Degree Year

2013

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Jim Walsh

Keywords

Dynamical systems, Mathematical climatology, Snowball Earth, Geometric singular perturbation theory, Legendre polynomials, Jormungand state, Fast-slow systems, Numerical simulations, Hysteresis, Ice-albedo feedback, Budyko-Widiasih Model

Abstract

The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis.

Included in

Mathematics Commons

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