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A New Approach for Dam Design Flood Estimation

Author(s): Alvaro A. Aldama; Aldo I. Ramirez

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Keywords: Design flood estimation; Joint return period; Storage reservoir design; Multivariate distribution; Peak flow rate; And runoff volume

Abstract: Design floods for dams and reservoirs are often estimated on the basis of flood frequency analyses. Such analyses employ data of maximum annual discharges recorded at or near the site where the dam will be built. Even though fewer dams are under construction nowadays than in the past, it is also necessary to revise design floods from time to time, as new data become available, especially when retrofitting plans are underway. A design flood is fully characterized by a hydrograph, which is routed through the reservoir in order to determine its flood control capacity and the spillway design discharge. Nevertheless, flood frequency analyses rely upon the estimation of probability distributions associated with peak discharges only. The determination of the design hydrograph is made by employing arbitrary procedures, such as assuming that its form is the same as the one corresponding to the hydrograph of the largest recorded flood. The simplest characterization of a hydrograph must involve, at least, its most important parameters, namely: peak discharge, time to peak and volume. The authors of this paper have developed a simple parameterization of hydrographs which is based on the use of Hermitian interpolants. Through the use of this parameterization, they have performed a sensitivity analysis that shows that the most important parameters in characterizing a hydrograph, in terms of the response of a reservoir are the peak discharge and the volume. On the basis of this result, a new approach for estimating the design flood of dams and reservoirs, has been developed and is presented in this paper. The method is based on the use of the bivariate extreme-value probability distribution of peak discharge and volume. Thus, an expression for the joint return period of these two parameters is derived. It is shown that an infinite number of pairs of values of peak discharge and volume possesses a given joint return period. Hence, in order to determine the design flood hydrograph, a nonlinear optimization problem is posed, whose solution represents the combination of values of peak discharge and volume that produces the worst effect on the reservoir for a given joint return period. An example involving the revision of the design flood of the “El Infiernillo” dam in Mexico is also presented.


Year: 1999

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