Application of the Semi-Lagrangian Method to a Spectral Model of the Shallow Water Equations

Abstract

Previous tests with grid-point numerical weather prediction models have shown that semi-Lagrangian schemes permit the use of time steps that are much larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian models, without reducing the accuracy of the forecasts. Thus model efficiency is improved because fewer time steps are needed to complete the forecast. In a first step to see if similar results can be achieved in spectral models, Ritchie, in a previous study, applied interpolating and noninterpolating semi-Lagrangian treatments of advection to the problem of simple advection by a steady wind field on a Gaussian grid. This present paper combines these treatments of advection with the semi-implicit scheme in a spectral model of the shallow water equations expressed in vector momentum form. Model formulations are presented and intercomparison experiments are performed. It is shown that both interpolating and noninterpolating semi-Lagrangian schemes can be applied accurately and stably to a spectral model of the shallow water equations with time steps that are much larger than the CFL limit for the corresponding Eulerian model.