*+Non-Boussinesq form of mixedlayer_restrat

[Hallberg-NOAA]

Revised the code in MOM_mixed_layer_restrat.F90 to work internally with thickness-based units for the restratification timescale calculation and other internal calculations, which eliminates the dependence in this module on the value of the Boussinesq reference density in non-Boussinesq mode. Several other minor issues (which might not change any answers in production runs) were also fixed. The changes with this commit include:

• When in non-Boussinesq mode, the mixed layer buoyancy gradients are determined from the average specific volume referenced to the surface pressure, rather than from the average potential density.

• Use find_ustar to set the friction velocities in the appropriate units in the various mixed_layer_restrat routines.

• A logical branch was added based on the correct mask for land or OBC points to avoid potentially ill-defined calculations of the magnitude of the Bodner parameterization streamfunction, some which were leading to NaNs.

• Set a tiny but nonzero default value for MIN_WSTAR2 to avoid NaNs in some calculations of the streamfunction magnitude.

• Within the function mu, the expression for dd was revised in a mathematically equivalent way to avoid any possibility of taking a fractional exponential power of a tiny negative number due to truncation errors, which was leading to NaNs in some cases while developing and debugging the other changes in this commit. This does not appear to change any answers in the existing test cases, perhaps because the mixed layer restratification "tail" is not being activated by setting TAIL_DH to be larger than 0.

• The addition of code to both mixedlayer_restrat_Bodner and mixedlayer_restrat_OM4 to determine the mixed layer thickness from its vertical extent when in non-Boussinesq mode.

This commit includes changes to the units of the Kv_restrat, ustar_min and wpup_filtered elements in the mixedlayer_restrat_CS type and the units of four arguments to the private function growth_time. CS%wpup_filtered also appears in the restart files generated with some mixed layer restratification settings, and it is rescaled to units of vertical distance or mass per unit area in the restart files depending on whether the model is Boussinesq.

There are 17 new or renamed internal variables, while the units of 21 internal variables were changed. 19 rescaling factors were cancelled out or replaced. There are also comments where variable units were corrected or added.

The rescaling of several chksum calls for thicknesses was modified to GV%H_to_mks to avoid any dependence on RHO_0 when non-Boussinesq.

No public interfaces are changed. All answers are bitwise identical in Boussinesq mode (at least when TAIL_DH=0.), but solutions will change in non-Boussinesq mode when mixed layer restratification is enabled, including changes to the units of a variable in the restart files.

[codecov]

Codecov Report

Merging #426 (f647e9f) into dev/gfdl (4c224e7) will decrease coverage by 0.03%.
The diff coverage is 59.09%.

❗ Current head f647e9f differs from pull request most recent head d5b1bc4. Consider uploading reports for the commit d5b1bc4 to get more accurate results

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Files Changed	Coverage Δ
...ameterizations/lateral/MOM_mixed_layer_restrat.F90	70.03% <59.09%> (-7.00%)	⬇️

... and 1 file with indirect coverage changes

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[adcroft]

This commit includes changes to the units of the Kv_restrat, ustar_min and wpup_filtered elements in the mixedlayer_restrat_CS

Is this only for the scaling tests or did the physical units change?

[marshallward]

Gaea regression: https://gitlab.gfdl.noaa.gov/ogrp/MOM6/-/pipelines/20377 ✔️