Accounting for Multiple Sources of Uncertainty in the Statistical Analysis of Holocene Sea Levels

Abstract:

We perform a Bayesian statistical analysis on historical and late Holocene rates of sea-level change. The data that form the input to the statistical model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. The aims are to estimate rates of sea-level change, to determine when modern rates of rise began and to observe how these rates have evolved over time. Many current methods for doing this use simple linear regression to estimate rates. This is often inappropriate as it is too rigid and it can ignore uncertainties that arise as part of the data collection exercise. This can lead to over-confidence in the sea-level trends being characterized.

The proposed model places a Gaussian process prior on the rate process (i.e. the process that determines how rates of sea-level are changing over time). The likelihood of the observed data is the integral of this process. When dealing with proxy reconstructions, the model is set in an errors-in-variables framework so as to take account of age uncertainty. It is also necessary to account for glacio-isostatic adjustment, which introduces a covariance between individual age and sea-level observations. This method allows for the estimation of the rate process with full consideration of all sources of uncertainty.

The model captures the continuous and dynamic evolution of sea-level change and results show that modern rates of rise are consistently increasing. Analysis of a global tide-gauge record (Church and White, 2011) indicated that the rate of sea-level rise increased continuously since 1880AD and is currently 1.9mm/yr (95% credible interval of 1.84 to 2.03mm/yr). Applying the model to a proxy reconstruction from North Carolina (Kemp et al., 2011) indicated that the mean rate of rise in this locality since the middle of the 19th century (current rate of 2.44 mm/yr with a 95% credible interval of 1.91 to 3.01mm/yr) is unprecedented in at least the last 2000 years.