Constraining past seawater δ¹⁸O and temperature records developed from foraminiferal geochemistry

Paired measurements of magnesium-to-calcium ratios (Mg/Ca) and the stable oxygen isotopic composition (δ¹⁸O) in foraminifera have significantly advanced our knowledge of the climate system by providing information on past temperature and seawater δ¹⁸O (δ¹⁸O_sw, a proxy for salinity and ice volume). However, multiple sources of uncertainty exist in transferring these downcore geochemical data into quantitative paleoclimate reconstructions. Here we develop a computational toolkit entitled Paleo-Seawater Uncertainty Solver (PSU Solver) that performs bootstrap Monte Carlo simulations to constrain these various sources of uncertainty. PSU Solver calculates temperature and δ¹⁸O_sw, and their respective confidence intervals using an iterative approach with user-defined errors, calibrations, and sea-level curves. Our probabilistic approach yields reduced uncertainty constraints compared to theoretical considerations and commonly used propagation exercises. We demonstrate the applicability of PSU Solver for published records covering three timescales: the late Holocene, the last deglaciation, and the last glacial period. We show that the influence of salinity on Mg/Ca can considerably alter the structure and amplitude of change in the resulting reconstruction and can impact the interpretation of paleoceanographic time series. We also highlight the sensitivity of the records to various inputs of sea-level curves, transfer functions, and uncertainty constraints. PSU Solver offers an expeditious yet rigorous approach to test the robustness of past climate variability inferred from paired Mg/Ca-δ¹⁸O measurements.