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Grid-scale noise in surface vertical tracer diffusion #110
@ChrisC28 noticed that there is grid-scale noise in monthly averages of these fields for the top 5-10 metres in the Indian Ocean:
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
I believe it could be ported to MOM5 with some effort.
Thanks @StephenGriffies for your detailed explanation.
Monthly mean salinity profiles (from
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