A three-dimensional variational single-Doppler velocity retrieval method with simple conservation equation constraint

In this paper, a new three-dimensional variational analysis scheme capable of retrieving three-dimensional winds from single Doppler observations of convective storms is developed. The method incorporates, in a single cost function, Doppler radar observations, a background field, smoothness and mass continuity constraints, and the residual of reflectivity or radial velocity conservation. By minimizing this cost function, an analysis with the desired fit to these constraints is obtained in a single procedure. In tests with both simulated and real thunderstorm cases, detailed structures of the storms are well retrieved in comparison with reference analysis. Unlike most kinematic retrieval methods, our scheme is capable of directly dealing with data voids. When an analysis background is available, say from a proximity sounding, a wind profiler, or a numerical model forecast, the method naturally blends Doppler radar observations with it. Thus, a smooth transition is obtained between data-rich and data-void areas. These features, among others, are important if the analysis is to be used to initialize storm-scale numerical models or for diagnostic studies of storm structures.