Accurate simulation of cloud microphysics is crucial in understanding cloud formation, precipitation processes, and ultimately, the future state of the climate. In practice, microphysical processes are evolved in time using low order integrators, e.g., forward Euler. Coupling among processes is infrequent, weak, and typically done via sequential and parallel splitting methods. This leads to large temporal contributions to the simulation error that can match or even exceed uncertainties in the microphysical parameterizations. In this work, we investigate the usage of advanced, high order time integration methods to improve the temporal accuracy and coupling. In particular, we consider high order explicit, implicit, implicit-explicit, and multirate Runge-Kutta methods implemented in the SUNDIALS suite of differential equation solvers. Our experiments are performed on a rainshaft model based on a subset of the Predicted Particle Properties (P3) scheme used in the Energy Exascale Earth System Model (E3SM). We found high order, adaptive Runge-Kutta schemes are more efficient than traditional low order operator splitting techniques over a wide range of tolerances and operating conditions. Further gains in efficiency and stability were made by treating rain evaporation and self-collision processes explicitly while treating the sedimentation process implicitly or with a smaller time step.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-867594