Clouds and Convective Self‐Aggregation in a Multimodel Ensemble of Radiative‐Convective Equilibrium Simulations

Abstract The Radiative‐Convective Equilibrium Model Intercomparison Project (RCEMIP) is an intercomparison of multiple types of numerical models configured in radiative‐convective equilibrium (RCE). RCE is an idealization of the tropical atmosphere that has long been used to study basic questions in climate science. Here, we employ RCE to investigate the role that clouds and convective activity play in determining cloud feedbacks, climate sensitivity, the state of convective aggregation, and the equilibrium climate. RCEMIP is unique among intercomparisons in its inclusion of a wide range of model types, including atmospheric general circulation models (GCMs), single column models (SCMs), cloud‐resolving models (CRMs), large eddy simulations (LES), and global cloud‐resolving models (GCRMs). The first results are presented from the RCEMIP ensemble of more than 30 models. While there are large differences across the RCEMIP ensemble in the representation of mean profiles of temperature, humidity, and cloudiness, in a majority of models anvil clouds rise, warm, and decrease in area coverage in response to an increase in sea surface temperature (SST). Nearly all models exhibit self‐aggregation in large domains and agree that self‐aggregation acts to dry and warm the troposphere, reduce high cloudiness, and increase cooling to space. The degree of self‐aggregation exhibits no clear tendency with warming. There is a wide range of climate sensitivities, but models with parameterized convection tend to have lower climate sensitivities than models with explicit convection. In models with parameterized convection, aggregated simulations have lower climate sensitivities than unaggregated simulations.

Introduction This supporting information contains the documentation for each model included in RCEMIP (Text S1), information on the sensitivity of the I org calculation to the assumptions in those calculation (Text S2, Table S1), as well as captions for Movies S1 to S65. Tables S2-S7 provide the anvil cloud fractions, temperatures, and heights for each simulation. Tables S8-S13 provide calculations of the net climate feedback parameter and change in cloud radiative effect in each model. This supporting information also includes additional figures to provide a complete view of the RCEMIP simulations. A series of figures shows snapshots of hourly-averaged precipitable water during the equilibrium state in each model in the simulations at 300 K (Figures S1-S5). The precipitable water is spatially homogenous in Figures S1 and S2, reflecting that the RCE small300, RCE small vert300, and RCE smal les300 simulations are un-aggregated (except UKMO-RA1-T), while there are regions of moister and drier air in Figures S3-S5, reflecting that the RCE large300 simulations are aggregated. Figures S6-S8 display the temporal evolution of y-averaged precipitable water, showing the rich structure of variability across scales. Figure S9 shows snapshots of hourly-averged outgoing longwave radiation in each GCM in the simulations at 300 K over a subset of the global domain that approximately matches the size of the CRM simulations. Figure S10 shows the precipitable water distribution in all simulations, in which the RCE large simulations have a strikingly broader distribution of precipitable water than the RCE small simulations.
Figures S11-S14 display average profiles for the simulations at 295 K, while Figures S15-S18 display average profiles for the simulations at 305 K. The equivalent profiles for simulations at 300 K are in the main text. The next set of figures display measures of the degree of aggregation. Figures S19-S20 show the metrics of aggregation for RCE large295 and RCE large305 (RCE large300 is in the main text). Figure S21 shows the rate of change of the aggregation metrics with warming from 295K-300K and 300K-305K. Figures  S22 and S23 show aggregation metrics in RCE large300 and their rate of change when I org is calculated using zero instead of four-point connectivity. Figures S24 and S25 show aggregation metrics in RCE large300 and their rate of change when the spatial variance of precipitable water scaled by its domain mean value is used as a moisture-based metric rather than the spatial variance of column relative humidity (as the latter may suffer from artifacts due to different specifications of vertical levels across models).
Figures S26-S28 display anvil cloud height, temperature, and fraction as a function of SST in which the models are split into those with explicit and parameterized convection. The equivalent plots for the entire ensemble of models are shown in the main text.
Text S1. Model Documentation Here we provide information about each model included in RCEMIP, including information about the dynamical core, physics packages, and grid settings for the RCE small, RCE large, and (if applicable) RCE small vert and RCE small les. S1.1. CRM/LES Models S1.1.1. CM1 CM1 (cm1r19.6; Bryan & Morrison, 2012) is used to perform both CRM and LES simulations. CM1 employs a Cartesian grid with Arakawa-C staggering and a compressible time-split, RK3, finite difference dynamical core (Wicker & Skamarock, 2002). The default advection schemes for CM1 are used (a 5th-order finite difference scheme for velocities and a 5th-order WENO scheme for scalars). The time step is variable with an average value of 18 s. RCE small has 108 x 108 x 74 grid points with 1 km horizontal grid spacing. RCE large has 2016 x 134 x 74 grid points with 3 km horizontal grid spacing. In both cases, the vertical levels are those specified by Wing et al. (2018). There is a sponge layer above 25 km. RCE small vert has 108 x 108 x 146 grid points with 1 km horizontal grid spacing while RCE small les has 540 x 540 x 146 grid points with 200 m horizontal grid spacing. The physics packages are RRTMG (Mlawer et al., 1997) for shortwave and longwave radiation, Morrison et al. (2009) double-moment for microphysics, and Jimenez et al. (2012) for the surface layer. No convection scheme is used. For CM1 and CM1-vert, the boundary layer scheme of Bryan and Rotunno (2009) is used, with no other sub-grid scale turbulence scheme. For CM1-LES, the Deardorff (1980) sub-grid scale turbulence scheme is used. S1.1.2. DALES, DALES-damping The Dutch Atmospheric Large-Eddy Simulation (DALES) model v4.2 (Heus et al., 2010) has a finite volume dynamical core, employs the anelastic approximation, and uses a Cartesian grid with an adaptive time step of ∼ 2 s. The RCE small configuration has 100 x 100 x 74 grid points with 1 km horizontal grid spacing, RCE small vert has 100 x 100 x 146 grid points with 1 km horizontal grid spacing, and RCE small les has 504 x 504 x 146 grid points with 200 m grid spacing. The vertical levels are a specified by Wing et al. (2018) and there is a sponge layer in the top 25% levels. The physics packages are RRTMG for shortwave and longwave radiation (Mlawer et al., 1997), Grabowski (1998); Khairoutdinov and Randall (2006) for microphysics, Deardorff (1980) for sub-grid scale turbulence and MOST for calculating the surface fluxes. DALES-damping is identical to DALES, with the addition of a damping of layer-averaged horizontal velocity towards zero, with a damping constant of 1 d −1 . The damping is added to decrease the build-up of strong winds in the stratosphere. S1.1.3. DAM Das Atmosphaerische Modell (DAM; Romps, 2008) has a finite volume dynamical core and uses a Cartesian grid. The RCE small configuration has 108 x 108 x 74 grid points with 1 km horizontal grid spacing. RCE large has 2592 x 144 x 74 grid points with 2.5 km horizontal grid spacing. The time step is variable between 7 and 20 s, depending on the CFL condition. The 74 vertical levels are stretched to a spacing of 500 m by 3 km, which is continued up to the model top of 33 km; there is no sponge layer. RRTMG is used for shortwave and longwave radiation and the Lin-Lord-Krueger scheme is used for microphysics. There is no sub-grid scale turbulence scheme and no boundary layer scheme; a bulk aerodynamic scheme is used for surface fluxes. S1.1.4. FV3 The GFDL-FV3CRM (Lin, 2004;Putman & Lin, 2007;Harris & Lin, 2013;Zhou et al., 2019) has a finite volume dynamical core and uses a Cartesian grid with a time step of 75 s. The RCE large configuration has 2048 x 128 x 79 grid points with 3 km horizontal grid spacing. There is a sponge layer in the top two levels. The physics packages are GFDL AM4 radiation, modified Lin microphysics (as in the GFDL microphysics in NGGPS), the GFDL AM4 PBL Lock scheme for boundary layer. There is no convection scheme and no sub-grid scale turbulence scheme. Output is not available for RCE small. S1.1.5. ICON-LEM The ICOsahedral Nonhydrostatic model (ICON) version 2.3.00 (Dipankar et al., 2015) is used to perform both CRM and LES simulations. ICON-LEM employs an icoshedraltriangular Arakawa-C grid with a non-hydrostatic dynamical core. The edge of each triangle is 1 km in the RCE small configuration and 3 km in the RCE large configuration. RCE small and RCE large use 5 s and 10 s time steps, respectively. After remapping to a Cartesian grid, the RCE small configuration has 100 x 100 x 75 grid points with a 1 km grid spacing and the RCE large configuration has 134 x 2000 x 75 grid points with a 3 km grid spacing. The vertical levels are geopotential height levels and extend up to 33.947 km, with a sponge layer starting at 19 km. RCE small vert has 100 x 100 x 156 grid points while RCE small les has 500 x 500 x 156 grid points. The physics packages are RRTMG (Mlawer et al., 1997) for shortwave and longwave radiation (called every 300 s), Seifert and Beheng (2006) two-moment mixed-phase bulk scheme for microphysics, and Smagorinsky boundary layer and sub-grid scale turbulence schemes. The RCE large simulations were initialized from RCE small simulations at 3 km grid spacing. S1.1.6. ICON-NWP ICON-NWP (Zängl et al., 2015) is the same as ICON-LEM in terms of the dynamical core and grid configuration, but uses different boundary layer, turbulence and cloud schemes. The physics packages are RRTMG (Mlawer et al., 1997) for shortwave and longwave radiation (called every 300 s), Seifert and Beheng (2006) two-moment mixedphase bulk scheme for microphysics, Raschendorfer (2001) boundary layer and sub-grid scale turbulence schemes, and a diagnostic cloud cover scheme by Martin Koehler. The RCE large simulations were initialized from RCE small simulations at 3 km grid spacing. S1.1.7. MESONH MESO-NH version 5.4.1 (Lac et al., 2018) employs the anelastic equation set on a fully staggered Cartesian Arakawa-C grid. RCE small has 100 x 100 x 74 grid points with 1 km horizontal grid spacing. RCE large has 2000 x 128 x 74 grid points with 3 km horizontal grid spacing. The vertical levels are those specified by Wing et al. (2018) with a sponge layer from 22 to 33 km. RCE small vert has 100 x 100 x 146 grid points with 1 km horizontal grid spacing. RCE small les has 500 x 500 x 146 grid points with 200 m horizontal grid spacing.The physics packages include RRTMG for longwave radiation, Fouquart and Bonnel (1980) for shortwave radiation (which are called every 900 s), the Pinty and Jabouille (1998) single-moment mixed microphysics scheme, the Pergaud, Masson, Malardel, and Couvreux (2009) eddy diffusivity mass flux scheme for shallow convection, and a 4th-order centered advection scheme for momentum variables and a PPM scheme for other variables. The LES simulations use the Cuxart, Bougeault, and Redelsperger (2000) 1.5 order closure TKE scheme withe the Deardorff (1980) mixing length while the other simulations use the same scheme but with the mixing length of Bougeault and Lacarrere (1989 (Tomita, 2008) for microphysics, and a Smagorinsky Lilly scheme with stability effects for sub-grid scale turbulence. S1.1.9. SAM-CRM The System for Atmospheric Modeling (SAM) version 6.11.2 (Khairoutdinov & Randall, 2003) is used to perform both CRM and LES simulations. SAM employs the anelastic equations on a fully staggered Arakawa C-type Cartesian grid. RCE small has 96 x 96 x 74 grid points with 1 km horizontal grid spacing and a 8 s time step. RCE large has 2048 x 192 x 74 grid points with 3 km horizontal grid spacing and a 12 s time step. The vertical levels are those specified by Wing et al. (2018) with the model top at 33 km and Newtonian damping of prognostic variables in the upper third of the model domain. RCE small vert has 96 x 96 x 146 grid points with 1 km horizontal grid spacing while RCE small les has 480 x 480 x 146 grid points with 200 m horizontal grid spacing. The physics packages include RRTMG for shortwave and longwave radiation, the original SAM one-moment microphysics scheme (Khairoutdinov & Randall, 2003) and a Smagorinksy sub-grid scale turbulence scheme. The original SAM advection scheme based on Smolarkiewicz' MPDATA scheme with a monotonic corrector is used. S1.1.10. SCALE SCALE version 5.2.5 (Nishizawa et al., 2015;Sato et al., 2015) employs a fully compressible equation set on a finite volume dynamical core on an Arakawa C-type Cartesian grid. RCE small has 96 x 96 x 74 grid points with 1 km horizontal grid spacing and a 6 s advection and physics time step. RCE large has 2048 x 128 x 74 grid points with 3 km horizontal grid spacing and a 12 s advection and time step. The dynamical time step is 1/3 of the advection and physics time step. The vertical levels are those specified by Wing et al. (2018) with a sponge layer from 22 to 33 km, in which only the vertical wind is damped. The physics packages include mstrnX (Sekiguchi & Nakajima, 2008) for shortwave and longwave radiation, which is called every 300 s, the Tomita (2008) six-class one-moment bulk microphysics scheme, and the Mellor-Yamada-Nakanishi-Niino (Nakanishi & Niino, 2004) boundary layer scheme. Surface fluxes are calculated from a bulk method using the universal function (Beljaars & Holtslag, 1991;D. K. Wilson, 2001) and sea surface roughness is parameterized by the Moon, Ginis, Hara, and Thomas (2007) method. A third order upwind difference advection scheme for both velocities and scalars was used. S1.1.11. UCLA-CRM The University of California, Los Angeles large-eddy simulation model (UCLA-LES) (Hohenegger & Stevens, 2016) employs finite difference equations on a Cartesian Arakawa-C grid with a third-order Runge-Kutta time-stepping scheme and dynamic time step based on the CFL criterium. RCE small has 96 x 96 x 75 grid points with 1 km horizontal grid spacing. RCE large has 1984 x 128 x 75 grid points with 3 km horizontal grid spacing. There is a sponge layer in the top six vertical levels. Shortwave and longwave radiation are computed as in Pincus and Stevens (2009), using the delta-four stream method and Monte Carlo sampling, but with updates to include cloud ice. The two-moment microphysics of Seifert and Beheng (2006) is used, which has cloud water, rain, ice snow, graupel, and hail as the hydrometeor species. A Smagorinsky sub-grid scale turbulence scheme is used; there is no boundary layer scheme. S1.1.12. UKMO-CASIM The UK Met Office idealized Model version 11.0 (Stratton et al., 2018) (UKMO-CASIM) has semi-implicit, semi-lagrangian (Wood et al., 2014) numerics and a Cartesian horizontal C-grid and vertical sigma-z C-P grid. RCE small uses 100 x 100 x 98 grid points with 1 km horizontal grid spacing. RCE large uses 2016 x 144 x 98 grid points with 3 km horizontal grid spacing. The vertical levels are step-stretched with a grid spacing of 60 m near the surface, increasing to a constant 250 m grid spacing between 5 and 13 km, and increasing to a constant 1000 m grid spacing from 30 to 40 km. There is a sponge layer that performs Rayleigh damping of prognostic variables, in which a timescale weight follows an exponential function of height from 24-40 km. The Suite of Community RAdiative Transfer codes based on Edwards and Slingo (SOCRATES) scheme (Edwards & Slingo, 1996;Manners et al., 2015) is used for shortwave and longwave radiation and the doublemoment Cloud AeroSol Interacting Microphysics (CASIM; Shipway & Hill, 2012;Hill et al., 2015) is used for microphysics. The Lock, Brown, Bush, Martin, and Smith (2000) boundary layer scheme with updates from Walters et al. (2019) and a Smagorinksy (1963) sub-grid scale turbulence scheme is also used. S1.1.13. UKMO-RA1-T, UKMO-RA1-T-hrad, UKMO-RA1-T-nocloud UKMO-RA1-T is the same as UKMO-CASIM except for the microphysics scheme and the use of a sub-grid cloud scheme based on Smith (1990), with uniform critical relative humidity of 0.99. The microphysics scheme is a single-moment scheme from D. R. Wilson and Ballard (1999) but with updates as in Walters et al. (2019). The UKMO-RA1-T RCE small simulations unexpectedly showed convective self-aggregation, so additional simulations (UKMO-RA1-T-hrad) were performed in which radiative heating tendencies were computed interactively but applied uniformly as domain-mean profiles to prevent aggregation; the RCE large UKMO-RA1-T simulations were initialized from the un-aggregated UKMO-RA1-T-hrad simulations. Additional simulations (UKMO-RA1-Tnocloud) were performed in which the sub-grid cloud scheme was disabled. S1.1.14. WRF-COL-CRM The Weather Research and Forecasting model (WRF) v3.5.1 (Skamarock et al., 2008) modified for performing RCE/WTG simulations (Wang et al., 2016;Martin et al., 2019), the same as used for WRF-GCM, has a conservative-form finite difference dynamical core on a Cartesian grid. The RCE small configuration has 100 x 100 x 74 grid points with 1 km horizontal grid spacing. The RCE large configuration has 2000 x 134 x 74 grid points with 3 km horizontal grid spacing. The time step is 20 seconds. The vertical levels are eta levels with the model top at approximately 33 km and a sponge layer in the top 5 km. The physics packages used are RRTMG (Iacono et al., 2008) for shortwave and longwave radiation, the Morrison et al. (2009) double-moment microphysics scheme, the YSU boundary layer scheme (Noh et al., 2003;Hong et al., 2006), and a horizontal Smagorinsky first-order closure for sub-grid scale turbulence. S1.1.15. WRF-CRM The Weather Research and Forecasting model (WRF) v3.9.1 (Skamarock et al., 2008) was used to perform RCE small simulations, with 100 x 100 x 74 grid points with 1 km horizontal grid spacing and a 6 s time step. For RCE large simulations, 2000 x 133 x 74 grid points with 3 km horizontal grid spacing and a 10 s time step were employed. The model top is set at 33 km with a sponge layer depth of 5 km from the model top. The physics packages include the Goddard for shortwave and longwave radiation schemes (Chou & Suarez, 1999;Chou et al., 2001) and the WDM6 (Lim & Hong, 2010) doublemoment cloud microphysics scheme. The YSU boundary layer scheme (Hong et al., 2006) coupled with Monin-Obukhov similarity (Jimenez et al., 2012) for the surface layer and 5-layer thermal diffusion scheme (Dudhia, 1996) are used as a surface option. S1.2. GCRMs S1.2.1. MPAS The Model for Prediction Across Scales-Atmosphere version 6.1 (MPAS) (Skamarock et al., 2012) is a nonhydrostatic atmospheric model with a finite element dynamical core that is here used in its global spherical configuration. MPAS uses C-grid discretization on a Voronoi unstructured grid. The RCE small configuration is a small sphere with a reduced Earth radius of ∼ 52km and 10,242 horizontal grid columns, which are interpolated to 180 x 90 latitude by longitude grid points in the output. The horizontal grid spacing is 1 km, which is interpolated to 2 • in the output. The time step is 6 seconds. The RCE large configuration is a sphere with reduced Earth radius of R E /8 and 1,024,002 horizontal grid columns, which are interpolated to 900 x 1800 latitude by longitude grid points in the output. The horizontal grid spacing is 3 km, which is interpolated to 0.2 • in the output. The time step is 15 seconds. Both RCE small and RCE large use 74 vertical levels as defined in (Wing et al., 2018), with a sponge layer above 25 km. The physics packages used are RRTMG (Mlawer et al., 1997;Iacono et al., 2008) for shortwave and longwave radiation, the WSM6 microphysics scheme (Hong et al., 2004), and the YSU boundary layer scheme (Noh et al., 2003).

S1.2.2. NICAM
The Non-hydrostatic Icosahedral Atmospheric Model (NICAM) version 16.3 (Satoh et al., 2014) employs the fully compressible equations on a spherical A-type grid, with time steps of < 8 s for dynamics, < 30 s for cloud microphysics, and 300 s for radiation. RCE small has 128 x 128 x 117 grid points with a horizontal grid spacing of 1 km, while RCE large has reduced Earth radius of R E /4 with a horizontal grid spacing of 3.5 km and 117 vertical levels. The vertical grid has stretched grid spacing with 200 m grid spacing in the free atmosphere, a model top at 33 km, and Newtonian damping of momentum and internal energy above 20 km. The physics packages include mstrnX for radiation (Sekiguchi & Nakajima, 2008) and the NICAM double moment microphysics (NDW6) scheme. The turbulent closure was calculated using level 2 of the Mellor-Yamada-Nakanishi-Niino scheme (Nakanishi & Niino, 2004) in both the planetary boundary layer and the free atmosphere. There is no convection scheme.

S1.2.3. SAM-GCRM
The global version of the System for Atmospheric Modeling (SAM) (Khairoutdinov & Randall, 2003) uses version 7.3 with a spherical latitude-longitude grid (Satoh et al., 2019). Like SAM-CRM, SAM-GCRM employs the same anelastic finite-difference equation set. The RCE large configuration has 2304 x 1152 x 74 grid points with 0.15625 • x 0.1545 • grid spacing and a reduced Earth radius of R E /4, which corresponds to a horizontal grid spacing of 4.25 km at the Equator. The time step is 12 s. There are rigid walls at 89 N and 89 S. The vertical levels are those specified by Wing et al. (2018), with a sponge layer starting at 20 km. The physics packages include RRTMG for shortwave and radiation, the original SAM one-moment microphysics scheme (Khairoutdinov & Randall, 2003) and a Smagorinksy sub-grid scale turbulence scheme. The RCE large simulations are initialized from the corresponding RCE small simulations with SAM-CRM. S1.3. GCMs/SCMs S1.3.1. CAM5-GCM The Community Atmosphere Model version 5 (CAM5) (Neale et al., 2012) is configured here with the spectral element dynamical core (Lauritzen et al., 2018) on a spherical grid for the GCM for RCE large and as the single column model SCAM5 with the Eulerian spectral transform dynamical core for RCE small. The physics time step is 1800 s, the dynamical time step is 300 s, and the simulations are run for 1200 days. RCE small is a single column with 30 vertical levels corresponding to a ∼ 320 km grid (T42), in which the time step is 1800 s for both physics and dynamics. RCE large has 48602 columns but is interpolated to a latitude-longitude grid of 192 x 288 columns, with a horizontal grid spacing of 0.9 x 1.25 degrees. There are 30 vertical levels that employ a terrain-following hybrid vertical coordinate and a sponge layer in the top 3 levels. The physics packages used are RRTMG (Mlawer et al., 1997;Iacono et al., 2008) for radiation, Morrison and Gettelman (2008) for microphysics, Park and Bretherton (2009) for boundary layer, Zhang and McFarlane (1995) for convection, and Bretherton and Park (2009) for sub-grid scale turbulenece. There are a few parameters that are different for SCAM5 and CAM5 due to the different dynamical cores used -[cldfrc sh1]: 0.07D0 vs. 0.04D0; [zmconv ke]: 3.0E-6 vs. 5.0E-6. S1.3.2. CAM6-GCM The Community Atmosphere Model version 6 (CAM6) (https://ncar.github.io/ CAM/doc/build/html/index.html) is configured here with the spectral element dynamical core (Lauritzen et al., 2018) on a spherical grid for the GCM for RCE large and as the single column model SCAM6 with the Eulerian spectral transform dynamical core for RCE small. The physics time step is 1800 s, the dynamical time step is 300 s, and the simulations are run for 1200 days. RCE small is a single column with 30 vertical levels corresponding to a ∼ 320 km grid (T42) in which the time step is 1800 s for both physics and dynamics. RCE large has 48602 columns but is interpolated to a latitude-longitude grid of 192 x 288 columns, with a horizontal grid spacing of 0.9 x 1.25 degrees. There are 32 vertical levels that employ a terrain-following hybrid vertical coordinate and a sponge layer in the top 3 levels. The physics packages used are RRTMG (Mlawer et al., 1997) for radiation, Gettelman and Morrison (2015) for microphysics, Zhang and McFarlane (1995) for convection, and CLUBB (Bogenschutz et al., 2013) for boundary layer and sub-grid scale turbulence. There are a few parameters that are different for SCAM6 and CAM6 due to the different dynamical cores used -[cldfrc sh1]: 0.07D0 vs. 0.04D0; [zmconv ke]: 3.0E-6 vs. 5.0E-6; [cldfrc premit]: 75000.0D0 vs. 25000.0D0. S1.3.3. CNRM-CM6-1 The CNRM climate model CNRM-CM6-1 is based on the atmospheric component ARPEGE-Climat Version 6.3 (Roehrig & coauthors, 2020;Voldoire & coauthors, 2019). Its dynamical core is spectral for linear terms (T127 truncature, ∼150km horizontal grid spacing) while all non-linear terms are computed on the associated reduced Gaussian grid with a two time-level semi-Lagrangian semi-implicit scheme and a 15 min time step. The model vertical grid consists of 91 hybrid sigma-pressure levels between the surface and 1 Pa, with smaller grid spacing in the boundary layer. The CNRM-CM6-1 physics packages include RRTMG (Mlawer et al., 1997) for longwave radiation and Fouquart and Bonnel (1980) for shortwave radiation, the Lopez (2002) single-moment microphysics scheme, the Cuxart et al. (2000) 1.5 order turbulence scheme, coupled to the Bougeault (1981) cloud scheme and a convection scheme unified for shallow and deep convection following Piriou, Redelsperger, Geleyn, Lafore, and Guichard (2007) and Guérémy (2011). S1.3.4. ECHAM6-GCM ECHAM version 6.3.04p1 is the atmospheric component of the MPI-M Earth System Model (Stevens et al., 2013) and employs a dry spectral-transform dynamical core on a spherical grid with a time step of 450 s. RCE large has 192 x 96 horizontal grid points with T63 resolution and 47 vertical levels, employing a hybrid sigma-pressure vertical coordinate up to 1 Pa and a sponge layer in the uppermost level. ECHAM6 does not have a single column set-up, so RCE large is initialized from the mean profile on the last day of a simulation with cloud-radiative effects switched off that was run for 30 days (an unaggregated simulation). The physics packages are PSrad/RRTMG (Iacono et al., 2008) for radiation, a one-moment bulk microphysics scheme (Lohmann & Roeckner, 1996), an eddy-diffusivity approach for boundary layer and sub-grid scale turbulence (Brinkop & Roeckner, 1995), the Nordeng scheme for convection (Nordeng, 1994), and the Sundqvist scheme for stratiform clouds (Sundqvist et al., 1989). S1.3.5. GEOS-GCM GEOS 5.21 (Molod et al., 2015; Arnold & Putman, 2018) employs a finite volume dynamical core (Lin, 2004) on a spherical, cubed sphere grid with a time step of 450 s for moist physics. RCE small employs a single column configuration corresponding to a grid spacing of 100 km and 72 hybrid levels. RCE large has 90 x 540 grid points with horizontal grid spacing of ∼ 100 km and 72 hybrid levels. The physics packages are RRTMG for longwave radiation and Chou (1990Chou ( , 1992 for shortwave radiation, the Bacmeister, Suarez, and Robertson (2006) single-moment microphysics scheme, Lock et al. (2000) and Louis, Tiedtke, and Geleyn (1982) for boundary layer, and the relaxed Arakawa-Schubert convection scheme (Moorthi & Suarez, 1992). S1.3.6. ICON-GCM ICON-A is the atmosphere component of the ICON Earth System Model (Giorgetta et al., 2018) which employs a finite volume dynamical core on an icosahedral grid with a time step of 4 minutes. RCE large has 20,480 grid points with a horizontal grid spacing of 158 km and 47 vertical levels, with the top level at 32.9 km and a sponge layer above 25 km. The physics packages are PSRAD (Pincus & Stevens, 2013) for radiation, a cloud microphysical scheme, the Tiedtke mass flux scheme for convection (Tiedtke, 1989) including updates by Nordeng (Nordeng, 1994), andMauritsen et al. (2007) for vertical diffusion. Because of a bug in the configuration, no cloud microphysics were calculated above a height of ∼ 16 km. S1.3.7. IPSL-CM6 IPSL-CM6A-LR (Hourdin & coauthors, 2020) employs a finite difference dynamical core on a longitude-latitude grid with a time step of 120 s. RCE large has 144 x 142 horizontal grid points and equal area grid spacing with 79 sigma-hybrid vertical levels. Output from the RCE small single column simulation is not available. The physics packages are RRTM (Mlawer et al., 1997) for longwave radiation and Fouquart and Bonnel (1980) and Morcrette (1991) for shortwave radiation, Le Treut and Li (1991) for microphysics, a thermal plume model for shallow convection (Hourdin et al., 2002(Hourdin et al., , 2019), a deep convection scheme based on the Emanuel mass flux scheme (Emanuel, 1991;Grandpeix et al., 2004) with ALE-triggering and ALP closure (Rio et al., 2013), and Yamada (1983) for sub-grid scale turbulence. Several statistical cloud schemes are used in the model -one for shallow clouds (Jam et al., 2013;Hourdin et al., 2019) coupled to the thermal plume model, one for deep convective clouds (Bony & Emanuel, 2001) coupled to the Emanuel convection scheme, and one for stratiform clouds (Madeleine et al., 2020).

S1.3.8. SAM0-UNICON
The Seoul National University Atmosphere Model Version 0 (SAM0-UNICON; Park et al., 2019) is a CAM5-based model that is configured with a spectral element dynamical core on a cubed-sphere mesh, a dynamics time step of 360 s, and a physics time step of 1800 s. The horizontal grid resolution is ne30 which corresponds to a grid spacing of 111 km at the equator. There are 30 hybrid sigma-pressure vertical levels with the midpoint height of the lowest model layer at the sigma pressure level of 0.9926 and the highest model interface at 0.00225 with approximately 1200 m vertical spacing. The physics packages are RRTMG (Iacono et al., 2008;Mitchell, 2002) for radiation, the Morrison and Gettelman (2008) double-moment microphysics scheme, the UW moist turbulence scheme for boundary layer (Bretherton & Park, 2009), UNICON for convection (Park, 2014). Note that SAM0-UNICON differs from CAM5 in its shallow and deep convection scheme and treatment of convective detrainment process in cloud macrophysics scheme (Park et al., 2017). S1.3.9. SP-CAM, SPX-CAM The Super-parameterized Community Atmosphere Model (SP-CAM) (Randall et al., 2016) employs a finite volume dynamical core with a spherical grid and a time step of 1800 s. RCE large has 288 x 192 horizontal grid points, corresponding to 1 degree grid spacing, and 26 hybrid pressure levels with a sponge layer at the model top. The radiation scheme is CAM-RT; all other physics parameterizations are represented via super-parameterization with an embedded cloud-resolving model (SAM) (Khairoutdinov & Randall, 2003). There are 32 CRM columns in each GCM grid cell with 4 km grid spacing and a CRM time step of 20 s. The CRM uses the bottom 24 CAM levels. The microphysics scheme is the SAM single-moment microphysics. The Multi-instance Super-parameterized Community Atmosphere Model (SPX-CAM; Phillips, 2018) differs from SP-CAM in that the surface fluxes are computed separately in each CRM grid column and are averaged back to the GCM. S1.3.10. UKMO-GA7.1 The Met Office Unified Model Global Atmosphere (GA7.1, CMIP6 model version) (Walters et al., 2019) employs a spherical grid with a 20 minute time step. RCE small employs a single column configuration with 85 vertical levels while RCE large has 192 x 144 horizontal grid points at N96 resolution corresponding to 130 km and 85 vertical levels. The vertical levels are height levels; most variables provided for RCEMIP are on "rho levels" but several are on "theta levels". The physics packages are detailed in Walters et al. (2019). S1.3.11. WRF-GCM The Weather Research and Forecasting model v3.5.1 (Skamarock et al., 2008), the same as is used for WRF-COL-CRM, employs the Advanced Research WRF (ARW) dynamical core on a Cartesian grid. The RCE large configuration is the same as for WRF-COL-CRM but has coarser horizontal resolution, fewer vertical levels, and employs convective parameterizations. The domain has 120 x 8 x 48 grid points, with a horizontal grid spacing of 50 km and a time step of 75 seconds. The vertical levels are eta levels (with hydrostatic pressure) with a model top of approximately 33 km and a sponge layer in the top 5 km. The physics packages used are RRTMG (Iacono et al., 2008) for shortwave and longwave radiation, the Morrison et al. (2009) double-moment microphysics scheme, the YSU boundary layer scheme (Noh et al., 2003;Hong et al., 2006), and a horizontal Smagorinsky first-order closure for sub-grid scale turbulence. Six different schemes are used: cps0 (no convective scheme), cps1 (Kain-Fritsch), cps2 (Betts-Miller-Janjic), cps3 (Grell-Freitas), cps4 (Simplified Arakawa Schubert), and cps6 (Tiedtke).

Text S2. Sensitivity of I org Calculation
The calculation of I org is sensitive to numerous details, some of which may not be readily apparent to the casual user. We present our approach to calculating I org to reveal these nuances and so that our results may be reproduced. We discuss three ways to calculate the cumulative distribution function and the sensitivity to the choice in number of connections used in identification of convective entities. Most differences in the calculation approach are small, but they can quickly accumulate for some models.
In addition to which variable and what threshold to use to identify convective pixels, as discussed in the main text's Appendix C, there are four primary considerations when setting up the I org calculation: 1. Periodic boundary conditions should be taken into account, as they allow for convective entities to span the boundaries and for those near the boundaries to consider nearest neighbors near the opposing boundary. 2. For global simulations, limiting the calculation to the tropical band where the curvature of Earth has very little impact on the calculation of distances between entities and the assumption of a cartesian grid can be reasonably applied.
3. The number of connective points by which to classify a group of convective pixels into a convective entitiy 4. Approach to calculating the cumulative density function (CDF, discussed further in S2.1.) The RCEMIP simulations employ doubly periodic boundary conditions for cloudresolving models (CRMs) and the global simulations are of course cyclic in the zonal direction. These boundary conditions are taken into account when identifying convective entities and their nearest neighbors. We limit the data in the I org calculation for global models to a tropical band of 30 • S-30 • N and thus must consider the band to be zonally re-entrant. However, the tropical band is not periodic in the meridional direction. The use of a tropical band, rather than the full global domain, is valid as long as the convective entities are significantly smaller than the tropical band, and as long as the aggregation is not so extreme that all convective activity occurs outside of the tropical band. This happens transiently prior to day 80 in the RCE large305 simulation in NICAM, so we only consider I org values after day 80 in this simulation.
For the calculation of I org in CRMs, we identify connected convective pixels as convective entities using four-point connectivity (considering adjacent pixels). We tested the sensitivity of the I org calculation to instead using eight-point connectivity (considering adjacent and diagonal pixels) and found it to be relatively insensitive to this choice. Fourpoint connectivity is also used for the GCM simulations, but given the parameterization of convection and coarse grid spacing, one individual convective pixel may be considered its own convective entity. Therefore, we also present results in which each convective pixel is considered to be independent (that is, using zero connectivity to identify convective entities). It is not clear which approach is more accurate. In the extreme limit of only a few clusters, the nearest neighbor distances between convective entities defined by four-point connectivity would be large and I org may be artificially low. With zero connectivity, on the other hand, I org is dominated by the small scales (i.e., how close convective pixels are to each other within a broader convective area) and may be artificially large. The actual differences depend on the structure of convection in a given model; I org is larger with zero connectivity in some models but smaller in others ( Figure S22). While the absolute value of I org is affected by the choice of connectivity, the dependence on SST and the inter-model spread is not ( Figure S23).
There are several approaches to the calculation of empirical CDF, discussed below. This paper uses Method II. The differences in the value of I org using the three different methods range across models from 0.001 to 0.081 with an average difference of 0.015 (∼ 2.5% error) when I org 's calculated from Method II and III were considered. All ECHAM6-GCM and WRF-GCM simulations and the warmest CAM5-GCM and CAM6-GCM simulations stand out as the models in which the ECDF method has the strongest impact on the I org calculation. This may be because ECHAM has the coarsest resolution of all GCMs and WRF-GCM has few grid points. The global cloud-resolving model (GCRM) simulations are the least impacted by the choice of ECDF method. Interestingly, these and other (relatively) higher resolution GCMs also have the least difference (and sometimes no difference) between them from the use of different nearest neighbor image processing packages (e.g., Pedregosa et al., 2011;Virtanen et al., 2020).
We note one additional possible source of error in the I org calculation: the nearest neighbor distances are calculated using the gridded indices of the centroids of the convec-tive entities. This calculation assumes a cartesian grid in which there is equal distance between indices in both horizontal directions. However, this is not always the case in the global simulations. For example, IPSL-CM6, the model with the coarsest resolution, has a grid spacing of 2.5 • in the zonal direction and ∼0.8 • in the meridional direction (for the latitude range we are considering) which is a difference in distance by a factor of three. However, when the data are interpolated onto a regular 1 • x1 • , the I org calculation differs by less than 1%, which is as small a difference as that which results from other choices. Therefore, we simply note it as a caveat.
These nuances of the I org calcluation are important to consider if it is desired to reproduce identical results. The sensitivity of the I org calculation in the GCMs, especially to choices as seemingly arbitrary as which ECDF method or which image processing package to use, suggest that I org is perhaps not a metric best suited for use in global models with coarse grids, at least when the absolute value of I org is of interest. The assumption that I org = 0.5 represents un-aggregated convection may not be valid in such models.

S2.1. ECDF Theory
The empirical cumulative distribution function, ECDF, is described by the following equation (van der Vaart, 1998): where N is the number of elements less or equal to t, n is the total number of elements, 1 x i ≤t is the indicator of event x i ≤ t, and the data, x, are independent and identically distributed. The methods described below will use the following list of numbers as example input and an example using a few models will follow the descriptions of the methods: x input = [0, 0, 1, 2, 2, 3]. Note each method sorts its input data from lowest to highest, but the example data, x input , is already sorted for simplicity. y output is a vector of values of the empirical CDF evaluated at x output , where this can be determined from x input (a vector of input data values) in several ways different ways (detailed below). The results of the three methods applied to example data are compared in Table S1.
with spacing between elements equal to and y output follows the following formula: which counts the number of elements of x input that are less than or equal to a particular element of the new x output . The results for our example are as follows: Method III: Method III is based on the MATLAB (MATLAB, 2019) ECDF function (Cox & Oakes, 1984;Lawless, 2002;Kleinbaum & Klein, 2005) which uses the Kaplan and Meier (1958) estimate of the CDF.
This method uses a temporary x list containing only unique elements of x input and then calculates a temporary y list containing the total amount of elements in x input that are less than or equal to an element in x temporary As a final step, a copy of the first element of x temporary is added to the beginning of the x temporary list and a zero is added to the beginning of the y temporary list. For our example: y temporary = 2 6 , 3 6 , 5 6 , 6 6 (10) Movie S1. Animation of hourly-averaged outgoing longwave radiation (OLR; W m 2 ) and precipitable water (PW; kg m −2 ) from day 65 to day 95 in RCE large simulations for CAM5-GCM. Note that the colorbar for PW is different in the 305K simulation. Movie S2. As in Movie S1 but for CAM6-GCM. Movie S3. As in Movie S1 but for CM1. Movie S4. As in Movie S1 but for CNRM-CM6-1. Movie S5. As in Movie S1 but for DAM. Movie S6. As in Movie S1 but for ECHAM6-GCM. Movie S7. As in Movie S1 but for daily-averaged PW only in FV3. Movie S8. As in Movie S1 but for GEOS-GCM. Movie S9. As in Movie S1 but for ICON-GCM. Movie S10. As in Movie S1 but for ICON-LEM. Movie S11. As in Movie S1 but for ICON-NWP. Movie S12. As in Movie S1 but for daily-averaged IPSL-CM6. Movie S13. As in Movie S1 but for MESONH. Movie S14. As in Movie S1 but for MPAS. Movie S15. As in Movie S1 but for NICAM. Movie S16. As in Movie S1 but for SAM0-UNICON. Movie S17. As in Movie S1 but for SAM-CRM. Movie S18. As in Movie S1 but for SAM-GCRM. Movie S19. As in Movie S1 but for SCALE. Movie S20. As in Movie S1 but for SP-CAM. Movie S21. As in Movie S1 but for SPX-CAM. Movie S22. As in Movie S1 but for UCLA-CRM. Movie S23. As in Movie S1 but for UKMO-GA7.1. Movie S24. As in Movie S1 but for UKMO-CASIM. Movie S25. As in Movie S1 but for UKMO-RA1-T. Movie S26. As in Movie S1 but for UKMO-RA1-T-nocloud. Movie S27. As in Movie S1 but for WRF-COL-CRM. Movie S28. As in Movie S1 but for WRF-CRM. Movie S29. As in Movie S1 but for WRF-GCM-cps0. Movie S30. As in Movie S1 but for WRF-GCM-cps1. Movie S31. As in Movie S1 but for WRF-GCM-cps2. Movie S32. As in Movie S1 but for WRF-GCM-cps3. Movie S33. As in Movie S1 but for WRF-GCM-cps4. Movie S34. As in Movie S1 but for WRF-GCM-cps6.  Model Dev., 11 , 1929Dev., 11 , -1969Dev., 11 , . doi: 10.5194/gmd-11-1929Dev., 11 , -2018 Lauritzen, P. H., Nair, R. D., Herrington, A., Callaghan, P., Goldhaber, S., Dennis, J.,         Table S9. Shortwave (λ SW = dR TOA,SW /dT ; Wm −2 K −1 ) and longwave (λ LW = dR TOA,LW /dT ;   Table S11. Net climate feedback parameter (λ = dR TOA /dT ; Wm −2 K −1 ) and cloud radiative   Figure S1.
Hourly-averaged precipitable water (kg m −2 ) at day 80 of the RCE small300 simulation for all cloud-resolving models.  Figure S2. Hourly-averaged precipitable water (kg m −2 )at day 80 of the RCE small300 (left column) and day 50 of the RCE small vert300 (middle column) and RCE small les300 (right column) simulations for CM1, DALES, DALES-damping, ICON LEM, MESONH, MicroHH, and SAM. Note that the radiative properties of ice clouds were erroneously configured in DALES and DALES-damping. DALES-damping-rad is a corrected version, shown for reference (note that it is the RCE small vert300 simulation that is shown despite it being in the column with LES simulations).   Figure S4.
Hourly-averaged precipitable water (kg m −2 ) at day 80 of the RCE large300 simulation for all global models. All models shown are GCMs with parameterized convection except MPAS, NICAM, and SAM, which are global cloud-resolving models that employ reduced Earth radius of R E /8, R E /4, and R E /4, respectively, and are shown to scale and, in the box, zoomed in. IPSL-CM6 is daily-averaged.  Figure S5. Hourly-averaged precipitable water (kg m −2 ) at day 80 of the RCE large300 simulation for all versions of WRF 3.5.1. The top panel for the WRF-COL-CRM configuration is the same is in Figure S3. The other panels show WRF in the cartesian RCE large300 configuration but with 50 km grid spacing and convective parameterizations.  Figure S6. Temporal evolution of hourly-and y-averaged precipitable water (kg m −2 ) in the RCE large300 simulations for CRMs over the first 100 days of simulation (y-axis) and the first 6000 km of the domain (x-axis).  Figure S7. Temporal evolution of hourly-and y-averaged precipitable water (kg m −2 ) in the RCE large300 simulations for GCMs (a-k) and GCRMs (l-n) over the first 100 days of simulation (y-axis) over a ∼6000 km zonal segment of the globe (x-axis). The PW is averaged meridionally within ∼400 km of the equator. Since MPAS employs a sphere of R E /8, a ∼4500 km zonal segment is shown, which is the entire domain. IPSL-CM6 is daily-averaged.  Figure S8. Temporal evolution of hourly-and y-averaged precipitable water (kg m −2 ) in the RCE large300 simulations for WRF-GCM over the first 100 days of simulation (y-axis) and the first 6000 km of the domain (x-axis).  Figure S9.

X -55
Hourly-averaged outgoing longwave radiation (Wm −2 ) at day 80 of the RCE large300 simulation for all GCMs, over a ∼6000 km x ∼400 km tropical band centered on the equator, to match the domain size of the CRM simulations (compare to Figure 4 in the main text). Since MPAS employs a sphere of R E /8, a ∼4500 km zonal segment is shown, which is the entire domain. IPSL-CM6 is daily-averaged. Figure S10. Probabability density function of precipitable water (PW; kg m −2 ) in RCE large simulations (left panels) and RCE small simulations (right panels) at 295 K (top), 300 K (middle), and 305 K (bottom). Each row represents the PDF for a particular model (ordered alphabetically). A row with no shading means that that model did not perform that particular simulation.  Figure S14.
Horizontal-mean total cloud condensate profile, averaged in time excluding the first 75 days of simulation of the RCE small (top row, a-d) and RCE large (bottom row, e-h) simulations at 295 K. TThe first column (a,e) includes all models that performed each type of simulation, where the black line is the ensemble mean, the blue shading shows the range across all models, and the orange lines indicate the interquartile range (IQR). The other columns display each sub-group of models: models with parameterized convection (second column; b,f), CRMs (third column; c,g), models that performed RCE small vert (dashed) and RCE small les (solid) simulations (panel d; RCE small les simulations are averaged over days 25-50), and GCRMs (panel h).  Figure S17. Domain-wide cloud fraction profile, averaged in time excluding the first 75 days of simulation of the RCE small (top row, a-d) and RCE large (bottom row, e-h) simulations at 305 K. The first column (a,e) includes all models that performed each type of simulation, where the black line is the ensemble mean, the blue shading shows the range across all models, and the orange lines indicate the interquartile range (IQR). The other columns display each sub-group of models: models with parameterized convection (second column; b,f), CRMs (third column; c,g), models that performed RCE small vert (dashed) and RCE small les (solid) simulations (panel d; RCE small les simulations are averaged over days 25-50), and GCRMs (panel h).  Figure S18. Horizontal-mean total cloud condensate profile, averaged in time excluding the first 75 days of simulation of the RCE small (top row, a-d) and RCE large (bottom row, e-h) simulations at 305 K. The first column (a,e) includes all models that performed each type of simulation, where the black line is the ensemble mean, the blue shading shows the range across all models, and the orange lines indicate the interquartile range (IQR). The other columns display each sub-group of models: models with parameterized convection (second column; b,f), CRMs (third column; c,g), models that performed RCE small vert (dashed) and RCE small les (solid) simulations (panel d; RCE small les simulations are averaged over days 25-50), and GCRMs (panel h).

Figure S19.
Degree of aggregation in RCE large295 based on subsidence fraction (red circles), I org (blue squares), and spatial variance of column relative humidity (green triangles) in all models, averaged in time excluding the first 75 days of simulation. The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line. Within each group of models, they are ordered according to their values of subsidence fraction. The two models for which subsidence fraction could not be computed are listed first. Box plots indicate the spread of each metric across models. Figure S20.
Degree of aggregation in RCE large305 based on subsidence fraction (red circles), I org (blue squares), and spatial variance of column relative humidity (green triangles) in all models, averaged in time excluding the first 75 days of simulation. The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line. Within each group of models, they are ordered according to their values of subsidence fraction. The two models for which subsidence fraction could not be computed are listed first. Box plots indicate the spread of each metric across models. Figure S21.
Rate of change of aggregation per degree K based on subsidence fraction (red circles), I org (blue squares), and spatial variance of column relative humidity (green triangles) in all models, based on the rate of change from 295 K to 300 K (filled symbols) and 300 K to 305 K (open symbols). The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line. Figure S22.
As in Figure 12 in the main text, but using zero connectivity to calculate I org in the GCMs rather than four-point connectivity. Degree of aggregation in RCE large300 based on subsidence fraction (red circles), I org (blue squares), and spatial variance of column relative humidity (green triangles) in all models, averaged in time excluding the first 75 days of simulation. The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line. Within each group of models, they are ordered according to their values of subsidence fraction. The two models for which subsidence fraction could not be computed are listed first. Box plots indicate the spread of each metric across models.
Rate of change of aggregation metrics in RCE_large Figure S23.
As in Figure 16 in the main text, but using zero connectivity to calculate I org in the GCMs rather than four-point connectivity. Shows the rate of change of the aggregation metrics from 295 K to 3005 K per degree K based on I org (blue squares), subsidence fraction (red circles), and spatial variance of column relative humidity (green triangles) in all models. The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line, each ordered according to their values of df sub /dSST . Box plots indicate the spread of each metric's rate of change across models, with outlier indicated with symbols. Figure S24.
As in Figure 12 in the main text, but using the spatial variance of precipitable water (PW) scaled by its domain mean value (green triangles) rather than column relative humidity. Degree of aggregation in RCE large300 based on subsidence fraction (red circles), I org (blue squares), and spatial variance of scaled PW (green triangles) in all models, averaged in time excluding the first 75 days of simulation. he models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line. Within each group of models, they are ordered according to their values of subsidence fraction. The two models for which subsidence fraction could not be computed are listed first.
Rate of change of aggregation metrics in RCE_large Figure S25.
As in Figure 16 in the main text, but using the spatial variance of precipitable water (PW) scaled by its domain mean value (green triangles) rather than column relative humidity. Shows the rate of change of the aggregation metrics from 295 K to 3005 K per degree K based on I org (blue squares), subsidence fraction (red circles), and spatial variance of scaled PW (green triangles) in all models. The models are ordered such that the models with explicit convection are to the left of the dashed line and models with parameterized convection are to the right of the dashed line, each ordered according to their values of df sub /dSST . Box plots indicate the spread of each metric's rate of change across models, with outlier indicated with symbols. Figure S26. Horizontal-and time-mean height at the location of the domain-wide anvil cloud peak as a function of SST in the RCE small simulations (a,b) and RCE large simulations (c,d), for models with explicit (a,c) and parameterized (b,d) convection. The dashed lines are linear regression lines of best fit. Figure S27. Horizontal-and time-mean temperature at the location of the domain-wide anvil cloud peak as a function of SST in the RCE small simulations (a,b) and RCE large simulations (c,d), for models with explicit (a,c) and parameterized (b,d) convection. The dashed lines are linear regression lines of best fit.  Figure S28. Domain-wide anvil cloud fraction as a function of SST in the RCE small simulations (a,b) and RCE large simulations (c,d), for models with explicit (a,c) and parameterized (b,d) convection. The anvil cloud fraction is shown as anomaly from its value in the simulation at 300 K. The dashed lines are linear regression lines of best fit.