A stability theorem for energy-balance climate models

Abstract

The paper treats the stability of steady-state solutions of some simple, latitude-dependent, energy-balance climate models. For north-south symmetric solutions of models with an ice-cap-type albedo feedback, and for the sum of horizontal transport and infrared radiation given by a linear operator, it is possible to prove a 'slope stability' theorem, i.e., if the local slope of the steady-state iceline latitude versus solar constant curve is positive (negative) the steady-state solution is stable (unstable). Certain rather weak restrictions on the albedo function and on the heat transport are required for the proof, and their physical basis is discussed.