch(1987), Miller and Fritsch (1990), Laing and Fritsch (1993a, b), Machado and Rossow(1993), Mapes and Houze (1993), Laing and Fritsch (1997), Zuidema (2003), and Hennon
et al. (2012), but some more recent studies have also used other types of satellite data suchas precipitation radar (Nesbitt et al. 2000; Schumacher and Houze 2003; Futyan and Genio
2007; Peters et al. 2009), microwave measurements of column water vapor (CWV) (Mapes
et al. 2009), and scatterometer winds (Mapes et al. 2009). While cloud clusters are often
identified by searching for large, contiguous cold cloud shields, more advanced techniques
search for the combined signature of deep convection and extensive stratiform cloud andprecipitation area. For example, higher stratiform rain fractions are associated withorganized convection, which can be diagnosed from satellite precipitation radar data
(Schumacher and Houze 2003), as are large optical thicknesses and low-cloud top

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pressures, which can distinguish a particular cloud regime (Tselioudis et al. 2010; Tanet al. 2013).
A significant fraction of the observational work on organized convection has focused on
mesoscale convective systems (MCSs), or a subset of them known as mesoscale convective
complexes (MCCs), which occur in both the tropics and mid-latitudes. A global climatology of MCCs, which are identified by a large ([105 km2 ), long-lasting ([6 h), quasicircular cold cloud shield, was compiled by Laing and Fritsch (1997) based on previous
regional studies (Miller and Fritsch 1990; Laing and Fritsch 1993a, b; Velasco and Fritsch1987).
Other studies have detailed the properties of, more generally, tropical cloud clusters anddeep convective systems. This includes studies on the structural characteristics andradiative properties of tropical high cloud systems (Machado and Rossow 1993), the life
cycles of deep convective systems (Futyan and Genio 2007; Mapes et al. 2009), the size
distribution of cloud clusters (Mapes and Houze 1993; Roca and Ramanathan 2000;
Zuidema 2003; Peters et al. 2009), and the spatial and temporal variability in cloud clusters
and their efficiency at producing tropical cyclones (Hennon et al. 2012). Studies have also
pointed out significant self-similarity between MCSs and convectively coupled equatorial
waves (Mapes et al. 2006; Kiladis et al. 2009).
Despite the fact that the occurrence of mesoscale organized convection makes up asmall fraction of the total frequency of cloud/precipitation features in the tropics (\6%,Mapes and Houze 1993; Nesbitt et al. 2000; Tan et al. 2013), it contributes a significant
proportion of total tropical cloudiness1 and about half of total tropical precipitation.2
Tropical cloud clusters therefore may modulate the radiative heating of the surface andatmosphere (e.g., Machado and Rossow 1993) and strongly influence the large-scale circulation, moisture distribution, and hydrological cycle. There is observational evidence
that the frequency of organized convection has increased across the tropics over the past
 30 years (Tselioudis et al. 2010) and that most of the regional increases in tropicalprecipitation over that period are associated with this increase (Tan et al. 2015). In addition
to their contribution to tropical cloudiness and precipitation, tropical cloud clusters also
play an important role as precursors to tropical cyclones, with globally 6.4% of tropicalcloud clusters developing into tropical cyclones each year (Hennon et al. 2012).
Another observational finding which may be relevant to self-aggregation is the evidence
that tropical precipitation has properties like those of a critical phenomenon. Peters andNeelin (2006) found that there is a power law increase in precipitation with CWV above a
critical CWV value, and a sharp peak in the variance of precipitation at the critical value.
Holloway and Neelin (2009) further found that free-tropospheric moisture plays a key rolein the transition to deep convection and linked the increase in precipitation with CWV to
an increase in the buoyancy of entraining plumes, which relates to the proposed moisture–
convection feedback in self-aggregation. Neelin et al. (2009) also noted that the atmosphere is near criticality a larger fraction of the time when it is over warm sea surface
temperatures (SSTs). Peters et al. (2009) found that precipitation clusters exhibited scale1

Mapes and Houze (1993) found that half of the very cold cloudiness was contributed by cloud clusters
greater than 2  104 km2 in size and half of the moderately cold cloudiness was contributed by cloudclusters greater than 105 km2 in size. Mapes (1993) found that 43% of the total cold cloud coverage in thetropics was associated with large superclusters.
2

Tan et al. (2013) found that the cloud regime associated with organized convection contributes 45% of
total tropical rainfall. Nesbitt et al. (2000) found that precipitation features that include an MCS contribute
38–55% of total rainfall in various regions of the tropics.

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free size distributions including much larger clusters near-critical CWV than below it,suggesting a possible link between clustering within the moist convective regions in idealized self-aggregation and near-critical CWV values.
While the literature on observations of tropical cloud clusters is extensive (only a small
segment of which was reviewed here), only a few studies have specifically looked forprocesses related to modeled self-aggregation using observations. The first such paper,
Tobin et al. (2012), used geostationary satellite infrared brightness temperature in snapshots of large tropical latitude-longitude boxes (10  10 ) to categorize observations by
their degree of convective organization. To do this, they devised the Simple Convective
Aggregation Index (SCAI) as a combined measure of cluster number and inter-cluster
distance, with cluster pixels defined as having brightness temperature below 240 K andwith larger SCAI corresponding to a less aggregated state. They found that cluster number
was statistically sufficient to discriminate between different levels of aggregation, so theyoften used the number of clusters as a metric for the degree of aggregation, with fewer
clusters corresponding to a more aggregated state. By controlling for measures of boxmean convective intensity and large-scale forcing, including rainfall from microwave
satellite data, SST from infrared satellite data, and vertical velocity from reanalyses, they
could compare atmospheric conditions for varying amounts of convective organization in a
way that was analogous to comparing different stages of aggregation in idealized models.
Tobin et al. (2012) found several similarities between their observational analyses andidealized simulations of self-aggregation. Holding large-scale SST and rainfall constant,they found that more aggregated states had a drier free troposphere in the non-convective
environment and, consequently, in the domain as a whole. They also found an increase inoutgoing longwave radiation (OLR) at the top of the atmosphere (by as much as 30 W m2 )with aggregation (Fig. 2a), mainly because of a reduction of mid-level and upper levelcloudiness. These main conclusions, in agreement with all studies of idealized self-aggregation in models, were also supported by a related paper, Tobin et al. (2013), whichlooked at smaller (3  3 ) domains using higher-resolution satellite brightness

Fig. 2 a Composites over many 10  10 snapshots of domain-averaged OLR from CERES and NOAA
for two different average rain rates for different satellite-derived cluster numbers, with fewer clusters
representing more aggregated convection. b Similar analysis for 3  3 snapshots of domain-averaged freetropospheric humidity derived from Meteosat Tb in the WV channel, for three different average rain rates. c
Domain-averaged AIRS relative humidity composited on the same 3  3 snapshots as in b for three cluster
number bins for a precipitation rate of 8 mm day1 . Figures from Tobin et al. (2012) (panel a) and Tobin
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temperature data (Fig. 2b, c), as well as Stein et al. (2017), which analyzed the vertical
cloud structure for different SCAI values using CloudSat–CALIPSO data.
On the other hand, Tobin et al. (2012, 2013) found some results that were inconclusive,
mixed, or contradictory when compared with modeling studies. For instance, Tobin et al.
(2012) found that surface turbulent heat fluxes increased both inside and outside convective regions when aggregation increased, whereas Tobin et al. (2013) found little
sensitivity of these fluxes to aggregation at the smaller scales they investigated (although
this discrepancy could be due to limitations in satellite retrievals of surface fluxes). In
idealized simulations, surface fluxes generally increase with self-aggregation (e.g.,
Bretherton et al. 2005; Wing 2014; Holloway and Woolnough 2016), with the increase due
to larger wind speeds in general and larger air–sea enthalpy disequilibrium in the dry
environment (Wing and Emanuel 2014). (Note that this modest increase in surface fluxes
for idealized models is also consistent with slightly larger atmospheric radiative coolingrates and precipitation rates in radiative–convective equilibrium after aggregation has
occurred.) Tobin et al. (2012, 2013) also found that the top-of-atmosphere net radiationbudget was not significantly affected by aggregation because increased OLR was offset bydecreased reflected shortwave radiation. This differs from idealized simulations discussed
by Wing and Cronin (2016), in which an increase in low-cloud fraction with aggregation
left reflected shortwave largely unchanged, leading to a net loss of radiation at the top of
atmosphere for aggregated conditions. Tobin et al. (2013) and Stein et al. (2017) bothfound evidence for an increase in low-cloud fraction with aggregation, while Tobin et al.
(2012) found the opposite, so the models are supported by at least some observational
studies regarding low-cloud changes.
In the next section, we briefly review processes found to be important for self-aggregation in models with a focus on links to observed convective organization.

2 Observational Perspectives on Processes Important for Idealized
Convective Aggregation
There are longstanding attempts to reconcile the well-observed clumping of tropicalconvection with simple theory (e.g., Mapes 1993). Randall and Huffman (1980) proposedthat clumping occurs when clouds can create an area around themselves that is morefavorable for future convection than areas further away. Numerical studies of self-aggregation have identified multiple processes involving convection–moisture–radiation feedbacks that are capable of doing exactly that. The diversity of processes that can lead toconvective aggregation may explain why it has been observed by multiple different
modeling groups using very different models, from high-resolution cloud-resolving models
to global climate models (GCMs) with parameterized convection. Additionally, different
feedbacks that lead to aggregation may be excited by different initial conditions.
We will mostly discuss self-aggregation in idealized settings: radiative convective
equilibrium (RCE) over constant uniform SST in non-rotating, three-dimensional, doubly
periodic square domains, though some rectangular and aquaplanet simulations will occasionally be discussed as well. It is worth noting that self-aggregation has been shown to berobust to the presence of rotation (Bretherton et al. 2005; Khairoutdinov and Emanuel2013; Bretherton and Khairoutdinov 2015; Davis 2015; Wing et al. 2016), vertical shear(Bretherton et al. 2005), diurnal cycle (Wing and Cronin 2016), two-dimensional or threedimensional settings (Held et al. 1993; Jeevanjee and Romps 2013), and an interactive

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ocean mixed layer (Bretherton et al. 2005; Hohenegger and Stevens 2016), and to occur aswell in global climate simulations with parameterized convection in aquaplanet non-rotating settings (Coppin and Bony 2015; Popke et al. 2013; Reed et al. 2015).
In this section, we briefly review the various processes leading to the self-aggregation of
convection in RCE simulations and the metrics used to quantify them, including thephysical processes that lead to aggregation from homogeneous initial conditions as well as
those which can maintain convective aggregation once it is established. We focus on thosewhich could be targeted in observations; a more complete review can be found in Wing
et al. (2017).

2.1 Metrics to Quantify Feedbacks
Several methods have been proposed to analyze the leading order feedbacks in simulations(and also possibly in observations). They all share the methodology of stratifying the data
by vertically integrated moist static energy (MSE). In the tropics, weak temperature gradients imply that horizontal variability of MSE is largely dictated by variability in CWV.
Using this methodology, different variables can be moisture-ranked.
Wing and Emanuel (2014) introduced an analysis framework employing a budget forthe spatial variance of MSE. Self-aggregation is associated with a very strong increase in
MSE variance. The equation for the time evolution of MSE variance allows one to estimate
the various contributions to the enhanced MSE variability. The terms of this budget include
the horizontal convergence or divergence of MSE, as well as the direct diabatic contributions from radiative and surface fluxes, i.e., whether a heating/moistening diabatic
tendency reinforces (positive feedback) or smoothes (negative feedback) MSE gradients.
The potential use of observations to calculate the diabatic terms in the MSE spatial
variance budget is discussed more in Sect. 2.4.
Note that these diabatic terms include the direct diabatic effects of radiative and surface
flux feedbacks, not the circulation that the diabatic terms generate. For instance a positive
shortwave (SW) feedback means anomalous SW heating in the high-MSE region and/or
anomalous SW cooling in the low-MSE region, thereby enhancing the MSE gradient. The
diabatic feedback term does not account for the dynamical response to this SW heating
distribution, which can also transport MSE up- or down-gradient. This transport is acomponent of the horizontal convergence term, but is not explicitly diagnosed separatelyfrom the other dynamical contributions in this framework. Another related issue is thatthese diagnostics are based on vertical integrals and hence do not explicitly capture thesensitivity to the vertical distribution of diabatic forcings found in Muller and Bony (2015).
Indeed diabatic tendencies applied at different heights can yield different MSE transports
since MSE varies strongly with height.
An assessment of both the direct diabatic effect and the indirect circulation and MSEtransport corresponding to a heating anomaly is achieved in model simulations with sensitivity runs in which diabatic terms are horizontally homogenized, removing both direct
and indirect effects, as done in Muller and Held (2012). This is obviously not possible withobservations. The remaining option is to analyze the circulation generated by diabatic
forcing and infer the MSE transport as done in Holloway and Woolnough (2016). The
visualization of the MSE transport is usually done with a stream function in moisture andheight space (Bretherton et al. 2005; Muller and Held 2012; Holloway and Woolnough2016). This quantifies the energy transport between the dry region and the moist region andhence determines whether it is up-gradient, which is typical of aggregation in idealized
model studies (e.g., Bretherton et al. 2005; Muller and Held 2012) though the total

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vertically integrated transport is not always up-gradient (e.g., Coppin and Bony 2015). Thisvisualization method is useful in simulations, where vertical profiles of vertical velocity as
a function of MSE are available, but it is not clear whether it is applicable to observations.
Also, quantifying the role played by radiation in the circulation requires vertical profiles ofradiation as a function of MSE (cf. Muller and Bony 2015), which are only beginning tobecome available in observations (e.g., Haynes et al. 2013). Section 5.3 explores possible
approaches to observing these profiles using ground-based instruments.
Bretherton et al. (2005) showed that they could capture the aggregation instability in asemiempirical toy model accounting for the sensitivity of radiative and surface fluxes, aswell as MSE convergence, to humidity. In their theoretical paper of convective aggregation, Craig and Mack (2013) take a somewhat similar approach, although the physicalprocesses are modeled differently (in particular the MSE convergence is modeled as adiffusive process). The end result is an expression of the rate of change of humidity as afunction of humidity itself oI=ot ¼ f ðIÞ ¼ dV=dI þ T, where I is the order parameter (inthis case column-integrated free-tropospheric water vapor), V(I) is a potential function, andT is a diffusive transport term. The minima of the functional V(I) are equilibrium values ofhumidity. The structure of the functional V(I) therefore highlights the appearance ofmultiple equilibria typical of self-aggregation, with the two minima corresponding to themoist and dry solutions. Although this framework allows for the identification of aggregation, it is unclear if it can be used to identify feedbacks involved in the aggregation
process. Aggregation from different feedbacks may have different signatures in thefunctional dependence V(I).
More work using theory, as well as idealized (and perhaps more realistic) simulations, isdesirable to compare conceptual frameworks and metrics of aggregation and determine
how these could be applied to observations.

2.2 Initiation Processes
At SSTs close to our current tropical climate (300 K or so), the leading physical process
behind the spontaneous self-aggregation of convection seems to be a ‘‘radiatively driven
cold pool’’ outside deep convection, as seen in a schematic from Coppin and Bony (2015)(Fig. 3). One or several dry regions appear and expand, with strong longwave radiative
cooling and subsidence yielding further drying. Moisture and convection are confined to
the rest of the domain, as the dry convection-free region expands. In the following, we
briefly review the various physical processes contributing to the formation of this radiatively driven cold pool for temperatures close to current tropical atmospheric temperatures,

Fig. 3 Aggregation processes for: (left) cold SSTs with radiatively driven cold pools, and (right) warm
SSTs with surface flux feedbacks. Figure adapted from Coppin and Bony (2015)

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and then we discuss the sensitivity of these processes to SST. A more complete review canbe found in Wing et al. (2017).

2.2.1 Longwave Radiation
As mentioned above, aggregation generally begins with the formation of a dry region withstrong radiative cooling. The strong longwave cooling in the dry region is largely induced
by low-level clouds (Muller and Held 2012; Muller and Bony 2015; Coppin and Bony
2015; Holloway and Woolnough 2016), although clear-sky cooling also contributes (Wingand Emanuel 2014; Wing and Cronin 2016).
Strong subsidence in dry regions, theoretically predicted by the RCE instability study ofEmanuel et al. (2014), further promotes the formation of low-level clouds. These in turnenhance the radiative cooling, forming radiatively driven cold pools in dry regions
responsible for the clumping of convection in the rest of the domain. Note that theseradiatively driven cold pools are colocated with the dry regions and therefore do not mix
boundary layer air between moist and dry regions, whereas ‘‘conventional cold pools’’(defined here as cold pools resulting from downdrafts caused by rain evaporation and/or
condensate loading) can propagate from moist to dry regions and tend to slow or weaken
aggregation (cf. Jeevanjee and Romps 2013).

2.2.2 Surface Fluxes
Feedbacks involving surface enthalpy fluxes favor the initiation of self-aggregation due tolarger surface winds in the moist, convecting area, which enhance the up-gradient MSE
transport associated with the radiatively driven cold pool discussed above. However, whilesensitivity runs with homogenized surface fluxes (no feedback) sometimes do not aggregate (Tompkins and Craig 1998; Bretherton et al. 2005; Wing 2014), they can aggregate
depending on the domain size, strength of the surface fluxes imposed, and availability ofradiative feedbacks (Muller and Held 2012; Holloway and Woolnough 2016). Therefore,
surface fluxes feedbacks are not critical for aggregation to occur, at least at current
temperatures.

2.2.3 Shortwave Radiation
The direct, diabatic effect of shortwave radiation is a positive feedback on aggregation due
to variations in the absorption of shortwave radiation by water vapor (Wing and Emanuel2014), but it is weaker than the longwave and surface flux feedbacks. In sensitivity
experiments that include both direct and indirect (dynamic response to the diabatic forcing)effects, shortwave feedbacks slightly oppose aggregation. Either way, the impact ofshortwave radiation appears to be secondary, at least at current temperatures.

2.2.4 Moisture–Convection Feedbacks
Moisture–convection feedbacks, in which convection moistens the atmosphere and is also
more likely to occur in moister conditions, amplify the instabilities leading to self-aggregation (Tompkins 2001; Mapes and Neale 2011; Emanuel et al. 2014). When radiation
feedbacks (which are normally required for self-aggregation) are suppressed while rain
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weaken aggregation), these moisture–convection feedbacks are strong enough to cause
aggregation on their own (Muller and Bony 2015; Holloway and Woolnough 2016). Thisappears to occur through a process similar to the coarsening process in Craig and Mack
(2013) in which initial perturbations of a bistable system grow over time. These feedbacks
are difficult to quantify directly, even in models, and they would also be difficult to target
in observations. A place to start (perhaps using field campaign data) would be to correlate
convective activity with moist (high MSE) locations and then to estimate the transport ofMSE (part of the convergence term in the MSE spatial variance budget) due to circulations
forced by this anomalous convective heating.

2.3 Sensitivity to SST
Several aspects of self-aggregation are sensitive to SST, such as its initiation mechanisms,
spatial scale, and perhaps degree of organization (Khairoutdinov and Emanuel 2010; Wing
and Emanuel 2014; Emanuel et al. 2014; Wing and Cronin 2016; Coppin and Bony 2015;
Abbot 2014; Holloway and Woolnough 2016). It is worth noting that self-aggregation isfound at temperatures much colder than our current climate, including 243 K in snowball
Earth simulations (Abbot 2014) and 280 K in long-channel experiments (Wing and Cronin2016), as well as much warmer (e.g., 310 K, Wing and Cronin 2016). The radiatively
driven cold pools discussed above seem to be most efficient at cold and current temperatures (Fig. 1, Coppin and Bony 2015), possibly because climate models with strong
positive low-cloud feedback (like the model used in that study) do not have any low clouds
at high temperatures. However, cloud radiative feedbacks may behave differently at muchcolder temperatures (Wing and Cronin 2016) and clear-sky longwave feedbacks arefavored by warm temperatures (Emanuel et al. 2014). At warm temperatures, surface-fluxwind feedbacks in the high-MSE convective region are the leading mechanism for selfaggregation in GCM simulations (Fig. 1, Coppin and Bony 2015).
In their semiempirical model of self-aggregation based on cloud-permitting simulationsat present-day temperatures, Bretherton et al. (2005) found a slightly stronger sensitivity ofradiative fluxes to moisture than that of surface fluxes. These sensitivities are likely to bedifferent at different temperatures.

2.4 Maintenance Processes
Given that the real tropical atmosphere is never starting from a homogeneous backgroundstate, as in the idealized simulations, the processes that maintain existing convective
aggregation may be easier to observe than those initiating it. While the strongest positive
feedbacks in the early stages of idealized self-aggregation are usually found in the dry
region, at later times strong consistently positive feedbacks are found only in the moist
region. Muller and Held (2012) and Muller and Bony (2015), which find low clouds to benecessary for the initiation of aggregation using mechanism denial experiments, find that
low clouds are not necessary to maintain self-aggregation in their simulations. Instead,high clouds in the moist regions and clear-sky longwave feedbacks can maintain aggregation (Muller and Held 2012; Wing and Emanuel 2014; Muller and Bony 2015; Wing andCronin 2016). Possible sensitivity of these maintenance processes to SST is discussed in
Sect. 4 below.
Surface flux feedbacks are neither necessary nor sufficient to maintain non-rotating
aggregation (Holloway and Woolnough 2016), at least at current climate temperatures.
Indeed, the surface flux feedback becomes negative in later stages of non-rotating

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aggregation, due to the opposing influences of surface winds and air–sea enthalpy disequilibrium (Wing and Emanuel 2014). However, surface flux feedbacks could behave
differently in simulations with an interactive SST calculated from surface energy balance.
Quantifying the strength of these maintenance feedbacks in observations would bedesirable. As in the simulations discussed earlier, the radiative and surface flux feedbacks
could be diagnosed by their contributions to the MSE spatial variance budget. These
require simultaneous measurements over a large area of the top-of-atmosphere and surface
radiative fluxes, as well as observed surface enthalpy fluxes and vertically integrated MSE.
Alternatively, an MSE temporal variance budget could be computed at a given location,
assuming that with time, both the dry and moist regions of aggregated convection would
pass over the station. Methods for estimating quantities needed to calculate these terms
using satellite data are explored in Sect. 5.1. The strength of the radiative and surface flux
feedbacks could also be correlated with the degree of aggregation as measured by SCAI
(defined in Tobin et al. 2012). Tobin et al. (2013) used SCAI calculated from observations
to suggest that intraseasonal variations of aggregation tend to amplify dynamical
anomalies. Similarly, recent work compositing on MJO events during the DYNAMO field
campaign has shown that radiation and, to a lesser extent, surface heat fluxes play animportant role in amplifying MJO variability (Sobel et al. 2014), revealing potential links
to the aggregation work proposed here.

3 Comparing the Idealized World to the Natural WorldIn addition to process-oriented studies, observations can also be used to test the realism of
the mean state, variability, and convective characteristics of the idealized models. Here we
explore similarities and differences between these aspects of idealized simulations of selfaggregation and observations. We also discuss processes that are not usually captured byidealized models, such as ocean interaction. Linking self-aggregation processes to environments with further complexity, such as non-uniform SST or the effects of land andorography, is not addressed here but deserves future investigation. The motivation for thissection is that, in order to have confidence in the relevance of self-aggregation processes
found in idealized simulations for observed convective organization, we need to be able tounderstand and explain differences between the idealized world and the natural world.

3.1 Time Scales of Self-Aggregation
One common critique of idealized self-aggregation is that the time scale of the aggregation
process is much longer than typical time scales for observed convective organization. Thisis a valid concern, but there are several rebuttals which are discussed below. First, there is abroad range of time scales for self-aggregation and disaggregation in the literature, andthese appear to depend on model, domain size, resolution, initial conditions, SST, and theinclusion or suppression of processes such as conventional cold pools. Second, self-aggregation from homogeneous initial conditions includes the spin-up of small-scale convective activity and clustering without pre-existing large-scale features, and while we canlearn a lot from these early stages they are not likely to occur simultaneously across a large
region in the real world where asymmetries are always present. Third, while it is likely thatthe processes important for idealized self-aggregation are not important for all types of
convective organization in nature, and may be less important for rapidly organizing123Surv Geophys (2017) 38:1199–1236

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convective systems, some types of organized convection (particularly on longer timescales) do show intriguing links to self-aggregation.
As mentioned in Wing et al. (2017), self-aggregation in idealized models can take
15–100 days or more to reach a relatively stable aggregated state when starting fromhomogeneous initial conditions (though the longer time scales likely relate to an initial
gestation period in some simulations which occurs before aggregation has started at all).
There is some sensitivity of this to domain size and grid scale (Muller and Held 2012).
When rain evaporation and conventional cold pools were suppressed, Holloway and
Woolnough (2016) found that the time scale decreased to only 8 days as opposed to
16 days in their control run, supporting the idea proposed in Jeevanjee and Romps (2013)that conventional cold pools slow or suppress aggregation in idealized simulations. Perhaps
also relevant to understanding processes that keep convective clusters organized in nature,
Muller and Held (2012) and Holloway and Woolnough (2016) both found a disaggregation
time scale (which is the time needed to return to a less aggregated equilibrium) as small as
10 days when simulations were initialized with an aggregated state and then interactive
radiation was suppressed.
Wing (2014) found that the spatial MSE variance grew with an e-folding time of11–13 days. As mentioned in Wing et al. (2017), this kind of exponential growth willlead to much larger scales in a given amount of time when starting from larger initialclustering, as is typically found in nature. In other words, much of the time scale for selfaggregation from homogeneous initial conditions may not be especially relevant to comparisons with nature because these time periods involve spinning up mesoscale activity
from extremely small initial length scales (and may also involve gestation periods before
aggregation begins at all). In fact, convective cluster growth across scales (but especially atlarger scales) was found to be linked to radiative feedbacks in near-global RCE channel
runs (including rotation) in Bretherton and Khairoutdinov (2015), with e-folding timescales of 6–14 days. Those authors suggest that diabatic feedbacks (mainly longwave
radiation feedback) may be especially important for large-scale convective organizationsuch as the MJO.

3.2 Mean Wind and Wind Shear
Most idealized RCE studies have no imposed mean wind or wind shear. While wind shear
can act to enhance some kinds of mesoscale organization such as squall lines (e.g., Houze
2004; Muller 2013), it has also been shown to slow or prevent self-aggregation in idealized
simulations such as those in Bretherton et al. (2005) and Khairoutdinov and Emanuel(2010), although the latter found that there was hysteresis, since an already aggregatedstate did not disaggregate with some levels of imposed shear.
Nonzero mean vertical velocity due to large-scale circulations is common in regions
containing organized tropical systems in nature but cannot occur for the domain mean in a
typical RCE setup. Global-scale simulations, however, do represent these circulations (e.g.,
Coppin and Bony 2015), and smaller RCE simulations can impose them (e.g., Su et al.
2000) or parameterize them using reference profiles and assumptions of weak temperatureor pressure gradients (e.g., Sessions et al. 2016). As these kinds of modeling studies
progress, there will be more opportunities to evaluate their simulated relationships between
aggregation and large-scale circulations using observations.

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3.3 Humidity Profiles
One of the potentially unrealistic aspects of self-aggregation as seen in idealized models
that needs to be reconciled with observations is the presence of very dry humidity profiles
that occur in the non-convecting areas of the domain. Since humidity plays a key role in allof the feedbacks important for self-aggregation, it is especially important to investigate thisissue. To that end, we include here some examples of humidity profiles (and the related
radiative heating profiles) in moist and dry areas of simulated self-aggregation. These
profiles are from the simulations presented by Wing and Cronin (2016). We show profiles
from two simulations: one with a square domain that is 1536 km  1536 km in the horizontal (sq) and one that is an elongated channel with dimensions of 12,288 km  192 km
in the horizontal (ch). The sq simulation has one circular, intensely precipitating moist
cluster while the ch simulation has multiple moist and dry bands. All other aspects of thesimulations are identical.3 Fig. 4 shows water vapor mixing ratio and relative humidity inthe moist and dry areas, averaged over the last 10 days of the two simulations. In Fig. 4a,the ‘‘moist’’ area is defined as the area where the CWV is greater than 80% of the
maximum CWV found in the last 10 days of simulation. The rest of the domain is classified as the ‘‘dry’’ area. Profiles using an alternate definition of moist and dry areas areshown in Fig. 4b, in which the ‘‘dry’’ and ‘‘moist’’ areas are the driest 10% and moistest
10% of the domain according to CWV. Here, we show profiles from both the developing
and mature stage of aggregation, using 5-day averages centered at day 10 and day 70,
respectively. Figure 4c, d show similar plots to Fig. 4a, b but for relative humidity, withranking done according to column relative humidity (CRH, defined as CWV divided bycolumn-integrated saturation specific humidity) instead of CWV.
As shown in Fig. 4, the water vapor mixing ratio and relative humidity are substantiallyreduced in the dry regions relative to the moist regions at all levels (including the boundary
layer), but most strongly in the mid-troposphere. The difference between the dry and moist
regions is stronger for the sq simulation than the ch simulation, reflecting the more extreme(and arguably less realistic) aggregation that occurs in square domain simulations. There issignificantly more radiative cooling in the dry regions than the moist regions, especially inthe lower troposphere (Fig. 5), which further amplifies the anomalies.
These results naturally lead to several questions about how representative these idealized simulations are of humidity variability in the real tropics. The behavior of thehumidity profiles across the different evolutionary states of aggregation in the simulations(from developing to mature aggregation) is interesting; substantial drying is present in theupper troposphere as early as day 10, but drying of the middle–lower troposphere andboundary layer does not appear until later in the simulation (Fig. 4b, d). One potential
avenue of research to link this to observations is to relate the evolution of humidity in thedry regions and the stage of aggregation to the altitude depth of the bimodality of water
vapor (Mapes 2001, 2016; Zhang et al. 2003). However, a more basic starting point is todetermine whether humidity in the tropics exhibits a similar range of variability between
dry and moist conditions: do humidity profiles as dry as the ones in simulated aggregation
exist in the real tropics?

3

SST = 305 K, no rotation, diurnal cycle of insolation at 19.45 N at perpetual Julian day 80.5, Rapid
Radiative Transfer Model (RRTM) radiation scheme, 3 km horizontal resolution, 64 vertical levels, rigid lid
at 28 km, doubly periodic lateral boundaries, initialized with white noise in boundary layer temperaturefield.

123

Surv Geophys (2017) 38:1199–1236

1213(a) 100(b) 100
Moist; chDry; chMoist; sqDry; sq

200
300

300
400

P (hPa)400

P (hPa)Moist; ch; day 10
Dry; ch; day 10
Moist; ch; day 70
Dry; ch; day 70
Moist; sq; day 10
Dry; sq; day 10
Moist; sq; day 70
Dry; sq; day 70

200

500
600

500
600

700

700

800

800

900

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1000

1000
0

5

10

15

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25

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5

10

g/kg

200

200

300

300

400

400

P (hPa)(d)100P (hPa)(c) 100

500
600

800

800

900

900

1000

1000
0.4

25

0.6

0.8

1

600
700

0.2

20

500

700

0

15

g/kg

0.6

0.8

1

0

0.2

0.4

Fig. 4 Profiles of water vapor mixing ratio (top panels) and relative humidity (bottom panels) in
simulations in elongated channel (solid lines) and square (dashed lines) domains. The left panels definemoist regions (blue) as area where CWV  0:8 maxðCWVÞ [or CRH  0:8 maxðCRHÞ in panel c], dry
regions (red) defined as the rest of the domain; the profiles are averaged over the last 10 days of thesimulation. The right panels show profiles from the moistest (shades of blue) and driest (shades of red) 10%of the domain, according to CWV [or CRH in d]. Profiles from both the developing (5-day average centeredat day 10; lighter colors) and mature (5-day average centered at day 70; darker colors) stages of aggregation
are plotted. a q where CWV [/\ 0.8 max (CWV), b q in moistest/driest 10% of domain, c RH where CRH[/\ 0.8 max (CRH) and d RH where CRH [/\ 0.8 max (CRH)

As a first step toward answering this question, we compare the humidity data from theidealized simulations in Wing and Cronin (2016) to twice-daily radiosondes from Nauru in
the Pacific warm pool. Figure 6 shows humidity profiles from 5 years of the Nauru
radiosondes. These data span the period from April 1, 2001 to August 16, 2006 and arefrom the former Atmospheric Radiation Measurement (ARM) site (Mather et al. 1998;
Long et al. 2016). The data, which include 3491 retained sondes, are described in moredetail in Holloway and Neelin (2009). Figure 6a shows mean specific humidity profiles of
two subsets of sondes divided by a CWV threshold of 0.8 times the 99th percentile of
CWV (55 mm, the 63rd percentile). Despite coming from a range of SSTs which are
generally a few degrees cooler than 305 K, these profiles look quite similar to the mixing
ratio profiles from the ch simulation shown in Fig. 4a, while the sq simulation in that

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1214

(a) 100

Moist; chDry; chMoist; sqDry; sq

200
300
400

P (hPa)Fig. 5 Profiles of radiative
heating rate in simulations inelongated channel (solid lines)
and square (dashed lines)
domains. a Moist regions (blue)
as area where
CWV  0:8 maxðCWVÞ, dry
regions (red) defined as the restof the domain; the profiles areaveraged over the last 10 days ofthe simulation. b Profiles fromthe moistest (shades of blue) anddriest (shades of red) 10% of thedomain, according to CWV.
Profiles from both the developing(5-day average centered at day
10; lighter colors) and mature (5day average centered at day 70;
darker colors) stages ofaggregation are plotted. a Qrad
where CWV[/\0.8 max (CWV)
and b Qrad in moistest/driest 10%of domain

Surv Geophys (2017) 38:1199–1236

500
600
700
800
900
1000
-6

-4

-2

0

2

4

K/day

(b) 100
200
300

P (hPa)400
500

Moist; ch; day 10
Dry; ch; day 10
Moist; ch; day 70
Dry; ch; day 70
Moist; sq; day 10
Dry; sq; day 10
Moist; sq; day 70
Dry; sq; day 70

600
700
800
900
1000
-6

-4

-2

0

2

K/day

figure shows much more spread between moist and dry profiles. Similarly, the extreme
moistest 10% and driest 10% of sondes in Fig. 6b are much more similar to those for day
70 of the ch simulation than for day 70 of the sq simulation in Fig. 4b; indeed, the extreme
10% quantiles in the sq simulation at day 70 within the lower and middle free troposphere
are much more extreme than even the extreme 1% quantiles for the sondes. The driest 10%
quantile in the sq simulation at day 70 suggests that air is subsiding from the upper
troposphere down to almost 900 hPa without encountering significant moistening by
mixing or convection, something not seen in the observations.
Figure 6c, d shows similar analysis to Fig. 6a, b but for relative humidity (defined withrespect to ice for temperatures below 0 C) and CRH. Note that, even for the driest 1% ofsondes, relative humidity in the boundary layer is always above 65% on average. The
corresponding profiles for the simulations in Fig. 4c, d are consistent with the ch simulation being more realistic than the sq simulation, at least regarding humidity variability.
Note that the near-surface relative humidity averaged for the driest 10% of the domain in
the sq simulation at day 70 is about 10% drier (in relative humidity units) than the averagefor the driest 1% of sondes at Nauru.

123Surv Geophys (2017) 38:1199–1236

1215

Nauru sondes

(a)

(b)

100

100
CWV < (0.8 * 99th pctl CWV)CWV > (0.8 * 99th pctl CWV)

P (hPa)200

lowest 1% CWV
lowest 10% CWV
highest 10% CWV
highest 1% CWV

200

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0

5

10

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0

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q (g/kg)

15

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80

100

q (g/kg)(c)

P (hPa)

10

(d)

100

100

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500

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700

800

lo 1% CRH
lo 10% CRH
hi 10% CRH
hi 1% CRH

800

900

900

CRH < (0.8 * 99pl CRH)
CRH > (0.8 * 99pl CRH)

1000
0

20

40

60

RH (%)

1000
80

100

0

20

40

60

RH (%)

Fig. 6 Nauru radiosondes: a mean profiles of water vapor specific humidity (g kg1 ) for all sondes withCWV greater than 0.8 times the 99th percentile of CWV and for all sondes less than this threshold, b mean
profiles for all sondes in the lowest 1%, lowest 10%, highest 10%, and highest 1% as ranked by CWV,c mean profiles of relative humidity (%) for all sondes with CRH greater than 0.8 times the 99th percentileof CRH and for all sondes less than this threshold, and d mean profiles of relative humidity for all sondes in
the lowest 1%, lowest 10%, highest 10%, and highest 1% as ranked by CRH

Table 1 compares surface observations of relative humidity at Nauru with relative
humidity at the lowest model level (37 m) in the ch simulation from Wing and Cronin(2016). The values for most of the percentiles are comparable, except the simulation has amuch lower minimum value than the Nauru observations (32.5% compared to 52.0%).
Figure 7 shows contour plots of all 3491 sondes ranked by CRH and divided into 100
equally populated bins. These show both relative humidity and saturation deficit (saturation
specific humidity minus specific humidity). A similar plot for the ch simulation from Wing
and Cronin (2016) is shown in Fig. 8, and Fig. 7d can be additionally compared with asimilar figure from day 90 of the square simulation at 305 K SST in Wing and Emanuel(2014, their Fig. 11). That figure shows that the square simulation has a large spread in
relative humidity between 1 and 2 km height of about 100% between moist and dry

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Table 1 Values of surface relative humidity (%) at Nauru (averaged from station data over 1 h centeredaround on each sonde launch time) and lowest model level (37 m) relative humidity (%) in the 305 K
Channel simulation from Wing and Cronin (2016)
Percentile

Nauru

Channel simulation

Minimum

52.0

32.5

1st

57.9

58.6

25th

70.8

69.9

50th

76.8

73.5

75th

82.3

77.5

99th

92.8

93.0

The statistics from the channel simulation are computed over the final 25 days of that simulation

regions, while the Nauru sondes show a spread of 60% at most in that layer and a muchlarger number of bins with small anomalies. The channel simulation (Fig. 8), on the other
hand, is much more comparable to the Nauru sondes, indicating that this simulation has
realistic humidity variability.
Radiosondes from other tropical locations, such as the Bay of Bengal and the eastern
tropical Pacific, also reveal significant variability in mid- and upper-tropospheric relative
humidity and little variation in boundary layer moisture (e.g., Zuidema et al. 2006; Zuidema and Mapes 2008), though these locations are subject to large-scale circulations thatcan bring remote influences from neighboring landmasses. Radiosondes from the equatorial Indian Ocean also demonstrate that most of the relative humidity variability is
contained within the middle troposphere (Johnson and Ciesielski 2013), where the signature of self-aggregation may be first detected (Mapes 2016).
There are reasons to expect that the Nauru sondes and tropical sondes from these otherlocations would not necessarily look exactly like idealized self-aggregation simulations (orindeed, would not be representative of tropical maritime observations more generally). For
instance, these sondes are generally launched from islands, which could have local effects
on convection, and transport of air from landmasses or higher latitudes could also cause
differences compared with idealized conditions. Additionally, we may not necessarily
think of idealized aggregated convection as something that would or should be representative of typical tropical conditions anyway.
However, since humidity variability is fundamentally linked to both the contributing
processes and large-scale impacts of self-aggregation, it is important to consider possible
reasons why the channel simulation appears to have more realistic humidity variability,
while the square simulation is too extreme. One possibility is that the channel simulation is‘‘getting the right answer for the wrong reason’’, for instance because its quasi-2D
geometry leads to a spurious strong wind shear similar to that found in 2D simulations in
Held et al. (1993). Although the channel simulation does have tropospheric along-channel
mean wind and vertical wind shear that are larger than values in the square simulation, thechannel values are of order 1 m s1 for both quantities, and this is not overly strong
compared with typical tropical mean values. The channel simulation is 192 km wide,
which allows for multiple convective systems and associated cold pools to exist andpropagate along the shorter dimension. Subsidence in the driest regions is actually stronger
in the channel simulation relative to the square simulation, though ascent in the moist
regions is weaker. While determining the reasons for the differences between the simulations is beyond the scope of this paper, it is likely that the channel simulation has more

123Surv Geophys (2017) 38:1199–1236

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P (hPa)Nauru sondes

(a)

(b)

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9.00

12.00

-5.00

P (hPa)saturation deficit (g/kg)

(d)

100

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Rank of sonde bin by CRH (low to high)
5

25

50

RH (%)

75

40

-2.50

60
0.00

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100

2.50

5.00

saturation deficit anom. (g/kg)

(c)

0

20

95

0

20

40

60

80

100

Rank of sonde bin by CRH (low to high)
-60

-30

0

30

60

RH anom. (%)

Fig. 7 Nauru radiosondes: a saturation deficit ðg kg1 Þ for all sondes ranked by CRH and averaged in 100
equally populated bins, b anomaly of each bin in a from the all-sonde mean saturation deficit at each level,c as in a but for relative humidity (%), and d as in c but for relative humidity

mixing and transport between convective and subsidence regions—animations (not shown)
reveal that boundaries between convective and subsidence regions are less stationary, andcloser to the center of subsidence regions, in the channel simulation.
While the above discussion does not definitively endorse one model domain geometry
over another, this type of analysis is informative in starting to address the extent to which
idealized aggregated convection is similar to organized convection in the real world, andwe hope that it helps frame future comparisons with other data. For instance, analysis
tracing air particles back to their time of last condensation within both a modeling

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Surv Geophys (2017) 38:1199–1236

P (hPa)Channel simulation

(a)

(b)

100

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0.00

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12.00

-5.00

P (hPa)saturation deficit (g/kg)

50

100

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150
0.00

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2.50

5.00

saturation deficit anom. (g/kg)

(c)

(d)

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0

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Rank of column by CRH (low to high)
5

25

50

75

RH (%)

0

50

100

150

200

250

Rank of column by CRH (low to high)
95

-60

-30

0

30

60

RH anom. (%)

Fig. 8 As in Fig. 7 but for channel simulation at 305 K from Wing and Cronin (2016). a Saturation deficit
ðg kg1 Þ for all sondes averaged over 192 km  48 km blocks and ranked by block-averaged CRH,
b anomaly of each block in a from the domain-mean saturation deficit at each level, c as in a but for relative
humidity (%), and d as in c but for relative humidity

construct and observations could be helpful (e.g., Pierrehumbert 1998), as well as aspectral analysis to determine if key time scales are matched within both.

3.4 Equatorial Wave Dynamics
Earth’s latitudinally varying rotational effects on large-scale horizontal motions result inequatorial wave dynamics which help shape tropical convective organization. For instance,
the MJO interacts with equatorially trapped moist Kelvin and Rossby waves, andthese dynamics are also important for the development of the Hadley Circulation, the123Surv Geophys (2017) 38:1199–1236

1219

inter-tropical convergence zone (ITCZ), and monsoons. While self-aggregation is generally defined not to include the effects of a latitudinally varying Coriolis parameter, a few
studies have looked for the processes that lead to self-aggregation in simulations that doinclude such effects. Bretherton and Khairoutdinov (2015) found that radiative feedbacks
were likely to be important mainly for large-scale convective organization in their nearglobal RCE channel runs. Arnold and Randall (2015) performed global aquaplanet simulations (using a superparameterization setup in which 2D CRMs are embedded in eachlarge-scale model grid cell) with uniform SST both with and without rotation and foundsimilarities in diabatic feedbacks between the self-aggregation in the non-rotating setup
and the MJO in the rotating setup. Holloway (2017) found that simulations of real nearequatorial case studies using a limited-area CRM setup also showed similarities to idealized self-aggregation, although the effects of suppressing interactive radiation were constrained by the imposed lateral boundary conditions. More studies are needed to probe
links between self-aggregation and convective organization that interacts with equatorial
wave dynamics.

3.5 Ocean Interaction and Feedback
Nearly all studies of self-aggregation have used atmosphere-only simulations. However,there are a few studies that have used coupled models, and they generally find that ocean
coupling slows or prevents self-aggregation. For instance, an interactive slab ocean
experiment slowed down self-aggregation in Bretherton et al. (2005), possibly because ofcloud shading. That experiment had a 60 W m2 imposed ocean cooling to represent largescale ocean or atmospheric transport, and after aggregation the SST cooled rapidly due toincreased longwave cooling. Khairoutdinov and Emanuel (2010) used a 2-m slab ocean but
homogenized the SST horizontally at each time step (thus removing effects like cloudshading) and also found that SST dropped after aggregation occurred. They noted hysteresis, since cooler SSTs could still maintain aggregation that had already been present but
could not sustain self-aggregation from homogeneous conditions. Popke et al. (2013)
performed global-tropics RCE runs using parameterized convection (with no rotation andhomogeneous solar forcing) coupled to a slab ocean and found that large convective
clusters formed along with transient SST anomalies. Reed et al. (2015) performed similar
global-tropics RCE runs and found that, although ocean coupling slows aggregationcompared to runs with fixed warm SSTs (302 K) in agreement with other studies, runs with
fixed cool SSTs (as low as 295 K) result in much less organization than runs with similar
SSTs and an interactive slab ocean, suggesting a possible link between ocean coupling andthe sensitivity of aggregation to SST.
Coppin and Bony (2017) also ran global-tropics RCE simulations without rotation andcoupled to a slab ocean and found that the coupled RCE system exhibits some internalvariability, arising from the interplay between SST, SST gradients and aggregation. The
time scale of this variability depends on the depth of the ocean mixed layer, and for a large
range of depths, it occurs at the interannual time scale, suggesting a possible link tointernal modes of variability in the real tropical ocean atmosphere system such as El NiñoSouthern Oscillation (ENSO). They also showed that, at this time scale, the relationshipbetween SST and aggregation could be very different from (or even opposite to) that foundin prescribed SST simulations or in coupled RCE simulations on long time scales.
Hohenegger and Stevens (2016) ran high-resolution coupled RCE runs (without
imposed ocean cooling, but with reduced solar insolation equivalent to that averaged over

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the full Earth rather than the tropics) and found that aggregation seemed to prevent a
runaway greenhouse effect, providing ‘‘radiator fins’’ to the idealized climate in the dry
subsiding regions analogous to the role of the subtropics proposed by Pierrehumbert(1995). They also found that slab oceans with small depths can slow or prevent selfaggregation, similar to studies mentioned above. This delay stems from the development of
SST gradients which cause a low-level circulation opposing the one that favors selfaggregation. Furthermore, Hohenegger and Stevens (2016) suggest that cloud feedbacks
and resulting aggregation and coupled equilibrium states are very different at high resolution using explicit convection versus similar runs using parameterized convection fromPopke et al. (2013), showing another example of model disagreement with regards to theseprocesses.
While atmosphere–ocean coupling has been extensively studied for large-scale tropicalconvective phenomena such as the MJO (cf. DeMott et al. 2015), observational work isneeded to explore the interactions between organized tropical convective systems and SST
or sea surface salinity across scales. Specifically, this analysis could look at processes
important for aggregation in idealized models.

4 Observational Perspectives on Aggregation in a Warming Climate
Several modeling studies suggest that convective aggregation depends on surface temperature, although the exact nature of this dependence remains uncertain. The initiation of
aggregation is found to occur more easily at certain temperatures (Coppin and Bony 2015),
particularly when considering a given domain size (Wing and Emanuel 2014). Once initiated, the clumping of aggregation in some studies tends to strengthen as the surface
temperature rises (Coppin and Bony 2015), though other studies find that the degree of
aggregation is relatively insensitive to SST (Wing and Cronin 2016; Holloway and
Woolnough 2016; Hohenegger and Stevens 2016). Several interpretations have been
proposed for the temperature dependence of the initiation mechanisms (Sect. 2.3). Some ofthem invoke the nonlinearity of the Clausius–Clapeyron relationship, the sensitivity of theclear-sky longwave radiative cooling of the atmospheric column to lower-troposphericlongwave opacity (Emanuel et al. 2014), or the sensitivity of the low-cloud cover totemperature (e.g., Coppin and Bony 2015; Wing and Cronin 2016; Holloway and Woolnough 2016), and these temperature dependences differ across models. On the other hand,
the interaction between temperature, high-cloud radiative effects, and dynamics has been
proposed by Bony et al. (2016) as a mechanism for stronger clumping of convection at theaggregated equilibrium state over warmer surfaces. That study argues that, owing to thedependence of static stability on temperature and pressure, as the climate warms anvil
clouds not only rise to a higher altitude but also shrink in horizontal area. This behavior,referred to as the ‘‘stability-iris’’ effect in Bony et al. (2016), concentrates the atmosphericcloud radiative effects of anvil clouds and enhances the horizontal gradients in atmosphericradiative cooling (enhancing the cooling in subsiding areas and reducing it in convective
areas), which could lead to enhanced convective aggregation.
Given the implications that a dependence of convective aggregation on temperature
may have for climate (Sect. 1.1), it is important to verify whether this dependence seen insome models is confirmed by observations. However, very few studies have investigatedthis issue so far. Long time series of convective aggregation indices have now been123

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produced (e.g., Tobin et al. 2012; Tan et al. 2015), but they have not been analyzed in thisperspective yet.
What has been investigated, on the other hand, is the temperature dependence of various
large-scale organized convective phenomena that share many characteristics with convective aggregation in idealized models. One of these is the MJO, which likely represents avery large-scale manifestation of convective aggregation in the tropics (Khairoutdinov andEmanuel 2010; Arnold and Randall 2015). There is modeling evidence that MJO activity
increases when the climate is warming (e.g., Caballero and Huber 2010; Arnold et al.
2015), though MJO-like behavior has been found even at temperatures as cold as 1  C(Pritchard and Yang 2016); this finding of increased MJO activity with increased SST inmodels is qualitatively consistent with observations that suggest linear increases in theintensity and number of MJO events over the last 50 years (Jones and Carvalho 2006).
Tropical cyclones likely constitute another spectacular manifestation of convective
aggregation. But unfortunately, no such consistency has yet been reached between theirmodeled and observed behavior with temperature. Idealized RCE simulations performed ina rotating framework suggest that the number of tropical cyclones decreases as surface
temperature rises, while their intensity and precipitation rate increases (Nolan et al. 2007;
Held and Zhao 2008; Khairoutdinov and Emanuel 2013). Climate projections made withgeneral circulation models also suggest such a tendency, although the relationship between
tropical cyclones and temperature very much depends on the metrics used for warming(Knutson et al. 2013). On the observational side, however, trends in tropical cyclones andtheir relationship to temperature remain elusive (Stocker et al. 2013). This is partly due tothe limited availability and quality of long-term historical records, but also to the large
number of global and regional factors that influence the occurrence and intensity of tropical
cyclones. In particular, it is difficult to disentangle a trend associated with global warmingfrom records which are either too short or associated with an insufficient geographicalsampling. Another source of complication stems from the fact that tropical cyclone activity
does not only depend on absolute surface temperature: it is also affected by factors such as
the temperature difference between the surface and the tropopause (Emanuel 1987), thelocal surface temperature relative to the tropical mean (Lin et al. 2015), the wind shear andmid-tropospheric humidity (Tang and Emanuel 2010), and the upper ocean stratification(Emanuel 2015), and these factors are strongly modulated by the decadal to multi-decadal
natural climate variability.
To confirm or refute modeling inferences regarding the temperature dependence of
convective aggregation, another approach consists of using observations to test the physical processes that contribute to this dependence in models. One such process is the
reduction of the anvil cloud amount as the climate warms (Bony et al. 2016). Someobservational studies suggest that, on average over the tropics, the anvil cloud amountdecreases as the surface temperature increases (Zelinka and Hartmann 2011; Igel et al.
2014) as shown in Fig. 9 reproduced from Igel et al. (2014), but other studies do not findstrong evidence for such a relationship (Stein et al. 2017). These differences may result
from methodological differences: in contrast with other studies, Stein et al. (2017) consider
the dependence of anvil cloud amounts on surface temperature for given precipitation andlarge-scale forcings, which amounts to comparing situations having a fairly similar convective mass flux, and therefore a weaker change in anvil cloud amount with temperature.
Also, Stein et al. (2017) and Igel et al. (2014) are only comparing local SSTs colocatedwith specific cloud scenes, whereas the reduction of anvil cloud amount with warming may
be more sensitive to the tropical mean SST, which is the metric used in Zelinka andHartmann (2011). And Igel et al. (2014) study anvil cloud per individual cloud object, not

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Fig. 9 Composites of anvil
cloud objects derived fromCloudSat observations: the widthof anvil clouds is found to
decrease as surface temperature
increases. From Igel et al. (2014)

total anvil fraction, but Stein et al. (2017) find that SCAI values increase with SST,
meaning that there are more (and smaller) anvil cloud clusters for warmer SSTs, which
could cancel out effects of smaller anvil size per cluster. Additional methodological differences may also contribute to these conflicting results, and they will have to be clarified.
More generally, several methodological issues complicate attempts to investigate therelationship between temperature and convective aggregation in observations. First, unlike
idealized modeling studies forced by uniform boundary conditions, the Earth’s climate is
associated with gradients in surface temperature which strongly influence large-scalevertical motions in the tropics. As is widely recognized, at the regional scale clouds andconvection are much more influenced by the large-scale atmospheric circulation than by
local surface temperature (Hartmann and Michelsen 1993; Bony et al. 1997). For thisreason, relationships between convective aggregation and surface temperature derived
from regional investigations do not necessarily reflect an intrinsic dependence of aggregation on temperature. Second, there is abundant evidence that the relationship between
temperature and water vapor or clouds can differ on short versus long time scales (e.g.,
Dessler 2010). Relationships inferred from observed climate variations on seasonal orinterannual time scales may thus differ from the temperature dependence of convective
aggregation on decadal time scales and under long-term climate change. Recent results
suggest that this might also be the case for coupled RCE simulations (Coppin and Bony2017), although the extent to which this result applies to other models remains unknown.
Finally, models suggest that convective aggregation can behave very differently in cold
and warm climates. For instance, Abbot (2014) predicted stronger convective aggregation
on a Snowball Earth than in the modern climate, but observations of clouds and convection

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are only available for a limited time period and thus for a very narrow range of surface
temperatures. To explore possible changes in convective aggregation in more drasticallydifferent ranges of temperature, one must consider paleoclimatic changes using proxy data.
Techniques of paleotempestology offer opportunities to reconstruct tropical cyclone
activity at different periods of the past and for a range of time scales (e.g., Liu and Fearn
2000; Donnelly and Woodruff 2007) and could be very useful for this purpose. The
isotopic composition of water is very sensitive to the organization of convection (e.g.,
Lawrence et al. 2004; Risi et al. 2008), and therefore long-term isotopic records (as well as
recent satellite observations of water isotopes) could be used to explore changes in convective organization with climate.

5 Future Observational Aspirations
Much remains to be done in terms of observing convective aggregation. Using satellite
observations, the variability of aggregation at different time scales could be investigated, as
well as its relationship to local and remote surface and atmospheric conditions. Besides
this, it would be nice to investigate whether the physical mechanisms found to play a rolein the initiation of aggregation in models can also be observed in nature. For instance, isthere evidence for the formation of radiatively driven cold pools in the dry areas of thetropics? Will future space missions such as the ADM-Aeolus wind lidar mission (Reitebuch 2012) help observe the interplay between low clouds and shallow circulations in thevicinity of deep convection? Will they help us observe radiatively driven cold pools? Can
we observe signs of convective self-aggregation? To address these questions, one may
analyze observations from field experiments such as those collected during AMIE/DYNAMO in the Indian ocean (Feng et al. 2015) or in the tropical Atlantic as part of the
NARVAL-EUREC4 A campaigns (Stevens et al. 2015; Bony et al. this issue). One may
also think of organizing a field campaign specially dedicated to these questions.
The ISSI workshop in February 2016 on ‘‘Shallow clouds and water vapor, circulationand climate sensitivity’’ brought together scientists using numerical simulations to study
convective organization with scientists at the forefront of observational work, including
experts on remote sensing of clouds and their environment. In this section, we present
some perspectives on novel approaches to using satellite data to observe convective
aggregation and the processes discussed above. Another paper (Lebsock this issue) alsopresents some promising new work along these lines using CloudSat and other A-Trainsatellites, complementing work by Stein et al. (2017). We also propose another possible
way forward using a ground-based observational network.

5.1 Evolution of Convective Organization Using Satellite Data
The physical processes of convective self-aggregation involve a range of elements from the
dynamics of convective systems to the thermodynamics of their rain-free environment. In
this section, we review recent work with unique ideas of exploiting the existing satellite
capability to study precipitating cloud systems and the surrounding atmosphere. The
potential utility of such satellite observations in addressing different aspects of convective
self-aggregation is also discussed.
The variability in the large-scale atmospheric state associated with a life cycle ofconvective systems has been examined with a suite of satellite measurements by Masunaga

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Surv Geophys (2017) 38:1199–1236(2012) and several subsequent papers. Since the sporadic nature of low-Earth orbiting(LEO) satellite overpasses with high-inclination orbits makes it difficult to continuously
monitor subdaily scale variations, the variability is statistically reproduced by projecting alarge number of snapshots obtained from multiple LEO satellites onto a composite timeseries. For instance, temperature and humidity profiles from the Atmospheric InfraredSounder (AIRS) aboard the Aqua satellite are combined with the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) so that the evolution of the ambient
sounding is constructed over the hours before and after convection develops (Masunaga2012).
Masunaga (2013) applied water and heat budget analysis to this composite time series.
The moisture and MSE (denoted by h) budget equations integrated vertically over the
troposphere are:ohqi þ hr  qvi ¼ E  P
ot

ð1Þ

o
hhi þ hr  hvi ¼ S þ Lv E þ hQR i;
ot

ð2Þ

and

where h  i designates the vertical integral over the whole troposphere, the overbar denotes
horizontal averaging over a large-scale [O(100 km)] domain, q is specific humidity, v ishorizontal wind, E is surface evaporation, P is surface precipitation, S is surface sensible
heat flux, Lv is the latent heat of vaporization, and QR is the radiative heating rate. Eachterm on the rhs of (1) and (2) is available from satellite observations and the tendency termon the lhs is evaluated from the composite time series, leaving as the only unknowns thesecond term of (1) and (2), that is, the horizontal convergence of moisture and MSE
convergence. The vertically integrated moisture and MSE convergences, although notdirectly measurable from satellites, are instead derived as the residual in the budget
equations. Note that the quantities calculated for these equations could also be used to

(a)

(b)
moisture convergenceevaporation (LE)surface precipitation (LPs)

(c)

(d)
LE + SMSE convergence

QR <0

Q >0
R

Fig. 10 Satellite-derived moisture and MSE budget parameters in composite time series associated with thedevelopment and dissipation of convection. a Moisture convergence (shaded), surface precipitation (solidline), and surface evaporation (dotted line) for the organized system regime, b as in a but for the isolated
cumulus regime, c MSE convergence (light-shaded), radiative heating (heavy shaded; red where positiveand blue where negative) on the top of MSE convergence, surface heat flux (dotted line) for the organizedsystem regime. d As in c but for the isolated cumulus regime. All parameters including precipitation andevaporation are plotted in energy flux units ðW m2 Þ123

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calculate the diabatic terms of the MSE spatial variance budget from Wing and Emanuel(2014) as suggested in Sect. 2.4.
Figure 10 shows the composite evolution of different budget terms for both the ‘‘organized system’’ and ‘‘isolated cumulus’’ regimes. These two regimes are separated byapplying different thresholds to the areal coverage of TRMM-detected precipitation cells(i.e.,\25% for isolated cumuli and[50% for organized systems), aimed at delineating theelements of atmospheric thermodynamics that are favorable or unfavorable for convective
organization (Masunaga 2014). The primary moisture source of precipitation is moisture
convergence during hours around the peak convection in the organized system regime(Fig. 10a), while precipitation nearly balances out the local moisture supply from surface
evaporation in the isolated cumulus regime (Fig. 10b). In both the regimes, evaporation
stays almost constant over time at  100–150 W m2 , which suffices to produce modest
rainfall from isolated cumuli but needs to be supplemented by a large dynamically driven
import of moisture to feed organized systems.
The dynamics specific to organized convective systems is illustrated in light of the MSE
budget (Fig. 10c), where MSE convergence stays overall negative but nearly vanishes tozero as convection intensifies (discussed in detail by Masunaga and L’Ecuyer 2014). The
zero MSE convergence, or neutral gross moist stability (GMS), implies that the import ofmoisture is just large enough to drive the large-scale adiabatic ascent and hence allows aself-sustaining growth of convection (Masunaga 2014). In the isolated cumulus regime(Fig. 10d), MSE convergence vanishes as in the organized system regime but the enhanced
radiative cooling, owing to reduced high clouds, appears to work against the further growthof convection that could otherwise occur.
Note that the composite time series above are not to be interpreted as convective selfaggregation itself being in progress. Idealized simulations demonstrate that convective
self-aggregation proceeds over a week or two (Tompkins 2001) or a few months(Bretherton et al. 2005; Wing and Emanuel 2014), which is a time scale substantiallylonger than the life cycle of individual convective systems (a few days at most) as depicted
in Fig. 10. The isolated cumulus regime and organized system regime, if put into thecontext of self-aggregation, may be each a representation of the states before and after the
self-aggregation takes place (or outside and inside the area of aggregated convection).
From this perspective, the convective self-aggregation could be considered as a ‘‘phasetransition’’ from the isolated cumulus regime to the organized system regime. Figure 10c,d suggests that a key role in the transition, if it occurs, would be the magnitude of radiative
cooling, which is in line with idealized simulations (Muller and Bony 2015) and theories of
convective self-aggregation (Emanuel et al. 2014). This hypothesis may be tested byseparating the composite analysis among different degrees of convective aggregation
using, for example, SCAI (Tobin et al. 2012). With the other environmental conditions
such as SST being equal, a set of composite time series constructed with different SCAI
values would provide an observational test bed to examine the self-aggregation processes
in the context of moisture and thermal budgets. This would be an interesting line ofresearch to pursue in the future.

5.2 Spaceborne Cloud Radar Approaches
Novel analyses of newer satellite assets that have not traditionally been applied to study
convection may offer potential for advancing our understanding of the coupled radiativeand hydrological responses to convective aggregation. There is growing acceptance of the

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utility of spaceborne cloud radars, in particular, for characterizing the distribution, internal
structure, spatial organization, updraft intensity, and radiative environments of convection.
New methods for discriminating precipitating scenes, isolating convective cores, andprofiling radiative fluxes and heating rates both within cloud and in the adjacent cloud-freepixels are becoming sufficiently mature to shed new light on the coupled energy and water
cycle impacts of convective aggregation (Haynes et al. 2009; Lebsock and L’Ecuyer 2011;
Henderson et al. 2013; Matus and L’Ecuyer 2017).
Igel and Heever (2015), for example, used CloudSat observations to establish a quantitative link between the area of convective anvils and the associated convective cores.
Unlike previous studies that relied on coarser or less direct methods for identifying convective updrafts, the high sensitivity and relatively high spatial resolution of the CloudSat
Cloud Profiling Radar (CPR) provide an unambiguous means of discriminating precipitating and non-precipitating pixels with associated ice cloud area and vertical structurefrom a single sensor. Examining nearly 5 years of CloudSat observations over the tropicaloceans, Igel et al. (2014) and Igel and Heever (2015) demonstrate that anvil widths systematically decrease while anvil temperatures become colder with increasing SST, as
discussed in Sect. 4. In addition, the width of associated cloud object pedestals (the cloudshapes at the base of the anvils) decreases with increasing SST. These findings could beconsistent with a trend toward more aggregated convection over warmer oceans, though it
should be noted that, as discussed in Sect. 4, these studies look only at anvil size per cloud
object, not at total cloud area or how individual cloud objects are spatially distributed.
Furthermore, these studies do not explicitly control for precipitation intensity or divide
observations into different large-scale circulation regimes, and they look at local SST
rather than tropics-wide SST. Stein et al. (2017) use CloudSat-CALIPSO data to link cloudamount to aggregation, showing larger areas of anvil cloud and less low cloud in regionswith less large-scale aggregation for a given large-scale rain rate, although they find lessdependence of anvil fraction on (local) SST as discussed in Sect. 4.
The greatest potential of cloud radar observations for advancing theories of convective
aggregation may, however, reside in recent efforts to infer internal dynamics and related
processes (Luo et al. 2010; Nelson et al. 2016). As convection evolves to a more aggregated state, there is reason to anticipate that convective buoyancy and entrainment rates
will change owing to the reduced convective area and cloud lateral boundaries. Luo et al.
(2010) used the difference between cloud top temperature (CTT) and that of the ambientenvironment at the radar-defined cloud top height (CTH) to estimate convective buoyancy
and entrainment rates in individual convective systems. CloudSat reflectivity observations
effectively remove the ambiguity between cloud top temperature and height, allowing
buoyancy to be estimated by comparing the observed CTT to the temperature at the CTH
in the environmental sounding. Entrainment rates are then estimated through iterative
application of an entraining plume model to obtain the best match with observed storm
vertical structure. Luo et al. (2010) paint a familiar picture of tri-modal tropical convection
made up of shallow, mid-level congestus, and deep convective modes (e.g., Johnson et al.
1999) but further characterize the composite dynamic processes within each mode. Nearly
all deep convection has negatively buoyant cloud tops and smaller entrainment rates whilecongestus can be separated into distinct ‘‘transient’’ and ‘‘terminal’’ modes with positive
and negative buoyancy (smaller and larger entrainment rates), respectively.
Given the challenges associated with directly observing the time evolution of convective cloud structures on the scales required to observe convective aggregation, it may beargued that composites of such observation-based estimates of dynamic and thermodynamic processes will be key to testing model-based inferences regarding the driving

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processes. It is very likely, for example, that transitions from scattered to aggregated statesof convection will be accompanied by a shift in the relative frequencies of convective
states, leading to corresponding changes in domain-mean buoyancy and entrainment rates
that may be measured through a similar approach. While Luo et al. (2010) do not characterize the properties of shallow convection, recent work has demonstrated that evaporation and condensation rates in shallow convection can also be inferred from cloud radarobservations, offering the potential to further address the role of shallow convection in thetransition from isolated to aggregated convection (Nelson et al. 2016).
Spaceborne cloud radar observations also offer potential for testing hypothesized
feedbacks and energy and water cycle impacts of convective aggregation. Luo et al. (2014)
use time-differenced infrared brightness temperatures to relate cloud top vertical velocities
to convective mass transport and precipitation efficiency, two central physical characteristics linking the causes and effects of convective aggregation. They demonstrate thatstronger updrafts correlate with higher precipitation echo-tops, increased convective mass
fluxes, and heavier rainfall throughout the tropics. While these studies do not definitively
test emerging theories concerning convective aggregation, they attest to the maturity ofnovel process-related datasets from cloud radar observations and suggest that pursuing new
ways of integrating spaceborne cloud radar into future studies of convective aggregation is
warranted.

5.3 Feasibility of a Ground-Based Observational Network
Simulations of convective aggregation have shown that there is a marked difference in thewater vapor profiles in the dry and moist regions (Fig. 4), and the longwave radiative
heating difference between the two regions (Fig. 5) results in an up-gradient flow justabove the boundary layer that works to further enhance this moisture gradient (Sect. 2).
This characteristic difference between dry and moist regions is an important indicator of
aggregation, and therefore something that a field experiment could target. In this section,
we discuss the feasibility of such an experiment (for instance as part of a field campaign)using currently available ground-based instruments.
6

Moist Profile
Dry Profile

5

5

4

4

3

Altitude [km AGL]

Altitude [km AGL]

6

2

3

2

1

1

0

0

0

5

10

Water Vapor [g kg-1]

15

-6

-4

-2

0

LW Heating Rate [K day-1]

Fig. 11 Water vapor mixing ratio profiles from a dry (black) and moist (gray) region of an RCE simulation(at day 30) where convective aggregation occurred (left), and the corresponding longwave radiative heating
rate profiles computed using the RRTM (right). The error bars on the heating rate profiles were computedby propagating the uncertainties in the Atmospheric Emitted Radiance Interferometer (AERI) retrieved
profiles through the RRTM

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An example of water vapor profiles from the dry and moist regions in a simulation of
aggregation from Muller and Bony (2015), along with longwave radiative heating rates incloud-free scenes computed using a radiative transfer model (RRTM; Mlawer et al. 1997),
are shown in Fig. 11. The differences in the shape of the water vapor profiles result in an
extra 2 K day1 clear-sky longwave cooling in the boundary layer. This boundary layer
cooling will be enhanced if there are shallow liquid water clouds at the top of the boundary
layer; cumulus are often seen in the dry regions of simulations that show aggregation.
The challenge of any field experiment that aims to investigate the results shown by
numerical simulations of convective aggregation is the ability to observe water vapor
profiles, especially in the boundary layer, with the needed accuracy to yield significant
differences in the computed radiative heating rate profiles (cf. Stevens et al. this issue).
Many different boundary layer thermodynamic profiling technologies are currently being
used; Wulfmeyer et al. (2015) provides a review of these instruments. Satellite sensors
have difficulty observing the thermodynamic structure of the boundary layer, especially ifthere are clouds in the scene; the limitations of satellite observations of water vapor also
affect reanalyses (Pincus et al. this issue). Thus, a network of multiple ground-based
remote sensors distributed over some area is the best option if a long duration dataset isdesired to observe the processes that lead to convective aggregation.
Of ground-based sensors, active remote sensors like water vapor Raman lidar anddifferential absorption lidar (DIAL) have a special appeal because of their vertical resolution and accuracy. However, there are no commercially available water vapor Raman
lidars or DIALs, and thus any network of lidars would consist of systems from multiple
research groups where each lidar would have its own sensitivity and uncertainties that may
make the analysis of a network of these datasets more challenging. However, there arecommercially available microwave radiometers and infrared spectrometers, and thus a
network composed only of one of these types of instrument would be homogeneous andpotentially easier to analyze.
Passive remote sensors like microwave radiometers and infrared spectrometers observe
radiance, and retrieval algorithms are needed to derive thermodynamic profiles from theseobservations. Several studies have investigated the accuracy and information content ofthese retrieved profiles. Löhnert et al. (2009) used an instrument system simulation
experiment to demonstrate that infrared spectrometers such as the Atmospheric Emitted
Radiance Interferometer (AERI, Knuteson et al. 2004a, b) have 2–4 times more information on both the temperature and water vapor profile than microwave radiometers,
which leads to improved accuracy in the AERI-retrieved profiles under clear-sky conditions. Blumberg et al. (2015) and Weckwerth et al. (2016) both confirmed that the AERIretrieved water vapor profile was more accurate than microwave radiometers below cloudbase or in cloud-free scenes using real observations.
A natural question is: Do the AERI retrievals have the sensitivity to distinguish between
the longwave radiative cooling rate profiles in the dry and moist columns seen in convective aggregation scenarios? If so, then the AERI would be a good choice to include inany ground-based network that is established to study convective aggregation fromobservations. The AERI retrieval algorithm developed by Turner and Löhnert (2014),
which is able to retrieve lower-tropospheric thermodynamic profiles in both clear andcloudy conditions, provides a complete error covariance matrix for each retrieval. Thermodynamic profiles derived from a Monte Carlo sampling of this error covariance matrix
were used to derive the RRTM to compute cloud-free longwave radiative heating profiles,
and the 1  r uncertainties at each level are shown in Fig. 11 (right). This demonstrates

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that the AERI has the accuracy to determine the radiative heating rate profiles in the twoclear-sky scenes. However, in moist convective regions, where clouds are numerous andcan dominate radiation fluxes, a combination of AERI and microwave radiometer retrievals
may be desirable to ensure sufficiently accurate humidity profiles (Löhnert et al. 2009;
Turner and Löhnert 2014). Furthermore, low clouds in the dry region contribute significantly to self-aggregation in numerical simulations, so it would also be desirable tomeasure vertical profiles of cloud water. This would enable a calculation of the total
radiative heating rate profiles. Cloud radars are the only type of instrument capable of thistype of measurement, but are likely prohibitively expensive to deploy in a network as
proposed here. A first step could be the deployment of ceilometers, which are a standard,relatively inexpensive, autonomous, weak lidar used primarily at airports to determine
cloud base height.
A main strength of microwave and AERI measurements is their ability to measurevertical profiles of moisture. If deployed in a network, the profilers in combination also
provide spatial context. A further extension integrates the surface-based measurementswith a satellite view of the CWV, thereby more fully interrogating the moisture budget
expressed in (1) (Hannah et al. 2016). The satellite can also be integrated with satellitederived perceptions of the precipitation and cloud distribution, while the surface-based
network provides further information on low clouds not easily detected from space and fills
in measurements in-between satellite overpasses, so that a rich, dense, three-dimensional
construction of a moisture field can be constructed that is large enough to encompass both
dry and moist regions. A remaining difficulty may be the typically short time spans for afield deployment, muddying an interpretation of self-aggregation from data. Nevertheless,high-resolution large-domain simulations coincident with such field observations, andcombined with observed surface fluxes and top-of-atmosphere radiative fluxes, will inspirea deeper confidence in the theory of self-aggregation derived from RCE simulations andhelp determine the relative importance of contributing processes.

6 Conclusions
Observing convective organization is not a new pursuit, as evidenced by the literature
review in this paper. But as we learn more about how convection clumps in idealized
models, there are new opportunities to formulate theories of fundamental convective
processes and test them (or at least gauge their plausibility) using observations. Models canalso be used at more realistic configurations to form a bridge between idealized simulations
and observations, and to help us better frame observational studies.
Insights from idealized simulations are already raising many new questions about how
the climate interacts with convective organization. But some findings are dependent onmodel setup or formulation, and the few existing observational studies of aggregation are
not completely consistent with each other or with some model findings—we encourage
recent efforts to organize an intercomparison of RCE in models over a range of complexities and configurations to help resolve these discrepancies. There is agreement
between models and observations that, as convection becomes clumped into fewer moist
regions, the subsidence regions become drier, resulting in a drier large-scale mean environment. This drying, and a reduction of upper-tropospheric stratiform cloud, leads tolarger OLR and stronger atmospheric cooling. However, how aggregation and its effects

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interact with local SST on short time scales and with tropics-wide SST on long time scales
is still uncertain in both models and observations, as discussed further below.
Initiation processes, such as radiatively driven cold pools and related shallow overturning circulations, are one obvious observational target. Maintenance processes may beeven easier to study in observations, since they can be studied in heterogeneous conditions
more typical of convection in nature. There are already links between convective selfaggregation processes in models and observed phenomena such as the MJO and tropical
cyclones, with feedbacks involving convection, clouds, moisture, radiation, and surface
fluxes being important. In fact, the difficulty of global weather and climate models tosimulate these phenomena may be related to problems with those models’ ability tosimulate aggregation processes, as mentioned in Wing et al. (2017).
Time scales are longer in idealized self-aggregation from homogeneous conditions thantypical time scales of observed growth of organized mesoscale convection, but we haveargued that this does not mean that idealized processes are not relevant for real organized
convection. This is because time scales vary a lot in idealized models, and exponential
growth implies shorter effective time scales when starting from already existing organization as is often found in nature. Furthermore, although the real world certainly contains
additional processes that can organize or disorganize convection (such as those reliant oncoastlines and orography), and these may dominate where they are faster or stronger thanself-aggregation processes, these are likely to be concentrated in particular regions and atparticular (especially smaller) space and time scales. This means that self-aggregation
processes may be favored in other regions and, perhaps, on larger spatial scales, and they
are still likely to be relevant for many phenomena and for climate. Feedbacks allowing forthe maintenance of idealized aggregation may also be important for maintaining organized
convection in nature, since disaggregation time scales are relatively short when longwave
radiation feedbacks are turned off in idealized simulations.
Some preliminary new findings show that an idealized simulation with elongatedchannel geometry has a more realistic representation of atmospheric humidity than asimulation with a square domain, which has too broad distribution of humidity and is too
dry in the driest regions when compared with radiosonde records from Nauru. This is an
example of how observations may be used to discriminate between different model configurations and address concerns that may otherwise cast doubt on the relevance of
aggregation studies in general. Determining the reason for the difference in humidity
between these two model configurations is beyond the scope of this paper, and somecaution should be exercised when interpreting these results until the reasons and theirrelationship to physical processes are better understood, since it is possible that the channel
simulation gets the ‘‘right answer for the wrong reason’’. However, possible reasons forthese humidity differences include differences in wind speed caused by stronger overturning circulations in the channel simulations, the development of slightly stronger mean
wind and wind shear in the channel simulations, or interactions between large-scale circulations and multiple convective regions causing increased proximity and mixing between
moist and dry regions.
Recent work has underlined the potential importance of the sensitivity of aggregation
processes to SST and climate change. There are exciting new processes being proposed,such as the ‘‘stability-iris’’ effect (Bony et al. 2016) that predicts smaller anvil fractions ina warmer climate. We are gaining an understanding of how organized convection andclimate change may interact, but new questions are being raised about the fidelity of ourmodels. The ability to represent both large-scale circulations and convective processes
adequately is still a challenge for idealized models, and the effects of more complex

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1231

processes such as ocean coupling are only beginning to be explored. There are also
challenges in using observations of the recent past to test model behavior in both idealized
and more realistic simulations of projected future climate. Specifically, we lack longobservational records, and studies of regional snapshots or individual cloud elements overshort time periods may not scale up to tropics-wide behavior on long time scales. There arealso differences in the SST dependence of initiation processes versus maintenance processes in idealized self-aggregation which need to be further explored in both models andobservations. But the problem of aggregation in a warming world is an important one anddeserves a sustained research effort.
In addition to encouraging the continuing endeavor of confronting self-aggregation
processes with observations in general, we have proposed several specific lines of work
which appear promising. These include:
•
•
•
•
•
•
•
•
•
•

existence, formation, and structure of radiatively driven cold pools
MSE spatial variance budget analysis
particle tracing back to last saturation (model and observations)radiosonde time scale analysis
changes in satellite-observed aggregation state and anvil fraction over last few decades(and further investigation of sensitivity to SST)
paleotempestology using long-term isotopic records
satellite analysis of link between water vapor isotopes and aggregation
multiple-satellite temporal evolution of MSE budget for aggregated convection
spaceborne radar to infer convective processes
ground-based observational network

While this list is a good start, there are surely other opportunities to further our knowledgeof aggregation processes in idealized models using observations. And as the field advances,
there will be more ideas to test and explore. We hope the work reviewed and proposed hereis the beginning of an exciting new engagement between modeling and observational
studies of organized convection.
Acknowledgements This paper arises from the International Space Science Institute (ISSI) workshop on‘‘Shallow clouds and water vapor, circulation and climate sensitivity’’. ARM data were used with thecooperation of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement Program
Climate Research Facility. We thank Kerry Emanuel, Robert Pincus, Thorwald Stein, James Ruppert, and an
anonymous reviewer for helpful comments. AAW acknowledges support from an NSF Postdoctoral
Research Fellowship under Award No. AGS-1433251. SB acknowledges support from ERC Grant No.
694768.
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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