nonzero method for xr.DataArray

np.nonzero to DataArray returns a wrong result,

In [4]: da = xr.DataArray(np.arange(12).reshape(4, 3), dims=['x', 'y'],
   ...:                   coords={'x': [0, 1, 2, 3], 'y': ['a', 'b', 'c']})
   ...: np.nonzero(da)
   ...: 
Out[4]: 
<xarray.DataArray (x: 2, y: 11)>
array([[0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3],
       [1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2]])
Coordinates:
  * x        (x) int64 0 1 2 3
  * y        (y) <U1 'a' 'b' 'c'

Problem description

Apparently, the dimensions and the coordinates conflict each other.
I think we can have our own nonzero method, which may return a Dataset consisting of indexes and appropriate coordinates.

Output of xr.show_versions()

Reproduce the reported result with the DataArray example and inspect how NumPy's nonzero dispatch interacts with xarray dimensions and coordinates. The issue names no implementation file or test; done would require an agreed nonzero behavior that preserves appropriate indexes and coordinates, plus regression coverage.