Optimization and sophistication of the super-droplet method for ultrahigh resolution cloud simulations

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.