The HPM method has been extended to the shallow water equations in spherical geometry. A number of test problems from the NCAR test set for shallow water equations were run. The results for Case 7 are reported in an article appearing in Atmospheric Science Letters.
Here is a movie of the geopototential height stereographic projection for Case 7 of the NCAR set over a 10 day interval: Analyzed 500mb Initial Conditions (800kB).