Single-Doppler velocity retrievals with Phoenix II data: clear air and microburst wind retrievals in the planetary boundary layer

A new three-dimensional single-Doppler velocity retrieval is introduced and tested with reflectivity and radial velocity data. 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. -from Authors