Well, there’s a paper in Theoretical and Applied Climatology by Jarl Kampen from the Environmental Policy Group and Research Methodology Group at Wageningen University and Research. Under the title “A methodological note on the making of causal statements
in the debate on anthropogenic global warming” (doi: 10.1007/s00704-010-0355-y), he puts forward some methodological caveats of climate change research based on mathematical and philosophical thoughts.
I have to admit, I do not really know what to think about it. There are so many points where I want to object or at least identify weaknesses, it’s kind of endless. On the other hand, it’s hard to really put the finger on the errors. Therefore I only want to say, that I have a problem with the foundation of his argumentation. Kampen starts from Popper‘s view of scientific theories and the necessity of falsifiers. My impression is, that he ignores much of the post-Popper philosophy of science (Kuhn and others).
Nevertheless Kampens paper is a provoking read and he probably is correct, that climate change research would benefit from the identification of falsifiers. However, these ought not to be purely mathematical but rather base on physics.