Before revision: Energy preserving reduced-order models are developed for the rotating thermal shallow water (RTSW) equation in the non-canonical Hamiltonian /Poisson form . The RTSW equation is discretized in space by the skew-symmetric finite-difference operators to preserve the Hamiltonian structure.
After revision: Energy preserving reduced-order models are developed for the rotating thermal shallow water (RTSW) equation in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-difference operators to preserve the Hamiltonian structure.