Selection and application of Copula functions with dependence on its tail right to the joint frequency analysis (Q, V) of annual floods
DOI:
https://doi.org/10.24850/j-tyca-14-05-03Keywords:
Copula Functions, Kendall's tau quotient, Spearman's rho coefficient, dependence at the upper tail, observed dependence, joint return periods, secondary return periodAbstract
The hydrological design of the reservoirs to be built or the revision of the existing ones, requires the estimation of the so-called Design Flood Hydrograph. The simplest and most approximate way to estimate such a hydrograph, for a determined joint return period, is through the bivariate Frequency Analysis of the maximum flow (Q) and the annual runoff volume (V) of the registered floods. Copula Functions (FC) are probabilistic models based on the dependence between Q and V, which easily establish their bivariate distribution, based on previously adopted marginal functions or distributions of any type, equal or different. The application of the FC in the hydrological estimates showed that a decisive aspect in their ideal selection is related to the dependence on the extreme right of the data ( ) and that which have ( ) certain FC. Therefore, in this study the FC are exposed: Student's t, Gumbel-Hougaard, Clayton Associate and Joe, which show increasing values . The values of are contrasted against the obtained in 16 random real records of Q and V, to establish the applicability of each cited FC. In addition, the record of 26 annual Q and V data of the inflow floods to the Adolfo López Mateos Dam (Humaya), in the state of Sinaloa, Mexico, is processed as a numerical application. Finally, the Conclusions are presented, which highlight the advantages of FC in the bivariate frequency analysis of floods.
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