In an article by Zhang et al., the authors describe how the (normalized) forecast errors of different renewable energy sources (like solar panels and wind mills) are correlated. To that end, they compute Pearson's correlation coefficient for different pairs of solar panels and wind mills. (See, for instance, page 5 of the paper.)

Now, these pairs of renewable energy sources are located at (approximately) the same place. I wonder how the Pearson correlation coefficient for the forecast error changes according to change in distance between the two energy sources. I guess that, the bigger the distance gets, the smaller the correlation coefficient becomes. At some point, it ought to be (almost) zero. Then the forecast error distributions are independent of one another.

So my questions are:

what is the relationship between the distance between two renewable energy sources and the Pearson correlation coefficient of their respective forecast error distributions? Are there any articles describing this relationship?

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