On peaks-over-threshold modeling of floods with zero-inflated Poisson arrivals under stationarity and nonstationarity

The peaks-over-threshold (POT) model with Poisson arrivals and generalized Pareto (GP) distributed exceedances remains a popular and useful tool for modelling hydrologic extremes. The use of the Poisson-GP model for flood frequency analysis requires the validation of the hypothesis that the distribution of the annual number of flood events may be described by a Poisson distribution. Such hypothesis is not always valid in practical applications. The present study concerns the use of an alternative distribution for modelling the annual number of floods-the zero-inflated Poisson (ZIP) distribution with two parameters. A ZIP-GP model for flood frequency analysis is proposed. This model is less restrictive than the Poisson-GP model since it allows for a more accurate description of the occurrence process in a POT framework if the fraction of years with no exceedances is significantly higher than the theoretical mass at zero of the Poisson distribution. Furthermore, a nonstationary model (NSZIP-GP) is presented, in which the parameters of the ZIP are allowed to change in time as a function of a covariate, which, even for stationary peak magnitudes, affects the annual maximum flood quantiles with a given non-exceedance probability. Applications of the ZIP-GP model to flood data from Northern Portugal and the evaluation of its performance relative to the Poisson-GP model, including assessments of quantile uncertainty, are presented. An illustrative application of the NSZIP-GP model, using the North Atlantic Oscillation as a covariate is also presented. The applications of both models include assessment of quantile uncertainty.