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Optimal fingerprinting is a standard method for detecting climate changes. Among the uncertainties taken into account by this method, one is the fact that the response to climate forcing is not known exactly, but in practice is estimated from ensemble averages of model simulations. This uncertainty can be taken into account using an Error-in-Variables model (or equivalently, the Total Least Squares method), and can be expressed through confidence intervals. Unfortunately, the predominant paradigm (likelihood ratio theory) for deriving confidence intervals is not guaranteed to work because the number of parameters that are estimated in the Error-in-Variables model grows with the number of observations. This paper discusses various methods for deriving confidence intervals and shows that the widely-used intervals proposed in the seminal paper by Allen and Stott are effectively equivalent to bias-corrected intervals from likelihood ratio theory. A new, computationally simpler, method for computing these intervals is derived. Nevertheless, these confidence intervals are incorrect in the "weak-signal regime". This conclusion does not necessarily invalidate previous detection and attribution studies because many such studies lie in the strong-signal regime, for which standard methods give correct confidence intervals. A new diagnostic is introduced to check whether or not a data set lies in the weak-signal regime. Finally, and most importantly, a bootstrap method is shown to give correct confidence intervals in both strong- and weak-signal regimes, and always produces finite confidence intervals, in contrast to the likelihood ratio method which can give unbounded intervals that do not match the actual uncertainty. [ABSTRACT FROM AUTHOR]

In this study, the potential predictability of the Northern America (NA) surface air temperature (SAT) was explored using an information-based predictability framework and two multiple model ensemble products: a one-tier prediction by coupled models (T1), and a two-tier prediction by atmospheric models only (T2). Furthermore, the potential predictability was optimally decomposed into different modes for both T1 and T2, by extracting the most predictable structures. Emphasis was placed on the comparison of the predictability between T1 and T2. It was found that the potential predictability of the NA SAT is seasonal and spatially dependent in both T1 and T2. Higher predictability occurs in spring and winter and over the southeastern US and northwestern Canada. There is no significant difference of potential predictability between T1 and T2 for most areas of NA, although T1 has higher potential predictability than T2 in the southeastern US. Both T1 and T2 display similar most predictable components (PrCs) for the NA SAT, characterized by the inter-annual variability mode and the long-term trend mode. The first one is inherent to the tropical Pacific sea surface temperature forcing, such as the El Nino-Southern Oscillation, whereas the second one is closely associated with global warming. In general, the PrC modes can better characterize the predictability in T1 than in T2, in particular for the inter-annual variability mode in the fall. The prediction skill against observations is better measured by the PrC analysis than by principal component analysis for all seasons, indicating the stronger capability of PrCA in extracting prediction targets. [ABSTRACT FROM AUTHOR]