Selection of Optimum Probability Distribution Model for Flood Flow in Lokoja Hydrological Station

Abstract

This research aimed to choose the optimum probability distribution function that best fits the historical time series of the Lokoja hydrologic station in the Niger/Benue River Basin in Nigeria. The flood data was collected from the National Inland Waterways Authority (NIWA) at Lokoja. The concept of flood frequency analysis (FFA) was applied in analyzing the extreme data using the annual maximum series (AMS). The observed data were fitted into four (4) probability distribution models, namely: Normal (N2), Gumbel (EV1), two-parameter Log-normal (LN2), and the generalized extreme value (GEV). A MATLAB program was used to simulate and model the FFA for both stations. Several pieces of literature on FFA were reviewed. Hydrologic data screening was carried out, using several statistical tests at a 5-percent level of significance, to ensure that the time series attained stationary, randomness and that the random samples are independently and identically distributed. The Pre-Whitening Analysis procedures were done to eliminate the visible trend and auto-correlation from the time series record. The method of moments (MoM) was used for statistical parameter estimation. The chi-square ( ) and the Kolmogorov-Smirnov (K-S) goodness of fit tests were performed at the 5-percent level of significance on the modeled data to determine the best-fit distribution from the four (4) frequency distributions. From the results obtained, it was found that the generalized extreme value (GEV) distribution is an optimum approximation of flood characteristics for the Lokoja hydrologic station in the Niger/Benue river basin. The Kolmogorov-Smirnov (K-S) and chi-square ( ) test statistics for Lokoja station are 0.8707 and 1.2044 respectively, which was the most reliable and thereby prove the GEV as the optimum distribution for Lokoja hydrologic station.