A Bayesian peaks-over-threshold analysis of floods in the Itajaí-açu River under stationarity and nonstationarity

Abstract

In this paper we revisit the case study of Silva et al. (Stoch Env Res Risk A. doi:10.1007/s00477-015-1072-y, 2015), the Itajai-acu River at Apiuna (Southern Brazil), with an augmented data set and Bayesian inferential techniques. Nonstationary Poisson-GP models are used to study the joint influence of El Nino-Southern Oscillation (ENSO) and of upstream flood control structures on the flood regime at the study site. The Nino3.4 DJF index and a dimensionless reservoir index are used as covariates. Prior belief about the GP shape parameter is elicited by fitting the GEV distribution to AMS samples from 138 sites in Southern Brazil with 40 or more years of data and deriving the distribution from the estimates of that parameter. Following a data-driven exploratory analysis, a Markov chain Monte Carlo (MCMC) procedure is used to sample from the posterior distribution of parameters. Model evaluation and selection used Bayes factors and two information criteria. Results show evidence that, while upstream dams play a significant, though small, role in reducing flood hazard, the influence of the climate covariate is stronger, and an increase in ENSO amplitude in the last decades has led to the occurrence of higher annual maximum floods. MCMC samples are used to derive the Bayesian predictive distribution of annual flood quantiles and design life levels. Uncertainty analyses based on the posterior distribution of parameters and quantiles are presented.