diff of cftime.Datetime

What happened?

A cftime variable returns a timedelta64[ns] when calling diff / + / - and it can then not be added/ subtracted from the original data.

What did you expect to happen?

We can add cftime timedeltas.

Minimal Complete Verifiable Example

import xarray as xr

air = xr.tutorial.open_dataset("air_temperature", use_cftime=True)

air.time + air.time.diff("time") / 2

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.

Relevant log output

air.time.variable.values[1:] - air.time.variable.values[:-1]

returns array([datetime.timedelta(seconds=21600), ...]) but then

xr.Variable(("time",), np.array([datetime.timedelta(0)]))

returns a dtype='timedelta64[ns]' array.

Anything else we need to know?

• See upstream PR: xarray-contrib/cf-xarray#441
• Similar to #7381 (but I don't think it's the same issue, feel free to close if you disagree)
• That might need a special data type for timedeltas of cftime.Datetime objects, or allowing to add 'timedelta64[ns]' to cftime.Datetime objects
• The casting comes from

https://github.com/pydata/xarray/blob/d8ec3a3f6b02a8b941b484b3d254537af84b5fde/xarray/core/variable.py#L366

https://github.com/pydata/xarray/blob/d8ec3a3f6b02a8b941b484b3d254537af84b5fde/xarray/core/variable.py#L272

Environment

Reproduce the provided cftime example with xarray. Start at xarray/core/variable.py around lines 272 and 366, where the issue identifies the timedelta casting. Done means that the result of diff and the + or - operations can be applied back to the original cftime data without an incompatible dtype.