A Finite-Element Formulation for the Vertical Discretization of Sigma-Coordinate Primitive Equation Models

TLDR: In this paper, a finite-element formulation for the vertical structure of primitive equation models has been developed, which is a variant of the Galerkin procedure in which the dependent variables are expanded in a finite, set of basis functions and then the truncation error is orthogonalized to each of the basis functions.

Abstract: A finite-element formulation for the vertical structure of primitive equation models has been developed. The finite-element method is a variant of the Galerkin procedure in which the dependent variables are expanded in a finite, set of basis functions and then the truncation error is orthogonalized to each of the basis functions. In the present case, the basis functions are Châpeau functions in sigma, the vertical coordinate. The procedure has been designed for use with a semi-implicit time discretization algorithm. Although this vertical representation has been developed for ultimate implementation in a three-dimensional finite-element model, it has been first tested in a spherical harmonic, baroclinic, primitive equations model. Short-range forecasts made with this model are very encouraging.