Practical issues with modeling extreme Brazilian rainfall

Accurately quantifying extreme rainfall is important for the design of hydraulic structures, for flood mapping and zoning and for disaster management. In order to produce maps of estimates of 25-year rainfall return levels in Brazil, we selected 893 shorter and 104 longer rainfall time series from the Agencia Nacional de Aguas (ANA), and applied the framework of extreme value theory. Care was needed to reduce the impact of poor data. Estimates of the shape parameter of the extreme-value model fitted to rainfall data are typically biased, so we discuss an empirical correction that takes into account not only the sample-size bias, but also a so-called penultimate approximation that we use to inform a Bayesian spatial latent variable model for the annual rainfall maxima. This model accounts for subtle patterns of spatial variation in the data and provides plausible return level estimates.