Simple albedo feedback models of the icecaps

A series of simple models of the albedo feedback mechanism and its effect on the global climate are solved analytically. All of the models are similar to one considered by Budyko. The seasonal variation in incident solar radiation is ignored. Emphasis is placed on the parameter dependence of the models' sensitivity to changes in the solar constant. It is found in all cases that increasing the efficiency of the poleward transport of energy increases this sensitivity. It is also suggested that knowledge of the partitioning of the transport between the atmosphere and the oceans is of considerable importance for estimating sensitivity. The stability of equilibrium states is determined from the properties of small perturbations away from equilibrium. It is observed that relaxation times of perturbations can be increased considerably by the albedo feedback mechanism. The effect of variations in the obliquity of the planet's orbit on sensitivity and stability is also analyzed. The results indicate that albedo feedback may increase the significance of obliquity variations on Mars, as well as on the Earth.