This paper compared the differences and similarities in the rainfall intensities predicted by four standard IDF equations for return periods between 5 and 40 years and for storm durations between 15 and 30 minutes. The empirical models employed for comparison on the development of standard IDF equations using historic data for Benin, Calabar, Port Harcourt, Onitsha and Warri meteorological stations, all in Southern Nigeria were available in literature. The strength and weakness of the different models were assessed using the mean ± standard deviation as range between intensities estimated for 5 and 40 years, and percent relative error between the observed and predicted rainfall intensities as performance criteria. The results obtained showed that there were significant differences in the rainfall intensities as predicted by the equation types. However, the IDF types-1 and 2 equations displayed lower range values in intensities for all returned periods. Types-1 and 2 equations predicted the lowest relative error of less than or equal to 6% in all stations considered. Because IDF studies are associated with hydrologic extremes, both types-1 and 2 equations are therefore recommended for hydrologic design of flood control structures. The study has advanced the understanding of the equations and further insight in their utility as hydrologic design tools.

The impact of climate change on the hydrologic system is widely recognized to be geographic location-specific, thus each geographic location should be assessed for the plausible impacts of climate change. Consequently, this research was conducted to assess the impact of climate change on Intensity-Duration-Frequency equations in Benin City, Nigeria. Trend analysis was performed using Mann-Kendall test while the Sen's slope method was used to estimate the magnitude of the change. The main results may be summarized as i. Statistically insignificant negative(downward) trends were observed for annual rainfall intensities for durations of 10 to 30-minute; ii. Both statistically insignificant downward and upward trends were obtained for durations above 45-minute except for 540-minute duration where a statistically significant positive trend was obtained. All statistical tests were conducted at 5% significance level. Since the statistical insignificant negative (downward) trends were obtained for rainfall durations of 10-30-minute, which is usually the range for inlet time generally applied for design of urban drainage systems. It implies therefore, that climate will pose negligible impacts on flood risk. Consequently the 34-year annual rainfall intensity series(the longest available) was used to develop IDF equations of the Wisner's equation type for return periods of 5-to 100-year. The explanatory power and accuracy of the IDF equations may be represented by the following inequalities; 0.40≤R2≤0.972; 2.55≤SEE≤4.31; 2.34≤RMSE≤3.96;0.044≤RSR≤0.056; 1.93≤MAE≤2.96. These inequalities indicate that the equations are very good for estimation of storm runoff and for design of drainage systems, and as input for urban drainage simulation modelling systems such as SWMM model.

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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.

The choice of optimum probability distribution model that would accurately simulate flood discharges at a particular location or region has remained a challenging problem to water resources engineers. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the quantile - probability relationship for planning, design and management of water resources systems, risk assessment in flood plains and flood insurance. 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 Generalised Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of five hydrological stations in the lower Niger River Basin in Nigeria. The choice of optimum probability distribution model was made 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), and probability plot correlation coefficient (PPCC). The results show that GEV is the optimum distribution in 3 stations, and LP3 in 2 stations. On the overall GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. Furthermore, GEV simulated discharges were in closest agreement with the observed flood discharges. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.