Small changes in the climate system can be sufficiently understood by assuming linear relationships between variables. However, many climate processes are non-linear by nature, and conclusions based on linear models and processes may in these cases no longer be valid. Non-linearity is a prerequisite for the existence of thresholds in the climate system: small perturbations or changes in the forcing can trigger large reorganisations if thresholds are passed. The result is that atmospheric and oceanic circulations may change from one regime to another. This could possibly be manifested as rapid climate change.

There is no clear definition of �rapid climate change�. In general, this notion is used to describe climate changes that are of significant magnitude (relative to the natural variability) and occur as a shift in the mean or variability from one level to another. In order to distinguish such changes from �extreme events�, a certain persistence of the change is required. Among the classical cases are spontaneous transitions from one preferred mode to another or transitions triggered by slowly varying forcing. This occurs in non-linear systems which have multiple equilibria (Lorenz, 1993). Evidence for the possibility of such transitions can be found in palaeoclimatic records (see Chapter 2, Section 2.4; and Stocker, 2000), in observations of changes in large-scale circulation patterns from the instrumental record (see Section 7.6.5.1), and contemporary observations of regional weather patterns (e.g., Corti et al., 1999).

Here, we briefly summarise non-linear changes that have captured attention in the recent literature and that have been assessed in this chapter:

• The Northern Hemispheric atmospheric circulation exhibits different regimes that are associated with the North Atlantic Oscillation. Recent analyses of observations suggest that relatively rapid regime changes are possible (see Section 7.2.6) and that they may have happened frequently in the past (Appenzeller et al., 1998). Several studies suggest that the recent changes may be a response to anthropogenic forcing, but our understanding of the processes generating NAO is not sufficient to have confidence in whether this is the case.
  
• Observed variability of ENSO suggests that a transition to more frequent El Niño occurred around 1976 (see Section 7.6.5.1). Current understanding of ENSO processes does not yet permit a distinction as to the extent this is a response to anthropogenic forcing versus part of the long-term natural variability of the tropical atmosphere-ocean system, or both (see also Chapter 2, Section 2.6.2).
• Results from most climate models suggest that the Atlantic thermohaline circulation slows down in response to global warming; some models simulate a complete shut-down if certain thresholds are passed (see Section 7.3.6 and Chapter 9, Section 9.3.4.3). Such a shut-down is in general not abrupt but evolves on a time-scale which is determined by the warming, i.e., a few decades to centuries. Processes for such an evolution are increasingly understood. As model resolution increases and high latitude processes are better represented in these models (sea ice, topography), additional feedbacks influencing the Atlantic THC will be investigated and their relative importance must be explored. This will lead to a better quantification of the overall stability of the THC.
  
• Large polar ice masses, ice shelves or even complete ice sheets may be destabilised by sea level rise (see Section 7.5 and Chapter 11, Section 11.3.3), thereby contributing to further sea level rise.
  
• Warming in the high latitudes may lead to significant reductions in sea ice and associated feedbacks may accelerate this development (see Box 7.1).
• Large-scale and possibly irreversible changes in the terrestrial biosphere and vegetation cover are thought to have occurred in the past when anthropogenic perturbation was negligible (e.g., the development of the Saharan desert, Claussen et al., 1999). These changes may be interpreted as non-linear changes triggered by slow changes in external forcing and thus cannot be excluded to occur in the future. Knowledge on these phenomena, however, is not advanced yet.

Reducing uncertainty in climate projections also requires a better understanding of these non-linear processes which give rise to thresholds that are present in the climate system. Observations, palaeoclimatic data, and models suggest that such thresholds exist and that transitions have occurred in the past. The occurrence of such transitions can clearly not be excluded in a climate that is changing. On the contrary, model simulations indicate that such transitions lie within the range of changes that are projected for the next few centuries if greenhouse gas concentrations continue to increase. A particular concern is the fact that some of these changes may even be irreversible due to the existence of multiple equilibrium states in the climate system.

Comprehensive climate models in conjunction with sustained observational systems, both in situ and remote, are the only tool to decide whether the evolving climate system is approaching such thresholds. Our knowledge about the processes, and feedback mechanisms determining them, must be significantly improved in order to extract early signs of such changes from model simulations and observations.

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