On use of the anelastic vertical vorticity equation in dual-Doppler analyses of the vertical velocity field

The potential for applying the anelastic vertical vorticity equation for dual-Doppler synthesis of the vertical wind field is explored. In particular, application of the vorticity equation as a weak variational constraint to retrieve the boundary condition field(s) is investigated. The Euler-Lagrange equations for a single boundary condition as well as a system of two opposing boundary conditions are presented. Since mass continuity is applied as a weak constraint during vertical velocity retrieval in the latter approach, a correction step to the horizontal wind fields is developed that ensures anelastic mass continuity is satisfied exactly in the final analysis.; The techniques are tested on ARPS simulations of the May 20, 1977 Del City supercell storm as well as a storm evolving in a typical dry microburst environment. Errors are introduced to the simulated radial wind observations, and the resulting analyses are compared against the traditional techniques that would most likely be applied in each of four data availability scenarios. These four scenarios were devised to address the scanning limitations of current operational and research radars. The results using simulated data indicate that the vorticity equation has the potential for significantly improving dual-Doppler analyses of the vertical velocity field in many common situations, and argue for the deployment of more rapid scanning research radars.