Abstract

A class of semi-implicit time integration schemes is proposed for use in atmospheric modelling. Various explicit predictor-corrector methods can be combined with an implicit treatment of the linear terms responsible for fast modes in order to improve computational stability. Linear analysis is used to identify promising algorithms. These are then tested in a finite volume shallow water model on an icosahedral grid. This framework has been developed at Environment Canada and will be extended to a more complete, three-dimensional atmospheric model in the future. Experiments with standard test cases show that the proposed time schemes allow for stable integrations with relatively long time-steps, while maintaining a sufficient level of accuracy. In particular, they are more robust than the traditional, single-stage semi-implicit method using the leapfrog discretisation and do not require a time filter to control the computational mode.