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Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models

Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models. Prepared by William Merkel USDA-NRCS National Water Quality and Quantity Technology Development Team Beltsville, Maryland. NRCS Hydrologic Models. WinTR-20 Computer Program for Project Formulation - Hydrology

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Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models

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  1. Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models Prepared by William Merkel USDA-NRCS National Water Quality and Quantity Technology Development Team Beltsville, Maryland WinTR-20 Course

  2. NRCS Hydrologic Models • WinTR-20 Computer Program for Project Formulation - Hydrology • WinTR-55 Urban Hydrology for Small Watersheds • Both programs are developed for Windows and are currently available in final release versions. WinTR-20 Course

  3. Project Goals • Incorporate Muskingum-Cunge Procedure into WinTR-20 and WinTR-55 Models • Develop procedure applicable to any cross section shape • Evaluate accuracy in comparison to dynamic wave routing WinTR-20 Course

  4. Muskingum Routing Method WinTR-20 Course

  5. Muskingum Routing Method • Based on conservation of mass equation • Relates reach storage to both inflow and outflow discharges • S = K { X I + ( 1 - X) O } • K and X are determined for the individual routing reach WinTR-20 Course

  6. Muskingum routing equation • O2 = C1 I1 + C2 I2 + C3 O1 • O2 = outflow at time 2 • I1 = inflow at time 1 • I2 = inflow at time 2 • O1 = outflow at time 1 • C1, C2, C3 = routing coefficients • C1 + C2 + C3 = 1.0 WinTR-20 Course

  7. X = distance, feet t = time, seconds O2 I2 t t I1 x O1 x Distance vs Time Solution Grid WinTR-20 Course

  8. Muskingum-Cunge Method • Derived from convection-diffusion equation (simplification of full dynamic equations) • K and X determined from hydraulic properties of the reach • K is a timing parameter, seconds • X is a diffusion parameter, no dimensions WinTR-20 Course

  9. Routing Coefficient - X • X = 1/2 { 1 - [ Q / (B So c ∆x )]} • Q = discharge, cubic feet / sec • B = width of cross section, feet • So = bed or friction slope, feet / feet • c = wave celerity, feet / second • ∆x = routing distance step, feet WinTR-20 Course

  10. Represent Rating Table by Power Curve to estimate celerity • Q = x A m and c = m Q / A • x and m are based on Xsec Q and A • for wide rectangular cross section, m = 5/3 • for triangular cross section, m = 4/3 • for natural channels, 1.2 ~ m ~ 1.7 WinTR-20 Course

  11. Routing Coefficient - K • K = ∆x / c , seconds • ∆x = routing distance step, feet • Distance step is based on hydraulic properties of reach • c = wave celerity, feet / second WinTR-20 Course

  12. Data Requirements – Rating Table • Elevation, feet • Discharge, cubic feet / second • Area, square feet • Top Width, feet • Friction Slope, feet / feet • Reach length (channel / flood plain) WinTR-20 Course

  13. Assumptions / Limitations • Equations developed for wide rectangular cross sections • width is top width • celerity is 5/3 velocity using Manning equation • Q is a reference discharge • What width, celerity, and Q should be used for flood plain cross sections ? WinTR-20 Course

  14. Channel Cross Section Plot WinTR-20 Course

  15. Channel Cross Section Rating Curve Plot WinTR-20 Course

  16. Channel Cross Section Wave Celerity versus Elevation Plot WinTR-20 Course

  17. Flood Plain Cross Section Plot WinTR-20 Course

  18. Flood Plain Cross Section Rating Curve Plot WinTR-20 Course

  19. Flood Plain Cross Section Wave Celerity versus Elevation Plot WinTR-20 Course

  20. Flood Routing Tests • Compared WinTR-20 with NWS FLDWAV • Prismatic reach assumed • tested variety of cross section shapes • tested variety of reach lengths, slopes, and inflow hydrographs • purpose was to determine limits WinTR-20 Course

  21. Evaluation of error in peak discharge • Compare peak discharge at end of reach • Q* = (Qpo - Qb) / (Qpi - Qb) • where: Qpi = peak inflow • Qpo = peak outflow • Qb = base flow WinTR-20 Course

  22. Results of constant coefficient solution - channel tests WinTR-20 Course

  23. Results of constant coefficient solution - flood plain tests WinTR-20 Course

  24. Results of constant coefficient solution - all cross section tests WinTR-20 Course

  25. Muskingum-Cunge Warning • It is always recommended to view the debug file WinTR-20 Course

  26. Muskingum-Cunge Warning • This happens mostly on long - flat reaches WinTR-20 Course

  27. Muskingum-Cunge Warning • The peak inflow and peak outflow can occur at the same time. WinTR-20 Course

  28. Muskingum-Cunge Warning • Changing the reach to a structure gives a more reasonable time shift. WinTR-20 Course

  29. Routing Meandering Channels • Channel and Flood Plain reach lengths may be different • Low ground elevation is dividing point of channel and flood plain flow • Flow area is adjusted (usually decreased) above the low ground elevation • Adjusted rating table may be viewed in debug output file (select Cross Section Rating Table) WinTR-20 Course

  30. Low Ground Bankfull Bankfull and Low Ground Elev. • Where bankfull and low ground elevations are different. WinTR-20 Course

  31. Application Strategy • Select one cross section to represent the WinTR-20 reach. • The velocity is the key factor to look at. • Picking a cross section with an average velocity will give reasonable results. • A computer program is being developed to derive an average rating from a group of HEC-RAS cross sections. WinTR-20 Course

  32. WinTR-20 Course

  33. The End WinTR-20 Course

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