Gravitational potential energy source/sink associated with different oceanic model parameterizations can be used as a criterion in evaluating model’s performance. The upper bound of energy associated with lateral diffusion/advection is estimated at 100GW. Parameterizations associated with energy much larger than the bound are unphysical.

    Gravitational Potential Energy (GPE) change due to horizontal/isopycnal/sigma eddy diffusion and advection is examined.  It is shown that GPE source/sink in isopycnal coordinates (0.076TW for diffusion and 0.3TW for advection) is closely linked to physical property distribution, such as temperature, salinity and velocity. Although isopycnal coordinates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eulerian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge. GPE source/sink due to stirring and cabbeling associated with sigma diffusion/advection are too big (130TW and 13TW), and they are not closely linked to physical property distribution. The excessive amount of GPE source/sink associated with sigma diffusion/advection raises a very serious question whether lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable.