Thanks for raising this issue @mathause. In hindsight this does not surprise me. Pandas's strict use of nanosecond-resolution datetimes and timedeltas was part of the motivation for the CFTimeIndex. While convenient, because it allows us to re-use code already written in pandas, holding the result of the difference between two CFTimeIndexes in a TimedeltaIndex clearly prevents us from taking the difference between distant dates.

Perhaps a more robust (yet more complex) solution for https://github.com/pydata/xarray/issues/2484 would be to write a version of a TimedeltaIndex that does not internally cast the timedeltas to type np.timedelta64[ns], and rather leaves them as datetime.timedelta objects, which are the actual result of subtracting two sequences of cftime.datetime objects.

Regarding the combine_by_coords issue, though, there might be an easier fix. Is there a reason that first_items is an Index of length-one Indexes? It's not clear to me why that needs to be the case.

https://github.com/pydata/xarray/blob/56c16e4bf45a3771fd9acba76d802c0199c14519/xarray/core/combine.py#L91

It appears if we just select the first value of each index (i.e. a cftime.datetime object in this example), e.g.

python first_items = pd.Index([index[0] for index in indexes]) pandas's rank method works properly and combine_by_coords produces the correct result:

```

xr.combine_by_coords([d1, d2, d3]).time <xarray.DataArray 'time' (time: 3)> array([cftime.DatetimeGregorian(4500, 12, 31, 0, 0, 0, 0, 4, 365), cftime.DatetimeGregorian(4600, 12, 31, 0, 0, 0, 0, 2, 365), cftime.DatetimeGregorian(5100, 12, 31, 0, 0, 0, 0, 0, 365)], dtype=object) Coordinates: * time (time) object 4500-12-31 00:00:00 ... 5100-12-31 00:00:00 ```

This happens in xr.combinde_by_coords. Note that the OverflowError is "ignored in: pandas._libs.algos.are_diff'". Soxr.combinde_by_coords` can return a wrong dataset (although this does not happen silently):

``` python

import xarray as xr i1 = xr.cftime_range("4500-12-31", periods=1) i2 = xr.cftime_range("4600-12-31", periods=1) i3 = xr.cftime_range("5100-12-31", periods=1)

d1 = xr.DataArray([0], dims=("time", ), coords={"time": ("time", i1)}).to_dataset(name="a") d2 = xr.DataArray([1], dims=("time", ), coords={"time": ("time", i2)}).to_dataset(name="a") d3 = xr.DataArray([2], dims=("time", ), coords={"time": ("time", i3)}).to_dataset(name="a")

xr.combine_by_coords([d1, d2, d3]).time ```

returns:

python <xarray.DataArray 'time' (time: 2)> array([cftime.DatetimeGregorian(4500-12-31 00:00:00), cftime.DatetimeGregorian(5100-12-31 00:00:00)], dtype=object) Coordinates: * time (time) object 4500-12-31 00:00:00 5100-12-31 00:00:00 note how d2 is missing.

Within xr.combine_by_coords the error happens here:

https://github.com/pydata/xarray/blob/7b4a286f59bc7d60d4e4d03be65562ff63f9b111/xarray/core/combine.py#L98

``` python import pandas as pd

indexes = [i1, i2, i3]

the code from _infer_concat_order_from_coords

first_items = pd.Index([index.take([0]) for index in indexes])

series = first_items.to_series() rank = series.rank(method="dense", ascending=ascending) order = rank.astype(int).values - 1

order

array([0, 1, 1]) ```

This causes the second item to be dropped.