A single-Doppler radar velocity retrieval method, based on an optimally determined moving frame of reference, is developed. This method enables the recovery of the complete three-dimensional wind field using reflectivity, and radial wind observations, detected by a single Doppler radar over multiple volume scans. This method first computes a set of optimal moving speeds (U, V, W), which can be functions of the height. It is considered optimal in the sense that when a reference frame is traveling at this speed, as much of the radar reflectivity, interpolated onto this frame can be conserved as possible. The perturbation velocities (u′, v′, w′) are then solved simultaneously, with respect to the moving speeds, by minimizing a cost function through the three-dimensional variational (3D-Var) approach. This cost function consists of a set of weak constraints, mainly the equation for radar reflectivity conservation, the continuity equation, the geometric relationship between the radar-observed radial wind and the Cartesian winds, and a smoothness filter. Finally, by adding the optimal moving speed to the perturbation velocities, a complete three-dimensional wind field is obtained.The performance of this method is tested under different scenarios, including cases with deep convections, embedded in an environment without mean wind, with constant mean wind, with vertical wind shear of the horizontal mean wind, and with differences in the radar observational time at each grid point within one volume scan are considered.This method is demonstrated to be feasible by applying it to recover the three-dimensional wind structure of a subtropical squall line from Doppler radar data, collected during the 1987 Taiwan Area Mesoscale Experiment (TAMEX).
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