Results from studies using pattern correlations were reported extensively in the SAR (for example, Santer et al., 1995, 1996c; Mitchell et al., 1995b). They found that the patterns of simulated surface temperature change due to the main anthropogenic factors in recent decades are significantly closer to those observed than expected by chance. Pattern correlations have been used because they are simple and are insensitive to errors in the amplitude of the spatial pattern of response and, if centred, to the global mean response. They are also less sensitive than regression-based optimal detection techniques to sampling error in the model-simulated response. The aim of pattern-correlation studies is to use the differences in the large-scale patterns of response, or "fingerprints", to distinguish between different causes of climate change.
Strengths and weaknesses of correlation methods
Pattern correlation statistics come in two types - centred and uncentred (see Appendix 12.3). The centred (uncentred) statistic measures the similarity of two patterns after (without) removal of the global mean. Legates and Davis (1997) criticised the use of centred correlation in detection studies. They argued that correlations could increase while observed and simulated global means diverge. This was precisely the reason centred correlations were introduced (e.g., Santer et al., 1993): to provide an indicator that was statistically independent of global mean temperature changes. If both global mean changes and centred pattern correlations point towards the same explanation of observed temperature changes, it provides more compelling evidence than either of these indicators in isolation. An explicit analysis of the role of the global mean in correlation-based studies can be provided by the use of both centred and uncentred statistics. Pattern correlation-based detection studies account for spatial auto-correlation implicitly by comparing the observed pattern correlation with values that are realised in long control simulations (see Wigley et al., 2000). These studies do not consider the amplitude of anthropogenic signals, and thus centred correlations alone are not sufficient for the attribution of climate change.
Wigley et al. (1998b) studied the performance of correlation statistics in an idealised study in which known spatial signal patterns were combined with realistic levels of internal variability. The statistics were found to perform well even when the signal is contaminated with noise. They found, in agreement with Johns et al. (2001), that using an earlier base period can enhance detectability, but that much of this advantage is lost when the reduced data coverage of earlier base periods is taken into account. They also found that reasonable combinations of greenhouse gas and aerosol patterns are more easily detected than the greenhouse gas pattern on its own. This last result indicates the importance of reducing the uncertainty in the estimate of aerosol forcing, particularly the indirect effects. In summary, we have a better understanding of the behaviour of pattern correlation statistics and reasons for the discrepancies between different studies.
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