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Rating Curve Development at Ungauged River Sites using Variable Parameter Muskingum Discharge Routing Method

Abstract

A physically based simplified discharge routing method, namely, the variable parameter Muskingum discharge-hydrograph (VPMD) routing method, having the capability of estimating the stage hydrographs simultaneously in channels with floodplains is presented herein. The upstream discharge hydrograph is routed using this VPMD method in different two-stage symmetrical trapezoidal compound cross section channel reaches. The performance of the VPMD method is evaluated by numerical experiments using the benchmark MIKE11 hydrodynamic model and the field data of the Tiber River in central Italy. The proposed method is capable of accurately routing the discharge hydrographs, corresponding stage hydrographs and synthesizing the normal rating curves at any downstream ungauged river site which is not affected by any downstream effects. This study can be helpful for various planning and management of river water resources in both the diagnostic and prognostic modes.

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References

  1. Ackers P (1993) Stage-discharge functions for two-stage channels: the impact of new research. J Inst Water Environ Manag 7(1):52–61

  2. ASCE (1993) Task committee on definition of criteria for evaluation of watershed models of the watershed management committee, irrigation and drainage division criteria for evaluation of watershed models. J Irrig Drain Eng ASCE 119(3):429–442

  3. Birkhead AL, James CS (1998) Synthesis of rating curves from local stages and remote discharge monitoring using nonlinear Muskingum routing. J Hydrol 205(1–2):52–65

  4. Danish Hydraulic Institute (DHI) (2003) User’s manual and technical references for MIKE 11 (version 2003b). Hørsholm, Denmark

  5. Ferrick MG (1985) Analysis of river wave types. Water Resour Res 21(2):209–220

  6. Franchini M, Lamberti P, Giammarco PD (1999) Rating curve estimation using local stages, upstream discharge data and a simplified hydraulic model. Hydrol Earth Syst Sci 3(4):541–548

  7. Fread, DL (1990) DAMBRK: The NWS Dam-Break Flood Forecasting Model. report, National Weather Service, Office of Hydrology, Silver Spring, Marryland, USA

  8. Garbrecht J, Brunner G (1991) Hydrologic channel-flow routing for compound sections. J Hydraul Eng ASCE 117(5):629–642

  9. Heatherman WJ (2004) Muskingum–Cunge revisited. World Water and Environmental Resources Congress 2004, ASCE, Edited by G Sehlke, DF Hayes, DK Stevens (June 2– July 1, 2004), Salt Lake City, Utah, USA

  10. Henderson FM (1966) Open channel flow. MacMillan and Co., New York

  11. McCarthy GT (1938) The unit hydrograph and flood routing. Conf. North Atlantic Div, U.S. Army Corps of Engineers, New London, Conn

  12. Moramarco T, Singh VP (2001) Simple method for relating local stage and remote discharge. J Hydrol Eng ASCE 6(1):78–81

  13. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models, Part-1: a discussion of principles. J Hydrol 10(3):282–290

  14. Natural Environment Research Council (NERC) (1975) Flood routing studies report, Vol. III. Institute of Hydrology, Wallingford

  15. O’Sullivan JJ, Ahilan S, Bruen M (2012) A modified Muskingum routing approach for floodplain flows: theory and practice. J Hydrol 470–471:239–254

  16. Perumal M (1992) The cause of negative initial outflow with the Muskingum method. Hydrol Sci J 37(4):391–401

  17. Perumal M (1994a) Hydrodynamic derivation of a variable parameter Muskingum method: 1 Theory and solution procedure. Hydrol Sci J 39(5):431–442

  18. Perumal M (1994b) Hydrodynamic derivation of a variable parameter Muskingum method: 2. verification. Hydrol Sci J 39(5):443–458

  19. Perumal M, Price RK (2013) A fully mass conservative variable parameter McCarthy–Muskingum method: theory and verification. J Hydrol 502:89–102. doi:10.1016/j.jhydrol.2013.08.023

  20. Perumal M, Ranga Raju KG (1998a) Variable parameter stage-hydrograph routing method: II. Evaluation. J Hydrol Eng ASCE 3(2):115–121

  21. Perumal M, Ranga Raju KG (1998b) Variable parameter stage-hydrograph routing method: I. Theory. J Hydrol Eng ASCE 3(2):109–114

  22. Perumal M, Ranga Raju KG (1999) Approximate convection diffusion equations. J Hydrol Eng ASCE 4(2):161–164

  23. Perumal M, Sahoo B (2007) Applicability criteria of the variable parameter Muskingum stage and discharge routing methods. Water Resour Res W05409 43(5):1–20. doi:10.1029/2006WR004909

  24. Perumal M, O’Connell PE, Ranga Raju KG (2001) Field applications of a variable parameter Muskingum method. J Hydrol Eng ASCE 6(3):196–207

  25. Perumal M, Moramarco T, Sahoo B, Barbetta S (2007) A methodology for discharge estimation and rating curve development at ungauged river sites. Water Resour Res W02412 43(2):1–22. doi:10.1029/2005WR004609

  26. Perumal M, Sahoo B, Moramarco T, Barbetta S (2009) Multilinear Muskingum method for stage-hydrograph routing in compound channels. J Hydrol Eng ASCE 14(7):663–670. doi:10.1061/(ASCE)HE.1943-5584.0000029

  27. Perumal M, Moramarco T, Sahoo B, Barbetta S (2010) On the practical applicability of the VPMS routing method for rating curve development at ungauged river sites. Water Resour Res 46(3):1–9. doi:10.1029/2009WR008103, W03522

  28. Price RK (1973) Flood routing methods for British rivers. Proc Inst Civ Engrs 55(12):913–930

  29. Price RK (1985) Flood routing. In: Novak P (ed) Developments in Hydraulic Engineering. chap. 4. Elsevier, New York, pp 129–173

  30. Price RK (2009) Volume conservative non-linear flood routing. J Hydraul Eng ASCE 135(10):838–845

  31. Sahoo B (2007) Variable parameter flood routing methods for hydrological analyses of ungauged basins. Ph.D. Thesis. Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee, India

  32. Sahoo B (2013) Field application of the multilinear Muskingum discharge routing method. Water Resour Manag 27:1193–1205. doi:10.1007/s11269-012-0228-5

  33. Tang X, Knight DW, Samuels P (1999) Variable parameter Muskingum-Cunge method for flood routing in a compound channel. J Hydraul Res IAHR 37(5):591–614

  34. Todini E (2007) A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach. Hydrol Earth Syst Sci 11:1645–1659

  35. US Army Corps of Engineers (2006a) HEC-RAS river analysis system user’s manual (version 4.0 beta). Rep. CPD-68, Hydrol Eng Cent, Davis, Calif

  36. US Army Corps of Engineers (2006b) Hydrologic modeling system HEC-HMS user’s manual (version 3.1.0). Rep. CPD-74A, Hydrol Eng Cent., Davis, Calif

  37. Weinmann PE (1977) Comparison of flood routing methods for natural rivers. Report No. 2/1977, Department of Civil Engineering, Monash University, Victoria, Australia

  38. Weinmann PE, Laurenson EM (1979) Approximate flood routing methods: a review. J Hydraul Div ASCE 105(12):1521–1526

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Acknowledgments

The authors thank the Umbria Region, CNR–IRPI Office of Perugia, Italy for providing the Tiber River data.

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Correspondence to Bhabagrahi Sahoo.

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Sahoo, B., Perumal, M., Moramarco, T. et al. Rating Curve Development at Ungauged River Sites using Variable Parameter Muskingum Discharge Routing Method. Water Resour Manage 28, 3783–3800 (2014). https://doi.org/10.1007/s11269-014-0709-9

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Keywords

  • Hydrograph
  • Rating curve
  • Routing
  • Ungauged river
  • Variable parameter
  • VPMD routing method