issues: 2212186122

What happened?

It is currently possible to create a Coordinates object where a variable shares a name with a dimension, but the variable is not 1D. This is explicitly forbidden by the xarray data model.

What did you expect to happen?

If you try to pass the resulting object into the Dataset constructor you get the expected error telling you that this is forbidden, but that error should have been raised by Coordinates.__init__.

Minimal Complete Verifiable Example

```Python In [1]: from xarray.core.coordinates import Coordinates

In [2]: from xarray.core.variable import Variable

In [4]: import numpy as np

In [5]: var = Variable(data=np.arange(6).reshape(2, 3), dims=['x', 'y'])

In [6]: var Out[6]: <xarray.Variable (x: 2, y: 3)> Size: 48B array([[0, 1, 2], [3, 4, 5]])

In [7]: coords = Coordinates(coords={'x': var}, indexes={})

In [8]: coords Out[8]: Coordinates: x (x, y) int64 48B 0 1 2 3 4 5

In [10]: import xarray as xr

In [11]: ds = xr.Dataset(coords=coords)

MergeError Traceback (most recent call last) Cell In[11], line 1 ----> 1 ds = xr.Dataset(coords=coords)

File ~/Documents/Work/Code/xarray/xarray/core/dataset.py:693, in Dataset.init(self, data_vars, coords, attrs) 690 if isinstance(coords, Dataset): 691 coords = coords._variables --> 693 variables, coord_names, dims, indexes, _ = merge_data_and_coords( 694 data_vars, coords 695 ) 697 self._attrs = dict(attrs) if attrs else None 698 self._close = None

File ~/Documents/Work/Code/xarray/xarray/core/dataset.py:422, in merge_data_and_coords(data_vars, coords) 418 coords = create_coords_with_default_indexes(coords, data_vars) 420 # exclude coords from alignment (all variables in a Coordinates object should 421 # already be aligned together) and use coordinates' indexes to align data_vars --> 422 return merge_core( 423 [data_vars, coords], 424 compat="broadcast_equals", 425 join="outer", 426 explicit_coords=tuple(coords), 427 indexes=coords.xindexes, 428 priority_arg=1, 429 skip_align_args=[1], 430 )

File ~/Documents/Work/Code/xarray/xarray/core/merge.py:731, in merge_core(objects, compat, join, combine_attrs, priority_arg, explicit_coords, indexes, fill_value, skip_align_args) 729 coord_names.intersection_update(variables) 730 if explicit_coords is not None: --> 731 assert_valid_explicit_coords(variables, dims, explicit_coords) 732 coord_names.update(explicit_coords) 733 for dim, size in dims.items():

File ~/Documents/Work/Code/xarray/xarray/core/merge.py:577, in assert_valid_explicit_coords(variables, dims, explicit_coords) 575 for coord_name in explicit_coords: 576 if coord_name in dims and variables[coord_name].dims != (coord_name,): --> 577 raise MergeError( 578 f"coordinate {coord_name} shares a name with a dataset dimension, but is " 579 "not a 1D variable along that dimension. This is disallowed " 580 "by the xarray data model." 581 )

MergeError: coordinate x shares a name with a dataset dimension, but is not a 1D variable along that dimension. This is disallowed by the xarray data model. ```

MVCE confirmation

• [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• [X] Complete example — the example is self-contained, including all data and the text of any traceback.
• [X] Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• [x] New issue — a search of GitHub Issues suggests this is not a duplicate.
• [X] Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

No response

Anything else we need to know?

I noticed this whilst working on #8872

Environment

main