The application of new distribution in determining extreme hydrologic events such as floods

Abstract. Climate change has already impacted global water resources, and it is expected to have even more severe consequences in the future. Advancing climate change will necessitate the use of new distributions that are more flexible in adapting to changes in stationarity or the presence of trends in the sample. In this work, we compare the best fit of three-parameter distributions such as lognormal, Generalized Extreme Value (GEV), Pearson type III, and a new extension of GEV – Dual Gamma Generalized Extreme Value Distribution (GGEV) under different trends in the time series and by adding criteria such as catchment area and peak flow magnitude. The research pertains to catchments in the temperate climate zone of Poland, covering 678 water gauges in 340 rivers. Based on a trend criterion, the GGEV distribution compared to the analyzed three-parameter distributions, and the GEV distribution compared to the other three-parameter distributions, were the best fit for most samples. Based on the trend criterion and catchment size it was found that the GEV distribution is best suited for micro- and meso-catchments, while the GGEV distribution is ideal for macro- to large-catchments where the series exhibits a trend, either positive or negative. The major benefit of the GGEV distribution is its flexibility when the data are influenced by temporal non-stationarities. The additional shape parameter compensates for the limitations of the other shape parameter in distributions with lighter tails. Analysis of the dependence relationships between environmental indicators such as geographic, physiographic and hydrological indicators and the distribution parameters is less conclusive. In order to test the risk of overparameterization and overfitting for the distributions with more parameters, Kolmogorov-Smirnov tests and K-Fold cross validation shows that the GEV and GGEV distributions perform better compared to the exponential and two-parameter lognormal distributions. As an overall conclusion, the study showed that for the analyzed samples in the temperate climate zone in the era of climate change, distributions that better respond to trends, like GGEV, are more likely to be applied.