Reclaiming the past: Using hierarchical Bayesian analysis to fill missing values in the tide gauge mean sea level record, with application to extreme value analysis

Abstract:

Tide gauge records of mean sea level are some of the most valuable instrumental time series of oceanic variability and change. Yet these time series sometimes have short record lengths and intermittently missing values. Such issues can limit the utility of the data, for example, precluding rigorous analyses of return periods of extreme mean sea level events and whether they are unprecedented.

With a view to filling gaps in the tide gauge mean sea level time series, we describe a hierarchical Bayesian modeling approach. The model, which is predicated on the notion of conditional probabilities, comprises three levels: a process level, which casts mean sea level as a field with spatiotemporal covariance; a data level, which represents tide gauge observations as noisy, biased versions of the true process; and a prior level, which gives prior functional forms to model parameters. Using Bayes' rule, this technique gives estimates of the posterior probability of the process and the parameters given the observations.

To demonstrate the approach, we apply it to 2,967 station-years of annual mean sea level observations over 1856-2013 from 70 tide gauges along the United States East Coast from Florida to Maine (i.e., 26.8% record completeness). The model overcomes the data paucity by sharing information across space and time. The result is an ensemble of realizations, each member of which is a possible history of sea level changes at these locations over this period, which is consistent with and equally likely given the tide gauge data and underlying model assumptions.

Using the ensemble of histories furnished by the Bayesian model, we identify extreme events of mean sea level change in the tide gauge time series. Specifically, we use the model to address the particular hypothesis (with rigorous uncertainty quantification) that a recently reported interannual sea level rise during 2008-2010 was unprecedented in the instrumental record along the northeast coast of North America, and that it had a return period of 850 years. Preliminary analysis suggests that this event was likely unprecedented on the coast of Maine in the last century.