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We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\delta}13C 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 (MSE = 0.003). The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time. This approach is suitable for reconstructing other paleoenvironmental variables using biological proxies., Comment: 27 pages, 7 figures

We evaluate relative sea level (RSL) trajectories for North Carolina, USA, in the context of tide-gauge measurements and geological sea-level reconstructions spanning the last $\mathord{\sim}$11,000 years. RSL rise was fastest ($\mathord{\sim}$7 mm/yr) during the early Holocene and slowed over time with the end of the deglaciation. During the pre-Industrial Common Era (i.e., 0--1800 CE), RSL rise ($\mathord{\sim}$0.7 to 1.1 mm/yr) was driven primarily by glacio-isostatic adjustment, though dampened by tectonic uplift along the Cape Fear Arch. Ocean/atmosphere dynamics caused centennial variability of up to $\mathord{\sim}$0.6 mm/yr around the long-term rate. It is extremely likely (probability $P = 0.95$) that 20th century RSL rise at Sand Point, NC, (2.8 $\pm$ 0.5 mm/yr) was faster than during any other century in at least 2,900 years. Projections based on a fusion of process models, statistical models, expert elicitation, and expert assessment indicate that RSL at Wilmington, NC, is very likely ($P = 0.90$) to rise by 42--132 cm between 2000 and 2100 under the high-emissions RCP 8.5 pathway. Under all emission pathways, 21st century RSL rise is very likely ($P > 0.90$) to be faster than during the 20th century. Due to RSL rise, under RCP 8.5, the current `1-in-100 year' flood is expected at Wilmington in $\mathord{\sim}$30 of the 50 years between 2050-2100., Comment: 13 main text pages, 4 figures, 4 supplemental pages. Published in Climatic Change

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., Comment: Published at http://dx.doi.org/10.1214/15-AOAS824 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)