A global semi-Lagrangian spectral model of the shallow water equations with variable resolution

A new formulation of a semi-implicit, semi-Lagrangian spectral method is given together with a conformal mapping of the underlying Gaussian grid. The mapping based on the Schmidt transformation focuses grid resolution on a particular region. The advective form of the vorticity–divergence equations allows the conformal map to be incorporated in a semi-Lagrangian transport step while maintaining an efficient spectral transform algorithm. The shallow water equations on the sphere are solved to test the variable resolution spectral model. By focusing on a specified location, local details of the flow are more accurately resolved. Accuracy and stability of the method are compared with uniform spectral solutions.