@pschwede well CO2 isnt really showing a delay there just looks that way because they have different zero values. Instead of trying to see if one line is to the left or right of the other pick out actually peaks and look how they line up. The peaks themselves mostly overlap on each other well.

In practice we dont just eye ball it in science. Im suggesting you do it here since i dont want to actually take the time it would take (months/weeks) to teach you statistics. In practice what we do is actually test for the stuff your saying with very specific formula. Those are covered int he full paper I linked.