March 2009WinTR-20 Course1 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

March 2009WinTR-20 Course2 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.

March 2009WinTR-20 Course3 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

March 2009WinTR-20 Course4 Muskingum Routing Method

March 2009WinTR-20 Course5 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

March 2009WinTR-20 Course6 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

March 2009WinTR-20 Course7 Distance vs Time Solution Grid X = distance, feet t = time, seconds t x I1 O1 I2 O2 x t

March 2009WinTR-20 Course8 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

March 2009WinTR-20 Course9 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

March 2009WinTR-20 Course10 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

March 2009WinTR-20 Course11 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

March 2009WinTR-20 Course12 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)

March 2009WinTR-20 Course13 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 ?

March 2009WinTR-20 Course14 Channel Cross Section Plot

March 2009WinTR-20 Course15 Channel Cross Section Rating Curve Plot

March 2009WinTR-20 Course16 Channel Cross Section Wave Celerity versus Elevation Plot

March 2009WinTR-20 Course17 Flood Plain Cross Section Plot

March 2009WinTR-20 Course18 Flood Plain Cross Section Rating Curve Plot

March 2009WinTR-20 Course19 Flood Plain Cross Section Wave Celerity versus Elevation Plot

March 2009WinTR-20 Course20 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

March 2009WinTR-20 Course21 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

March 2009WinTR-20 Course22 Results of constant coefficient solution - channel tests

March 2009WinTR-20 Course23 Results of constant coefficient solution - flood plain tests

March 2009WinTR-20 Course24 Results of constant coefficient solution - all cross section tests

March 2009WinTR-20 Course25 Muskingum-Cunge Warning It is always recommended to view the debug file

March 2009WinTR-20 Course26 Muskingum-Cunge Warning This happens mostly on long - flat reaches

March 2009WinTR-20 Course27 Muskingum-Cunge Warning The peak inflow and peak outflow can occur at the same time.

March 2009WinTR-20 Course28 Muskingum-Cunge Warning Changing the reach to a structure gives a more reasonable time shift.

March 2009WinTR-20 Course29 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)

March 2009WinTR-20 Course30 Bankfull and Low Ground Elev. Where bankfull and low ground elevations are different. Bankfull Low Ground

March 2009WinTR-20 Course31 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.

March 2009WinTR-20 Course32

March 2009WinTR-20 Course33 The End The End