Deep-sea coral δ¹³C: A tool to reconstruct the difference between seawater pH and δ¹¹B-derived calcifying fluid pH

The boron isotopic composition (δ¹¹B) of coral skeleton is a proxy for seawater pH. However, δ¹¹B-based pH estimates must account for the pH difference between seawater and the coral calcifying fluid, ΔpH. We report that skeletal δ¹¹B and ΔpH are related to the skeletal carbon isotopic composition (δ¹³C) in four genera of deep-sea corals collected across a natural pH range of 7.89-8.09, with ΔpH related to δ¹³C by ΔpH = 0.029 × δ¹³C + 0.929, r² = 0.717. Seawater pH can be reconstructed by determining ΔpH from δ¹³C and subtracting it from the δ¹¹B-derived calcifying fluid pH. The uncertainty for reconstructions is ±0.12 pH units (2 standard deviations) if estimated from regression prediction intervals or between ±0.04 and ±0.06 pH units if estimated from confidence intervals. Our new approach quantifies and corrects for vital effects, offering improved accuracy relative to an existing δ¹¹B versus seawater pH calibration with deep-sea scleractinian corals.