Approximate Bayesian inference for spatial flood frequency analysis
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Extreme floods cause casualties, widespread property damage, and damage to vital civil infrastructure. Predictions of extreme floods within gauged and ungauged catchments is crucial to mitigate these disasters. A Bayesian framework is proposed for predicting extreme floods using the generalized extreme-value (GEV) distribution. The methodological challenges consist of choosing a suitable parametrization for the GEV distribution when multiple covariates and/or latent spatial effects are involved, balancing model complexity and parsimony using an appropriate model selection procedure, and making inference based on a reliable and computationally efficient approach. We propose a latent Gaussian model with a novel multivariate link function for the location, scale and shape parameters of the GEV distribution. This link function is designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape parameter. Structured additive regression models are proposed for the three parameters at the latent level. Each of these regression models contains fixed linear effects for catchment descriptors. Spatial model components are added to the two first latent regression models, to model the residual spatial structure unexplained by the catchment descriptors. To achieve computational efficiency for large datasets with these richly parametrized models, we exploit a Gaussian-based approximation to the posterior density. This approximation relies on site-wise estimates, but, contrary to typical plug-in approaches, the uncertainty in these initial estimates is properly propagated through to the final posterior computations. We applied the proposed modeling and inference framework to annual peak river flow data from 554 catchments across the United Kingdom. The framework performed well in terms of flood predictions for ungauged catchments.
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