Gilles Bellon
email: gilles.bellon@meteo.fr

David Coppin

in Modeling Earth Systems (JAMES

Subsidence favors convective self-aggregation in a convection-permitting model • Two stationary states, one aggregated, the other non-aggregated can exist for the same subsidence • In the aggregated stationary state, the area of the convective region adjusts in response to subsidence

manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES)

Abstract

Simulations using the convection-permitting MesoNH model with imposed vertical motion document the influence of large-scale circulation on convective self-aggregation. Results show that subsidence favors self-aggregation in this model and that this sensitivity includes a hysteresis: for weak subsidence, only one stationary state is found, without aggregation; for moderate subsidence, two stationary states are found, one with aggregation and one without; for large subsidence, only the aggregated stationary state is found. In that state, the area covered by deep convection decreases with subsidence. Using the variance of column moist static energy (MSE) as a metric for aggregation, we detail the role of physical processes in the development or maintenance of aggregation.

Solar radiation always contributes positively to aggregation. The effect of terrestrial radiation results from a competition between the effects of the top-of-atmosphere and surface fluxes, and can therefore vary in amplitude and change sign both with time in transient simulations and with subsidence intensity in stationary state. The effect of turbulent surface fluxes also result from a competition between the effect of air-sea thermodynamic contrast and the wind-induced contribution, and it can also vary very significantly. The contribution of MSE transport within the model domain also changes from negative to positive as the intensity of subsidence is increased because the shallow circulation accelerates and causes a change of sign in the gross moist stability associated with this circulation.

Plain Language Summary

In the tropical atmosphere, deep convective clouds are sometimes scattered randomly over a region, but most often they are organised spatially in cloud ensembles, such as tropical storms, with regions without deep clouds surrounding these ensembles. In idealized numerical simulations of the tropical atmosphere, spontaneous spatial organisation also occurs and is called convective self-aggregation. Although some of the characteristics of observed spatially organised convection match those of modeled self-aggregation, it is still unclear whether the mechanisms yielding observed and modeled phenomena are the same. This study contributes to this line of inquiry by studying the influence of largescale atmospheric circulation on self-aggregation. Results show that subsidence favors self-aggregation; this sensitivity is highly non-linear and includes a hysteresis. Varying subsidence also appears as a way to document varying roles of the physical processes (radiation, surface fluxes, transport) in the development or maintenance of aggregation.

Introduction

Convective self-aggregation is the spontaneous spatial organization of deep convective clouds in one or a few convective regions surrounded by dry regions in which convection is limited to the boundary layer. It has been documented in a number of atmospheric models of various levels of complexity (see [START_REF] Wing | Convective selfaggregation in numerical simulations: A review[END_REF], for a review) in an idealized configuration known as radiative-convective equilibrium (RCE), in which there is no rotation and no transport of water or energy into or out of the simulation domain.

Many processes appear involved in the arising of self-aggregation: clear-sky and cloud radiative contrasts [START_REF] Tompkins | Radiative-convective equilibrium in a three-dimensional cloud-ensemble model[END_REF][START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Stephens | Radiative-convective feedbacks in idealized states of radiative-convective equilibrium[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF]Wing & Emanuel, 2014;[START_REF] Muller | What favors convective aggregation and why?[END_REF][START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF][START_REF] Becker | Imprint of the convective parameterization and sea-surface temperature on large-scale convective selfaggregation[END_REF][START_REF] Yang | Boundary layer height and buoyancy determine the horizontal scale of convective self-aggregation[END_REF], wind-induced surface heat fluxes [START_REF] Tompkins | Radiative-convective equilibrium in a three-dimensional cloud-ensemble model[END_REF][START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF][START_REF] Becker | Imprint of the convective parameterization and sea-surface temperature on large-scale convective selfaggregation[END_REF], shallow circulations [START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF][START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF][START_REF] Shamekh | Self-aggregation of convective clouds with interactive sea surface temperature[END_REF], cold pools [START_REF] Tompkins | Organization of tropical convection in low vertical wind shears: The role of cold pools[END_REF][START_REF] Jeevanjee | Convective self-aggregation, cold pools, and domain size[END_REF][START_REF] Haerter | Convective self-aggregation as a cold pool-driven critical phenomenon[END_REF], and which processes are dominant seem highly dependent on models and surface boundary conditions.

Nevertheless, the combination of these processes can be translated into two main mechanisms, which have resulted in the development of simple models of self-aggregation: a radiative-convective instability [START_REF] Emanuel | Radiative-convective instability[END_REF][START_REF] Beucler | Moisture-radiative cooling instability[END_REF] and an upgradient energy transport due to a shallow circulation [START_REF] Naumann | A conceptual model of a shallow circulation induced by prescribed low-level radiative cooling[END_REF][START_REF] Naumann | A moist conceptual model for the boundary layer structure and radiatively driven shallow circulations in the trades[END_REF].

Even though these mechanisms originate from different processes and different regions of the atmosphere, they do not exclude one another.

The observed atmosphere shares many characteristics of self-aggregated simulations (see [START_REF] Holloway | Observing convective aggregation[END_REF], for a review), but the relationship between self-aggregation and the observed organization of convection is still unclear. Considering the potential impact of changes in organized convection on climate change [START_REF] Wing | Self-aggregation of deep convection and its implications for climate[END_REF], bridging the gap between idealized simulations and realistic situations has become a priority. Many steps have been attempted in this direction, such as the inclusion of rotation [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Khairoutdinov | Rotating radiative-convective equilibrium simulated by a cloud-resolving model[END_REF][START_REF] Merlis | Surface temperature dependence of tropical cyclone-permitting simulations in a spherical model with uniform thermal forcing[END_REF], of a hot spot (Shamekh et al., 2020a), of the diurnal cycle [START_REF] Haerter | Diurnal self-aggregation[END_REF][START_REF] Tompkins | Impact of a mixed ocean layer and the diurnal cycle on convective aggregation[END_REF] or the coupling with a simple model of the upper ocean [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Hohenegger | Coupled radiative convective equilibrium simulations with explicit and parameterized convection[END_REF][START_REF] Coppin | Internal variability in a coupled general circulation model in radiative-convective equilibrium[END_REF][START_REF] Yang | Boundary layer diabatic processes, the virtual effect, and convective self-aggregation[END_REF][START_REF] Shamekh | Self-aggregation of convective clouds with interactive sea surface temperature[END_REF].

The present work is a step in another direction, investigating whether self-aggregation changes with large-scale circulation, for example between the ascending and subsiding regions of the Walker circulation or between phases of slow intraseasonal waves. To address this question, we use a convection-permitting model with an imposed large-scale vertical motion of which we systematically vary the intensity. We consider that, as long as the large-scale forcing is horizontally homogeneous, such as uniform SST and horizontally uniform imposed vertical motion, convective aggregation results from sub-domain processes and can be termed self-aggregation. Section 2 presents our model, its configuration, and the methodology used in the analysis of our simulations. Section 3 presents our results before our conclusions in Section 4.

Method

Convection-permitting simulations

We use the mesoscale nonhydrostatic atmospheric model Meso-NH version 5.2.2 [START_REF] Lafore | The Meso-NH Atmospheric Simulation System. Part I: Adiabatic formulation and control simulations[END_REF][START_REF] Lac | Overview of the Meso-NH model version 5.4 and its applications[END_REF] at kilometer resolution that explicitly resolves cloud ensembles. Meso-NH is developed jointly by the Laboratoire d'Aérologie (LA) and the Centre National des Recherche Météorologiques (CNRM). Cloud microphysical processes are represented by a single-moment bulk scheme [START_REF] Pinty | A mixed-phased cloud parameterization for use in a mesoscale non-hydrostatic model: simulations of a squall line and of orographic precipitation[END_REF]) that tracks five different types of hydrometeors (cloud liquid water and ice, rain, graupel, and snow).

Turbulence is solved by a three-dimensional scheme using a prognostic equation for the turbulent kinetic energy with a 1.5-order closure scheme and the turbulent mixing length given by the mesh size [START_REF] Cuxart | A turbulence scheme allowing for mesoscale and large-eddy simulations[END_REF]. The eddy-diffusivity mass-flux scheme of [START_REF] Pergaud | A parameterization of dry thermals and shallow cumuli for mesoscale numerical weather prediction[END_REF] is used to represent dry thermals in the atmospheric boundary layer and unresolved shallow convective clouds. Radiation calculations use the RRTM scheme for longwave [START_REF] Morcrette | Radiation and cloud radiative properties in the European Centre for Medium Range Weather Forecasts forecasting system[END_REF][START_REF] Morcrette | The surface downward longwave radiation in the ECMWF forecast system[END_REF] and [START_REF] Fouquart | Computations of solar heating of the earth's atmosphere: A new parameterization[END_REF] for shortwave. Surface processes and interactions with the atmosphere are simulated by the SURFEX model [START_REF] Masson | The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of earth surface variables and fluxes[END_REF] in which oceanic surface fluxes are computed using bulk formulae with exchange coefficients parameterized by the ECUME scheme [START_REF] Belamari | Report on uncertainty estimates of an optimal bulk formulation for surface turbulent fluxes. Marine EnviRonment and Security for the European Area-Integrated Project (MERSEA IP)[END_REF].

In our reference configuration, the domain is a doubly-periodic 300-km square on the horizontal and tops vertically at 25 km. The horizontal grid spacing is 3 km and there are 47 stretched vertical layers with a thickness of 75 m at the surface and 800 m at the top. Diffusion and damping are used in the top levels to prevent unrealistic reflection of vertically propagating waves. The time step is 20 s. There is no mean wind and no rotation. SST is fixed to the typical tropical value of 301 K and solar parameters are set constant at the equatorial equinox. Since self-aggregation is sensitive to domain size and horizontal resolution [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF][START_REF] Jeevanjee | Convective self-aggregation, cold pools, and domain size[END_REF][START_REF] Muller | What favors convective aggregation and why?[END_REF], Section 3 of the Supplementary material explores the sensitivity of our results to resolution and domain size with experiments with horizontal grid spacing of 4 km and experiments with horizontal domain size of 150 km.

First, the model is run in Radiative-Convective Equilibrium (RCE), which is the stationary state the atmosphere would reach in the absence of large-scale energy transport. We initialize this simulation with typical average tropical profiles of the thermodynamic variables (20-year average at (10 • N, 180 • ) from ERA-Interim reanalysis) and no wind. A white noise of 0.1 K is added to the first 5 levels to initiate sub-domain variability (i.e., horizontal in-homogeneity within the domain), with maximum amplitude at 30 m. This simulation is performed for 200 days of model time. The model domain is small compared to the scales on which RCE is usually observed [START_REF] Jakob | Radiative convective equilibrium and organized convection: An observational perspective[END_REF].

The best real-world analog to this configuration is a small equatorial region with zero vertical motion, either in a transition region between a convergence zone and a region of subsidence or between phases of a large-scale wave, with the caveat that large-scale conditions often change on timescales shorter than the characteristic time scales of selfaggregation.

Second, we perform a series of experiments with imposed large-scale mean subsidence w(z) (as usual, the overbar denotes horizontal average). We impose a profile of vertical velocity typical of large-scale tropical variability [START_REF] Kiladis | Convectively coupled equatorial waves[END_REF][START_REF] Kiladis | Zonal and vertical structure of the madden-julian oscillation[END_REF], with a maximum intensity in the mid-troposphere: w(z) ∝ sin (πz/H) with H = 14 km. The amplitude of subsidence is controlled by multiplicative parameter M . M = 1 corresponds to a downward vertical mass flux M of 1 g m -2 s -1 , typical of the suppressed phase of the Madden Julian Oscillation [START_REF] Johnson | Structure and properties of Madden-Julian Oscillations deduced from DYNAMO sounding arrays[END_REF][START_REF] Sperber | Propagation and the vertical structure of the madden-julian oscillation[END_REF][START_REF] Adames | Three-dimensional structure and evolution of the vertical velocity and divergence fields in the mjo[END_REF]. The RCE simulation corresponds to M = 0 (w = 0 m s -1 ). Figure 1a illustrates the profile of vertical velocity for a few values M . The mean subsidence is im-posed uniformly on the horizontal and adds a transport term in the prognostic equations of momentum, energy, and moisture as in classical test cases (e.g., [START_REF] Redelsperger | A gcss model intercomparison for a tropical squall line observed during toga-coare. i: Cloud-resolving models[END_REF][START_REF] Janiga | Mjo moisture budget during dynamo in a cloudresolving model[END_REF]. These transport terms follow the flux formulation introduced in previous studies of stationary states [START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 1. comparison over uniform surface conditions[END_REF][START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 2. comparison over nonuniform surface conditions[END_REF], using the horizontalmean, time-mean RCE thermodynamic profiles as reference profiles for the atmosphere outside the domain (based on the last 90 days of the simulation with M = 0); this formulation is to avoid an unrealistically dry free troposphere.

We will call "external transport" (EXTR) the import or export associated with the imposed circulation w and "internal transport" (INTR) the intra-domain transport associated with the internal circulations (u, v, w ), with the prime denoting the deviation from the horizontal average w.

M is the control parameter for our series of numerical experiments; it is first increased systematically from zero to 2.5 and then systematically decreased from 2.5 to zero. As initial conditions, simulations use the final state of the previous simulation or the simulation with the nearest value of M . If a transition to another regime occurs in a simulation, simulations with very similar M (down to increments of 0.1) are performed and the possible existence of a hysteresis is investigated. For each value of M , simulations are integrated in time until they reach stationary state, which is diagnosed by looking at the difference between the last two 10-day segments of the simulation. If the maximum difference between the segment-mean, horizontalmean liquid-water potential temperature profiles is smaller than 0.1 K and the maximum difference between the segment-mean, horizontal-mean total water is smaller than 0.1 g/kg, then the simulation is considered to have reached stationary state. This can take over 200 model days in the cases with a transition between regimes. We also lengthen the simulations to 300 days for M closest to a transition threshold (aggregated stationary state for M = 0.5 and non-aggregated stationary state with M = 1.5) to ascertain the stability of these stationary states. We use the last 50 days of the simulations to describe the stationary state. In the following, we use the term "equilibrium" interchangeably with "stationary state", even if the model exhibits internal variability and only the domain-mean, 10-day statistics do not vary in time.

Moist static energy analysis

As in previous studies [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF]Wing & Emanuel, 2014;[START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF][START_REF] Becker | Imprint of the convective parameterization and sea-surface temperature on large-scale convective selfaggregation[END_REF], we base our analysis of convective aggregation on the moist static energy (MSE) h including the effect of ice condensate ("frozen MSE"):

h = C p T + Φ + L v q v -L f q i , (1)
with C p the heat capacity of air at constant pressure, T the temperature, Φ the geopotential, L v the latent heat of evaporation, q v the water vapor mixing ration, L f the latent heat of fusion, and q i the ice water mixing ratio.

In particular, we examine the sub-domain variability of the column-integrated MSE:

[h] = zt 0 hρ 0 dz, (2)
with z t the altitude of the top of the model and ρ 0 the reference density profiles in the anelastic approximation. The brackets denote a vertical integration.

First, we use the sub-domain Probability Distribution Function (PDF) to determine whether convection is aggregated or not in a given equilibrium. Using optimization least-square algorithms (interior-point and Levenberg-Marquardt algorithms), we approximate the PDF of [h] in stationary state by a normal distribution or the sum of two log-normal distributions. If the PDF of [h] is best approximated by a unimodal, normal distribution, we consider that the convection in that equilibrium is not aggregated.

If the PDF of [h] is best approximated by the sum of two log-normal distributions, we consider that the convection in that stationary state is aggregated. Note that we also tried to approximate the PDFs of [h] with a log-normal distribution and the sum of two normal distributions but in no case was one of these the best approximation. Because of the small horizontal gradients of temperature in the tropical free troposphere and the small quantity of ice water in the air, the horizontal variability of [h] follows closely that of the column-integrated water vapor [q v ], also known as precipitable water (PW); the same method using PDFs of PW yields very similar results (not shown).

Figure 2a shows the PDFs of [h] for two stationary states obtained for M = 1.5.

In the non-aggregated case (orange line), the PDF of [h] is clearly unimodal and very peaked at its maximum. In the aggregated case (red line), the PDF of [h] is bimodal, and well approximated by the sum of two log-normal distributions; one mode with low regions. This allows us to diagnose the respective areas of these regions and to analyse aggregated stationary states in a two-column framework, with one convective column and one dry column similarly to some studies on the climate of the whole tropics [START_REF] Pierrehumbert | Thermostats, radiator fins, and the local runaway greenhouse[END_REF][START_REF] Bellon | Large-scale and evaporation-wind feedbacks in a box model of the tropical climate[END_REF][START_REF] Bellon | Analysis of the tropical climate variability in a two-column framework[END_REF].

Third, since convective aggregation corresponds to an increase in the sub-domain variability of MSE, we can use the budget of MSE to diagnose the processes that influence the sub-domain variance of [h] following the method introduced by [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF] which has become standard [START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF][START_REF] Bretherton | Convective self-aggregation feedbacks in near-global cloud-resolving simulations of an aquaplanet[END_REF][START_REF] Holloway | The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations[END_REF][START_REF] Becker | Imprint of the convective parameterization and sea-surface temperature on large-scale convective selfaggregation[END_REF][START_REF] Pope | Cloud-radiation interactions and their contributions to convective self-aggregation[END_REF]: the processes that increase the variance of MSE aggregate convection and those that decrease the variance of MSE homogenize convection. The column-integrated budget of MSE can be written:

d[h] dt = [∂ z (ρ 0 w) h cv ] -[∇ • (ρ 0 uh)] + ∆R + T SHF, (3)
with h cv = h where the imposed circulation is horizontally divergent (∂ z (ρ 0 w) < 0) and h cv is the horizontally averaged MSE in RCE h RCE where the imposed circulation is horizontally convergent (∂ z (ρ 0 w) > 0); u = (u, v) is the horizontal velocity, ∆R is the convergence of the radiative fluxes across the atmospheric column, and T SHF is the surface turbulent heat flux (i.e., the sum of the sensible and latent heat fluxes). On the right-hand side, the first term is the external transport and the second term is the internal transport. In practice, the internal transport is computed as a residual from this column-integrated MSE budget.

-9-manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES)

By using Equation (3) for the perturbation [h ] of column-integrated MSE, we can diagnose the role of the different processes in the evolution of the variance of [h], following [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF]:

d[h ] 2 dt = 2[h ] d[h ] dt = 2[h ][∂ z (ρ 0 w) h cv ] -2[h ][∇ • (ρ 0 uh)] + 2[h ]∆R + 2[h ]T SHF . (4)
The radiative flux convergence can be decomposed into the sum of solar ("shortwave") and terrestrial ("longwave") contributions:

∆R = ∆R SW + ∆R LW , (5)
And ∆R, ∆R SW , and ∆R LW can be written as the difference between the net upward flux at the surface and the net upward flux at the top of the atmosphere:

∆R = F SRF -F TOA , (6)
and corresponding expressions for ∆R SW and ∆R LW . The contribution of radiation to the time evolution of the variance of [h] can be decomposed into contributions from solar and terrestrial radiation and/or from surface and top-of-the-atmosphere fluxes:

2[h ]∆R = 2[h ]∆R SW + 2[h ]∆R LW , (7)
and

2[h ]∆R = 2[h ]F SRF -2[h ]F TOA . (8)
The turbulent surface fluxes are modelled by so-called bulk formula:

T SHF = ρ 0 C d V s δh, (9)
with C d a parameter called drag coefficient, V s is the near-surface wind speed, and δh is the difference between the saturated MSE at the sea surface temperature and the nearsurface MSE. Still following [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF], the contribution of turbulent surface fluxes to the time evolution of the variance of [h] can be decomposed into contri-butions from the variability of the air-sea thermodynamic contrast, from the surface-wind variability (also called Wind-Induced Surface Heat Exchange -WISHE -effect), and from the co-variation of the two, which is generally a small term that can be neglected:

2[h ]T SHF ≈ 2ρ 0 C d V s [h ]δh + 2ρ 0 C d [h ]u s • u s V s δh, (10)
with u s the near-surface velocity (V s = ||u s ||). Note that with constant SST, the anomaly of the air-sea MSE contrast is just the opposite of the anomaly h s of near-surface

MSE: δh = -h s , and [h ]δh = -[h ]h s .

Gross moist stability

For a given circulation, the normalized gross moist stability (NGMS) is the amount of MSE exported from region by unit of latent heat imported into this region (see Ray- On the contrary, if the NGMS is negative, the circulation is a positive feedback. We will be interested in the NGMS of the internal circulation in the aggregated stationary state:

N GM S = - [∇ • (ρ 0 uh)] m [∇ • (ρ 0 uq v )] m , (11)
with [•] m indicates the column-integrated average over the moist, convective region.

Results

In the following, we present simulations with non-aggregated initial conditions for M = 0, 0.5, 1, 1.5, 1.6, 2, 2.5 and simulations with aggregated initial conditions for M = 0, 0.4, 0.5, 1, 1.3, 1.5, 2, 2.5. We have also performed simulations with M < 0 (mean ascending motion) with non-aggregated initial conditions, and obtained only non-aggregated stationary states with a sensitivity to M similar to the cases with M > 0, so these simulations are not presented here.

Hysteresis and multiple stationary states

In our configuration, Meso-NH does not exhibit self-aggregation in RCE (M = 0) unlike many similar models used in previous studies. In configurations more favorable to self-aggregation (e.g., with larger horizontal domain or reduced horizontal resolution), Meso-NH does simulate self-aggregation in RCE (see Section 3 of the Supplementary material for an example).

For 0 ≤ M ≤ 1.5, all simulations with non-aggregated initial conditions yield non-aggregated equilibria. For M ≥ 1.6, the simulations with non-aggregated initial conditions (which are the final state of the non-aggregated equilibrium with M = 1.5) yield an aggregated equilibrium. For 0.5 ≤ M ≤ 2.5, all simulations with aggregated initial conditions yield aggregated equilibria. For M ≤ 0.4, the simulations with aggregated initial conditions (which are the final state of the aggregated equilibrium with M = 0.5) yield a non-aggregated equilibrium. Figure 3 shows the daily mean PW for one day of the simulations in equilibrium for M = 0, 0.5, 1, 1.5, 2, 2.5. Only stationary states reached by the model are shown in this figure; if, for a value of M , only one map is shown, this means that the same stationary state was obtained, irrespective of initial conditions.

For 0.5 ≤ M ≤ 1.5, we obtain multiple equilibria (one non-aggregated and one aggregated); the initial conditions determine which equilibrium is reached by each simulation.

For the non-aggregated equilibria (Fig. What our set of simulations shows is that subsidence favors convective aggregation in Meso-NH, but not in a linear way in which aggregation would increase progressively with M : subsidence destabilizes the non-aggregated equilibrium for a threshold M N A between 1.5 and 1.6, and only the aggregated equilibrium is stable for larger values of M . And aggregation is unstable for weak subsidence, up to a threshold M A between 0.4 and 0.5 and can only develop for stronger subsidence.

We investigate how the hysteresis in Meso-NH is sensitive to horizontal resolution and domain size in Section 3 of the Supplementary material. Overall, we find that the threshold M A for the existence of the aggregated equilibrium is reduced in configurations more favorable to self-aggregation (coarser resolution, larger domain), and so is the threshold M N A for destabilization of the non-aggregated equilibrium.

In aggregated cases, for M = 0.5 and 1, the subsiding region appears as a patch;

for M = 2.5, the patch corresponds to the convective region; and the equilibrium for M = 1.5 and 2 are intermediary cases. These situations are reminiscent of the successive transient phases in simulations of self-aggregation (e.g., Wing & Emanuel, 2014):

in these simulations, aggregation starts with the formation of a cold, dry patch that progressively extends and corals convection into a limited region of the domain. The study of the dynamics of this patch, often called "radiative cold pool" is the focus of some of the work on the fundamental mechanisms of self-aggregation [START_REF] Naumann | A conceptual model of a shallow circulation induced by prescribed low-level radiative cooling[END_REF][START_REF] Naumann | A moist conceptual model for the boundary layer structure and radiatively driven shallow circulations in the trades[END_REF].

In our simulations, we obtain dry patches (and moist patches) of varying sizes. Using the method described in Section 2.2, we can diagnose the relative area of the convective region. Figure 2b shows this relative area for the aggregates equilibria as a function of M : it decreases with increasing subsidence (i.e., increasing M ), from 0.78 for M = 0.5 to 0.16 for M = 2.5. This suggests that large-scale transport can have an effect on the scale of aggregation additionally to diabatic effects [START_REF] Bretherton | Convective self-aggregation feedbacks in near-global cloud-resolving simulations of an aquaplanet[END_REF][START_REF] Beucler | A budget for the size of convective selfaggregation[END_REF] and buoyancy processes in the atmospheric boundary layer (Yang, 2018a).

Sensitivity to subsidence

Figure 4 shows the equilibrium profiles of thermodynamic variables averaged over the horizontal domain for varying values of M : the difference ∆θ between the equilibrium profiles of potential temperature θ(z) and its profile in RCE (Figure 4a), the water vapor and water condensate mixing ratios q v and q c (Figures 4b,c). Figure A1 in the Appendix also shows the profiles on MSE and the profiles in moist and dry regions of the aggregated equilibria. In average over the domain, aggregated equilibria are more convectively stable, drier and less cloudy than the corresponding non-aggregated equilibria for the same subsidence. This is a well-known difference between aggregated and non-aggregated states since the earliest studies of self-aggregation [START_REF] Held | Radiative-convective equilibrium with explicit two-dimensional moist convection[END_REF] that is also observed [START_REF] Tobin | Observational evidence for relationships between the degree of aggregation of deep convection, water vapor, surface fluxes, and radiation[END_REF][START_REF] Holloway | Observing convective aggregation[END_REF][START_REF] Stein | Observed relationships between cloud vertical structure and convective aggregation over tropical ocean[END_REF]. The dif-ference in stability is explained by intense convection in the moist regions of the aggregated equilibria, which is more concentrated than the scattered convection in the nonaggregated equilibria and occurs in a moister environment. The effect of convective entrainment on convective updrafts is smaller in the moist region of the aggregated state than in the non-aggregated state, so that the free-tropospheric temperature is more closely tied to the boundary-layer MSE and warmer. In the aggregated equilibria, the free-tropospheric temperature profile in the moist region is communicated to the whole domain by transient gravity waves and the overturning circulation. This overturning circulation also dries the dry regions very efficiently, resulting in an overall drier and less cloudy aggregated equilibria than the corresponding non-aggregated equilibria. Figure A1b shows that the moist regions of the aggregated equilibria are actually moister than the RCE, while the dry regions are essentially devoid of moisture and cloud.

Overall, subsidence dries both the aggregated equilibria and the non-aggregated equilibria and increases the contrast between the two regimes. In the non-aggregated regime, as M increases, subsidence reduces convection by drying the entire domain (see Fig. 4b);

this results in reduced cloudiness (see Fig. 4c) as well as slightly reduced boundary-layer MSE (see Fig. A1a) and increased updraft dilution, which yield less convectively stable temperature profiles (see Fig. 4a). For values of M beyond M N A , the subsidence drying is sufficient to inhibit widespread convection and the non-aggregated equilibrium becomes unstable, only the aggregated equilibria exists. In the aggregated regime, the main adjustment is a change in the relative area of the moist and dry regions: as M increases, the moist region becomes smaller (see Fig. 2b) and it becomes moister, more convective, and more cloudy (see Fig. A1b,c). The decrease in updraft dilution in the moist region explains the increasingly warm free troposphere (see Fig. 4a) and the decrease in the area of the moist region explains the decrease in domain-average humidity and cloudiness with increasing M (see Fig. 4b,c). Essentially, as M increases, evaporation from the entire domain is transported to a smaller and smaller fraction of the domain where convection remains.

Figure 5 shows the different terms of the domain-averaged energy and water bud- Two-column models [START_REF] Pierrehumbert | Thermostats, radiator fins, and the local runaway greenhouse[END_REF][START_REF] Bellon | Large-scale and evaporation-wind feedbacks in a box model of the tropical climate[END_REF] have long shown that the relative area of the moist column/region is one of the most important control parameters for their equilibrium and can therefore modulate strongly the equilibrium response to an external forcing; some studies have postulated that changes in the area of moist and cloudy regions might be an important feedback to anthropogenic climate change [START_REF] Mauritsen | Missing iris effect as a possible cause of muted hydrological change and high climate sensitivity in models[END_REF]. Our kilometer-resolution model does simulate such a stabilizing feedback to an external forcing, which makes the aggregated equilibrium more resilient to the imposed drying than the non-aggregated equilibrium. This suggests that the change in the area of the moist region is a factor in the instability of the aggregated equilibrium for M < M A : the dry region becomes too small to withstand perturbations associated with the internal variability of the model and disappears, yielding a non-aggregated equilibrium after a long adjustment.

Mechanisms at equilibrium

In this section, we use the analysis of the MSE budget described in Section 2.2.2

to understand which processes contribute to the stability or instability of the non-aggregated and aggregated equilibria. In the non-aggregated equilibria (see Fig. 6a), all diabatic processes (radiation and surface turbulent fluxes) tend to aggregate convection and therefore destabilize the equilibria, while both internal and external transports decrease aggregation and stabilize the equilibria. While the effect of solar radiation and turbulent surface fluxes is not very sensitive to the imposed subsidence, the effect of terrestrial radiation and transport increases with M (in absolute value). In all aggregated equilibria (Figure 6b), solar radiation reinforces aggregation and external transport weakens aggregation; the surface-flux term is small and positive for small M and increasingly unfavorable to aggregation as M increases: the effect of terrestrial radiation and internal transport vary significantly with M even changing sign between low M , for which terrestrial radiation favors aggregation and internal transport opposes it, and large M , for which terrestrial radiation opposes aggregation and internal transport favors it.

To better understand these terms, Figure 7 shows the contributions of each percentile of [h] to these terms for the aggregated equilibria with M = 0.5, 1.5, and 2.5.

Because these contributions are physically similar in the non-aggregated equilibria and in the aggregated equilibria with M = 0.5, we do not show a corresponding figure for the non-aggregated ones.

Solar radiation:

The effect of absorption by humidity is larger than that of reflection by clouds at the top of the atmosphere which is partially offset by an opposite effect at the surface. Moister, larger-MSE atmospheric columns absorb more solar radiation than dry, low-MSE ones and solar radiation therefore amplifies contrasts in [h],

with a larger contribution from dry columns (not shown). This contribution therefore systematically favors aggregation, and more so if the MSE and humidity contrasts increase, i.e for high M . These results are consistent with previous studies (see Wing et al., 2018).

Terrestrial radiation: This term has been widely identified as crucial to the triggering of aggregation [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF][START_REF] Holloway | The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations[END_REF][START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF], with a particularly large positive contribution of the driest, lowest-MSE columns that form the radiative cold pool(s) in the early stages of a transition from a non-aggregated to an aggregated state. This term was also iden-tified in some simulations as dominant in the maintenance of aggregation (Wing & Emanuel, 2014), although the contribution of the driest columns at equilibrium is negative. Most of our results are consistent with these previous studies: in the non-aggregated equilibrium, the terrestrial term favors aggregation and it is the only positive term that increases significantly with increasing M , suggesting that terrestrial radiation is the process that causes the instability of the non-aggregated equilibrium for M > M N A (see Fig. 6a).

In most of the aggregated equilibria (for M ≤ 1.6), the terrestrial term is also positive, and it is one of the largest terms for small M ; but this term decreases with M and even becomes negative, unfavorable for convection, for M ≥ 2 (see Fig. 6a). This sensitivity to M results from a competition between the sensitivity of the surface terrestrial flux and that of the top-of-the-atmosphere flux: moist atmospheric columns cause a larger greenhouse effect than dry columns and therefore emit less towards space, but also more towards the surface. Since, at constant SST, the surface emits a fixed terrestrial flux, moist columns lose less terrestrial radiation to space and more to the surface than dry columns. The competition between surface and top-of-the-atmosphere fluxes plays out differently depending on the humidity of the column: Figure 7 shows that in very dry atmospheric columns, the surface flux dominates and the terrestrial contribution of these columns to aggregation is negative, similarly to [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF]. The physics behind this nonlinear behavior are fairly straightforward. In the dry region, the free troposphere is very dry, so that the effective radiative temperature is es-sentially that of the top of the boundary layer, not much colder than the surface temperature. A decrease in low-level humidity causes less emission by the lower troposphere but also more transmission of the upward surface flux. These two effects largely compensate each other in the net upward flux at the top of the boundary layer and at the top of the atmosphere, making the outgoing longwave radiation little sensitive to lowlevel humidity (Fig. 8c). On the other hand, a reduced downward emission from the lower troposphere associated with a decrease in low-level humidity increases the net upward flux at the surface (Fig. 8d). In the moist region, the more usual greenhouse effect of moisture and clouds is at play: the lower and middle troposphere is essentially opaque to terrestrial radiation, the effective temperature of downward emission and therefore the net surface flux are insensitive to changes in column moisture (Fig. 8d). On the other hand, outgoing longwave radiation is very sensitive to hydrometeors, an increase in column humidity corresponds to an increase in cloudiness, which raises the equivalent level of emission to space and therefore lowers the effective temperature, resulting in a decrease of the outgoing longwave radiation (Fig. 8c).

This physical reasoning is consistent with the simple two-layer radiative model in [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF] (see their Figure 12 and Equation ( 13))) : the divergence of the terrestrial radiative flux across the atmospheric column systematically increases with the emissivity (or humidity) of the upper layer (or free troposphere) and decreases with the emissivity of the lower layer (or boundary layer). In the moist region, both emissivities tend to covary (convection mixes humidity vertically) and moister atmospheric columns cool less than drier ones. But in the dry region, the emissivity of the free troposphere is almost fixed and the column radiative cooling mostly responds to changes in the emissivity of the boundary layer: columns with a moister boundary layer cool more than drier ones.

As M increases, the area of the dry region increases, resulting in an increasingly larger negative contribution of the dry columns to the terrestrial radiative effect. In the dry regions, the sensitivity of the top-of-the atmosphere flux to [h] also decreases, resulting in an increasingly negative contribution of the driest regions (see Fig. 7). In the moist columns, the sensitivity of both the surface and top-of the-atmosphere fluxes to [h] increases, with a dominant effect of the latter (greenhouse effect), resulting in an increasingly positive contribution of the moistest columns, but this effect is limited to an in-creasingly small region. As a result, the overall effect of terrestrial radiation on aggregation decreases and even becomes negative.

Surface fluxes: In the non-aggregated equilibria, the turbulent surface heat fluxes favor aggregation (see Fig. 6a). This is also true for the aggregated equilibrium with M = 0.5, although this effect is very small compared to the other terms. For M > 0.5, we find that surface fluxes limit aggregation in the aggregated equilibria, and increasingly so as M is increased. In general, previous studies have found a supporting role for surface fluxes during self-aggregation [START_REF] Tompkins | Radiative-convective equilibrium in a three-dimensional cloud-ensemble model[END_REF][START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF][START_REF] Holloway | The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations[END_REF]Wing & Emanuel, 2014) rather than a crucial role, and [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF]; [START_REF] Holloway | The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations[END_REF] noted that this effect becomes unfavorable once aggregation has occurred. Our results are broadly consistent, with a surface-flux effect that generally tends to destabilize whichever equilibrium the model is in, but the sensitivity of the surface-flux term to M (Fig. 6) suggests that surface fluxes are not solely nor fundamentally responsible for the instability of either the non-aggregated equilibrium at large M or the aggregated equilibrium at low M .

The surface-flux effect can be decomposed as the sum of two effects (plus a nonlinear term), one resulting from air-sea thermodynamic contrast and one from the surface wind, as shown in Equation ( 10). As pointed out by [START_REF] Wing | Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simulations[END_REF], these two effects are competing to determines the net TSHF effect in moist regions: in convective regions, the near surface air has larger MSE in columns of larger MSE, and the reduced air-sea contrast yields smaller turbulent surface heat fluxes; on the other hand the surface gustiness tends to increase the surface fluxes. Overall, the surface-wind effect is predominant and surface fluxes favor aggregation in these regions. This is apparent in our results as well: in the non-aggregated equilibria (see Fig. 6a), convection occurs over the whole domain and overall surface-flux effect favors convection; and the contribution of moist regions in the aggregated equilibria is positive as well (see Fig. 7). But in the dry regions of the aggregated equilibria, the boundary layer is ventilated and dried by the overturning circulation, the air-sea thermodynamic contrast can become quite large and its effect becomes much larger than the weak surface-wind effect, yielding a net negative contribution to aggregation. Note also that the sum of the two effects does not match the total TSHF effect for the lowest and highest percentiles of [h], pointing to a significant non-linear effect in these columns. As the imposed subsidence is increased (see Fig. 7), the area of the dry region increases and the associated negative contribution as well.

Additionnally, the effect of the thermodynamic contrast in the moist region becomes larger as they become moister (see Fig. A1). As a result, the surface-flux effect changes sign for M > 0.5 and becomes increasingly negative as M is increased.

Internal transport: Overall, internal transport by the overturning circulation has been shown to transport energy downgradient in the aggregated regime [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF]Wing & Emanuel, 2014;[START_REF] Muller | What favors convective aggregation and why?[END_REF][START_REF] Wing | Self-aggregation of convection in long channel geometry[END_REF], even if its contribution to the [h ] 2 exhibits very large variability. This is typical of a deep circulation with positive gross moist stability that exports upper-tropospheric air with large MSE from the convective regions to the dry regions, and imports surface, lower-MSE air from the dry regions into the moist regions. But almost all RCE experiments have shown that this internal transport has a positive effect on aggregation at some stage during the process of self-aggregation [START_REF] Bretherton | An energy-balance analysis of deep convective self-aggregation above uniform sst[END_REF][START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF]Wing & Emanuel, 2014;[START_REF] Muller | What favors convective aggregation and why?[END_REF]. This positive effect is attributed to a shallow circulation, with inflow in the boundary layer and outflow in the lower free troposphere, which results from radiative cooling at the top of the boundary layer in dry regions. This circulation transports energy upgradient, from dry to moist regions, because the humidity contrast between the boundary layer and the lower free troposphere results in a negative gross moist stability associated with this circulation. Our results

show that in the non-aggregated equilibria, internal transport is the main effect that prevents aggregation by redistributing energy between atmospheric columns (see Fig. 6a).

It increases as M approaches the threshold of instability M N A , suggesting that it constitutes a negative, stabilizing feedback for this equilibrium and that the initial destabilization of this equilibrium for M > M N A is not due to internal transport. In the aggregated equilibria, internal transport has a negative effect on aggregation for small M but changes sign as M is increased and becomes the largest positive effect on aggregation for large M (see Fig. 6b). Indeed, this change of signs is associated with a change of sign in the gross moist stability, from positive to negative, as diagnosed following Equation (11) and shown in Figure 2b. The change in sign of the gross moist stability results from the changes in circulation rather than changes in thermodynamic profiles: Figure A1a shows that the stratification in h increases slightly with M , which increases the gross moist stability, while Figure 1 shows very significant changes in the overturning circulation. Figure 1b shows the intensity of the overturning circulation as the upward mass Figure 1a further investigates this peculiar sensitivity of the overturning circulation by showing the horizontally averaged vertical velocity w m in the convective region and w d in the dry region, as well as the mean vertical velocity over the whole domain, which is the imposed w. The striking feature of Figure 1a is the relative insensitivity of the vertical velocity w d in the dry region to changes of M . In the tropical free troposphere, horizontal energy advection is negligible and, in equilibrium, vertical advection balances diabatic heating (e. g., [START_REF] Sobel | Modeling tropical precipitation in a single column[END_REF], which is exclusively radiative in cloudfree regions. The vertical speed can be approximated by:

w d ≈ - ṙ ∂ z θ , ( 12
)
with ṙ the radiative cooling rate on potential temperature. Because humidity in the dry regions of our aggregated equilibria is determined by transport (both internal and ex-ternal), it only decreases slightly with increasing M (see Fig. A1b) and the emissivity of the dry free troposphere in both the terrestrial and solar ranges decreases slightly with increasing M . The associated decrease of greenhouse effect results in a slight increase in the radiative cooling ṙ with increasing M . This increase is compensated by an increase in the stability ∂ z θ (see Fig. 4), and, following Equation ( 12), the subsidence w d is not sensitive to M , as seen in Figure 1a. By continuity, the vertical velocity in the dry region constrains the vertical velocity in the convective region. As M is increased, the imposed subsidence w increases and, considering a fixed, radiatively controlled subsidence w d in the dry region, the vertical velocity in the convective region w m is contrained by w d and the imposed horizontal average w; since w = Aw m + (1 -A)w d , we have:

w m = - 1 A ((1 -A)w d -w) , ∂w m ∂M = 1 A w M - 1 A 2 ∂A ∂M (w -w d ) (13)
which shows that the sensitivity of w m results from the linear variation of w with M and the decrease of relative area A of the convective region (see Fig. 2b) with M . The two effects are opposite but the latter is largely dominant in the boundary layer and upper troposphere where w -w d is large, resulting in an increase in w m with increasing M :

subsidence in an increasingly large region has to be compensated by an increasingly faster ascending motion in a smaller and smaller convective region. But in the mid-troposphere where w/M is maximum, the first effect is dominant and w m decreases with M : ascending motion decreases in the convective region to ensure that the horizontal average matches w. This yields the increase in shallow overturning circulation, the decrease in deep circulation and the development of the upper-tropospheric overturning circulation with increasing M , and consequently the decrease and change of sign of the gross moist stability. The distribution of vertical speed profile as a function of [h] (not shown) shows that this decrease of the deep circulation corresponds, within the moist region, to a decrease in the low-and mid-tropospheric vertical ascent in convective updrafts and the upward shift of subsidence in downdrafts around them.

For M ≈ 2.5, w's minimum at 7 km of altitude reaches the radiatively controlled w d (see Fig. 1b) and the subsidence at that altitude in the dry region is exclusively imposed; Equation (13) shows that w m ≈ w at this altitude, and there is no internal com-ponent in the circulation at this altitude, as seen in Figure 1a. This ensures the stability of the aggregated equilibrium by causing a large negative gross moist stability and a positive effect of internal circulation on aggregation; but it also means that the convective column is, in average, subsiding at this altitude, which is a situation whose physical realism is questionable.

Figure 7 suggests that the details beyond this overall effect of internal transport are complex. It shows that within each of the dry and moist regions, contributions change sign, with negative contributions from the moderate values of MSE and positive contributions from extreme values for M = 0.5 and 1.5. This suggests that the profiles of vertical velocity exhibit a large variability within these regions, resulting in a negative gross moist stability only in very dry and very moist columns.

External transport systematically opposes aggregation because it exports MSE from each atmospheric column and imports MSE typical of the RCE. Its overall effect is a relaxation towards the RCE profiles in each column. The amplitude of its contribution increases with the deviation from the RCE, i.e. with MSE contrasts.

Mechanisms of aggregation and disaggregation

The simulation with M = 1.6 and non-aggregated initial conditions yields an aggregated stationary state and the simulation with M = 0.4 and aggregated initial conditions yields a non-aggregated stationary state. These simulations provide opportunities to investigate the mechanisms responsible for aggregation as in previous studies (e.g., Wing & Emanuel, 2014;[START_REF] Muller | What favors convective aggregation and why?[END_REF] and those responsible for disaggregation.

Figure 9a shows the time evolution of the variance of MSE in the simulation with M = 1.6 and non-aggregated initial conditions taken from the final state of the simulation with M = 1.5, during the first 100 days of the simulation. The increase in variance between day 30 and day 60 of the simulation is characteristic of aggregation. Note that self-aggregation is slow in this simulation compared to our other simulations and among the slowest documented in previous studies [START_REF] Wing | Convective selfaggregation in numerical simulations: A review[END_REF]; we can attribute this to the weak instability of the non-aggregated state for M = 1.6. Figure 9b shows the effects of the different physical processes on the rate of change of [h ] 2 . It shows a gradual increase of the aggregating effect of terrestrial radiation starting at day 20 followed by a change of sign of the effect of internal transport at day 30 that goes from in-hibiting aggregation to driving aggregation until day 60. Afterwards, the effect of internal transport exhibits large variability, with a moderately supporting role in average, as in equilibrium (see Fig. 6b). Figure 9b suggests that other processes react to aggregation rather than drive it: the effect of solar radiation is a positive feedback on aggregation (because moister columns absorb more solar radiation), the effect of external transport is a negative feedback (because external transport acts as a relaxation towards the RCE profiles), and the effect of surface fluxes goes from destabilizing the non-aggregated state (due to the dominant wind-induced effect) to limiting aggregation in the aggregated state (due to the dominant effect of air-sea thermodynamic contrast), as can be expected from the equilibrium effects (see Fig. 6). Figure 9c Figure 9d shows the time evolution of the distribution of internal-transport contribution per MSE percentile. It shows that the drying effect of shallow circulation on the driest columns starts around day 30, about 10 days after the terrestrial effects. Internal transport appears to respond to the terrestrial effect rather than to initiate aggregation. But between day 40 and 60, internal transport is the largest contributor to aggregation (see Fig. 7b), with a major contribution of the driest column from which shallow circulation removes moisture and MSE.

Figure 10a shows the time evolution of [h ] 2 in the simulation with M = 0.4 and aggregated initial conditions taken from the final state of the simulation with M = 0.5, during the second 100 days of the simulation. The decrease in variance between day 150 and day 180 of the simulation is characteristic of disaggregation. The fact that the simulation stays in an aggregated state for a period of time about 5 times the characteristic time scale of transition suggests that the aggregated stationary state with M = 0.4 is metastable, and that the variability in this aggregated state constitutes a stochastic forcing capable of destabilizing this metastable state. This simulation was run for 250 days of model time and the non-aggregated stationary state appears stable; it is also similar to the non-aggregated stationary state for M = 0.5, and this suggests that continuing the simulation would not yield another period of aggregated convection. We can see that the amplitude minimum of the internal-transport contribution around day 145 originates in the second decile of [h] (see Fig. 10d), at the margins between the dry and moist regions of this aggregated state. This drying effect on the columns in this second decile causes an increase of air-sea thermodynamic contrast that results in an increase of the surface fluxes and a moistening of these dry regions around day 150 (see Fig. 10c). This is followed by a large negative contribution of internal transport in this decile around day 155, with an additional negative contribution from the moderately humid columns (seventh and eighth deciles). This pattern is maintained, with decreasing amplitude, until disaggregation is complete.

Further analysis of the vertical distribution of these contributions (not shown) confirms that the second decile of [h] is indeed where the crucial changes operate to yield disaggregation. These changes involve wave patterns extending from the surface to the mid-troposphere, not just a simple change in the shallow circulation as could have been expected. We therefore attribute the variability of the internal transport contribution to generic internal atmospheric variability. The role of internal transport is therefore twofold: on long time scales (∼ 50 days), it systematically opposes aggregation; on short time scales (∼ 5 days), it acts as a stochastic forcing which can destabilize the aggregated equilibrium and trigger disaggregation.

Summary and conclusion

Using the convection-permitting configuration of the non-hydrostatic model MesoNH, this article investigates the sensitivity of convective self-aggregation to large-scale circulation. In our configuration, the model's radiative-convective equilibrium exhibits scattered convection over the whole domain and no aggregation; this non-aggregated stationary state is stable for weak to moderate subsidence, up to the order of magnitude of subsidence associated with intraseasonal variability. For moderate to intense subsidence, there is a second stable stationary state with aggregated convection in one region of the domain and no deep convection outside of that region. There is a significant range of subsidence for which both the non-aggregated and the aggregated stationary states are stable. This hysteresis, mentioned in previous work [START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF][START_REF] Muller | What favors convective aggregation and why?[END_REF][START_REF] Coppin | Physical mechanisms controlling the initiation of convective self-aggregation in a general circulation model[END_REF], appears clearly in our series of experiments. Subsidence is therefore favorable to aggregation, but in a highly non-linear fashion: in this model with a non-aggregated RCE, it creates a second, aggregated stationary state and even-tually destabilizes the non-aggregated state. These results are consistent with previous studies that found that anything making convection more difficult enhances or favors aggregation [START_REF] Becker | Imprint of the convective parameterization and sea-surface temperature on large-scale convective selfaggregation[END_REF][START_REF] Tompkins | Organization of tropical convection in low vertical wind shears: Role of updraft entrainment[END_REF].

In the aggregated steady state, the fraction A of the horizontal domain covered by the moist region varies significantly with the subsidence, from 0.78 for M = 0.5 to 0.16 for M = 2.5. This shows that the processes that control A are very complex: external forcing plays a strong role additionally to diabatic processes [START_REF] Beucler | A budget for the size of convective selfaggregation[END_REF] and buoyancy-based scalings (Yang, 2018a). In our model configuration, there is an upper bound to A for weak subsidence, beyond which the dry region is destabilized and disaggregation occurs.

The behavior of the model can be explained by arguments on moisture and convective processes: free-tropospheric advective drying inhibits convection and makes scattered convection unsustainable if the subsidence is sufficiently strong; aggregation limits this drying and concentrates convective instability in a fraction of the domain. We can also explain our results in terms of energy. Subsidence imports MSE into the domain, which the model has to eliminate to maintain stationarity, mostly through radiation since the fixed SST limits the variation of turbulent surface fluxes. In a non-aggregated state with horizontally homogeneous humidity, maintaining convection while drying the column to reduce the greenhouse effect and radiate more energy to space becomes impossible for strong subsidence. In an aggregated state, the dry region is the radiator fins of [START_REF] Pierrehumbert | Thermostats, radiator fins, and the local runaway greenhouse[END_REF]; it looses energy radiatively. The model can adjust to increases of subsidence by increasing the area of the dry region at the expense of the runaway-greenhouse moist region. This is similar to the mechanism known as the iris effect in the case of a response to SST changes [START_REF] Mauritsen | Missing iris effect as a possible cause of muted hydrological change and high climate sensitivity in models[END_REF][START_REF] Saint-Lu | Observational evidence for a stability iris effect in the tropics[END_REF]. Small dry regions as in the aggregated cases with M = 0.5, 1 are surprising and might be influenced by the limited horizontal size of the domain. An interesting perspective to this study is to test the robustness of our results to a large increase in domain size.

The analysis of column MSE variance can shed some light on the physical processes that favor or prevent aggregation and our results are generally consistent with past studies (in particular Wing & Emanuel, 2014). In the non-aggregated stationary states, the transport within the domain and outside of the domain by the imposed subsidence prevents aggregation, while all the diabatic processes (radiation and surface fluxes) tend to aggregate convective clouds, with a dominant role of the terrestrial radiation. In the aggregated stationary state, while some physical processes exhibit a systematic effect on aggregation (solar radiation favorable to aggregation, external transport unfavorable to aggregation), the others exhibit a change in sign: terrestrial radiation is favorable to aggregation and internal transport is unfavorable to aggregation for moderate subsidence, and they have the opposite effect for large subsidence. In the case of the terrestrial radiation, this change of sign results from the competition between the sensitivities of the surface and top-of-atmosphere fluxes to the atmospheric emissivity. For the internal transport, changes in the vertical profile of vertical velocity cause an intensification of a shallow circulation and a change in the gross-moist stability associated with the overturning circulation. The effect of turbulent surface fluxes also differs from case to case because it results from a competition between the effect of air-sea thermodynamics contrast (unfavorable to convection) and the wind-induced effect (favorable to convection).

Whether the two equilibria we obtained would remain if the thermodynamic state of our model domain interacted with the large-scale circulation is unclear. Parameterizations of the large-scale vertical motion [START_REF] Kuang | Modeling the interaction between cumulus convection and linear gravity waves using a limited-domain cloud system-resolving model[END_REF][START_REF] Sessions | Multiple equilibria in a cloud-resolving model using the weak temperature gradient approximation[END_REF][START_REF] Herman | Wtg cloud modeling with spectral decomposition of heating[END_REF] do yield multiple equilibria [START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 1. comparison over uniform surface conditions[END_REF][START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 2. comparison over nonuniform surface conditions[END_REF][START_REF] Sessions | Convective response to changes in the thermodynamic environment in idealized weak temperature gradient simulations[END_REF][START_REF] Sessions | The role of radiation in organizing convection in weak temperature gradient simulations[END_REF], one with ascent and deep convection, the other with subsidence and only shallow convection. In such parameterizations, the temperature difference with the reference RCE profile determines the vertical motion: although these parameterizations differ, overall a cooler profile favors subsidence and a warmer profile favors ascent. Figure 4a suggests that the non-aggregated equililibrium would sustain or enhance subsidence while the aggregated equilibrium would cause ascent, which could destabilize the aggregated state. We can speculate two possible outcomes: one in which our model would yield the same equilibria as in the previous studies [START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 1. comparison over uniform surface conditions[END_REF][START_REF] Daleu | Intercomparison of methods of coupling between convection and large-scale circulation: 2. comparison over nonuniform surface conditions[END_REF][START_REF] Sessions | Multiple equilibria in a cloud-resolving model using the weak temperature gradient approximation[END_REF][START_REF] Sessions | Convective response to changes in the thermodynamic environment in idealized weak temperature gradient simulations[END_REF][START_REF] Sessions | The role of radiation in organizing convection in weak temperature gradient simulations[END_REF]) and another in which a limit cycle would arise, with aggregation decreasing subsidence, eventually disaggregating convection, and the non-aggregated state then causing subsidence, eventualy yielding aggregation.

We also investigate the mechanisms of two transient simulations, one with non-aggregated initial conditions and large subsidence that leads to aggregation, and one with aggregated initial conditions and weak subsidence that leads to disaggregation. In the first one, findings are again generally consistent with past studies [START_REF] Muller | Detailed investigation of the self-aggregation of convection in cloud-resolving simulations[END_REF]Wing & Emanuel, 2014;[START_REF] Muller | What favors convective aggregation and why?[END_REF], with an early contribution to aggregation from terrestrial radiation followed by a positive feedback from solar radiation, while the internal transport exhibits large variations and contributes significantly to aggregation in the transient phase. To our knowledge, the physical processes involved in convective disaggregation are documented for the first time; in our simulation, internal transport is the main process responsible for disaggregation, not only because it generally opposes aggregation but also because its large variability creates a stochastic forcing that destabilizes the aggregated state.

The differences in the value of A and the roles of the different feedbacks between our simulations is similar to the differences between models documented in the literature (see [START_REF] Wing | Convective selfaggregation in numerical simulations: A review[END_REF]. This suggests that some inter-model differences might be explained by the differences in both the model physics and the model configurations. The sensitivity to large-scale circulation appears to provide an opportunity to document different feedbacks and behaviors within the same model.

This sensitivity might also be relevant to analyze observations. In particular, it might explain why the spatial organization of convection vary with the intraseasonal or seasonal variability; for example it might explain why convection is more organized in the decaying phase of the MJO than in the active phase [START_REF] Sakaeda | The behaviors of intraseasonal cloud organization during dynamo/amie[END_REF].

Appendix A Thermodynamic profiles in the aggregated stationary state

As a complement to Figure 4, we present here additional profiles of the thermodynamic variables at equilibrium. Figure A1 shows the deviation from the RCE for the equilibrium profiles of moist static energy h (Fig. A1a), water vapor mixing ration (Fig. A1b), and condensed water mixing ratio (Fig. A1c) in the non-aggregated (dashed lines)

and aggregated (solid lines) equilibria; for the aggregated equilibria, the profiles in the dry region (dash-dotted lines) and moist region (dotted lines) are also shown. Figure A1b,c confirms that the non-aggregated equilibria with M > 0 are drier and less cloudy than the RCE. It also shows that the dryness and reduced cloudiness in the aggregated equilibria results from the extremely dry, cloud-free dry region whose area increases with increasing M ; the convective region is moister and more cloudy than the RCE, and more so with increasing M , but its contribution to the horizontal average decreases with the decreasing relative area A of the convective region. Evaporation in an increasingly large dry region is transported to a shrinking fraction of the horizontal domain where it fuels an increasingly intense convection.

Figure A1a shows that, for moist static energy, the deviation from the RCE is dominated by the contribution from humidity in the lower troposphere and from the changes in dry stability (see Fig. 4a) in the upper troposphere. Again, in the aggregated equilibria, the deviation in the lower to mid-troposphere is dominated by the contribution from the dry region; the moist region is much less stratified than the dry region. vapor mixing ratio q v , and (c) water condensate mixing ratio q c for the non-aggregated (dashed lines) and the aggregated (solid lines) stationary states. vapor mixing ratio q v , and (c) water condensate mixing ratio q c for the mean in the nonaggregated (dashed lines) and the aggregated (solid lines) stationary state, as well as for the convective region (dotted lines) and the dry region (dash-dotted lines) in the aggregated stationary state.

Figure 1 :

 1 Figure 1: Profiles of (a) imposed average vertical velocity w (solid lines), vertical velocity in the convective region w m (dotted lines) and in the dry region w d (dash-dotted lines) for aggregated stationary states; (b) internal vertical mass flux in the convective region.

  [h] corresponds to the dry regions of the domain while the mode with high [h] corresponds to the convective regions. Second, in the aggregated stationary states, we use the approximate distribution to determine the border between the convective and the suppressed, dry regions of the domain. A threshold [h] c is defined as the value of [h] for which the values of the two log-normal distributions summed to obtain the approximated distribution are equal (see dotted black line on Figure 2)a. The gridpoints with [h] > [h] c are considered part of the convective regions and the regions with [h] < [h] c are considered part of the dry

Figure 2 :

 2 Figure 2: (a) Probability Distribution Function of the column-integrated MSE [h] for the non-aggregated stationary state (orange line, scaled by a factor 1/4) and the aggregated stationary state (red line), as well as its approximation by the sum (red dash-dotted line) of two log-normal distributions (red dotted and dashed lines), for M = 1.5. The threshold column-integrated MSE [h] c between the convective and dry regions is indicated (black dotted line); (b) Fractional area A of the convective region and normalized gross convective stability N GM S associated with the internal circulation in the aggregated stationary state, as a function of the intensity of the subsidence M .

  mond et al., 2009, for a review on gross moist stability). It measures how efficiently the circulation transports energy from convergence zones, which are regions of large [h], to dry regions with low [h]. It sets the sign and amplitude of the feedback of this circulation on anomalies of [h]: if the NGMS is positive, the circulation exports energy from the convergence zones and therefore reduces their large [h] and imports energy into the low-[h], dry regions; the circulation is therefore a negative feedback to anomalies of [h].

  3 a,b,c,d), regions of high and low PW are small and distributed randomly over the domain. For the aggregated equilibria (Fig. 3e,f,g,h,i), two regions of contrasted PW appear: the low-PW region is the dry region and the high-PW region is the moist, convective region characteristic of aggregation. Maps of Outgoing Longwave Radiation (OLR) and precipitation are shown in Section 1 of the Supplementary material (Figs S1 and S2); they confirm the aggregated or non-aggregated nature of the stationary states reached by our simulations.

  gets. It shows that the turbulent surface fluxes of heat and water (green bars) are not very sensitive to the subsidence, which can be explained by the weak sensitivity of the boundary-layer temperature and humidity which are mostly controlled by the SST. Adjustment to subsidence drying and warming is through a reduction in precipitation (Figs.5a,b) and an increase in atmospheric radiative cooling(Figs. 5c,d). Aggregation decreases domain-averaged subsidence drying (Figs.5a,b) because, while convection maintains a moist profile over the whole domain in the non-aggregated equilibrium, part of the domain is dry in the aggregated equilibrium and air exported from this region does not export much moisture. With increasing subsidence, this dry region expands and this moderation of the moisture export is enhanced. Aggregation also causes larger radiative cooling (Figs.5c,d) because the dry region experiences little greenhouse effect due to its low humidity and absence of cloudiness. As a result, the aggregated equilibrium is more resilient to subsidence than the non-aggregated equilibrium, which becomes unstable for M > M N A . If M is further increased, up to a value typical of the subsiding branch of the Hadley circulation (M = 4.5), deep convection is eventually inhibited in the aggregated equilibrium, as shown in Section 2 of the Supplementary material.

  Figure 6 shows the contribution of the different diabatic and transport terms to the change in the column-MSE variance [h ] 2 for all our simulations that reach a stationary state, in which the sum of these terms is zero. Positive terms increase MSE in regions of large MSE and/or decrease MSE in regions of low MSE; they therefore tend to increase the MSE variance and favor convective aggregation; negative terms tend to decrease aggregation.

  Figure 7 also shows that the top-of-the-atmosphere flux dominates in the moist columns -at least in most of the columns in the moist region as defined by [h] > [h] c -and the terrestrial contribution of these columns to aggregation is positive. The latter contribution is dominant for small M and the former becomes dominant at large M .

Figure 8

 8 Figure8illustrates this surface/top-of-the-atmosphere competition by showing the daily average of MSE, column terrestrial heating, downward top-of-the-atmosphere and upward surface terrestrial fluxes for one day of the aggregated equilibrium with M = 1.5 -the same day for which PW is shown in Figure3g. We see that the column terrestrial cooling (Fig.8b) is maximum around the limit between the moist and dry regions; it decreases both towards the moistest regions at the center of the convective regions and towards the driest regions in the dry, low-MSE region. Figure8c and d clearlyshow that this sensitivity is controlled by the top-of-the-atmosphere flux in the moist region and by the surface flux in the dry region.

  Journal of Advances in Modeling Earth Systems(JAMES) flux in the convective region (which equals the downward mass flux in the dry region).For M = 0.5, this mass flux is largest in the boundary layer (between 1 and 2 km of altitude), almost constant in the free troposphere up to 10 km and vanishes between 10 and 12 km, at the model tropopause. This corresponds to the superposition of a shallow circulation, with convergence in the boundary layer and divergence in the lower free troposphere, and a deep circulation, with convergence in the boundary layer and divergence in the upper troposphere. As the imposed subsidence is increased from M = 0.5 to 1.5, the mass flux increases in the lower troposphere, which corresponds to a further increase in the shallow circulation. If the imposed subsidence is further increased from M = 1.5 to 2.5, the mass flux decreases in the mid-troposphere; this corresponds to an increase in the shallow circulation (with an upward expansion of the lower-free-tropospheric divergence layer), a decrease in the deep circulation, and the development and intensification of an upper-tropospheric circulation with convergence between 7 and 10 km of altitude and divergence above. For M = 2.5, there is no more deep circulation, only the shallow and upper-tropospheric circulations. Shallow circulations are associated with a negative gross moist stability, deep and upper-tropospheric circulations with positive gross moist stability. In our aggregated equilibria, the combined gross moist stability of these three circulations decreases with the increase in the shallow circulation and with the transition from a deep circulation to an upper-tropospheric circulation. As a result, the gross moist stability decreases with M and even becomes negative.

  shows the time evolution of the distribution of terrestrial radiative contribution per MSE percentile. The increase in the destabilizing terrestrial contribution starting at day 20 of the simulation is dominated by the low MSE percentiles, i.e. by the dry regions. At day 20, the driest regions are still occasionally convective so changes in humidity are spread over the depth of the troposphere, and the sensitivity of terrestrial flux divergence across the troposphere is dominated by that of the top-of-the-atmosphere flux (not shown): increases in humidity therefore yield an increased greenhouse effect and a warming of the column. By day 40, the driest columns have little moisture in the free-troposphere and changes in humidity are limited to the boundary layer; as a result, the sensitivity of terrestrial flux divergence across the troposphere is dominated by that of the surface flux (not shown), which is negative as in the stationary state (see Fig.7b). Dry columns with positive contributions dominated by the top-of-the-atmosphere are no longer the driest, their [h] is close to the horizontal average (see dashed line indicating [h] = 0 in Fig.7c). At the same time; the moistest columns become moister and this contributes positively to aggregation because of the dominating top-of-the-atmosphere greenhouse effect. The positive contribution of the moderately dry columns and very moist column dominates and explain the overall positive contribution of terrestrial radiation to aggregation.

Figure

  Figure 10b shows the contribution to the change of [h ] 2 from the different physical processes. Internal transport appears to control the variability of the trend in [h ] 2and exhibits a large variability on time scales of a few weeks, as in all aggregated states (also seen on Fig.9bafter day 50, and generally true for all aggregated equilibria). This provides the stochastic forcing mentioned above. Another process that contributes to the disaggregation is the turbulent surface heat fluxes whose contribution is generally small, but crucially becomes unfavorable to aggregation around day 150. It seems that following a minimum (in amplitude) of the negative contribution of the internal transport around day 145 that causes an increase in the variance of [h] (see Fig.10a), the surface fluxes damp this variance and the subsequent amplitude maximum of the negative internal transport around day 155 triggers disaggregation. The contributions from other processes are not as active in the disaggregation process: terrestrial radiation attempts to maintain aggregation, while solar radiation is a positive feedback on aggregation. Finally, external transport contributes a little to disaggregation, but as a negative feedback on aggregation rather than a driver of disaggregation. Analysis of the simulation with the same initial conditions and M = 0 yields similar results except for the timing of disaggregation which happens very early in the simulation (not shown).

Figure

  Figure 10c and d show the distribution per percentiles of the contributions of the turbulent surface heat fluxes and internal transport to the change of the variance of [h].

  Journal of Advances in Modeling Earth Systems (JAMES)

Figure 3 :

 3 Figure 3: Maps of precipitable water for a typical day in the non-aggregated stationary state (a,b,c,d) and the aggregated stationary state (e,f,g,h,i).

Figure 4 :

 4 Figure 4: Profiles of (a) deviation of potential temperature from the RCE, (b) water

Figure 5 :

 5 Figure5: Terms of the domain-averaged budgets of water (a,b) and energy (c,d) for the non-aggregated (a,c) and aggregated (b,d) equilibria. "E" denotes evaporation,"P" precipitation, "EXTR" external transport by the imposed subsidence, "TSHF" turbulent surface heat fluxes, and "∆R" the column radiative heating.

Figure 6 :

 6 Figure 6: Effects of physical processes on the (absence of) change in the variance [h ] 2 of column-integrated MSE in (a) the non-aggregated stationary state and (b) the aggregated stationary state, for different values of the subsidence intensity M . EXTR indicates external transport; INTR indicates internal transport; ∆R LW indicates terrestrial radiation; ∆R SW indicates solar radiation; TSHF indicates turbulent surface heat fluxes.

Figure 7 :

 7 Figure 7: Contributions of the different processes to the change of the variance [h ] 2 in the aggregated stationary state as a function of the percentile of [h], for (a) M = 0.5, (b) M = 1.5, and (c) M = 2.5: contribution of the external transport EXTR (dark blue), internal transport INTR (blue), terrestrial radiation ∆R LW (red), which can be decomposed into a top-of-the-atmosphere term F TOA LW (dotted dark red) and a surface term F SRF LW (dashed dark red), solar radiation ∆R SW (yellow), and turbulent surface fluxes TSHF (green), which can be decomposed into a term from air-sea thermodynamic contrast TSHF δh (dashed dark green), a term from surface wind (TSHF Vs , dotted dark green), and a non-linear term. The percentiles corresponding to the average column MSE ([h ] = 0) and the threshold between dry and moist regions ([h] = [h] c ) are indicated (dashed black lines).

Figure 8 :

 8 Figure 8: Maps of (a) column-integrated MSE [h] for a typical day in the aggregated stationary state for M = 1.5; (b) corresponding column-integrated radiative heating; corresponding (c) net downward terrestrial radiative flux at the top of the atmosphere and (d) net upward terrestrial radiative flux at the surface. Isoline [h] = [h] c is shown in all panels (dashed line) and isoline [h] = 0 is shown in (a).

Figure A1 :

 A1 Figure A1: Profiles of deviation from the RCE of (a) moist static energy h, (b) water

manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES)

Acknowledgments

We thank the MesoNH team for their frequent help. We also acknowledge the support of the New Zealand eScience Infrastructure (NeSI) high-performance computing facilities and consulting support as part of this research. New Zealand's national facilities are provided by NeSI and funded jointly by NeSI's collaborator institutions and through the Ministry of Business, Innovation and Employment's Research Infrastructure programme (https://www.nesi.org.nz). G.B. was supported by the Glavish-Buckley Lectureship and D. C. by the Glavish Postdoctoral Fellowship at the University of Auckland. The MesoNH model can be downloaded from the MesoNH webpage (http://mesonh.aero.obs-mip.fr/mesonh55)

and simulations used in this study are available via the Open Science Foundation (https://osf.io/qyudz/). We thank Chris Holloway and two other reviewers for their helpful comments.