check_inputs is too strict with multivariate coordinates

[coxipi]

Setup Information

• Xclim version: '0.50.1-dev.1'
• Python version:
• Operating System:

Description

I think I should be able to use stacked periods & variables together:

ref, sim  = [stack_periods(ds, window=30) for ds in [ref, sim]]
daref,dasim  = [sdba.stack_variable(ds, window=30) for ds in [ref, sim]]
sdba.EmpiricalQuantileMapping.train(ref=daref.isel(period=0), hist=dasim.isel(period=0)).adjust(sim=dasim.isel(period=1))

Steps To Reproduce

from xclim.core.calendar import stack_periods
from xclim import sdba
from xclim.testing import open_dataset
ds = open_dataset("sdba/ahccd_1950-2013.nc")

# success
ds = stack_periods(ds, window=30)
sdba.BaseAdjustment._check_inputs(*[ds.isel(period=0), ds.isel(period=1)], group=sdba.Grouper("time"))

da = sdba.stack_variables(ds)
# fail
sdba.BaseAdjustment._check_inputs(*[da.isel(period=0), da.isel(period=1)], group=sdba.Grouper("time"))

This comes from this very strict comparison on multivariate coordinates mvcrds:

if mvcrds and (
    not all(mvcrds[0].equals(mv) for mv in mvcrds[1:])
            or len(mvcrds) != len(inputs)
        ):
            coords = {mv.name   for mv in mvcrds}
            raise ValueError(
                f"Inputs have different multivariate coordinates: {', '.join(coords)}."
            )

Additional context

I guess we want to be very strict with a multivariate coordinate because it's a weird object? period is a special type of coordinate where we accept in the context of bias adjustment, it can differ on various datasets

I could skip_input_checks or drop the period coordinate, it's just a bit impractical

Contribution

• I would be willing/able to open a Pull Request to address this bug.

Code of Conduct

• I agree to follow this project's Code of Conduct