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Abstract: Starting from the evident idea that the design of the spillway, that is, the capacity of the spillway and the volume allocated for flood regulation, in dams where this volume is considerable, depends on the maximum discharge and the volume of the inflows entering the reservoir; a large number of studies have been developed based on the fitting of bivariate probability distribution functions for these two variables. This paper presents an analysis that provides arguments to support the authors' opinion that the use of bivariate functions for the estimation of design floods in dams with considerable regulation capacity is not convenient. Instead, the method developed at the Institute of Engineering of UNAM is proposed.
Keywords: Probability distribution function, discharge-duration curve for return period, joint return period, base time, design floods shape
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1. Introduction
Bivariate distribution functions have been widely used since the mid-1990s for the estimation of design floods in reservoirs with significant regulation capacity, considering both peak discharge and flood volume (see, for example, the works of [1-6]; among others. Three fundamental aspects can be identified that make it difficult-if not impossible-to achieve successful results in the application of bivariate methods: (1) the criteria used to define the volume of annual maximum flood events and to form peak discharge-volume pairs; (2) the definition of the design or failure domain based on the bivariate probability distribution function of the peak discharge-volume pairs (i.e., the definition of the joint return period); and (3) the criteria used to shape the design hydrographs. This study will primarily focus on the first aspect, with brief consideration of the second and third. In contrast, the method developed by the Institute of Engineering overcomes the limitations associated with the use of bivariate distribution functions for the estimation of design hydrographs in dams with significant regulation capacity.
1.1 Definition of Annual Maximum Flood Volumes
The selection of the base time for flood events allows for the definition of annual maximum flood volumes, which are then incorporated into the series of peak discharges and volumes used to estimate the joint distribution function of these two variables. However, only a few studies explicitly present the criteria proposed for this calculation. Some of these include: Pegram and Deacon,1992...