[Mitgcm-support] Cause for small degradation of SST

[mitgcm-support at dev.mitgcm.org]

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It was shown before that, the assimilation improves the comparison of
subsurface temperature with TAO data, but degraded SST slightly (see
here)[1] . After looking at the assimilation more closely, salinity
effect doesn't seem to be a major cause for the smalll degradation of
SST because there are a few points outside the warm pool where SST is
also degraded. Another possible explanation is offerred below. Temporal
evolution of temperature is governed by dT/dt = (1) surface heat flux +
(2) advection + (3) diffusion The assimilation assumes model errors to
be due to uncertainties in surface forcings and initial condition (the
latter is less important in the tropics due to the fast time scale). The
adjustment of heat flux aims to reflect error associated (1). The
adjustment of wind stress aims to reflect error associated with (2)
(horizontal advection as well as heaving). Error of (3) was not
accounted for. In fact, the adjoint assimilation model uses a crude
formulation of diffusion (i.e., time-mean mixing coefficients
pre-computed by KPP). So it's not surprising to see improvement below
the mixed layer (where much of dT/dt is apparently due to advection),
and degradation in the mixed layer where diffusion is very important.
There are 2 ways to improve SST: (1) use full kpp in the forward model
to minimize model error associated with diffusion in the mixed layer,
and (2) treat mixing coefficient as time-dependent control variables.

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[1] http://escher.jpl.nasa.gov:2000/hosts/escher/escher4/medea/tlee/FIG_FORUM/plot_statt_ave.jpg