Joint frequency analysis of peak flow and volumes of floods with Gumbel marginals
DOI:
https://doi.org/10.24850/j-tyca-14-03-01Keywords:
Design floods, bivariate Gumbel distributions, conditional distributions of the Logistic model, joint empirical probabilities, validation of the Logistic model, hybrid univariate return periods, joint return periodsAbstract
For two decades, the estimation of Design Floods of reservoirs has been addressed with the simplest multivariate approach, the bivariate. This has been accepted because it was proven that the reservoirs are not time sensitive to maximum flow, moreover, that such flow and volume are correlated with each other and the latter, with the total duration of the flood hydrograph. In this study, the bivariate Gumbel distribution or Logistics model was adjusted to the 61 annual data of peak flow and volume of floods entering the Adolfo Ruiz Cortines (Mocúzari) dam in the Río Mayo of the state of Sonora, Mexico. This process comprehends the following eight stages: (1) selection and testing of records to be processed; (2) verification of the randomness of the annual records; (3) acceptance of Gumbel marginal functions; (4) estimation of the joint empirical probabilities; (5) validation of the Logistic model; (6) verification of probability constraints; (7) estimation of design events, peak flow and volume, hybrid univariates, and (8) estimation of joint design events. In stage 1, first a subjective selection is made and then it is verified with the PPCC Test. Stage 2 is carried out based on the Wald-Wolfowitz Test. Stages 3 and 5 use the Kolmogórov-Smirnov Test. In stage 7, design flows are defined, and volumes are obtained by regression and conditional probability. In contrast, in stage 8, several peak flow and volume events are obtained, belonging to the subgroup of critical pairs, in the graphs of the joint return period T'(Q,V). Towards the last part of this work, conclusions are formulated, which highlight the advantages of the bivariate joint frequency analysis and the simplicity of application and testing of the Logistic model.
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