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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.

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.

This paper discusses the effects of cloud turbulence, turbulent entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet size spectrum. We simulate an ensemble of idealized turbulent cloud parcels that are subject to entrainment events modeled as a random process. Entrainment events, subsequent turbulent mixing inside the parcel, supersaturation fluctuations, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. Quantities characterizing the turbulence intensity, entrainment rate, CCN concentration, and the mean fraction of environmental air entrained in an event are all specified as independent external parameters. Cloud microphysics is described by applying Lagrangian particles, the so-called superdroplets. These are either unactivated CCN or cloud droplets that grow from activated CCN. The model accounts for the addition of environmental CCN into the cloud by entraining eddies at the cloud edge. Turbulent mixing of the entrained dry air with cloudy air is described using the classical linear relaxation to the mean model. We show that turbulence plays an important role in aiding entrained CCN to activate, and thus broadening the droplet size distribution. These findings are consistent with previous large-eddy simulations (LESs) that consider the impact of variable droplet growth histories on the droplet size spectra in small cumuli. The scheme developed in this work is ready to be used as a stochastic subgrid-scale scheme in LESs of natural clouds.

Spectral width of the cloud droplet spectrum is important for radiative properties and drizzle/rain development in warm ice‐free clouds. We use an adiabatic rising parcel model to study activation and diffusional growth of cloud droplets, focusing on the spectral width evolution, and contrasting clean and polluted environments. A comprehensive droplet growth equation is used that includes kinetic, solute, and surface tension effects. We show that those effects have an appreciable impact on the spectral width evolution above the cloud base. Without those effects, the droplet area standard deviation should not change once activation is completed. In contrast, simulation results show that the area standard deviation does increase with height, especially for weak updrafts and polluted environments. Implications of those results for cloud modeling, especially applying conventional bin microphysics, are discussed. Plain Language Summary Shape of the droplet spectrum is an important parameter affecting cloud radiative properties as well as drizzle and rain development in warm ice‐free clouds. We consider formation and growth of cloud droplets in an air parcel rising across the subcloud layer, reaching the cloud base, and continuing its rise carrying cloud droplets growing by condensation of water vapor. We focus on the evolution of the spectrum shape. We show that the simplified droplet growth equation often applied in cloud simulations is not accurate enough to faithfully predict shape of the droplet spectrum aloft, especially in polluted weak‐updraft shallow clouds such as a continental stratocumulus. Key Points Evolutions of cloud droplet spectral width in an adiabatic parcel rising through cloud base differ between clean and polluted environments Smaller droplet sizes make the solute and surface tension effects more influential for spectral width evolutions in polluted clouds Conventional bin microphysics are not suitable for studying weak‐updraft shallow polluted clouds such as continental stratocumulus

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

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.

This paper introduces a new scheme available in the library of algorithms for representing cloud microphysics in numerical models named libcloudph++. The scheme extends the particle-based microphysics scheme with a Monte Carlo coalescence available in libcloudph++ to the aqueous-phase chemical processes occurring within cloud droplets. The representation of chemical processes focuses on the aqueous-phase oxidation of the dissolved SO2 by O3 and H2O2. The particle-based microphysics and chemistry scheme allows for tracking of the changes in the cloud condensation nuclei (CCN) distribution caused by both collisions between cloud droplets and aqueous-phase oxidation.The scheme is implemented in C++ and equipped with bindings to Python. The scheme can be used on either a CPU or a GPU, and is distributed under the GPLv3 license. Here, the particle-based microphysics and chemistry scheme is tested in a simple 0-dimensional adiabatic parcel model and then used in a 2-dimensional prescribed flow framework. The results are discussed with a focus on changes to the CCN sizes and comparison with other model simulations discussed in the literature.

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.

This paper presents an approach to locally predict homogeneity of the subgrid-scale turbulent mixing in large-eddy simulation of shallow clouds applying double-moment warm-rain microphysics. The homogeneity of subgrid-scale mixing refers to the partitioning of the cloud water evaporation due to parameterized entrainment between changes of the mean droplet radius and changes of the mean droplet concentration. Homogeneous and extremely inhomogeneous mixing represent two limits of possible scenarios, where the droplet concentration and the mean droplet radius remains unchanged during the microphysical adjustment, respectively. To predict the subgrid-scale mixing scenario, the double-moment microphysics scheme is merged with the approach to delay droplet evaporation resulting from entrainment. Details of the new scheme and its application in the Barbados Oceanographic and Meteorological Experiment (BOMEX) shallow convection case are discussed. The simulated homogeneity of mixing varies significantly inside small convective clouds, from close to homogeneous to close to extremely inhomogeneous. The mean mixing characteristics become more homogeneous with height, reflecting increases of the mean droplet size and the mean turbulence intensity, both favoring homogeneous mixing. Model results are consistent with microphysical effects of entrainment and mixing deduced from field observations. Mixing close to homogeneous is predicted in volumes with the highest liquid water content (LWC) and strongest updraft at a given height, whereas mixing in strongly diluted volumes is typically close to extremely inhomogeneous. The simulated homogeneity of mixing has a small impact on mean microphysical characteristics. This result agrees with the previous study applying prescribed mixing scenarios and can be explained by the high humidity of the clear air involved in the subgrid-scale mixing.

The plane-parallel model for the parameterization of clouds in global climate models is examined in order to estimate the effects of the vertical profile of the microphysical parameters on radiative transfer calculations for extended boundary layer clouds. The vertically uniform model is thus compared to the adiabatic stratified one.