Machine Learning based vertical diffusivity in EPBL mixing scheme used for ocean surface boundary layer

[aakashsane]

Requesting to add a few subroutines to the EPBL vertical mixing module. 
These changes enhances the existing vertical diffusivity used in EPBL with machine learning, and makes it constrained on second moment closure. Using symbolic regression and empirical fitting, a shape function ( g(\sigma) ) has been formulated that responds to changes in the surface forcing (Latitude, wind stress, surface buoyancy flux, boundary layer depth). g(\sigma) goes from zero to 1 and its skewness changes as per surface forcing conditions. The velocity scale, v_0, is an approximation that depends on (Coriolis f, ustar, and surface buoyancy flux).
When v_0 is combined with g(\sigma) and multiplied by the energetics based boundary layer depth h, i.e \nu = . g(\sigma) X v_0 X h, we get a diffusivity which is constrained on a second moment closure.

The subroutines are activated by using the flags:

1. Equation_Discovery_shape = True
2. Equation_Discovery_velocity = True
3. Equation_Discovery_velocity_h = False
4. activates the new equation for shape function. 2. Activates velocity scale equations that approximate neural networks as described in Sane et al. 2023. 3. Is a new velocity scale that includes boundary layer depth as input and agrees with well known scaling.
   Either 2. or 3. should be 'True', both cannot be True or False.

The new subroutines have been tested by running the OM4 configuration (Adcroft et al. 2019) and comparing the simulation against observations (SST from WOA and Mixed Layer Depth from ARGO). The equations are approximating the neural networks. The neural network based diffusivity has been published in Sane et al. 2023 ( https://doi.org/10.1029/2023MS003890 ) and the equations based diffusivity will soon be submitted for a publication.
The changes have also been tested using the scale test.

All the commits can be squashed into one as only the latest is relevant.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 40.94%. Comparing base (f90b071) to head (992f266).
Report is 5 commits behind head on dev/gfdl.

Additional details and impacted files

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  Branches      15834     1013   -14821     
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- Hits          30829     2165   -28664     
+ Misses        47509     2938   -44571     
+ Partials       5815      185    -5630     

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[adcroft]

I can't (shouldn't) make the final approval on this since I'm involved in the research, but there are some obvious things that need to be changed before someone else reviews the PR. Once these are cleaned up, my take is it will be smooth sailing.

You added several files that I think should not be included:

• .testing/tc4/Makefile is generated by autoconf using the Makefile.in template
• .testing/gen_data.dSYM/Contents.Info.plist - looks like something leftover from your a mac build process
• .testing/gen_grid.dSYM/Contents.Info.plist - ditto

Please remove these files. I believe the only file you meant to submit changes for is MOM_energetic_PBL.F90. There's also a real variable with missing unit documentation which I added a separate inline comment for.

[adcroft]

This real variable needs units in the comment (looks like it should be the same as CS%vo)

[aakashsane]

Thanks for pointing it out.
I have completed:

1. Units added to that variable.
2. All the files mentioned above have been deleted.

[adcroft]

I've just been discussing with Bob, and we think we need to add a new version of get_param to solve a problem that has been highlighted by this PR, namely that we're adding 16 run-time parameters, for one scheme, when they could be a single line. We'll look into adding a vector default option and get back to this PR shortly.