Abstract
The Muskingum model is one of the most popular models for hydrologic channel flood routing. However, as the parameters of this model are estimated by analyzing both inflow and outflow data, the application of this model to an ungauged channel reach has been limited. In this study, as a solution to this problem, a methodology is proposed to estimate the parameters of the Muskingum model using the basin characteristics representing the inlet and outlet of the channel reach. That is, the Muskingum model could be expressed as a combination of the linear reservoir model and the Dirac delta function, whose weighting factors are determined as a function of the Muskingum model parameter . It was also found that the storage coefficient of the linear reservoir model is expressed by both the Muskingum model parameters and . Finally, it was shown that the Muskingum model parameters can be estimated using the information of concentration time and storage coefficient representing the inlet and outlet of the given channel reach. In the application example with the observed data from the dam discharge experiment in the Geum River Basin, Korea, it was shown that the Muskingum model parameters could be reasonably estimated to be very close to those estimated by the conventional graphical method.
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Acknowledgments
This research was supported by a grant (14AWMP-B082564-01) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of the Korean government.
References
Agirre, U., Goni, M., Lopez, J. J., and Gimena, F. N. (2005). “Application of a unit hydrograph based on subwatershed division and comparison with Nash’s instantaneous unit hydrograph.” Catena, 64(2–3), 321–332.
Barbetta, S., Moramarco, T., Franchini, M., Melone, F., Brocca, L., and Singh, V. P. (2011). “Case study: Improving real time stage forecasting Muskingum model by incorporating the rating curve model.” J. Hydrol. Eng., 540–557.
Brutsaert, W. (2005). Hydrology: An introduction, Cambridge University Press, Cambridge, U.K.
Cho, H. (2008). “A study on the optimization of parameters for Muskingum routing method.” J. Korean Soc. Ind. Appl., 11(1), 27–34.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw-Hill, New York.
Geum River Flood Control Office. (2003). “Flood alert system: Sapgyo Stream, Gap Stream and Geum River Basin.” Gongju, Korea.
Gill, M. A. (1978). “Flood routing by the Muskingum method.” J. Hydrol., 36(3–4), 353–363.
Heerdegen, R. G., and Reich, B. M. (1974). “Unit hydrographs for catchments of different sizes and dissimilar regions.” J. Hydrol., 22(1–2), 143–153.
Jeong, J. H., and Yoon, Y. N. (2007). Design practices in water resources, Goomi Press, Seoul.
JSCE (Japan Society of Civil Engineers). (1986). “The collection of hydraulic formulae.” Tokyo.
Karahan, H., Gurarslan, G., and Geem, Z. W. (2013). “Parameter estimation of the nonlinear Muskingum flood-routing model using a hybrid harmony search algorithm.” J. Hydrol. Eng., 352–360.
Lee, J., Yoo, C., and Sin, J. (2013). “Theoretical backgrounds of basin concentration time and storage coefficient and their empirical formula.” J. Korea Water Resour. Assoc., 46(2), 155–169.
McCarthy, G. T. (1938). “The unit hydrograph and flood routing.” Conf. of North Atlantic Division, U.S. Army Corps of Engineers, New London, CT.
MOCT (Ministry of Construction and Transportation). (2006). “Establishment of comprehensive flood mitigation plan for the Han River Basin.” Seoul.
MOCT (Ministry of Construction and Transportation). (2007). “Guidelines for flood estimation.” Seoul.
Ouyang, A., Tang, Z., Li, K., Sallam, A., and Sha, E. (2014). “Estimating parameters of Muskingum model using an adaptive hybrid PSO algorithm.” Int. J. Pattern Recognit. Artif. Intell., 28(1), 1–29.
Overton, D. E. (1966). “Muskingum flood routing of upland streamflow.” J. Hydrol., 4, 185–200.
Park, B. J., Gang, G. S., and Jeong, G. S. (1997). “A flood routing for the downstream of the Kum River Basin due to the Teachong Dam discharge.” J. Korea Water Resour. Assoc., 30(2), 131–141.
Russel, S. O., Sunnell, G. J., and Kenning, B. F. (1979). “Estimating design flows for urban drainage.” J. Hydraul. Div., 105(1), 43–52.
Venetis, C. (1969). “The IUH of the Muskingum channel reach.” J. Hydrol., 7(4), 444–447.
Viessman, W., Lewis, G. L., and Knapp, J. W. (1989). Introduction to hydrology, Harper and Row, New York.
Wang, G. T., and Chen, S. (1996). “A linear spatially distributed model for a surface rainfall-runoff system.” J. Hydrol., 185(1–4), 183–198.
Wilson, E. M. (1974). Engineering hydrology, Macmillan, London.
Yoo, C., and Kim, H. (2010). “Hydrologic re-analysis of Muskingum channel routing method: A linear combination of linear reservoir and linear channel models.” J. Korea Water Resour. Assoc., 43(12), 1051–1061.
Yoo, C., Lee, J., Park, C., and Jun, C. (2014). “Method for estimating concentration time and storage coefficient of the Clark model using rainfall-runoff measurements.” J. Hydrol. Eng., 626–634.
Yoo, C., Sin, J., and Jun, C. H. (2013). “Parameter decision of Muskingum channel routing method based on the linear system assumption.” J. Korea Water Resour. Assoc., 46(5), 449–463.
Yoon, Y. N. (2007). Hydrology: Fundamental and application, Cheongmoongak Press, Gyeonggido, Korea.
Information & Authors
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Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jul 18, 2016
Accepted: Nov 29, 2016
Published ahead of print: Feb 23, 2017
Published online: Feb 24, 2017
Published in print: Jul 1, 2017
Discussion open until: Jul 24, 2017
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