Getting DataArrays from netCDF4 files correctly and without hassle

Context

Consider a netCDF4 file with a group structure. For example, the following toy:

import netCDF4 as nc
# netCDF4 file
f = nc.Dataset('simple_hierarchy.nc', 'w')
# coordinates in root
f.createDimension('x', 3)
f.createVariable('x', 'f4', ('x',), fill_value=False)
f['x'][:] = [1.1, 2.2, 3.3]
f.createDimension('y', 2)
f.createVariable('y', 'f4', ('y',), fill_value=False)
f['y'][:] = [-0.9, -1.8]
# variables in root
f.createVariable('u', 'i1', (), fill_value=False)
f.createVariable('v', 'u1', ('x','y'), fill_value=False)
# group
f.createGroup('g')
g = f['g']
# new/modified coordinates in g
g.createDimension('y', 3)
g.createVariable('y', 'f4', ('y',), fill_value=False)
g['y'][:] = [-0.9, -1.8, -2.7]
# variable in g
g.createVariable('w', 'u1', ('x', 'y'), fill_value=False)
f.close()

Current behavior

1. It is currently a hassle to get a DataArray from variable in a group with multiple non-coordinate variables:

   >>> xr.open_dataarray('simple_hierarchy.nc')
   …
   ValueError: Given file dataset contains more than one data variable. 
   Please read with xarray.open_dataset and then select the variable you want.
   >>> xr.open_dataarray('simple_hierarchy.nc', group='v')
   xr.open_dataarray('simple_hierarchy.nc', group='v')
   …
   OSError: [Errno group not found: v] 'v'
   >>> xr.open_dataarray('simple_hierarchy.nc', drop_variables='u')
   <xarray.DataArray 'v' (x: 3, y: 2)>
   array([[120, 219],
          [178, 172],
          [  9, 127]], dtype=uint8)
   Coordinates:
     * x        (x) float32 1.1 2.2 3.3
     * y        (y) float32 -0.9 -1.8
   

2. Also, coordinates defined at a group level closer tot the root are not taken into account:

   >>> xr.open_dataarray('simple_hierarchy.nc', group='g')
   <xarray.DataArray 'w' (x: 3, y: 3)>
   array([[216, 219, 178],
          [172,   9, 127],
          [  0,   0,  64]], dtype=uint8)
   Coordinates:
     * y        (y) float32 -0.9 -1.8 -2.7
   Dimensions without coordinates: x
   

   So the DataArray is not loaded correctly, as part of its defining coordinates are missing.

Suggested behavior

1. Add a variable kwarg in the open_dataarray method:

   >>> xr.open_dataarray('simple_hierarchy.nc', variable='v')
   <xarray.DataArray 'v' (x: 3, y: 2)>
   array([[120, 219],
          [178, 172],
          [  9, 127]], dtype=uint8)
   Coordinates:
     * x        (x) float32 1.1 2.2 3.3
     * y        (y) float32 -0.9 -1.8
   

2. Have the function that loads variables go up the group hierarchy to see if some coordinate arrays can be found for dimensions lacking them within this group:

   >>> xr.open_dataarray('simple_hierarchy.nc', group='g')
   <xarray.DataArray 'w' (x: 3, y: 3)>
   array([[216, 219, 178],
          [172,   9, 127],
          [  0,   0,  64]], dtype=uint8)
   Coordinates:
     * x        (x) float32 1.1 2.2 3.3
     * y        (y) float32 -0.9 -1.8 -2.7
   

   I guess care needs to be taken as well upon writing to netCDF, to make sure no spurious dimension/coordinate definitions are added.

Version

xarray 0.9.6

Start with the open_dataarray entry point and reproduce the toy netCDF4 hierarchy described in the issue. Implement the requested variable selection and parent-group coordinate lookup, then verify that grouped variables load with all defining coordinates and that existing behavior remains correct.