Diagnosis of wave activity in a heavy-rainfall event

Three general wave-activity laws with an inclusion of ageostrophic winds are derived in a nonhydrostatic dynamic framework by introducing an arbitrary scalar phi into potential vorticity theorem. The wave activity theory may be applied to diagnoses of mesoscale weather systems. It is shown that the general wave-activity densities cannot represent monochromatic wave but slowly varying wave train. They cannot be transported through the surface of perturbation scalar phi(e) and can neither be created nor destroyed within a layer bounded by the two phi(e) surfaces. The general wave-activity law associated with perturbation vertical velocity is embodied by setting the arbitrary scalar phi to specific humidity, equivalent potential temperature, and virtual potential temperature, respectively. The simulation data of a heavy-rainfall event by the ARPS model are used to calculate the three specific wave-activity densities and to study their laws. It is shown that the three specific wave-activity densities are closely related to the simulated rain rate. This suggests that they may serve as track for detecting precipitation. The variation of moist wave-activity density is mainly caused by the wave-activity flux divergence associated with the vertical component of perturbation pressure gradient force.