The response to anthropogenic changes in climate forcing occurs against a backdrop of natural internal and externally forced climate variability that can occur on similar temporal and spatial scales. Internal climate variability, by which we mean climate variability not forced by external agents, occurs on all time-scales from weeks to centuries and millennia. Slow climate components, such as the ocean, have particularly important roles on decadal and century time-scales because they integrate high-frequency weather variability (Hasselmann, 1976) and interact with faster components. Thus the climate is capable of producing long time-scale internal variations of considerable magnitude without any external influences. Externally forced climate variations may be due to changes in natural forcing factors, such as solar radiation or volcanic aerosols, or to changes in anthropogenic forcing factors, such as increasing concentrations of greenhouse gases or sulphate aerosols.

Definitions
The presence of this natural climate variability means that the detection and attribution of anthropogenic climate change is a statistical �signal-in-noise� problem. Detection is the process of demonstrating that an observed change is significantly different (in a statistical sense) than can be explained by natural internal variability. However, the detection of a change in climate does not necessarily imply that its causes are understood. As noted in the SAR, the unequivocal attribution of climate change to anthropogenic causes (i.e., the isolation of cause and effect) would require controlled experimentation with the climate system in which the hypothesised agents of change are systematically varied in order to determine the climate�s sensitivity to these agents. Such an approach to attribution is clearly not possible. Thus, from a practical perspective, attribution of observed climate change to a given combination of human activity and natural influences requires another approach. This involves statistical analysis and the careful assessment of multiple lines of evidence to demonstrate, within a pre-specified margin of error, that the observed changes are:

• unlikely to be due entirely to internal variability;
• consistent with the estimated responses to the given combination of anthropogenic and natural forcing; and
• not consistent with alternative, physically plausible explanations of recent climate change that exclude important elements of the given combination of forcings.

Limitations
It is impossible, even in principle, to distinguish formally between all conceivable explanations with a finite amount of data. Nevertheless, studies have now been performed that include all the main natural and anthropogenic forcing agents that are generally accepted (on physical grounds) to have had a substantial impact on near-surface temperature changes over the 20th century. Any statement that a model simulation is consistent with observed changes can only apply to a subset of model-simulated variables, such as large-scale near-surface temperature trends: no numerical model will ever be perfect in every respect. To attribute all or part of recent climate change to human activity, therefore, we need to demonstrate that alternative explanations, such as pure internal variability or purely naturally forced climate change, are unlikely to account for a set of observed changes that can be accounted for by human influence. Detection (ruling out that observed changes are only an instance of internal variability) is thus one component of the more complex and demanding process of attribution. In addition to this general usage of the term detection (that some climate change has taken place), we shall also discuss the detection of the influence of individual forcings (see Section 12.4).

Detection and estimation
The basic elements of this approach to detection and attribution were recognised in the SAR. However, detection and attribution studies have advanced beyond addressing the simple question �have we detected a human influence on climate?� to such questions as �how large is the anthropogenic change?� and �is the magnitude of the response to greenhouse gas forcing as estimated in the observed record consistent with the response simulated by climate models?� The task of detection and attribution can thus be rephrased as an estimation problem, with the quantities to be estimated being the factor(s) by which we have to scale the model-simulated response(s) to external forcing to be consistent with the observed change. The estimation approach uses essentially the same tools as earlier studies that considered the problem as one of hypothesis testing, but is potentially more informative in that it allows us to quantify, with associated estimates of uncertainty, how much different factors have contributed to recent observed climate changes. This interpretation only makes sense, however, if it can be assumed that important sources of model error, such as missing or incorrectly represented atmospheric feedbacks, affect primarily the amplitude and not the structure of the response to external forcing. The majority of relevant studies suggest that this is the case for the relatively small-amplitude changes observed to date, but the possibility of model errors changing both the amplitude and structure of the response remains an important caveat. Sampling error in model-derived signals that originates from the model�s own internal variability also becomes an issue if detection and attribution is considered as an estimation problem � some investigations have begun to allow for this, and one study has estimated the contribution to uncertainty from observational sampling and instrumental error. The robustness of detection and attribution findings obtained with different climate models has been assessed.

Extensions
It is important to stress that the attribution process is inherently open-ended, since we have no way of predicting what alternative explanations for observed climate change may be proposed, and be accepted as plausible, in the future. This problem is not unique to the climate change issue, but applies to any problem of establishing cause and effect given a limited sample of observations. The possibility of a confounding explanation can never be ruled out completely, but as successive alternatives are tested and found to be inadequate, it can be seen to become progressively more unlikely. There is growing interest in the use of Bayesian methods (Dempster, 1998; Hasselmann, 1998; Leroy, 1998; Tol and de Vos, 1998; Barnett et al., 1999; Levine and Berliner, 1999; Berliner et al., 2000). These provide a means of formalising the process of incorporating additional information and evaluating a range of alternative explanations in detection and attribution studies. Existing studies can be rephrased in a Bayesian formalism without any change in their conclusions, as demonstrated by Leroy (1998). However, a number of statisticians (e.g., Berliner et al., 2000) argue that a more explicitly Bayesian approach would allow greater flexibility and rigour in the treatment of different sources of uncertainty.

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