Abstract
A new three-dimensional single-Doppler velocity retrieval is introduced and tested with reflectivity and radial velocity data gathered during the Phoenix II field program near Boulder, Colorado. This retrieval is based on reflectivity conservation (with provision for raindrop fall speed), the incompressibility condition, and a temporal constraint on the velocity field. Two temporal constraints are considered: velocity stationarity and Taylor's frozen turbulence approximation (velocity stationarity in a moving reference frame). It is demonstrated that either of these temporal constraints can be used to derive a second conserved scalar from the original conserved scalar (reflectivity). This two-scalar system is, in general, overdetermined, but a least-squares formulation reduces the problem to a Poisson equation for a pseudostreamfunction. The requisite boundary conditions arise naturally from the least-squares formulation and require only single-Doppler measurements for their evaluation.
The new retrieval is tested with Phoenix II data for an optically clear convective planetary boundary layer (22 June 1984) and for a moderate reflectivity microburst (31 May 1984). The input data consist of three consecutive volume scans of radial velocity and reflectivity data from an X-band Doppler radar (NOAA radar C). To validate the retrievals, the retrieved winds are projected into the direction of a second Doppler radar (NOAA radar D) and a direct comparison made with the observed radial winds of that second radar. Experiments focus on data smoothing, optimal time constraints, and raindrop terminal velocity parameterizations. For an optimal treatment of these processes, good agreement is found between the observed and retrieved wind components in both datasets.
