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On the Branching Structure of Diffusive Climatological Models

P. G. DrazinSchool of Mathematics, University of Bristol, Bristol BS8 1TW England

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D. H. GriffelSchool of Mathematics, University of Bristol, Bristol BS8 1TW England

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Abstract

We consider the general structure of the equilibrium solutions of simple, zonally averaged, energy-balance climatological models with diffusive heat transport and a nonlinear ice albedo feedback. The relation between the appearance of unstable modes and the bifurcation of equilibrium solutions is elucidated, in particular the relation between antisymmetric modes and bifurcation of asymmetric equilibrium solutions. Numerical solution of a specific model, which has been shown by others to possess an equilibrium solution similar to the present climate of the earth, shows that as well as the several previously known symmetric equilibrium solutions, it possesses asymmetric solutions, including ones with an ice cap at only one pole. One of these types of asymmetric solutions is shown to be stable for values of parameters which represent present conditions on earth.

Abstract

We consider the general structure of the equilibrium solutions of simple, zonally averaged, energy-balance climatological models with diffusive heat transport and a nonlinear ice albedo feedback. The relation between the appearance of unstable modes and the bifurcation of equilibrium solutions is elucidated, in particular the relation between antisymmetric modes and bifurcation of asymmetric equilibrium solutions. Numerical solution of a specific model, which has been shown by others to possess an equilibrium solution similar to the present climate of the earth, shows that as well as the several previously known symmetric equilibrium solutions, it possesses asymmetric solutions, including ones with an ice cap at only one pole. One of these types of asymmetric solutions is shown to be stable for values of parameters which represent present conditions on earth.

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