Author:

Keywords:

flood, Nile, extremes

Abstract:

In many applications of water engineering, the accurate description of extreme surface water states, i.e. flooding, and their recurrence rates, is of primary importance. The description can be done either based on long-term time series of measurements or long-term simulation results from mathematical models, and through application of extreme value analysis. In this analysis, the tail of the distribution describing the probability of occurrence of extreme events is analyzed and modeled by a separate distribution. When the analysis is done for river discharges or water levels at flow gauging stations, river flooding (over bank storage) often disturbs the results. In the current paper, the influence of river flooding on the extreme value analysis is discussed based on river flow data in Sudan. Rivers where flooding influences are present were selected. They include the Blue Nile at Ed Deim at the border with Ethiopia, river Rahad at Hawata, river Dinder at Gwasi, river Jur at Wau, and rivers Pibor and Akobo (tributaries of River Sobat). Calibration of the probability distributions (flood frequency curves) has been done based on the central part of the distributions as well as their tails. The tail of the distribution is the upper segment with high values for the quantiles, having small probabilities of occurrence or high return periods. A separate analysis of the general behaviour of the tail of the distribution can be done based on the ‘extreme value theory’ as presented by Fisher & Tippet (1928) and Pickands (1975). By means of so-called quantile – quantile plots (Q-Q plots), anomalies in the tail behaviour can be recognized in an easy visual way, as shown by Beirlant et al. (1996) and Willems (1998). The distributions considered for this study are the ‘classical’ ones, with parameters calibrated using the method of moments (MOM), probability weighted moments (PWM), and the maximum likelihood method (ML). Hosking and Wallis (1987) have given an overview of these statistical methods and their application. Because a normal tail was found for all selected rivers in Sudan, the candidate distributions were evaluated in the exponential Q-Q plot. It was concluded from this analysis that the observations do follow an EV1/Gumbel distribution, but not for the full range of extremes. For discharges higher than a specific value, the observations bend down which might be explained by the influence of flooding along the river. Therefore, it was suggested to calibrate separate distributions for the two subpopulations: the observations during (a) non-flooding conditions and, (b) flooding conditions. It is assumed that the “non-flooded” extremes follow closely the extreme value distribution of rainfall – runoff discharges from the catchment upstream of the river discharge stations. They therefore reflect the natural upstream flow conditions without flooding influence. Both distributions (conditions (a) and (b)) have separate applications in water engineering.