Investigating the goodness-of-fit of ten candidate distributions and estimating high quantiles of extreme floods in the lower Limpopo River Basin, Mozambique

Abstract

We compare ten candidate distributions for their goodness-of-fit in modelling the annual maximum daily flood heights in the lower Limpopo River Basin, Mozambique. The ten candidate distributions compared in this study are Generalised Gamma (GG), two-parameter Gamma, three-parameter Gamma, two-parameter lognormal, three-parameter lognormal, log-Pearson Type 3 (LP3), Generalised Extreme Value (GEV), two-parameter Weibull, three-parameter Weibull, and Gumbel distribution. The GEV, Gumbel, and GG were the best three distributions at Sicacate based on their ability to model the tails. The three-parameter Gamma, three-parameter lognormal and GEV were the best three distributions at Chokwe. Among the parameter estimation methods used were the maximum likelihood method and the method of L-moments. Goodness-of-fit was evaluated by means of Kolmogorov-Smirnov and Anderson-Darling tests, as well as P-P plots and simulation studies to check whether the distribution could mimic the observed values. Results of the expected return periods and probable high quantiles at both sites Chokwe (upstream) and Sicacate (downstream) indicated that the 13 m flood height of the year 2000 was way higher than the 100-year-flood height and had a return period in excess of 250 years based on the best fitting distributions, implying that it has a very small likelihood of being equalled or exceeded at least once in 250 years.