Actually, I used fewer words. I don't think you understand what the authors are doing. They are modeling temperature T per year as a sum of four terms: T = E + S + V + R---(E)l Nino, (S)solar irradiance, (V)olcanic activity, and (R)emaining factors. Then they subtract E, S, and V. Then they show that R fits a super-linear curve. Why there would be no "statistically valid way" to do this is beyond me, the authors, and the article's peer reviewers. If this is "bad methodology", lodge your complaints on https://pubpeer.com/.
1) Their model is inherently dumb. The system is much more complicated and inseparable.
2) They openly admit that “subtracting E, S and V”, as you say, cannot actually be done.
3) They’re arbitrarily removing sources of variation so that they can claim “significance” in a narrow window. The entire exercise is designed to achieve a predetermined outcome, and statistical significance cannot be calculated in those circumstances.
