Support freq="W" in standardized indices

[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?

• Add support for weekly standardized indices

Does this PR introduce a breaking change?

No

Other information:

I realize that xclim and climate_indices treat zero-inflated distributions differently. I will investigate which library does it correctly and include changes if needed

EDIT: I believe xclim has the correct implementation. The probability of zeroes should be determined in the fitting procedure, not by using the full dataset. The idea is when you compute a CDF, a zero value should be mapped to the prob_of_zero in the calibration period. That is the same logic as using the fitting params of the distribution in the calibration period to compute the CDF in the full dataset.

I confirmed this is also how it's done in the case of the R package (SPEI), although I find some steps a bit weird, but I'm not too familiar with R.

[coxipi]

I could not get "max-lik" to work with the R package, just got NaNs. But I hacked the xclim SPI to be able to use lmoments3 (it should be modified to be able to accept lmoments3) and the results are quite similar

This is not the case as I add zeros, the treatment seems different. I really have the impression there are errors in the code, but I'm not too proefficient in R:

      # Calculate CDF on `x` using `f_params`
      cdf_res <- switch(distribution,
        "log-Logistic" = lmom::cdfglo(x[ff], f_params),
        "Gamma" = lmom::cdfgam(x[ff], f_params),
        "PearsonIII" = lmom::cdfpe3(x[ff], f_params)
      )
      # Adjust for `pze` if distribution is Gamma or PearsonIII
      if (distribution == "Gamma" | distribution == "PearsonIII") {
        spei[ff, s] <- qnorm(pze + (1 - pze) * pnorm(spei[ff, s]))
      }

      # Store the standardized values
      spei[ff, s] <- qnorm(cdf_res)

The x above is the full timeseries, and the zeroes were never removed. The zeroes were removed for the calibration that computes f_params. After that, it seems that the #Adjust is just cancelled by the #Store? Or is there something very different with the "<-" relative to "=" when you just append non-null values?

I use the same precip time series, but I artifically added 0's The result I get with xclim seems more heatlhy:

[coxipi]

All in all, the weekly resampling seems to work well. On the question of the treatment of zeroes, climate-indices, R package, and xclim, all seem to work differently. I'm starting to think I have the right implementation, but if anyone wants to chip in, I would be glad if someone wants to give a fresh look on this

[coxipi]

If the calendar is not appropriate, there will simply be problems with resampling or groupby ? Is that sufficient for documentation purposes?

[aulemahal]

I would say yes. Xarray will fail.

The error is ValueError: Invalid frequency string provided. I wish it would say that it's because cftime doesn't support W, but still I don't think we need to add more safeguards.

W (business week) doesn't make sense in non-real calendars, I think users would be aware of that.

[aulemahal]

Looks good! But I thought the solution for lmoments3 was the opposite.

[coxipi]

I don't know why #1892 was not closed, I thought it was automatic