Semi-Lagrangian treatment of advection on the sphere with accurate spatial and temporal approximations

This paper is devoted to the numerical solution of the transport equation on the sphere, aimed at the implementation of accurate spatial interpolation procedures and of accurate reconstruction of the characteristic lines in a semi-Lagrangian framework. Since nonregular grid and pole singularity can both affect accuracy of the numerical approximation, proper account is taken for these problems. It is shown on a literature test case that accurate spatial approximation highly improves the accuracy of the method, having a greater impact than accurate temporal approximation. The algorithms can be introduced into general circulation models, where accurate temporal approximation is expected to play a major role.