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Abstract
Zero dimensional climate models of the Budyko-Sellers type are investigated when weak periodic forcing with a period of 105 years and a relative amplitude of 10−3 and stochastic (white noise) forcing are acting as external influences.
The first model has steady states at T 2−ΔT, T 2 and T2+Ar where T 2 and ΔT may vary. The albedo as a function of temperature has a parabolic shape. Investigating the influence of the periodic forcing alone it is shown that temperature changes between a glacial and an interglacial period of a correct order of magnitude may be predicted if ΔT∼25K or ΔT∼30K. The approximate method used for the solution of the stochastic problems permits solutions for ΔT>20K. For such values it is shown that the stochastic forcing combined with the periodic forcing describes transitions from one steady state to another with a period of 105 years and with a realistic value of the intensity of the stochastic forcing. However, the implied temperature difference between the two steady states is large compared to present estimates of the temperature change from a glacial to an interglacial period.
The second model is designed for small temperature differences between the two stable steady states. It is shown in this case by numerical integrations that the periodic forcing cannot produce the desired temperature changes. On the other hand, the combined effects of periodic and stochastic forcing can in this case describe climate transitions between steady states having a temperature difference of 4–5 K.