An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme

Abstract The semi‐implicit semi‐Lagrangian integration technique enables numerical weather prediction models to be run with much longer timesteps than permitted by a semi‐implicit Eulerian scheme. the choice of timestep can then be made on the basis of accuracy rather than stability requirements. to realize the full potential of the technique, it is important to maintain second‐order accuracy in time; this has previously been achieved by applying it in the context of a three‐time‐level integration scheme. In this paper we present a two‐time‐level version of the technique which yields the same level of accuracy for half the computational effort. Unlike other efficient two‐time‐level schemes, ours does not rely on operator splitting. We apply this scheme to a variable‐resolution barotropic finite‐element regional model with a minimum gridlength of 100 km, using timesteps of up to three hours. the results are verified against a control run with uniformly high resolution, and are shown to be of similar accuracy to those of a semi‐implicit Eulerian integration with a timestep of 10 minutes.