Fig. 2: Power spectra of coral Sr/Ca, δ¹⁸O, and instrumental SST.

a A comparison of the uncorrected (S_proxy) and corrected (S_clim) spectra estimated from coral Sr/Ca and δ¹⁸O with the power spectral density (PSD) of instrumental SST (ERSSTv5 & OISSTv2) evaluated for the locations and time periods for which there were Sr/Ca and δ¹⁸O data. Spectra represent averages across all pairs of coral records analyzed in this study. For a and b, units have been converted to Kelvin by multiplying Sr/Ca and δ¹⁸O based spectra by 1/0.06² and 1/0.22² respectively. b No. of pairs and the number of unique records contributing to the mean power spectra at each frequency for coral derived data. c Power spectral density of the uncorrected coral proxy records, shared (climate) and noise components estimated using the stacked records method. For proxy-based power spectra, shaded regions indicate 68 and 95% confidence intervals estimated by record-wise bootstrapping. Bootstrapped interval estimation was not possible for timescales with contributions from less than about 20 coral pairs (the precise number was dependent on the variation of the given statistic).