Bivariate Statistical Approach to Check Adequacy of Dam Spillway
Publication: Journal of Hydrologic Engineering
Volume 10, Issue 1
Abstract
The problem of selecting the appropriate design flood is a constant concern to dam engineering and, in general, in the hydrological practice. Overtopping represents more than 40% of dam failures in the world. The determination of the design flood is based in some cases on the -year quantile of flood peak, and in other cases considering also the -year quantile of flood volume. However, flood peak and flood volume have a positive (strong or weak) dependence. To model properly this aspect a bivariate probability distribution is considered using the concept of 2-Copulas, and a bivariate extreme value distribution with generalized extreme value marginals is proposed. The peak–volume pair can then be transformed into the correspondent flood hydrograph, representing the river basin response, through a simple linear model. The hydrological safety of dams is considered checking adequacy of dam spillway. The reservoir behavior is tested using a long synthetic series of flood hydrographs. An application to an existing dam is given.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research was partially supported by MURST via the project “Hydrological Safety of Impounded Rivers.” The support of “Progetto Giovani Ricercatori” is also acknowledged.
References
American Society of Civil Engineers (ASCE). (2000). “Dam safety.” Policy Statement 280, New York.
Berga, L. (1998). “New trends in hydrological safety.” Dam safety, L. Berga, ed., Balkema, Rotterdam, The Netherlands, 1099–1110.
Bras, R. L. (1990). Hydrology: An introduction to hydrologic science, Addison-Wesley, Reading, Mass.
Carriere, J. F. (1994). “A large sample test for one-parameter families of copulas.” Commun. Stat: Theory Meth., 23(5), 1311–1317.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1998). Applied hydrology, McGraw–Hill, Singapore.
Committee on Failures and Accidents to Large Dams of the United States Committeee on Large Dams. (1975). “Lessons from dam incidents, USA.” ASCE∕USCOLD, New York.
De Almeida, A. B., and Viseu, T. (1997). “Dams and valley: A present and future challenge.” Proc., Int. NATO Workshop on Dams and Safety Management at Downstream Valleys, Lisbon, Portugal, A. B. De Almeida, and T. Viseu, eds., Balkema, Rotterdam, The Netherlands, 3–25.
Deheuvels, P. (1979). “La fonction de dependence empirique et ses proprietes. Un test non parametrique d’independence.” Acad. Roy. Belg. Bull. Cl. Sci., 65(5), 274–292.
De Michele, C., and Salvadori, G. (2003). “A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas.” J. Geophys. Res., [Atmos.], 108(D2), ACL 15-1–ACL 15-11.
Genest, C., and Rivest, L. (1993). “Statistical inference procedures for bivariate archimedean copulas.” J. Am. Stat. Assoc., 88(423), 1034–1043.
Gumbel, M. E. J. (1960). “Distributions des valeurs extrêmes en plusieurs dimensions.” Publ. Inst. Stat. Univ. Paris, 9, 171–173.
Hosking, J. R. M. (1990). “ -moments: Analysis and estimation of distributions using linear combinations of order statistics.” J. R. Stat. Soc. Ser. B. Methodol., 52, 105–124.
Joe, H. (1997). Multivariate models and dependence concepts, Chapman and Hall, London.
Kottegoda, N. T., and Rosso, R. (1997). Statistics, probability and reliability for civil and environmental engineers, McGraw–Hill, New York.
Nash, J. E. (1957). “The form of the instantaneous unit hydrograph.” IAHS Publication, 45(3–4), 114–121.
Nelsen, R. B. (1999) An introduction to copulas, Springler, New York.
Salvadori, G., and De Michele, C. (2004). “Analytical calculation of storm volume statistics involving Pareto-like intensity-duration marginals.” Geophys. Res. Lett., 31, L04502.
Soil Conservation Service. (1972). “Hydrology.” National engineering handbook, Sec. 4, Soil Conservation Service, U.S. Department of Agriculture, Washington, D.C.
Zoppou, C. (1999). “Reverse routing of flood hydrographs using level pool routing.” J. Hydraul. Eng., 4(2), 184–188.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 10 • Issue 1 • January 2005
Pages: 50 - 57
Copyright
© 2005 ASCE.
History
Received: Mar 17, 2003
Accepted: May 6, 2004
Published online: Jan 1, 2005
Published in print: Jan 2005
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.