1. WinTR-20 Course February 20151 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

2. WinTR-20 Course February 20152 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.

3. WinTR-20 Course February 20153 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

4. WinTR-20 Course February 20154 Muskingum Routing Method

5. WinTR-20 Course February 20155 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

6. WinTR-20 Course February 20156 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

7. WinTR-20 Course February 20157 Distance vs Time Solution Grid X = distance, feet t = time, seconds t x I1 O1 I2 O2 x t

8. WinTR-20 Course February 20158 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

9. WinTR-20 Course February 20159 Routing Coefficient - X X = 1/2 { 1 - [ Q / (B S o c ∆x )]} –Q = discharge, cubic feet / sec –B = width of cross section, feet –S o = bed or friction slope, feet / feet –c = wave celerity, feet / second –∆x = routing distance step, feet

10. WinTR-20 Course February 201510 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

11. WinTR-20 Course February 201511 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

12. WinTR-20 Course February 201512 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)

13. WinTR-20 Course February 201513 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 ?

14. WinTR-20 Course February 201514 Channel Cross Section Plot

15. WinTR-20 Course February 201515 Channel Cross Section Rating Curve Plot

16. WinTR-20 Course February 201516 Channel Cross Section Wave Celerity versus Elevation Plot

17. WinTR-20 Course February 201517 Flood Plain Cross Section Plot

18. WinTR-20 Course February 201518 Flood Plain Cross Section Rating Curve Plot

19. WinTR-20 Course February 201519 Flood Plain Cross Section Wave Celerity versus Elevation Plot

20. WinTR-20 Course February 201520 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

21. WinTR-20 Course February 201521 Evaluation of error in peak discharge Compare peak discharge at end of reach Q* = (Q po - Q b ) / (Q pi - Q b ) where: Q pi = peak inflow Q po = peak outflow Q b = base flow

22. WinTR-20 Course February 201522 Results of constant coefficient solution - channel tests

23. WinTR-20 Course February 201523 Results of constant coefficient solution - flood plain tests

24. WinTR-20 Course February 201524 Results of constant coefficient solution - all cross section tests

25. WinTR-20 Course February 201525 Muskingum-Cunge Warning It is always recommended to view the debug file

26. WinTR-20 Course February 201526 Muskingum-Cunge Warning This happens mostly on long - flat reaches

27. WinTR-20 Course February 201527 Muskingum-Cunge Warning The peak inflow and peak outflow can occur at the same time.

28. WinTR-20 Course February 201528 Muskingum-Cunge Warning Changing the reach to a structure gives a more reasonable time shift.

29. WinTR-20 Course February 201529 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)

30. WinTR-20 Course February 201530 Bankfull and Low Ground Elev. Where bankfull and low ground elevations are different. Bankfull Low Ground

31. WinTR-20 Course February 201531 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.

32. WinTR-20 Course February 201532

33. WinTR-20 Course February 201533 The End The End