Copula-Based Flood Frequency Analysis at Ungauged Basin Confluences: Nashville, Tennessee
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 7
Abstract
Many cities are located at or near the confluence of streams where availability of water resources may be enhanced to sustain user needs while also posing an increased flooding risk from multiple tributaries. An accurate flood-frequency estimator that models the joint flood potential at a basin confluence is needed. Given that long-term flow observations are often unavailable, estimating flood-frequency at ungauged basin confluences proves challenging. Through the use of copulas, this case study demonstrates how an improved flood-frequency analysis can be performed for stream confluences at Nashville, Tennessee. The approach involves four major steps: initial data quality control, fitting of marginal distributions of tributary peak flows, construction of a suitable copula dependence structure, and identification of flood-frequency at the confluence point based on synthesized peak flows. This case study may help researchers and practitioners develop a better understanding of joint flood-frequency with consideration of upstream dam regulation among several contributing watersheds.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Gratitude is expressed to Mr. Lester King of USACE, who organized and provided the daily streamflow observation of J. Percy Priest Dam. The authors would also like to thank Dr. Richard Medina, Mr. Kevin Stewart, editors and the anonymous reviewers for their helpful suggestions. The first author contributed to this work on his own personal time.
References
Ang, A. H., and Tang, W. H. (1975). Probability concepts in engineering planning and design, Wiley, Hoboken, NJ.
Ashkar, F., El-Jabi, N., and Issa, M. (1998). “A bivariate analysis of the volume and duration of low-flow events.” Stoch. Hydrol. Hydraul.SHHYEK, 12(2), 97–116.
Beersma, J. J., and Buishand, T. A. (2004). “Joint probability of precipitation and discharge deficits in the Netherlands.” Water Resour. Res.WRERAQ, 40(12), W12508.
Cunnane, C. (1988). “Methods and merits of regional flood frequency analysis.” J. Hydrol. (Amsterdam)JHYDA7, 100(1–3), 269–290.
Durrans, S. R., Eiffe, M. A., Thomas, J. W. O., and Goranflo, H. M. (2003). “Joint seasonal/annual flood frequency analysis.” J. Hydrol. Eng.JHYEFF, 8(4), 181–189.
Farr, T. G., et al. (2007). “The shuttle radar topography mission.” Rev. Geophys.REGEEP, 45(2), 1–33.
Favre, A. C., Adlouni, S. EI, Perreault, L., Thiemonge, N., and Bobee, B. (2004). “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res.WRERAQ, 40(1), W01101.
Flynn, K. M., Kirby, W. H., and Hummel, P. R. (2006). “User’s manual for program peakFQ, annual flood-frequency analysis using bulletin 17B guidelines.” Techniques and Methods 4-B4, U.S. Geological Survey, Reston, VA.
Genest, C., Favre, A. C., Béliveau, J., and Jacques, C. (2007). “Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data.” Water Resour. Res.WRERAQ, 43(9), W09401.
Genz, A., and Bretz, F. (2002). “Comparison of methods for the computation of multivariate -probabilities.” J. Comput. Graph. Stat., 11(4), 950–971.
Griffis, V. W., and Stedinger, J. R. (2007a). “Log-Pearson Type 3 distribution and its application in flood frequency analysis. I: Distribution characteristics.” J. Hydrol. Eng.JHYEFF, 12(5), 482–491.
Griffis, V. W., and Stedinger, J. R. (2007b). “Log-Pearson Type 3 distribution and its application in flood frequency analysis. II: Parameter estimation methods.” J. Hydrol. Eng.JHYEFF, 12(5), 492–500.
Griffis, V. W., and Stedinger, J. R. (2009). “Log-Pearson Type 3 distribution and its application in flood frequency analysis. III: Sample skew and weighted skew estimators.” J. Hydrol. Eng.JHYEFF, 14(2), 121–130.
Grimaldi, S., and Serinaldi, F. (2006). “Design hyetographs analysis with 3-copula function.” Hydrol. Sci. J.HSJODN, 51(2), 223–238.
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis, 1st Ed., Cambridge University Press, New York.
Hydrology Subcommittee of the Interagency Advisory Committee on Water Data. (1981). “Guidelines for determining flood frequency.” Bulletin 17B, Office of Water Data Collection, U.S. Geological Survey, Reston, VA.
Kao, S.-C., and Govindaraju, R. S. (2008). “Trivariate statistical analysis of extreme rainfall events via Plackett family of copulas.” Water Resour. Res.WRERAQ, 44(2), W02415.
Karmakar, S., and Simonovic, S. P. (2009). “Bivariate flood frequency analysis. Part 2: A copula-based approach with mixed marginal distributions.” J. Flood Risk Manage., 2(1), 32–44.
Kite, G. W., and Stuart, A. (1977). Frequency and risk analysis in hydrology, Water Resources Public, Fort Collins, CO.
Knight, R. (2010a). High flows in TN rivers estimated, news release, U.S. Geological Survey, Reston, VA.
Knight, R. (2010b). “How does the May 2010 flood compare with historical flooding in middle TN?” U.S. Geological Survey. 〈http://tn.water.usgs.gov/flood/mill_harpeth_cumberland_final.pdf〉 (Oct. 20, 2010).
Kotz, S., Balakristhnan, N., and Johnson, N. L. (2000). Continuous multivariate distributions volume 1: Models and applications, Wiley, Hoboken, NJ.
Kundzewicz, Z. W. (2007). “Prediction in ungauged basins—A systemic perspective.” Proc., PUB Kick-off Meeting, Int. Association of Hydrological Sciences (IAHS), Rennes, France.
Laio, F. (2004). “Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters.” Water Resour. Res.WRERAQ, 40(9), W09308.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models part I—A discussion of principles.” J. Hydrol. (Amsterdam)JHYDA7, 10(3), 282–290.
Nelsen, R. B. (2006). An introduction to copulas, Springer-Verlag, New York.
Rao, A. R., and Hamed, K. H. (2000). Flood frequency analysis, CRC Press, Boca Raton, FL.
Renard, B., and Lang, M. (2007). “Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology.” Adv. Water Resour.AWREDI, 30(4), 897–912.
Salvadori, G., and De Michele, C. (2004). “Frequency analysis via copulas: theoretical aspects and applications to hydrological events.” Water Resour. Res.WRERAQ, 40(12), W12511.
Scott, A. G. (2009). “Project evaluation of investigation and analysis of floods from small drainage areas in New Mexico: A progress report.” U.S. Dept. of the Interior, U.S. Geological Survey, Washington, DC.
Shiau, J., Feng, S., and Nadarajah, S. (2007). “Assessment of hydrological droughts for the Yellow River, China, using copulas.” Hydrol. ProcessesHYPRE3, 21(16), 2157–2163.
Singh, V. P., Jain, S. K., and Tyagi, A. (2007). Risk and reliability analysis: A handbook for civil and environmental engineers, ASCE, Reston, VA.
Sklar, A. (1959). Fonctions de répartition à dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8, 229–231 (in French).
Smith, O. E., Adelfang, S. I., and Tubbs, J. D. (1982). “A bivariate gamma probability distribution with application to gust modelling.” NASA Technical Rep. TM-82483, NASA, Washington, DC.
U.S. Army Corps of Engineers. (1994). “Engineering and design—hydrologic engineering analysis concepts for cost-shared flood damage reduction studies.” Engineer Pamphlets EP 1110-2-10, U.S. Army Corps of Engineers, Washington, DC.
U.S. Geological Survey. (2002). “The national flood frequency program, Version 3: A computer program for estimating magnitude and frequency of floods for ungaged sites”, Water-Resources Investigations Rep. 02-4168, U.S. Army Corps of Engineers, Washington, DC.
Vogel, R. M., Thomas, W. O. Jr., and McMahon, T. A. (1993). “Flood-flow frequency model selection in southwestern United States.” J. Water Resour. Plann. Manage.JWRMD5, 119(3), 353–366.
Wang, Q. J. (2001). “A Bayesian joint probability approach for flood record augmentation.” Water Resour. Res.WRERAQ, 37(6), 1707–1712.
Wang, C., Chang, N. B., and Yeh, G. T. (2009). “Copula-based flood frequency (COFF) analysis at the confluence of river systems.” Hydrol. ProcessesHYPRE3, 23(10), 1471–1486.
Yue, S. (2000). “The bivariate lognormal distribution to model a multivariate flood episode.” Hydrol. ProcessesHYPRE3, 14(14), 2575–2588.
Yue, S., and Rasmussen, P. (2002). “Bivariate frequency analysis: Discussion of some useful concepts in hydrological application.” Hydrol. ProcessesHYPRE3, 16(14), 2881–2898.
Yue, S., and Wang, C. Y. (2004). “A comparison of two bivariate extreme value distributions.” Stoch. Environ. Res. Risk Assess., 18(2), 61–66.
Zhang, L., and Singh, V. P. (2006). “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng.JHYEFF, 11(2), 150–164.
Zhang, L., and Singh, V. P. (2007). “Bivariate rainfall frequency distributions using Archimedean copulas.” J. Hydrol. (Amsterdam)JHYDA7, 332(1–2), 93–109.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 17 • Issue 7 • July 2012
Pages: 790 - 799
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Nov 14, 2009
Accepted: Jul 18, 2011
Published online: Jul 20, 2011
Published in print: Jul 1, 2012
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.