Assessment Performance of 3-Parameter Probability ‎Distributions for At-site Annual Streamflow in the ‎Blue Nile Basin ‎

Abstract

Many investigators have been applied various probability distributions for flood discharges at-site or region, however, there is no scientific judge about the best distribution to accurate the flood discharge estimations. In practice, different probability distributions are taken into account, and the best distribution is then applied to create the percentile quantiles. This paper introduces the assessment of three probability distributions that have three parameters; Generalized Extreme Value (GEV), Generalized Pareto (GPA) and Generalized Logistic (GLO) using L-moments (LM) method to estimate their parameters using annual peak discharge series of three hydrological stations on Blue River Basin and Atbara River in Sudan. Cunnane plotting position formula is considered to test the applicable probability distribution that gives good estimations in tails. The Q-Q relation with coefficient of determination (R2) is adopted to present the consistency process of the estimates and their corresponding of observed annual peak data. L-moment ratio diagram (LMRD) as suggested by Hosking and Walish (1993) is also performed to measure the discordance of probability distributions. Further, the evaluation performance of probability distributions can be measured by using three comparison criteria; root mean square error (RMSE), mean absolute deviation index (MADI) and relative root mean square error (RRMSE). The results indicated that GLO distribution generally shows the best fit followed by GEV distribution; however the GEV distribution gave more realistic in upper tail than others. It may be recommended as the appropriate probability distribution for annual peak discharge at-site in Blue Nile.

Keywords

• probability distributions
• l-moment
• comparison criteria
• l-moments diagram
• return period