Allow creating DataArrays with nD coordinate variables

Closes pydata#2233
Closes pydata#8106

xarray/core/dataarray.py

@@ -119,21 +119,14 @@ def _check_coords_dims(shape, coords, dims):
                 f"dimensions {dims}"
             )
 
-        for d, s in zip(v.dims, v.shape):
+        for d, s in v.sizes.items():
             if s != sizes[d]:
                 raise ValueError(
                     f"conflicting sizes for dimension {d!r}: "
                     f"length {sizes[d]} on the data but length {s} on "
                     f"coordinate {k!r}"
                 )
 
-        if k in sizes and v.shape != (sizes[k],):
-            raise ValueError(
-                f"coordinate {k!r} is a DataArray dimension, but "
-                f"it has shape {v.shape!r} rather than expected shape {sizes[k]!r} "
-                "matching the dimension size"
-            )
-
 
 def _infer_coords_and_dims(
     shape, coords, dims

xarray/tests/test_dataarray.py

@@ -7073,3 +7073,23 @@ def test_error_on_ellipsis_without_list(self) -> None:
         da = DataArray([[1, 2], [1, 2]], dims=("x", "y"))
         with pytest.raises(ValueError):
             da.stack(flat=...)  # type: ignore
+
+
+def test_nD_coord_dataarray():
+    # should succeed
+    da = DataArray(
+        np.ones((2, 4)),
+        dims=("x", "y"),
+        coords={
+            "x": (("x", "y"), np.arange(8).reshape((2, 4))),
+            "y": ("y", np.arange(4)),
+        },
+    )
+    da2 = DataArray(np.ones(4), dims=("y"), coords={"y": ("y", np.arange(4))})
+
+    _, actual = xr.align(da, da2)
+    assert_identical(da2, actual)
+
+    expected = da.drop_vars("x")
+    _, actual = xr.broadcast(da, da2)
+    assert_identical(expected, actual)