Scaling Approaches to Quasigeostrophic Theory for Moist, Precipitating Air

Abstract

Abstract Quasigeostrophic (QG) theory is of fundamental importance in the study of large-scale atmospheric flows. In recent years, there has been growing interest in extending the classical QG plus Ekman friction layer model (QG–Ekman) to systematically include additional physical processes known to significantly contribute to real-life weather phenomena. This paper lays the foundation for combining two of these developments, namely, Smith and Stechmann’s family of precipitating quasigeostrophic (PQG) models on the one hand, and the extension of QG–Ekman for dry air by a strongly diabatic layer (DL) of intermediate height (QG–DL–Ekman) on the other hand. To this end, Smith and Stechmann’s PQG equations for soundproof motions are first corroborated within a general asymptotic modeling framework starting from a full compressible flow model. The derivations show that the PQG model family is naturally embedded in the asymptotic hierarchy of scale-dependent atmospheric flow models introduced by one of the present authors. Particular emphasis is then placed on an asymptotic scaling regime for PQG that accounts for a generic Kessler-type bulk microphysics closure and is compatible with QG–DL–Ekman theory. The detailed derivation of a moist QG–DL–Ekman model is deferred to a future publication.