Earth-average temperature: A time delay approach

Earth-average temperature is investigated using a simple energy balance model of the Budyko-Sellers-Ghil type expressed as a delay-differential equation describing the absorption and reflection of incoming solar radiation and surface-reflected infrared radiation. Cloud albedos for both radiations and the surface albedo as affected by ice coverage are assumed to depend upon the temperature that existed some time ago, introducing a time delay into the model. A variety of steady and oscillatory states are possible for Earth-average temperature, assuming plausible functions for the albedos, blackbody cooling, and suitable delay times. Multiple true steady states and multiple transient pseudo steady states as well as periodic, chaotic, and square-wave relaxation-oscillations result. The bifurcation structure relating the appearance of these phenomena to system parameters is explored. This very simple climate model exhibits complex behavior in global temperature without solar variation or environmental perturbation. Bifurcations exist at which small changes in parameters lead to destabilization of steady states and dramatic changes in qualitative behavior.