Another reason why simple discretizations of rotated diffusion operators cause problems in ocean models: Comments on "Isoneutral diffusion in a z-coordinate ocean model"

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and vershooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not.