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

A time-dependent focusing grid works together with the formulation of a semi-implicit, semi-Lagrangian spectral method for the shallow-water equations in a rotated and stretched spherical geometry. The conformal mapping of the underlying discrete grid based on the Schmidt transformation, focuses grid on a particular region or path with variable resolution. A new advective form of the vorticity-divergence equations allows for the conformal map to be incorporated while maintaining an efficient spectral transform algorithm. A shallow water model on the sphere is used to test the spectral model with variable resolution. We are able to focus on a specified location resolving local details of the flow. More importantly, we could follow the features of the flow at all time.