Abstract
The selection of optimum probabilistic model of extreme floods as a crucial step for flood frequency analysis has remained a formidable challenge for the scientific and engineering communities to address. Presently, there is no scientific consensus about the choice of probability distribution model that would accurately simulate flood discharges at a particular location or region. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the design quantile - probability relationship. This paper presents the evaluation of five probability distributions models; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria. Additionally, Q-Q plots were used to compliment the selection process. The choice of optimum probability distribution model was based on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR). Goodness – of – fit assessment reveals that GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. In comparison with WMO (1989) survey of countries on distribution types currently in use for frequency analysis of extremes of floods shows that GEV is standard in one country, while PR3 is a standard in 7 countries, and LP3 is standard in 7 countries. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.
Highlights
IntroductionThis paper presents the evaluation of five probability distributions models; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria
The selection of optimum probabilistic model of extreme floods as a crucial step for flood frequency analysis has remained a formidable challenge for the scientific and engineering communities to address
Several probability distribution models have been considered in different situations, for the probabilistic modelling of extreme events, such as Generalized Extreme Value (GEV), Lognormal (2 and 3), Gamma (Gam), Gumbel Extreme Value type 1 (EV1), Log-Pearson Type 3(LP3), Pearson Type 3 (PR3)
Summary
This paper presents the evaluation of five probability distributions models; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria. The steps in flood frequency analysis are: i) selection of data series type; ii) data screening; iii) choice of parameter estimation method; iv) assessment of uncertainties associated with the parameters and quantiles; v) goodness – of –fit tests. Rahman [11] studied the selection of probability distribution for atsite flood frequency analysis in Australia and identified LP3, GEV and generalized pareto-distribution (GPO) as the top three best-fit distributions. To the best of my knowledge, and literature search, there was no prior study on the hydrological stations being evaluated; namely Benue River at Umaisha, Makurdi, Ibi, and Yola
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
