A Variable Resolution Global Model Based upon Fourier and Finite Element Representation

Abstract

Abstract We describe the development and preliminary testing of a numerical scheme designed to predict the global circulation which can also telescope into local subdomains of enhanced vertical and horizontal resolution. The accuracy of the method appears intermediate to the accuracy of purely spectral and grid point models, but it is especially well suited to study certain practical predictability problems within limited area domains. The approach is based upon separate Galerkin approximations in longitude and latitude. The longitude variation is discretized in terms of truncated Fourier series, while the latitude structure of the Fourier amplitudes is depicted as sums of piecewise continuous linear functions (finite elements). The vertical structure is also described in terms of finite elements. The technique is especially well suited to fine resolution of polar caps within which a given wavenumber truncation ensures enhanced local resolution in longitude, and where a refined element size can also be im...