Low-dimensional models can give insight into the climate system, in particular its response to externally imposed forcing such as the anthropogenic emission of greenhouse gases. Here, we use the Lorenz system, a chaotic dynamical system characterized by two "regimes", to examine the effect of a weak imposed forcing. We show that the probability density functions (PDF's) of time-spent in the two regimes are exponential, and that the most dramatic response to forcing is a change in the frequency of occurrence of extremely persistent events, rather than the weaker change in the mean persistence time. This enhanced sensitivity of the "tails" of the PDF's to forcing is quantitatively explained by changes in the stability of the regimes. We demonstrate similar behavior in a stochastically forced double well system. Our results suggest that the most significant effect of anthropogenic forcing may be to change the frequency of occurrence of persistent climate events, such as droughts, rather than the mean.
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