A Three-Dimensional Semi-Lagrangian Scheme for the Canadian Regional Finite-Element Forecast Model

Abstract

The coupling of a semi-Lagrangian treatment of horizontal advection with a semi-implicit treatment of gravitational oscillations permits longer timesteps than those allowed by a semi-implicit Eulerian scheme. The timestep is then limited by the stability of the explicit treatment of vertical advection. To remove this stability constraint, we propose the use of the semi-Lagrangian advection scheme for both horizontal and vertical advection. This is done in the context of the Canadian regional finite-element weather forecast model that includes a parameterization of the most relevant sub-grid-scale processes. It is shown that the three-dimensional semi-Lagrangian scheme produces stable, accurate integrations using timesteps that far exceed the stability limit for the Eulerian model.