Comparison of full and empirical Bayes approaches for inferring sea-level changes from tide-gauge data

Tide-gauge data are one of the longest instrumental records of the ocean, but these data can be noisy, gappy, and biased. Previous studies have used empirical Bayes methods to infer the sea-level field from tide-gauge records but have not accounted for uncertainty in the estimation of model parameters. Here we compare to a fully Bayesian method that accounts for uncertainty in model parameters, and demonstrate that empirical Bayes methods underestimate the uncertainty in sea level inferred from tide-gauge records. We use a synthetic tide-gauge data set to assess the skill of the empirical and full Bayes methods. The empirical-Bayes credible intervals on the sea-level field are narrower and less reliable than the full-Bayes credible intervals: the empirical-Bayes 95% credible intervals are 42.8% narrower on average than are the full-Bayes 95% credible intervals; full-Bayes 95% credible intervals capture 95.6% of the true field values, while the empirical-Bayes 95% credible intervals capture only 77.1% of the true values, showing that parameter uncertainty has an important influence on the uncertainty of the inferred sea-level field. Most influential are uncertainties in model parameters for data biases (i.e., tide-gauge datums); letting data-bias parameters vary along with the sea-level process, but holding all other parameters fixed, the 95% credible intervals capture 92.8% of the true synthetic-field values. Results indicate that full Bayes methods are preferable for reconstructing sea-level estimates in cases where complete and accurate estimates of uncertainty are warranted.