Selection of the best probability models for daily annual maximum rainfalls in Egypt

Twelve commonly used probability distributions are evaluated to identify the most suitable model that could provide accurate extreme rainfall estimates in Egypt. Three popular parameter estimation methods are applied: the method of moments, L-moments and maximum likelihood. The performance of the models is evaluated based on several numerical and graphical goodness-of-fit criteria. The proposed procedure is applied to annual maximum daily rainfall data from a network of 31 stations located in Egypt. The results indicate that no single distribution performed the best at all stations. Log-Normal, Log-Pearson Type III and Exponential are the top three distributions for the frequency analysis of daily annual extreme rainfalls in Egypt, i.e. they are selected as the “optimum” models for 23%, 19% and 19% of the total stations, respectively. In contrast, the distributions: Normal, Gumbel, Logistic and Generalized Logistic are not suitable for describing the extreme rainfalls in the country. The performances of both L-moments and maximum likelihood methods are almost equal and much better than that of the method of moments. Additionally, Depth-Duration-Frequency curves were established for 18 stations by using the “optimum” model, which can support the design of hydraulic structures. The findings from this study would be helpful for rainfall frequency analysis in similar arid countries.