Discontinuous Fronts as Exact Solutions to Precipitating Quasi-geostrophic Equations

Abstract

Atmospheric fronts include cold fronts, warm fronts, and stationary fronts, and they can be idealized as boundaries between two air masses with different temperatures and other properties. Simple exact solutions have previously been presented through the Margules relations, but they are lacking in two aspects: they do not propagate and they do not involve water vapor, clouds, or precipitation. Here, these two aspects are included by considering the recently derived precipitating quasi-geostrophic (PQG) equations. The PQG equations are shown to have exact solutions that are discontinuous fronts with jumps in temperature, winds, and total water. A phase change of water occurs at the location of the front, and the front propagates at a speed that is related to the rainfall velocity, jump magnitudes, and front geometry. Exact formulas for the front's properties are presented, including the classical Margules relations and many additional relations involving moisture. Estimates of physical parameters are used as an initial assessment of the realism of the model fronts. Through consideration of alternative representations of atmospheric dynamics, it is suggested that the phase change of water and the fall velocity of rain are key aspects of the PQG equations that allow propagating, discontinuous fronts.