Solving a North-type energy balance model using boundary integral methods

Abstract. Simplified climate models such as energy balance models (EBMs) are useful conceptual tools, in part because their reduced complexity often allows for studies using analytical methods. In this paper, we solve a North-type EBM using a boundary integral method (BIM). The North-type EBM is a diffusive one-dimensional EBM with a non-linear albedo feedback mechanism. We discuss this approach in light of existing analytical techniques for this type of equation. Subsequently, we test the proposed method by solving multiple North-type EBMs with a zonally symmetric continent featuring an altered ice-albedo feedback dynamic. We demonstrate that the introduction of a continent results in new equilibrium states characterized by multiple ice edges and ice belts. Furthermore, we show that the BIM serves as an efficient framework for handling unconventional ice distributions and model configurations for North-type EBMs.