Effects of Symmetry in a Diffusive Energy Balance Model

TL;DR

This paper analyzes how symmetry and continent placement affect equilibrium states and bifurcations in a North-type Energy Balance Model using analytical and numerical methods.

Contribution

It introduces a detailed analysis of symmetry effects on climate model equilibria and bifurcations, highlighting the impact of continent placement on system dynamics.

Findings

Symmetry increases the number of bifurcations and equilibria.

Continent placement significantly influences bifurcation sensitivity.

The bifurcation structure offers insights into complex climate dynamics.

Abstract

In this paper, we solve a North-type Energy Balance Model (EBM) using an analytical method, the Boundary Integral Method. This approach is discussed in light of existing analytical techniques for this type of equation. We use the method to demonstrate that the placement of a zonally symmetric continent, with an altered ice-albedo feedback dynamic, introduces new equilibrium states. A finite difference algorithm is implemented to solve the time-dependent equation and assess the stability of the equilibrium states, along with a numerical perturbation scheme. Bifurcation diagrams are drawn and we show that the bifurcation curve is extremely sensitive to the placement of a continent. The continent is initially configured with meridional symmetry, and we investigate how the system dynamics respond to a gradual reduction of the system's symmetry properties. We find that meridional symmetry increases the number of fold bifurcations and equilibria. Additionally, we discuss how the emerging bifurcation structures may provide insights into the complex dynamics involved as one ascends the climate model hierarchy.