A dynamics approach to a low-order climate model

James Walsh,Esther Widiasih

doi:10.3934/dcdsb.2014.19.257

Abstract

Energy Balance Models (EBM) are conceptual models which have proved useful in the study of planetary climate. The focus of EBM is placed on large scale climate components such as incoming solar radiation, albedo, outgoing longwave radiation and heat transport, and their interactions. Until recently, their study has centered on equilibrium solutions of an associated model equation, with no consideration of the dynamical nature of these solutions. In this paper we continue and expand upon recent efforts aimed at placing EBM in a more mathematical, dynamical systems context. In particular, the dynamical behavior of several variants of the Budyko-Sellers model, all but one of which involve the movement of glaciers, is shown to reduce to the study of the system on an attracting one-dimensional invariant manifold in an appropriately defined state space.

Highlights

Mathematical models of planetary climate run the gamut from low-order models, through intermediate complexity models, and up to highly sophisticated planetary system models [11]
Low-order models, the analysis of which can be amenable to dynamical systems techniques, are often formulated via finitedimensional approximations to systems of PDEs derived from the associated physics
Latitudedependent energy balance models, such as those introduced by Budyko and Sellers in 1969, have been extensively studied

Summary

Introduction

Mathematical models of planetary climate run the gamut from low-order models, through intermediate complexity models, and up to highly sophisticated planetary system models [11]. We outline the proof of a theorem due to Widiasih [41] concerning the dynamics of the coupled temperature– ice line model.

Results

Conclusion