Reconstructing seawater δ18O from paired coral δ18O and Sr/Ca ratios: Methods, error analysis and problems, with examples from Tahiti (French Polynesia) and Timor (Indonesia)

We compare several statistical routines that may be used to calculate δ18Osw and SSS from paired coral Sr/Ca and δ18O measurements. Typically, the δ18Ocoral-SST relationship is estimated by linear regression of coral δ18O vs. SST. If this method is applied, evidence should be given that at a particular site SST and SSS do not co-vary. In the tropical oceans, SST and δ18Osw (SSS) often co-vary, and this will bias the estimate of the regression slope of δ18Ocoral-SST. Using a stochastic model, we show that covariance leads to a bias in the coefficients of the univariate regression equations. As the slope of the δ18Ocoral-SST relationship has known, we propose to insert this value for γ1 in the regression models. This requires that the constants of the regression equations are removed. To omit the constants, we propose to center the regression equations (i.e., to remove the mean values from the variables). The statistical error propagation is calculated to assess our ability to resolve past variations in δ18Osw (SSS). At Tahiti, we find that the combined analytical uncertainties of coral δ18O and Sr/Ca equal the amplitude of the seasonal cycle of δ18Osw (SSS). Therefore, we cannot resolve the seasonal cycle of SSS at Tahiti. At Timor, the error of reconstructed δ18Osw (SSS) is lower than the magnitude of seasonal variations of δ18Osw (SSS), and the seasonal cycle of δ18Osw (SSS) can be resolved.