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

Abstract. In hydrology, statistics of extremes play an important role in the use of time series analysis as well as in planning, design and operation of hydrotechnical structures and water systems. In particular, probability distributions are used to estimate and forecast floods. However, in order to use distributions, the data must be random, with a change-point and should not have a trend. Unfortunately, the data being analyzed are not independent, which is very often due to the anthropogenic impact, among other factors. In situations where various processes generate rainfall and floods in river basins, the use of mixed distributions is recommended. However, an accurate estimation of multiple parameters derived from a mixture of distributions can be difficult, which is the biggest disadvantage of this approach. Therefore, as an alternative, we propose a new extension of the GEV distribution – the Dual Gamma Generalized Extreme Value Distribution (GGEV) developed by Nascimento, Bourguignony and Leão (2016). We compared this distribution with selected 3-parameter distributions: Pearson type III, Log-Normal, Weibull and Generalized Extreme Value. In addition, various methods of estimating 3-parameter distributions were used. As a case study, rivers from Poland and the Czech Republic were investigated, because this has a significant impact on water management in the Upper Oder basin due to the strategic water reservoirs and other hydrotechnical constructions, either existing or planned. Currently, there are no clearly indicated distributions for the Upper Oder basin. Therefore, our aim was to approximate them. Two methods were used, namely the Annual Maximum (AM) and the Peaks Over Threshold (POT). In the latter case, two methods for determining the threshold were used, namely: the Mean of the Annual Maximum River Flows (MAMRF) and the Hill plot. Hence, the basic 3-parameter Weibull distribution, with parameters estimated using the modified method of moments and the maximum likelihood estimation, yielded a better fit to the observation series in the AM and POT methods. For the AM and POT (MAMRF, Hill plot) methods, the GGEV turned out to be the best-fitted distribution according to the Mean Absolute Relative Error (MARE). The GGEV distribution can be used as an alternative to mixed distributions in various samples, both homogeneous and heterogeneous. This distribution turned out to be the best fit especially for the sample whose independence is affected by the presence of a GGEV water reservoir.