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Whereas it is now widely accepted that cumulus cloud sizes are power‐law distributed, characteristic exponents reported in the literature vary greatly, generally taking values between 1 and >3. Although these differences might be explained by variations in environmental conditions or physical processes organizing the cloud ensembles, the use of improper fitting methods may also introduce large biases. To address this issue, we propose to use a combination of maximum likelihood estimation and goodness‐of‐fit tests to provide more robust power‐law fits while systematically identifying the size range over which these fits are valid. The procedure is applied to cloud size distributions extracted from two idealized high‐resolution simulations displaying different organization characteristics. Overall, power‐laws are found to be outperformed by alternative distributions in almost all situations. When clouds are identified based on a condensed water path threshold, using power‐laws with an exponential cutoff yields the best results as it provides superior fits in the tail of the cloud size distributions. For clouds identified using a combination of water content and updraft velocity thresholds in the free troposphere, no substantial improvement over pure power‐laws can be found when considering more complex two‐parameter distributions. In this context however, exponential distributions provide results that are as good as, if not better than power‐laws. Finally, it is demonstrated that the emergence of scale free behaviors in cloud size distributions is related to exponentially distributed cloud cores merging as they are brought closer to each other by underlying organizing mechanisms. Plain Language Summary Clouds constitute an important element of the climate system reflecting incoming solar radiation and emitting infra‐red radiation that heats the atmosphere. The net radiative impact of clouds however depends on many factors including their size. It is thus of prime importance to characterize the size of clouds, in particular convective clouds, and understand the underlying processes controlling them. In this study, a numerical model is used to simulate two convective situations at horizontal resolutions providing a fine description of cloud processes. After identifying individual clouds and calculating their size, statistical methods are employed to characterize the cloud size distributions. Depending on the situation, cloud size distributions are found to be best represented by either power‐laws with an exponential cutoff or exponential functions. Pure power‐laws, which constitute the most popular model used to represent cloud size distributions, are generally found to yield poorer fits. Finally, it is demonstrated that power‐laws in cloud size distributions emerge when individual cloud cores, that are exponentially distributed in size, are brought closer to each other and merge as the cloud ensemble organizes. Key Points A combination of statistical methods is used to fit cloud size distributions from two simulated convective cloud ensembles Depending on the situation, exponential distributions and power‐laws with an exponential cutoff may constitute superior alternatives to pure power‐laws The merging of individual cloud cores is found to control the emergence of power‐law cloud size distributions

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical consistency, and smooth integration into ESMs. Here, a two-step method is presented to improve a climate model with data-driven parameterizations. First, we incorporate a physically consistent cloud cover parameterization—derived from storm-resolving simulations via symbolic regression, preserving interpretability while enhancing accuracy—into the ICON global atmospheric model. Second, we apply the gradient-free Nelder–Mead optimizer to automatically recalibrate the hybrid model against Earth observations, tuning in nested stages (2-, 7-, 30- and 365-day runs) to ensure stability and tractability. The tuned hybrid model substantially reduces long-standing biases in cloud cover—particularly over the Southern Ocean (by 75%) and subtropical stratocumulus regions (by 44%)—and remains robust under +4K surface warming. These results demonstrate that interpretable machine-learned parameterizations, paired with practical tuning, can efficiently and transparently strengthen ESM fidelity.

The lack of consensus as to how entrainment and detrainment must be represented in convection parameterizations highlights the need for in-depth investigations of the processes driving lateral mixing in clouds. Direct estimates of entrainment and detrainment rates are here obtained from high-resolution simulations of shallow cumulus convection using a method that isolates the contributions from various competing processes. Moreover, cloud-averaged entrainment and detrainment rates are computed and correlated with bulk cloud and environmental properties. Detrainment is found to dominate in the middle of the cloud layer, and is locally driven by evaporation along cloud edges. Entrainment and detrainment events also occur due to changes in updraft velocity, but vertical acceleration and deceleration balance each other on average to yield no net entrainment/detrainment. In contrast, entrainment at cloud base is mostly related to condensation in dry updrafts surrounding the clouds, whereas detrainment at the top of the cloud layer is driven by buoyancy reversal. Cloud-averaged entrainment and detrainment rates both correlate preferentially with in-cloud vertical pressure gradients at all altitudes, but not with cloud-core buoyancy. No significant influence of environmental moisture on entrainment/detrainment was found, probably because of the very humid shell surrounding each cloud. Overall, these results suggest that entrainment and detrainment result from two concurring processes: a cloud-scale circulation driven by vertical pressure gradients, and small-scale, turbulent-like motions along the core edges generating mixing and, again, vertical pressure gradients.

Properly predicting the rapid transition from shallow to precipitating atmospheric convection within a diurnal cycle over land is of great importance for both weather prediction and climate projections. In this work, we consider that a cumulus cloud is formed due to the transport of water mass by multiple updrafts during its lifetime. Cumulus clouds then locally create favorable conditions for the subsequent convective updrafts to reach higher altitudes, leading to deeper precipitating convection. This mechanism is amplified by the cold pools formed by the evaporation of precipitation in the sub‐cloud layer. Based on this conceptual view of cloud–cloud interactions which goes beyond the one cloud equals one–plume picture, it is argued that precipitating clouds may act as predators that prey on the total cloud population, such that the rapid shallow–to–deep transition can be modeled as a simple predator–prey system. This conceptual model is validated by comparing solutions of the Lotka‐Volterra system of equations to results obtained using a high‐resolution large‐eddy simulation model. Moreover, we argue that the complete diurnal cycle of deep convection can be seen as a predator–prey system with varying food supply for the prey. Finally, we suggest that based on the present conceptual model, new unified cloud‐convection parameterizations can be designed which may lead to improved representations of the transition from shallow to precipitating continental convection. Plain Language Summary The rapid transition from shallow to precipitating convection over land is still poorly represented by weather and climate models. In this work, we argue that this is due to the fact that the convective parameterization schemes only consider the interaction between the clouds and their environment, which is a slow process, and do not consider cloud–cloud interactions during the transition, which is a fast process. We show that this latter interaction can be modeled as a predator–prey process, and we show how a very simple dynamical model for cloud population can lead to improved prediction for the precipitation rate and cloud cover over land. Key Points A conceptual picture for cumulus cloud populations based on cloud–updraft interaction is discussed The local shallow preconditioning and the cold pool feedback imply a predator–prey type of interaction in the cloud–precipitation system A simple predator–prey model shows good agreement with idealized numerical simulations for the rapid shallow–to–deep transition

This article details corrections to: Schwarz, M, Savre, J, Sudhakar, D, Quaas, J and Ekman, AML. 2024. The Transition from Aerosol- to Updraft-Limited Susceptibility Regime in Large-Eddy Simulations with Bulk Microphysics. Tellus B: Chemical and Physical Meteorology, 76(1): 32–46. DOI: https://doi.org/10.16993/tellusb.94

Large-eddy simulation (LES) is often used as a benchmark simulation in climate science and is suggested as a fundamental tool to examine, e.g., marine cloud brightening. Therefore, it is necessary to critically evaluate if these high-resolution models can skillfully simulate expected physical phenomena. This study focuses on the first indirect aerosol effect in warm stratocumulus clouds. We investigate if an LES code with explicit aerosol-cloud interactions and a widely used two-moment bulk microphysical scheme can reproduce well-known cloud droplet number susceptibility regimes previously identified by observations and supported by detailed parcel model simulations—the updraft-limited regime (typically occurring at high aerosol number concentrations and low updraft speeds) and the aerosol-limited regime (typically occurring at low aerosol number concentrations and high updraft speeds). Our simulations show that the LES in its default configuration cannot reproduce the two regimes if the initial droplet radius of newly activated droplets (rid) is estimated by integrating the wet aerosol size distribution. The main reason is related to the relatively coarse (but commonly used) time step in the model (Δt ≈ 1s), which is too long to resolve relevant microphysical processes adequately at high aerosol concentrations. A regime transition does occur if the timestep is decreased to Δt ≈ 0.1s and if a renormalization procedure is applied, which limits the number of activated droplets so that the water mass of the newly activated droplets cannot exceed the available amount of supersaturated water vapor. Another way to obtain a regime transition is to increase rid to values >1 µm. However, a clear recommendation for the choice of rid cannot be made upon physical arguments. An alternative solution could be to introduce a sub-time-stepping or adaptive time-stepping algorithm to calculate droplet formation and growth, particularly for updraft-limited conditions. Our study highlights the importance of critically evaluating LES results to guarantee that relevant physical processes are properly represented.

Persistent systematic errors in Earth system models (ESMs) arise from difficulties in representing the full diversity of subgrid, multiscale atmospheric convection and turbulence. Machine learning (ML) parameterizations trained on short high‐resolution simulations show strong potential to reduce these errors. However, stable long‐term atmospheric simulations with hybrid (physics + ML) ESMs remain difficult, as neural networks (NNs) trained offline often destabilize online runs. Training convection parameterizations directly on coarse‐grained data is challenging, notably because scales cannot be cleanly separated. This issue is mitigated using data from superparameterized simulations, which provide clearer scale separation. Yet, transferring a parameterization from one ESM to another remains difficult due to distribution shifts that induce large inference errors. Here, we present a proof‐of‐concept where a ClimSim‐trained, physics‐informed NN convection parameterization is successfully transferred to ICON‐A. The scheme is (a) trained on adjusted ClimSim data with subtracted radiative tendencies, and (b) integrated into ICON‐A. The NN parameterization predicts its own error, enabling mixing with a conventional convection scheme when confidence is low, thus making the hybrid AI‐physics model tunable with respect to observations and reanalysis through mixing parameters. This improves process understanding by constraining convective tendencies across column water vapor, lower‐tropospheric stability, and geographical conditions, yielding interpretable regime behavior. In Atmospheric Model Intercomparison Project‐style setups, several hybrid configurations outperform the default convection scheme (e.g., improved precipitation statistics). With additive input noise during training, both hybrid and pure‐ML schemes lead to stable simulations and remain physically consistent for at least 20 years, demonstrating inter‐ESM transferability and advancing long‐term integrability. Clouds and thunderstorms are difficult to simulate accurately in climate models because they typically occur at scales smaller than the model's grid. This necessitates the use of approximations for these processes, so‐called parameterizations, which often introduce errors. Machine learning (ML) offers a new way to improve these models, but ML can be unstable and doesn't always behave well when employed in different models or with different conditions. In this study, we develop a new hybrid method that combines machine learning with established physical principles to better simulate the influence of atmospheric convection. Our approach learns from high‐fidelity climate simulations and can adjust its behavior based on how confident the ML model is in its predictions. This helps the model stay stable and accurate, even when it is used in a different climate model. Furthermore, a small amount of noise is added during training to improve the long‐term stability of our ML model. We tested our method in the ICON climate model and found that it is accurate and stable in year‐long simulations, while remaining stable and reliable over periods of 20 years. This work shows that blending physics with machine learning can lead to more accurate and robust climate models. An machine learning convection parameterization trained on ClimSim and coupled to ICON achieves stable and accurate 20‐year Atmospheric Model Intercomparison Project simulations Physics‐informed loss, confidence‐guided mixing, and noise‐augmented training enhance conservation, accuracy, and stability, respectively The scheme can be tuned with observations by mixing in the conventional scheme when neural network confidence is low in moist, unstable regimes

This paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model–Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAM-Fluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as ). ATHAM-Fluidity operates on two- and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite–Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.

In this work, cloud ensemble statistics are extracted from idealized radiative–convective equilibrium simulations performed at horizontal grid spacings Δ ranging from 2 km to 125 m. At the coarsest resolution, convection remains randomly distributed in space such that the equilibrium statistical mechanics theory proposed by Craig and Cohen in 2006 (CC06; assumes Poisson distributed clouds and exponential mass flux distributions) remains valid. Using classical organization metrics, clustering is already observed at Δ = 1 km, but substantial deviations between the simulated cloud ensemble statistics and CC06 are only observed for grid spacings Δ < 500 m. At these resolutions, the cloud mass flux distributions exhibit heavy tails and cloud counts become overdispersed (higher variance than a Poisson distribution). These changes in ensemble statistics are accompanied by a shift in subcloud organization patterns as well as with the fact that individual cloudy updrafts start to be resolved. Consequently, a horizontal grid spacing no larger than 250 m is recommended, not only to properly resolve the dynamics of individual convective clouds, but also to capture the mesoscale organization of the cloud ensemble. Finally, it is shown that the CC06 theory and our high-resolution results including mesoscale organization may be reconciled if one considers 1) areas smaller than approximately 2 km in size, corresponding roughly to the narrow bands along which clouds develop almost randomly; and 2) individual cloud cores instead of cloud objects, core mass fluxes being shown to generally follow exponential distributions.

Large‐eddy simulations of mixed‐phase Arctic clouds by 11 different models are analyzed with the goal of improving understanding and model representation of processes controlling the evolution of these clouds. In a case based on observations from the Indirect and Semi‐Direct Aerosol Campaign (ISDAC), it is found that ice number concentration, Ni, exerts significant influence on the cloud structure. Increasing Ni leads to a substantial reduction in liquid water path (LWP), in agreement with earlier studies. In contrast to previous intercomparison studies, all models here use the same ice particle properties (i.e., mass‐size, mass‐fall speed, and mass‐capacitance relationships) and a common radiation parameterization. The constrained setup exposes the importance of ice particle size distributions (PSDs) in influencing cloud evolution. A clear separation in LWP and IWP predicted by models with bin and bulk microphysical treatments is documented and attributed primarily to the assumed shape of ice PSD used in bulk schemes. Compared to the bin schemes that explicitly predict the PSD, schemes assuming exponential ice PSD underestimate ice growth by vapor deposition and overestimate mass‐weighted fall speed leading to an underprediction of IWP by a factor of two in the considered case. Sensitivity tests indicate LWP and IWP are much closer to the bin model simulations when a modified shape factor which is similar to that predicted by bin model simulation is used in bulk scheme. These results demonstrate the importance of representation of ice PSD in determining the partitioning of liquid and ice and the longevity of mixed‐phase clouds. Key Points Constrained LES of mixed‐phase Arctic clouds from 11 models are analyzed Ice water path differences are attributed to assumed ice size distributions Bulk schemes with gamma size distributions agree better with bin schemes