Global well-posedness of a model for precipitating convection with hydrostatic pressure under fast autoconversion and rain evaporation conditions

Abstract

Moist convection in the tropical atmosphere involves the interaction of deep precipitating clouds that can be organized into different patterns and propagate long distances. Their modeling to predict their evolution can be done with PDE-based models but it requires the parametrization of different cloud micro-physical processes. Simplified models can maintain a balance between complexity and precision, and can still capture qualitative observations made in nature. In this work, we prove global existence and uniqueness of a model for precipitating turbulent convection. The model considers a moisture dynamics with phase changes. It assumes fast auto-conversion and rain evaporation together with a hydrostatic pressure approximation. We also show positivity of the variables associated to moisture and equivalent potential temperature. The existing literature is discussed and the new challenges in this model are highlighted.