quad_util_mod rotations

Reported in the standup that the quad_utils_mod may have problems when the quad is rotated at 45 degrees.

model_mods that would be affected by this:

• cam-fv
• mom6 (unreleased)
• quad_utils is used by people with their own DART development for TIEGCM

Not confirmed (yet).

There is no record of the error (or fix) in the log:
https://github.com/NCAR/DART/commits/main/models/utilities/quad_utils_mod.f90

There is the namelist option do_rotate (default .false.)
https://github.com/NCAR/DART/blob/16595cad595b6349605c9bc8e021c7ecc2c2391a/models/utilities/quad_utils_mod.f90#L2179

The notes talk about the degenerate case where the grid is rotated 90 degrees:
https://github.com/NCAR/DART/blob/16595cad595b6349605c9bc8e021c7ecc2c2391a/models/utilities/quad_utils_mod.f90#L2201-L2202

Mentioned at the standup (note I might not be recalling this correctly): cam-se has a fix for this rotation problem. Is this it?
https://github.com/NCAR/DART/blob/16595cad595b6349605c9bc8e021c7ecc2c2391a/models/cam-se/model_mod.f90#L2531

Q. Why does cam-se not use quad_utils_mod?
Q. What is the goal of rotating?
Q. Why is the default do_rotate = .false.?

I think quad_interp_mod is a generalization (and replacement?) for the original POP model_mod interpolation code:
https://github.com/NCAR/DART/blob/16595cad595b6349605c9bc8e021c7ecc2c2391a/models/utilities/quad_utils_mod.f90#L894-L897
Q. Can we switch out the POP model_mod code?

There are 21 fixmes is the quad_util_mod module.

Other quad_util_mod issues:

• see https://github.com/NCAR/DART/issues/249 for a note only only one of the quad_utils routines checking for missing values in the state.

• Note from pull #247

  quad_utils_mod.f90 uses  invals(4, nitems)
  cam-fv/model_mod.f90 uses quad_vals(ens_size,4) !< array of interpolated values
  

  which seems ripe for bugs such as https://github.com/NCAR/DART/issues/246. I'm not sure why the change
  in order was made, maybe should be reverted.

⚠️ Note the rotation in quad_utils_mod does not match the comment, the rotation is clockwise rather than counterclockwise. https://github.com/NCAR/DART/issues/833#issuecomment-2730460445