[MITgcm-support] diagnosing numerical diffusion

[Ryan Abernathey]

Hello,

We are working on closing the tracer variance budget in a way that is
consistent with MITgcm numerics. In the variance budget, the distinction
between advection and diffusion is crucial, because diffusion leads to
dissipation, while advection does not. The biggest challenge is that the
nonlinear advection schemes introduce numerical diffusion even with
explicit diffusion set to zero, resulting in a dissipation of variance. We
would like to quantify this effect locally at each grid point.

The idea we have come up with is to define a residual advective flux as the
difference between the advective flux estimated via naive centered
differences (i.e the way the diagnostics such as UVELTH are computed in
pkg/diagnostics/diagnostics_fill_state.F) and the "true" advective flux
calculated by the GAD package (i.e. the diagnostics such as ADVx_TH as
calculated in pkg/generic_advdiff/gad_calc_rhs.F). Our thinking is that
this will tell us something about the "extra" flux introduced by the
nonlinear scheme.

I know that variance is not conserved exactly. We just want to do the best
we can. I am emailing the list to find whether you think this idea is sane
or not. If any of you numerical gurus has a better idea about how this can
be done, I would love to hear your suggestions.

Best,
Ryan
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