Integrated Frequency Analysis of Extreme Flood Peaks and Flood Volumes Using the Regionalized Quantiles of Rainfall Depths as Auxiliary Variables
Publication: Journal of Hydrologic Engineering
Volume 13, Issue 3
Abstract
In its 1988 report, the U.S. National Research Council identified principles to be followed in order to improve estimation of extreme flood quantiles. In spite of the many advances attained by more recent research on extreme flood estimation, the NRC principles remain useful recommendations to be considered, which are used in the methodology to be described herein. According to the proposed method, flood peaks that have exceeded an arbitrary threshold and their associated flood volumes are modeled as a marked point process. The estimation method consists of separately estimating the marginal density function of flood volumes and the density function of flood peaks conditioned on volumes. The annual probability distribution of flood peaks can then be estimated by double integrating the product of both densities. Regionalized quantiles of rainfall depths have been used as auxiliary variables for guiding the estimation of the upper tail of the marginal density function of flood volumes by postulating simple assumptions regarding the rainfall-runoff transformation under extreme conditions. The inclusion of the regional frequency analysis of rainfall depths, for the same duration as that of flood volumes, is performed by fitting a regional two-component extreme value distribution to rainfall data observed at a number of gauging stations within a homogeneous region. This paper summarizes the basic ideas of the method and the details of its application to a watershed in southeastern Brazil.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers wish to acknowledge the support of FAPEMIG (“Fundação de Amparo à Pesquisa do Estado de Minas Gerais”) to this research through Grant No. UNSPECIFIEDCRA576/01. The writers would like to thank the anonymous reviewers for their valuable comments and suggestions.
References
Benito, G., and Thorndycraft, V. R., eds. (2004). Systematic, paleoflood and historical data for the improvement of flood risk estimation—Methodological guidelines, 1st Ed., CSIC—Centro de Ciências Medioambientales, Madrid, Spain.
Beran, M., Hosking, J. R. M., and Arnell, N. (1986). “Comment on ‘Two component extreme value distribution for flood frequency analysis’ by F. Rossi, M. Fiorentino, and P. Versace.” Water Resour. Res., 22(2), 263–266.
Bradley, A. A., and Potter, K. W. (1992). “Flood frequency analysis of simulated flows.” Water Resour. Res., 28(9), 2375–2385.
Cleveland, W. S. (1979). “Robust locally weighted regression and smoothing scatterplots.” J. Am. Stat. Assoc., 74(368), 829–836.
Companhia de Pesquisa de Recursos Minerais (CPRM). (2001). Regionalização de vazões. Sub-Bacias 40 e 41: Relatório Final. Vazões Máximas, Vol. 4, CPRM/ANEEL, Belo Horizonte, Brazil.
Duband, D., Michel, C., Garros, H., and Astier, J. (1988). “Estimating extreme value floods and the design flood by the gradex method.” Proc., 16th Int. Congress on Large Dams, San Francisco, 1009–1047.
Fernandes, W., and Naghettini, M. (2005). “Relação adimensional entre vazões médias diárias máximas e volumes de cheia para a bacia do rio Pará, no estado de Minas Gerais.” Proc., XVI Simpósio Brasileiro de Recursos Hídricos, João Pessoa, Brazil.
Fiorentino, M., Gabriele, S., Rossi, F., and Versace, P. (1987). “Hierarchical approach for regional flood frequency analysis.” Regional flood frequency analysis, V. P. Singh, ed., Reidel, Dordrecht, 35–49.
Gabriele, S., and Arnell, N. W. (1991). “A hierarchical approach to regional flood frequency analysis.” Water Resour. Res., 26(6), 1281–1289.
Guillot, P., and Duband, D. (1967). “La méthode du gradex pour le calcul de la probabilité des crues à partir des pluies.” Proc., Floods and Their Computation—Proceedings of the Leningrad Symp., IASH Publication No. 84, 560–569.
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis—An approach based on L moments, 1st Ed., Cambridge Univ. Press, Cambridge, U.K.
House, P. K., Webb, R. H., Baker, V. R., and Levish, D. R., eds. (2001). Ancient floods, modern hazards: Principles and application of paleoflood hydrology, AGU Water Science and Application Series, Vol. 5, American Geophysical Union, Washington, D.C.
Lima, A. A. (2004). “Metodologia integrada para determinação da enchente de projeto de estruturas hidráulicas por meio de séries sintéticas de precipitação emodelos chuva-vazão.” MS thesis, Programa de Pós-Graduação em Saneamento, Meio Ambiente e Recursos Hídricos—UFMG, Belo Horizonte, Brazil.
More, J. J., Garbow, B. S., and Hillstrom, K. E. (1980). “User’s guide to Minpack I.” Publ. No. ANL-80-74, Argonne National Laboratory, Argonne, Ill.
Naghettini, M., Nascimento, N. O., Thimotti, T., Lima, A. A., and Silva, F. E. O. (2002). Modelo Rio Grande de Simulação Hidrológica para Previsão de Vazões de Curto Prazo: Formulação Teórica, Departamento de Engenharia Hidráulica e Recursos Hídricos da UFMG, Belo Horizonte, Brazil.
Naghettini, M., Potter, K. W., and Illangasekare, T. (1996). “Estimating the upper-tail of flood-peak frequency distributions using hydrometeorological information.” Water Resour. Res., 32(6), 1729–1740.
National Research Council (NRC). (1988). Estimating probabilities of extreme floods, 1st Ed., National Academy Press, Washington, D.C.
Rogers, W. F. (1980). “A pratical model for linear and nonlinear runoff.” J. Hydrol., 46, 1–78.
Rossi, F., Fiorentino, M., and Versace, P. (1984). “Two-component extreme value distribution for flood frequency analysis.” Water Resour. Res., 20(7), 847–856.
Singh, V. P., and Aminian, H. (1986). “An empirical relation between volume and peak of direct runoff.” Water Resour. Bull., 22(5), 725–730.
Swain, R. E., England, J. F., Bullard, K. L., and Raff, D. A. (2004). “Hydrologic hazard curve estimating procedures.” Dam Safety Research Program Research Report No. DSO-04-08, U.S., Dept. of Interior, Bureau of Reclamation, Denver.
Todorovic, P., and Zelenhasic, E. (1970). “A stochastic model for flood analysis.” Water Resour. Res., 6(6), 1641–1648.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: Feb 12, 2007
Accepted: Jun 8, 2007
Published online: Mar 1, 2008
Published in print: Mar 2008
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.