MBCn - Why an univariate adjustment before applying NpdfTransform?

[sylvainmarchi]

Setup Information

Xclim version: 0.52.0
Python version: 3.10.14
Operating System: Linux

Context

I would like to apply the MBCn algorithm to Euro-CORDEX data. I followed this helpful tutorial:
https://xclim.readthedocs.io/en/stable/notebooks/sdba.html#Fourth-example-:-Multivariate-bias-adjustment-with-multiple-steps-(Cannon,-2018)

I successfully reproduced the example. However, I’m curious about why a univariate adjustment is performed before applying the N-dimensional probability density function transform. I understand that the univariate adjustments are used afterward, but in Cannon (2018), isn’t the NpdfTransform applied to the standardized raw data?

Perhaps it doesn’t make much difference. I tested using the raw standardized stacked data, and it produces similar (by eye, I haven't investigated much) results. I thought the reason might be related to the convergence speed of the algorithm. However, the E-score converges similarly in both cases.

Thanks for sharing your thoughts on this and for taking the time to develop this useful package.

Sylvain

Steps To Reproduce

$ pip install foo --bar

[coxipi]

Hi Sylvain,

You are right, in (Cannon, 2018), we first have:

1. Npdf transform on raw standarized data
2. Univariate QDM on raw data
3. Reorder QDM-adjusted (output of 2.) using the Npdf transformed data (output of 1.)

In the xclim notebook you point out, we had:

1. Univariate QDM on raw data
2. Npdf transform on QDM-adjusted and standarized data
3. Reorder QDM-adjusted (output of 1.) using the Npdf transformed data (output of 2.)

I also concluded there was not much difference, but in newer version of xclim, we follow the exact methology proposed in (Cannon, 2018).

Both the standardization and univariate QDM are now performed in a single class MBCn in recent versions of xclim, you can see recent notebooks for more information (I found out the first two cells in the MBCn example in the latest sdba.ipynb don't serve any purpose, this might be a bit confusing, I will fix this for future releases)

Let me know if you have more questions.

Cheers,
Éric