Exploration of a simple model for ice ages
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Exploration of a simple model for ice ages A. C. Fowler · R. E. M. Rickaby · E. W. Wolff
Received: 18 April 2012 / Accepted: 23 June 2012 © Springer-Verlag 2012
Abstract We argue that, while Milankovi´c variations in solar radiation undoubtedly have a major influence on the timing of the Quaternary ice ages, they are partly incidental to their underlying causes. Based on observations of the significance of CO2 , we propose a conceptually simple (but complicated in detail) energy balance type model which has the ability to explain the underlying oscillatory nature of ice ages. We are led to develop a model which combines ice sheet growth and atmospheric energy balance with ocean carbon balance. In order to provide results which mimic the basic features of the observations, we develop novel hypotheses as follows. The succession of the most recent ice ages can be explained as being due to an oscillation due to the interaction of the growing northern hemisphere ice sheets and proglacial lakes which form as they migrate south. The CO2 signal which faithfully follows the proxy temperature signal can then be explained as being due to a combination of thermally activated ocean biomass production, which enables the rapid CO2 rise at glacial terminations, and enhanced glacial carbonate weathering through the exposure of continental shelves, which enables CO2 to passively follow the subsequent glacial cooling cycle. Milankovi´c variations provide for modulations of the amplitude and periods of the resulting signals.
A. C. Fowler (B) MACSI, University of Limerick, Limerick, Republic of Ireland e-mail: [email protected] A. C. Fowler OCIAM, University of Oxford, Oxford, UK R. E. M. Rickaby Department of Earth Sciences, University of Oxford, Oxford, UK E. W. Wolff British Antarctic Survey, High Cross, Madingley Road, Cambridge, UK
123
Int J Geomath
Keywords Ice ages · Milankovi´c · Energy balance model · Proglacial lakes · Carbonate weathering Mathematics Subject Classification
86A40
Contents 1 A critique of the Milankovi´c theory of ice ages 2 Background and outline . . . . . . . . . . . . 3 A simple model of ocean carbon . . . . . . . . 3.1 The carbon cycle . . . . . . . . . . . . . 3.2 The ocean-atmosphere model . . . . . . . 3.3 An application to post-Eocene cooling . . 3.4 An application to global warming . . . . . 4 Climate and ice sheet models . . . . . . . . . 4.1 A simple climate model . . . . . . . . . . 4.2 Nucleation and growth of ice sheets . . . 5 Combined ice and carbon model . . . . . . . . 5.1 The full dimensionless model . . . . . . . 5.2 The onset of ice ages . . . . . . . . . . . 6 Proglacial lake formation . . . . . . . . . . . 6.1 Glacial retreat . . . . . . . . . . . . . . . 6.2 The proglacial lake equation . . . . . . . 7 Rapid CO2 rise . . . . . . . . . . . . . . . . . 7.1 Continental shelf exposure . . . . . . . . 7.2 River chemistry . . . . . . . . . . . . . . 7.3 Bioproduction . . . . . . . . . . . . . . . 8 Numerical results . . . . . . . . . . . . . . . . 8.1 Numerical method . . . . . . .
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