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Grid-scale noise in surface vertical tracer diffusion #110

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aekiss opened this Issue Sep 12, 2018 · 7 comments

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aekiss commented Sep 12, 2018

@ChrisC28 noticed that there is grid-scale noise in monthly averages of these fields for the top 5-10 metres in the Indian Ocean:

	float salt_vdiffuse_impl(time, st_ocean_sub01, yt_ocean_sub01, xt_ocean_sub01) ;
		salt_vdiffuse_impl:long_name = "implicit vert diffusion of Practical Salinity" ;
	float salt_vdiffuse_diff_cbt(time, st_ocean_sub01, yt_ocean_sub01, xt_ocean_sub01) ;
		salt_vdiffuse_diff_cbt:long_name = "vert diffusion due to diff_cbt for Practical Salinity" ;
	float temp_vdiffuse_impl(time, st_ocean_sub01, yt_ocean_sub01, xt_ocean_sub01) ;
		temp_vdiffuse_impl:long_name = "implicit vert diffusion of heat" ;
	float temp_vdiffuse_diff_cbt(time, st_ocean_sub01, yt_ocean_sub01, xt_ocean_sub01) ;
		temp_vdiffuse_diff_cbt:long_name = "vert diffusion of heat due to diff_cbt" ;

e.g. in /g/data3/hh5/tmp/cosima/access-om2-01/01deg_jra55v13_iaf/output090/ocean/rregionindian_ocean_west.nc

screen shot 2018-09-12 at wed 12-9 10 14am
screen shot 2018-09-12 at wed 12-9 10 16am
(these salt fluxes also have blocky features due to the salt restoring used: #74)

screen shot 2018-09-12 at wed 12-9 10 17am 1
screen shot 2018-09-12 at wed 12-9 10 18am

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russfiedler commented Sep 12, 2018

The blockiness was an issue that we kind of glossed over yesterday at the start of the TWG meeting. i.e. implement "patch" interpolation for the salt field to be used in restoring.

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aekiss commented Sep 15, 2018

Agreed - another reason to smooth this restoring field.

FWIW MLD and vorticity look OK in this region (though MLD has some blockiness from the restoring).

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aekiss commented Sep 15, 2018

...however MLD has grid-scale noise in the equatorial Pacific and Atlantic (click to enlarge):

screen shot 2018-09-15 at sat 15-9 6 25pm

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nichannah commented Sep 16, 2018

Is this motivation to try again with the 2nd order conservative mapping option for the 0.1 deg? The software we used has had another release since we set up the 1 and 0.25 deg remapping.

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aekiss commented Dec 6, 2018

here's the blocky salt restoring issue #74

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StephenGriffies commented Dec 6, 2018

I have two comments, diametrically opposed but nonetheless relevant.

A/ I expect to see a noisy tendency from the diffusion operator in regions of high forcing and eddy activity. The reason is that the diffusion operator is the Laplacian of the tracer field, so that the operator preferentially hits the high wave number (i.e., noisy) portion of the tracer field. The resulting tracer field is smoothed since the diffusion operator acts to dissipate the high wave number power.

A checkerboard or zig-zag example is useful to consider. Namely, let the tracer have structure sin(2pi *k), where k is the vertical grid cell index. This zig-zag vertical pattern will be smoothed by the diffusion operator. But if we look at the tendency arising from the diffusion operator, it will indeed be noisy, which again is what it should be since diffusion is preferentially dissipating the noise.

One way to test the above hypothesis is to look at the tracer field to see if it too is noisy. My guess is that it will be less noisy than the diffusion operator, which means the diffusion is doing what it should do. Namely, it is acting to kill variance that is piling up at the grid scale due to the direct cascade of tracer variance.

B/ Richardson number based vertical mixing schemes, such as KPP, often produce noise in the tracer field and mixed layer depth due to decoupling between adjacent columns. This issue tends to be well seen in the tropics.

It is a well known problem that arises since the 1d vertical mixing schemes allow for columns to partly decouple, especially in regions where Coriolis is small. Hallberg has a proposed fix for MOM6 that seems to work. It is based on a particular choice for grid averaging for computing the Richardson number. He introduced the code just recently into MOM6. Look for

subroutine Calc_kappa_shear_vertex

in

https://github.com/NOAA-GFDL/MOM6/blob/dev/gfdl/src/parameterizations/vertical/MOM_kappa_shear.F90

I believe it could be ported to MOM5 with some effort.

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aekiss commented Dec 7, 2018

Thanks @StephenGriffies for your detailed explanation.

SSS is indeed smooth, e.g. this daily average from /g/data3/hh5/tmp/cosima/access-om2-01/01deg_jra55v13_iaf/output090/ice/OUTPUT/iceh.2000-02-01.nc
screen shot 2018-12-07 at fri 7-12 10 58am

Depth profiles of the monthly-mean implicit vertical salt diffusion have opposite extrema at the surface and the first level down at noisy points
screen shot 2018-12-07 at fri 7-12 10 28am

whereas depth profiles at non-noisy points have only the surface extremum
screen shot 2018-12-07 at fri 7-12 10 26am

Monthly mean salinity profiles (from /g/data3/hh5/tmp/cosima/access-om2-01/01deg_jra55v13_iaf/output090/ocean/ocean.nc) look smooth and unremarkable at the noisy points:
screen shot 2018-12-07 at fri 7-12 11 20am
...with no obvious difference from at the non-noisy points:
screen shot 2018-12-07 at fri 7-12 11 30am
(ignore the horizontal lines with no marker points - these are a plotting glitch).

So
A/ I think you're right, diffusion is doing its job well and keeping the salinity field vertically smooth. On the other hand, this could be interpreted as compensating errors, i.e. the diffusion is compensating for spurious generation of grid-scale variance by other terms, so the diffusion is unphysical?

B/ This column decoupling could well be what is producing the variance in the horizontal. Thanks for the link to Bob's MOM6 fix.

We used the KDS75 grid, with surface vertical resolution of about 1.1m. Perhaps there are some tweaks we could adopt from your recent KPP paper (Van Roekel et al 2018)?

It is worth noting that the Indian Ocean figures in the posts above are monthly averages. This animation of two consecutive months from /g/data3/hh5/tmp/cosima/access-om2-01/01deg_jra55v13_iaf/output090/ocean/rregionindian_ocean_west.nc shows there's little persistence in the noise from one monthly average to the next. So I expect there is some cancellation of the noise in the monthly average, i.e. the noise at each timestep is larger (perhaps much larger, depending on the timescale of the processes generating this noise).

screen shot 2018-12-07 at fri 7-12 10 13am

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