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Climate of the Past An interactive open-access journal of the European Geosciences Union
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Discussion papers | Copyright
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 22 May 2018

Research article | 22 May 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Climate of the Past (CP).

An Energy Balance Model for Paleoclimate Transitions

Brady Dortmans, William F. Langford, and Allan R. Willms Brady Dortmans et al.
  • Department of Mathematics and Statistics, University of Guelph, 50 Stone Road West, Guelph, ON, N1G 2W1, Canada

Abstract. A new energy balance model (EBM) is presented and is used to study Paleoclimate transitions. While most previous EBMs dealt only with the globally averaged climate, this new EBM has three variants: Arctic, Antarctic and Tropical climates. This EBM incorporates the greenhouse warming effects of both carbon dioxide and water vapour, and also includes ice-albedo feedback. The main conclusion to be drawn from the EBM is that the climate system possesses multiple equilibrium states, both warm and frozen, which coexist mathematically. While the actual climate can exist in only one of these states at any given time, the climate can undergo transitions between the states, via mathematical saddlenode bifurcations. This paper proposes that such bifurcations have actually occurred in Paleoclimate transitions. The EBM is applied to the study of the Pliocene Paradox, the Glaciation of Antarctica and the so-called warm, equable climate problem of both the mid-Cretaceous Period and the Eocene Epoch. In all cases, the EBM is in qualitative agreement with the geological record.

Brady Dortmans et al.
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Brady Dortmans et al.
Brady Dortmans et al.
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Short summary
In geology and in paleoclimate science, most changes are caused by well-understood forces acting slowly over long periods of time. However, in highly nonlinear physical systems, mathematical bifurcation theory predicts that small changes in forcing can cause major changes in the system, in a short period of time. This paper explores some sudden changes, in the paleoclimate history of the Earth, where it appears that bifurcation theory gives a more satisfying explanation than uniformitarianism.
In geology and in paleoclimate science, most changes are caused by well-understood forces acting...