  We propose a comprehensive Bayesian hierarchical model for monthly maxima of
instantaneous flow in river catchments. The Gumbel distribution is used as the
probabilistic model for the observations, which are assumed to come from
several catchments. Our suggested latent model is Gaussian and designed for
monthly maxima, making better use of the data than the standard approach using
annual maxima. At the latent level, linear mixed models are used for both the
location and scale parameters of the Gumbel distribution, accounting for
seasonal dependence and covariates from the catchments. The specification of
prior distributions makes use of penalised complexity (PC) priors, to ensure
robust inference for the latent parameters. The main idea behind the PC priors
is to shrink toward a base model, thus avoiding overfitting. PC priors also
provide a convenient framework for prior elicitation based on simple notions of
scale. Prior distributions for regression coefficients are also elicited based
on hydrological and meteorological knowledge. Posterior inference was done
using the MCMC split sampler, an efficient Gibbs blocking scheme tailored to
latent Gaussian models. The proposed model was applied to observed data from
eight river catchments in Iceland. A cross-validation study demonstrates good
predictive performance.
