Extended Data Fig. 7: Timing of peak warming in noise-proxy reconstructions.

a, As for the CWP panel in Fig. 3, but with reconstructions using noise proxies. Colours in maps indicate the century with the largest ensemble-based probability of containing the warmest 51-year period within the Common Era (see Methods). Maps show the 25 reconstruction realizations, each consisting of six 100-member ensemble reconstructions, for the R-FDR-screened (n = 66) noise-proxy networks (see Methods). b, The global area fraction of peak warmth in each century for each reconstruction method. Top, real proxies (screened); middle, average values across the 25 screened (n = 66) noise-proxy reconstruction ensembles; bottom, average values across the 25 force-screened (n = 210) noise-proxy reconstruction ensembles. c, Fraction of global area having the CWP warm peak within the twentieth century for all three noise-proxy types described in the Methods. Large grey boxplots represent noise-proxy reconstructions across all methods. Grey filled circles show individual noise-proxy reconstructions across all methods. Coloured boxplots show noise-proxy results for the individual reconstruction methods (with colours as in b). Vertical red lines show real proxy reconstructions for both unscreened and screened networks. Boxplots are across 25 reconstruction experiments; centre lines represent median; boxes represent the interquartile range; whiskers show the 95% range. All noise-proxy experiments across all methods yield a weaker spatial agreement of maximum-century 51-year warming compared with the real data reconstructions. The more ‘traditional’ statistical reconstruction methods (CPS, PCR and CCA) mostly exhibit smaller areas of twentieth-century warming in the noise reconstructions than do the other methods (GraphEM, AM and DA; see Methods). A possible explanation for this difference is that the traditional methods are designed to yield reconstructions with as little variance loss as possible independently of data uncertainty (see, for example, ref. ⁶²). Reconstructed temperatures over the full Common Era thus exhibit fluctuations with a magnitude comparable to the calibration period in all noise experiments. By contrast, the newer methods usually generate reconstructed variance that is inversely proportional to the errors in the input data. Thus they converge towards zero with increasing data uncertainty and decreasing coherence among the input data, as is the case in the noise-proxy experiments. For these methods, this results in noise-proxy reconstructions with little temperature variance before the calibration period, and thus a higher probability that the twentieth-century warming exceeds earlier warm periods in magnitude. For a general discussion of the results, see Methods.