Topological Climate Change and Anthropogenic Forcing

The mathematical theory of bifurcation is applied to an energy balance model of the Earth’s climate. Bifurcation theory explains how nonlinear systems can exhibit drastically different solutions when certain parameters, though varied gradually, cause catastrophic changes. Such a model is better able to forecast major changes in the climate than traditional methods that capture gradual variations. This thesis presents the first mathematical proof of the existence of a cusp bifurcation in a paleoclimate energy balance model. This result leads to rational explanations for three outstanding problems of paleoclimate science: the Pliocene paradox, the abruptness of the Eocene-Oligocene transition, and the warm, equable Cretaceous-Eocene climate problem. The refinement of this paleoclimate energy balance model using modern climate data adapts it to modern day and near-future parameters up to the year 2300, focusing on climate forcing caused by human activity. Results suggest an even greater future warming effect in the Arctic and Antarctic than currently projected, as a result of a bifurcation that causes a jump to a much warmer climate state in these regions.