A Bayesian Hierarchical Model for Reconstructing Sea Level from the Common Era: From Raw Data to Rates of Change

Abstract:

We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ¹³C) sea-level indicators preserved in dated cores of salt-marsh sediment. The 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 δ¹³C values). (2) A chronology developed from a Bchron age-depth model. (3) An 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, USA. Results from our new Bayesian transfer function (B-TF), with and without the δ¹³C proxy, are compared to those from a widely-used weighted-averaging transfer function (WA-TF). The incorporation of secondary proxy information into the model in a formalized way results in smaller vertical uncertainties for reconstructed relative sea level. The vertical uncertainty from the multi proxy B-TF is ~30% smaller on average compared to the WA-TF. We evaluate the performance of both transfer functions by comparing reconstructed relative sea level to historic tide-gauge measurements. The multi proxy B-TF most accurately reconstructs the relative sea-level changes observed in the tide-gauge record. The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time.