A Bayesian Hierarchical Model for Reconstructing Sea Levels: From Raw Data to Rates of Change

We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\delta}13C proxy and compare our results to those from a widely-used weighted-averaging transfer function (WA-TF). The formal incorporation of a second proxy into the B-TF model results in smaller vertical uncertainties and improved accuracy for reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ~28% smaller on average compared to the WA-TF. When evaluated against historic tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the RSL changes observed in the instrumental record (MSE = 0.003). The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time. This approach is suitable for reconstructing other paleoenvironmental variables using biological proxies.