[Mitgcm-support] Choosing constant diffusivities for package MIX

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Choosing constant diffusivities for package MIX
===============================================

Package MIX requires up to five input files.  These are:

 mix_viscArFile = vertical viscosity
 mix_diffKrFile = vertical diffusivity
 mix_KAPGMwFile = isopycnal diffusivity
 mix_K13File    = zonal isopycnal slope * 2
 mix_K23File    = meridional isopycnal slope * 2

The last two files are needed to reconstruct diffusivity
tensor.

Input files can specify either constant or time-varying
coefficients.  This posting discusses initial choice of
"constant" coefficients for the 1997 adjoint model
optimization.  The coefficients are based on 1997 output
files from control run c20000630:

 KPPAZave_08_08.*
 KPPKZTave_08_08.*
 KAPGMave_08_08.*
 K13ave_08_08.*
 K23ave_08_08.*

Input files were created using
triton:~dimitri/mitgcm/output/tscop_global/c20000630y1997/mk_mean3.m
Follows a summary of what was done for each input file.

KAPGM1997mean:
Used 1997-mean isopycnal diffusivity.

K131997mean_lim_p02 and K231997mean_lim_p02:
Used 1997-mean isopycnal slopes but with 10-day-average
values clipped to +/-.02 (1% slope) to avoid problem
with large slopes discussed in an earlier posting:
http://escher.JPL.NASA.GOV:2000/HyperNews/get/forums/cvslog/2/12.html

KPPAZ1997meanKPPsummer and KPPKZT1997meanKPPsummer:
These are the vertical viscosity and diffusivity files,
respectively.  The files contain summer mean KPP values
north of 15 deg N and south of 15 deg S; they contain annual
mean values within an equatorial band (10 deg S to 10 deg N);
in the transition areas the averaging period going away from
the equatorial band decreases by 20 days per grid point, until
only the summer months are included in the average.  This
scheme is needed because an earlier test using annual mean
mixing coefficients everywhere was dominated by winter-time
convections and destroyed surface seasonal cycle.  The next
two figures illustrate this effect.

http://escher.jpl.nasa.gov:2000/hosts/triton/dm1/dimitri/mitgcm/output/tscop_global/c20000630y1997/FIGS/FIG2.ps
http://escher.jpl.nasa.gov:2000/hosts/triton/dm1/dimitri/mitgcm/output/tscop_global/c20000630y1997/FIGS/FIG3.ps

Top panel of first figure is a meridional slice of annual
mean vertical diffusivity in the Atlantic.  Note how the
diffusivity values are dominated by wintertime convection,
especially in the North Atlantic.

Middle panel shows a 10-day average of vertical diffusivity
during boreal summer.  Notice that the annual mean vertical
diffusivity is up to 4 orders of magnitude larger than
typical summer values.

Bottom panel shows vertical diffusivities constructed from
mean summer profiles as discussed above.  Notice that the
the large values due to winter convection are gone and that
there is no sharp transitions between equatorial band and
rest of domain.  The justification for withholding winter
mixing from the average is that winter convection will be
separately accomodated by the models convection scheme.

Second figure shows results from three separate model
integrations with 1997 surface boundary conditions.  The
three panels show vertical profiles of temperature anomaly
at a location of deep convection in the North Atlantic
as a function of 1997 calendar day.  Top panel is from the
control integration c20000630.  It displays a seasonal cycle
as expected.  Thin black line is the KPP OBL depth.  Middle
panel shows results when using annual mean vertical
diffusivity.  The seasonal cycle is unrealistic because deep
convection occurs all year round. Bottom panel shows results
when using summer mean diffusivity as discussed earlier.
Although different from the control integration (top panel)
the seasonal cycle is much more realistic than in the middle
panel.