島 伸一郎

Abstract Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing super-droplet method (SDM) and a 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 super-drops 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.

Clouds play a central role in climate physics by interacting with precipitation, radiation, and circulation. Although the self-aggregation of clouds is a fundamental problem in convective organization, a theoretical explanation of how it occurs has not been established owing to its complexity. Here, we introduce an idealized mathematical model of the phenomenon in which the state of the system is represented solely by the atmospheric columns' vertically integrated water vapor content. By analyzing the nonlinear dynamics of this simplified system, we mathematically elucidated the mechanisms that determine the onset of self-aggregation and the spatial scale of the self-aggregated state. Nonlocal coupling between atmospheric columns makes the system bistable with dry and moist equilibria, reflecting the effect of circulation driven by horizontal differential heating due to convection and radiation. The bistable self-aggregated state is realized when destabilization by nonlocal coupling triggered by finite-amplitude disturbances in the uniform state overwhelms the stabilization by diffusion. For globally coupled systems in which all the columns are equally coupled, the perturbation of the maximum wavelength has the maximum growth rate. A solution with an infinitely long wavelength exists, which can be understood as the dynamical system's heteroclinic trajectories describing the steady state's spatial evolution. In contrast, for nonlocally coupled systems with finite filter lengths, perturbation of the wavelength close to the characteristic length of the coupling is preferred. The results revealed that the balance between nonlocal coupling and diffusion is essential for understanding convective self-aggregation.

Abstract Estimating the states of chaotic cellular automata (CA) based on noisy imperfect data is challenging due to the nonlinearity and discreteness of the dynamical system.This paper proposes particle filter (PF)-based data assimilation (DA) for three-state chaotic CA and demonstrates that the PF-based DA can predict the present and future state even with noisy and sparse observations.The chaotic CA used in the present study comprised a competitive system of $land$, $grass$, and $sheep$.To the best of the authors' knowledge, this is the first application of DA to chaotic CA.The performance of DA for different observation sets was evaluated in terms of observational error, density, and frequency, and a series of sensitivity tests of the internal parameters in the DA was conducted.The inflation and localization parameters were tuned according to the sensitivity tests.

Abstract. The 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). Then, the weak electric effect on a cumulus cloud is investigated by size resolved cloud model with particle treatment of the super-droplet method. The results show that with CS treatment, the electrostatic force contributes a larger effect on cloud evolution than previous research. With a 3 % lower charge limit of the maximum charge amount of the droplet, the domain total precipitation with CS treatment for droplets with opposite signs is 52.5 % higher than that with the no charge (NC) setting. Compared with previous work by Khain et al. (2004), with the multi-image-dipole treatment of CS, the amount of precipitation is 5.42 % higher. It is found that the charged droplets could affect cloud formation even when the droplet charge is lower charge limit. High pollution levels result in greater sensitivity to electro-coalescence. The results show that when the charges 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 CS method would require 30 % longer computation time than before, it is worthwhile to include it in cloud, weather, and climate models.

Abstract. 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 13 8242×3072 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.

Galactic cosmic rays are one of the possible mediators of the solar influence on climate. However, the impacts of GCR on clouds and climate systems are not fully understood. In this paper, we show that the high-altitude clouds associated with deep convective activities are responding to the decadal-scale cycles of GCRs and that the susceptible areas are seasonally variable. Most notable responses were found in August over tropical land areas, suggesting that the susceptivity of clouds to GCRs depends on the depth of convective activities and the abundance of aerosol precursor materials. Furthermore, following the activation of high-altitude cloud formation, an increase in sea surface temperature (SST) gradient was observed over the Pacific. Although the response of sea surface temperature to solar activity has mostly been discussed as mediated by solar radiations, we propose that another mechanism is possible: through the impact of GCRs on clouds and the resultant changes in atmospheric circulations.

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.

<jats:p>Abstract. 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. </jats:p>

<jats:p>Abstract. 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. </jats:p>

10th International Cloud Modeling Workshop: What: More than 120 cloud modeling researchers participated in a virtual workshop to discuss recent progress in representing dynamics-microphysics interactions in numerical models and pathways to improve our understanding across a variety of scales. When: 26-30 July 2021. Where: Online.

Abstract. This study provides comparisons of aerosol representation methods incorporated into a regional-scale nonhydrostatic meteorology–chemistry model (NHM-Chem). Three options for aerosol representations are currently available: the five-category non-equilibrium (Aitken, soot-free accumulation, soot-containing accumulation, dust, and sea salt), three-category non-equilibrium (Aitken, accumulation, and coarse), and bulk equilibrium (submicron, dust, and sea salt) methods. The three-category method is widely used in three-dimensional air quality models. The five-category method, the standard method of NHM-Chem, is an extensional development of the three-category method and provides improved predictions of variables relating to aerosol–cloud–radiation interaction processes by implementing separate treatments of light absorber and ice nuclei particles, namely, soot and dust, from the accumulation- and coarse-mode categories (implementation of aerosol feedback processes to NHM-Chem is still ongoing, though). The bulk equilibrium method was developed for operational air quality forecasting with simple aerosol dynamics representations. The total CPU times of the five-category and three-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 simulated surface concentrations and depositions of bulk chemical species of the three-category method were not significantly different from those of the five-category method. However, the internal mixture assumption of soot/soot-free and dust/sea salt particles in the three-category method resulted in significant differences in the size distribution and hygroscopicity of the particles. The unrealistic dust/sea salt complete mixture of the three-category method induced significant errors in the prediction of the mineral dust-containing cloud condensation nuclei (CCN), which alters heterogeneous ice nucleation in cold rain processes. The overestimation of soot hygroscopicity by the three-category method induced errors in the BC-containing CCN, BC deposition, and light-absorbing aerosol optical thickness (AAOT). Nevertheless, the difference in AAOT was less pronounced with the three-category method 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 terms of total properties, such as aerosol optical thickness (AOT) and CCN, the results of the three-category method were acceptable.

<jats:p>Abstract. 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. </jats:p>

In the atmosphere,microphysicsrefers 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.

The model performance of a regional-scale meteorology-chemistry model (NHM-Chem) has been evaluated for the consistent predictions of the chemical, physical, and optical properties of aerosols. These properties are essentially important for the accurate assessment of air quality and health hazards, contamination of land and ocean ecosystems, and regional climate changes due to aerosol-cloud-radiation interaction processes. Currently, three optional methods arc available: the five-category non-equilibrium method, the three-category non-equilibrium method, and the bulk equilibrium method. These three methods are suitable for the predictions of regional climate, air quality, and operational forecasts, respectively. In this paper, the simulated aerosol chemical, physical, and optical properties and their consistency were evaluated using various observation data in East Asia. The simulated mass, size, and deposition of SO42- and NH4+ agreed well with the observations, whereas those of NO3-, sea salt, and dust needed improvement. The simulated surface mass concentration (PM10 and PM2.5) and spherical extinction coefficient agreed well with the observations. The simulated aerosol optical thickness (AOT) and dust extinction coefficient were significantly underestimated.

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.

Abstract. 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.

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 100/80m to 6.25/5m. 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 12.5/10m, 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.

We developed a data assimilation system based on a particle filter approach with the spatially explicit individual-based dynamic global vegetation model (SEIB-DGVM). We first performed an idealized observing system simulation experiment to evaluate the impact of assimilating the leaf area index (LAI) data every 4 days, simulating the satellite-based LAI. Although we assimilated only LAI as a whole, the tree and grass LAIs were estimated separately with high accuracy. Uncertain model parameters and other state variables were also estimated accurately. Therefore, we extended the experiment to the real world using the real Moderate Resolution Imaging Spectroradiometer (MODIS) LAI data and obtained promising results.

We take into consideration the evolution of particle size in a monodisperse aerosol population during activation and deactivation of cloud condensation nuclei (CCN). Our analysis reveals that the system undergoes a saddlenode bifurcation and a cusp catastrophe. The control parameters chosen for the analysis are the relative humidity and the particle concentration. An analytical estimate of the activation timescale is derived through estimation of the time spent in the saddle-node bifurcation bottleneck. Numerical integration of the system coupled with a simple air-parcel cloud model portrays two types of activation/deactivation hystereses: one associated with the kinetic limitations on droplet growth when the system is far from equilibrium, and one occurring close to equilibrium and associated with the cusp catastrophe. We discuss the presented analyses in context of the development of particle-based models of aerosolcloud interactions in which activation and deactivation impose stringent time-resolution constraints on numerical integration.

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.

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.

洋上の浅い層積雲にエアロゾルと雲の相互作用が及ぼす影響を, 持続的にエアロゾルが形成される理想化された気象システムの数値計算により調べる. 雲微物理過程の数値計算には超水滴法を使い, エアロゾル・雲粒・降水粒子のふるまいを統一的に計算する.大気流体場は準圧縮近似の下で音波モードとそれ以外を分割して数値計算する. 初期のエアロゾル数密度によらず系は数日後にある定常状態に落ち着くこと, その定常状態はエアロゾル生成率が大きくなるに伴い積雲から層雲に転移することを見る. 今回のモデルでは, 気相や液相での化学反応までは考慮していないためエアロゾルと雲の相互作用が完全に表現できてはおらず, また数値計算も鉛直２次元で行うため, この結果はあくまで予備的なものである.The influence of aerosol-cloud interactions on the behavior of marine stratocumulus is investigated through numerical simulations of an idealized meteorological system in which aerosols are formed continuously. The super-droplet method is used for the simulation of cloud microphysical processes, with which the time evolution of aerosol/cloud/precipitation particles is calculated in a unified manner. For the simulation of atmospheric fluid dynamical processes, the quasi-compressible approximation and the sound mode splitting method are applied. The system gradually evolves to reach its final steady state in a few days, which is irrelevant to the initial number density of aerosols. A transition of the final steady state from cumuli to strati occurs when the aerosol formation rate is increased. Because the chemical reaction in the gas phase and the liquid phase is not incorporated, the model is not detailed enough to describe aerosol-cloud interactions. Further, the numerical simulations are performed in two dimensions. For these reasons, the results obtained are still all preliminary

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.

A novel, particle-based, probabilistic approach for the Simulation of cloud microphysics is proposed, which is named the super-droplet method (SDM). This method enables the accurate simulation of cloud microphysics with a less demanding cost in Computation. SDM is applied to a warm-cloud system, which incorporates sedimentation, condensation/evaporation and stochastic coalescence. The methodology to couple super-droplets and a non-hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the stochastic coalescence of super-droplets agrees fairly well with the solutions of the stochastic coalescence equation. The behaviour of the model is evaluated using a simple test problem, that of a shallow maritime cumulus formation initiated by a warm bubble. Possible extensions of SDM are briefly discussed. A theoretical analysis suggests that the Computational cost of SDM becomes lower than the spectral (bin) method when the number of attributes - the variables that identify the state of each super-droplet - becomes larger than some critical value, which we estimate to be in the range 2 similar to 4. Copyright (C) 2009 Royal Meteorological Society

A new methodology for the, simulation of multiscale processes, 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.

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.

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 nonlocality 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 rotating 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.

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.

A tube conveying a large amount of fluid with a free outlet does not sit<br /> still. We construct and analyze a nonlinear evolution equation describing such<br /> phenomena. Two types of boundary conditions at the inlet are considered, one<br /> for which it is clamped and one for which it is hinged. Analyzing the linear<br /> stability of the trivial solution, we find that with the former boundary<br /> conditions, it exhibits a ``flutter&#039;&#039; instability, while with the latter<br /> boundary conditions, it exhibits a ``rotation&#039;&#039; instability. These<br /> instabilities and the nonlinear behaviors of the system are also studied<br /> numerically.