xarray v 2023.9.0: ```ValueError: unable to infer dtype on variable 'time'; xarray cannot serialize arbitrary Python objects```

What happened?

I tried to save an xarray dataset with datetimes as data for its time dimension to a nc file with to_netcdf and got the error ValueError: unable to infer dtype on variable 'time'; xarray cannot serialize arbitrary Python objects.

What did you expect to happen?

I expected xarray to automatically detect these were datetimes, and convert them to whatever format xarray likes to work with internally to dump it into a CF compatible file, following what is described at https://github.com/pydata/xarray/issues/2512 .

Minimal Complete Verifiable Example

import xarray as xr
import datetime

times = [datetime.datetime(2024, 1, 1, 1, 1, 1, tzinfo=datetime.timezone.utc), datetime.datetime(2024, 1, 1, 1, 1, 2, tzinfo=datetime.timezone.utc)]

data = [1, 2]

xr_result = xr.Dataset(
    {
        'time':
        xr.DataArray(dims=["time"],
                     data=times,
                     attrs={
                         "standard_name": "time",
                     }),
        #
        'data':
        xr.DataArray(dims=["time"],
                     data=data,
                     attrs={
                         "_FillValue": "NaN",
                         "standard_name": "some_data",
                     }),
    }
)

xr_result.to_netcdf("test.nc")

MVCE confirmation

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

The example is available as a notebook viewable at:

https://github.com/jerabaul29/public_bug_reports/blob/main/xarray/2024_01_24/xarray_and_datetimes.ipynb

Environment

Start with the provided minimal example and trace the Dataset.to_netcdf path for the datetime-valued time variable. Confirm the behavior with a focused regression test, and consider the issue complete when the example serializes successfully to a CF-compatible netCDF file without the dtype error.