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\begin{document}

\title{Investigating the Causes and Impacts of Convective Organization in a
High Resolution Atmospheric GCM}



\author[1]{Bosong Zhang}%
\author[2]{Brian Soden}%
\author[3]{Gabriel Vecchi}%
\author[3]{Wenchang Yang}%
\affil[1]{University of Miami}%
\affil[2]{Univ. Miami, Miami}%
\affil[3]{Princeton University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
A \textasciitilde{} 50 km resolution atmospheric general circulation
model (GCM) is used to investigate the impact of radiative interactions
on spatial organization of convection, the model's mean state, and
extreme precipitation events in the presence of realistic boundary
conditions. Mechanism-denial experiments are performed in which
synoptic-scale feedbacks between radiation and dynamics are suppressed
by overwriting the model-generated atmospheric radiative cooling rates
with its monthly-varying climatological values. When synoptic-scale
radiative interactions are disabled, the annual mean circulation and
precipitation remain almost unchanged, however tropical convection
becomes less aggregated, with an increase in cloud fraction and relative
humidity in the free troposphere but a decrease in both variables in the
boundary layer. Changes in cloud fraction and relative humidity in the
boundary layer exhibit more sensitivity to the presence of radiative
interactions than variations in the degree of aggregation. The less
aggregated state is associated with a decrease in the frequency of
extreme precipitation events, coincident with a decrease in the
dynamical contribution to the magnitude of extreme precipitation. At
regional scales, the spatial contrast in radiative cooling between dry
and moist regions diminishes when radiative interactions are suppressed,
reducing the upgradient transport of energy, degree of aggregation and
frequency of extreme precipitation events. However, the mean width of
the tropical rain belt remains almost unaffected when radiative
interactions are disabled. These results offer insights into how
radiation-circulation coupling affects the spatial organization of
convection, distributions of clouds and humidity, and weather extremes.%
\end{abstract}%



\sloppy


\textbf{Investigating the Causes and Impacts of Convective Organization
in a High Resolution Atmospheric GCM}

Bosong Zhang\textsuperscript{1}, Brian J. Soden\textsuperscript{1}

\emph{1. Rosenstiel School of Marine and Atmospheric Science}

\emph{University of Miami, Miami, Florida}

Gabriel A. Vecchi\textsuperscript{2, 3}, Wenchang
Yang\textsuperscript{2}

\emph{2. Department of Geosciences, Princeton University}

\emph{Princeton, NJ}

\emph{3. High Meadows Environmental Institute, Princeton University}

\emph{Princeton, NJ}

To be submitted to \emph{JAMES}

2021

Corresponding author address: Bosong Zhang, Rosenstiel School of Marine
and Atmospheric Science, University of Miami, 4600 Rickenbacker
Causeway, Miami, FL 33149, USA. (bosong.zhang@rsmas.miami.edu)

\section*{Abstract}

{\label{abstract}}

A \textasciitilde{} 50 km resolution atmospheric general circulation
model (GCM) is used to investigate the impact of radiative interactions
on spatial organization of convection, the model's mean state, and
extreme precipitation events in the presence of realistic boundary
conditions. Mechanism-denial experiments are performed in which
synoptic-scale feedbacks between radiation and dynamics are suppressed
by overwriting the model-generated atmospheric radiative cooling rates
with its monthly-varying climatological values. When synoptic-scale
radiative interactions are disabled, the annual mean circulation and
precipitation remain almost unchanged, however tropical convection
becomes less aggregated, with an increase in cloud fraction and relative
humidity in the free troposphere but a decrease in both variables in the
boundary layer. Changes in cloud fraction and relative humidity in the
boundary layer exhibit more sensitivity to the presence of radiative
interactions than variations in the degree of aggregation. The less
aggregated state is associated with a decrease in the frequency of
extreme precipitation events, coincident with a decrease in the
dynamical contribution to the magnitude of extreme precipitation. At
regional scales, the spatial contrast in radiative cooling between dry
and moist regions diminishes when radiative interactions are suppressed,
reducing the upgradient transport of energy, degree of aggregation and
frequency of extreme precipitation events. However, the mean width of
the tropical rain belt remains almost unaffected when radiative
interactions are disabled. These results offer insights into how
radiation-circulation coupling affects the spatial organization of
convection, distributions of clouds and humidity, and weather extremes.



\textbf{Key Points}

\begin{itemize}
\tightlist
\item
  Radiative coupling strengthens the degree of aggregation and extreme
  precipitation.
\item
  Radiative coupling modulates the distribution of clouds and relative
  humidity.
\item
  Radiative coupling in the boundary layer has comparable impacts on
  convective organization, clouds and humidity as does radiative
  coupling in the free troposphere.
\end{itemize}

\textbf{Plain Language Summary}

Interplays between radiation, clouds and convection are well studied in
numerical simulations under idealized boundary conditions (e.g.,
spatially uniform sea surface temperatures, no wind shear, etc.).
However, it remains unclear how they interact with each other in more
realistic situations with the presence of sea surface temperature
gradients and a large-scale background circulation. In this study we
examine the impact of synoptic-scale radiative coupling on convective
organization, clouds, and precipitation extremes using a
\textasciitilde{}50 km resolution atmospheric general circulation model.
When synoptic-scale radiative coupling is disabled, we find that the
mean circulation and rainfall remain almost unaffected. However,
convection becomes less organized without radiative coupling, which is
due to the diminished spatial contrast in radiative cooling between dry
and moist regions. Also, both daily precipitation and mid-tropospheric
updrafts exhibit a reduction in the probability of their extreme values
when radiative coupling is disabled. In addition, we find that radiative
coupling can modulate the distribution of clouds and relative humidity.
These findings highlight the importance of synoptic-scale interactions
between radiation and convection even in realistic situations, and
motivates the comparison of model simulations and observations.



\section*{1 Introduction}

{\label{introduction}}

The tendency for convection to organize from isolated convective
updrafts into spatially coherent clusters has long been recognized in
numerical model simulations (Bretherton et al., 2005; Held et al., 1993;
Tompkins, 2001). This aggregation of convection occurs even in the
presence of uniform boundary conditions (self-organization) and not only
impacts the intensity of precipitation events (Bao \& Sherwood, 2019),
but also modulates the larger-scale thermodynamic and radiative
properties of the tropics (e.g., Bony et al. (2020)). Increased
aggregation is associated with increased spatial variance of moisture;
dry regions become drier and moist regions become moister (Dai \& Soden,
2020). The increased spatial variance of moisture directly impacts both
the intensity of precipitating systems and the larger-scale radiative
fluxes (Bony et al., 2020; Bony et al., 2016; Bretherton et al., 2005;
Wing et al., 2020).

The net effect of more aggregated convection is to dry the tropical free
troposphere, particularly in cloud-free regions, resulting in a net loss
of longwave radiation to space (Bretherton et al., 2005). This
large-scale influence of aggregation has been proposed as a potential
thermostat that may regulate the sensitivity of the tropics to radiative
forcing (Mauritsen \& Stevens, 2015). However, the interaction with
radiation involves feedbacks. The amplification and expansion of dry
regions is believed to play a key role in triggering aggregation, and
radiative feedbacks involving both clouds and water vapor are essential
for maintaining the aggregation in idealized models (Wing et al., 2017).
Additionally, the relative importance of clear versus cloudy sky
radiative processes is not well understood, as is the contributions of
shortwave (SW) versus longwave (LW) radiation.

There is a long history of observational studies of convective
organization (see Holloway et al. (2017) for a recent review). Most
recently, Bony et al. (2020) found that increased aggregation in the
tropics is associated with a reduction in high cloud cover, a drier free
troposphere in the non-convective environment and increased emission of
infrared radiation to space. These features lead to a net radiative
cooling of the tropics.

Precipitation extremes are largely controlled by the amount of moisture
present in the atmosphere (Allen \& Ingram, 2002; Pall et al., 2007;
Trenberth, 1999) and also atmospheric convergence (Liu et al., 2020),
whereas the global-mean precipitation is constrained by the global-mean
radiative cooling. From an energy balance perspective, latent heating
into the atmosphere must be balanced by atmospheric radiative cooling
given that heat capacity of the atmosphere is negligible (Allen \&
Ingram, 2002). In model simulations, the change in extreme precipitation
in response to increases in greenhouse gases is found to depend on the
magnitude of warming (Pendergrass et al., 2015) and the change in
convective organization (Muller, 2013; Pendergrass et al., 2016). In
observations, the degree of aggregation at regional scales has also been
connected with extreme rainfall events (Dai \& Soden, 2020).

Climate model projections indicate that the thermodynamic constraint
based on the Clausius-Clapeyron relation is a good predictor for extreme
precipitation changes in a warmer climate for regions where changes in
the circulation are small (Pall et al., 2007). However, this may not be
the case for regions with large changes in the atmospheric circulation,
such as the tropics (Emori \& Brown, 2005; Vecchi \& Soden, 2007) or for
tropical cyclones (Knutson et al., 2013; Liu et al., 2020). Indeed,
several studies suggest that the sensitivity of tropical precipitation
extremes is substantially larger than that predicted from the
Clausius-Clapeyron relationship (Allan \& Soden, 2008; Norris et al.,
2019; O'gorman, 2015; Westra et al., 2013).

Among different factors contributing to radiative cooling of the
atmosphere, cloud radiative effects (CRE) have been received
considerable attentions. The Clouds On-Off Klimate Intercomparison
Experiment (COOKIE) is designed to investigate the role of CRE in the
climate system (Stevens et al., 2012). This project compares simulations
with clouds that are transparent to radiation (``clouds-off'') and those
including CRE (``clouds-on''). Using output from the COOKIE project,
Fermepin and Bony (2014) showed that low cloud radiative effects
increase tropical precipitation and strengthen winds near ocean surface.
However, Li et al. (2015) found that CRE can decrease precipitation in
the tropics but increase it at middle-to-high latitudes. Recently,
Medeiros et al. (2021) reported that extreme precipitation over tropical
ocean is strengthened by CRE. While mean precipitation and large-scale
circulation can be affected by removing CRE, it is unclear how
precipitation, especially extreme precipitation, will respond if
radiative-convective interactions are disabled.

In idealized models, studies found that interactive radiation is key to
convective aggregation over a limited domain (Muller \& Bony, 2015;
Muller \& Held, 2012; Wing \& Emanuel, 2014; Yang, 2018). In simulations
of radiative convective equilibrium without rotation, Bao and Sherwood
(2019) found that extreme daily precipitation gets stronger when
convection is more aggregated with fully interactive radiation. Most
research on the coupling of clouds and radiation on smaller time/space
scales has focused on the impact of radiative feedbacks on convective
organization. These studies typically have been performed using high
resolution, radiative equilibrium simulations under very idealized
settings. This makes it difficult to ascertain the importance of
cloud-circulation feedbacks under more realistic situations (e.g., in
the presence of the SST gradients or wind shears that are present in our
planet). It also makes it more challenging to evaluate the model
simulations with observations.

In this study, we examine the impact of radiative interactions on the
spatial organization of convection and extreme precipitation events
under realistic boundary conditions. Instead of completely removing the
CRE, which dramatically changes the mean circulation and rainfall in a
model (e.g., as is done in COOKIE), synoptic-scale radiative
interactions are suppressed by prescribing radiative cooling rates using
their monthly climatological values. This enables us to examine the
behavior of two versions of a model with nearly identical large-scale
circulations but with differing degrees of convective organization. Our
simulations highlight the role of synoptic-scale radiative coupling in
enhancing convective aggregation and extreme precipitation by increasing
the horizontal gradient of radiative cooling which provides an
upgradient transport of energy from dry to moist regions.

\section*{2 Methods}

{\label{methods}}

\emph{a. Model and experiments}

We use the High-Resolution Atmospheric Model (HiRAM; Zhao et al. (2009))
developed at the Geophysical Fluid Dynamics Laboratory (GFDL). All
simulations are conducted with prescribed climatological monthly means
of sea surface temperature (SST) and sea ice from Hadley Centre Sea Ice
and Sea Surface Temperature (HadISST) dataset (Rayner et al., 2003)
based on the 20-year period from 1986 to 2005, and are integrated for 50
years with constant atmospheric CO\textsubscript{2}, greenhouse gases
and aerosol concentrations (at 1990 levels). The first simulation
(referred to as the Control run) follows the default model configuration
and thus has fully interactive radiation. The second simulation
(referred to as the ClimRad run) overwrites the model-generated
atmospheric radiative cooling rates with its monthly-varying
climatological values computed from the Control run. Specifically, the
overwriting process is implemented as follows: (a) monthly atmospheric
radiative cooling rates are retrieved from the last 20 years of the
Control run; (b) a multiyear average is applied to the 20-year data to
get monthly-varying climatological radiative cooling rates; and (c) each
time when the radiation code is called in the ClimRad run, the
atmospheric radiative cooling rates are overwritten by its
monthly-varying climatological values that are temporally interpolated
to the current time step. A summary of these simulations is listed in
Table 1. These simulations are also used in Zhang et al. (2021).

\emph{b. Degree of Convective Aggregation}

Different metrics have been used to quantify the degree of aggregation
under different circumstances such as the ``organization index'' that
detects organized convective features using satellite observed infrared
brightness temperatures (Bony et al., 2020; Tompkins \& Semie, 2017),
subsidence fraction (Coppin \& Bony, 2015), the spatial variance of
column relative humidity (Wing \& Cronin, 2016) and the spatial variance
of column integrated water vapor (Dai \& Soden, 2020; Wing et al.,
2020). In this study, we characterize the spatial organization of
convection using subsidence fraction, which is computed as the
fractional area covered by subsidence based on daily vertical pressure
velocity at 500 hPa \(\left(\omega_{500}\right)\). We note that using the spatial
variance of column integrated water vapor yields similar results.

\section*{3 Results}

{\label{results}}

\subsection*{a. Mean circulation and
precipitation}

{\label{a.-mean-circulation-and-precipitation}}

Figure 1 shows the zonal mean meridional overturning circulation in the
Control and ClimRad runs. Overall the difference between the two
simulations is very small, indicating that the mean circulation remains
almost unchanged without radiative interactions. Also, we note that
suppressing radiative interactions has little impact on the magnitude of
the global-mean precipitation because the overwriting approach applied
in the ClimRad run does not change the magnitude of the global-mean
radiative cooling of the atmosphere. Overall the atmospheric energy
budget remains nearly unaffected in the ClimRad run.

\subsection*{b. Convective aggregation, cloud and relative
humidity}

{\label{b.-convective-aggregation-cloud-and-relative-humidity}}

Although the mean circulation is essentially the same between the
Control and ClimRad runs, suppressing radiative interactions
significantly changes features related to synoptic-scale convection.
Figure 2 shows probability density functions (PDFs) of daily subsidence
fraction in the Control and ClimRad runs computed over the entire
tropics (30\selectlanguage{ngerman}°S--30°N). Small (large) values of daily subsidence fraction
in the ClimRad run are more (less) frequent than those in the Control
run, indicating that convection becomes less aggregated when radiative
interactions are suppressed. These results are in line with previous
numerical simulations with an aquaplanet configuration (Coppin \& Bony,
2015) and in convection-resolving models (Muller \& Bony, 2015; Muller
\& Held, 2012; Yang, 2018).

Using satellite observations, Bony et al. (2020) found that the spatial
organization of deep convection can modulate high-level clouds and
relative humidity in the free troposphere, which further impacts the
tropical radiation budget. Based on an ensemble of radiative-convective
equilibrium simulations, Wing et al. (2020) showed similar results in
which the occurrence of convective self-aggregation reduces high cloud
coverage and dries the mid-troposphere. Here, we investigate how clouds
and relative humidity respond to suppressed radiative interactions
(Figure 3). Negative values are found in the upper troposphere over the
tropics for the Control run minus the ClimRad run, indicating that a
more aggregated state is associated with fewer high-level clouds. Also,
we find that the free troposphere is in general drier in the Control run
than that in the ClimRad run (Figure 4). The reduction in high-level
clouds and mid-tropospheric relative humidity in the Control run is
qualitatively consistent with observations (Bony et al., 2020; Holloway
et al., 2017; Stein et al., 2017; Tobin et al., 2013; Tobin et al.,
2012) and other model simulations (Bretherton et al., 2005; Wing et al.,
2017; Wing \& Emanuel, 2014; Wing et al., 2020). This shows that, even
when the large-scale circulations are nearly identical, differences in
the spatial organization of convection can alter the mean state of the
free troposphere.

However, the responses in cloud fraction and relative humidity are not
vertically uniform. We find that the Control run has an overall increase
in cloud fraction and relative humidity in the boundary layer, which may
not be directly linked with the degree of aggregation. Previous results
on the relationship between convective aggregation and low cloud
fraction are inconclusive. While an increase in low-level clouds with
aggregation is found in Tobin et al. (2013) and Stein et al. (2017),
Tobin et al. (2012) found the opposite result. Recently, Wing et al.
(2020) found that most radiative-convective equilibrium simulations
agree on an increase in low-level clouds with convective
self-aggregation, although such increase is less robust in magnitude.
They proposed that the difference in horizontal grid spacing, rather
than the occurrence of self-aggregation itself, may contribute to the
increase in low-level clouds. In addition, lower tropospheric stability
may also play a role in modulating low-level clouds (Bony et al., 2020).
When lower-tropospheric stability increases, more moisture is trapped in
the boundary layer, which promotes the formation of low-level clouds
(Wood \& Bretherton, 2006). However, the impact of lower tropospheric
stability on low-level clouds is thought to be independent of the degree
of aggregation as noted by Bony et al. (2020). Here we use estimated
inversion strength (\emph{EIS} ), defined as\(EIS=LTS-\Gamma_{m}^{850}\left(z_{700}-LCL\right)\), to
represent the stability in the boundary layer. LTS stands
for lower tropospheric stability and is computed as\(LTS=\theta_{700}-\theta_{1000}\)
where \(\theta_{700}\) and\(\theta_{1000}\) are potential
temperatures at 700 hPa and 1000 hPa respectively (Klein \& Hartmann,
1993); \(\Gamma_{m}^{850}\) is

Among different factors contributing to the low cloud fraction,
radiative interactions with boundary layer clouds could make a
difference. In the boundary layer, the coupling between clouds,
radiation, turbulence and entrainment was first documented by Lilly
(1968). Strong longwave radiative cooling at the cloud top promotes
vertical mixing and drives turbulent eddies, which transports moisture
from the sea surface upward and maintains the cloud amount (Bretherton
et al., 2004b; Wood, 2012). Additionally, strong radiative cooling at
the cloud top increases relative humidity in the boundary layer. Higher
relative humidity further promotes the formation of low-level clouds
(Brient \& Bony, 2012). In the ClimRad run, the coupling between
radiation and low-level clouds is disabled, which may explain the
reduction in both relative humidity and cloud fraction in the boundary
layer.

To explore the sensitivity of clouds and relative humidity to the
vertical structure of radiative coupling, we conduct two other
simulations: one is referred to as ClimRadFT, in which the overwriting
procedure is only applied to the free troposphere, whereas radiation in
the boundary layer is fully interactive; the other is referred to as
ClimRadBL, in which only radiation in the boundary layer is fixed while
that in the free troposphere is interactive (see Table 1 for more
details). Compared to the Control run, we find that changes in low-level
clouds and lower-tropospheric relative humidity in the ClimRadBL run are
similar to those in the ClimRad runs (Figure 3 and Figure 4). In
contrast, the differences in tropical low-level clouds and relative
humidity in the boundary layer are reduced between the Control and
ClimRadFT runs (Figure 3 and Figure 4). However, we note that the
ClimRadBL and ClimRadFT runs exhibit similar changes in lower
tropospheric stability compared to the Control run (Figure S1). This
suggests that it is the direct effects of radiative coupling in the
boundary layer that is primarily responsible for the changes in
low-level clouds and relative humidity in the ClimRad run, rather than
the influence of radiative processes in the free troposphere on lower
tropospheric stability.

In addition, the changes in low-level clouds and relative humidity are
found to be, at least from a qualitative perspective, independent of
variations in the degree of aggregation. A comparison of the PDFs of
daily subsidence fraction from the Control, ClimRad, ClimRadFT and
ClimRadBL runs is shown in Figure 5. Compared to the Control run, the
other three simulations exhibit an overall reduction in the degree of
aggregation although the magnitude of such reduction varies among them.
The qualitatively consistent change in the degree of aggregation cannot
explain the differing responses in cloud fraction and relative humidity,
indicating that variations in the degree of aggregation may not be a
leading factor in modulating the distribution of cloud and humidity.
Here, the coupling between radiation, cloud and humidity plays a more
important role in maintaining the model's mean state.

\subsection*{c. Response in extreme
precipitation}

{\label{c.-response-in-extreme-precipitation}}

Previous idealized modeling studies showed that extreme daily
precipitation becomes weaker when convective aggregation is inhibited
(Bao \& Sherwood, 2019). To examine the response in extreme
precipitation to suppressed radiative interactions, we compute the
annual maximum daily precipitation (\(P_{e}\)) at each grid
point. While the difference in \(P_{e}\) between the Control
and ClimRad runs is small at middle-to-high latitudes, a significant
reduction in \(P_{e}\)is found across the tropics in the
ClimRad run (Figure 6, left), which indicates that suppressing radiative
interactions reduces the strength of extreme daily precipitation. At
each grid point, \(P_{e}\) can be estimated by a physical
scaling diagnostic (O'Gorman \& Schneider, 2009; Pfahl et al., 2017;
Sugiyama et al., 2010):

\begin{equation}
\begin{matrix}P_{e}\sim-\left\{\omega_{e}\left.\ \frac{dq_{s}}{\text{dp}}\right|_{\theta^{*}}\right\}\#\left(1\right)\\
\end{matrix}\nonumber \\
 \end{equation}

where \(\omega_{e}\) is the annual maximum daily vertical pressure
velocity, \(q_{s}\) is the saturation specific humidity,
\(p\) is the pressure and \(\theta^{*}\) is the
saturation equivalent potential temperature. Here \(\left\{\bullet\right\}\)
means a mass-weighted vertical integral over the troposphere. We show
that the scaling approach reproduces the spatial patterns of
\(P_{e}\) in both simulations, leading to a consistent
reduction in the scaling when radiative interactions are suppressed
(Figure 6, right).

Eq. 1 can be used to decompose changes in extreme precipitation into
thermodynamic and dynamic contributions. A thermodynamic scaling is
implemented by replacing \(\omega_{e}\) in Eq. 1 with long-term
averaged vertical velocity at each grid point, whereas a dynamic scaling
is the difference between the full scaling and the thermodynamic scaling
(Pfahl et al., 2017). There is little difference in the thermodynamic
contribution between the Control and ClimRad runs (Figure S2, left)
because both runs are forced by the same SSTs and
CO\textsubscript{2}concentrations. However, the spatial patterns of
difference in dynamic contribution (Figure S2, right) largely resemble
the spatial patterns of difference in \(P_{e}\) and the
scaling, indicating that suppressing radiative interactions primarily
reduces the dynamical contribution to extreme precipitation.

To verify the robustness of our results, probability distributions of
daily precipitation and updrafts across the tropics (30\selectlanguage{ngerman}°S--30°N) are
compared between these two simulations. Figure S3 shows the base-10
logarithm of the probability that daily precipitation and
mid-tropospheric updrafts (\(\omega_{500}<0\)) exceed a particular
value in the Control and ClimRad runs. We find that both variables
exhibit a reduction in the probability of exceedance toward its extreme
values in the ClimRad run, indicating that suppressing radiative
interactions reduces the frequency of extreme convective events. We note
that suppressing radiative interactions also reduces the temporal
variance of daily precipitation (Figure S4).

Having demonstrated the impact of suppressing radiative interactions on
convective organization, we next explore the physical mechanisms which
underlie these changes. To do that we first divide the tropics
into\(10\times 10\) regional blocks (Figure 7, top). Within each
block, the grid point with the local maximum precipitation is
identified, which later becomes the new center of that block. The
recentered blocks are then composited based on their domain mean
precipitation. Here we show composites of precipitation in the Control
run for blocks with domain mean precipitation \textless{}5, 5--10,
10--15 and \textgreater{}15 mm day\textsuperscript{-1} (Figure 7,
bottom). Note that composites of precipitation in the ClimRad run show
similar results (not shown). However, the number of blocks per year
(referred to as \(N_{b}\)) in each bin is different between
the Control and ClimRad runs. Boxplots of\(N_{b}\) normalized
by the median value in the Control run are shown in Figure 8 (top). In
the \textgreater{}15 mm day\textsuperscript{-1} bin,\(N_{b}\)
is reduced in the ClimRad run, which means that blocks with heavy
precipitation happen less frequently when radiative interactions are
suppressed. Through this block-by-block analysis, we can also compare
the degree of aggregation over blocks with similar amplitude of domain
mean precipitation. A comparison of PDFs of daily subsidence fraction
between the Control and ClimRad runs are shown in Figure 8 (bottom).
Higher probabilities of large subsidence fraction are found in the
Control run, indicating that suppressing radiative interactions leads to
an overall reduction in aggregation across convective systems of
different intensities, which is consistent with the results shown in
Figure 2.

In idealized models, it is found that the upgradient transport of moist
static energy (Neelin \& Held, 1987) plays an important role in
convective aggregation (Bretherton et al., 2005; Muller \& Bony, 2015;
Muller \& Held, 2012). Here, radiative cooling and circulation are
composited over bins as shown in Figure 8. Following Bretherton et al.
(2005), we use column relative humidity (CRH), defined as the ratio of
water vapor path to the saturation water vapor path of the atmospheric
column (Bretherton et al., 2004a; Raymond, 2000), to represent the
degree of dryness at each grid point within a block. Next, all grid
points in a block are sorted from lowest to highest CRH and the
circulation is represented by an effective streamfunction
\(\Psi\), which is computed as a horizontal integral over
vertical velocity starting with the driest grid point. The
streamfunction \(\Psi\) at a certain grid point can be
interpreted as an accumulation of vertical mass flux over grid points
that are drier than the target grid point. Primarily, the streamfunction
is thought to capture the exchange of moist static energy between dry
and moist regions (Bretherton et al., 2005).

Figure 9 shows the streamfunction \(\Psi\) and radiative
cooling rates in the Control and ClimRad runs. In the Control run, when
the domain mean precipitation is small, the circulation is weak and
there is little contrast in radiative cooling between dry and moist
regions, especially in the lower troposphere. As the domain mean
precipitation increases, the circulation gets stronger, with its
low-level component below \textasciitilde{}850 hPa moving air from dry
to moist regions. Although the magnitude of radiative cooling in dry
regions does not change much, the radiative cooling reduces
significantly in moist regions as domain mean precipitation increases,
which is equivalent to adding anomalous radiative heating there. As a
result, the horizontal gradient of radiative cooling is enhanced, which
promotes the low-level circulation and thus the upgradient transport of
energy. In comparison, the enhanced horizontal gradient of radiative
cooling shown in the Control run is missing in the ClimRad run,
indicating that suppressing radiative interactions inhibits the
horizontal gradient of radiative cooling from increasing, which explains
why the degree of aggregation and extreme precipitation events are
reduced in the ClimRad run.

\subsection*{d. Meridional width of the tropical rain
belt}

{\label{d.-meridional-width-of-the-tropical-rain-belt}}

Recent studies measure the width of tropical ascending regions by the
fraction of vertical pressure velocity at 500 hPa less than zero in the
tropics (Su et al., 2020; Su et al., 2019). Given the same domain,
greater ascending fraction corresponds to smaller subsidence fraction.
While in section 3b we show that daily subsidence fraction in the
tropics is reduced without radiative interactions. On longer time
scales, the mean vertical pressure velocity at 500 hPa exhibits little
difference between the Control and ClimRad runs (not shown). However,
this definition may not be an appropriate measure of the meridional
width of zonal mean Hadley circulation or the width of the intertropical
convergence zone (ITCZ), as noted by Su et al. (2020). Therefore, other
metrics are required to quantify the width of the tropical rain belt.
Based on observations, Popp and Bony (2019) reported a strong link
between zonal convective clustering (CC) and the tropical rain belt:
when convection becomes more clustered in the zonal direction, the
meridional width of tropical rain belt increases and exhibits a
double-peak structure. However, it remains unclear how CC is related to
the width of ITCZ in climate models (Popp et al., 2020b). In section 3b,
we show that suppressing radiative interactions reduces the degree of
aggregation across the tropics. Thus, convection should become less
clustered in the zonal direction as well without radiative interactions.
Here, two metrics are used to characterize zonal CC: i) the
precipitation-inferred CC index, which is defined as monthly mean of the
meridionally averaged daily zonal standard deviation of precipitation
from 6°S to 6°N normalized by the daily mean precipitation over the same
region (Popp \& Bony, 2019); and ii) the dynamically inferred CC index,
which is defined as the monthly average of the daily zonal fraction of
positive values of the meridional-mean vertical pressure velocity at 500
hPa between 6°S to 6°N (Popp et al., 2020a). Also, we only consider
months during which the tropical precipitation distribution is symmetric
about the equator with the tropical precipitation asymmetry index (Hwang
\& Frierson, 2013; Popp \& Bony, 2019) less than 0.4. Another two
metrics are used to quantify the ITCZ width: i) the
precipitation-inferred ITCZ width, which is defined as the area mean of
precipitation from 15°S to 15°N divided by the area mean of
precipitation from 6°S to 6°N (Popp \& Bony, 2019); and ii) the
dynamically inferred ITCZ width, which is defined by the contiguous
width in degrees latitude of zonal mean ascent region at 500 hPa around
the absolute maximum of zonal mean precipitation (Byrne \& Schneider,
2016; Popp \& Bony, 2019).

Scatter plots of zonal CC and the ITCZ width in the Control and ClimRad
runs are shown in Figure 10. Positive temporal correlations are found
between zonal CC and the ITCZ width using either precipitation or
dynamically inferred metrics in both simulations, which is consistent
with observations (Popp \& Bony, 2019). We note that the mean ITCZ width
exhibits little difference between the Control and ClimRad runs, which
is supported by Figure S5 and Figure S6 based on precipitation minus
evaporation. These results indicate that suppressing radiative
interactions has little impact on the mean ITCZ width. In comparison,
the mean value of zonal CC is reduced in the ClimRad run, which comes as
no surprise since the degree of aggregation is also reduced without
radiative interactions as illustrated in section 3b. Based on model
simulations participating in CMIP5 (Taylor et al., 2012), Popp et al.
(2020b) showed that biases in CC cannot explain biases in the ITCZ width
and no dominant mechanism could explain the link between the temporal
variability of CC and that of the ITCZ width. However, they found a
tendency for models with higher spatial resolution to exhibit stronger
links between zonal CC and the dynamically inferred ITCZ width. In this
study, suppressing radiative interactions has a robust impact on zonal
CC but little impact on the mean ITCZ width. One possibility is that
while the degree of aggregation/clustering is more sensitive to
synoptic-scale radiation-circulation coupling (i.e. the spatial contrast
in radiative cooling), the ITCZ width is more dependent on the long-term
averaged large-scale circulation in this GCM.

\section*{4 Summary and Discussion}

{\label{summary-and-discussion}}

This study examines the impact of radiative interactions on the spatial
organization of convection, the distribution of clouds and relative
humidity, and extreme daily precipitation events. We show that
suppressing radiative interactions does not alter the mean circulation
much but reduces the degree of convective aggregation. The reduction in
the degree of aggregation is associated with an increase in high cloud
coverage and relative humidity in the free troposphere and a decrease in
the boundary layer. These differing responses of cloud and humidity are
found to be sensitive to radiative interactions and, to some extent,
independent of variations in the degree of aggregation.

Additionally, a less aggerated state due to suppressed radiative
interactions is associated with a decrease in the frequency of extreme
precipitation events due to a reduction in the dynamic contribution,
i.e., a weakening of the strongest updrafts. At regional scales,
suppressing radiative interactions diminishes the horizontal gradient of
radiative cooling from dry to moist regions, weakening the upgradient
transport of energy and reducing the degree of aggregation. However, the
mean ITCZ width shows little difference with and without radiative
interactions.

While our results show that the impact of radiative interactions on the
degree of aggregation and extreme precipitation is not overwhelmed by
the presence of realistic SST gradients, it is worth mentioning that the
model response to suppressed radiative interactions shows considerable
spatial variability. Overall, stronger signals are found in the tropics
than those at mid to high latitudes. Signals over sea surfaces are also
more robust than those over land ones. These spatially heterogeneous
responses indicate that local environment may play a role in determining
the extent to which radiative interactions impact extreme weather
extremes and convective aggregation. In addition, our simulations are
performed with prescribed SSTs, which essentially excludes the possible
impact of changes in the degree of aggregation on SSTs. It remains
unclear whether and how changes in the degree of aggregation affect
SSTs, and if yes, how changes in SSTs would feedback onto interactions
between radiation and convection. Future studies may explore these
issues using fully coupled GCMs.

\section*{Acknowledgement}

{\label{acknowledgement}}

This research was supported by NOAA Awards NA18OAR4310269 and
NA18OAR4310418, and Department of Energy Award DE-SC0021333. HiRAM
simulations are performed on the Princeton University Research Computing
systems. The data sets produced in this study are available from
https://tigress-web.princeton.edu/\textasciitilde{}bosongz/.



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\section*{Tables}

{\label{tables}}

Table 1 A list of the simulations conducted in this study.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Experiment name & SST forcing & CO\textsubscript{2} forcing &
Radiation\tabularnewline
\midrule
\endhead
Control & 1986-2005 Average & Fixed & Fully Interactive\tabularnewline
ClimRad & 1986-2005 Average & Fixed & Prescribed
Climatology\tabularnewline
ClimRadFT & 1986-2005 Average & Fixed & Prescribed Climatology in the
Free Troposphere (from \textasciitilde{}850 hPa and above); Fully
Interactive in the Boundary Layer (below \textasciitilde{}850
hPa)\tabularnewline
ClimRadBL & 1986-2005 Average & Fixed & Prescribed Climatology in the
Boundary Layer (below \textasciitilde{}850 hPa); Fully Interactive in
the Free Troposphere (from \textasciitilde{}850 hPa and
above)\tabularnewline
\bottomrule
\end{longtable}

\section*{Figures}

{\label{figures}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1 Annual mean, zonal mean meridional circulation by stream
function (unit:\(\times 10^{10}\text{\ kg\ }s^{-1}\)) in the Control run (top), ClimRad run
(middle) and their difference (bottom).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2 PDFs of the subsidence fraction in the Control and ClimRad runs
over the entire tropics. The two PDFs are significantly different based
on the Kolmogorov-Smirnov two-sample test with \emph{p value} less than
0.01.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3 Vertical distribution of zonal mean cloud fraction (unit: \%)
in the Control run (top row), the ClimRad, ClimRadFT and ClimRadBL runs
(middle row, from left to right) and their difference (bottom row). The
y-axis (pressure) is of logarithmic scale.

\textsuperscript{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4 Same as Figure 3 but for vertical distribution of zonal mean
relative humidity (unit: \%).

\textsuperscript{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5 A comparison of PDFs of the subsidence fraction in the Control,
ClimRad, ClimRadFT and ClimRadBL runs over the entire tropics.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6 Maps of annual maximum precipitation (left; units: mm
day\textsuperscript{-1}) and precipitation extremes scaling (right;
units: mm day\textsuperscript{-1}) in the Control run (top), ClimRad run
(middle) and their difference (bottom).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7 The top row shows\(10\times 10\) blocks across the tropics
while the bottom row shows composites of precipitation in the Control
run for different domain mean precipitation bins: \textless{}5, 5--10,
10--15 and \textgreater{}15 mm day\textsuperscript{-1} (from left to
right).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8 The top row shows boxplots of normalized \(N_{b}\) in
the Control run (red) and the ClimRad run (blue), while the bottom row
shows PDFs of subsidence fraction.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\par\null

Figure 9 Composites of CRH-sorted streamfunction (contours; the thicker
solid line shows zero values) and radiative cooling rates (colors; K
day\textsuperscript{-1}) for the Control run (top) and the ClimRad run
(bottom) for different domain average precipitation bins.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10 Scatter plots of two metrics for the zonal CC (x-axis) and two
metrics for the ITCZ width (y-axis) in the Control run (red) and the
ClimRad run (blue). Mean values of the zonal CC (the ITCZ width) are
marked with triangles (asterisks). Results are computed over months
during which the tropical precipitation distribution is symmetric about
the equator.

\textsuperscript{}

\textbf{Supplementary}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure S1 Zonal mean difference in EIS for Control -- ClimRad (the red
line), Control -- ClimRadBL (the blue line), and Control -- ClimRadFT
(the orange line).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

Figure S2 Same as Figure 6 but for the thermodynamic contribution (left;
units: mm day\textsuperscript{-1}) and the dynamic contribution (right;
units: mm day\textsuperscript{-1}). See texts in section 3c for more
details.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

Figure S3 Logarithmic probabilities of exceedance for daily
precipitation (left) and daily updrafts at 500 hPa (right) over grid
points within the tropics (30\selectlanguage{ngerman}°S--30°N) for the Control run (red lines)
and the ClimRad run (blue lines).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

Figure S4 Maps of temporal variance of daily precipitation (units:
\(\times 10^{3}\)mm\textsuperscript{2} day\textsuperscript{-2}) in the
Control run (top), ClimRad run (middle) and their difference (bottom).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

Figure S5 Zonal mean P minus E (units: mm day\textsuperscript{-1})
averaged over all months (left) and over months during which the
tropical precipitation distribution is symmetric about the equator
(right).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

Figure S6 Maps of P minus E (units: mm day\textsuperscript{-1}) for the
Control run (top) and the ClimRad run (bottom) averaged over all months
(left) and over months during which the tropical precipitation
distribution is symmetric about the equator (right).

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