Developing a Slow Moist Variable for a Compressible Atmosphere with Clouds

Clouds are one of the greatest challenges in atmospheric physics. They are the leading source of uncertainty in climate change predictions, and rainfall is arguably the most challenging quantity to predict in weather forecasts. Our theoretical understanding of clouds also lags behind our understanding of a ``dry'' atmosphere. In recent years a new conserved quantity, called the “M” variable, was shown to describe the slow component of moisture in the atmosphere. for a simplified set of equations, called the Boussinesq equations. Here we seek to develop an M quantity for the more general compressible set of equations. In particular, we show that the energy for an atmosphere with clouds, can be decomposed into three components that correspond with pressure perturbations (acoustic/sound waves), buoyancy, and a slow moist latent energy which is points towards a compressible definition of the “M” variable.