HAMILTONIAN TRUNCATION OF THE SHALLOW-WATER EQUATION

In this Letter, we describe a truncation of the Eulerian description of the shallow water equation of climate modeling to a finite-dimensional Hamiltonian system. The technique is to use an isomorphism from a semidirect product Poisson manifold to a direct product of Poisson manifolds, both of whose components are truncatable to finite-dimensional Poisson manifolds, based on Moser's theorem on volume elements.