Evaluation of Plotting Position Formulae for Pearson Type 3 Distribution in Three Hydrological Stations on the Niger River

In this study, eight unbiased plotting position formulae recommended for Pearson Type 3 distribution were evaluated by comparing the simulated series of each formula with the annual maximum series (AMS) of River Niger at Baro, Koroussa and Shintaku hydrological stations, each having data length of 51years, 53 years and 58 years respectively.

The parameters of Pearson Type 3 distribution were computed by the method of moments with corrections for skewness. While the fitting of Pearson Type 3 distribution proceeds with the development of flood – return period (Q-T) relationship, followed by application of the derived Q- T relation to compute simulated discharges for comparison with AMS of the study stations.

The plotting position formulae were evaluated on the basis of optimum values of the statistically goodness-of-fit of probability plot correlation coefficient (PPCC), relative root mean square error (RRMSE), percent bias (PBIAS), mean absolute error (MAE) and Nash-sutcliffe efficiency (NSE), across the stations.

The plotting position formulae were ranked on scale of 1 to 8. Thus a plotting formula that best simulates the empirical observations using the goodness-of-measures was scored “1” and so on. The individual scores per plotting position were summed across the gof tests to obtain the total score.

The study show that Chegodayev is the best plotting position formula for Baro, Weibull is the best plotting position Formula for Kourassou and Shintaku hydrological stations. The overall performances of the eight plotting position formulae across the hydrological stations show that weibull distribution is the overall best having scored 27, seconded by Chegodayev with 30 and thirdly, Beard with 38.

The Pearson Type 3 distribution had been found one of the best probability distribution model of flood flow in Nigeria and this study was conducted to gain in-depth knowledge of the distribution. Finally, this study recommends extension of the studies to Log-Pearson Type 3 distribution.