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In the atmosphere, microphysics refers to the microscale processes that affect cloud and precipitation particles and is a key linkage among the various components of Earth's atmospheric water and energy cycles. The representation of microphysical processes in models continues to pose a major challenge leading to uncertainty in numerical weather forecasts and climate simulations. In this paper, the problem of treating microphysics in models is divided into two parts: (i) how to represent the population of cloud and precipitation particles, given the impossibility of simulating all particles individually within a cloud, and (ii) uncertainties in the microphysical process rates owing to fundamental gaps in knowledge of cloud physics. The recently developed Lagrangian particle‐based method is advocated as a way to address several conceptual and practical challenges of representing particle populations using traditional bulk and bin microphysics parameterization schemes. For addressing critical gaps in cloud physics knowledge, sustained investment for observational advances from laboratory experiments, new probe development, and next‐generation instruments in space is needed. Greater emphasis on laboratory work, which has apparently declined over the past several decades relative to other areas of cloud physics research, is argued to be an essential ingredient for improving process‐level understanding. More systematic use of natural cloud and precipitation observations to constrain microphysics schemes is also advocated. Because it is generally difficult to quantify individual microphysical process rates from these observations directly, this presents an inverse problem that can be viewed from the standpoint of Bayesian statistics. Following this idea, a probabilistic framework is proposed that combines elements from statistical and physical modeling. Besides providing rigorous constraint of schemes, there is an added benefit of quantifying uncertainty systematically. Finally, a broader hierarchical approach is proposed to accelerate improvements in microphysics schemes, leveraging the advances described in this paper related to process modeling (using Lagrangian particle‐based schemes), laboratory experimentation, cloud and precipitation observations, and statistical methods. Plain Language Summary In the atmosphere, microphysics—the small‐scale processes affecting cloud and precipitation particles such as their growth by condensation, evaporation, and melting—is a critical part of Earth's weather and climate. Because it is impossible to simulate every cloud particle individually owing to their sheer number within even a small cloud, atmospheric models have to represent the evolution of particle populations statistically. There are critical gaps in knowledge of the microphysical processes that act on particles, especially for atmospheric ice particles because of their wide variety and intricacy of their shapes. The difficulty of representing cloud and precipitation particle populations and knowledge gaps in cloud processes both introduce important uncertainties into models that translate into uncertainty in weather forecasts and climate simulations, including climate change assessments. We discuss several specific challenges related to these problems. To improve how cloud and precipitation particle populations are represented, we advocate a “particle‐based” approach that addresses several limitations of traditional approaches and has recently gained traction as a tool for cloud modeling. Advances in observations, including laboratory studies, are argued to be essential for addressing gaps in knowledge of microphysical processes. We also advocate using statistical modeling tools to improve how these observations are used to constrain model microphysics. Finally, we discuss a hierarchical approach that combines the various pieces discussed in this article, providing a possible blueprint for accelerating progress in how microphysics is represented in cloud, weather, and climate models. Key Points Microphysics is an important component of weather and climate models, but its representation in current models is highly uncertain Two critical challenges are identified: representing cloud and precipitation particle populations and knowledge gaps in cloud physics A possible blueprint for addressing these challenges is proposed to accelerate progress in improving microphysics schemes

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.

The sensitivity of simulated nonprecipitating cumulus clouds to grid length was investigated using a large‐eddy simulation model coupled to a particle‐based Lagrangian cloud microphysical model (LCM) and an Eulerian cloud microphysical model (ECM). For the sensitivity experiment, the horizontal/vertical grid length was decreased from 100/80 m to 6.25/5 m. The results of the sensitivity experiment indicated a similar dependency of cloud cover (CC) on the grid length in the LCM and ECM, which is critical for the radiative properties of clouds. CC increased with a shorter grid length, and numerically converged with a horizontal/vertical grid length of 12.5/10 m, although the three‐dimensional cloud field and turbulence properties in the cloud layer did not numerically converge and the cloud fields simulated by the LCM and ECM differed. The dependency of CC on grid length originated from the dependency of the turbulence structure in the subcloud layer. Roll convection was clearly simulated in the subcloud layer using a short grid length, but it was gradually obscured with increasing grid length. With a long grid length, the shear production term of turbulent kinetic energy near the surface, which is critical for dominating roll convection, was not simulated because of insufficient vertical layers near the surface. On the other hand, with a short grid length, the number of layers close to the surface was sufficient to reproduce the shear production term, and roll convection was clearly reproduced. Key Points A grid refinement study was conducted using Lagrangian and Eulerian microphysical models coupled with the same dynamical core Numerical convergence of shallow cloud cover was achieved using a grid length of 12.5 m in both the Lagrangian and Eulerian models The roll convection was clear with a smaller grid length, and the strong upward velocity below cloud led to numerical convergence

Cloud microphysical processes occur at the smallest end of scales among cloud-related processes and thus must be parameterized not only in large-scale global circulation models (GCMs) but also in various higher-resolution limited-area models such as cloud-resolving models (CRMs) and large-eddy simulation (LES) models. Instead of giving a comprehensive review of existing microphysical parameterizations that have been developed over the years, this study concentrates purposely on several topics that we believe are understudied but hold great potential for further advancing bulk microphysics parameterizations: multi-moment bulk microphysics parameterizations and the role of the spectral shape of hydrometeor size distributions; discrete vs “continuous” representation of hydrometeor types; turbulence-microphysics interactions including turbulent entrainment-mixing processes and stochastic condensation; theoretical foundations for the mathematical expressions used to describe hydrometeor size distributions and hydrometeor morphology; and approaches for developing bulk microphysics parameterizations. Also presented are the spectral bin scheme and particle-based scheme (especially, super-droplet method) for representing explicit microphysics. Their advantages and disadvantages are elucidated for constructing cloud models with detailed microphysics that are essential to developing processes understanding and bulk microphysics parameterizations. Particle-resolved direct numerical simulation (DNS) models are described as an emerging technique to investigate turbulence-microphysics interactions at the most fundamental level by tracking individual particles and resolving the smallest turbulent eddies in turbulent clouds. Outstanding challenges and future research directions are explored as well.

The super-droplet method (SDM) is a particle-based numerical scheme that enables accurate cloud microphysics simulation with lower computational demand than multi-dimensional bin schemes. Using SDM, a detailed numerical model of mixed-phase clouds is developed in which ice morphologies are explicitly predicted without assuming ice categories or mass–dimension relationships. Ice particles are approximated using porous spheroids. The elementary cloud microphysics processes considered are advection and sedimentation; immersion/condensation and homogeneous freezing; melting; condensation and evaporation including cloud condensation nuclei activation and deactivation; deposition and sublimation; and coalescence, riming, and aggregation. To evaluate the model's performance, a 2-D large-eddy simulation of a cumulonimbus was conducted, and the life cycle of a cumulonimbus typically observed in nature was successfully reproduced. The mass–dimension and velocity–dimension relationships the model predicted show a reasonable agreement with existing formulas. Numerical convergence is achieved at a super-particle number concentration as low as 128 per cell, which consumes 30 times more computational time than a two-moment bulk model. Although the model still has room for improvement, these results strongly support the efficacy of the particle-based modeling methodology to simulate mixed-phase clouds.

A series of simulations employing the superdroplet method (SDM) for representing aerosol, cloud, and rain microphysics in large-eddy simulations (LES) is discussed. The particle-based formulation treats all particles in the same way, subjecting them to condensational growth and evaporation, transport of the particles by the flow, gravitational settling, and collisional growth. SDM features a Monte Carlo–type numerical scheme for representing the collision and coalescence process. All processes combined cover representation of cloud condensation nuclei (CCN) activation, drizzle formation by autoconversion, accretion of cloud droplets, self-collection of raindrops, and precipitation, including aerosol wet deposition. The model setup used in the study is based on observations from the Rain in Cumulus over the Ocean (RICO) field project. Cloud and rain droplet size spectra obtained in the simulations are discussed in context of previously published analyses of aircraft observations carried out during RICO. The analysis covers height-resolved statistics of simulated cloud microphysical parameters such as droplet number concentration, effective radius, and parameters describing the width of the cloud droplet size spectrum. A reasonable agreement with measurements is found for several of the discussed parameters. The sensitivity of the results to the grid resolution of the LES, as well as to the sampling density of the probabilistic Monte Carlo–type model, is explored.

The phenomenon of electric fields applied to droplets, inducing droplet coalescence, is called the electro-coalescence effect. An analytic expression for electro-coalescence with the accurate electrostatic force for a pair of droplets with opposite-sign charges is established by treating the droplets as conducting spheres (CSs). To investigate this effect, we applied a weak electric field to a cumulus cloud using a cloud model that employs the super-droplet method, a probabilistic particle-based microphysics method. This study employs a two-dimensional (2D) large-eddy simulation (LES) in a flow-coupled model to examine aerosol microphysics (such as collision–coalescence enhancement, velocity fluctuations, and supersaturation fluctuations) in warm cumulus clouds without relying on subgrid dynamics. In the simulation, we assume that droplets carry opposite-sign charges and are well mixed within the cloud. The charge is not treated as an individual particle attribute. To assess fluctuation effects, we conducted 50 simulations with varying pseudo-random number sequences for each electro-coalescence treatment. The results show that, with CS treatment, the electrostatic force contributes a larger effect on cloud evolution than in previous research. With a lower charge limit of the maximum charge amount on the droplet, the domain total precipitation with CS treatment for droplets with opposite signs is higher than that with the no-charge (NC) setting. Compared to previous work, the multi-image dipole treatment of CS results in higher precipitation. It is found that the electro-coalescence effect could affect rain formation even when the droplet charge is at the lower charge limit. High pollution levels result in greater sensitivity to electro-coalescence. The results show that, when the charge ratio between two droplets is over 100, the short-range attractive electric force due to the multi-image dipole would also significantly enhance precipitation for the cumulus. It is indicated that, although the accurate treatment of the electrostatic force with the CS method would require 30 % longer computation time than before, it is worthwhile to include it in cloud, weather, and climate models.

A particle-based cloud model was developed for meter- to submeter-scale-resolution simulations of warm clouds. Simplified cloud microphysics schemes have already made meter-scale-resolution simulations feasible; however, such schemes are based on empirical assumptions, and hence they contain huge uncertainties. The super-droplet method (SDM) is a promising candidate for cloud microphysical process modeling and is a particle-based approach, making fewer assumptions for the droplet size distributions. However, meter-scale-resolution simulations using the SDM are not feasible even on existing high-end supercomputers because of high computational cost. In the present study, we overcame challenges to realize such simulations. The contributions of our work are as follows: (1) the uniform sampling method is not suitable when dealing with a large number of super-droplets (SDs). Hence, we developed a new initialization method for sampling SDs from a real droplet population. These SDs can be used for simulating spatial resolutions between meter and submeter scales. (2) We optimized the SDM algorithm to achieve high performance by reducing data movement and simplifying loop bodies using the concept of effective resolution. The optimized algorithms can be applied to a Fujitsu A64FX processor, and most of them are also effective on other many-core CPUs and possibly graphics processing units (GPUs). Warm-bubble experiments revealed that the throughput of particle calculations per second for the improved algorithms is 61.3 times faster than those for the original SDM. In the case of shallow cumulous, the simulation time when using the new SDM with 32–64 SDs per cell is shorter than that of a bin method with 32 bins and comparable to that of a two-moment bulk method. (3) Using the supercomputer Fugaku, we demonstrated that a numerical experiment with 2 m resolution and 128 SDs per cell covering 138242×3072 m3 domain is possible. The number of grid points and SDs are 104 and 442 times, respectively, those of the highest-resolution simulation performed so far. Our numerical model exhibited 98 % weak scaling for 36 864 nodes, accounting for 23 % of the total system. The simulation achieves 7.97 PFLOPS, 7.04 % of the peak ratio for overall performance, and a simulation time for SDM of 2.86×1013 particle ⋅ steps per second. Several challenges, such as incorporating mixed-phase processes, inclusion of terrain, and long-time integrations, remain, and our study will also contribute to solving them. The developed model enables us to study turbulence and microphysics processes over a wide range of scales using combinations of direct numerical simulation (DNS), laboratory experiments, and field studies. We believe that our approach advances the scientific understanding of clouds and contributes to reducing the uncertainties of weather simulation and climate projection.

The super-droplet method (SDM) is a Lagrangian particle-based numerical scheme for cloud microphysics. In this work, a series of simulations based on the DYCOMS-II (RF02) setup with different horizontal and vertical resolutions are conducted to explore the grid convergence of the SDM simulations of marine stratocumulus. The results are compared with the double-moment bulk scheme (SN14) and model intercomparison project (MIP) results. In general, all SDM and SN14 variables show a good agreement with the MIP results and have similar grid size dependencies. The stratocumulus simulation is more sensitive to the vertical resolution than to the horizontal resolution. The vertical grid length DZ ≪ 2.5 m is necessary for both SDM and SN14. The horizontal grid length DX < 12.5 m is necessary for the SDM simulations. DX ≤ 25 m is sufficient for SN14. We also assess the numerical convergence with respect to the super-droplet numbers. The simulations are well converged when the super-droplet number concentration (SDNC) is larger than 16 super-droplets per cell. Our results indicate that the super-droplet number per grid cell is more critical than that per unit volume at least for the stratocumulus case investigated here. Our comprehensive analysis not only offers guidance on numerical settings essential for accurate stratocumulus cloud simulation but also underscores significant differences in liquid water content and cloud macrostructure between SDM and SN14. These differences are attributed to the inherent modeling strategies of the two schemes. SDM's dynamic representation of aerosol size distribution through wet deposition markedly contrasts with SN14's static approach, influencing cloud structure and behavior over a 6 h simulation. Findings reveal sedimentation's crucial role in altering aerosol distributions near cloud tops, affecting the vertical profile of cloud fraction (CF). Additionally, the study briefly addresses numerical diffusion's potential effects, suggesting further investigation is needed. The results underscore the importance of accurate aerosol modeling and its interactions with cloud processes in marine stratocumulus simulations, pointing to future research directions for enhancing stratocumulus modeling accuracy and predictive capabilities.

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