SUMMARY

The local balance equation for the total energy in numerical ocean general circulation models (OGCMs) gen-erally possesses nonconservative production/destruction terms that result from physical inconsistencies between the dynamical and thermodynamical equations used by such models. Because such production/destruction terms are most likely to be unphysical, they are potentially responsible for spurious forces in the momentum equations and for spurious diabatic terms in the thermodynamic equations, and hence likely associated with potential errors in the simulated ocean currents and water masses. Assessing the importance of such terms requires a strategy to identify and quantify them. It is the main purpose of this paper to develop a theoretical framework forming the basis for a practical determination of such terms. At least four main sources of errors are identified. They arise from, by decreasing order of importance: 1) the kinetic energy dissipation term that in reality would be converted into heat, but which is “hanging ” in OGCMs; 2) assuming potential or conservative temperature to be a conservative quantity; 3) the interaction of the Boussinesq approximation with the parameterisations of turbulent mixing of temperature and salinity; 4) some adiabatic compressibility effects due to the Boussinesq approximation. In principle, a fifth source of error in the form of spurious numerical energy sources/sinks must also exist in OGCMs. Apart from 1), most of the nonconservative energy sources/sinks are not sign definite, allowing for possibl