Articles | Volume 11, issue 1
Earth Syst. Dynam., 11, 281–289, 2020
https://doi.org/10.5194/esd-11-281-2020
Earth Syst. Dynam., 11, 281–289, 2020
https://doi.org/10.5194/esd-11-281-2020

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. 
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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.
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