Radiative-convective Equilibrium Research Articles

Recent advances in research on tropical cyclogenesis

This review article summarizes recent (2014–2019) advances in our understanding of tropical cyclogenesis, stemming from activities at the ninth International Workshop on Tropical Cyclones. Tropical cyclogenesis involves the interaction of dynamic and thermodynamic processes at multiple spatio-temporal scales. Studies have furthered our understanding of how tropical cyclogenesis may be affected by external processes, such as intraseasonal oscillations, monsoon circulations, the intertropical convergence zone, and midlatitude troughs and cutoff lows. Additionally, studies have furthered our understanding of how tropical cyclogenesis may be affected by internal processes, such as the organization of deep convection; the evolution of the “pouch” structure; the role of friction; the development of the moist, warm core; the importance of surface fluxes; and the role of the mid-level vortex. A relatively recent class of idealized, numerical simulations of tropical cyclogenesis in radiative-convective equilibrium have highlighted the potential importance of radiative feedbacks on tropical cyclogenesis. We also offer some recommendations to the community on future directions for tropical cyclogenesis research.

A new set of atmosphere and evolution models for cool T–Y brown dwarfs and giant exoplanets

We present a new set of solar metallicity atmosphere and evolutionary models for very cool brown dwarfs and self-luminous giant exoplanets, which we term ATMO 2020. Atmosphere models are generated with our state-of-the-art 1D radiative-convective equilibrium code ATMO, and are used as surface boundary conditions to calculate the interior structure and evolution of 0.001–0.075 M⊙ objects. Our models include several key improvements to the input physics used in previous models available in the literature. Most notably, the use of a new H–He equation of state including ab initio quantum molecular dynamics calculations has raised the mass by ~1−2% at the stellar–substellar boundary and has altered the cooling tracks around the hydrogen and deuterium burning minimum masses. A second key improvement concerns updated molecular opacities in our atmosphere model ATMO, which now contains significantly more line transitions required to accurately capture the opacity in these hot atmospheres. This leads to warmer atmospheric temperature structures, further changing the cooling curves and predicted emission spectra of substellar objects. We present significant improvement for the treatment of the collisionally broadened potassium resonance doublet, and highlight the importance of these lines in shaping the red-optical and near-infrared spectrum of brown dwarfs. We generate three different grids of model simulations, one using equilibrium chemistry and two using non-equilibrium chemistry due to vertical mixing, all three computed self-consistently with the pressure-temperature structure of the atmosphere. We show the impact of vertical mixing on emission spectra and in colour-magnitude diagrams, highlighting how the 3.5−5.5 μm flux window can be used to calibrate vertical mixing in cool T–Y spectral type objects.

Convective Dynamics and the Response of Precipitation Extremes to Warming in Radiative–Convective Equilibrium

AbstractTropical precipitation extremes are expected to strengthen with warming, but quantitative estimates remain uncertain because of a poor understanding of changes in convective dynamics. This uncertainty is addressed here by analyzing idealized convection-permitting simulations of radiative–convective equilibrium in long-channel geometry. Across a wide range of climates, the thermodynamic contribution to changes in instantaneous precipitation extremes follows near-surface moisture, and the dynamic contribution is positive and small but is sensitive to domain size. The shapes of mass flux profiles associated with precipitation extremes are determined by conditional sampling that favors strong vertical motion at levels where the vertical saturation specific humidity gradient is large, and mass flux profiles collapse to a common shape across climates when plotted in a moisture-based vertical coordinate. The collapse, robust to changes in microphysics and turbulence schemes, implies a thermodynamic contribution that scales with near-surface moisture despite substantial convergence aloft and allows the dynamic contribution to be defined by the pressure velocity at a single level. Linking the simplified dynamic mode to vertical velocities from entraining plume models reveals that the small dynamic mode in channel simulations (2% K−1) is caused by opposing height dependences of vertical velocity and density, together with the buffering influence of cloud-base buoyancies that vary little with surface temperature. These results reinforce an emerging picture of the response of extreme tropical precipitation rates to warming: a thermodynamic mode of about 7% K−1 dominates, with a minor contribution from changes in dynamics.

Responses of Mean and Extreme Precipitation to Different Climate Forcing Under Radiative-Convective Equilibrium

Understanding the responses of mean and extreme precipitation to climate change is of great importance. Previous studies have mainly focused on the responses to prescribed sea surface warming or warming due to increases of CO2. This study uses a cloud-resolving model under the idealization of radiative–convective equilibrium to examine the responses of mean and extreme precipitation to a variety of climate forcings, including changes in prescribed sea surface temperature, CO2, solar insolation, surface albedo, stratospheric volcanic aerosols, and several tropospheric aerosols. The different responses of mean precipitation are understood by examining the changes in the surface energy budget. It is found that the cancellation between shortwave scattering and longwave radiation leads to a small dependence of the mean precipitation response on forcings. The responses of extreme precipitation are decomposed into three components (thermodynamic, dynamic, and precipitation efficiency). The thermodynamic components for all climate forcings are similar. The dynamic components and the precipitation-efficiency components, which have large spreads among the cases, are negatively correlated, leading to a small dependence of the extreme precipitation response on the forcings.

Axisymmetric Hadley Cell Theory with a Fixed Tropopause Temperature Rather than Height

Abstract Axisymmetric Hadley cell theory has traditionally assumed that the tropopause height (Ht) is uniform and unchanged from its radiative–convective equilibrium (RCE) value by the cells’ emergence. Recent studies suggest that the tropopause temperature (Tt), not height, is nearly invariant in RCE, which would require appreciable meridional variations in Ht. Here, we derive modified expressions of axisymmetric theory by assuming a fixed Tt and compare the results to their fixed-Ht counterparts. If Tt and the depth-averaged lapse rate are meridionally uniform, then at each latitude Ht varies linearly with the local surface temperature, altering the diagnosed gradient-balanced zonal wind at the tropopause appreciably (up to tens of meters per second) but the minimal Hadley cell extent predicted by Hide’s theorem only weakly (≲1°) under standard annual-mean and solsticial forcings. A uniform Tt alters the thermal field required to generate an angular-momentum-conserving Hadley circulation, but these changes and the resulting changes to the equal-area model solutions for the cell edges again are modest (<10%). In numerical simulations of latitude-by-latitude RCE under annual-mean forcing using a single-column model, assuming a uniform Tt is reasonably accurate up to the midlatitudes, and the Hide’s theorem metrics are again qualitatively insensitive to the tropopause definition. However imperfectly axisymmetric theory portrays the Hadley cells in Earth’s macroturbulent atmosphere, evidently its treatment of the tropopause is not an important error source.

Climate Sensitivity and the Direct Effect of Carbon Dioxide in a Limited-Area Cloud-Resolving Model

AbstractEven in a small domain, it can be prohibitively expensive to run cloud-resolving greenhouse gas warming experiments due to the long equilibration time. Here, a technique is introduced that reduces the computational cost of these experiments by an order of magnitude: instead of fixing the carbon dioxide concentration and equilibrating the sea surface temperature (SST), this technique fixes the SST and equilibrates the carbon dioxide concentration. Using this approach in a cloud-resolving model of radiative–convective equilibrium (RCE), the equilibrated SST is obtained as a continuous function of carbon dioxide concentrations spanning 1 ppmv to nearly 10 000 ppmv, revealing a dramatic increase in equilibrium climate sensitivity (ECS) at higher temperatures. This increase in ECS is due to both an increase in forcing and a decrease in the feedback parameter. In addition, the technique is used to obtain the direct effects of carbon dioxide (i.e., the rapid adjustments) over a wide range of SSTs. Overall, the direct effect of carbon dioxide offsets a quarter of the increase in precipitation from warming, reduces the shallow cloud fraction by a small amount, and has no impact on convective available potential energy (CAPE).

Deflating Super-puffs: Impact of Photochemical Hazes on the Observed Mass–Radius Relationship of Low-mass Planets

Abstract The observed mass–radius relationship of low-mass planets informs our understanding of their composition and evolution. Recent discoveries of low-mass, large-radius objects (“super-puffs”) have challenged theories of planet formation and atmospheric loss, as their high inferred gas masses make them vulnerable to runaway accretion and hydrodynamic escape. Here we propose that high-altitude photochemical hazes could enhance the observed radii of low-mass planets and explain the nature of super-puffs. We construct model atmospheres in radiative-convective equilibrium and compute rates of atmospheric escape and haze distributions, taking into account haze coagulation, sedimentation, diffusion, and advection by an outflow wind. We develop mass–radius diagrams that include atmospheric lifetimes and haze opacity, which is enhanced by the outflow, such that young (∼0.1–1 Gyr), warm (T eq ≥ 500 K), low-mass objects (M c < 4 M ⊕) should experience the most apparent radius enhancement due to hazes, reaching factors of three. This reconciles the densities and ages of the most extreme super-puffs. For Kepler-51b, the inclusion of hazes reduces its inferred gas mass fraction to <10%, similar to that of planets on the large-radius side of the sub-Neptune radius gap. This suggests that Kepler-51b may be evolving toward that population and that some warm sub-Neptunes may have evolved from super-puffs. Hazes also render transmission spectra of super-puffs and sub-Neptunes featureless, consistent with recent measurements. Our hypothesis can be tested by future observations of super-puffs’ transmission spectra at mid-infrared wavelengths, where we predict that the planet radius will be half of that observed in the near-infrared.

On the Cooling-to-Space Approximation

AbstractThe cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.

Global variability in radiative-convective equilibrium with a slab ocean under a wide range of CO2 concentrations

In radiative-convective equilibrium (RCE), radiative cooling of the troposphere is roughly balanced by the vaporization enthalpy set free by precipitating moist convection. Many earlier studies restricted the investigation of RCE to the dynamics of the atmosphere with constant boundary conditions including prescribed surface temperature. We investigate a GCM setup where a slab ocean is coupled to the atmosphere, and we explore a wide range of CO2 concentrations. We obtain reliable statistical quantities from thousand-year-long simulations. For moderate CO2 concentrations, we find unskewed temporal variations of 1–2 K in global mean surface temperature, with an almost constant climate sensitivity of 2 K. At CO2 concentrations beyond four times the preindustrial value, the climate sensitivity decreases to nearly zero as a result of episodic global cooling events as large as 10 K. The dynamics of these cooling events are investigated in detail and shown to be associated with an increase in large-scale low-level stratiform cloudiness in the subsiding region, which is a result of penetrative shallow convection being capped by an inversion and thus not ventilating the lower troposphere. These dynamics depend on the CO2 concentration: both through the effect of temperature on stratification and through the changing spatial scale of organization of the flow, which determines the spatial scale and temporal coherence of the stratiform cloud sheets.

Self‐Aggregation of Convection in Spatially Varying Sea Surface Temperatures

AbstractThe phenomenon of self‐aggregation of convection was first identified in convection‐permitting simulations of radiative convective equilibrium, characterized by homogeneous boundary conditions and in the absence of planetary rotation. In this study, we expose self‐aggregation of convection to more complex, nonhomogeneous boundary conditions and investigate its interaction with convective aggregation, as forced by large‐scale variations in sea surface temperatures (SSTs). We do this by conducting radiative convective equilibrium simulations on a spherical domain, with SST patterns that are zonally homogeneous but meridionally varying. Due to the meridional contrast in SST, a convergence line first forms, mimicking the Intertropical Convergence Zone. We nevertheless find that the convergence line breaks up and contracts zonally as a result of the self‐aggregation of convection. The contraction is significant, being here more than 50% of the original extent. The stability of the convergence line is controlled by the strength of the meridional circulation, which depends upon the imposed SST contrast. However, the process of self‐aggregation, once it is initiated, is insensitive to the strength of the SST contrast. The zonal contraction is accompanied by a slight meridional expansion and a moistening of the high latitudes, where SSTs are low. The moistening of the high latitudes can be understood from the fact that the convective cluster intensifies and expands its moist meridional low‐level outflow when it self‐aggregates zonally. Overall, our results suggest that the Intertropical Convergence Zone may be unstable to the self‐aggregation of convection, that self‐aggregation may serve as a precursor to the formation of atmospheric rivers, and that longer convergence lines are more likely to exist in regimes with strong SST gradients.

Evaluating the Future of Lightning in Cloud‐Resolving Models

AbstractTwo proxies for lightning predict very different responses to global warming: the CAPE times precipitation proxy predicts a large increase in lightning over both the continental United States and the tropical oceans, while the ice flux proxy predicts a small increase over the United States and a decrease over the tropical oceans. To date, however, these proxies have been studied only in global climate models with parameterized convection. Here, cloud‐resolving simulations are used to assess their predictions of future lightning rates. Over the United States, all proxies predict a large increase in the lightning rate in the range of 8–16%/K. On the other hand, in the tropics as modeled by radiative convective equilibrium, half of the proxies predict an increase (of 5–12%/K), while the other half predict a decrease (of 1–4%/K). The reasons for the different responses of these proxies is explored, but it remains unclear which proxy is best suited to predicting future lightning rates.

Analyzing Atmospheric Temperature Profiles and Spectra of M Dwarf Rocky Planets

Abstract The James Webb Space Telescope (JWST) will make it possible to comprehensively measure the thermal emission spectra of rocky exoplanets orbiting M dwarfs and thus characterize their atmospheres. In preparation for this opportunity, we present model atmospheres for three M-dwarf planets particularly amenable to secondary eclipse spectroscopy—TRAPPIST-1b, GJ 1132b, and LHS 3844b. Using three limiting cases of candidate atmospheric compositions (pure H2O, pure CO2, and solar abundances) we calculate temperature–pressure profiles and emission spectra in radiative-convective equilibrium, including the effects of a solid surface. We find that the atmospheric radiative transfer is significantly influenced by the cool M-star irradiation; H2O and CO2 absorption bands in the near-infrared are strong enough to absorb a sizeable fraction of the incoming stellar light at low pressures, which leads to temperature inversions in the upper atmosphere. The non-gray band structure of gaseous opacities in the infrared is hereby an important factor. Opacity windows are muted at higher atmospheric temperatures, so we expect temperature inversions to be common only for sufficiently cool planets. We also find that pure CO2 atmospheres exhibit lower overall temperatures and stronger reflection spectra compared to models of the other compositions. We estimate that for GJ 1132b and LHS 3844b we should be able to distinguish between different atmospheric compositions with JWST. The emission lines from the predicted temperature inversions are currently hard to measure, but high-resolution spectroscopy with future extremely large telescopes may be able to detect them.

Surface Moisture Exchange Under Vanishing Wind in Simulations of Idealized Tropical Convection

AbstractUnder radiative‐convective equilibrium (RCE), surface moisture fluxes drive convection, while convection‐driven winds regulate surface fluxes. Most simulations of RCE do not resolve the boundary‐layer turbulence that drives near‐surface winds due to too coarse grid spacing and instead parameterize its effects by enforcing a minimum wind speed in the computation of the ocean‐atmosphere exchange. We show from RCE simulations with fully resolved boundary‐layer turbulence that capturing wind dynamics at low speeds impacts the spatially averaged surface moisture flux, as well as its spatial distribution. A minimum wind speed constraint of only 1 m s−1 leads to ∼10% increase in spatially averaged surface flux in the evolution towards RCE and reduces the surface flux differences between windy and calm regions with more than a factor of two. Hence, the ability of simulations to let wind vanish is key in representing the wind‐induced surface heat exchange feedback and is potentially important in convective self‐aggregation.

Re-Examining the First Climate Models: Climate Sensitivity of a Modern Radiative–Convective Equilibrium Model

Abstract We revisit clear-sky one-dimensional radiative–convective equilibrium (1D-RCE) and determine its equilibrium climate sensitivity to a CO2 doubling (ECS) and associated uncertainty. Our 1D-RCE model, named konrad, uses the Rapid Radiative Transfer Model for GCMs (RRTMG) to calculate radiative fluxes in the same way as in comprehensive climate models. The simulated radiative feedbacks are verified by a line-by-line radiative transfer model, with which we also investigate their spectral distribution. Changing the model configuration of konrad enables a clear separation between the water vapor and the lapse rate feedbacks, as well as the interaction between the two. We find that the radiative feedback and ECS are sensitive to the chosen relative humidity profile, resulting in an ECS range of 2.09–2.40 K. Using larger CO2 forcings we find that the radiative feedback changes up to 10% for surface temperatures of 291–299 K. Although the ECS is similar to previous studies, it arises from the compensation of a larger clear-sky forcing (4.7 W m−2) and more strongly negative feedbacks (−2.3 W m−2 K−1). The lapse rate feedback and the feedback from the interaction of lapse rate and humidity compensate each other, but the degree of compensation depends on the relative humidity profile. Additionally, the temperature profile is investigated in a warming climate. The temperature change at the convective top is half as large as at the surface, consistent with the proportionally higher anvil temperature hypothesis, as long as the humidity is consistently coupled to the temperature profile.

Collapse of the General Circulation in Shortwave-absorbing Atmospheres: An Idealized Model Study

Abstract The response of the general circulation in a dry atmosphere to various atmospheric shortwave absorptivities is investigated in a three-dimensional general circulation model with gray radiation. Shortwave absorption in the atmosphere reduces the incoming radiation reaching the surface but warms the upper atmosphere, significantly shifting the habitable zone toward the star. The strong stratification under high shortwave absorptivity suppresses the Hadley cell in a manner that matches previous Hadley cell scalings. General circulation changes may be observable through cloud coverage and superrotation. The equatorial superrotation in the upper atmosphere strengthens with the shortwave opacity, as predicted based on the gradient wind of the radiative–convective equilibrium profile. There is a sudden drop of equatorial superrotation at very low shortwave opacity. This is because the Hadley cell in those cases are strong enough to fill the entire troposphere with zero momentum air from the surface. A diurnal cycle (westward motion of substellar point relative to the planet) leads to acceleration of the equatorial westerlies in general, through the enhancement of the equatorward eddy momentum transport, but the response is not completely monotonic, perhaps due to the resonance of tropical waves and the diurnal forcing.

A 1D RCE Study of Factors Affecting the Tropical Tropopause Layer and Surface Climate

Abstract There are discrepancies between global climate models regarding the evolution of the tropical tropopause layer (TTL) and also whether changes in ozone impact the surface under climate change. We use a 1D clear-sky radiative–convective equilibrium model to determine how a variety of factors can affect the TTL and how they influence surface climate. We develop a new method of convective adjustment, which relaxes the temperature profile toward the moist adiabat and allows for cooling above the level of neutral buoyancy. The TTL temperatures in our model are sensitive to CO2 concentration, ozone profile, the method of convective adjustment, and the upwelling velocity, which is used to calculate a dynamical cooling rate in the stratosphere. Moreover, the temperature response of the TTL to changes in each of the above factors sometimes depends on the others. The surface temperature response to changes in ozone and upwelling at and above the TTL is also strongly amplified by both stratospheric and tropospheric water vapor changes. With all these influencing factors, it is not surprising that global models disagree with regard to TTL structure and evolution and the influence of ozone changes on surface temperatures. On the other hand, the effect of doubling CO2 on the surface, including just radiative, water vapor, and lapse-rate feedbacks, is relatively robust to changes in convection, upwelling, or the applied ozone profile.

A Conceptual Spectral Plume Model for Understanding Tropical Temperature Profile and Convective Updraft Velocities

Abstract The tropical tropospheric temperature is close to but typically cooler than that of the moist adiabat. The negative temperature deviation from the moist adiabat manifests a C-shape profile and is projected to increase and stretch upward under warming in both comprehensive climate models and idealized radiative–convective equilibrium (RCE) simulations. The increased temperature deviation corresponds to a larger convective available potential energy (CAPE) under warming. The extreme convective updraft velocity in RCE increases correspondingly but at a smaller fractional rate than that of CAPE. A conceptual model for the tropical temperature deviation and convective updraft velocities is formulated to understand these features. The model builds on the previous zero-buoyancy model but replaces the bulk zero-buoyancy plume by a spectrum of entraining plumes that have distinct entrainment rates and are positively buoyant until their levels of neutral buoyancy. Besides the negative temperature deviation and its increasing magnitude with warming, this allows the spectral plume model to further predict the C-shape profile as well as its upward stretch with warming. By representing extreme convective updrafts as weakly entraining plumes, the model is able to reproduce the smaller fractional increase in convective velocities with warming as compared to that of CAPE. The smaller fractional increase is mainly caused by the upward stretch in the temperature deviation profile with warming, which reduces the ratio between the integrated plume buoyancy and CAPE. The model thus provides a useful tool for understanding the tropical temperature profile and convective updraft velocities.

Dry and Semidry Tropical Cyclones

AbstractIt is widely believed that tropical cyclones are an intrinsically moist phenomenon, requiring evaporation and latent heat release in cumulus convection. Recent numerical modeling by Mrowiec et al., however, challenged this conventional wisdom by finding the formation of axisymmetric dry tropical cyclones in dry radiative–convective equilibrium (RCE). This paper addresses ensuing questions about the stability of dry tropical cyclones in 3D, the moist–dry vortex transition, and whether existing theories for intensity, size, and structure apply to dry cyclones. A convection-permitting model is used to simulate rotating 3D RCE, with surface wetness (0–1) and surface temperature (240–300 K) smoothly varying between dry and moist states. Tropical cyclones spontaneously form and persist for tens of days in both moist and dry/cold states, as well as part of the relatively moist/warm intermediate parameter space. As the surface is dried or cooled, cyclones weaken, both in absolute terms and relative to their potential intensities. Dry and semidry cyclones have smaller outer radii but similar-sized or larger convective centers compared to moist cyclones, consistent with existing structural theory. Strikingly, spontaneous cyclogenesis fails to occur at moderately low surface wetness values and intermediate surface temperatures of 250–270 K. Simulations with time-varying surface moisture and sea surface temperatures indicate this range of parameter space is a barrier to spontaneous genesis but not cyclone existence. Dry and semidry tropical cyclones in rotating RCE provide a compelling model system to further our understanding of real moist tropical cyclones.

Limits on the Extent of the Solsticial Hadley Cell: The Role of Planetary Rotation

Abstract The role of planetary rotation in limiting the extent of the cross-equatorial solsticial Hadley cell (SHC) is investigated using idealized simulations with an aquaplanet general circulation model run under perpetual-solstice conditions. Consistent with previous studies that include a seasonal cycle, the SHC extent increases with decreasing rotation rate, and it occupies the entire globe for sufficiently low planetary rotation rates. A simple theory for the summer-hemisphere extent of the SHC is constructed in which it is assumed that the SHC occupies regions for which a hypothetical radiative–convective equilibrium state is physically unattainable. The theory predicts that the SHC extends farther into the summer hemisphere as the rotation rate is decreased, qualitatively reproducing the behavior of the simulations, but it generally underestimates the simulated SHC extent. A diagnostic theory for the summer-hemisphere SHC extent is then developed based on the assumptions of slantwise convective neutrality and conservation of angular momentum within the Hadley cell. The theory relates the structure of the SHC in the summer hemisphere to the distribution of boundary layer entropy in the dynamically equilibrated simulations. The resultant diagnostic for the SHC extent generalizes the convective quasi-equilibrium-based constraint of Privé and Plumb, in which the position of rain belts is related to maxima in the low-level entropy distribution.

Convection and Climate: What Have We Learned from Simple Models and Simplified Settings?

We ask what fundamental insights about the relationship of tropical convection to climate have arisen from recent investigations using simplified models. The vertical distribution of relative humidity should remain approximately constant in a changed climate. The temperature of clouds in the upper troposphere should also remain effectively constant for climate changes likely to occur in response to human-induced warming. The fractional coverage of convective clouds will likely decrease slightly with warming, but it is not known how the albedo and net radiative effect of tropical convective clouds will change. The areal extent and net radiative effect of tropical convective clouds depend on the interactions of radiation, cloud physics, and turbulence within the extended upper-level ice clouds. SST gradients develop naturally as a result of the aggregation of convection and large-scale thermodynamics and circulation act to couple the cloud properties and the SST. Radiative-convective equilibrium continues to provide insight into the structure and energy balance of the atmosphere by incorporating the interactions among radiation, cloud physics, and atmospheric motion.