| Abstract: | In this paper, a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps. First, the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method, avoiding a weighting parameter specification step. Compared with conventional dual-Doppler wind synthesis approaches, this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process, which is one of the main sources of errors. Then, through the accelerated Liebmann method, the vertical velocity is further re-estimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause. The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation. Compared with the method proposed by O'Brien, this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability. Furthermore, the method proposed in this paper is applied to Doppler radar observation of a squall line process. It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display (VAD) method, and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations. There is a good correspondence between the divergence field of the derived wind field and the vertical velocity. And, the horizontal and vertical circulations within and around the squall line, as well as strong updrafts, the associated downdrafts, and associated rear inflow of the bow echo, are analyzed well. It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations. |
