What happened?

As a follow up of this comment: https://github.com/pydata/xarray/issues/6752#issuecomment-1236756285 I'm currently trying to implement a custom NetCDF4 backend that allows me to also handle multiindices when loading a NetCDF dataset using xr.open_dataset.

I'm using the following two functions to convert the dataset to a NetCDF compatible version and back again: https://github.com/pydata/xarray/issues/1077#issuecomment-1101505074.

Here is a small code example:

Creating the dataset

```python import xarray as xr import pandas

def create_multiindex(**kwargs): return pandas.MultiIndex.from_arrays(list(kwargs.values()), names=kwargs.keys())

dataset = xr.Dataset() dataset.coords["observation"] = ["A", "B"] dataset.coords["wavelength"] = [0.4, 0.5, 0.6, 0.7] dataset.coords["stokes"] = ["I", "Q"] dataset["measurement"] = create_multiindex( observation=["A", "A", "B", "B"], wavelength=[0.4, 0.5, 0.6, 0.7], stokes=["I", "Q", "I", "I"], ) ```

Saving as NetCDF

python from cf_xarray import encode_multi_index_as_compress patched = encode_multi_index_as_compress(dataset) patched.to_netcdf("multiindex.nc")

And loading again

python from cf_xarray import decode_compress_to_multi_index loaded = xr.open_dataset("multiindex.nc") loaded = decode_compress_to_multiindex(loaded) assert loaded.equals(dataset) # works

Custom Backend

While the manual patching for saving is currently still required, I tried to at least work around the added function call in open_dataset by creating a custom NetCDF Backend:

```python

registered as netcdf4-multiindex backend in setup.py

class MultiindexNetCDF4BackendEntrypoint(NetCDF4BackendEntrypoint): def open_dataset(self, args, handle_multiindex=True, kwargs): ds = super().open_dataset(args, **kwargs)

    if handle_multiindex:  # here is where the restore operation happens:
        ds = decode_compress_to_multiindex(ds)

    return ds

```

The error

```python

loaded = xr.open_dataset("multiindex.nc", engine="netcdf4-multiindex", handle_multiindex=True) # fails

File ~/.local/share/virtualenvs/test-oePfdNug/lib/python3.8/site-packages/xarray/core/variable.py:2795, in IndexVariable.data(self, data) 2793 @Variable.data.setter # type: ignore[attr-defined] 2794 def data(self, data): -> 2795 raise ValueError( 2796 f"Cannot assign to the .data attribute of dimension coordinate a.k.a IndexVariable {self.name!r}. " 2797 f"Please use DataArray.assign_coords, Dataset.assign_coords or Dataset.assign as appropriate." 2798 )

ValueError: Cannot assign to the .data attribute of dimension coordinate a.k.a IndexVariable 'measurement'. Please use DataArray.assign_coords, Dataset.assign_coords or Dataset.assign as appropriate. ```

but this works: ```python

loaded = xr.open_dataset("multiindex.nc", engine="netcdf4-multiindex", handle_multiindex=False) loaded = decode_compress_to_multiindex(loaded) assert loaded.equals(dataset) ```

So I'm guessing xarray is performing some operation on the dataset returned by the backend, and one of those leads to a failure if there is a multiindex already contained.

What did you expect to happen?

I expected that it doesn't matter wheter decode_compress_to_multi_index is called inside the backend or afterwards, and the same dataset will be returned each time.

Minimal Complete Verifiable Example

Python See above.

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

No response

Anything else we need to know?

I'm also open to other suggestions how I could simplify the usage of multiindices, maybe there is an approach that doesn't require a custom backend at all?

Environment

What happened?

When upgrading to 2022.6.0.rc0 from 2022.3.0 I noticed a possible unexpected breaking change in the Dataset.indexes property. MultiIndices are now listed for each dimension they apply for as well as once for the multi index itself when accessing dataset.indexes.

What did you expect to happen?

Same behaviour as before, see example below.

Minimal Complete Verifiable Example

```Python

execute with 2022.3.0 and 2022.6.0.rc0 to see the differences

import pandas import xarray as xr

def _create_multiindex(**kwargs): return pandas.MultiIndex.from_arrays(list(kwargs.values()), names=kwargs.keys())

ds = xr.Dataset() ds.coords["measurement"] = _create_multiindex( observation=["A", "A", "B", "B"], wavelength=[0.4, 0.5, 0.6, 0.7], stokes=["I", "Q", "I", "I"], )

for name, idx in ds.indexes.items(): print(name, idx) ```

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 Output with version 2022.3.0:

measurement MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], names=['observation', 'wavelength', 'stokes'])

Output with version 2022.6.0.rc0:

measurement MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') observation MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') wavelength MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') stokes MultiIndex([('A', 0.4, 'I'), ('A', 0.5, 'Q'), ('B', 0.6, 'I'), ('B', 0.7, 'I')], name='measurement') ```

Anything else we need to know?

No response

Environment