Toward multiscale simulation of moist flows with soundproof equations

This paper discusses the incorporation of phase changes of the water substance that accompany moist atmospheric flows into the all-scale atmospheric model based on soundproof equations. A specific issue involves developing a theoretical basis and practical implementation to include pressure perturbations associated with atmospheric circulations, from small scale to global, into representations of moist thermodynamics. In small-scale modeling using soundproof equations, pressure perturbations are obtained from the elliptic pressure solver and are typically excluded from the moist thermodynamics. This paper argues that in larger-scale flows, at least the hydrostatic component of the pressure perturbation needs to be included because pressure variation in synoptic weather systems may affect moist thermodynamics in a way comparable to the temperature variations. As an illustration, two idealized test problems are considered: the small-scale moist thermal rising in a stratified environment and the moist mesoscale flow over idealized topography. The paper compares numerical solutions obtained with a fully compressible acoustic mode-resolving model and with two versions of the anelastic model, either including or excluding anelastic pressure perturbations in moist thermodynamics. The two versions of the anelastic model are referred to as the generalized and standard anelastic. In agreement with the scaling arguments, only negligible differences between anelastic and compressible solutions are simulated. Incorporation of the anelastic pressure perturbations into moist thermodynamics paves the way for future studies where larger-scale moist dynamics will be considered.