Radiative–convective equilibrium (RCE) has long been used as an idealization of the climate system. In a greenhouse atmosphere, convection must balance the radiative heat loss of the atmosphere, making radiative–convective equilibrium the simplest possible description of the climate system . For this reason, there is a rich history of modeling RCE, mostly as a one-dimensional problem e.g.,. These early studies of RCE helped formulate an understanding of the basic characteristics of climate and the first estimates of climate sensitivity . Early work with two-dimensional simulations of RCE studied the relationship between convection and environmental structures . In recent years, as it became possible to perform more computationally intensive numerical simulations of RCE, there has been a revival in the use of RCE to study a variety of problems in tropical meteorology and climate. One common configuration is to simulate RCE with a three-dimensional numerical model with explicitly resolved convection over domain lengths of 100–1000 km e.g.,. The RCE state is achieved by prescribing uniform solar insolation and a horizontally uniform boundary condition (constant sea surface temperature (SST) or a slab ocean model) and initializing the model with random noise. There is also a growing body of work employing RCE in general circulation models (GCMs) with parameterized clouds and convection e.g.,.

The popularity of RCE arises from the fact that it remains the simplest way to phrase many important questions about the climate system. RCE has been extensively used to help answer questions such as how the representation of subgrid-scale processes influences the coupling of clouds and convection to the climate system e.g.,, and how this coupling depends on temperature e.g.,. RCE has been used to study the predictability of mesoscale rainfall e.g.,, tropical anvil clouds , and precipitation extremes e.g.,, as well as how the land surface influences the climate state , or the rectifying effects of surface heterogeneity in the form of islands e.g.,. RCE has also been used as a background state for tropical cyclone studies e.g.,. A central theme arising in many of these studies, and related to the formation of tropical cyclones and the Madden–Julian Oscillation , is the role of convective aggregation, which often arises spontaneously in studies of RCE using explicit and parameterized convection (, and references therein). It remains an open question as to how and whether the real atmosphere self-aggregates, and to what extent this is important for the properties of the climate system , in part because these aspects of the simulations appear sensitive to how the models are formulated e.g.,.

Assessing the structural sensitivity of simulations of RCE is hindered by the absence of a common baseline. Past studies differ in many, seemingly unessential details, which makes them hard to compare and determine which aspects of the simulations are robust. These range from different prescriptions of boundary conditions, such as incoming solar radiation, to different specifications of atmospheric composition, to different treatments of the upper atmosphere, or surface properties such as albedo. To provide context for the many studies that have been performed so far, and to provide a starting point for the many studies to come, a common baseline would be helpful. In this paper, we propose such a baseline in the form of a model intercomparison study, RCEMIP. A standard configuration of RCE is a useful framework for model development and evaluation , but in addition to providing a fixed point for past and future studies, such an intercomparison can itself address important questions related to RCE, such as establishing which features of the RCE state are consistent across models and which vary across configurations. Already, groups are beginning to compare RCE solutions using general circulation models with parameterized physics on large domains, to simulations on smaller domains with finer grids, to solutions using cloud-resolving models e.g.,. No other framework is accessible by so many of the varied models used to study the climate system, as in addition to cloud-resolving models, general circulation models, and single-column models, large-eddy simulation models and even Earth system models of intermediate complexity could be applied to the problem of RCE. Hence, through the definition of a common baseline, it should be possible to encourage the study of this canonical representation of the climate system using an even wider range of models, which is important for evaluating the generality of previous work on RCE. In addition to the simplicity and accessibility of the RCE framework, its importance lies in its similarities to substantial aspects of the real atmosphere; in general, RCE states are thought to correspond to convective regions over the tropical western Pacific warm pool, in terms of thermal structure (RCE has also been considered to represent the whole tropical belt, in which there is no large-scale vertical motion on average over the tropics and an approximate moist adiabatic thermal structure). There have already been some efforts to consider RCE simulations within a hierarchy of models; for example, and compared cloud feedbacks between a GCM in a realistic configuration and in RCE, and compared the structure of tropical convective systems between Earth-like aqua-planet experiments and RCE. A standard configuration of RCE would enable more of these types of comparisons.

Given this backdrop, in what follows, we describe the proposed model intercomparison study, RCEMIP, and more specifically detail the questions it will be used to address. In Sect. 2, we state the main scientific questions that this initiative will address. Subsequent sections specify the experimental design, including the required output and diagnostics. Finally, to give a flavor and better guide to those who wish to participate in this study, in Sect. 5, we present some sample results from three different models.

The three themes that RCEMIP has been designed for are as follows:

What is the response of clouds to warming and the climate sensitivity in RCE?

The first theme of RCEMIP, clouds and climate sensitivity, is motivated by the fact that cloud feedbacks are the largest source of uncertainty in estimates of climate sensitivity and depend on processes that are largely parameterized in global climate models e.g.,. The role of convection in cloud feedbacks is central to a better understanding of global and regional climate changes, as pointed out by the WCRP Grand Challenge on Clouds, Circulation, and Climate Sensitivity . RCEMIP, which includes both cloud-resolving models (CRMs) and GCMs, is uniquely situated to determine the response of certain types of clouds to warming, without the complications of topography, latitudinal insolation gradients, and the associated dynamical disturbances. Recent work has suggested a thermodynamic mechanism for a decrease in anvil cloud fraction with warming in several GCMs and a CRM , but the robustness of this response across a wider range of models has yet to be determined. For example, one other CRM finds the opposite response, an increase in anvil cloud fraction with warming . Changes in the amount and height of anvil clouds with warming have strong implications for cloud feedbacks, and the coupling between temperature, cloud amount, and circulation may contribute to a narrowing of convective areas – both of which could lead to a type of iris effect . The net feedback parameter of the RCE state may be computed, which is reminiscent of the use of single-column model simulations of RCE for the very first estimates of climate sensitivity, but now RCE can be simulated in much more advanced models that allow relative humidity and clouds to vary, including models that allow for the generation of large-scale circulations by self-aggregation. The climate sensitivity of RCE simulations would reflect the fundamental characteristics of each model's representation of tropical clouds and convection, as opposed to Coupled Model Intercomparison Project (CMIP)-type simulations, which include many additional complexities such as ice–albedo feedbacks and interactions between clouds and midlatitude baroclinic eddies. A potentially important factor in determining the climate sensitivity of RCE is the extent to which a given model's convection self-aggregates and how the aggregation changes with warming. Self-aggregation has been hypothesized to be important for climate and climate sensitivity because both numerical simulations e.g., and observational analyses e.g., indicate the mean atmospheric state is drier and more efficient at radiating heat to space when convection is more aggregated. Much remains to be understood, however, about how the self-aggregation in idealized simulations is borne out in the real atmosphere . The role of self-aggregation in climate is therefore an aspect of climate sensitivity that RCEMIP will target.

The manner and extent to which self-aggregation is temperature dependent is strongly related to the impact of aggregation on climate sensitivity but remains unresolved . Therefore, the second theme of RCEMIP is about the dependence of the degree of convective self-aggregation on temperature (for instance, whether convection becomes more or less aggregated in a warmer climate). Not only does the degree of self-aggregation have implications for climate feedbacks, changing convective organization has also been shown to be one mechanism for increases in extreme precipitation with warming . Changes in the amount of organized convection have also been linked to observed regional tropical precipitation increases . In addition, the fact that self-aggregation generates large-scale overturning circulations allows us to ask the more general question of how tropical circulation regimes change with climate. In CRMs with domain geometries capable of containing multiple self-aggregated regions, there is the additional possibility of examining interactions between clouds, convection, and circulation in a framework that explicitly simulates both convection and the large-scale circulation in which it is embedded, which is a rare combination . Across both CRMs and GCMs, RCEMIP will be able to assess how circulation strength depends on temperature.

The final theme of RCEMIP, and the most critical, is the robustness of the RCE state, its changes with warming, and representation of self-aggregation across the spectrum of models. The broader implications of the results from the first two themes, regarding clouds and aggregation, depend in part on our ability to establish a consistent picture of the RCE state; identifying which features and responses are robust across models is essential. The evaluation of the robustness of the RCE state should include a comparison of baseline characteristics, such as profiles of humidity and cloudiness and the radiative cooling rate and mean surface precipitation rate at which equilibrium is reached, but could have a more lasting impact on theories of tropical climate by also including a determination of the universality of theoretical invariances or relationships found in a single model. For example, relative humidity has been argued to be a function of temperature only by and radiative flux divergence has been found to be a nearly universal function of temperature . Such invariances could simplify thinking about the response of RCE, and perhaps the actual tropics, to warming, but there is a lack of understanding of their robustness across models. In addition, a comparison of the inter-model spread in climate sensitivity of the RCE simulations with the inter-model spread of CMIP6 simulations would be informative. Despite the simplicity of the RCE setup, there is the potential for a wide range of behavior given how essential clouds and convective processes are to determining the RCE state, and the myriad of different ways these processes are represented in models. Further, while multiple common features and mechanisms have emerged across different studies of self-aggregation , the behavior of self-aggregation of convection across a wide range of models set up in a consistent manner has not been fully characterized. RCEMIP will enable us to better determine the robustness of self-aggregation and its sensitivities, an important step to understanding its role in climate.

The experimental design of RCEMIP is to require a small set of experiments that are designed to maximize the utility of the RCEMIP simulations in answering the questions about clouds, climate sensitivity, and self-aggregation posed above while minimizing the effort required by the modeling groups.

We request output following the conventions of CMIP6 (see http://clipc-services.ceda.ac.uk/dreq/index.html for variable descriptions). If possible, the output should be “CMOR-ized”, such that the output variable names and units are the same as in CMIP6. All variables should be saved for the entirety of each RCE_small and RCE_large simulation. For CRMs, the variables should be output on the model levels and on the native x/y grid. For GCMs, the variables should be output on model levels and the native grid (groups may additionally interpolate to the standard CMIP6 pressure levels if they desire). If the native GCM grid is not latitude–longitude, then the output should also be interpolated to a latitude–longitude grid. The output format should be NetCDF, and will be uploaded to a shared data server, which will facilitate analysis and comparison of the simulations.

Table  shows a preliminary list of models that are confirmed to participate in RCEMIP. We expect this list to grow with participation from other modeling groups and scientists across the world.

Several preliminary simulations using the RCEMIP configuration have been performed using the System for Atmospheric Modeling (SAM), version 6.8.2 , a CRM, NICAM, version 15, a GCRM , and the Community Atmosphere Model (CAM), version 5 , a GCM. We show here sample results from those test simulations as an example of what the RCEMIP simulations might look like; this is not intended as a comprehensive comparison.

Figures – show example results from a cloud-resolving model simulation of RCE, using SAM with the settings configured as described in Sect.  (with the exception of the q0 values in the analytic profiles used to initialize the RCE_small simulations at 295 and 305 K; q0=18.65 gkg-1 was used for all simulations shown here). Figure  shows outgoing longwave radiation (indicating deep convective clouds) and precipitation rate from the end of a RCE_small simulation at 300 K; the convection is quasi-random in space and time. Figure  shows outgoing longwave radiation and precipitation rate from a RCE_large simulation at 300 K. The convection is aggregated into several large clusters. Self-aggregation is characterized by the development of anomalously moist and dry regions, as can be seen by plots of daily mean water vapor path at day 10 (Fig. a) and day 90 (Fig. b) of the large-domain SAM simulation. This does not occur in the small-domain simulation (Fig. ); while the domain dries out slightly, the daily mean water vapor path is spatially homogenous. The moist static energy variance budget can be used to diagnose the physical mechanisms contributing to self-aggregation (Fig. ). The domain average moist static energy variance increases over 2 orders of magnitude over the course of the simulation, indicating the moistening of moist areas and drying of dry areas (Fig. a). Figure b shows the contributions of different feedbacks to that growth in moist static energy variance; in this case, it is the surface flux and longwave radiation feedbacks.

Figure  shows an example result from a global simulation of RCE with explicit convection, using NICAM in a global, non-rotating, spherical configuration with a real Earth radius and a 14 km horizontal grid spacing. Figure  shows a snapshot of outgoing longwave radiation (OLR) and precipitation rate, which is similar to Figs. –. The convection has spontaneously organized into clusters. Differences in aggregation properties, such as cluster sizes, can be seen between the results shown in Figs.  and , which may stem from the domain geometry, the horizontal resolution, or other details, as mentioned in Sect. . Note that, in this example simulation, slightly different values of the solar constant, zenith angle, surface albedo, and minimum wind speed in the surface flux calculation were used than those described in the RCEMIP protocol (434 Wm-2, 0∘, and 2 ms-1, respectively). The simulation was initialized from zonally averaged profiles of a coarser-resolution simulation.

Figures – show example results from a series of GCM simulations of RCE, using CAM5 with the spectral element dynamical core on a cubed–sphere grid with ne30 resolution, which corresponds to ∼100 km grid spacing. More details on the version of CAM5 (including the physics packages) used for these simulations can be found in . Figure  shows a snapshot of OLR and precipitation rate for the set of three RCEMIP experiments, which can be compared to Figs. , , and . Figure  shows a snapshot of water vapor path (at the same time as displayed in Fig. ). There is a large cluster of clouds and precipitation in each of the simulations at 300 and 305 K, while the precipitation in the simulation at 295 K is somewhat more scattered. The simulation at 305 K appears to be the most aggregated, with a single hemisphere-scale, intensely precipitating cluster and little cloud cover or precipitation elsewhere on the globe. It is also evident from Fig.  that the range of water vapor path values is largest in the simulation at 305 K, with the largest values occurring where the clouds and precipitation are clustered.

The above results indicate what RCEMIP simulations might look like in three different model types. Here, we provide a brief example of how the simulations can be compared to each other to determine the robustness of the RCE state and its response to warming across the spectrum of models. One of the objectives of RCEMIP is to examine the changes in clouds with warming. Figure  shows that high clouds shift upward with warming and decrease in extent in the SAM and CAM simulations but increase in extent in the NICAM simulations. The decrease in high cloud fraction in the SAM simulations occurs in both the small- and large-domain simulations (without and with convective aggregation). The degree of convective aggregation can be diagnosed using the subsidence fraction metric, for example (SF; Sect. 4.2.3). In the SAM CRM simulation, the subsidence fraction increases over the first ∼40 days of each simulation, indicating the increasing aggregation of convection and development of large areas of subsiding air (Fig. ). The mean subsidence fraction over the last 25 days decreases with increasing SST, but there is large variability in the subsidence fraction. The equilibrium value of the subsidence fraction is between ∼0.65 and 0.7 in the SAM simulations, while it is higher (∼0.7–0.8) in the NICAM and CAM simulations, indicating that the convection is more aggregated in the global simulations. The subsidence fraction does not depend monotonically on SST in either the NICAM or CAM simulations.

RCEMIP has been designed to be as simple as possible in order to maximize participation, foster a community of modelers of RCE, and allow for scientific progress on each of our three themes with a minimum of simulations. We recognize that the initial simulations will not necessarily be a definitive representation of the RCE state, for reasons such as lack of boundary closure in some CRMs, distortions of shallow clouds, sensitivity to microphysical formulations, and other sources of bias that we might not be aware of yet. Our vision for the evolution of RCEMIP is that the simulations proposed here serve as a starting point that will allow us to establish a baseline, enable progress on the scientific objectives presented in Sect. 2, and based on the results, inform subsequent experimentation. RCEMIP presents an exceptional opportunity for the participants to explore other issues, which we hope will form the basis for a second phase of RCEMIP. Here, we provide a few suggestions that we think are promising avenues forward but leave open the possibility for other directions that could evolve from the results of the first RCEMIP simulations.

Radiative–convective equilibrium is an idealization of the tropical atmosphere that, over the past five decades, has led to advances in our understanding of the vertical temperature structure of the tropics, the scaling of the hydrological cycle with warming, climate sensitivity, interactions between convection and radiation, and the development of large-scale circulations. With a coordinated intercomparison including both cloud-resolving models and general circulation models with parameterized convection, RCEMIP will help answer important questions surrounding changes in clouds and convective activity with warming, cloud feedbacks, and climate sensitivity, and the aggregation of convection and its role in climate. In addition, the simple premise of RCE will allow the results of RCEMIP to be connected to theory, as well as serve as a useful framework for model development and evaluation. RCEMIP distinguishes itself from many other intercomparisons because of its ability to involve many model types (SCMs, CRMs, GCRMs, GCMs, LES); the comparison between model types is vital as increasingly higher resolutions are possible in climate-scale global modeling. RCEMIP is specifically designed to determine how models of different types represent the same phenomena and thus provides a basis for testing models with parameterized convection against models that simulate convection directly. In doing so, RCEMIP will help us answer some of the most important questions in climate science.