PERFORMANCE OF THE PROBABILITY DISTRIBUTIONS FOR PLOTTING POSITIONS IN ESTIMATING THE MAXIMUM DISCHARGES OF ADHAIM RIVER

Abstract

In this study, the peak discharges of Adhaim River were plotted against their hydrologic years. Two probability distributions and five plotting positions formulas were fitted to the annual maximum discharges AMD. The performances of the probability distributions with plotting position formulas were evaluated using the coefficients of determination R², root mean square errors RMSE, Mean Absolute Percent Error MAPE, and absolute differences between predicted and observed discharges. The annual maximum discharges of Adhaim River vary in magnitude from 111 to 3520 m³/sec for record periods. The mean of annual maximum discharges 753 m³/sec. The Lognormal LN and Log-Person type III LP3 distributions have the highest R² using Weibull plotting position formula WPP of 0.992 and 0.989, respectively. The LN had minimum RMSE and MAPE of 69.13 and 7.3%, respectively, when conformed with California plotting position CPP. The LP3 had minimum RMSE and MAPE of 93.6 and 6.5% respectively when conformed with Chegadayev plotting position CHPP. The minimum absolute differences at return periods of 25, 50,100, and 200 years were obtained when LN conformed with Hazen plotting position HPP and when LP3 conformed with CPP.