Groupby exclude dimension

Is there some way to do a groupby operation where some dimension is excluded from the operation, e.g., a vectorized version of something like this:

vertlevels = [ds.vel.sel(nVertLevels=i).groupby('y').mean() for i in ds.nVertLevels]
xavgvel = xr.concat(vertlevels, 'nVertLevels')

The application here is to average 3D data in the x coordinate to the unique y coordinates, but not the vertical coordinate.

Thus, we are basically looking for something that allows a coordinate to be excluded from the groupby operation, e.g., in this case the vertical coordinate. Ideally this would also be possible within the context of the groupby_bins operation.

Any ideas on how this should work or a pointer on how to implement this type of operation more cleanly with existing infrastructure is greatly appreciated. This appears to be related to #324 and especially (perhaps identically) #924.

cc @vanroekel, @shoyer, @jhamman, @rabernat, @MaximilianR

Start by reading related issues #324 and #924, then inspect the existing groupby and groupby_bins behavior described by the example. Done should provide a defined way to exclude the vertical dimension while grouping by y, including the requested groupby_bins case.