Abrupt Change, Thresholds, and Hysteresis

According to the definition given in Chapter 1, a climatic response faster than a change in forcing would be called abrupt. Such a rapid response would not occur as a result of small perturbations about a reference state, but only if a threshold was crossed; after that, a new state would be rapidly approached. Systems that exhibit such behavior often show hysteresis; that is, even if the perturbation has ceased after leading to the crossing of a threshold, the system does not return to its original state. Box 1.1 showed a

Box 3.1 Thresholds and Hysteresis

FIGURE 3.1

Many simple physical systems exhibit abrupt change, as demonstrated in the simple diagram presented in Box 1.1. The more complex figure (Figure 3.1 ) provides a schematic view of hysteresis in the thermohaline circulation. The upper branch denotes climate states in which the THC is strong and North Atlantic temperatures are relatively high (similar to present conditions). The lower branch represents a much-reduced or collapsed THC, in which the Atlantic meridional heat flux by the ocean is small. A given perturbation (indicated by the horizontal arrows) in the freshwater balance of the North Atlantic (precipitation plus runoff minus evaporation) first causes transitions from an initial state 1 to state 2. The reverse perturbation then causes a transition back to state 1, or to state 3. Three structurally different responses are possible for the same pair of perturbations, depending on whether threshold values (dashed line) are crossed. This, in turn, depends on where state 1 is, relative to the threshold: a) small, reversible response; b) large, reversible response; c) large, irreversible response (Stocker and Marchal, 2000).



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