Adds twcrps for ensembles

[nicholasloveday]

About

This pull request includes:

• twCRPS for ensembles implementation
• A twCRPS convenience function tail_twcrps_for_ensembles for threshold weighting of the tail
• improvements to the crps_for_ensembles tests (it can now take xr.datasets and broadcasting is tested)

Tutorial

The tutorial is expected to be completed in a separate pull request.

Further extensions

In the future, I can to add other convenience functions for different kinds of threshold weighting (e.g., interval)

Checklist

Development for new xarray-based metrics

• Works with n-dimensional data and includes reduce_dims, preserve_dims, and weights args.
• Typehints added
• Docstrings complete and followed Napoleon (google) style
• Reference to paper/webpage is in docstring
• Add error handling
• Imported into the API

Testing of new xarray-based metrics

• 100% unit test coverage
• Test that metric is compatible with dask.
• Test that metrics work with inputs that contain NaNs
• Test that broadcasting with xarray works
• Test both reduce and preserve dims arguments work
• Test that errors are raised as expected
• Test that it works with both xr.Dataarrays and xr.Datasets

Documentation

• Add the score to the API documentation
• Add the score to the included list of metrics and tools

[nicholasloveday]

I should also mention that I compared the results from tail_twcrp_for_ensemble to the crps_cdf implementation with equivalent weights and found that the results converged with increasing sample size (even more so with method="fair")

[rob-taggart]

Looks good @nicholasloveday . Some suggestions for docstrings

[Steph-Chong]

1. Allen et al. (2023) (https://doi.org/10.1137/22M1532184) is paywalled. (Except for the supplementary materials, which are freely available). Is there also a non-paywalled reference available for these metrics? (I realise there isn't always a good, non-paywalled reference available).

2. I was looking at how Tail twCRPS for Ensembles and twCRPS for Ensembles appear in included.md when rendered (see: https://scores.readthedocs.io/en/228-documentation-testing-branch/included.html). They look good as is. However, I was wondering, should they perhaps be included as nested items underneath "Continuous Ranked Probability Score (CRPS) for Ensembles" - in a similar fashion to how the CRPS for CDFs functions appear in included.md? I really have no opinion on this - I imagine it is fine either way - I just wanted to raise the question.

[tennlee]

I did this a number of days ago and didn't realise it hadn't shown. Apologies.

[nicholasloveday]

1. Allen et al. (2023) (https://doi.org/10.1137/22M1532184) is paywalled. (Except for the supplementary materials, which are freely available). Is there also a non-paywalled reference available for these metrics? (I realise there isn't always a good, non-paywalled reference available).

   2. I was looking at how Tail twCRPS for Ensembles and twCRPS for Ensembles appear in included.md when rendered (see: https://scores.readthedocs.io/en/228-documentation-testing-branch/included.html). They look good as is. However, I was wondering, should they perhaps be included as nested items underneath "Continuous Ranked Probability Score (CRPS) for Ensembles" - in a similar fashion to how the CRPS for CDFs functions appear in included.md? I really have no opinion on this - I imagine it is fine either way - I just wanted to raise the question.

1. There is a preprint on arXiv https://arxiv.org/abs/2202.12732 . Many of our references in scores are behind paywalls, but by Googling the title you can usually find the PDF. I'll leave this as is until we make a decision to additionally add links to non-paywalled articles everywhere, but I definitely think that it's worthwhile to consider.
2. Potentially. What I have done is consistent with how twMSE and MSE appear in the documentation. I'll leave it as is unless someone has a strong opinion on it.

[nicholasloveday]

Thank you for those helpful reviews. I have pushed up the changes.