Articles | Volume 11, issue 1
Research article
17 Mar 2020
Research article |  | 17 Mar 2020

π-theorem generalization of the ice-age theory

Mikhail Y. Verbitsky and Michel Crucifix

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Cited articles

Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J.I., Takahashi, K., and Blatter, H.: Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume, Nature, 500, 190–194, 2013. 
Barenblatt, G. I.: Scaling, Cambridge University Press, Cambridge, 2003. 
Berger, A. and Loutre, M. F.: Insolation values for the climate of the last 10 million years, Quaternary Sci. Rev., 10, 297–317, 1991. 
Buckingham, E.: On physically similar systems; illustrations of the use of dimensional equations, Phys. Rev., 4, 345–376, 1914. 
Chalikov, D. V. and Verbitsky, M. Y.: Modeling the Pleistocene ice ages, Adv. Geophys., 32, 75–131, 1990. 

The requested paper has a corresponding corrigendum published. Please read the corrigendum first before downloading the article.

Short summary
Using the central theorem of dimensional analysis, the π theorem, we show that the relationship between the amplitude and duration of glacial cycles is governed by a property of scale invariance that does not depend on the physical nature of the underlying positive and negative feedbacks incorporated by the system. It thus turns out to be one of the most fundamental properties of the Pleistocene climate.
Final-revised paper