A Variational Method for the Analysis of Three-Dimensional Wind Fields from Two Doppler Radars

Abstract

This paper proposes a new method of dual-Doppler radar analysis based on a variational approach. In it, a cost function, defined as the distance between the analysis and the observations at the data points, is minimized through a limited memory, quasi-Newton conjugate gradient algorithm with the mass continuity equation imposed as a weak constraint. The analysis is performed in Cartesian space. Compared with traditional methods, the variational method offers much more flexibility in its use of observational data and various constraints. Using the radar data directly at observation locations avoids an interpolation step, which is often a source of error, especially in the presence of data voids. In addition, using the mass continuity equation as a weak instead of strong constraint avoids the error accumulation and the subsequent somewhat arbitrary adjustment associated with the explicit vertical integration of the continuity equation. The current method is tested on both model-simulated and observed datasets of supercell storms. It is shown that the circulation inside and around the storms, including the strong updraft and associated downdraft, is well analyzed in both cases. Furthermore, the authors found that the analysis is not very sensitive to the specification of boundary conditions and to data contamination. The method also has the potential for retrieving, with reasonable accuracy, the wind in regions of single-Doppler radar coverage.