Annual variability in a conceptual climate model: snapshot attractors, hysteresis in extreme events, and climate sensitivity.

In a conceptual model of global atmospheric circulation, the effects of annually periodic driving are investigated. The driven system is represented in terms of snapshot attractors, which may remain fractal at all times. This is due to the transiently chaotic behavior in the regular parameter regimes of the undriven system. The driving with annual periodicity is found to be relatively fast: There is a considerable deviation from the undriven case. Accordingly, the existence of a hysteresis loop is identified, namely, the extremal values of a given variable depend not only on the actual strength of the insolation but also on the sign of its temporal change. This hysteresis is due to a kind of internal memory. In the threshold-dependence of mean return times of various extreme events, a roughly exponential scaling is found. Climate sensitivity parameters are defined, and the measure of certain types of extremal behavior is found to be strongly susceptible to changes in insolation.