HR: 08:45h
AN: H41A-04 INVITED [Abstracts]
TI: Bivariate estimation of dam design floods
AU: * Aparicio, J
EM: japaricio@tlaloc.imta.mx
AF: Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Progreso, Jiutepec, Mor
62550, Mexico
AU: Ramírez, A
EM: aramirez@tlaloc.imta.mx
AF: Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Progreso, Jiutepec, Mor
62550, Mexico
AU: Aldama, Á
EM: aaldama@tlaloc.imta.mx
AF: Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Progreso, Jiutepec, Mor
62550, Mexico
AB:
Design floods for dams and reservoirs are often estimated on the basis of flood frequency analysis. This method
consists of fitting a theoretical extreme-value probability distribution to the maximum annual flow rate data
collected at a streamflow gauging station, thus enabling the hydrologist to estimate, via extrapolation, the flow rate
or peak discharge corresponding to a given design return period. It is often the case that medium- to large-sized
dams are designed by using return periods of up to 10,000 years.
Even though fewer dams are under construction nowadays than in the past, it is also necessary to revise design
flood 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 often rely
upon the estimation of probability distributions associated with peak discharges only. The determination of the
design hydrograph is usually made through 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 characteristics, namely: peak discharge, time to peak and
volume. However, the authors of this paper have performed a sensitivity analysis that shows that the two most
important parameters in characterizing a hydrograph, in terms of the response of a reservoir are the peak
discharge and the runoff volume.
Furthermore, experience demonstrates that the response of some reservoirs may be more sensitive to the flood
runoff volume than to its peak discharge. Thus it is highly desirable to address the problem of characterizing the
whole design hydrograph in a probabilistic framework.
On the basis of these results, a new approach for estimating the design flood of dams and reservoirs has been
developed. The method is based on the use of the bivariate extreme-value 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 peak discharge and volume possess a given joint return period.
Hence, in order to determine the design flood hydrograph, a nonlinear optimization problem is posed. The
solution of this problem represents the combination of values of peak discharge and volume that produces the
worst effect on the reservoir for a given joint return period. The worst effect is obtained by choosing the
combination of peak discharge and volume that produces the highest level of the water surface and, by
correspondence, the highest flow through the spillway.
The methodology was applied to the revision of several dams in Mexico finding that some of them are not as safe
as it was supposed.
DE: 1800 HYDROLOGY
DE: 1808 Dams
DE: 1817 Extreme events
SC: Hydrology [H]
MN: 2007 Joint Assembly