[ENHANCEMENT] a closer look into the pastas CCF function

[dbrakenhoff]

When developing code to visualize the cross-correlation between synthetically generated heads based on actual rainfall, I noticed that pastas CCF function does not produce correlations that match the block response function. The pastas implementation is based on the pearson correlation coefficient whereas the CCF I developed uses np.correlate which uses a different definition of correlation.

According to theory, the cross-correlation should be equal to the block response as long as autocorrelation in the stress time series is not obfuscating the relationship. The example below shows the known block-response used to create a synthetic head time series. The different color bar plots show the computed CCF using different methods. The pastas CCF method clearly produces a very different result from the CCF (original). Also the block-response matches nicely with the CCF-PW computation, whereas it looks nothing like the pastas CCF result.

Things to check:

• difference between pastas and my CCF is not just some scaling issue?
• ...

This issue replaces #352 and #350. Cross-correlation developments will be programmed as a pastas plugin in the future once we settle on a plugin architecture.

[mbakker7]

Are there references to the different approaches of computing the CCF?
Would be useful here, but especially in the doc string.
But the new CCF-PW seems like the way to go.

[raoulcollenteur]

Do we have some code and script with a simple example to compute the CCF? perhaps a benchmark where we know the theoretical values like in the ACF benchmark..https://pastas.readthedocs.io/en/master/benchmarks/autocorrelation.html