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Climate of the Past An interactive open-access journal of the European Geosciences Union
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Volume 12, issue 2 | Copyright
Clim. Past, 12, 525-542, 2016
https://doi.org/10.5194/cp-12-525-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 29 Feb 2016

Research article | 29 Feb 2016

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

Niamh Cahill1,2, Andrew C. Kemp3, Benjamin P. Horton4,5, and Andrew C. Parnell1 Niamh Cahill et al.
  • 1School of Mathematics and Statistics, CASL, Earth Institute, University College Dublin, Ireland
  • 2Dept. of Biostatistics and Epidemiology, School of Public Health, University of Massachusetts Amherst, USA
  • 3Dept. of Earth and Ocean Sciences, Tufts University, USA
  • 4Department of Marine & Coastal Sciences and Institute of Earth, Ocean, & Atmospheric Sciences, Rutgers University, USA
  • 5The Earth Observatory of Singapore and the Asian School of the Environment, Nanyang Technological University, Singapore

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 = 0.003m2). 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.

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We propose a Bayesian model for the reconstruction and analysis of former sea levels. The model provides a single, unifying framework for reconstructing and analyzing sea level through time with fully quantified uncertainty. We illustrate our approach using a case study of Common Era (last 2000 years) sea levels from New Jersey.
We propose a Bayesian model for the reconstruction and analysis of former sea levels. The model...
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