1. ERT 246 Hydrology & Water Resources Eng.
FLOOD ROUTING
ERT 246 Hydrology & Water Resources Eng.

2. Flow Routing Q t Q
Procedure to determine the flow hydrograph at a point on a watershed from a known hydrograph upstream
As the hydrograph travels, it
attenuates
gets delayed t Q t Q t

3. Why route flows? Q t
Account for changes in flow hydrograph as a flood wave passes downstream
This helps in
Calculate for storages
Studying the attenuation of flood peaks

4. Types of flow routing Lumped/hydrologic Distributed/hydraulic
Flow is calculated as a function of time alone at a particular location
Governed by continuity equation and flow/storage relationship
Distributed/hydraulic
Flow is calculated as a function of space and time throughout the system
Governed by continuity and momentum equations

5. Lumped flow routing Three types Level pool method (Modified Puls)
Storage is nonlinear function of Q
Muskingum method
Storage is linear function of I and Q
Series of reservoir models
Storage is linear function of Q and its time derivatives

6. S and Q relationships

7. Level pool routing
Procedure for calculating outflow hydrograph Q(t) from a reservoir with horizontal water surface, given its inflow hydrograph I(t) and storage-outflow relationship

8. Wedge and Prism Storage
Positive wedge I > Q
Maximum S when I = Q
Negative wedge I < Q

9. Hydrologic River Flood Routing
Basic Equation

10. Hydrologic river routing (Muskingum Method)
Wedge storage in reach
Advancing
Flood
Wave
I > Q
K = travel time of peak through the reach
X = weight on inflow versus outflow (0 ≤ X ≤ 0.5)
X = 0  Reservoir, storage depends on outflow, no wedge
X =  Natural stream
Receding
Flood
Wave
Q > I

11. Continuity Equation in Difference Form
Referring to figure, the continuity equation in difference form can be expressed as 2 ) O 1 (O I (I _ t S + - = D

12. Derivation of Muskingum Routing Equation
By Muskingum Model,
at t = t2, S2 = K [X I2 + (1 - X)O2]
at t = t1, S1 = K [X I1 + (1 - X)O1]
Substituting S1, S2 into the continuity equation and after some algebraic manipulations, one has
O2 = Co I2 + C1 I1 + C2 O1
Replacing subscript 2 by t +1 and 1 by t, the Muskingum routing equation is
Ot+1 = Co It+1 + C1 It + C2 Ot, for t = 1, 2, …
where ; ; C2 = 1 – Co – C1
Note: K and t must have the same unit.
Routing

13. Muskingum Routing Equation
where C’s are functions of x, K, Dt and sum to 1.0

14. Muskingum Equations where C0 = (– Kx + 0.5Dt) / D
C2 = (K – Kx – 0.5Dt) / D
D = (K – Kx + 0.5Dt)
Repeat for Q3, Q4, Q5 and so on.

15. Estimating Muskingum Parameters, K and x
Graphical Method:
Referring to the Muskingum Model, find X such that the plot of XIt+ (1-X)Ot (m3/s) vs St (m3/s.h) behaves almost nearly as a single value curve. The assume value of x lies between 0 and 0.3.
The corresponding slope is K.

16. Example 8.4: Estimating the value of x and K.
Try and error to get the nearly straight line graph.

17. Muskingum Routing Procedure
Given (knowns): O1; I1, I2, …; t; K; X
Find (unknowns): O2, O3, O4, …
Procedure:
(a) Calculate Co, C1, and C2
(b) Apply Ot+1 = Co It+1 + C1 It + C2 Ot starting from t=1, 2, … recursively.

18. Example 8.5 Given K and x. Initial outflow, Q also given. Solution:
Calculate Co, C1, and C2
C0 = (– Kx + 0.5Dt)/ D
C1 = (Kx + 0.5Dt)/ D
C2 = (K – Kx – 0.5Dt)/ D
D = (K – Kx + 0.5Dt)

19. Solution:
Route the following flood hydrograph through a river reach for which K=12.0hr and X=0.20. At the start of the inflow flood, the outflow flood, the outflow discharge is 10 m3/s.
Time (hr) 6 12 18 24 30 36 42 48 54
Inflow (m3/s) 10 20 50 60 55 45 35 27 15

20. Reservoir Routing
Reservoir acts to store water and release through control structure later.
Inflow hydrograph
Outflow hydrograph
S - Q Relationship
Outflow peaks are reduced
Outflow timing is delayed
Max Storage

21. Inflow and Outflow

22. Inflow and Outflow
I1 + I2 – Q1 + Q S2 – S1 = 2 2 Dt

23. Inflow & Outflow Day 3 = change in storage / time
Repeat for each day in progression

24. Determining Storage Evaluate surface area at several different depths
Use available topographic maps or GIS based DEM sources (digital elevation map)
Outflow Q can be computed as function of depth for either pipes, orifices, or weirs or combinations

25. Typical Storage -Outflow
Plot of Storage in vs. Outflow in Storage is largely a function of topography
Outflows can be computed as function of elevation for either pipes or weirs
Combined S
Pipe Q

26. Comparisons: River vs. Reservoir Routing
Level pool reservoir
River Reach

27. Flood Control
Structural Measures
Non-structural Methods