Diagnostics of diapycnal diffusion in z-level ocean models

In general ocean circulation models (OGCMs) diapycnal diffusion arises not only from the discretisation of the explicit diffusion, but also by numerically induced diffusion, caused, e.g., by common discretisations of advective transport. In the present study, three different diagnostics to analyse the mean diapycnal diffusivities of individual tracers (vertically and horizontally) are introduced: (i) The divergence method based on the work of Ledwell et al. (1998) infers the mean diapycnal diffusivity from the advection-diffusion equation. (ii) The tracer flux method based on the work of Griffies et al. (2000), that determines the diapycnal flux crossing an isopycnal layer, is modified for the analysis of mean diapycnal diffusivities of a passive tracer. (iii) The variance method based on the work of Morales Maqueda and Holloway (2006) is a more general approach as the diapycnal diffusion is analysed by the variance decay of the total tracer concentration. These methods can be used for the analysis of the diffusivity of passive tracer independent of the model set-up, e.g. the advection scheme used, but support only information about mean diapycnal diffusivity of that tracer field rather than for each individual layer. The applicability of these methods is tested in a set of 1- and 2-dimensional case studies. The effect of vertical advection and of diverging and converging isopycnals is shown separately. In all three methods used, the transformation of the tracer onto isopycnals leads to errors in the diagnosed diffusivities. It turns out that the tracer flux method is the most robust method and therefore the method of choice. In order to keep the errors as small as possible, longer time mean values should be analysed.