A dynamics approach to a low-order  climate model

James Walsh; Esther Widiasih

doi:10.3934/dcdsb.2014.19.257

Article Contents

2014, Volume 19, Issue 1: 257-279. Doi: 10.3934/dcdsb.2014.19.257

This issue Previous Article Wellposedness and regularity for a degenerate parabolic equation arising in a model of chemotaxis with nonlinear sensitivity Next Article Dirichlet series for dynamical systems of first-order ordinary differential equations

A dynamics approach to a low-order climate model

James Walsh^1, and
Esther Widiasih^2,

1.
Department of Mathematics, Oberlin College, 10 N. Professor St, Oberlin, OH 44074
2.
Department of Mathematics, University of Hawai'i West Oahu, 91-1001 Farrington Hwy, Kapolei, HI, 96707

Received: April 30, 2012

Revised: July 31, 2013

Published: December 2013

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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.

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Mathematics Subject Classification: Primary: 35Q86; Secondary: 37N10, 86A40.

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