On the Significance and Use of the Generalized Moist Potential Vorticity Equation

In this paper, the continuity and thermodynamic equations including moisture forcings were derived. Using these two equations and the basic momentum equation of local Cartesian coordinates, the budget equation of generalized moist potential vorticity (GMPV) was derived. The GMPV equation is a good generalization of the Ertel potential vorticity (PV) and moist potential vorticity (MPV) equations. The GMPV equation is conserved under adiabatic, frictionless, barotropic, or saturated atmospheric conditions, and it is closely associated with the horizontal frontogenesis and stability of the real atmosphere. A real case study indicates that term diabatic heating could be a useful diagnostic tool for heavy rainfall events.