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OK great. We can meditate on it for a while, no great rush! Thanks for engaging.

we would either have to raise an error or automatically transpose the second variable. Neither option sounds great to me.

Agree, I was thinking we'd transpose the second one, but fair if you think too invasive

Maybe this would be fine. We already do automatic alignment, and this is really not that much different.

It would be a breaking change, though, so we would need to roll it out slowly.

Perhaps this could be relaxed now that Python's dict always preserves the order in which items are added.

Ah OK. If we relaxed that, what would the order be? Just the order they were initially added, and so at least consistent through time (though not necessarily with the variables)?

Yes, that's right.

One potential concern is that this would expose a detail of xarray's data model that would not be easy for users to control. I can imagine that we might have internal xarray methods that inadvertently change dimension order.

So maybe this would make sense only if we also do your other suggested change (enforcing a consistent dimension order throughout a Dataset).

we would either have to raise an error or automatically transpose the second variable. Neither option sounds great to me.

Agree, I was thinking we'd transpose the second one, but fair if you think too invasive

Perhaps this could be relaxed now that Python's dict always preserves the order in which items are added.

Ah OK. If we relaxed that, what would the order be? Just the order they were initially added, and so at least consistent through time (though not necessarily with the variables)?

Consistent dimension ordering is usually a best practice, but I'm not sure we want to enforce it. If a user explicitly supplies two variables, with dimensions ('x', 'y') and ('y', 'x'), respectively, we would either have to raise an error or automatically transpose the second variable. Neither option sounds great to me.

As for the current order in ds.dims, right now we use sorted order. Mostly this is because I didn't want to need to use an OrderedDict for keeping track of dimensions on datasets, and until recently Python dict order was entirely arbitrary. Perhaps this could be relaxed now that Python's dict always preserves the order in which items are added.

What do we think about attempting to enforce a dimension order throughout the dataset? That would solve these issues for free.

We already have some order in .dims & .sizes. Could we transpose all dimensions to that ordering after any operation?

(Maybe this doesn't need to be strictly enforced, but we'd at least set the expectation that dimensions could be reordered to that dimension order at any time)

Or are there uses to having different dimension order throughout a dataset?

```python In [45]: ds Out[45]: <xarray.Dataset> Dimensions: (lat: 25, lon: 53, time: 2920) Coordinates: * lat (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0 * lon (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0 * time (time) datetime64[ns] 2013-01-01 ... 2014-12-31T18:00:00 Data variables: air (time, lat, lon) float32 ... Attributes: Conventions: COARDS title: 4x daily NMC reanalysis (1948) description: Data is from NMC initialized reanalysis\n(4x/day). These a... platform: Model references: http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

In [46]: ds.dims Out[46]: Frozen(SortedKeysDict({'lat': 25, 'time': 2920, 'lon': 53}))

In [47]: ds.sizes Out[47]: Frozen(SortedKeysDict({'lat': 25, 'time': 2920, 'lon': 53})) ```

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What if we just supplied an output_dims kwarg to apply_ufunc or apply_raw?

We could do that, but how to do we handle specifying output dimensions for a Dataset function? Maybe use a dict?

This is part of why a helper function starts to make sense to me.

What if we just supplied an output_dims kwarg to apply_ufunc or apply_raw?

I started trying to implement this in apply_ufunc and then realized why I hadn't done so before: it's really not clear how to match up input/output arguments if there are more than one of each. We could do something special for there first input/output but that could be more confusing than helpful.

This is probably better reserved for the simpler apply_raw(https://github.com/pydata/xarray/issues/1618).

At this point, I think I'm +1 on either automatically restoring dimension order or providing some option to do so (with restoring as the default). I'm still getting used to apply_ufunc so I'm not sure I feel strongly enough to make this call yet though.

I wonder if it would make sense to simply change the behavior of apply_ufunc so existing dimensions always get restored to their original location, and only new dimensions remain at the end. It seems like this is almost always desirable.