abstract

• Design floods (DF) give dimension for hydrological security to the hydraulic protection works. The most reliable estimate is obtained through the univariate frequency analysis (FA), which represents the maximum annual flows available, with an appropriate probability distribution function (PDF), to estimate the predictions sought. In this study, the FA is carried out with the trivariate approach, processing a base record of flows QX and two other auxiliaries, QY and QZ, which are correlated to; the first and have the same amplitude. The verification of the simultaneous character of the QX, QY and QZ flows (that they belong to the same event analyzed) is described in detail. The joint trivariate PDF of flows was obtained using the Gumbel-Hougaard Copula function, which showed an excellent fit and reproduced the observed dependency on flows. A numerical application exposed here processed 43 annual flows and was carried out at the hydrometric stations, Tempoal as base, and El Cardón and Terrerillos as auxiliaries of the Tempoal river system of Hydrological Region No. 26 (Pánuco), Mexico. In order to obtain the ideal marginal PDFs, the Moment Ratios Diagram L was used and, in addition, the Kappa and Wakeby PDFs were applied to contrast predictions. Finally, conclusions are formulated, which highlight the importance of the trivariate approach, based on regional dependence, to validate the behavior in magnitudes of the DF estimated with the univariate approach.

publication date

• 2025-01-01

published in

• Tecnologia y Ciencias del Agua  Journal

keywords

• asymmetric trivariate CF; design events; Frank and Gumbel-Hougaard CF; Kendall's tau ratio; secondary return period; symmetric multivariate CF; upper tail and observed dependences design; flooding; frequency analysis; hydraulic property; hydrological response; probability density function

Digital Object Identifier (DOI)

• 10.24850/j-tyca-2025-01-08

PubMed ID

start page

• 381

end page

• 441

volume

• 16

issue

• 1