Weighted sum/mean/cumsum

While thinking about #99, I would also consider adding a module for weighted mean/sum/cumsum to xgcm. I have been using my own code so far (https://github.com/jbusecke/xarrayutils/blob/master/xarrayutils/weighted_operations.py).

Currently I would use someting like this

from xarrayutils.weighted_ops import weighted_mean
w_mean = weighted_mean(da['varname'], da['weightname'], dims=['xc', 'yc'])

I would really like if I could do something like this in xgcm with a full dataset:

from xgcm import Grid
grid = Grid(ds)

ds_mean = grid.mean(['X', 'Y'], weights='area')

This would use the internal logic resulting from #99 and weigh all variables with the appropriate area depening on its dimensions.

@rabernat, would you consider this something that could make it into xgcm? This would obviously not be the first thing on the list, but I wanted to put it out here.

[rabernat]

@dhruvbalwada - thanks for weighing in! (No pun intended 🤣 )

Here we are talking about reductions operations happening in grid space. Like a zonal mean or mean over the domain. It’s something we already do every day when we do

(ds.SST * ds.rA).sum()

(area-weighted sum of SST)

The “weight” concept in xhistogram is about something related but different: what weights to assign to each point when calculating a histogram. The weights themselves will indeed often be the same arrays.

We could potentially attach histogram methods to xgcm Grids which would automatically figure out the weights.

[jbusecke]

Closed via #162