Appendix B: Calibrating Coral del18O for SSS Monthly Relationships: Growth rate and bulk sampling effects limit our ability to evaluate del18O from the slow-growing Bermuda coral as an SSS proxy on monthly time-scales. However, for comparison to the literature we examine the del18O data on monthly time-scales. The del18O of the coral (delOc) is negatively correlated to Hydrostation S SST and positively correlated to Hydrostation S SSS (Figure S4). Over the calibration period (1976-1997), monthly coral del18O values range from -4.63 to -2.92 permil. The correlation coefficient (r^2) of monthly delOc is 0.69 to SST and 0.32 to SSS. Hydrostation S SST and SSS are correlated (r^2 = 0.31) over this time period and thus the coral delOc–SST and delOc–SSS correlations are not fully independent. The correlation of del18O to Sr/Ca (r^2 = 0.70) is strong, as expected from both proxies’ dependence on SST. Regressions of monthly del18O to SST and monthly Sr/Ca to del18O are regularly reported in the literature. Reported del18O to SST slopes range from -0.101 to -0.179 permil/degC [Bagnato et al., 2004; Cardinal et al., 2001; deVilliers et al., 1995; Dunbar et al., 1994; Gagan et al., 1998; Guilderson et al., 1994; McCulloch et al., 1994; Smith et al., 2006; Watanabe et al., 2003]. The slope of -0.105 permil/degC found in this study is at the shallow end of reported results. Reported Sr/Ca to del18O slopes range from 0.27 to 0.30 mmol/mol/permil (with one reported value of 0.18 [Cardinal et al., 2001] from a coral growing less than 3 mm/year) [Beck et al., 1992; Cardinal et al., 2001; McCulloch et al., 1994; Smith et al., 2006], equivalent to our slope of 0.28 mmol/mol/permil. Kinetic disequilibrium models indicate that slow growing corals should more closely approach thermodynamic equilibrium than faster growing corals [McConnaughey, 1989a; McConnaughey, 1989b]. Fewer growth (kinetic) effects during calcification are expected to impact the del18O of these slow-growing coral species. This should include effects found within and between colonies [deVilliers et al., 1995; Guilderson and Schrag, 1999; Linsley et al., 1999; McConnaughey, 1989b; McConnaughey, 2003]. However, in addition to kinetic effects, the del18O of slow-growing corals will be further complicated by growth structure and smoothing during bulk sampling [Cohen et al., 2004; Goodkin et al., 2005; Swart et al., 2002]. Therefore, when examining oxygen isotopes to investigate salinity, consideration of inter-annual changes (rather than monthly changes) is critical. Mean-Annual Relationship: The relationships among mean-annual del18O, SST, and SSS are analyzed over the same time period as Sr/Ca, from 1976-1997 with the exclusion of years missing instrumental data. First, del18O of the water (delOw) was calculated using Hydrostation S SSS instrumental data and the following thermocline equilibrium equation [Schmidt, 1999]: delOw = 0.49 * (SSS) -17 eqn. (B.1) A limited set of measurements of delOw (permil) and salinity (psu) from the Bermuda Atlantic Time Series (BATS) and from Surf Bay Beach, Bermuda indicate that SSS provides a reasonable estimate for delOw at this location [Goodkin, 2007]. Mean-annual delOc has the expected negative relationship to SST and positive correlation to delOw (SSS) (Figures S5a and S5b). Therefore, we began by using a multivariate model in which delOc (permil) was linearly regressed against SST (degC) and delOw (permil): delOc = –0.138 (±0.250) * SST + 0.990 (±1.35) * delOw – 1.26 (±5.47) (2 sigma, 95% conf., r^2 = 0.17, Fsig = 0.3092, rmsr of delOw = 0.098 permil, se on delOc = 0.108 permil) eqn. (B.2) Statistically this regression is insignificant (Fsig greater than 0.01). In examining Figure S5, we can see the impacts of using this regression to reconstruct salinity. Equation B.2 does not sufficiently describe delOc, underestimating the range seen during the calibration period, when either Hydrostation S or Sr/Ca-based SST is used with Hydrostation S delOw (Figure S5c). DelOw is also calculated by inverting equation B.2 and using both Hydrostation S and Sr/Ca-based SST with the measured delOc. The model dictates that reconstructed delOw over the calibration period will have a 1:1 relationship with the instrumental based delOw (Figure S5d). However, the range of reconstructed delOw (0.6 – 1.1 permil) overestimates the range seen at Hydrostation S (0.8 – 1.1permil) by a factor of 3, and the rmsr error of 0.098 permil for the reconstructed delOw is very large. Therefore, we developed a second model. In this model, instead of regressing delOc vs both SST and delOw, we subtracted delOw (permil) from delOc (permil) and linearly regressed the difference against SST (degC). Linear regression of delOc – delOw versus SST returns the following result: delOc – delOw = –0.139 (±0.226) * (SST) – 1.26 (±5.22) (2 sigma, 95 percent conf., r^2 = 0.10, Fsig = 0.2378, rmsr of delOw = 0.10 permil, se on delOc – delOw = 0.104 permil) eqn. (B.3) At a 95 percent confidence interval, this equation is also insignificant and also has a large rmsr for delOw of 0.10 permil. One potential problem with this method is that we are differing two large values (delOc and delOw) to calculate a small residual, and if the errors in delOc and delOw are large, than we have little constraint on the resulting difference. Figure S6 shows that switching to a single variant regression of delOc - delOw vs. SST does not improve the relationship. As shown in Figure S6d, delOw variability is still overestimated, and the error in reconstructed delOw remains large. It is important to mention that the inclusion of growth rate in either of these regressions (eqns. B.2 or B.3) does not improve the significance. In addition, the added growth rate term is never statistically significant (p is never less than 0.1). This result implies that either growth rate has a much smaller impact on del18O relative to SST and SSS than it does on Sr/Ca relative to SST or that the added noise of the del18Oc coral record from salinity or vital effects cannot be fully described by growth. As discussed in the main text, mean annual delOc shows a flat or slightly decreasing trend (-0.0003 permil/year) from 1782-1998, and coral Sr/Ca-based reconstructed SST shows an increasing trend (Figure S7). Because the delOc data do not show a strong trend opposing the SST trend, the two records imply that historical mean-annual SSS (delOw) was fresher than today. Both equations B.2 and B.3, which return very similar results, applied to the 218 year record of delOc using coral SST estimates demonstrate a trend of increasing SSS (delOw) from the late 1700s to today. However, due to the lack of significance in either regression model, we are unable to robustly transform the results into a quantitative salinity change over this period. Winter Relationship: The relationship between winter-time (Dec.-March) del18O, SST and SSS is evaluated over the same calibration time period as mean-annual del18O (1976-1997). Winter trace element ratios have shown no growth impacts, and therefore, are expected to have less vital and or sampling effects than the mean-annual reconstruction. The same two models are used as for the mean-annual calibrations. We begin by describing delOc (permil) as a function of both SST (degC) (Figure S8a) and delOw (Figure S8b). The multi-variant regression returns the following result: delOc = -0.117 (±0.100)*(SST) + 1.48 (±1.42)*(delOw) -2.28 (±2.26) (2 sigma, 95 percent conf., r2 = 0.34, Fsig = 0.0299, rmsr of delOw = 0.08 permil, se = 0.125 permil) eqn. (B.4) The winter-time results for the multi-variant regression are comparable to the mean-annual results. The relationship described by eqn. B.4 is statistically significant. DelOc calculated with Hydrostation S delOw and either Hydrostation S and Sr/Ca-based reconstructed SST underestimate variability relative to the delOc of the coral (Figure S8c). Reconstructed delOw both with SST records and the coral delOc show the expected (or close to expected) ratio of 1:1 relative to the estimated Hydrostation S delOw. However, the delOw reconstructed range of 0.7-1.1 permil is close to three times the instrumental range of 0.8-1.0 permil (Figure S8d), and size of the error is substantial relative to the signal. The winter-time multi-variant regression fails to describe the delOc-SST-delOw relationship. We also investigated the single variant model in which delOc - delOw is regressed against SST. A linear regression of delOc - delOw (permil) versus winter-time SST (deg C) returns the following results (Figure S9): delOc - delOw = –0.112 (±0.097) * (SST) – 1.93 (±1.98) (2 sigma, 95 percent conf., r^2 = 0.23, Fsig = 0.0331, rmsr of delOw = 0.12 permil, se of delOc= 0.123 permil) eqn. (B.5) At a 95 percent confidence interval, this equation is significant, with a large amount of noise amongst the data (Figure S9a). Using either the instrumental or Sr/Ca-based reconstructed SST, the delOw is still not accurately reconstructed, with a range of 0.6-1.2 permil compared to the Hydrostation S delOw range of 0.8-1.0 permil (Figure S9d). All of the delOc regressions serve to underestimate variability in delOc and overestimate variability in delOw. Ideally, we could examine these data over average periods as was done with the winter Sr/Ca to reduce the influence of noise. However, due to limited salinity data this will reduce the number of points in the regression, diminishing statistical evaluations. The winter-time 218 year long record shows strong qualitative results in agreement with mean-annual record. delOc shows a slightly increasing or no trend through time (Figure S10a) which combined with an increasing trend in the Sr/Ca-based reconstructed SST implies an increasing salinity (delOw) from the late 1700s until today. Both models overestimate variability in delOw, and therefore, cannot be used as a quantitative tool for reconstructing SSS. However, both models do return the result of increasing salinity, confirming the first order interpretation of the data. References Bagnato, S., B. K. Linsley, S. S. Howe, G. M. Wellington, and J. 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Hantoro, Oxygen isotope systematics in Diploastrea heliopora: New coral archive of tropical paleoclimate, Geochimica Et Cosmochimica Acta, 67, 1349-1358, 2003. Figure S4: From coral BB 001, monthly d18O from 1976-1997 regressed linearly against monthly Hydrostation S SST (a) and SSS (b). Monthly BB 001 Sr/Ca regressed linearly against monthly BB 001 d18O. Figure S5: Results of a multivariate regression of mean-annual delOc versus SST and delOw. a) Coral measured delOc versus Hydrostation S SST. b) Coral measured delOc versus Hydrostation S delOw (SSS). c) Reconstructed delOc using eqn. B.2 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. d) Reconstructed delOw using eqn. B.2 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOw. Figure S6: Results of a single variate regression of mean-annual delOc – delOw versus SST. a) Coral measured delOc – delOw versus Hydrostation S SST. b) Reconstructed delOc – delOw using eqn. B.3 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. c) Reconstructed delOc using eqn. B.3 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. d) Reconstructed delOw using eqn. B.3 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOw. Figure S7: Two hundred year records of mean-annual data or derived records of a) Coral measured delOc, b) Coral-based Sr/Ca reconstructed SST, c) Reconstructed delOw using eqn. B.2 and coral-based Sr/Ca reconstructed SST, d) Reconstructed delOw using eqn. B.3 and coral-based Sr/Ca reconstructed SST. Linear trends with time are shown by shaded lines. Figure S8: Results of a multivariate regression of winter-time delOc versus SST and delOw. a) Coral measured delOc versus Hydrostation S SST. b) Coral measured delOc versus Hydrostation S delOw. c) Reconstructed delOc using eqn. B.4 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. d) Reconstructed delOw using eqn. B.4 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOw. Figure S9: Results of a single variant regression of winter-time delOc – delOw versus SST. a) Coral measured delOc – delOw versus Hydrostation S SST. b) Reconstructed delOc – delOw using eqn. B.5 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. c) Reconstructed delOc using eqn. B.5 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOc. d) Reconstructed delOw using eqn. B.5 and both Hydrostation S SST (solid) and coral Sr/Ca reconstructed SST (shaded) versus measured delOw. Figure S10: Two hundred year records of winter-time data or derived records of a) Coral measured delOc, b) Coral-based Sr/Ca reconstructed SST, c) Reconstructed delOw using eqn. B.4 and coral-based Sr/Ca reconstructed SST, d) Reconstructed delOw using eqn. B.5 and coral-based Sr/Ca reconstructed SST. Linear trends with time are shown by shaded lines.