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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.

Marine stratocumulus clouds play an important role in the planet’s radiation budget by reflecting the incident solar radiation. Some studies have shown that the uncertainty in temperature projections in global warming simulations is mainly caused by the representation of marine low clouds in global climate models. Using the Super Droplet Method (SDM), an advanced and highly accurate particle-based numerical simulation method for cloud microphysics, the characteristics and morphology of the simulated clouds are closer to those of natural clouds. We explore separately how small a grid length is necessary for accurate simulations of stratocumulus using the SDM and a double-moment scheme called SN14 which is a traditional and simpler cloud microphysics scheme and how many Super-droplet number per grid is required for an accurate simulation using SDM. This result can be used as a reference for future related research, saving computational resources while ensuring the accuracy of the simulation. The results of both schemes are compared with the results of model intercomparison project (MIP) results showing a good agreement. The difference of results of SDM and SN14 could be explained by the numerical diffusion and different performance of aerosol particles. The former is a numerical calculation error that is present in the simulation of SN14 but not in the SDM. SDM can simulate the motion and microphysical processes of aerosol particles more accurately, so it explicitly calculates the process of aerosol removal, and this would make the cloud holes larger and longer lasting. The results of this comparison also suggest that cloud-aerosol interactions could be critical to understanding the behavior and morphology of marine stratocumulus. We hope that our findings on the mechanisms of cloud-aerosol interactions will provide new insights for future studies and help us understand stratocumulus clouds.

A particle-based cloud model was developed for ultrahigh-resolution numerical simulation of warm clouds. Simplified cloud microphysics schemes have already made meter-scale numerical experiments feasible; however, such schemes are based on empirical assumptions, and hence, they contain huge uncertainties. The super-droplet method (SDM) is promising for cloud microphysical process modeling; it is based on a particle-based approach and does not make any assumptions for the droplet size distributions. However, meter-scale numerical experiments using the SDM are not feasible even on the existing high-end supercomputers because of its high computational cost. In the present study, we optimized and sophisticated the SDM for ultrahigh resolution 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 centimeter and meter scales. (2) We improved the SDM algorithm to achieve high performance by reducing data movement and simplifying loop bodies by applying the concept of effective resolution. The improved algorithms can be applied to Fujitsu A64FX processor, and most of them are also effective on other many-core CPUs and graphics processing units (GPUs). Warm bubble experiments revealed that the particle-steps per time for the improved algorithms is 57.6 times faster than those for the original SDM. In the case of shallow cumuli, the simulation times when using the new SDM with 64–128 SDs per cell are shorter than those for a bin method with 32 bins and are comparable to those for a two-moment bulk method. (3) Using supercomputer Fugaku, we demonstrated that a numerical experiment with 2 m resolution and 128 SDs per cell covering 13,8242 × 3,072 m3 domain is possible. The number of grids and SDs are 104 and 442 times, respectively, those of the current state-of-the-art experiment. Our numerical model exhibited perfect weak scaling up to 36,864 nodes, which account for 23 % of the total system. The simulation achieves 7.97 PFLOPS, 7.04 % of peak ratio for overall performance, and the simulation time for SDM is 2.86 × 1013 particle·steps/s. Several challenges, such as optimization for mixed-phase clouds, inclusion of terrain, and long-time integrations, still remain, and our study will also contribute toward solving them. The developed model enables us to study turbulence and microphysics processes over a wide range of scales using combinations of 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.

In this study, the super droplet-method (SDM) is used in large-eddy simulations of an isolated cumulus congestus observed during the 1995 Small Cumulus Microphysics Study field project in order to ...

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.

In this presentation, we summarize the main results of Shima et al. (2019). The super-droplet method (SDM) is a particle-based numerical algorithm that enables accurate cloud microphysics simulation with lower computational demand than multi-dimensional bin schemes. Using SDM, we developed a detailed numerical model of mixed-phase clouds in which ice morphologies are explicitly predicted without assuming ice categories or mass-dimension relationships. Ice particles are approximated as 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; collision-coalescence, -riming, and -aggregation. To evaluate the model's performance, we conducted a 2D large-eddy simulation of a cumulonimbus. The results well capture characteristics of a real cumulonimbus. 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/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. Shima, S., Sato, Y., Hashimoto, A., and Misumi, R.: Predicting the morphology of ice particles in deep convection using the super-droplet method: development and evaluation of SCALE-SDM 0.2.5-2.2.0/2.2.1, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2019-294, 1-83, 2019.

The impact of spatial resolution on the simulation of trade wind cumuli was investigated. The super-droplet method, an efficient stochastic Lagrangian cloud microphysical model, was used to reduce uncertainties due to the empirical parameterisation of cloud microphysics and numerical diffusion for advection, which is inevitable in an Eulerian cloud microphysical model. We showed for the first time that cloud cover numerically converged with a grid resolution of 12.5 m. Our grid refinement analysis elucidated a significant contribution of small cumulus clouds to total cloud cover, as such cumuli are generated by small-scale updrafts that can be resolved only at a fine resolution.

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; collision-coalescence, -riming, and -aggregation. To evaluate the model's performance, a 2D large-eddy simulation of a cumulonimbus was conducted, and the results well capture characteristics of a real cumulonimbus. 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/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 regional-scale meteorology – chemistry model (NHM-Chem v1.0) has been developed. Three options for aerosol representations are currently available: the 5-category non-equilibrium (Aitken, soot-free accumulation, accumulation internally mixed with soot, dust, and sea-salt), 3-category non-equilibrium (Aitken, accumulation, and coarse), and bulk equilibrium (submicron, dust, and sea-salt) methods. These three methods are suitable for the predictions of regional climate, air quality, and operational forecasts, respectively. The total CPU times of the 5-category and 3-category methods were 91 % and 44 % greater than that of the bulk method, respectively. The bulk equilibrium method was shown to be eligible for operational forecast purposes, namely, the surface mass concentrations of air pollutants such as O3, mineral dust, and PM2.5. The 3-category method was shown to be eligible for air quality simulations, namely, mass concentrations and depositions. However, the internal mixture assumption of soot/soot-free and dust/sea-salt particles in the 3-category method resulted in significant differences in the size distribution and hygroscopicity of the particles. Even though the 3-category method was not designed to simulate aerosol-cloud-radiation interaction processes, its performance in terms of bulk properties, such as aerosol optical thickness (AOT) and cloud condensation nuclei (CCN), was acceptable. However, some specific parameters exhibited significant differences or systematic errors. The unrealistic dust/sea-salt complete mixture of the 3-category method induced significant errors in the prediction of mineral dust containing CCN. The overestimation of soot hygroscopicity by the 3-category method induced errors in BC-containing CCN, BC deposition, and absorbing AOT (AAOT). The difference in AAOT was less pronounced because the overestimation of the absorption enhancement was compensated by the overestimation of hygroscopic growth and the consequent loss due to in-cloud scavenging.

In this study we present a series of LES simulations employing the Super-Droplet Method (SDM) for representing aerosol, cloud and rain microphysics. SDM is a particle-based and probabilistic approach in which a Monte-Carlo type algorithm is used for solving the particle collisions and coalescence process. The model does not differentiate between aerosol particles, cloud droplets, drizzle or rain drops. Consequently, it covers representation of such cloud-microphysical processes as: CCN activation, drizzle formation by autoconversion, accretion of cloud droplets, self-collection of raindrops and precipitation including aerosol wet deposition. Among the salient features of the SDM, there are: (i) the robustness of the model formulation (i.e. employment of basic principles rather than parametrisations) and (ii) the ease of comparison of the model results with experimental data obtained with particle-counting instruments. The model set-up used in the study is based on observations from the Rain In Cumulus over Ocean (RICO) field project (the GEWEX Cloud System Study Boundary Layer Cloud Working Group RICO case). Cloud and rain droplet size spectrum features obtained in the simulations are compared with previously published aircraft observations carried out during the RICO field project. The analysis covers height-resolved statistics of simulated cloud microphysical parameters such as droplet number concentration, effective radius, and the width of the cloud droplet size spectrum. 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 discussed.

A novel simulation model of cloud microphysics is developed, which is named Super-Droplet Method (SDM). SDM enables accurate calculation of cloud microphysics with reasonable cost in computation. A simple SDM for warm rain, which incorporates sedimentation, condensation/evaporation, stochastic coalescence, is developed. The methodology to couple SDM and a non-hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the coalescence of super-droplets agrees fairly well with the solution of stochastic coalescence equation. A preliminary simulation of a shallow maritime cumulus formation initiated by a warm bubble is presented to demonstrate the practicality of SDM. Further discussions are devoted for the extension and the computational efficiency of SDM to incorporate various properties of clouds, such as, several types of ice crystals, several sorts of soluble/insoluble CCNs, their chemical reactions, electrification, and the breakup of droplets. It is suggested that the computational cost of SDM becomes lower than spectral (bin) method when the number of attributes $d$ becomes larger than some critical value, which may be $2\sim4$.

We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.

The method of precisely simulating a cloud microphysical process in a comparatively reasonable calculation cost has been developed by introducing the new concept that is called a super-droplet. Currently, the multi-physics simulations of the cumulus cloud formation and the rainfall have been tested, by coupling the super-droplet method with the macro-scale non-hydrostatic atmospheric model. Several characteristics of each water droplet, such as the positions in the atmosphere, the numbers of water droplets at those positions and the radii, are derived precisely in the simulation using super-droplet method.Several visualizations also have been tried for analyzing the data of this simulation. In the present paper, visualization of light transport in the cumulus cloud and around it is discussed by focusing optical characteristics of the water droplets which have been obtained by the multi-physics coupled cloud simulation.

A simple mean-field idea is applicable to the pattern dynamics of large assemblies of limit-cycle oscillators with non-local coupling. This is demonstrated by developing a mathematical theory for the following two specific examples of pattern dynamics. Firstly, we discuss propagation of phase waves in noisy oscillatory media, with particular concern with the existence of a critical condition for persistent propagation of the waves throughout the medium, and also with the possibility of noise-induced turbulence. Secondly, we discuss the existence of an exotic class of patterns peculiar to non-local coupling called chimera where the system is composed of two distinct domains, one coherent and the other incoherent, separated from each other with sharp boundaries.

A new methodology for the simulation of multiscale pro-cesses, called Macro-Micro Interlocked (MMI) Simulation, is introduced. The MMI simulation is carried out by the two-way connection of different numerical models, which may handle macroscopic and microscopic dynamics, respectively. The MMI simulation are applied to several multiscale phenomena, for instance, cloud formation, gas detonation, and plasma dynamics. The results indicate that the MMI simulation provide us an effective and prospective framework for multiscale simulation.

Rotating spiral waves without phase singularity are found to arise in a certain class of three-component reaction-diffusion systems of biological relevance. It is argued that this phenomenon is universal when some chemical components involved are diffusion-free. Some more detailed mathematical and numerical analyses are carried out on a complex Ginzburg-Landau equation with non-local coupling to which the original system is reduced close to a codimension-two parameter set., 11 pages, 5 figures

Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a paradigmatic three-component reaction-diffusion model. The origin of this anomalous spiral dynamics is the effective non-locality in coupling, whose effect is stronger for weaker coupling. There exists a critical coupling strength which is estimated from a simple argument. Detailed mathematical and numerical analyses are carried out in the extreme case of weak coupling for which the phase reduction method is applicable. Under the assumption that the mean field pattern keeps to rotate steadily as a result of a statistical cancellation of the incoherence, we derive a functional self-consistency equation to be satisfied by this space-time dependent quantity. Its solution and the resulting effective frequencies of the individual oscillators are found to agree excellently with the numerical simulation., Comment: 10 pages, 6 figures