A General Framework for the Asymptotic Analysis of Moist Atmospheric Flows

We deal with asymptotic analysis for the derivation of partial differential equation models for geophysical flows in the Earth’s atmosphere with moist process closures, and we study their mathematical properties. Starting with the Navier–Stokes equations for dry air, we put the seminal papers of Klein, Majda et al. in a unified context and then discuss the appropriate extension to moist air. In particular, we deal with the scale-independent distinguished limit for the universal parameters of atmospheric motion for moist air, with the Clausius–Clapeyron relation that links saturation vapor pressure and air temperature, and with the mathematical formulation of phase changes associated with cloud formation and rain production. We conclude with a discussion of the precipitating quasi-geostrophic models introduced by Smith and Stechmann. Our intent is, on the one hand, to convey the problems arising at the modeling stage to mathematicians; on the other hand, we want to present the relevant mathematical methods and results to meteorologists.