| An Energy Balance Model (EBM) is an example of a minimum complexity climate model, constructed to build an understanding of the ice albedo feedback mechanism in a planet. The first EBM was conceptualized by Mihail Budyko in 1969 and various versions of it were studied by many since then, with the most recent formulation by Ka Kit Tung in 2007. None of these studies, however, proposed a model describing the movement of the ice line, which is crucial in understanding the albedo feedback process. In my thesis, I will propose a new formulation which includes a mechanism admitting this iceline movement.The formulation is a multiple time scale system of difference equations in which the equation that governs the infinite dimensional variable (the fast equation) is coupled with an equation that dictates the one dimensional variable (the slow equation). Using techniques from Dynamical Systems, I will show that there exists one dimensional center stable manifold, and thus, the analysis of the dynamics reduces to a simple system in one dimension. Finally, I will analyze some properties of the planet suggested by this model. |
