Single-Doppler Wind Retrieval in the Moving Frame of Reference

Abstract

A single Doppler radar analysis scheme is developed, and three-dimensional wind fields am retrieved from single Doppler radar reflectivity and radial velocity fields. The retrieval is based on two assumptions: 1) the Lagrangian conservation of the radar reflectivity and 2) the steadiness of the eddy structures in the wind field. To least violate these assumptions, a moving frame of reference is found where (in the least square sense) the observations are as stationary as possible. Multiple time levels of observations are used to avoid ill-conditioned computations. The retrieval equations, that is, the conservation equation of reflectivity and the relationship between the total wind and its radial component for several time levels, form a simple linear system. This linear system is overdetermined with respect to the three unknown Cartesian components u, v, and w of the vector wind. Thus u, v, and w are solved in the least square sense. Dual Doppler radar analyses are performed to provide verifications for the single-Doppler retrievals. The results show very good agreement between the wind fields from single-Doppler retrievals and the dual-Doppler analyses. The important findings from various experiments include that 1) the weighting of each term in the cost function is crucial to the retrieval accuracy; 2) performing the retrievals in the moving frame improves the results significantly; and 3) proper filtering in space and time can reduce errors in retrieved wind fields. Two independent cases are studied to test the robustness of the scheme.