+Add MOM_check_scaling.F90 and MOM_scaling_check.F90

[Hallberg-NOAA]

Added two new modules, the MOM6-specific MOM_check_scaling.F90 and the generic
framework module MOM_scaling_check.F90, to assess the uniqueness of the unit
scaling factors for all of the variables used by MOM6. If there are overlaps in
scaling factors for different units, this also identifies and suggests alternate
scaling factors with less overlaps. This commit includes the introduction of
the new publicly visible routines check_scaling_factors(), scales_to_powers()
and check_MOM6_scaling_factors. This new capability does not do anything for
sufficiently low levels of model verbosity, and it is silent if the scaling
factors are unique, or if less than 2 dimensions are being rescaled. All
answers and output files are bitwise identical, but there can be additional
messages to stdout.

[codecov]

Codecov Report

Merging #49 (4b8645f) into dev/gfdl (65998cd) will increase coverage by 0.07%.
The diff coverage is 47.13%.

@@             Coverage Diff              @@
##           dev/gfdl      #49      +/-   ##
============================================
+ Coverage     28.94%   29.02%   +0.07%     
============================================
  Files           242      244       +2     
  Lines         71553    71850     +297     
============================================
+ Hits          20714    20854     +140     
- Misses        50839    50996     +157     

Impacted Files	Coverage Δ
src/framework/MOM_unique_scales.F90	7.14% <7.14%> (ø)
src/core/MOM_check_scaling.F90	99.21% <99.21%> (ø)
src/core/MOM.F90	58.44% <100.00%> (+0.02%)	⬆️

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[adcroft]

This is a nice innovation, and as usual, properly working code. However:

1. I don't understand the use of two modules here. These could easily be one module and not change the functionality currently coded. The naming MOM_check_scaling and MOM_scaling_check do not help me know which level I'm looking at. I note the module descriptions are identical which must be corrected. Some of subroutine descriptions are so similar one would think the modules duplicate each other when infact one does the work and the other does the set up. One module seems to make sense, or if there's a real reason to not join them, a clearer description of the two levels.
2. Please change the verbosity in one of the TCs so that this code gets 100% coverage.
3. The regular comments about how units work have very useful information (e.g. L13-17 of the new modules) but this will not be found or referenceable. I suggest moving this into a dedicated .dox about units and scaling so we can refer to this documentation.

[Hallberg-NOAA]

Thank you for the review @adcroft

1. There are two modules because one (the smaller one) is specific to the physical parts of MOM6, while the other one (in the framework directory) is a set of model-agnostic tools and checks that can be used by MOM6, SIS2, various biogeochemical packages (like COBALT, TOPAZ, etc.) or anything else. However, I see that having such similar names will be very confusing. I could rename the latter to framework/MOM_scaling_check_framework.F90, but that seems rather long. Any suggestions for a better name?

2. Triggering this code requires the simultaneous rescaling of 2 or more dimensions, whereas the TC testing (by design) only tests one dimension at a time. One possibility that this opens up is that we could test all of the rescaled dimensions in the TCs at once, and then only trigger the tests of each individual dimension if that fails. However, that would add complexity to the driver for the TCs. Curiously, running a test that gets us to ~100% coverage would require this not use the settings that actually uniquely rescale all of the dimensions used in MOM6, as otherwise the code does not need to seek a set of values that do uniquely rescale all of the dimensions!

3. Improving this documentation is a good idea. I will prepare a .dox file describing the units as a separate PR. I am also preparing a proper manuscript about this for submission to the peer reviewed literature.

[adcroft]

1. Understood.
2. tc0 does not run as far as a the call to call check_MOM6_scaling_factors(CS%GV, US) but if you add a unit test s/r that sets up GV and US, then we could trivially update tc0 to test multiple dimensions always and thus exercise the code. Let's discuss...
3. And we must remember to add the link to the paper in the .dox file when it's available

[Hallberg-NOAA]

I have renamed one of the two new modules for help differentiate them, and I have added a new .dox file describing the unit scaling. However, I think that changes to the overall structure of the TC testing to exercise this new code goes beyond the scope of this PR. I now believe that this PR is ready to be reevaluated.

[marshallward]

Gaea regression: https://gitlab.gfdl.noaa.gov/ogrp/MOM6/-/pipelines/14676 ✔️

[marshallward]

Will merge after approval from @adcroft