ABSTRACT The use of copula functions in hydrology has increased significantly, as they allow for more precise hydrograph estimation by incorporating the joint behavior of key variables. However, modeling runoff events with three variables – flow, volume, and duration – presents challenges, especially due to the complexity in defining and discretizing the duration variable. This study evaluates the role of duration and proposes a methodology to estimate trivariate design hydrographs, giving priority to duration alongside flow and volume. A case study is presented for the La Angostura dam in Mexico, using a hybrid peak selection method combining the threshold and annual maxima approaches. Marginal distributions are estimated using maximum likelihood with genetic algorithms for single and mixed population models. Symmetrical and asymmetrical Archimedean trivariate copulas are applied, with the Clayton copula identified as the most appropriate model. Joint return periods are computed using the OR and Kendall's definitions. The proposed system allows any user-defined hydrograph shape to be applied to the estimated flow, volume, and duration values, ensuring flexibility in design representation. The results show that prioritizing duration enables the estimation of reliable hydrographs: short durations yield higher peaks and volumes, while longer ones lead to attenuated responses, improving the consistency of hydrological design.
Maya et al. (Fri,) studied this question.