Journal cover Journal topic
Climate of the Past An interactive open-access journal of the European Geosciences Union
Clim. Past, 12, 525-542, 2016
http://www.clim-past.net/12/525/2016/
doi: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
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 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  =  0.003 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.

Citation: Cahill, N., Kemp, A. C., Horton, B. P., and Parnell, A. C.: A Bayesian hierarchical model for reconstructing relative sea level: from raw data to rates of change, Clim. Past, 12, 525-542, doi:10.5194/cp-12-525-2016, 2016.
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Short summary
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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