Order of spatial filtering/ time averaging not interchangeable in the presence of variable ice-mask

So I reprocessed all the data with the refactored code (see #66) and ran a sanity test to check the assumption that we can compute the small scale decomposition (some simple algebra + filtering) on the time averaged flux fields instead of computing the decomposition on the daily time scale (hugely expensive) and then average in time.

Using the appendix data I computed both versions for a smaller time window (1 year) of the CM2.6 data, and plotted the difference:

This shows the difference relative to the daily decomposition which is averaged afterwards.

✅ in the open ocean the assumption holds as expected ❌ there are large local differences up to 50% in the regions that are covered by the ice-mask for part of the time

It seems to me that something in the filtering treatment of boundaries (nans) violates our assumption. Not sure what that is, but I think this deserves some more consideration.

Thankfully this does not actually change the global averages much (less than 2% difference), and thus I think we can move ahead with the paper and I propose we do not actually compute the decomposition on each timestep and average.

Keen for feedback from @ocean-transport/collab_team here.

ocean-transport / scale-aware-air-sea

Order of spatial filtering/ time averaging not interchangeable in the presence of variable ice-mask #67