Diagnostics of diapycnal diffusion in z-level ocean models

Abstract

In general ocean circulation models (OGCMs) diapycnal diffusion arises notonly from the discretisation of the explicit diffusion, but also by numericallyinduced diffusion, caused, e.g., by common discretisations of advectivetransport.In the present study, three different diagnostics to analyse the meandiapycnal diffusivities of individual tracers (vertically and horizontally) areintroduced: (i) The divergence method based on the work of Ledwellet al. (1998) infers the mean diapycnal diffusivity from theadvection-diffusion equation. (ii) The tracer flux method based on the workof Griffies et al. (2000), that determines the diapycnal flux crossing anisopycnal layer, is modified for the analysis of mean diapycnal diffusivitiesof a passive tracer. (iii) The variance method based on the work ofMorales Maqueda and Holloway (2006) is a more general approachas the diapycnal diffusion is analysed by the variance decay of the totaltracer concentration.These methods can be used for the analysis of the diffusivity of passivetracer independent of the model set-up, e.g. the advection scheme used, butsupport only information about mean diapycnal diffusivity of that tracerfield rather than for each individual layer. The applicability of thesemethods is tested in a set of 1- and 2-dimensional case studies. The effectof vertical advection and of diverging and converging isopycnals is shownseparately. In all three methods used, the transformation of the tracer ontoisopycnals leads to errors in the diagnosed diffusivities. It turns out thatthe tracer flux method is the most robust method and therefore the methodof choice. In order to keep the errors as small as possible, longer time meanvalues should be analysed