A Two-Time-Level Semi-Lagrangian Semi-implicit Scheme for Spectral Models

Recently, it has been demonstrated that the semi-implicit semi-Lagrangian technique can be successfully coupled with a three-time-level spectral discretization of the barotropic shallow-water equations. This permits the use of time steps that are much larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian model, without loss of accuracy. In this paper we show that it is possible to further quadruple the efficiency of semi-implicit semi-Lagrangian spectral models beyond that already demonstrated. A doubling of efficiency accrues from the use of the stable and accurate two-time-level scheme described herein. For semi-implicit semi-Lagrangian spectral models a further doubling of efficiency can be achieved by using a smaller computational Gaussian grid than the usual one, without incurring the significant loss of stability and accuracy that is observed for the corresponding Eulerian spectral model in analogous circumstances.