Use of the Vorticity Equation in Dual-Doppler Analysis of the Vertical Velocity Field

Abstract

The anelastic vertical vorticity equation is imposed as a flow constraint in dual-Doppler wind analysis techniques, with emphasis on improving retrievals of the vertical velocity field. Several new techniques in which the vorticity equation is imposed as a weak constraint are presented. In one method, the vorticity equation is used to obtain the vertical velocity boundary condition field required when mass continuity is used as a strong constraint. In a second method, the vorticity equation is used to solve for the set of two boundary condition fields required when the vertical velocity is expressed in a ?weak constraint form.? A final correction step to the horizontal wind field ensures that mass continuity is satisfied exactly in the final analysis. This latter method can be easily adapted to retrieve a single boundary condition when an opposing boundary condition can be accurately assessed using another method. These new analysis techniques are tested and compared with each other and to common traditional approaches in which the vorticity equation is not used. These tests use simulated data sampled from Advanced Regional Prediction System (ARPS) simulations of a supercell thunderstorm and of a thunderstorm evolving in a typical dry microburst environment. The results suggest that the vorticity equation holds significant potential for improving dual-Doppler analyses of the vertical velocity field, especially under less than optimal data coverage.