Conservation Properties of the Hamiltonian Particle-Mesh method for the Quasi-Geostrophic Equations on a sphere

The Hamiltonian particle-mesh (HPM) method is used to solve the Quasi-Geostrophic model generalized to a sphere, using the Spherepack modeling package to solve the Helmholtz equation on a colatitude-longitude grid with spherical harmonics. The predicted energy conservation of a Poisson system is shown to be approximately retained and statistical mean-eld theory is veried.