Correlation of two positive signals

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I have many signals that look as following - enter image description here

I wish to calculate correlations (closeness) of any pair of such signals. The problem is that the signal is all positive, so any method produces some positive correlations even if the signals are not related (no negative values which may help to nullify the result in case of unrelated signals).

Can anyone suggest a method, or better, some references of how to calculate correlations of strictly positive signals?