A Bayesian Hierarchical Spatiotemporal Model With Physical Barriers for Extreme Sea‐Level Prediction in Ireland

Rising seas raise the vulnerability of coastal regions through higher extreme sea levels. This paper estimates extreme sea levels at gauged and ungauged coastal locations around Ireland and the West Coast of Great Britain, using a Bayesian hierarchical extreme‐value model with spatiotemporal random effects. The annual maxima of tidal residuals are modelled with the blended Generalized Extreme Value (bGEV) distribution, whose location quantile varies in space and time through a latent Gaussian field, and coastlines enter the model as physical barriers that constrain spatial correlation. Inference uses the integrated nested Laplace approximation (INLA) with the stochastic partial differential equation (SPDE) representation, applied to 44 tide gauges around Ireland and Great Britain covering 1968 to 2025. We compare the barrier model with an otherwise identical stationary model. The two models produce nearly identical location surfaces, return levels, and uncertainty at gauged coastal sites. The stationary model is preferred by WAIC and leave‐group‐out cross‐validation, though the two are indistinguishable when predicting the same held‐out sites, where the barrier formulation offers a more physically consistent representation of coastal connectivity at no cost in accuracy. We also examine the assumption that the spread and the shape of the distribution are constant across the domain: the spread varies with the geometry of the basin while the shape does not, although a regional covariate on the spread adds little once the spatiotemporal field is present. Return levels are reported with full posterior uncertainty, obtained by propagating joint posterior draws of the latent field and the bGEV parameters through the return‐level function. A linear time trend is not identifiable in these data, since an apparent trend arises from confounding with the temporal random field, so we report return levels for the observed period and do not extrapolate; a physically based projection conditioned on climate‐model output would be the proper route to future estimates.