Analytical Solution to a Simple Climate Model with Diffusive Heat Transport

Abstract

A simple radiative balance climate model is presented which includes the ice feedback mechanism, zonal averaging, constant homogeneous cloudiness, and ordinary diffusive thermal heat transfer. The simplest version of the model with only one free parameter is solved explicitly in terms of hypergeometric functions and is used to study ice sheet latitude as a function of solar constant. A multiple branch structure of this function is found and discussed along with comparison to earlier results. A stability analysis about the equilibrium solutions shows that the present climate as well as an ice-covered earth are stable while an intermediate solution is unstable for small perturbations away from equilibrium.