Trivariate flood frequency analysis (Q, Q , V , D ) through Copula Functions

The trivariate flood frequencies analysis, of the maximum flow (Q), Q ), the runoff volume (V) V ) and the total duration (D), D ), allows to estimate with greater accuracy the Hydrograph of the Design Flood. To process available joint annual records of Q and V , it was proposed to estimate D as the duration of the Gamma hydrograph up to 0.1 % of Q . Then, each record of Q , V and D is searched for its ideal probability distribution to obtain the marginal functions. Next, the Copula Function (CF) CF ) that best represents the joint variables Q-V, V , Q-D D and V-D D is adopted. For these searches and the subsequent trivariates, we worked with the CF s of Clayton, Frank, Gumbel-Hougaard and Joe. In both cases, the selection of the best CF is based on the fit errors between the empirical and theoretical probabilities. For the triads of data Q , V , and D , the symmetrical and asymmetrical best-fit CF s of the four families mentioned were sought. Next, the joint return periods of type OR, AND and Kendall are calculated. The latter allow the estimation of the design events of Q , V and D . The trivariate frequency analysis is described for the 55 annual floods of the La Cu & ntilde;a hydrometric station of the Hydrological Region No. 12-3 (Santiago River), Mexico. Finally, the conclusions are formulated, which highlight the simplicity of the trivariate frequency analysis, when performed with CF .