Simplified two-layer models of precipitating atmosphere and their properties

Abstract

We derive a two-layer rotating shallow-water model for a moist atmosphere with water vapor condensation and related diabatic heating. Moist convection is represented by additional mass exchanges between the layers, which are determined from the moist enthalpy conservation principle, and related to the precipitation. Various boundary conditions at the lower and upper boundaries may be used. We show that the model reproduces in appropriate limits the main simplified models used previously in the literature for description of the large-scale moist-convective dynamics and precipitation fronts, namely the linear two-layer baroclinic models, the nonlinear two-layer quasigeostrophic model, and the nonlinear one-layer moist-convective rotating shallow-water model. We study the properties of the equations of the model, with special attention to the hyperbolicity loss, which is inherent to multilayer shallow-water models, and to the front propagation. Numerical illustrations of these properties are given with the help of a recently proposed high-resolution finite-volume numerical scheme with precipitation sources/sinks.