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Representation of cloud microphysics is a key aspect of simulating clouds. From the early days of cloud modeling, numerical models have relied on an Eulerian approach for all cloud and thermodynamic and microphysics variables. Over time the sophistication of microphysics schemes has steadily increased, from simple representations of bulk masses of cloud and rain in each grid cell, to including different ice particle types and bulk hydrometeor concentrations, to complex schemes referred to as bin or spectral schemes that explicitly evolve the hydrometeor size distributions within each model grid cell. As computational resources grow, there is a clear trend toward wider use of bin schemes, including their use as benchmarks to develop and test simplified bulk schemes. We argue that continuing on this path brings fundamental challenges difficult to overcome. The Lagrangian particle-based probabilistic approach is a practical alternative in which the myriad of cloud and precipitation particles present in a natural cloud is represented by a judiciously selected ensemble of point particles called superdroplets or superparticles. The advantages of the Lagrangian particle-based approach when compared to the Eulerian bin methodology are explained, and the prospects of applying the method to more comprehensive cloud simulations—for instance, targeting deep convection or frontal cloud systems—are discussed.

Stochasticity of the collisional growth of cloud droplets is studied using the super-droplet method (SDM) of Shima et al.(2009). Statistics are calculated from ensembles of simulations of collision–coalescence in a single well-mixed cell. The SDM is compared with direct numerical simulations and the master equation. It is argued that SDM simulations in which one computational droplet represents one real droplet are at the same level of precision as the master equation. Such simulations are used to study fluctuations in the autoconversion time, the sol–gel transition and the growth rate of lucky droplets, which is compared with a theoretical prediction. The size of the coalescence cell is found to strongly affect system behavior. In small cells, correlations in droplet sizes and droplet depletion slow down rain formation. In large cells, collisions between raindrops are more frequent and this can also slow down rain formation. The increase in the rate of collision between raindrops may be an artifact caused by assuming an overly large well-mixed volume. The highest ratio of rain water to cloud water is found in cells of intermediate sizes. Next, we use these precise simulations to determine the validity of more approximate methods: the Smoluchowski equation and the SDM with multiplicities greater than 1. In the latter, we determine how many computational droplets are necessary to correctly model the expected number and the standard deviation of the autoconversion time. The maximal size of a volume that is turbulently well mixed with respect to coalescence is estimated at Vmix  =  1.5  ×  10−2 cm3. The Smoluchowski equation is not valid in such small volumes. It is argued that larger volumes can be considered approximately well mixed, but such approximation needs to be supported by a comparison with fine-grid simulations that resolve droplet motion.

A numerical cloud model with Lagrangian particles coupled to an Eulerian flow is adapted for distributed memory systems. Eulerian and Lagrangian calculations can be done in parallel on CPUs and GPUs, respectively. The fraction of time when CPUs and GPUs work simultaneously is maximized at around 80 % for an optimal ratio of CPU and GPU workloads. The optimal ratio of workloads is different for different systems because it depends on the relation between computing performance of CPUs and GPUs. GPU workload can be adjusted by changing the number of Lagrangian particles, which is limited by device memory. Lagrangian computations scale with the number of nodes better than Eulerian computations because the former do not require collective communications. This means that the ratio of CPU and GPU computation times also depends on the number of nodes. Therefore, for a fixed number of Lagrangian particles, there is an optimal number of nodes, for which the time CPUs and GPUs work simultaneously is maximized. Scaling efficiency up to this optimal number of nodes is close to 100 %. Simulations that use both CPUs and GPUs take between 10 and 120 times less time and use between 10 to 60 times less energy than simulations run on CPUs only. Simulations with Lagrangian microphysics take up to 8 times longer to finish than simulations with Eulerian bulk microphysics, but the difference decreases as more nodes are used. The presented method of adaptation for computing clusters can be used in any numerical model with Lagrangian particles coupled to an Eulerian fluid flow.

The impact of giant sea salt aerosols released from breaking waves on rain formation in marine boundary layer clouds is studied using large-eddy simulations (LES). We perform simulations of marine cumuli and stratocumuli for various concentrations of cloud condensation nuclei (CCN) and giant CCN (GCCN). Cloud microphysics are modeled with a Lagrangian method that provides key improvements in comparison to previous LES of GCCN that used Eulerian bin microphysics. We find that GCCN significantly increase precipitation in stratocumuli. This effect is strongest for low and moderate CCN concentrations. GCCN are found to have a smaller impact on precipitation formation in cumuli. These conclusions are in agreement with field measurements. We develop a simple parameterization of the effect of GCCN on precipitation, accretion, and autoconversion rates in marine stratocumuli.

Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing (AON) superdroplet method (SDM) and a deterministic version of SDM (dSDM) that applies a fractional approach similar to the average impact method. In LES, variabilities driven by microphysics and by flow realizations are separated using the “piggybacking” technique. Rain initiation averaged over many realizations of the box model is delayed, and rain variability increases as the number of superdrops per collision volume N SD is decreased using SDM. In contrast, rain initiation time using SDM in LES is insensitive to N SD for 32 ≤ N SD ≤ 512. This is explained through the interaction between LES grid boxes, each acting as a separate collision volume. Variability across the ensemble of LES collision volumes using SDM results in rain quickly initiating in some of the LES grid cells at low N SD and leading to a similar overall timing of rain initiation from the cloud compared to simulations with high N SD . There is a ∼20% decrease in the total rain mass and mean rain flux as N SD is increased from 32 to 256, with little additional change as N SD is increased from 256 to 512. The fractional coalescence approach in dSDM leads to reduced microphysical variability and a 15–18-min delay in rain initiation compared to SDM. An additional LES ensemble with microphysical variability feeding back to the dynamics shows that flow variability dominates the impact of microphysical variability on rain properties. Thus, flow variability must be constrained to isolate impacts of microphysical variability.

The Kinematic Driver-Aerosol (KiD-A) intercomparison was established to test the hypothesis that detailed warm microphysical schemes provide a benchmark for lower-complexity bulk microphysics schemes. KiD-A is the first intercomparison to compare multiple Lagrangian cloud models (LCMs), size bin-resolved schemes, and double-moment bulk microphysics schemes in a consistent 1D dynamic framework and box cases. In the absence of sedimentation and collision–coalescence, the drop size distributions (DSDs) from the LCMs exhibit similar evolution with expected physical behaviors and good interscheme agreement, with the volume mean diameter ( D vol ) from the LCMs within 1%–5% of each other. In contrast, the bin schemes exhibit nonphysical broadening with condensational growth. These results further strengthen the case that LCMs are an appropriate numerical benchmark for DSD evolution under condensational growth. When precipitation processes are included, however, the simulated liquid water path, precipitation rates, and response to modified cloud drop/aerosol number concentrations from the LCMs vary substantially, while the bin and bulk schemes are relatively more consistent with each other. The lack of consistency in the LCM results stems from both the collision–coalescence process and the sedimentation process, limiting their application as a numerical benchmark for precipitation processes. Reassuringly, however, precipitation from bulk schemes, which are the basis for cloud microphysics in weather and climate prediction, is within the spread of precipitation from the detailed schemes (LCMs and bin). Overall, this intercomparison identifies the need for focused effort on the comparison of collision–coalescence methods and sedimentation in detailed microphysics schemes, especially LCMs.

The representation of subtropical stratocumulus and trade‐wind cumulus clouds by preliminary versions of Integrated Forecasting System (IFS) and ICON km‐scale global coupled climate models is explored. These models differ profoundly in their strategy to represent subgrid‐scale processes. The IFS employs complex parameterizations, including eddy‐diffusivity mass‐flux and convection schemes. ICON applies a minimal set of paramaterizations, including the Smagorinsky‐Lilly closure. Five‐year simulations are performed and evaluated for their representation of cloud albedo, its variability with environmental parameters and the vertical structure of the atmospheric boundary layer in eight regions: four corresponding to canonical Atlantic and Pacific stratocumulus and four in their downstream trades. For stratocumulus, both models capture the albedo's mean, annual cycle, and its relationship with the parameters relevant for low cloudiness, including lower tropospheric stability. They simulate an expected thermodynamic vertical structure of a stratocumulus‐topped boundary layer. ICON largely exhibits a lower cloud base and inversion height than IFS. We speculate the disagreement can be attributed to the contrasting treatment of subgrid mixing and cloud top entrainment. In the case of trade‐wind cumulus, both models well differentiate the cloud amount, the character of annual cycles and parameter correlations, and the vertical structure from the upstream stratocumulus. The annual cycles and parameter correlations reflect the dry and wet periods. Both models overestimate mean albedo and underestimate the strength of trade‐wind inversion. With an additional ICON run, we demonstrate the strong sensitivity of stratocumulus and the weaker response of trade‐wind cumulus to the treatment of subgrid mixing. Plain Language Summary Low‐level clouds over tropical oceans play an important role in regulating climate and shaping its response to changes because they reflect much of the incoming solar radiation. We explore how the two types of such clouds ‐ stratocumulus and trade‐wind cumulus ‐ are simulated by the two novel global climate models: Integrated Forecasting System (IFS) and ICON. The models cover the Earth with the grid cells of about 5 km. They differ in handling the processes occurring at the scales smaller than the grid cell. The IFS employs sophisticated routines while ICON adopts a much simpler approach with limited options for adjustments. Our analysis focused on eight regions over the Atlantic and Pacific: four corresponding to frequent stratocumulus cover and four dominated by trade‐wind cumulus. Both models simulate average stratocumulus amount and the changes of its properties throughout the year in agreement with satellite observations. Their skill is comparable despite differing modeling strategy. In the case of trade‐wind cumulus, both models overestimate the cloud amount, yet cumuli structures appear in the expected regions and follow the changes characteristic of dry and wet seasons. Additionally, we demonstrate that simulated stratocumulus amount depends sensitively on the strength of the mixing between the cloud and the warm dry air above. Key Points Early versions of IFS and ICON km‐scale global climate models satisfactorily simulate albedo and vertical structure for subtropical clouds Despite distinct approaches to sub‐grid parameterizations, the models achieve comparable skills in the stratocumulus regions Stratocumulus exhibits strong sensitivity to the treatment of cloud top mixing by sub‐grid turbulence scheme

This study presents the first model intercomparison of aerosol‐cloud‐turbulence interactions in a controlled cloudy Rayleigh‐Bénard Convection chamber environment, utilizing the Pi Chamber at Michigan Technological University. We analyzed simulated cloud chamber‐averaged statistics of microphysics and thermodynamics in a warm‐phase, cloudy environment under steady‐state conditions at varying aerosol injection rates. Simulation results from seven distinct models (DNS, LES, and a 1D turbulence model) were compared. Our findings demonstrate that while all models qualitatively capture observed trends in droplet number concentration, mean radius, and droplet size distributions at both high and low aerosol injection rates, significant quantitative differences were observed. Notably, droplet number concentrations varied by over two orders of magnitude between models for the same injection rates, indicating sensitivities to the model treatments in droplet activation and removal and wall fluxes. Furthermore, inconsistencies in vertical relative humidity profiles and in achieving steady‐state liquid water content suggest the need for further investigation into the mechanisms driving these variations. Despite these discrepancies, the models generally reproduced consistent power‐law relationships between the microphysical variables. This model intercomparison underscores the importance of controlled cloud chamber experiments for validating and improving cloud microphysical parameterizations. Recommendations for future modeling studies are also highlighted, including constraining wall conditions and processes, investigating droplet/aerosol removal (including sidewall losses), and conducting simplified experiments to isolate specific processes contributing to model divergence and reduce model uncertainties. Plain Language Summary Understanding how tiny particles (aerosols) interact with clouds and turbulence is essential for improving weather forecasts and climate predictions, as these interactions play a crucial role in determining the properties and evolution of clouds. In this study, we compared different numerical cloud models that simulate these interactions within a controlled laboratory environment, the Pi Chamber at Michigan Technological University. We examined how these models simulated the formation and growth of cloud droplets when aerosols were injected at different rates into the chamber. Our findings show that while all models generally captured the expected trends in cloud droplet size and number concentrations, there were significant quantitative differences. These differences suggest that model results are sensitive to the different model treatments on how droplets are formed and removed, as well as how fluxes from the chamber walls are represented. Despite these differences, the models generally agreed on the overall relationships between aerosol amounts and cloud properties, matching laboratory observations. This study highlights the value of using cloud chamber experiments to test and improve these models. We suggest that to reduce model uncertainties, future research should focus on better defining the conditions at the chamber walls and investigating how particles are removed from the chamber. Key Points This study presents the first model intercomparison to study aerosol‐cloud‐turbulence interactions in a convection‐cloud chamber All models capture the observed microphysical response to varying aerosol injection rates, but large inter‐model discrepancies are present The study underscores the importance of laboratory experiments for validating and improving microphysical representation in cloud models

Numerical convergence of the collision–coalescence algorithm used in Lagrangian particle-based microphysics is studied in 2D simulations of an isolated cumulus congestus (CC) and in box and multi-box simulations of collision–coalescence. Parameters studied are the time step for coalescence and the number of super-droplets (SDs) per cell. A time step of 0.1 s gives converged droplet size distribution (DSD) in box simulations and converged mean precipitation in CC. Variances of the DSD and of precipitation are not sensitive to the time step. In box simulations, mean DSD converges for 103 SDs per cell, but variance of the DSD does not converge as it decreases with an increasing number of SDs. Fewer SDs per cell are required for convergence of the mean DSD in multi-box simulations, probably thanks to mixing of SDs between cells. In CC simulations, more SDs are needed for convergence than in box or multi-box simulations. Mean precipitation converges for 5×103 SDs, but only in a strongly precipitating cloud. In cases with little precipitation, mean precipitation does not converge even for 105 SDs per cell. Variance in precipitation between independent CC runs is more sensitive to the resolved flow field than to the stochasticity in collision–coalescence of SDs, even when using as few as 50 SDs per cell.

A new anelastic large-eddy simulation (LES) model with an Eulerian dynamical core and Lagrangian particle-based microphysics is presented. The dynamical core uses the multidimensional positive-definite advection transport algorithm (MPDATA) advection scheme and the generalized conjugate residual pressure solver, whereas the microphysics scheme is based on the super-droplet method. Algorithms for coupling of Lagrangian microphysics with Eulerian dynamics are presented, including spatial and temporal discretizations and a condensation substepping algorithm. The model is free of numerical diffusion in the droplet size spectrum. Activation of droplets is modeled explicitly, making the model less sensitive to local supersaturation maxima than models in which activation is parameterized. Simulations of a drizzling marine stratocumulus give results in agreement with other LES models. It is shown that in the super-droplet method a relatively low number of computational particles is sufficient to obtain correct averaged properties of a cloud, but condensation and collision–coalescence have to be modeled with a time step of the order of 0.1 s. Such short time steps are achieved by substepping, as the model time step is typically around 1 s. Simulations with and without an explicit subgrid-scale turbulence model are compared. Effects of modeling subgrid-scale motion of super-droplets are investigated. The model achieves high computational performance by using graphics processing unit (GPU) accelerators.