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 delta O-18 and SSS from paired coral Sr/Ca and delta O-18 measurements. Typically, the delta O-18(coral)-SST relationship is estimated by linear regression of coral delta O-18 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 delta O-18(sw) (SSS) often co-vary, and this will bias the estimate of the regression slope of delta O-18(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 delta O-18(coral)-SST relationship has known, we propose to insert this value for gamma(1) 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 delta O-18(sw) (SSS). At Tahiti, we find that the combined analytical uncertainties of coral delta O-18 and Sr/Ca equal the amplitude of the seasonal cycle of delta O-18(sw) (SSS). Therefore, we cannot resolve the seasonal cycle of SSS at Tahiti. At Timor, the error of reconstructed delta O-18(sw) (SSS) is lower than the magnitude of seasonal variations of delta O-18(sw) (SSS), and the seasonal cycle of delta O-18(sw) (SSS) can be resolved. (c) 2008 Elsevier Ltd. All rights reserved.