Heavy rainfall frequency analysis in the Benin section of the Niger and Volta Rivers basins: is the Gumbel's distribution a one-size-fits-all model?

Abstract

West African populations are increasingly exposed to heavy rainfall events which cause devastating floods. For the design of rainwater drainage facilities (to protect populations), practitioners systematically use the Gumbel distribution regardless of rainfall statistical behaviour. The objective of this study is twofold. The first is to update existing knowledge on heavy rainfall frequency analysis in West Africa to check whether the systematic preference for Gumbel's distribution is not misleading, and subsequently to quantify biases induced by the use of the Gumbel distribution on stations fitting other distributions. Annual maximum daily rainfall of 12 stations located in the Benin sections of the Niger and Volta Rivers' basins covering a period of 96 years (1921–2016) were used. Five statistical distributions (Gumbel, GEV, Lognormal, Pearson type III, and Log-Pearson type III) were used for the frequency analysis and the most appropriate distribution was selected based on the Akaike (AIC) and Bayesian (BIC) criteria. The study shows that the Gumbel's distribution best represents the data of 2/3 of the stations studied, while the remaining 1/3 of the stations fit better GEV, Lognormal, and Pearson type III distributions. The systematic application of Gumbel's distribution for the frequency analysis of extreme rainfall is therefore misleading. For stations whose data best fit the other distributions, annual daily rainfall maxima were estimated both using these distributions and the Gumbel's distribution for different return periods. Depending on the return period, results demonstrate that the use of the Gumbel distribution instead of these distributions leads to an overestimation (of up to +6.1 %) and an underestimation (of up to −45.9 %) of the annual daily rainfall maxima and therefore to an uncertain design of flood protection facilities. For better validity, the findings presented here should be tested on larger datasets.