A Bayesian hierarchical model for reconstructing relative sea level: from raw data to rates of change

Niamh Cahill,Benjamin P Horton,Andrew C Kemp,Andrew C Parnell

doi:10.5194/cp-12-525-2016

Abstract

Abstract. We present a Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) a new Bayesian transfer (B-TF) function for the calibration of biological indicators into tidal elevation, which is flexible enough to formally accommodate additional proxies; (2) an existing chronology developed using the Bchron age–depth model, and (3) an existing Errors-In-Variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. Our approach is illustrated using a case study of Common Era sea-level variability from New Jersey, USA We develop a new B-TF using foraminifera, with and without the additional (δ13C) 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 (mean square error = 0.003 m2). The Bayesian hierarchical model provides a single, unifying framework for reconstructing and analyzing sea-level change through time. This approach is suitable for reconstructing other paleoenvironmental variables (e.g., temperature) using biological proxies.

Highlights

Paleoenvironmental reconstructions describe Earth’s response to past climate changes and offer a context for current trends and analogs for anticipated future changes (e.g., Mann et al, 2009)
The response curves are estimated from a multinomial distribution parameterized by a probability vector p, which is the probability of a species being present at a given tidal elevation
(1) A Bayesian transfer (B-TF) for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies such as bulk sediment δ13C. (2) An existing chronology developed from a BTF with an existing chronology module (Bchron) age– depth model

Summary

Introduction

Paleoenvironmental reconstructions describe Earth’s response to past climate changes and offer a context for current trends and analogs for anticipated future changes (e.g., Mann et al, 2009). The ecological preferences of biological proxies observed in modern environments are used to derive a paleoenvironmental reconstruction from their counterparts preserved in dated sediment cores under the assumption that their ecological preferences were unchanged through time (e.g., Juggins and Birks, 2012). This approach commonly utilizes data consisting of one environmental variable and counts from multiple proxy species (e.g., Imbrie and Kipp, 1971; Fritz et al, 1991; Birks, 1995). Numerical techniques known as transfer functions formalize the relationship between biological assemblages and the environmental variable.

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Conclusion