Two-time-level semi-Lagrangian modeling of precipitating clouds

This paper discusses two-time-level semi-Lagrangian approximations for the bulk warm-rain microphysics embedded in the framework of an anelastic cloud model. The central theoretical issue is a semi-Lagrangian integration of the rain-evolution equation. Because departure points of rain trajectories differ from those of flow trajectories and the terminal velocity of the precipitation depends on the concentration of the precipitation itself, effective semi-Lagrangian approximations are not necessarily straightforward. Some simplifying assumptions are adopted that compromise formal accuracy and computational efficiency of the method. Theoretical considerations are illustrated with idealized simulations of precipitating thermal convection and orographically forced clouds. Comparisons with corresponding results obtained using a more traditional, flux-form Eulerian cloud model document highly competitive performance of the semi-Lagrangian approach. Although derived for the warm-rain parameterization, the method presented in this paper is universal; that is, it may be easily extended to any standard microphysical parameterization, including ice physics or detailed microphysics.