A Three-Dimensional Variational Data Analysis Method with Recursive Filter for Doppler Radars

In this paper, a new method of dual-Doppler radar wind analysis based on a three-dimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasi-Newton conjugate-gradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem. The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumulation associated with such integration is avoided. As a result, the method is less sensitive to the vertical boundary uncertainties.