Roadmap to ECCO V4r4 support

[anthony-meza]

xbudget requires a few more functions to support ECCO V4r4. Ideally, the work done here will also allow xbudget to be extended to all xgcm grids that include face connections.

• Including an inverse or reciprocal operation that can be used in the yaml files. ECCO V4r4 does not output LHS tendencies directly, instead they can be inferred from daily snapshots.
  For example, the volume/mass tendency for a grid cell is given by
  $$\frac{\eta(x,y,t+\Delta t)-\eta(x,y,t)}{\Delta t}\frac{\mathrm{volcello}}{\mathrm{deptho}(x,y)}$$

• Create a grid/face_connection-aware lateral_convergence function. Ideally, we would just use thexgcm function grid.diff_2d_vector, but xgcm.0.9.0 currently gives errors. I have a lateral_convergence function for the LLC90 grid that we can use to prototype while we develop a solution to this issue.

• Add an ECCO_V4r4.yaml file

• Upload a small example Zarr file to Zenodo that can be used in a reproducible ECCO V4r4 budget notebook

[anthony-meza]

Anything I missed? @hdrake

[hdrake]

Seems like your bullet-point 1 would also require a time-difference operation, unless this was performed in a pre-processing step, no?

The only other thing missing is that we would need to add test coverage for all of these new features.

[anthony-meza]

I think the difference operation in xbudget already handles a lot of this out of the box.If the daily snapshots required to calculate Eulerian tendencies are stored as bounds (e.g. ETA_bounds lives on time_bounds), we can define the xgcm.Grid T axis like:

grid = Grid(ds, coords={“T”: {“center”: “time”, “outer”: “time_bounds”}})
Then, difference(ETA_bounds) will return the difference two snapshots on the centered time coordinate. This is because xbudget will detect that ETA_boundslives on a staggered coordinate.

I think dt (i.e., difference(time_bounds)) can be calculated in the same way but I haven't tried this yet. Right now I calculate dt manually as a preprocessing step.

So far, I have the been able to close the mass and heat budgets in xbudget this way. I'll be cleaning up my code and sending pull requests over early next week!

[hdrake]

Oh, registering time as a coordinate is a great idea that should also streamline a lot of the operations in xwmb!

Would be great to see a PR for this!