One-side-limited slopes bug with MEKE_GM_SRC_ALT=True.

[Hallberg-NOAA]

There is a bug in the application of KHTH_SLOPE_MAX to the slopes used to calculate the Potential energy released by the GM mixing for use by MEKE when MEKE_GM_SRC_ALT is true. Specifically the lines Slope_x_PE(I,j,k) = MIN(Slope,CS%slope_max) and its counterpart for Slope_y_PE (MOM_thickness_diffuse.F90, lines 928 and 1210) do limit positive slopes, but they do not limit negative slopes. As a result, this breaks rotational consistency, among other problems.

Obviously the solution to this bug is to replace this with something like Slope_x_PE(I,j,k) = MAX(MIN(Slope,CS%slope_max), -1.*CS%slope_max), but it could change answers for anyone using this option. To the best of my knowledge, we at GFDL are not currently using MEKE_GM_SRC_ALT in any cases, but because this code came from NCAR originally, it seems like this issue is best handled via dev/NCAR in case someone at NCAR is using it.

[Hallberg-NOAA]

This bug is being addressed via NOAA-GFDL#620, which retains adds the new runtime parameter MEKE_GM_SRC_ALT_SLOPE_BUG to correct it, but leaves the bug in place by default. Because we are not yet using MEKE_GM_SRC_ALT = True at GFDL, we would not mind if this bug were just fixed in the code, but adding this bug-fix flag does seem like the right approach in case someone is using this option. With this bug-fix enabled, we are able to get rotationally symmetric solutions when MEKE_GM_SRC_ALT = True.

[iangrooms]

I don't think NCAR is using MEKE_GM_SRC_ALT = True right now. I played with that option when I was exploring MEKE configurations with no equilibrium-restoring, but ended up not using it. This discussion summarizes the options we're currently exploring. It's of course great that this bug is being fixed; my comment is just to say that the fix is not urgent for us.