FIX: Standardize method applied on individual variables in OTC/dOTC

[coxipi]

Pull Request Checklist:

• This PR addresses an already opened issue (for bug fixes / features)
  • This PR fixes #xyz
• Tests for the changes have been added (for bug fixes / features)
  • (If applicable) Documentation has been added / updated (for bug fixes / features)
• CHANGELOG.rst has been updated (with summary of main changes)
  • Link to issue (:issue:number) and pull request (:pull:number) has been added

What kind of change does this PR introduce?

• The mean and std in the 'standardize' normalization method of OTC/dOTC now is correctly applied on each variable individually
• While we're at it, I suggest changing the argument transform to normalization which I feel is more specific and informative. Also, in optimal_transport, we should follow the snake convention, numIterMax -> num_iter_max (I guess this was done to imitate the signature of ot.emd, but I think we need to stick to a standard in xclim functions)

Does this PR introduce a breaking change?

• transform -> normalization in input arguments.

Other information:

[Zeitsperre]

This seems like a fine change. The transform signature is very new, so no need for a deprecation warning message. Just need to update the CHANGELOG.

[coxipi]

@SarahG-579462 Thoughts on these changes? Especially transform -> normalization which is a matter of taste.

[coveralls]

coverage: 89.393%. remained the same
when pulling 1999981 on fix_dotc_standardization
into 32cb8f5 on main.

[coxipi]

It's a step in the right direction, but I realze that's not even what I had in mind for the standardization. Right now, we just remove the mean/std of the cells, but those are simply evenly distributed. So, it doesn't say much about the distributions at hand, we don't have the information of the probability of each cell (or the count). Perhaps a proper standardization would not work well, but this remains to be seen

[SarahG-579462]

This looks good. Did you want to include your work with the time step vs grid cell motion, or do you want that in a different PR?

[coxipi]

Maybe the dOTC evolution through cells (more fidel to the paper) can wait another PR.

But, as I was refering in my last comment, I don't think what we were doing previously is what I had in mind for standardization. Both are interesting in their own way, and don't yield very different results as far as I can see. The new use muX to weight over different cells, in this way we truly standardize the time series X and not its grid (which are just the position of the bins without their count, this is why I need to use muX to obtain a proper weighting)

    def _standardize(grid, mu):
        mu0 = mu.reshape(len(mu), 1)
        mean = (mu0*grid).sum(axis=0)
        std =  np.sqrt((mu0*(grid**2-mean**2)).sum(axis=0))
        return (grid-mean)/std
   
    # this actually computes  `( X - mean(X) ) / std(X)`
    if normalization == "standardize":
        gridX = _standardize(gridX, muX)
        gridY = _standardize(gridY, muY)

    # this is the old way, it computes `(gridX - mean(gridX) ) / std(gridX)`
    elif normalization  == "standardize_cells":
        gridX = (gridX - gridX.mean(axis=0)) / gridX.std(axis=0)
        gridY = (gridY - gridY.mean(axis=0)) / gridY.std(axis=0)
        

The differences are not huge though:

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[coxipi]

I'll just merge this PR now, other changes can be in another PR.