On peaks-over-threshold modeling of floods with zero-inflated Poisson arrivals under stationarity and nonstationarity
2014
Silva, Artur Tiago | Portela, Maria Manuela | Naghettini, Mauro
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.
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