Evaluation of Semi-Implicit and Explicit Sedimentation Approaches in the Two-Moment Cloud Microphysics Scheme of ICON

Abstract. In the ICOsahedral Nonhydrostatic (ICON) model, the Seifert-Beheng two-moment microphysics scheme is one approach to simulate clouds with different hydrometeor classes. In this bulk description, sedimentation is modeled by advecting the first two moments (number and mass densities) of the hydrometeor size distributions with velocities derived from fitting a generalized gamma distribution to the moments. This method implicitly relies on the diffusive properties of the numerical advection schemes to obtain results in closer agreement with the exact spectral solution. The implementation in ICON offers both a semi-implicit and largely untested explicit method for sedimentation. Currently, the semi-implicit scheme is substantially slower on graphics processing units (GPUs), which is particularly relevant considering the recent rise of GPUs in supercomputing; this raises the question of whether the explicit scheme is a viable alternative.

We provide a detailed examination of both sedimentation schemes, their differences, and underlying assumptions. Using idealized one-dimensional experiments, we identify a minor issue in the default semi-implicit scheme (flux limiter artifacts) and propose a solution. Additionally, we show that the explicit scheme exhibits less numerical diffusion, though some diffusion is crucial for accurate bulk sedimentation. We caution that in the future, finer grid resolutions may result in insufficient diffusion, especially for the explicit scheme. An analysis of six case studies with thunderstorms reveals that the explicit scheme gives rise to more jagged patterns in the hydrometeor profiles, although without concerning instabilities. Furthermore, some differences in hail and graupel precipitation rates can be attributed to different ways of considering the microphysical source terms (e.g., hydrometeor interactions) during the sedimentation step.