Flood Frequency Analysis Using the Gamma Family Probability Distributions

• Published in: Water (Basel) Vol. 15; no. 7; p. 1389
• Main Authors: Ilinca, Cornel, Anghel, Cristian Gabriel
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2023
• Subjects: Approximation; Case studies; chi; Distribution (Probability theory); Expected values; Flood frequency; Floods; Frequency analysis; Hydrology; Hydrometric stations; inverse chi; Kritsky–Menkel; Least squares method; Methods; Parameter estimation; Pearson; Probability; Probability distribution; pseudo-Weibull; Romania; Skewness; Statistical analysis; Statistical distributions; Statistics; Wilson–Hilferty; Romania
• ISSN: 2073-4441; 2073-4441
• DOI: 10.3390/w15071389

This article presents six probability distributions from the gamma family with three parameters for the flood frequency analysis in hydrology. The choice of the gamma family of statistical distributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the improvement of the estimation of maximum flows, including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected parameters, was researched and is an element of novelty. The linear moments method performs better than the method of ordinary moments because it avoids the choice of skewness depending on the origin of the flows, and is the method practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented, such as quantile functions, the exact and approximate relations for estimating parameters, and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river to verify the proposed methodology. The performance of this distributions is evaluated using Kling–Gupta and Nash–Sutcliff coefficients.