Effects of feedbacks for an energy balance model on a circle

Abstract

A simple, North like, energy balance model on a circle is studied using boundary formulations derived with Green's functions for the stationary case, and a pseudo-spectral and finite difference solution for the time dependent case. The bifurcation software Auto-07p is also applied. The boundary formulation solution can be solved analytically in most cases, and is solved for bifurcation diagrams. Segmenting the circle into water and continent areas adds additional feedback mechanisms, whose effects are investigated through the bifurcation diagram form in different cases, and the stability of the bifurcation branches. It is found that additional feedback mechanisms result in smaller, step by step, drop offs in stationary state temperature when varying the solar constant.