A Three-Dimensional Variational Approach for Deriving the Thermodynamic Structure Using Doppler Wind Observations—An Application to a Subtropical Squall Line

Abstract

A newly designed retrieval scheme based on three-dimensional variational analysis is used to extract the thermodynamic field of a weather system from Doppler wind measurements. As compared with the traditional retrieval method, with this formulation the proposed scheme is able to find a set of optimal solutions for the pressure and buoyancy perturbations that, in the least squares sense, will simultaneously satisfy three momentum equations and a simplified thermodynamic equation. Therefore, the products of the retrieval are the complete thermodynamic fields in three dimensions. To test the performance of this method in real cases, it is applied to the analysis of a subtropical squall line. The required wind data were synthesized by two C-band Doppler radars during the 1987 Taiwan Area Mesoscale Experiment (TAMEX). The emphasis of this study is devoted to an examination of the validity of the retrieved thermodynamic structure, especially along the vertical direction. The results indicate that the distributions of the retrieved thermodynamic parameters are consistent with the kinematic structure and can be reasonably explained by the conceptual model of a squall line. Evidence is collected that strongly supports the validity of the derived thermodynamic structure. Thus, the applicability of this new retrieval scheme is demonstrated.