On the effects of symmetry in the energy balance on a sphere

Abstract

Simple climate models have gathered much attention as they have suggested the possibility of abrupt climate change associated with tipping points. Several simple climate models are found to have multiple equilibria, but in most cases similar equilibria do not appear or become too difficult to find in complex, fully coupled earth system models. In this thesis, we investigate a simple climate model, an energy balance model on a sphere, and we highlight a possible factor in the behavioral discrepancy between many simple, low-dimensional models and earth system models. A hypothesis is put forward and investigated regarding the effects of symmetry and the presence of multiple equilibria in this simple model. A novel application of boundary integral methods in the context of energy balance models is presented, and used to find semi-analytical solutions to the stationary energy balance equation. The hypothesis is eventually refuted and a new hypothesis is formulated based on the evidence presented: Symmetry violations in energy balance models cause the steady state solutions to become more similar. This is discussed in light of earth system models and how a similar dynamic would make the detection of multiple equilibra challenging in earth system models.