Before revision:  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 . The accuracy and computational efficiency of the ROMs are shown by a numerical test problem .
After revision:  total mass, total buoyancyand total potential vorticity , by the reduced-order solutions are demonstrated which ensures the long term stability of the solutions while exhibiting several orders of magnitude computational speedup over the FOM .