Natura non facit saltus—nature does not take jumps. Modern science has thoroughly shattered this tenet of the Aristotelian school of thought. Long-term observations and experimental insights have demonstrated convincingly that smooth, or regular, behavior is an exception rather than a rule. Available records of climate variability, for example, reveal sudden fluctuations of key variables at all time scales. Large, abrupt climate changes evident in Greenland ice-core records (known as Dansgaard-Oeschger oscillations—Dansgaard et al., 1993) and episodic, massive discharges of icebergs into the North Atlantic (known as Heinrich events—Bond et al., 1992) are obvious examples of irregular behavior as a result of weak external forcing. Ecosystems also display discontinuous responses to changing ambient conditions, such as changes in disturbance regimes (Holling, 1992a; Peterson et al., 1998) and species extinctions (Pounds et al., 1999). Irreversible changes in ecosystems are triggered by disturbances (e.g., Gill, 1998), pests (e.g., Holling, 1992b), and shifts in species distributions (Huntley et al., 1997). Irregular behavior is accepted as a major aspect of the dynamics of complex systems (Berry, 1978; Schuster, 1988; Wiggins, 1996; Badii and Politi, 1997).

A quantitative entity behaves "irregularly" when its dynamics are discontinuous, nondifferentiable, unbounded, wildly varying, or otherwise ill-defined. Such behavior often is termed singular, particularly in catastrophe theory (Saunders, 1982), and illustrates how smooth variations of driving forces can cause abrupt and drastic system responses. The occurrence, magnitude, and timing of singularities are relatively difficult to predict, which is why they often are called "surprises" in the literature.

It is important to emphasize that singular behavior is not restricted to natural systems. There has been speculation, for example, about possible destabilization of food markets, public health systems, and multilateral political agreements on resource use, but solid evidence rarely has been provided (e.g., Döös, 1994; Hsu, 1998). Rigorous scientific analysis of certain classes of singular socioeconomic phenomena is emerging (Bunde and Schellnhuber, 2000), but huge cognitive gaps remain in this field.

Singularities have large consequences for climate change vulnerability assessments. Unfortunately, most of the vulnerability assessment literature still is focusing on a smooth transition from what is assumed to be an equilibrium climate toward another equilibrium climate (often 1xCO₂ to 2xCO₂). This means that most impact assessments still implicitly assume that climate change basically is a "well-behaved" process. Until recently, only a few authors have emphasized the importance of discontinuous, irreversible, and extreme events to the climate problem (e.g., Lempert et al., 1994; Nordhaus, 1994a; Schellnhuber, 1997); concerns about the impacts of these events and their consequences for society now are becoming much more common. Singularities could lead to rapid, large, and unexpected impacts on local, regional, and global scales. Anticipating and adapting to such events and their impacts would be much more difficult than responding to smooth change, even if these responses must be made in the face of uncertainty. Furthermore, singularities considerably complicate the search for optimal emissions reduction strategies that are based on, for example, benefit-cost analysis or tolerable emissions strategies that are based on, as another example, the precautionary principle.

This section reviews and synthesizes relevant available information on the impacts of singular behavior of (components of) the climate system or singular impacts of climate change and draws conclusions about the consequences for vulnerability assessments. Because no generally accepted framework to assess singularities of climate change exists, an illustrative typology of singularities is discussed first. The different characteristics of each class in this typology justify why insights from this section contribute to two separate reasons for concern: extreme weather events and large-scale singularities.

The causes of singularities are diverse, but most can be grouped in the categories of nonlinearity, complexity, and stochasticity. Choices about how to assess singular climate impacts depend strongly on the factors generating such behavior. The first two categories arise in a largely deterministic context, so their incidence can be assessed with proper models. The latter is probabilistic, however, rendering its incidence basically unpredictable. Only statistical properties can be analyzed. Predictability (and consequently adaptability) is directly related to the stochastic nature of the underlying dynamics.

The first, and most obvious, class of singularities is caused by strongly nonlinear or discontinuous functional relationships. A conspicuous case is the critical threshold, where responses to a continuous change in a driving variable bring about sudden and severe impacts, such as extinction events. Changes in mean climate can increase the likelihood of crossing these thresholds. Even one of the simplest physical thresholds in the climate system—the melting point of ice—could induce singular impacts. For example, thawing of permafrost regions would be induced by only a few degrees of warming (Pavlov, 1997) and would severely affect soil and slope stability, with disastrous effects on Arctic infrastructure such as oil pipelines (see Section 16.2.5 and SAR WGII Section 11.5.3). Section 19.3 extensively illustrates the occurrence of critical thresholds that are relevant for bleaching of coral reefs (a temperature threshold) and coastal mangroves (a sea-level rise threshold).

Complexity itself is a second potential cause for singular behavior in many systems. Complex systems, of course, are composed of many elements that interact in many different ways. Anomalies in driving forces of these systems generally distort interactions between constituents of the system. Positive feedback loops then can easily push the systems into a singular response. (Note that complexity is by no means synonymous with nonlinearity!)

Complex interactions and feedbacks gradually have become a focal point of global and climate change investigations: Several illustrative studies, for example, deal with the interplay between atmosphere, oceans, cryosphere, and vegetation cover that brought about the rapid transition in the mid-Holocene from a "green" Sahara to a desert (Brovkin et al., 1998; Ganopolski et al., 1998; Claussen et al., 1999), with the mutual amplification of regional climate modification and unsustainable use of tropical forests as mediated by fire (Cochrane, 1999; Goldammer, 1999; Nepstad et al., 1999) and with the dramatic disruptions possibly inflicted on Southern Ocean food webs and ecological services by krill depletion resulting from dwindling sea-ice cover (see Brierly and Reid, 1999; see also Section 16.2.3).

The third category, stochasticity, captures a class of singularities that are triggered by exceptional events. In the climate context, these are, by definition, extreme weather events such as cyclones and heavy rains (see Table 3-10). Their occurrence is governed by a generally well-behaved statistical distribution. The irregular character of extreme events stems mainly from the fact that, although they reside in the far tails of this distribution, they nonetheless occur from time to time. Therefore, they could affect downstream systems by surprise and trigger effects that are vastly disproportional to their strength. Climate change also could lead, however, to changes in probability distributions for extreme events. Such changes actually could cause serious problems because the risk and consequences of these transitions are difficult to quantify and identify in advance. The impacts caused by these events have not yet been explored, although they should constitute an essential aspect of any impact and adaptation assessment.

The impacts of extreme event consequences of stochastic climate variability, however, have begun to attract researchers' attention in a related context. As noted in Chapter 18, changes in mean climate can increase the likelihood that distributed weather will cross thresholds where the consequences and impacts are severe and extreme. This variant of stochastic singularity therefore can change in frequency even if the probability of extreme weather events, measured against the mean, is unaffected by long-term trends.

There also is a fourth type that generally arises from a combination of all other singularity categories. This type—sometimes referred to as "imaginable surprises" (Schneider et al., 1998; see also Chapter 1)—represents conceivable global or regional disruptions of the operational mode of the Earth system. Such macro-discontinuities may cause damages to natural and human systems that exceed the negative impacts of "ordinary" disasters by several orders of magnitudes.

Responses to climate change can alter their character from singular to regular—and vice versa—as they cascade down the causal chain: geophysical perturbations, environmental impacts, sectoral and socioeconomic impacts, and societal responses. Only the last three are climate change effects in the proper sense, but the first is important because it translates highly averaged indicators of climate change into the actual trigger acting at the relevant scale. Most singular geophysical perturbations create singular impacts—which may, in turn, activate singular responses. One therefore might assume that singularities tend to be preserved down such a cascade. Singular events also can arise further down the causal chain. Purely regular geophysical forcing, for example, can cause singular impacts, and singular socioeconomic responses may result from regular impacts.

Harmful impacts of climate change generally can be alleviated by adaptation or exacerbated by mismanagement (see, e.g., West and Dowlatabadi, 1999; Schneider et al., 2000a; see also Chapter 18). Climate-triggered singular phenomena can generate substantial impacts because their predictability and manageability are low. Such impacts would be considerably reduced if they could be "regularized" by appropriate measures. For example, an ingenious array of seawalls and dikes could transform an extreme storm surge into a mundane inundation that could be controlled by routine contingency procedures. So too could a long-term policy of retreat from the sea. However, inappropriate flood control structures could wreak havoc, particularly because they foster a false sense of security and actually inspire further coastal development.

In summary, singularities tend to produce singularities, as a rule; regularities may turn into singularities under specific conditions, and singularities can be regularized by autonomous ecological processes or judicious societal measures. Defining the propagation of singular events in the causal cascade or opportunities to convert them into regular events remains a major research challenge.

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