NUMERICAL VARIATIONAL ANALYSIS FORMULATED UNDER THE CONSTRAINTS AS DETERMINED BY LONGWAVE EQUATIONS AND A LOW-PASS FILTER

Abstract

The ?timewise localized? variational formalism of the numerical variational analysis method is used (1) to filter and suppress unnecessary high-frequency noises contained in initial and forecast fields and (2) to obtain dynamically sound initial values in the areas lacking data. A set of nonlinear longwave equations and a low-pass filter minimizing local changes are used in this paper as dynamical constraints. Also proposed in this study is a technique to assure the convergence of a numerical solution of the nonlinear Euler equations by an iterative process. Three applications of the method are presented. The first two examples demonstrate that the initial guess in the iterative process influences significantly the speed of convergence. The last example is an application to the 500-mb analysis of hurricane Dora, 1964, and demonstrates a reasonable analysis in the data-sparse area where the hurricane was located at 1200 GMT on Sept. 8, 1964.