Open Access
June 2015 Modeling sea-level change using errors-in-variables integrated Gaussian processes
Niamh Cahill, Andrew C. Kemp, Benjamin P. Horton, Andrew C. Parnell
Ann. Appl. Stat. 9(2): 547-571 (June 2015). DOI: 10.1214/15-AOAS824


We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The input data to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. These data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. The model we propose places a Gaussian process prior on the rate of sea-level change, which is then integrated and set in an errors-in-variables framework to take account of age uncertainty. The resulting model captures the continuous and dynamic evolution of sea-level change with full consideration of all sources of uncertainty. We demonstrate the performance of our model using two real (and previously published) example data sets. The global tide-gauge data set indicates that sea-level rise increased from a rate with a posterior mean of 1.13 mm/yr in 1880 AD (0.89 to 1.28 mm/yr 95% credible interval for the posterior mean) to a posterior mean rate of 1.92 mm/yr in 2009 AD (1.84 to 2.03 mm/yr 95% credible interval for the posterior mean). The proxy reconstruction from North Carolina (USA) after correction for land-level change shows the 2000 AD rate of rise to have a posterior mean of 2.44 mm/yr (1.91 to 3.01 mm/yr 95% credible interval). This is unprecedented in at least the last 2000 years.


Download Citation

Niamh Cahill. Andrew C. Kemp. Benjamin P. Horton. Andrew C. Parnell. "Modeling sea-level change using errors-in-variables integrated Gaussian processes." Ann. Appl. Stat. 9 (2) 547 - 571, June 2015.


Received: 1 July 2014; Revised: 1 March 2015; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499920
MathSciNet: MR3371325
Digital Object Identifier: 10.1214/15-AOAS824

Keywords: Bayesian statistics , errors-in-variables , integrated Gaussian processes , proxy reconstruction , tide gauge

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 2 • June 2015
Back to Top