Abstract
There is a growing tendency to assess safety of dams by mathematical and statistical methods in hydrosystem engineering. This chapter presents the application of risk and uncertainty analysis to dam overtopping based on univariate and bivariate flood frequency analyses by applying Gumbel logistic distribution. The bivariate frequency analyses produced six inflow hydrographs with a joint return period of 100 years. Afterward, the overtopping risk of the Doroudzan Dam was evaluated for all six inflow hydrographs by considering quantile of flood peak discharge, initial depth of water in the reservoir, and discharge coefficient of spillway as uncertain variables and using two uncertainty analysis methods; Monte Carlo simulation and Latin hypercube sampling. Finally, the results of both univariate and bivariate frequency analyses were compared to show the significance of bivariate analysis on dam overtopping.
Goodarzi, E., Mirzaei, M., & Ziaei, M. (2012). Evaluation of Dam Overtopping Risk Based on Univariate and Bivariate Flood Frequency Analyses. Canadian Journal of Civil Engineering, 39(4), 374–387. doi:10.1139/l2012-012.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aldama, A., & Ramirez, A. (1999). A new approach for dam design flood estimation. In: Proceeding of the IAHR Congress, Graz, Austria 22–27 Aug 1999.
Bobee, B., & Rasmussen, P. F. (1994). Statistical analysis of annual flood series, in Trends in Hydrology (I). J. Menon (ED.), Council of scientific research integration (pp. 117–135). India.
Choulakian, V., El-Jabi, N., & Moussi, J. (1990). On the distribution of flood volume in partial duration series analysis of flood phenomena. Stochastic Hydrology and Hydraulics, 4, 217–226.
Chow, V. T. (1964). Handbook of Applied Hydrology. New York: McGrawHill.
Correia, F. N. (1987). Multivariate partial duration series in flood risk analysis. In V. P. Singh (Ed.), Hydrologic frequency modeling (pp. 541–554) Reidel Publishing Company, Dordrecht, The Netherlands.
Cunnane, C. (1988). Methods and merits of regional flood frequency analysis. Journal of Hydrology, 100, 269–290.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., & Rosso, R. (2005). Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydraulic Engineering, 10(1), 50–57.
Escalante, C., & Domı′nguez, J. (1997). Parameter estimation for bivariate extreme value distribution by maximum entropy. Hydrological Science and Technological Journal, 13, 1–10.
Goel, N. K., Seth, S. M., & Chandra, S. (1998). Multivariate modeling of flood flows. Journal of Hydraulic Engineering Division of the American Society of Civil Engineers, 124(2), 146–155.
Gumbel, E. J., & Mustafi, C. K. (1967). Some analytical properties of bivariate extreme distributions. Journal of American Statistical Association, 62, 569–588.
Hable, O. (2001). Multidimensional probabilistic design concept for the estimation of the overtopping probability of dams. PhD thesis, Technical University of Graz, Austria.
Johnson, N. L., & Kotz, S. (1972). Distribution in statistics: Continuous multivariate distributions. New York: Wiley.
Kelly, K. S., Krzysztofowicz, R., & 3 1. (1997). A bivariate meta-Gaussian density for use in hydrology. Stochastic Hydrology and Hydraulics, 11, 17.
Krstanovic, P. F., & Singh, V. P. (1987). A multivariate stochastic flood analysis using entropy. In V. P. Singh, (Ed.), Hydrologic frequency modeling (pp. 515–539) Reidel Publishing Company, Dordrecht, The Netherlands.
Kuo, J. T., Hsu, Y. C., Tung, Y. K., Yeh, K. C., & Wu, J. D. (2007a). Dam overtopping risk assessment considering inspection program. Journal of Stochastic Environment Resource Risk Assessment, 22(3), 303–313.
Loganathan, G. V., Kuo, C. Y., & Yannaccone, J. (1987). Joint probability distribution of stream flows and tides in estuaries. Nordic Hydrological, 18, 237–246.
McCuen, R. (2005). Hydrologic analysis and design. New Jersey: Pearson Prentice Hall.
Raynal, J.A. (1985). Bivariate extreme value distributions applied to flood frequency analysis Ph. D. dissertation, Civil Engineering Department, Colorado State University.
Raynal, J.A., & Salas, J.D. (1987). Multivariate extreme value distributions in hydrological analyses. In Water for the future: hydrology in perspective. J. Galambos (Ed.) Extreme value theory and applications (pp. 111–119) 164, IAHS Publication, UK.
Sackl, B., and Bergmann, H. (1987). A bivariate flood model and its application. V. P. Singh (Ed.), Hydrologic frequency modeling (pp. 571–582). Dordrecht: D. Reidel Publishing Company.
Salvadori, G., & De Michele, C. (2004). Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resources Research, 40(12), 511–528. doi:10.1029/2004WR003133.
Singh, V.P., Jain, S.K., & Tyagi, A.K. (2007). Risk and reliability analysis. American Society of Civil Engineers (pp 783). Reston, Virginia: ASCE Press.
Singh, K., & Singh, V. P. (1991). Derivation of bivariate probability density functions with exponential marginals. Stochastic Hydrology and Hydraulics, 5, 55–68.
Tung, Y. K., Yen, B. C., & Melching, C. S. (2005). Hydrosystems Engineering Reliability Assessment and Risk Analysis. New York: McGraw–Hill Professional.
Yanmaz, A., & Gunindi, M. (2008). Assessment of overtopping reliability and benefits of a flood detention dam. Canadian Journal of Engineering, 1177–1182.
Yen, B.C, (1979). Safety factor in hydrologic and hydraulic engineering design. In: E. A. McBean, K. W. Hipel, T. E. Unny (Eds) Reliability in water resources management (pp. 389–407) Highlands Ranch: Water Resources Publications.
Yue, S. (1999). Applying the bivariate normal distribution to flood frequency analysis. Water International, 24(3), 248–252.
Yue, S. (2001). A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrological Processes, 15, 1033–1045.
Yue, S., & Rasmussen, P. (2002). Bivariate frequency analysis: Discussion of some useful concepts in hydrological applications. Hydrological Processes, 16, 2881–2898.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Goodarzi, E., Ziaei, M., Teang Shui, L. (2013). Evaluation of Dam Overtopping Risk Based on Univariate and Bivariate Flood Frequency Analyses. In: Introduction to Risk and Uncertainty in Hydrosystem Engineering. Topics in Safety, Risk, Reliability and Quality, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5851-3_6
Download citation
DOI: https://doi.org/10.1007/978-94-007-5851-3_6
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5850-6
Online ISBN: 978-94-007-5851-3
eBook Packages: EngineeringEngineering (R0)