TypeError: '_ElementwiseFunctionArray' object does not support item assignment

What happened:
I am attempting to mask specific time_bnds coordinate points using loc, but am receiving TypeError: '_ElementwiseFunctionArray' object does not support item assignment.

This happens with datasets that have encoded (raw) time coordinates, then decoding with xr.decode_cf() before attempting to mask the time_bnds.

What you expected to happen:

The time_bnds coordinate points selected using .loc should mask properly

Minimal Complete Verifiable Example:

MVCE 1 -- breaks with encoded time coordinates then decoded using xr.decode_cf()

import numpy as np
import xarray as xr

time_encoded = xr.DataArray(
    name="time",
    data=[675348.5, 675378.0, 675407.5],
    dims=["time"],
    attrs={
        "bounds": "time_bnds",
        "units": "days since 0001-01-01",
        "calendar": "proleptic_gregorian",
        "axis": "T",
        "long_name": "time",
        "standard_name": "time",
    },
)
time_bnds_encoded = xr.DataArray(
    name="time_bnds",
    data=[[675333.0, 675364.0], [675364.0, 675392.0], [675392.0, 675423.0]],
    dims=["time", "bnds"],
)

ds = xr.Dataset(
    coords={"time": time_encoded}, data_vars={"time_bnds": time_bnds_encoded}
)
ds = xr.decode_cf(ds, decode_times=True)
ds["time_bnds"].loc[dict(time="1850-01")] = np.nan

MVCE 2 -- works fine with decoded time coordinates

import cftime
import numpy as np
import xarray as xr

time_decoded = xr.DataArray(
    name="time",
    data=np.array(
        [
            cftime.DatetimeProlepticGregorian(
                1850, 1, 16, 12, 0, 0, 0, has_year_zero=True
            ),
            cftime.DatetimeProlepticGregorian(
                1850, 2, 15, 0, 0, 0, 0, has_year_zero=True
            ),
            cftime.DatetimeProlepticGregorian(
                1850, 3, 16, 12, 0, 0, 0, has_year_zero=True
            ),
        ],
        dtype="object",
    ),
    dims=["time"],
    attrs={
        "bounds": "time_bnds",
        "axis": "T",
        "long_name": "time",
        "standard_name": "time",
    },
)
time_decoded.encoding = {
    "units": "days since 0001-01-01",
    "calendar": "proleptic_gregorian",
}
time_bnds_decoded = xr.DataArray(
    dims=["time", "bnds"],
    data=[
        [np.nan, np.nan],
        [
            cftime.DatetimeProlepticGregorian(
                1850, 2, 1, 0, 0, 0, 0, has_year_zero=True
            ),
            cftime.DatetimeProlepticGregorian(
                1850, 3, 1, 0, 0, 0, 0, has_year_zero=True
            ),
        ],
        [
            cftime.DatetimeProlepticGregorian(
                1850, 3, 1, 0, 0, 0, 0, has_year_zero=True
            ),
            cftime.DatetimeProlepticGregorian(
                1850, 4, 1, 0, 0, 0, 0, has_year_zero=True
            ),
        ],
    ],
)

ds = xr.Dataset(
    coords={"time": time_decoded}, data_vars={"time_bnds": time_bnds_decoded}
)
ds["time_bnds"].loc[dict(time="1850-01")] = np.nan

Anything else we need to know?:

The workaround is to perform .load() after xr.decode_cf()

import numpy as np
import xarray as xr

time_encoded = xr.DataArray(
    name="time",
    data=[675348.5, 675378.0, 675407.5],
    dims=["time"],
    attrs={
        "bounds": "time_bnds",
        "units": "days since 0001-01-01",
        "calendar": "proleptic_gregorian",
        "axis": "T",
        "long_name": "time",
        "standard_name": "time",
    },
)
time_bnds_encoded = xr.DataArray(
    name="time_bnds",
    data=[[675333.0, 675364.0], [675364.0, 675392.0], [675392.0, 675423.0]],
    dims=["time", "bnds"],
)

ds = xr.Dataset(
    coords={"time": time_encoded}, data_vars={"time_bnds": time_bnds_encoded}
)
ds = xr.decode_cf(ds, decode_times=True)
ds.load()
ds["time_bnds"].loc[dict(time="1850-01")] = np.nan

Log Output

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /Users/vo13/repositories/xcdat/qa/xr_6015.py:27
     [23](https://file+.vscode-resource.vscode-cdn.net/Users/vo13/repositories/xcdat/qa/xr_6015.py:23) ds = xr.Dataset(
     [24](https://file+.vscode-resource.vscode-cdn.net/Users/vo13/repositories/xcdat/qa/xr_6015.py:24)     coords={"time": time_encoded}, data_vars={"time_bnds": time_bnds_encoded}
     [25](https://file+.vscode-resource.vscode-cdn.net/Users/vo13/repositories/xcdat/qa/xr_6015.py:25) )
     [26](https://file+.vscode-resource.vscode-cdn.net/Users/vo13/repositories/xcdat/qa/xr_6015.py:26) ds = xr.decode_cf(ds, decode_times=True)
---> [27](https://file+.vscode-resource.vscode-cdn.net/Users/vo13/repositories/xcdat/qa/xr_6015.py:27) ds["time_bnds"].loc[dict(time="1850-01")] = np.nan

File /opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:246, in _LocIndexer.__setitem__(self, key, value)
    [243](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:243)     key = dict(zip(self.data_array.dims, labels))
    [245](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:245) dim_indexers = map_index_queries(self.data_array, key).dim_indexers
--> [246](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:246) self.data_array[dim_indexers] = value

File /opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:892, in DataArray.__setitem__(self, key, value)
    [887](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:887) # DataArray key -> Variable key
    [888](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:888) key = {
    [889](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:889)     k: v.variable if isinstance(v, DataArray) else v
    [890](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:890)     for k, v in self._item_key_to_dict(key).items()
    [891](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:891) }
--> [892](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/dataarray.py:892) self.variable[key] = value

File /opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/variable.py:866, in Variable.__setitem__(self, key, value)
    [863](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/variable.py:863)     value = np.moveaxis(value, new_order, range(len(new_order)))
    [865](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/variable.py:865) indexable = as_indexable(self._data)
--> [866](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/variable.py:866) indexing.set_with_indexer(indexable, index_tuple, value)

File /opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:1012, in set_with_indexer(indexable, indexer, value)
   [1010](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:1010)     indexable.oindex[indexer] = value
   [1011](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:1011) else:
-> [1012](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:1012)     indexable[indexer] = value

File /opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:660, in LazilyIndexedArray.__setitem__(self, key, value)
    [658](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:658) self._check_and_raise_if_non_basic_indexer(key)
    [659](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:659) full_key = self._updated_key(key)
--> [660](https://file+.vscode-resource.vscode-cdn.net/opt/miniconda3/envs/xcdat_dev/lib/python3.11/site-packages/xarray/core/indexing.py:660) self.array[full_key] = value

TypeError: '_ElementwiseFunctionArray' object does not support item assignment

Environment:

Start by reproducing the two minimal examples around xr.decode_cf(), DataArray.loc assignment, and the traceback through xarray's indexing path. Confirm that the encoded-time case fails before load() and the decoded case succeeds; done means the encoded-time assignment works without requiring load(), with a regression test for the reported example.