Fitting flood frequency distributions using the annual maximum series and the peak over threshold approaches

Abstract

Flood frequency plays an important role in the design of hydraulic structures as well as in the management of fisheries and aquatic resources. There are two types of flood frequency analyses, namely the annual maximum series (AMS) analysis and the partial duration series analysis (or peak over threshold, POT). The POT analysis consists of studying discharge data above a specific threshold (or truncation level), whereas the AMS method uses maximum annual discharge data. Both the AMS (generalized extreme value – GEV distribution) and POT (generalized Pareto – GP and exponential – Exp distributions) were used to calculate flood frequencies for four hydrometric stations within the Miramichi River basin of New Brunswick. A simple method was proposed for the selection of truncation levels, that is, values corresponding to 1, 1.5 and 2 flood counts per year. Considering multiple truncation levels in the POT analysis has the advantage of providing more results that are used to identify which level provides a better fit of the flood data. Both the GEV (AMS) and GP (POT) distributions best represented flood data within the Miramichi River whereas the Exp (POT) distribution did not fit well the data, especially for floods with high return periods (>25 years). Results showed the truncation level at a flood count of 1 (highest truncation level) for the POT method, generally provided a better fit of floods with high return periods (>25 years). Moreover, lower truncation levels tended to provide flood estimates with less uncertainties (lower coefficient of variation, as tested using a jackknife technique). Finally, results showed that both the AMS and POT methods are complementary in flood frequency analyses. The AMS is the more classic approach to flood frequency analyses; however, the POT provides a better characterization of floods (e.g. magnitude, duration and flood volume).