*Non-Boussinesq revision of MOM_thickness_diffuse

[Hallberg-NOAA]

Refactored thickness_diffuse when in non-Boussinesq mode to avoid any dependencies on the Boussinesq reference density, and to translate the volume streamfunction into the mass streamfunction using an appropriately defined in-situ density averaged to the interfaces at velocity points. This form follows the suggestions of Appendix A.3.2 of Griffies and Greatbatch (Ocean Modelling, 2012) when in non-Boussinesq mode. Thickness_diffuse_full was also revised to work properly in non-Boussinesq mode (and not depend on the Boussinesq reference density) when no equation of state is used.

As a part of these changes, the code now uses thickness-based streamfunctions and other thickness-based internal calculations in MOM_thickness_diffuse. For example, the overturning streamfunctions with this change are now in m3/s in Boussinesq mode, but kg/s in non-Boussinesq mode. These changes use a call to thickness_to_dz to set up a separate variable with the vertical distance across layers, and in non-Boussinesq mode they use tv%SpV_avg to estimate in situ densities. Additional debugging checksums were added to thickness_diffuse.

The code changes are extensive with 15 new or renamed internal variables, and changes to the units of 9 other internal variables and 3 arguments to the private routine streamfn_solver. After this change, GV%Rho, GV%Z_to_H and GV%H_to_Z are no longer used in any non-Boussinesq calculations (12 such instances having been elimated). Because some calculations have to be redone with the separate thickness and dz variables, this will be more expensive than the original version.

No public interfaces are changed, and all answers are bitwise identical in Boussinesq or semiBoussinesq mode, but they will change in non-Boussinesq mode when the isopycnal height diffusion parameterization is used.

[codecov]

Codecov Report

Merging #420 (b7b912a) into dev/gfdl (6102be2) will decrease coverage by 0.01%.
The diff coverage is 53.01%.

❗ Current head b7b912a differs from pull request most recent head ae3b269. Consider uploading reports for the commit ae3b269 to get more accurate results

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Files Changed	Coverage Δ
...arameterizations/lateral/MOM_thickness_diffuse.F90	46.00% <53.01%> (-0.30%)	⬇️

... and 1 file with indirect coverage changes

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[StephenGriffies]

As noted by @Hallberg-NOAA , the code changes are extensive. But they are limited to this module for the purpose of updating to allow for non-Bouss option. I did not scrutinize the full suite of code. But the proposed changes to the streamfunction, via Appendix A3.2 of Griffies and Greatbatch (2012), are sensible.

I suggest we move forward with this code.

[marshallward]

Gaea regression: https://gitlab.gfdl.noaa.gov/ogrp/MOM6/-/pipelines/20023 ✔️