Abstract

The concentrations of calcium, magnesium, and sulphate in seawater have changed over the Phanerozoic. We know this from data describing how the concentration of each element has changed, but additionally we have independent constraints on the Mg/Ca ratio of seawater through time. We also know the residence time of each of the elements and therefore have some sense of how rapidly each might have changed. Leveraging all this information together is a statistical challenge. We illustrate some of these challenges and demonstrate how we have combined Markov Chain Monte Carlo with Gaussian Processes to improve our understanding of how the concentrations of these elements have evolved through time. In particular, we improve uncertainty propagation, finding that the uncertainty in calcium concentrations is higher than previously thought (which has implications for palaeo saturation state). Overall, our method produces robust time series with uncertainty which describe how ocean composition has evolved over the Phanerozoic.