TECHNICAL PAPERS
Oct 12, 2010

Synthetic Design Hydrographs Based on Distribution Functions with Finite Support

Publication: Journal of Hydrologic Engineering
Volume 16, Issue 5

Abstract

The primary characteristics that influence the potential of defining a synthetic design hydrograph (SDH), are the hydrograph shape, peak discharge (Qp), volume (V), and duration (D). This paper studies the advantages and shortcomings of using simple distribution functions with finite support (namely, beta and generalized standard two-sided power distributions) to represent and synthesize direct runoff hydrographs. The relationships among Qp, V, D, and distribution parameters are explored on a few flood events selected by a recursive digital filter algorithm and an overthreshold approach. The results obtained indicate that the adopted procedure provides a good compromise between simplicity and accuracy for building SDHs with two assigned flood characteristics (e.g., Qp and V) and a defined shape.

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Acknowledgments

The writers wish to thank Dr. Attilio Castellarin (Università di Bologna, Italy) for kindly providing the data used in this study. The work was partly carried out under the project “Preliminary Study of Hydraulic Risk within the Basins of Rio Torbido, Torrente Rigo, Torrente Vezza, and the Related Subbasins Located in the Viterbo Administrative Province” supported by Provincia di Viterbo and Tiber River Basin Authority.

References

Ashkar, F., and Rousselle, J. (1983). “Some remarks on the truncation used in partial flood series models.” Water Resour. Res., 19(2), 477–480.
Bogena, H., Kunkel, R., Schöbel, T., Schrey, H. P., and Wendland, F. (2005). “Distributed modeling of groundwater recharge at the macroscale.” Ecol. Model., 187(1), 15–26.
Brath, A., and Montanari, A. (2000). “The effects of the spatial variability of soil infiltration capacity in distributed flood modelling.” Hydrol. Processes, 14(15), 2779–2794.
Brath, A., and Montanari, A. (2003). “Sensitivity of the peak flows to the spatial variability of the soil infiltration capacity for different climatic scenarios.” Phys. Chem. Earth, 28(6–7), 247–254.
Chapman, T. G. (1999). “A comparison of algorithms for stream flow recession and baseflow separation.” Hydrol. Processes, 13(5), 701–714.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw-Hill, New York.
Cleveland, W. S. (1994). The elements of graphing data, Hobart Press, Summit, NJ.
Eckhardt, K. (2005). “How to construct recursive digital filters for baseflow separation.” Hydrol. Processes, 19(2), 507–515.
Elek, P., and Zempléni, A. (2009). “Modelling extremes of time-dependent data by Markov-switching structures.” J. Stat. Plann. Infer., 139(6), 1953–1967.
Filliben, J. J. (1975). “The probability plot correlation coefficient test for normality.” Technometrics, 17(1), 111–117.
Furey, P. R., and Gupta, V. K. (2001). “A physically based filter for separating base flow from streamflow time series.” Water Resour. Res., 37(11), 2709–2722.
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., 43, W09401.
Grimaldi, S., and Serinaldi, F. (2006). “Asymmetric copula in multivariate flood frequency analysis.” Adv. Water Resour., 29(8), 1155–1167.
Karmakar, S., and Simonovic, S. (2008). “Bivariate flood frequency analysis: Part 1. Determination of marginals by parametric and nonparametric techniques.” J. Flood Risk Manage., 1(4), 190–200.
Karmakar, S., and Simonovic, S. (2009). “Bivariate flood frequency analysis. Part 2: A copula-based approach with mixed marginal distributions.” J. Flood Risk Manage., 2(1), 32–44.
Kling, H., and Nachtnebel, H. P. (2009). “A method for the regional estimation of runoff separation parameters for hydrological modelling.” J. Hydrol. (Amsterdam), 364(1–2), 163–174.
Kneip, A., and Gasser, T. (1992). “Statistical tools to analyze data representing a sample of curves.” Ann. Stat., 20(3), 1266–1305.
Koenker, R. (2005). Quantile regression, Cambridge University Press, New York.
Kottegoda, N. T., and Rosso, R. (2008). Applied statistics for civil and environmental engineers, 2nd Ed., Wiley-Blackwell, Chichester, UK.
Kotz, S., and van Dorp, J. R. (2004). “Uneven two-sided power distributions with applications in econometric models.” Stat. Methods Appl., 13(3), 285–313.
Laio, F. (2004). “Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters.” Water Resour. Res., 40, W09308.
Longobardi, A., and Villani, P. (2008). “Baseflow index regionalization analysis in a mediterranean area and data scarcity context: Role of the catchment permeability index.” J. Hydrol. (Amsterdam), 355(1–4), 63–75.
Lyne, V. D., and Hollick, M. (1979). “Stochastic time-variable rainfall-runoff modelling.” Hydrology and Water Resources Symp., Institution of Engineers Australia, Pert, Australia, 89–92.
Malamud, B. D., and Turcotte, D. L. (2006). “The applicability of power-law frequency statistics to floods.” J. Hydrol. (Amsterdam), 322(1–4), 168–180.
Merleau, J., Perreault, L., Angers, J.-F., and Favre, A.-C. (2007). “Bayesian modeling of hydrographs.” Water Resour. Res., 43, W10432.
Mugo, J. M., and Sharma, T. C. (1999). “Application of a conceptual method for separating runoff components in daily hydrographs in Kimakia forest catchments, Kenya.” Hydrol. Processes, 13(17), 2931–2939.
Nadarajah, S. (2007). “Probability models for unit hydrograph derivation.” J. Hydrol. (Amsterdam), 344(3–4), 185–189.
Nathan, R. J., and McMahon, T. A. (1990). “Evaluation of automated techniques for base flow and recession analyses.” Water Resour. Res., 26(7), 1465–1473.
Pramanik, N., Panda, R. K., and Sen, D. (2010). “Development of design flood hydrographs using probability density functions.” Hydrol. Processes, 24(4), 415–428.
Ramsay, J. O., and Silverman, B. W. (2005). Functional data analysis, 2nd Ed., Springer, New York.
Sauquet, E., Ramos, M.-H., Chapel, L., and Bernardara, P. (2008). “Streamflow scaling properties: Investigating characteristic scales from different statistical approaches.” Hydrol. Processes, 22(17), 3462–3475.
Serinaldi, F. (2009a). “Copula-based mixed models for bivariate rainfall data: An empirical study in regression perspective.” Stoch. Environ. Res. Risk Assess., 23(5), 677–693.
Serinaldi, F. (2009b). “Assessing the applicability of fractional order statistics for computing confidence intervals for extreme quantiles.” J. Hydrol. (Amsterdam), 376(3-4), 528–541.
Smakhtin, V. (2001). “Low flow hydrology: A review.” J. Hydrol. (Amsterdam), 240(3–4), 147–186.
Snyder, F. F. (1938). “Synthetic unit-graphs.” Trans., Am. Geophys. Union, 19(2), 447–454.
Sokolov, A. A., Rantz, S. E., and Roche, M. (1976). “Methods of developing designflood hydrographs.” Flood computation methods compiled from world experience, UNESCO, Paris.
Spongberg, M. E. (2000). “Spectral analysis of base flow separation with digital filters.” Water Resour. Res., 36(3), 745–752.
Szilagyi, J., and Parlange, M. B. (1998). “Baseflow separation based on analytical solutions of the Boussinesq equation.” J. Hydrol. (Amsterdam), 204(1-4), 251–260.
Tallaksen, L. M. (1995). “A review of baseflow recession analysis.” J. Hydrol. (Amsterdam), 165(1–4), 349–370.
Tan, S. B. K., Lo, E. Y.-M., Shuy, E. B., Chua, L. H. C., and Lim, W. H. (2009a). “Generation of total runoff hydrographs using a method derived from a digital filter algorithm.” J. Hydrol. Eng., 14(1), 101–106.
Tan, S. B. K., Lo, E. Y.-M., Shuy, E. B., Chua, L. H. C., and Lim, W. H. (2009b). “Hydrograph separation and development of empirical relationships using single-parameter digital filters.” J. Hydrol. Eng., 14(3), 271–279.
Todorovic, P., and Zelenhasic, E. (1970). “A stochastic model for flood analysis.” Water Resour. Res., 6(6), 1641–1648.
van Dorp, J. R., and Kotz, S. (2003). “Generalized trapezoidal distributions.” Metrika, 58(1), 85–97.
Villarini, G., Serinaldi, F., and Krajewski, W. F. (2008). “Modeling radar-rainfall estimation uncertainties using parametric and non-parametric approaches.” Adv. Water Resour., 31(12), 1674–1686.
Werner, A. D., Wood, M., Simmons, C. T., and Lockington, D. A. (2008). “Salinograph trends as indicators of the recession characteristics of stream components.” Hydrol. Processes, 22(16), 3020–3028.
Yue, S. (2001). “A bivariate gamma distribution for use in multivariate flood frequency analysis.” Hydrol. Processes, 15(6), 1033–1045.
Yue, S., Ouarda, T., Bobée, B., Legendre, P., and Bruneau, P. (1999). “Gumbel mixed model for flood frequency analysis.” J. Hydrol. (Amsterdam), 226(1-2), 88–100.
Yue, S., Ouarda, T., Bobée, B., Legendre, P., and Bruneau, P. (2002). “Approach for describing statistical properties of flood hydrograph.” J. Hydrol. Eng., 7(2), 147–153.

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Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 16Issue 5May 2011
Pages: 434 - 446

History

Received: Apr 16, 2010
Accepted: Oct 8, 2010
Published online: Oct 12, 2010
Published in print: May 1, 2011

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Authors

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Francesco Serinaldi
Dipartimento di Geologia e Ingegneria Meccanica, Naturalistica e Idraulica per il Territorio—GEMINI, Università della Tuscia, Via S. Camillo de Lellis snc, 01100 Viterbo, Italy (corresponding author). E-mail: [email protected]
Salvatore Grimaldi
Dipartimento di Geologia e Ingegneria Meccanica, Naturalistica e Idraulica per il Territorio—GEMINI, Università della Tuscia, Via S. Camillo de Lellis snc, 01100 Viterbo, Italy; also Honors Center of Italian Universities-H2CU, “Sapienza” Università di Roma, Via Eudossiana 18, 00184 Rome, Italy.

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