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 δ¹⁸O_sw and SSS from paired coral Sr/Ca and δ¹⁸O measurements. Typically, the δ¹⁸O_coral-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 δ¹⁸O_sw (SSS) often co-vary, and this will bias the estimate of the regression slope of δ¹⁸O_coral-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 δ¹⁸O_coral-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 δ¹⁸O_sw (SSS). At Tahiti, we find that the combined analytical uncertainties of coral δ¹⁸O and Sr/Ca equal the amplitude of the seasonal cycle of δ¹⁸O_sw (SSS). Therefore, we cannot resolve the seasonal cycle of SSS at Tahiti. At Timor, the error of reconstructed δ¹⁸O_sw (SSS) is lower than the magnitude of seasonal variations of δ¹⁸O_sw (SSS), and the seasonal cycle of δ¹⁸O_sw (SSS) can be resolved.