What happened?

This issue originates from this discussion where I was trying to figure out the best way to replace coordinate values in a MultiIndex level. I found that removing the level with reset_index and replacing the coordinate level with assign_coords works except when removing level leaves you with a MultIndex with only one level. In this case a ValueError is thrown.

What did you expect to happen?

I expect that removing and replacing a coordinate level would work the same independent of the number of levels in the MultiIndex.

Minimal Complete Verifiable Example

```Python import numpy as np import pandas as pd import xarray as xr

Replace the coordinates in level 'one'. This works as expected.

midx = pd.MultiIndex.from_product([[0,1,2], [3, 4], [5,6]], names=("one", "two","three")) mda = xr.DataArray(np.random.rand(12, 3), [("x", midx), ("y", range(3))])

new_coords = mda.coords['one'].values*2 mda.reset_index('one', drop=True).assign_coords(one= ('x',new_coords)).set_index(x='one',append=True) #Works

Drop the two level before had such that the intermediate state has a multindex

with only the 'three' level, this throws a ValueError

mda.reset_index('two',drop=True).reset_index('one', drop=True).assign_coords(one= ('x',new_coords)) #ValueError

We can intialize a data array with only two levels and only drop the 'one'

level, which gives the same ValueError. This shows that the problem is not

due to something with dropping the 'two' level above, but something inherent

to dropping to a state with only one multinddex level

midx = pd.MultiIndex.from_product([[0,1,2], [3, 4]], names=("one", "two")) mda = xr.DataArray(np.random.rand(6, 2), [("x", midx), ("y", range(2))])

new_coords = mda.coords['one'].values*2 mda.reset_index('one', drop=True).assign_coords(one= ('x',new_coords)).set_index(x='one',append=True) #ValueError ```

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.

Relevant log output

```Python

First example, starting from 3 level multiindex and dropping two levels

ValueError Traceback (most recent call last) c:\Users\aspit\Git\Learn\xarray\replace_coord_issue.py in <module> 15 # Drop the two level before had such that the intermediate state has a multindex 16 # with only the 'three' level, this throws a ValueError ---> 17 mda.reset_index('two',drop=True).reset_index('one', drop=True).assign_coords(one= ('x',new_coords))

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\common.py in assign_coords(self, coords, **coords_kwargs) 590 data = self.copy(deep=False) 591 results: dict[Hashable, Any] = self._calc_assign_results(coords_combined) --> 592 data.coords.update(results) 593 return data 594

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\coordinates.py in update(self, other) 160 other_vars = getattr(other, "variables", other) 161 self._maybe_drop_multiindex_coords(set(other_vars)) --> 162 coords, indexes = merge_coords( 163 [self.variables, other_vars], priority_arg=1, indexes=self.xindexes 164 )

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in merge_coords(objects, compat, join, priority_arg, indexes, fill_value) 564 collected = collect_variables_and_indexes(aligned) 565 prioritized = _get_priority_vars_and_indexes(aligned, priority_arg, compat=compat) --> 566 variables, out_indexes = merge_collected(collected, prioritized, compat=compat) 567 return variables, out_indexes 568

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in merge_collected(grouped, prioritized, compat, combine_attrs, equals) 252 253 _assert_compat_valid(compat) --> 254 _assert_prioritized_valid(grouped, prioritized) 255 256 merged_vars: dict[Hashable, Variable] = {}

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in _assert_prioritized_valid(grouped, prioritized) 199 common_names_str = ", ".join(f"{k!r}" for k in common_names) 200 index_names_str = ", ".join(f"{k!r}" for k in index_coord_names) --> 201 raise ValueError( 202 f"cannot set or update variable(s) {common_names_str}, which would corrupt " 203 f"the following index built from coordinates {index_names_str}:\n"

ValueError: cannot set or update variable(s) 'one', which would corrupt the following index built from coordinates 'x', 'one', 'three': <xarray.core.indexes.PandasMultiIndex object at 0x00000225AA4B5200>

Second Example Starting from two level multindex and dropping one level

ValueError Traceback (most recent call last) c:\Users\aspit\Git\Learn\xarray\replace_coord_issue.py in <module> 11 12 new_coords = mda.coords['one'].values*2 ---> 13 mda.reset_index('one', drop=True).assign_coords(one= ('x',new_coords)).set_index(x='one',append=True)

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\common.py in assign_coords(self, coords, **coords_kwargs) 590 data = self.copy(deep=False) 591 results: dict[Hashable, Any] = self._calc_assign_results(coords_combined) --> 592 data.coords.update(results) 593 return data 594

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\coordinates.py in update(self, other) 160 other_vars = getattr(other, "variables", other) 161 self._maybe_drop_multiindex_coords(set(other_vars)) --> 162 coords, indexes = merge_coords( 163 [self.variables, other_vars], priority_arg=1, indexes=self.xindexes 164 )

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in merge_coords(objects, compat, join, priority_arg, indexes, fill_value) 564 collected = collect_variables_and_indexes(aligned) 565 prioritized = _get_priority_vars_and_indexes(aligned, priority_arg, compat=compat) --> 566 variables, out_indexes = merge_collected(collected, prioritized, compat=compat) 567 return variables, out_indexes 568

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in merge_collected(grouped, prioritized, compat, combine_attrs, equals) 252 253 _assert_compat_valid(compat) --> 254 _assert_prioritized_valid(grouped, prioritized) 255 256 merged_vars: dict[Hashable, Variable] = {}

c:\Users\aspit\anaconda3\envs\dataanalysis\lib\site-packages\xarray\core\merge.py in _assert_prioritized_valid(grouped, prioritized) 199 common_names_str = ", ".join(f"{k!r}" for k in common_names) 200 index_names_str = ", ".join(f"{k!r}" for k in index_coord_names) --> 201 raise ValueError( 202 f"cannot set or update variable(s) {common_names_str}, which would corrupt " 203 f"the following index built from coordinates {index_names_str}:\n"

ValueError: cannot set or update variable(s) 'one', which would corrupt the following index built from coordinates 'x', 'one', 'two': <xarray.core.indexes.PandasMultiIndex object at 0x00000225AA53C9E0> ```

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS ------------------ commit: None python: 3.9.7 | packaged by conda-forge | (default, Sep 29 2021, 19:15:42) [MSC v.1916 64 bit (AMD64)] python-bits: 64 OS: Windows OS-release: 10 machine: AMD64 processor: Intel64 Family 6 Model 142 Stepping 12, GenuineIntel byteorder: little LC_ALL: None LANG: None LOCALE: ('English_United States', '1252') libhdf5: 1.12.1 libnetcdf: 4.8.1 xarray: 2022.6.0 pandas: 1.3.4 numpy: 1.21.4 scipy: 1.7.3 netCDF4: 1.5.8 pydap: None h5netcdf: 1.0.2 h5py: 3.7.0 Nio: None zarr: None cftime: 1.5.1.1 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: 1.3.5 dask: 2022.02.1 distributed: 2022.2.1 matplotlib: 3.4.3 cartopy: None seaborn: None numbagg: None fsspec: 2022.7.1 cupy: None pint: 0.18 sparse: None flox: None numpy_groupies: None setuptools: 59.1.0 pip: 21.3.1 conda: None pytest: 6.2.5 IPython: 7.29.0 sphinx: None