The sensitivity of response of climatic characteristics in a two-level general circulation model to small changes in solar radiation

A two-level, quasi-geostrophic, β-plane, general circulation model is developed, incorporating a time-dependent surface energy balance equation and a time-dependent heating function at the 500 mb level, with an associated feedback relationship. This system enables the surface temperature distribution to be evaluated as a function of time in the model, and so allows an associated variable spatial distribution of surface albedo to be carried in the model, including a simulated “snow and ice” edge. The effect on the model of successive small changes in solar radiation (of ½% up to a total of 3%) are then studied by carrying out numerical experiments over long time periods, these being sufficiently long (involving a total time of integration of 1800 model days) to produce oscillations in model heating and albedo distributions about asymptotic mean values. The successive latitudinal positions of the, zonally averaged, “snow and ice” edge agree approximately with those calculated by Gordon and Davies (1974) using a modified form of the statical energy balance method of Budyko (1969). However, the experiments also showed that the greater the reduction made in solar radiation the greater was the ensuing amplitude of spatial movement of the associated albedo distribution, implying a strong tendency towards instability of the simulated edge as the reduction approached a value of 3%.