Further application of the theory of stochastic perturbation of deterministic systems to simple climate models

A previous paper (Sutera 1981) considered the effect of stochastic perturbation on the long‐term behaviour of a highly idealized energy‐balanced model of zero spatial dimension. It was shown that, in the presence of stochastic perturbations, transitions between different stable equilibria, or ‘climates’, of the model become possible. the expected time for a stochastically perturbed model solution to leave the attractor basin of a stable equilibrium is called the ‘exit time’. the ‘exit time’ must be considered as an important new parameter characterizing model behaviour. In order to illustrate the methodology described in Sutera (1981) we apply these general considerations to a spatially one‐dimensional Budyko‐Sellers model. In fact, using two different heat capacity formulations, we test the sensitivity of such a model to stochastic perturbations. an interesting physical result, common to both versions of the model, is that, if the noise level is confined below a certain value, then the solution corresponding to an ‘ice‐covered earth’ will never be experienced.