Balanced Flow in Moist Dynamics with Phase Changes

Atmospheric flows are often decomposed into low-frequency (balanced) and high-frequency (unbalanced) waves. For dry atmospheric dynamics, a single mode, the potential vorticity, is enough to recover the balanced flow and determine its evolution. Here we show that a moist atmosphere with phase changes requires the inclusion of additional balanced modes arising from the moisture. The traditional potential vorticity mode with the inclusion of these new moist modes allow for the formulation of an inversion principle to recover the balanced flow, even when phase changes are present. This moist balanced flow can then be used to determine the decomposition of all atmospheric variables, including moisture, into balanced and unbalanced components.