A rigorous treatment of moist convection in a single column

TL;DR

This paper develops a rigorous mathematical framework for modeling moist convection in a single atmospheric column, analyzing stability, evolution, and solutions to better understand atmospheric dynamics.

Contribution

It introduces a measure valued solution concept for moist convection and proves its existence, advancing the mathematical understanding of atmospheric column models.

Findings

Conditions for stable steady states are established.

The evolution under upward displacement can lead to instability.

Existence of measure valued solutions is proven.

Abstract

We study a single column model of moist convection in the atmosphere. We state the conditions for it to represent a stable steady state. We then evolve the column by subjecting it to an upward displacement which can release instability, leading to a time dependent sequence of stable steady states. We propose a definition of measure valued solution to describe the time dependence and prove its existence.