Trivariate flood frequency analysis (Q, V, D) through Copula Functions
DOI:
https://doi.org/10.24850/j-tyca-2024-05-02Keywords:
Copula functions, Kendall's tau ratio, observed dependence, symmetric multivariate Copula Functions, asymmetric trivariate Copula Functions, joint return periods, design eventsAbstract
The trivariate flood frequencies analysis, of the maximum flow (Q), the runoff volume (V) and the total duration (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) that best represents the joint variables Q-V, Q-D and V-D is adopted. For these searches and the subsequent trivariates, we worked with the CFs 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 CFs 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 Cuña 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.
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