Quadratic Galerkin Finite Element Schemes for the Vertical Discretization of Numerical Forecast Models

Abstract

A finite element scheme with second-order basis functions is introduced for vertical discretization using a spectral model for horizontal discretization. The basis functions are required to be continuous, and no assumption is made concerning the continuity of their derivatives. The quadratic elements require about the same computation time as linear elements. The performance of this scheme was investigated by a series of test forecasts, which resulted in an improved forecast skill for the finite element scheme. Fifty-day integrations showed a substantial impact of the discretization on the model climate.