Quantifying uncertainty in coral Sr/Ca-based SST estimates from Orbicella faveolata: A basis for multi-colony SST reconstructions

The Sr/Ca in massive corals can be used as a proxy for sea surface temperature (SST) in shallow tropical to sub-tropical regions; however, the relationship between Sr/Ca and SST varies throughout the ocean, between different species of coral, and often between different colonies of the same species. We aimed to quantify the uncertainty associated with the Sr/Ca-SST proxy due to sample handling (e.g., micro-drilling or analytical error), vital effects (e.g., among-colony differences in coral growth), and local-scale variability in microhabitat. We examine the intra- and inter-colony reproducibility of Sr/Ca records extracted from five modern Orbicella faveolata colonies growing in the Dry Tortugas, Florida, USA. The average intra-colony absolute difference (AD) in Sr/Ca of the five colonies during an overlapping interval (1997-2008) was 0.055 ± 0.044 mmol mol-1 (0.96 ºC) and the average inter-colony Sr/Ca AD was 0.039 ± 0.01 mmol mol-1 (0.51 ºC). All available Sr/Ca-SST data pairs from 1997-2008 were combined and regressed against the HadISST1 gridded SST data set (24 ºN and 82 ºW) to produce a calibration equation that could be applied to O. faveolata specimens from throughout the Gulf of Mexico/Caribbean/Atlantic region after accounting for the potential uncertainties in Sr/Ca-derived SSTs. We quantified a combined error term for O. faveolata using the root-sum-square (RMS) of the analytical, intra-, and inter-colony uncertainties and suggest that an overall uncertainty of 0.046 mmol mol-1 (0.81 ºC, 1σ), should be used to interpret Sr/Ca records from O. faveolata specimens of unknown age or origin to reconstruct SST. We also explored how uncertainty is affected by the number of corals used in a reconstruction by iteratively calculating the RMS error for composite coral time-series using two, three, four, and five overlapping coral colonies. Our results indicate that maximum RMS error at the 95% confidence interval on mean annual SST estimates is 1.4 ºC when a composite record is made from only two overlapping coral Sr/Ca records. The uncertainty decreases as additional coral Sr/Ca data are added, with a maximum RMS error of 0.5 ºC on mean annual SST for a five-colony composite. To reduce uncertainty to under 1 ºC, it is best to use Sr/Ca from three or more coral colonies from the same geographic location and time period.