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WinTR-20 Course February 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

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WinTR-20 Course February 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.

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WinTR-20 Course February 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

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WinTR-20 Course February Muskingum Routing Method

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WinTR-20 Course February 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

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WinTR-20 Course February 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

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

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WinTR-20 Course February 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

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WinTR-20 Course February 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

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WinTR-20 Course February 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

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WinTR-20 Course February 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

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WinTR-20 Course February 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)

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WinTR-20 Course February 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 ?

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WinTR-20 Course February Channel Cross Section Plot

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WinTR-20 Course February Channel Cross Section Rating Curve Plot

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

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WinTR-20 Course February Flood Plain Cross Section Plot

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

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

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WinTR-20 Course February 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

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WinTR-20 Course February 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

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

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

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

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

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

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

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

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WinTR-20 Course February 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)

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

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WinTR-20 Course February 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.

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WinTR-20 Course February

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WinTR-20 Course February The End The End

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