Modelling the dependence structure of rainfall depth and duration by Gumbel's copula

This article underlines the dependence structure of hydrological variables: rain depth and duration. The dependence is investigated by chi plot and Kendall (K) plot and measured by two rank correlation coefficients: Kendall's τ and Spearman's ρ. The joint distribution of the depth—duration couple is built using Gumbel's copula. The durations are fitted by GEV distribution and the depths by extended three-parameter Burr XII. For adequacy of marginals, the Anderson-Darling test is used. The copula's goodness of fit among three models (Gumbel, Frank and Clayton) is realised by: (a) comparison between empirical versions of the functions K, J, M, L and R and their theoretical versions, and (b) bivariate χ2 test. This approach by copulas allows the reconstruction by simulation of a sample of rain depth—rainfall duration from Saddine 1 station (35°48′06″N; 9°04′09″E).