MILANKOVICH CYCLES, POSITIVE FEEDBACK AND SYSTEM SWITCHING BETWEEN STABLE STATES, A MODEL FOR GLACIAL - INTERGLACIAL REPETITIONS

The Quaternary climate record suggests that the Earth system has the ability to switch between two generally stable states, one cold that corresponds to glacial maxima and a second warmer state like that active during the Holocene. Systems of this type are likely to be controlled by a positive feedback that creates multiple possible steady states. For example, when a coupling causing feedback has the mathematical form of a logistics curve, the system may contain three steady states, two stable and one unstable that separates regions of stability. If "properly" tuned, the feedback can cause the system to switch between states when subjected to a cyclical forcing.

In this paper a model of a positive feedback subjected to a cyclical forcing is presented and related to Earth's climate system. Systems with positive feedback and a single steady state that moves in response to continuous forcing can enhance small changes in insolation. However, it cannot produce a response pattern similar to Quaternary temperature change. In contrast, a three state system can experience large and rapid change in temperature, have different time scales for warm and cold periods, and switch from warm to cold and from cold to warm states at different temperatures, all characteristic of the Earth's Quaternary climate pattern. The model suggests that feedbacks involving, temperature, ice, albedo, carbon dioxide and energy transfer between tropics and polar regions are able to enhance the effects of the Milankovitch cycle. The strength of feedback is relatively weak during glacial maxima and minima but strengthens during periods of ice advance and retreat. Other implications of the model include the possibility that small amounts of warming might prevent a future switch to cold conditions and that Snowball Earth is incompatible with current climate dynamics.