Application of the Semi-Lagrangian Method to Global Spectral Forecast Models

Abstract

ABSTRACT Since the original demonstration of the efficiency advantage of the semi-Lagrangian semi-implicit method over a decade ago by André Robert, this numerical integration scheme is being used in an increasing range of atmospheric models. Most of the applications have been in grid point models, where it has been shown that this method permits the use of time steps that are much larger than those permitted by the Courant-Friedrich-Levy (CFL) criterion for the corresponding Eulerian models. In this paper we concentrate on its application in spectral models. A review of the steps towards its operational implementation in global spectral forecast models is presented. Linear stability and geometric aspects are considered for the problem of simple advection on the Gaussian grid that is used in spectral models. Nonlinear stability, accuracy and efficiency of the approach are illustrated by its application to a spectral model of the shallow water equations. Application in multilevel spectral primitive equations models is demonstrated with the Canadian Global Spectral Forecast Model and a high resolution version of the ECMWF Forecast Model.