Reverse Flood Routing in Rivers Using Linear and Nonlinear Muskingum Models
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Volume 26, Issue 6
Abstract
One of the key factors for flood modeling and control is the flood hydrograph, which is not always available due to lack of flood discharge observations. In reverse flow routing, hydraulic or hydrological calculations are performed from the downstream end to the upstream end. In the present study, a reverse flood routing approach is developed based on the Muskingum model. The storage function is conceptualized as linear and five different nonlinear forms. The Euler and the fourth-order Runge–Kutta numerical methods are used for solving the storage models. The shuffled complex evolution (SCE) algorithm is used for optimization of the flood routing parameters. The models are calibrated and validated with theoretical and actual hydrographs. The results indicate that the proposed methodology could substantially (up to almost 82%) improve comparison with observed inflows. The practical applicability of the proposed methodology is also validated in real river systems.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon request.
Acknowledgments
The authors appreciatively acknowledge the valuable comments offered by the editors and anonymous reviewers in improving the technical contents of this paper.
References
Abdulwahid, M. H., and K. N. Kadhim. 2013. “Application of inverse routing methods to Euphrates river (IRAQ).” Int. J. Civ. Eng. Technol. 4 (1): 97–109.
Akbari, G. H., A. H. Nezhad, and R. Barati. 2012. “Developing a model for analysis of uncertainties in prediction of floods.” J. Adv. Res. 3 (1): 73–79. https://doi.org/10.1016/j.jare.2011.04.004.
Artichowicz, W., and R. Szymkiewicz. 2009. “Inverse integration of the open channel flow equations.” In Vol. I of Proc., 11th International Symp. on Water Management and Hydraulic Engineering, 89–96. Skopje, Macedonia: Univ. of Skopje.
Ayvaz, M. T., and G. Gurarslan. 2017. “A new partitioning approach for nonlinear Muskingum flood routing models with lateral flow contribution.” J. Hydrol. 553 (Oct): 142–159. https://doi.org/10.1016/j.jhydrol.2017.07.050.
Badfar, M. 2015. “Developing a model for reverse flood routing in rivers.” M.Sc. thesis, Dept. of Civil Engineering, Univ. of Sistan and Baluchestan.
Barati, R. 2011. “Parameter estimation of nonlinear Muskingum models using Nelder-Mead simplex algorithm.” J. Hydrol. Eng. 16 (11): 946–954. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000379.
Barati, R. 2013. “Application of excel solver for parameter estimation of the nonlinear Muskingum models.” KSCE J. Civ. Eng. 17 (5): 1139–1148. https://doi.org/10.1007/s12205-013-0037-2.
Barati, R., S. Rahimi, and G. H. Akbari. 2012. “Analysis of dynamic wave model for flood routing in natural rivers.” Water Sci. Eng. 5 (3): 243–258.
Battjes, J. A., and R. J. Labeur. 2017. Unsteady flow in open channels. New York: Cambridge University Press.
Bruen, M., and J. C. I. Dooge. 2007. “Harmonic analysis of the stability of reverse routing in channels.” Hydrol. Earth Syst. Sci. Discuss. 11 (1): 559–568.
Brutsaert, W. 2005. Hydrology: An introduction. New York: Cambridge University Press.
Cheng, S. J., and R. Y. Wang. 2002. “An approach for evaluating the hydrological effects of urbanization and its application.” Hydrol. Process. 16 (7): 1403–1418. https://doi.org/10.1002/hyp.350.
Chow, V. 1959. Open channel hydraulics. New York: McGraw-Hill.
Chow, V. T., D. R. Maidment, and L. W. Mays. 1988. Applied hydrology, 572. Singapore: McGraw-Hill.
Contractor, D. N., and J. W. Jenson. 2000. “Simulated effect of vadose infiltration on water levels in the Northern Guam Lens Aquifer.” J. Hydrol. 229 (3–4): 232–254. https://doi.org/10.1016/S0022-1694(00)00157-8.
Das, A. 2009. “Reverse stream flow routing by using Muskingum models.” Sadhana 34 (3): 483–499. https://doi.org/10.1007/s12046-009-0019-8.
Dooge, J., and M. Bruen. 2005. “Problems in reverse routing.” Acta Geophys. Pol. 53 (4): 357.
D’Oria, M., P. Mignosa, and M. G. Tanda. 2012. “Reverse level pool routing: Comparison between a deterministic and a stochastic approach.” J. Hydrol. 470 (Nov): 28–35. https://doi.org/10.1016/j.jhydrol.2012.07.045.
D’Oria, M., P. Mignosa, and M. G. Tanda. 2014. “Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems.” Adv. Water Resour. 63 (Jan): 143–151. https://doi.org/10.1016/j.advwatres.2013.11.007.
D’Oria, M., and M. G. Tanda. 2012. “Reverse flow routing in open channels: A Bayesian geostatistical approach.” J. Hydrol. 460 (Aug): 130–135. https://doi.org/10.1016/j.jhydrol.2012.06.055.
Duan, Q. 2003. “Global optimization for watershed model calibration.” Calibration Watershed Models 6: 89–104.
Duan, Q., V. Gupta, and S. Sorooshian. 1993. “Shuffled complex evolution approach for effective and efficient global minimization.” J. Optim. Theory Appl. 76 (3): 501–521. https://doi.org/10.1007/BF00939380.
Duan, Q., S. Sorooshian, and V. Gupta. 1992. “Effective and efficient global optimization for conceptual rainfall-runoff models.” Water Resour. Res. 28 (4): 1015–1031. https://doi.org/10.1029/91WR02985.
Duan, Q., S. Sorooshian, and V. Gupta. 1994. “Optimal use of the SCE-UA global optimization method for calibrating watershed models.” J. Hydrol. 158 (3–4): 265–284. https://doi.org/10.1016/0022-1694(94)90057-4.
Easa, S. M. 2014. “New and improved four-parameter non-linear Muskingum model.” Proc. Inst. Civ. Eng. 167 (5): 288.
Easa, S. M., R. Barati, H. Shahheydari, E. J. Nodoshan, and T. Barati. 2014. “Discussion: New and improved four-parameter non-linear Muskingum model.” Water Manage. 167 (10): 612–615.
Eckhardt, K., and J. G. Arnold. 2001. “Automatic calibration of a distributed catchment model.” J. Hydrol. 251 (1–2): 103–109. https://doi.org/10.1016/S0022-1694(01)00429-2.
Ehteram, M., et al. 2018. “Improving the Muskingum flood routing method using a hybrid of particle swarm optimization and bat algorithm.” Water 10 (6): 807.
Eli, R. N., J. M. Wiggert, and D. N. Contractor. 1974. “Reverse flow routing by the implicit method.” Water Resour. Res. 10 (3): 597–600. https://doi.org/10.1029/WR010i003p00597.
Eusuff, M. M., and K. E. Lansey. 2004. “Optimal operation of artificial groundwater recharge systems considering water quality transformations.” Water Resour. Manage. 18 (4): 379–405. https://doi.org/10.1023/B:WARM.0000048486.46046.ee.
Gavilan, G., and M. H. Houck. 1985. “Optimal Muskingum River routing.” In Proc., Computer Applications in Water Resources, 1294–1302. Reston, VA: ASCE.
Gill, M. 1978. “Flood routing by Muskingum method.” J. Hydrol. 36 (3–4): 353–363. https://doi.org/10.1016/0022-1694(78)90153-1.
Gupta, H. V., S. Sorooshian, and P. O. Yapo. 1999. “Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration.” J. Hydrol. Eng. 4 (2): 135–143. https://doi.org/10.1061/(ASCE)1084-0699(1999)4:2(135).
Kang, L., L. Zhou, and S. Zhang. 2017. “Parameter estimation of two improved nonlinear Muskingum models considering the lateral flow using a hybrid algorithm.” Water Resour. Manage. 31 (14): 4449–4467. https://doi.org/10.1007/s11269-017-1758-7.
Koussis, A. D. 2009. “Assessment and review of the hydraulics of storage flood routing 70 years after the presentation of the Muskingum method.” Hydrol. Sci. J. 54 (1): 43–61. https://doi.org/10.1623/hysj.54.1.43.
Koussis, A. D., K. Mazi, S. Lykoudis, and A. A. Argiriou. 2012. “Reverse flood routing with the inverted Muskingum storage routing scheme.” Nat. Hazards Earth Syst. Sci. 12 (1): 217–227.
McCarthy, G. 1938. “The unit hydrograph and flood routing North Atlantic division.” In Proc., Conf. of North Atlantic Division, US Army Corps of Engineers. Providence, RI: US Army Corps of Engineers.
Mertens, J., H. Madsen, L. Feyen, D. Jacques, and J. Feyen. 2004. “Including prior information in the estimation of effective soil parameters in unsaturated zone modeling.” J. Hydrol. 294 (4): 251–269. https://doi.org/10.1016/j.jhydrol.2004.02.011.
Niazkar, M., and S. H. Afzali. 2017. “New nonlinear variable-parameter Muskingum models.” KSCE J. Civ. Eng. 21 (7): 2958–2967. https://doi.org/10.1007/s12205-017-0652-4.
Perumal, M., and B. Sahoo. 2007. “Applicability criteria of the variable parameter Muskingum stage and discharge routing methods.” Water Resour. Res. 43 (5): 1–20.
Price, R. K., W. A. Y. S. Fernando, and D. P. Solomatine. 2006. “Inverse modeling for flood propagation.” In Proc., 7th Int. Conf. on Hydroinformatics. Nice, France: Research Pub.
Sadeghi, S. H., and J. K. Singh. 2010. “Derivation of flood hydrographs for ungauged upstream subwatersheds using a main outlet hydrograph.” J. Hydrol. Eng. 15 (12): 1059–1069. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000275.
Saghafian, B., M. H. Jannaty, and N. Ezami. 2015. “Inverse hydrograph routing optimization model based on the kinematic wave approach.” Eng. Optim. 47 (8): 1031–1042. https://doi.org/10.1080/0305215X.2014.941289.
Sivapragasam, C., R. Maheswaran, and V. Venkatesh. 2008. “Genetic programming approach for flood routing in natural channels.” Hydrol. Processes Int. J. 22 (5): 623–628. https://doi.org/10.1002/hyp.6628.
Sorooshian, S., Q. Duan, and V. K. Gupta. 1993. “Calibration of rainfall-runoff models: Application of global optimization to the Sacramento soil moisture accounting model.” Water Resour. Res. 29 (4): 1185–1194. https://doi.org/10.1029/92WR02617.
Spada, E., M. Sinagra, T. Tucciarelli, S. Barbetta, T. Moramarco, and G. Corato. 2017. “Assessment of river flow with significant lateral inflow through reverse routing modeling.” Hydrol. Process. 31 (7): 1539–1557. https://doi.org/10.1002/hyp.11125.
Szymkiewicz, R. 1993. “Solution of the inverse problem for the Saint Venant equations.” J. Hydrol. 147 (1–4): 105–120. https://doi.org/10.1016/0022-1694(93)90077-M.
Szymkiewicz, R. 2010. Vol. 83 of Numerical modeling in open channel hydraulics. New York: Springer.
Tung, Y. 1985. “River flood routing by nonlinear Muskingum method.” J. Hydraul. Eng. 111 (12): 1447–1460. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:12(1447).
van Griensven, A., and W. Bauwens. 2003. “Concepts for river water quality processes for an integrated river basin modeling.” Water Sci. Technol. 48 (3): 1–8. https://doi.org/10.2166/wst.2003.0145.
Vatankhah, A. R. 2014. “Evaluation of explicit numerical solution methods of the Muskingum model.” J. Hydrol. Eng. 19 (8): 06014001. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000978.
Vatankhah, A. R. 2015. “Discussion of ‘application of excel solver for parameter estimation of the nonlinear Muskingum models’ by Reza Barati.” KSCE J. Civ. Eng. 19 (1): 332–336. https://doi.org/10.1007/s12205-014-1422-1.
Wilson, E. M. 1974. Engineering hydrology. Hampshire, UK: MacMillan.
Yapo, P. O., H. V. Gupta, and S. Sorooshian. 1996. “Automatic calibration of conceptual rainfall-runoff models: Sensitivity to calibration data.” J. Hydrol. 181 (1–4): 23–48. https://doi.org/10.1016/0022-1694(95)02918-4.
Zoppou, C. 1999. “Reverse routing of flood hydrographs using level pool routing.” J. Hydrol. Eng. 4 (2): 184–188. https://doi.org/10.1061/(ASCE)1084-0699(1999)4:2(184).
Zucco, G., G. Tayfur, and T. Moramarco. 2015. “Reverse flood routing in natural channels using genetic algorithm.” Water Resour. Manage. 29 (12): 4241–4267. https://doi.org/10.1007/s11269-015-1058-z.
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Journal of Hydrologic Engineering
Volume 26 • Issue 6 • June 2021
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© 2021 American Society of Civil Engineers.
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Received: May 28, 2020
Accepted: Jan 21, 2021
Published online: Mar 25, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 25, 2021
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