  Extreme floods cause casualties, and widespread damage to property and vital
civil infrastructure. We here propose a Bayesian approach for predicting
extreme floods using the generalized extreme-value (GEV) distribution within
gauged and ungauged catchments. A major methodological challenge is to find a
suitable parametrization for the GEV distribution when covariates or latent
spatial effects are involved. Other challenges involve balancing model
complexity and parsimony using an appropriate model selection procedure, and
making inference using a reliable and computationally efficient approach. Our
approach relies on a latent Gaussian modeling framework with a novel
multivariate link function designed to separate the interpretation of the
parameters at the latent level and to avoid unreasonable estimates of the shape
and time trend parameters. Structured additive regression models are proposed
for the four parameters at the latent level. For computational efficiency with
large datasets and richly parametrized models, we exploit an accurate and fast
approximate Bayesian inference approach. We applied our proposed methodology to
annual peak river flow data from 554 catchments across the United Kingdom (UK).
Our model performed well in terms of flood predictions for both gauged and
ungauged catchments. The results show that the spatial model components for the
transformed location and scale parameters, and the time trend, are all
important. Posterior estimates of the time trend parameters correspond to an
average increase of about $1.5\%$ per decade and reveal a spatial structure
across the UK. To estimate return levels for spatial aggregates, we further
develop a novel copula-based post-processing approach of posterior predictive
samples, in order to mitigate the effect of the conditional independence
assumption at the data level, and we show that our approach provides accurate
results.
