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An energy preserving reduced order model is developed for the nontraditionalshallow water equation (NTSWE) with full Coriolis force. The NTSWE in thenoncanonical Hamiltonian/Poisson form is discretized in space by finitedifferences. The resulting system of ordinary differential equations isintegrated in time by the energy preserving average vector field (AVF) method.The Poisson structure of the NTSWE in discretized exhibits a skew-symmetricmatrix depending on the state variables. An energy preserving, computationallyefficient reduced-order model (ROM) is constructed by proper orthogonaldecomposition with Galerkin projection. The nonlinearities are computed for theROM efficiently by discrete empirical interpolation method. Preservation of thesemi-discrete energy and the enstrophy are shown for the full order model, andfor the ROM which ensures the long term stability of the solutions. Theaccuracy and computational efficiency of the ROMs are shown by two numericaltest problems

Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation