Calculating the heavy rainfall and flood flow by mathematical and statistical methods (Case study of Selbe River, Central Mongolia)

This study evaluates 5 most commonly used distribution methods, i.e., Exponential, Generalized Extreme Value (GEV), Pearson III, Gamma, and Lognormal for the flood frequency analysis in the area Selbe-Dambadarjaa hydrological station located in the center of Ulaanbaatar. The study was done for 2, 5, 10-, 20-, 50- and 100-year return periods by using annual maximum discharge data from 1984-2023 (34 yr) for Selbe River at Dambadarjaa hydrological station. The parameter estimation of the distributions was compared using the maximum likelihood method (MLE) and the linear moment method (LM) and evaluated using the relative absolute error. The results of the linear moment method the distribution parameter with less error than the maximum likelihood method. The goodness-of-fit test was applied to the fitted distributions Kolmogorov-Smirnov at a 5% significance level. The result indicates that Pearson III and GEV were the top two distributions at the Selbe River while Lognormal, and Exponential were least fitted having ranks 4-5, respectively. According to the Pearson III distribution, which can represent the peak flow curve of the Selbe River, the flood magnitudes for 1,2,5,10,20 and 50 % exceedance probability at Selbe-Dambadarjaa hydrological station are 42.6, 34.4, 24.0, 16.6, 10.1 and 3.34 m³/s, respectively. From the distribution calculation, it can be concluded that the magnitude of the flood in 2023 is a 5% catastrophic flood that repeats once every 20 years.