A pseudoenergy wave-activity relation for ageostrophic and non-hydrostatic moist atmosphere

By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Since this system of equations includes the effects of water substance, mass forcing, diabatic heating, and dissipations, the derived wave-activity relation generalizes the previous result for a dry atmosphere. The Casimir function used in the derivation is a monotonous function of virtual potential vorticity and virtual potential temperature. A virtual energy equation is employed (in place of the previous zonal momentum equation) in the derivation, and the basic state is stationary but can be three-dimensional or, at least, not necessarily zonally symmetric. The derived wave-activity relation is further used for the diagnosis of the evolution and propagation of meso-scale weather systems leading to heavy rainfall. Our diagnosis of two real cases of heavy precipitation shows that positive anomalies of the virtual pseudoenergy wave-activity density correspond well with the strong precipitation and are capable of indicating the movement of the precipitation region. This is largely due to the cyclonic vorticity perturbation and the vertically increasing virtual potential temperature over the precipitation region. (paper)