1. Flood Routing definitions
lag
Q(t)
Peak flow attenuation
Inflow at x
Outflow at x+Dx
Recession limb
Rising limb tp
time
c Dt x
time t
time t+Dt

2. Flood Routing methods Hydraulic Hydrologic
Uses both dynamic and continuity equations
Allows backwater effects to be modelled
Solution advanced by timestep Dt
Hydrologic
Uses only continuity equation
Cannot model backwater effects
Solution advanced downstream by Dx

3. Kinematic Wave Equation
Continuity with no lateral inflow yields: Q
Q+Q x
t+ t t A
For quasi-uniform flow:
Substitute and separate variables to get wave eq. or
where c = dQ/dA is wave celerity

4. Space-Time Coordinates
Time t
a Dx
Flow Q4 unknown 3 8 4 5 6
Nucleus Dt
b Dt 1 7 2 Dx
Distance x

5. Continuity Around the Nucleus8 7 6 5 4 3 2 1
bdt
adx

6. Generalized Muskingum equation
Let
and get Q4=f(Q1 , Q2 , Q3)
Collecting terms,
Setting b = 0.5 yields
where

7. Deriving the Diffusion equation
Non-centered finite difference scheme creates a numerical error or
Convert the Wave equation to a Diffusion equation
Diffusion coefficient is related to channel conveyance

8. Determine weighting coefficients
Compare the two equations for the diffusion coeff. D
f(a,b,D)=0 leads to multiple sets of (a,b) coordinates for any value of D.

9. Numerical Stability Criteria
Condition for numerical stability is
Unstable

10. Limits for Dx and Dt For b = 0.5 and From parts 1 & 2 or
For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N = 2,3,4...

11. Limits for Dx and Dt For b = 0.5 and From parts 1 & 2 or
For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N=2,3,4...
From parts 2 & 3 or
For very short channels, use routing time-step equal to sub-multiple of hydrology time step, dt=Dt/N, N=2,3,4...

12. MIDUSS 98 Route Command

13. MIDUSS 98 Route Command Details of last conduit design are displayed
Estimated values of weighting coefficients
User can change computed X or K values
Changes to Dx or Dt reported for information

14. Results of Route command

15. Calculating celerity