Energetics of lateral eddy diffusion/advection：Part Ⅳ. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy (GPE) source and sink due to stirring and cabbeling associated with sigma diffusion/advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography;the excessive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advection diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffusion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.