Semi-Lagrangian Advection on a Cubic Gnomonic Projection of the Sphere

Abstract

The cubic gnomonic projection of the sphere proposed by Sadourny (1972) is revisited. The gnomonic grid possesses six panels and has the major attraction of being quasi-uniform. Advection is performed using the semi-Lagrangian procedure of McGregor (1993). The departure points are determined accurately, even near panel boundaries. The accuracy is enhanced by a simple grid transformation which provides elements possessing more uniform area. For test cases of solid-body rotation, the semi-Lagrangian scheme performs more accurately on a gnomonic grid than on a standard Gaussian latitude-longitude grid having a similar number of grid points. The scheme is computationally efficient and can be coded without conditional jumps or calls to trigonometric functions.