Abstract
We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles. Filippov’s theory of differential inclusions is used to analyze the system, which can be viewed as a nonsmooth geometric singular perturbation problem. We prove the existence of a unique limit cycle, corresponding to the Earth’s glacial cycles. The diffusive heat transport component of the model is ideally suited for investigating the competing temperature gradient and transport efficiency feedbacks, each associated with ice-albedo feedback. It is the interplay of these feedbacks that determines the maximal extent of the ice sheet. In the nonautonomous setting, model glacial cycles persist when subjected to external forcing brought on by changes in Earth’s orbital parameters over geologic time. The system also exhibits various bifurcation scenarios as key parameters vary.
Highlights
Earth’s climate has varied drastically over long time scales, cycling between warmer interglacial periods and very cold glacial states
The beginning of a glacial cycle is characterized by a slow descent into a much colder world, in which massive ice sheets advanced into North America and Eurasia, fed by the moisture resulting from a corresponding drop in sea level of about 350 feet [1]
We present a new conceptual model of the glacial cycles in which the latitudinal transport of heat is modeled as a diffusive process
Summary
Earth’s climate has varied drastically over long time scales, cycling between warmer interglacial periods and very cold glacial states (ice ages). At the onset of a glacial age, a descending ice sheet leads to an increase in the surface temperature gradient, due to the increased albedo in the polar region This leads to a positive feedback in that the poleward transport of heat and moisture by the atmosphere, with the moisture precipitating out as snow on the glacier, is enhanced, all things being equal [23]. We investigate the interaction between this negative feedback and the positive temperature gradient feedback described above in the conceptual model, ODE setting We do this in part by assuming the diffusive meridional transport efficiency parameter is smaller during a glacial advance, relative to that during a glacial retreat, due to the ice cover
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