Bivariate frequencies analysis of annual floods through practical approach of the Copula functions
DOI:
https://doi.org/10.24850/j-tyca-15-02-01Keywords:
Families of Copula functions, Kendall's tau quotient, Spearman's rho coefficient, joint empirical probabilities, right-tail dependency, joint return periods, critical eventsAbstract
The study of hydrological safety in reservoirs is carried out with the so–called Design Flood Hydrograph. The simplest estimation of such a graph is based on the bivariate frequency analysis (BFA), by defining its maximum flow (Q) and volume (V), associated with a joint design return period. The Copula functions (CF) are based on the dependence between Q and V, and define the bivariate distribution by means of the previously adopted marginal univariate functions. The practical approach adopted uses CF with a single fit parameter and selects the most appropriate, based on the dependence shown by the joint record of Q and V, at the far-right end of its empirical distribution. Moreover, the practical approach compares and ratifies the adopted CF, against several of common use in the BFA. The above, using the fitting errors between the empirical and theoretical bivariate probabilities. Due to their importance, the search for marginal distributions was carried out based on the L quotient diagram, adopting the best three and comparing them to the highly versatile Kappa and Wakeby functions. The BFA of the 55 annual floods registered in the La Cuña hydrometric station of the Hydrological Region No. 12-3 (Santiago River), Mexico was carried out. Four joint design return periods were defined and the calculation of their AND curves is detailed. Finally, several Conclusions are cited which highlight the advantages of the use of CF in flood BFAs.
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