Analysis of the Gal-Chen–Zhang Single-Doppler Velocity Retrieval

The authors present herein an analysis of a single-Doppler velocity retrieval (SDVR) technique whereby the unobserved wind components are determined from single-Doppler radar data. The analysis is designed to provide information about the behavior and/or sensitivity of the SDVR scheme as a function of various internal and external parameters as well as about observational errors and weights. Results presented for retrieval of both the mean and local flow indicate that the SDVR breaks down if the reflectivity gradient vanishes or if a reflectivity isoline is locally perpendicular to the radar beam. In the absence of reflectivity or radial velocity errors, the mean flow solution is independent of the integration area, the radar location, the signal wavenumber, and the weights. Given perfect radial wind information, error in the reflectivity field degrades the solution. Contrary to the error-free solution, the solution with error depends on the integration area. Error statistics indicate that radial wind information alone is not sufficient to retrieve the local wind. Reduced error norms reveal that an optimal (i.e., reduced error norms) integration area exists that is dependent upon the length of time between radar volume scans, suggesting that the velocity field is not stationary (as was assumed) over these scans.