Daily maximum rainfall estimation by best-fit probability distribution in the source region of Indus River

Extreme events of precipitation can be guessed from best-fit probability distribution which is found through frequency analysis. The choice of best-fit probability distribution from several available distributions is a major problem. The goal of this research was the estimation of daily maximum precipitation using best-fitted probability distribution for observed data of 50 stations of the source region of Indus River from 1961 to 2015. Nine commonly used probability distributions were applied and methods of moments were used to find the parameters of applied distributions. Three goodness-of-fit tests were employed and the best-fitted probability model was selected whose sum of values from these goodness-of-fit tests was minimum. Generalized extreme value was selected as the best-fitted probability distribution on 54% of the rainfall stations, followed by log-Pearson type 3 (14% of the stations), Gamma (12% of the stations), Weibull type 3 (12% of the stations), Weibull (4% of the stations), log-normal (2% of the stations), and extreme value type 1 (2% of the stations). Then, using the best-fitted probability model at each of the rainfall station, daily maximum rainfall was estimated against different return periods. The models to minimize the threats of flooding and damages can be developed using the results of this study.