Modeling sea-level change using errors-in-variables integrated Gaussian processes

TL;DR

This paper introduces a Bayesian Gaussian process model that accounts for multiple uncertainties, including age errors, to analyze historical and recent sea-level change data, revealing unprecedented recent rise rates.

Contribution

It presents a novel errors-in-variables Gaussian process framework for modeling sea-level change with comprehensive uncertainty quantification.

Findings

Sea-level rise rate increased from 1.13 mm/yr in 1880 to 1.92 mm/yr in 2009

2000 AD rise rate in North Carolina is 2.44 mm/yr, unprecedented in 2000 years

Model effectively captures continuous sea-level change with uncertainty considerations.

Abstract

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.