Evaluation of the Dual Gamma Generalized Extreme Value distribution for flood events in Poland

Abstract

Climate change has already affected global water resources and 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 trends and other non-stationarities. In this paper we compare three-parameter distributions, such as the lognormal (LN3), the Generalized Extreme Value (GEV), and the Pearson type III (P3), with the Dual Gamma Generalized Extreme Value (GGEV) distribution. The GGEV is a four-parameter extension of the GEV. The comparison is made under different trend conditions and takes into account the differences in the catchment area and peak flow magnitude. The research pertains to basins in the temperate climate zone of Poland and includes data from 678 water gauges located on 340 rivers. Based on the 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 the catchment size, GEV is best suited for micro- and meso-catchments, while GGEV is ideal for macro- to large catchments when the series exhibits a trend, either positive or negative. The major benefit of GGEV is its flexibility when the data are influenced by temporal non-stationarities. The additional shape parameter of GGEV compensates for the limitations of the other shape parameter in distributions with lighter tails. Analysis of the dependence relationships between the environmental indicators, such as the 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, the Kolmogorov–Smirnov test and the K-fold cross-validation were used. They show that the GEV and GGEV distributions perform better compared to the exponential and the two-parameter lognormal distributions. As an overall conclusion, the study shows that, for the analyzed samples from the temperate climate zone in the era of climate change, distributions that better capture trends, such as GGEV, perform more effectively.