A Simple Monte Carlo Approach to Estimate the Uncertainties of SST and δ18Osw Inferred From Coral Proxies

Abstract

The skeletons of massive corals inhabiting tropical and subtropical oceans grow over centuries. The chemical and isotopic compositions of their skeletons reflect changes in the marine environment and provide an archive of sea surface temperature (SST) and salinity at a high temporal resolution spanning decades to centuries. Stable oxygen isotope ratios in coral skeletons (δ18Oc) are an excellent proxy for SST and the stable oxygen isotopic composition in seawater (δ18Osw). Variations in δ18Osw serve as a hydrological proxy and are routinely estimated by subtracting the SST component from δ18Oc. The SST component of δ18Oc is inferred from coral Sr/Ca (SST proxy). Both Sr/Ca and δ18Oc are converted to SST units based on Sr/Ca- and (δ18Oc–δ18Osw)-SST calibrations. However, the exact slope values of the Sr/Ca-SST and (δ18Oc–δ18Osw)-SST calibrations are challenging to assess, which hampers the reliable estimation of SST, δ18Osw, and their uncertainties. Here, we present a simple Monte Carlo approach to estimate variations in SST and δ18Osw together with their confidence intervals. Our approach improves on previous error propagation methods by including intercolonial differences of calibration slopes in addition to analytical errors. In addition, Monte Carlo experiments using adjusted errors suggest that uncertainties in the calibration slopes have a minor influence on estimates of SST and δ18Osw.