Appendix A: Calibrating Winter SST to Winter Sr/Ca We begin evaluating the winter Sr/Ca-SST regression by looking at three Bermuda corals (BB 001, BER 002, BER 003) from the same location. All three corals show a statistically significant (Fsig = 0.0004, 0.0938, and 0.0106 respectively) inverse relationship between winter-time (Dec-March) Sr/Ca and Hydrostation S SST over the calibration period (1976-1997) (Figure S1). Linear regressions of winter Sr/Ca to winter SST for each coral yield statistically equivalent (1 degC) slopes and intercepts with an average slope of -0.039 mmol/mol/degC and an intercept of 10.2 mmol/mol. Unlike previous work done on mean-annual calibrations for these corals, adding growth rate either through inter-annual changes [Goodkin et al., 2005] or colony averages [Goodkin et al., 2007] does not improve these winter-time calibrations. This confirms the previous conclusion that growth rate effects resulting from any of the proposed mechanisms [Goodkin et al., 2005] are not impacting the winter Sr/Ca between corals or between winters. Winter-time Sr/Ca appears to reflect SST in a linear fashion. The calibrations for winter Sr/Ca shown in Figure S1, however, are based on a small range of variability and do not provide a realistic SST reconstruction over the length of the multi-century record. The low Sr/Ca to SST slope (-0.039 mmol/mol/degC) tends to overestimate past variations in SST. The BB 001-Hydrostation S winter-time calibration applied to the long record shows winter SSTs as high as 27 deg C in the 1960s and as low as 15 deg C in the 1850s, a range that is greater than the current seasonal cycle. This result implies a possible problem with the above calibrations in that the noise is overwhelming the signals and biasing the regression. In order to address this influence of noise, the long record from BB 001 was correlated to HadISST from 1870-1999 to increase the length and range of signal of the calibration period (Figure S2). HadISST is a compilation of regional observational SST measurements [Rayner et al., 2003]. For our calibration, we use HadISST data over the gridded area 31-33 degrees North and 64-65 degrees West. The results of a type I regression of both yearly and five year binned Sr/Ca to SST are shown in Table S1. Increasing the length of the calibration data sets and then diminishing noise through averaging the SST records into 5-year bins succeeds at increasing the significance of the reconstructions and decreasing the root mean square of the residuals (rmsr) and standard error (se), relative to the Hydrostation S and HadISST inter-annual winter calibration. The slope doubles relative to the inter-annual winter Sr/Ca to Hydrostation S relationship and triples in the 5-year binned analysis. This supports the hypothesis that the 25-year Hydrostation S calibration period provides too shallow a Sr/Ca vs. SST slope likely because of a small range in interannual temperature variability and thus low signal-to-noise ratio for application to multi-century reconstructions. The same exercise was not undertaken for the mean-annual record because influences of growth rate require multiple colonies for calibration, and without longer records from multiple colonies, we cannot extend the calibration window. A study by Cohen and Thorrold (2007) using laser ablation techniques supports the conclusion that the method used in this study accurately captures the winter record without growth rate influences. In addition, they find a non-growth dependent calibration slope of Sr/Ca to SST using the full seasonal cycle of 0.096 mmol/mol/degC in agreement with the non-growth winter slope found here. The five-year binned calibration (eqn. A.2) (see Table S1) returns a slope of -0.0972 mmol/mol/degC. As with the mean-annual data, Sr/Ca reconstructed winter-time SSTs on yearly and five year binned time-scales were generated for the entire 218 year record by inverting equations A.1 and A.2. Error propagation was performed for the five year binned winter-time calibration (eqn. A.2) using standard error propagation methods (e.g., [Bevington, 1969]) as detailed in Goodkin (2007). Error propagation returns an average SST error of ±0.4 degC over the long, 5-year binned record (Figure S3). References Bevington, P. R., Chapter 4: Propagation of Error. in Data Reduction and Error Analysis for the Physical Sciences, pp. 56-65, McGraw Hill, United States of America, 1969. Cohen, A. L., and S. R. Thorrold, Recovery of temperature records from slow-growing corals by fine scale sampling of skeletons, Geophysical Research Letters, doi:10.1029/2007GL030967, 2007. Goodkin, N. F., K. Hughen, and A. C. Cohen, A multi-coral calibration method to approximate a universal equation relating Sr/Ca and growth rate to sea surface temperature, Paleoceanography, 22, 10.1029/2006PA001312, 2007. Goodkin, N. F., K. Hughen, A. C. Cohen, and S. R. Smith, Record of Little Ice Age sea surface temperatures at Bermuda using a growth-dependent calibration of coral Sr/Ca, Paleoceanography, 20, PA4016, doi:4010.1029/2005PA001140, 2005. Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, W. C. Kent, and A. Kaplan, Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century, Journal of Geophysical Research, 108, 4407, 2003. Table S1 Figure S1: Coral winter-time (Dec., Jan., Feb. and March) Sr/Ca and Hydrostation S (solid, grey) SST plotted versus year (a) and linearly (b) for BB 001 (solid line, circles), for BER 002 (small dashes, squares), and for BER 003 (large dashes, triangles). Figure S2: BB 001 winter-time (Dec.-March) Sr/Ca (shaded) and HadISST (solid) plotted versus year for a) inter-annual (r^2 = 0.13, rmsr = 1.03 degC), b) five-year bins (r^2 = 0.35, rmsr = 0.36 degC), and c) linearly with inter-annual (shaded, circles), and five year bins (solid, squares). Figure S3: A) Five-year winter-time Sr/Ca versus time and B) Reconstructed five-year averaged winter-time SST from 1781-1999. Uncertainty resulting from error propagation (1 sigma) is shown by shaded lines. Coral SSTs are reconstructed from Sr/Ca using five year averaged calibration (eqn. A.2).