Dynamics of the Budyko Energy Balance Model

TL;DR

This paper develops a dynamical systems framework for the Budyko energy balance model by incorporating ice line dynamics, resulting in a more precise mathematical formulation and analysis of climate behavior.

Contribution

It introduces a novel formulation of the Budyko model as an integro-difference equation coupled with ice line dynamics, revealing an attracting invariant manifold.

Findings

The model possesses an attracting one-dimensional invariant manifold.

The formulation captures known solutions with increased mathematical precision.

The approach enhances understanding of climate system stability and bifurcations.

Abstract

A dynamical system derived from a conceptual climate model is investigated. The model is often referred to as Budyko-Sellers type Energy Balance Model (EBM), or in short, the Budyko model. The focus of this study is on the mathematical formulation that further develops the model by capturing the ice line dynamics, and thereby places the Budyko model in dynamical systems framework. The classical Budyko EBM is represented here as an integro-difference equation, then coupled with an ice line equation. The resulting infinite dimensional system is shown to possess an attracting one dimensional invariant manifold. The novel formulation captures solutions that others have previously obtained while also making the formulation and the analysis of the model more precise.