Hydrological Drought Frequency Analysis in Water Management Using Univariate Distributions

The study of extreme phenomena in hydrology generally involves frequency analysis and a time series analysis. In this article we provide enough mathematics to enable hydrology researchers to apply a wide range of probability distributions in frequency analyses of hydrological drought. The article presents a hydrological drought frequency analysis methodology for the determination of minimum annual flows, annual drought durations and annual deficit volumes for exceedance probabilities common in water management. Eight statistical distributions from different families and with different numbers of parameters are used for the frequency analysis. The method of ordinary moments and the method of linear moments are used to estimate the parameters of the distributions. All the mathematical characteristics necessary for the application of the eight analyzed distributions, for the method of ordinary moments and the method of linear moments, are presented. The performance of the analyzed distributions is evaluated using relative mean error and relative absolute error. For the frequency analysis of the annual minimum flows, only distributions that have a lower bound close to the annual minimum value should be used, a defining characteristic having the asymptotic distributions at this value. A case study of hydrological drought frequency analysis is presented for the Prigor River. We believe that the use of software without the knowledge of the mathematics behind it is not beneficial for researchers in the field of technical hydrology; thus, the dissemination of mathematical methods and models is necessary. All the research was conducted within the Faculty of Hydrotechnics.