Diagnostics of diapycnal diffusion in z-level ocean models

Abstract

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.

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