New diagnostics for CMIP7: bigthetao200, thetao200

[adcroft]

The CMIP7 data request asks for tracers interpolated to a specific depth of 200m, e.g. thetao200 , bigthetao200

The variables requested at 200m depth include physical variables like Oday.bigthetao200 and Oday.thetao200, as well as BGC variables such as Oday.co3200, Oday.co3satarag200, Oday.o2200, Oday.ph200, Oday.phyc200, and Oday.chl200.

We can leverage the interpolation capability recently added to the remapping class for the t17d diagnostic (see pull request: #1001).

For the t17d diagnostic, depth is defined as the distance from the free-surface, which Baylor argued is most compatible with the products they intend to compare against. The challenge with using this definition for thetao200 is that the 3D mask can vary in time if the ocean column thickness varies above and below 200m. Using z*=-200 instead of z=ssh-200 seems to be little different to an interpolation error, so I suggest we can live with this.

Open questions:
[x] - definition of depth?
[ ] - availability of 200m diagnostic for other scalars?
[ ] - generalization to other depths?

Edit: I did a 180 on the definition of "depth", ending up reversed from OP

[iangrooms]

I agree that z*=-200 m is a reasonable interpretation of depth here. I doubt that the request envisioned having to deal with the fact that in some places 200 m below the surface can be either in the ocean or under the seafloor depending on when you look.

[adcroft]

I drafted some code, and when doing so realized that there is some extra overhead with computing z* for this diagnostic; z* requires knowing the total column thickness which is an extra loop.

My original concern with using z was a time-varying mask but we can define a static mask with G%bathyT(i,j)>200. If sea-level drops such that d_from_ssh reaches the bottom we can just use the bottom temperature for thetao200. This is less computation and is still in the category of not-too-much-difference.

For now, I've made the diagnostic either thetao200 or bigthetao200 depending on which is actually being used for the state variable. Accommodating both diagnostics in both potential- and conservative-temperature modes is a tedious lift.

[adcroft]

This is the layer average temperature in a z* coordinate config centered at 202.15m

and thetao200 using z=ssh-200 approach

The masking is working and values look right.