Least Squares Retrieval of Microburst Winds from Single-Doppler Radar Data

Abstract

A least squares (LS) method is developed for retrieving low-altitude winds from single-Doppler radar scans. The method is tested with Denver airport microburst data and the results compared with the previously developed simple adjoint (SA) method. It is found that the LS method is slightly superior to the SA method for the microburst data obtained with fast radar scans (?τ ≈ 60 s) but will become inferior to the SA method if the radar scans are twice as long (?τ ≈ 120 s). Four previously developed detailed techniques for the SA method are used to improve the LS retrievals, and these include (i) using multiple-time-level data, (ii) imposing the weak divergence and weak vorticity constraints, (iii) retrieving the eddy coefficient and time-mean forcing term, and (iv) using the, observed time-mean radial wind as a weak constraint. Because the control equation is used as a weak constraint in a finite-difference form, the LS method depends more on the smoothness constraints but is less sensitive to equation error and is computationally much more efficient than the SA method. An objective way for the selections of weights is also proposed and tested in this paper.