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).