A general framework for the asymptotic analysis of moist atmospheric flows

TL;DR

This paper develops a unified asymptotic analysis framework for moist atmospheric flows, extending existing models for dry air to include moist processes, phase changes, and cloud formation, with implications for meteorology and mathematics.

Contribution

It introduces a comprehensive asymptotic framework for moist atmospheric flows, integrating phase changes and cloud processes into existing models for the first time.

Findings

Unified treatment of dry and moist atmospheric models

Extension of scale-independent limits to moist air

Mathematical formulation of cloud formation and rain processes

Abstract

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 quasigeostrophic (PQG) models introduced by Smith & 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.