Incomplete similarity of the ice-climate system

Abstract. Reconstruction and explanation of past climate evolution using proxy records is the essence of paleoclimatology. In this study, we use dimensional analysis and concepts of similarity to recognize theoretical limits of such forensic inquiries. Specifically, we demonstrate that incomplete similarity in the dynamical ice-climate system implies the absence of physical similarity in conglomerate similarity parameters. It means that major events of the past such as, for example, the middle-Pleistocene transition could have been produced by different physical processes, and, therefore, the task of disambiguation of the historical paleo-records may be fundamentally difficult, if not impossible. It also means that any future scenario may not have a unique cause and, in this sense, the orbital time-scale future may be to some extent insensitive to specific physical circumstances.