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.