Anelastic and compressible simulation of moist deep convection

Moist deep convection is an example of a nonhydrostatic atmospheric flow that involves multiscale dynamics and extreme ranges of the temperature, pressure and humidity accompanied by strong vertical velocities. We compare anelastic and compressible solutions for two benchmark moist deep convection tests, 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 timesteps or a novel implicit scheme allowing timesteps as long as these used in the anelastic model. A unified numerical framework facilitates direct comparisons of results obtained with anelastic and compressible models.

The anelastic and compressible rising thermal solutions agrees not only with each other, but also with previously-published compressible benchmark solution based on the comprehensive representation of moist dynamics and thermodynamics. Anelastic and compressible supercell solutions agrees well for various versions of anelastic and compressible models even for cloud updrafts exceeding 10$\%$ of the speed of sound. The nonhydrostatic pressure perturbations turned 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 model applied.