March 2009WinTR-20 Course1 Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models...

March 2009 WinTR-20 Course 1

Muskingum-Cunge Flood Muskingum-Cunge Flood Routing Procedure in NRCS Routing Procedure in NRCS Hydrologic ModelsHydrologic Models

Prepared by William Merkel

USDA-NRCS National Water Quality and Quantity Technology Development Team

Beltsville, Maryland


NRCS Hydrologic ModelsNRCS 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.


Project GoalsProject 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


Muskingum Routing MethodMuskingum Routing Method


Muskingum Routing MethodMuskingum 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


Muskingum routing equationMuskingum 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


Distance vs Time Solution GridDistance vs Time Solution Grid

X = distance, feet t = time, seconds

t

xI1 O1

I2 O2

x

t


Muskingum-Cunge MethodMuskingum-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, secondsX is a diffusion parameter, no

dimensions


Routing Coefficient - XRouting 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


Represent Rating Table by Power Represent Rating Table by Power Curve to estimate celerityCurve to estimate celerityQ = x A m and c = m Q / A

x and m are based on Xsec Q and Afor wide rectangular cross section,

m = 5/3for triangular cross section, m = 4/3for natural channels, 1.2 ~ m ~ 1.7


Routing Coefficient - KRouting 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


Data Requirements – Rating TableData Requirements – Rating Table

Elevation, feetDischarge, cubic feet / secondArea, square feetTop Width, feetFriction Slope, feet / feetReach length (channel / flood plain)


Assumptions / LimitationsAssumptions / 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 ?


Channel Cross Section PlotChannel Cross Section Plot


Channel Cross Section Rating Channel Cross Section Rating Curve PlotCurve Plot


Channel Cross Section Wave Channel Cross Section Wave Celerity versus Elevation PlotCelerity versus Elevation Plot


Flood Plain Cross Section PlotFlood Plain Cross Section Plot


Flood Plain Cross Section Rating Flood Plain Cross Section Rating Curve PlotCurve Plot


Flood Plain Cross Section Wave Flood Plain Cross Section Wave Celerity versus Elevation PlotCelerity versus Elevation Plot


Flood Routing TestsFlood Routing Tests

Compared WinTR-20 with NWS FLDWAV

Prismatic reach assumedtested variety of cross section

shapestested variety of reach lengths,

slopes, and inflow hydrographspurpose was to determine limits


Evaluation of error in peak Evaluation of error in peak dischargedischargeCompare peak discharge at end of

reachQ* = (Qpo - Qb) / (Qpi - Qb)

where: Qpi = peak inflow

Qpo = peak outflow

Qb = base flow


Results of constant coefficient Results of constant coefficient solution - channel testssolution - channel tests


Results of constant coefficient Results of constant coefficient solution - flood plain testssolution - flood plain tests


Results of constant coefficient Results of constant coefficient solution - all cross section testssolution - all cross section tests


Muskingum-Cunge WarningMuskingum-Cunge Warning

It is always recommended to view the debug file



This happens mostly on long - flat reaches



The peak inflow and peak outflow can occur at the same time.


Muskingum-Cunge WarningMuskingum-Cunge Warning Changing the

reach to a structure gives a more reasonable time shift.


Routing Meandering ChannelsRouting 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)


Bankfull and Low Ground Elev.Bankfull and Low Ground Elev.

Where bankfull and low ground elevations are different.

BankfullLow Ground


Application StrategyApplication 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.


The EndThe End

March 2009WinTR-20 Course1 Muskingum-Cunge Flood Routing Procedure in NRCS Hydrologic Models...

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