Neoproterozoic glacial ages in a nonsmooth conceptual model

Abstract

There is widespread agreement that ice sheets flowed into the ocean in tropical latitudes at sea level during the Earth's past. Whether these extreme ice ages were snowball Earth events, with the entire surface covered in ice, or whether ocean water remained ice free in regions about the equator, continues to be controversial. For the latter situation to occur, the effect of positive ice albedo feedback would have to be damped to stabilize an advancing ice sheet shy of the equator. In this paper we analyze a conceptual model comprised of a zonally averaged surface temperature equation coupled to a dynamic ice line equation. This difference equation model is aligned with the cold world of these great glacial episodes through an appropriately chosen albedo function. Using the spectral method, the analysis leads to a nonsmooth singular perturbation problem. The Hadamard graph transform method is applied to prove the persistence of an invariant manifold, thereby providing insight into model behavior. A stable climate state with the ice line resting in tropical latitudes, but with open water about the equator, is shown to exist. Also presented are local smooth and nonsmooth bifurcations as parameters related to atmospheric carbon dioxide concentrations and the efficiency of meridional heat transport, respectively, are varied.

Publisher

IOP Publishing

Publication Date

7-30-2018

Publication Title

Journal of Physics Communications

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1088/2399-6528/aab748

Keywords

Nonsmooth invariant manifold, Singular perturbation, Neoproterozoic Era ice ages

Language

English

Format

text

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