A Variational Analysis Method for Retrieval of Three-Dimensional Wind Field from Single-Doppler Radar Data

Abstract

Abstract A variational method for retrieval of the three-dimensional wind field from single-Doppler radar observations is developed and tested. The method uses the conservation equation for reflectivity and the continuity equation as a constraining model. Weak and strong constraint formalisms in data analysis am reviewed and compared using a one-dimensional advection equation for reflectivity considered as a passive tracer. The authors show that a model equation should be used as a weak constraint when the model does not predict exactly the evolution of the observations (such as the conservation equation for reflectivity). Consequently, the variational method presented here combines both formalisms: the conservation equation for reflectivity is used as a weak constraint, while the continuity equation is used as a strong constraint. The method is applied to retrieve detailed three-dimensional wind field of a microburst observed by two C-band Doppler radars during the Phoenix II Convective Boundary Layer Ex...