MuskingumCunge Flood Routing Procedure in NRCS Hydrologic Models

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

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.

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

4
Muskingum Routing Method
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

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

7
Distance vs Time Solution Grid

• X distance, feet
• t time, seconds

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

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

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

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

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)

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 ?

14
Channel Cross Section Plot
15
Channel Cross Section Rating Curve Plot
16
Channel Cross Section Wave Celerity versus
Elevation Plot
17
Flood Plain Cross Section Plot
18
Flood Plain Cross Section Rating Curve Plot
19
Flood Plain Cross Section Wave Celerity versus
Elevation Plot
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

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

22
Results of constant coefficient solution -
channel tests
23
Results of constant coefficient solution - flood
plain tests
24
Results of constant coefficient solution - all
cross section tests
25
Muskingum-Cunge Warning

• It is always recommended to view the debug file

26
Muskingum-Cunge Warning

• This happens mostly on long - flat reaches

27
Muskingum-Cunge Warning

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

28
Muskingum-Cunge Warning

• Changing the reach to a structure gives a more
  reasonable time shift.

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)

30
Bankfull and Low Ground Elev.

• Where bankfull and low ground elevations are
  different.

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.

32
(No Transcript)
33
The End