New Formulations of Dual-Doppler Wind Analysis

Abstract

New formulations of three-dimensional dual-Doppler wind analysis are presented. The new formulations are conceptually simple, preserve the radial nature of the wind observations, involve only one analysis step (i.e., all constraints are imposed in one functional), and are in a form in which the well-posed condition can most readily be checked. These techniques minimize functionals that incorporate the anelastic mass conservation equation and the radial wind observations as strong or weak constraints. The minimizations are accomplished by appealing directly to the Euler?Lagrange equations and proceed most naturally in the ?coplane? cylindrical polar coordinate system. In one method, the anelastic mass conservation equation is applied as a weak constraint, while the radial wind observations are imposed as strong constraints. This results in an algorithm similar to the Armijo wind analysis but with provision for vertical velocity data specification on both upper and lower boundaries (as in the O?Brien adjustment). In another method, the anelastic mass conservation equation is imposed as a strong constraint, while the radial wind observations are used as weak constraints. In a third method, both mass conservation and the radial wind observations are used as weak constraints. In each of the latter two formulations, the analysis reduces to solving a second-order linear partial differential equation, the solution of which is unique. As in Armijo?s research, the shape of the analysis domains must be suitably restricted if the problems are to be well posed.