Predicting extreme surges from sparse data using a copula‐based hierarchical Bayesian spatial model

A hierarchical Bayesian model is proposed to quantify the magnitude of extreme surges on the Atlantic coast of Canada with limited data. Generalized extreme value distributions are fitted to surges derived from water levels measured at 21 buoys along the coast. The parameters of these distributions are linked together through a Gaussian field whose mean and variance are driven by atmospheric sea‐level pressure and the distance between stations, respectively. This allows for information sharing across the original stations and for interpolation anywhere along the coast. The use of a copula at the data level of the hierarchy further accounts for the dependence between locations, allowing for inference beyond a site‐by‐site basis. It is shown how the extreme surges derived from the model can be combined with the tidal process to predict potentially catastrophic water levels.