Anelastic and compressible simulation of moist deep convection

Anelastic and compressible solutions are compared for two moist deep convection benchmarks, a two-dimensional thermal rising in a saturated moist-neutral deep atmosphere, and a three-dimensional supercell formation. In the anelastic model, the pressure applied in the moist thermodynamics comes from either the environmental hydrostatically balanced pressure profile in the standard anelastic model or is combined with nonhydrostatic perturbations from the elliptic pressure solver in the generalized anelastic model. The compressible model applies either an explicit acoustic-mode-resolving scheme requiring short time steps or a novel implicit scheme allowing time steps as large as those used in the anelastic model. The consistency of the unified numerical framework facilitates direct comparisons of results obtained with anelastic and compressible models. The anelastic and compressible rising thermal solutions agree not only with each other but also with the previously published compressible benchmark solution based on the comprehensive representation of moist dynamics and thermodynamics. In contrast to earlier works focusing on the formulation of moist thermodynamics, the compatibility of the initial conditions is emphasized and its impact on the benchmark solutions is documented. The anelastic and compressible supercell solutions agree well for various versions of anelastic and compressible models even for cloud updrafts reaching 15% of the speed of sound. The nonhydrostatic pressure perturbations turn out to have a negligible impact on the moist dynamics. Numerical and physical details of the simulations, such as the advection scheme, spatial and temporal resolution, or parameters of the subgrid-scale turbulence, have a more significant effect on the solutions than the particular equation system applied.