A new estimation of Numerical Diffusivity from Improved Tracer Variance Budget in Eddy-resolving Ocean Simulation

Quantifying how much mixing there is in ocean model solutions is essential for model evaluation and comparison because it is directly related to tracer distribution and water mass transformation, yet also affects the energetics through dissipation and potential energy production. A new tracer variance diagnostic is used that distinguishes between transport and destruction in each direction thus allowing estimation, from the destruction term, of the numerical diffusivity in all directions. The method applies to any finite-volume discretization of the advection-diffusion equation and to most vertical coordinates since it accounts for the evolution of grid-cell thickness.

An idealized, southern-ocean-like eddy-resolving channel, similar to Hill et al., 2012, is used to evaluate the new method in comparison with others. Various advection schemes are considered, including those previously reported but also new high-order, weighted essentially non-oscillatory (WENO) advection schemes. By exploiting this method's specific capability, some averaged diagnostics including vertical profiles of variance destruction and effective diffusivity are presented. Methods to derive a diapycnal effective diffusivity are discussed and results are compared with other estimations.

Reference:
Hill, C, D Ferreira, J-M Campin, J Marshall, R Abernathey and N Barrier,
Controlling spurious diapycnal mixing in eddy-resolving height-coordinate
ocean models – Insights from virtual deliberate tracer release experiments,
Ocean Modelling, 45-46, pp 14-26, 2012, doi:10.1016/j.ocemod.2011.12.001