Before revision:  The nonlinearities in the ROM are efficiently computed by discrete empirical interpolation method (DEIM) . Preservation of the energy (Hamiltonian), and other conserved quantities ; total mass, total buoyancyand total potential vorticity , by the reduced-order solutions are demonstrated which ensures the long term stability of the reduced-order solutions .
After revision:  The nonlinearities in the ROM are efficiently computed by discrete empirical interpolation method (DEIM) . Preservation of the energy (Hamiltonian), and other conserved quantities , i.e. mass, buoyancy, and total vorticity show that the reduced-order solutions are demonstrated which ensures the long term stability of the reduced-order solutions .