1. Flood Routing Applied Hydrology

2. Flow Routing
Channel Routing
Reservoir Routing

3. Routing
Routing is the process of predicting temporal and spatial variation of a flood wave as it travels through a river (or channel reach or reservoir.
Two types of routing can be performed:
Hydrologic Routing
Hydraulic Routing

4. Hydrologic Routing
In hydrologic routing techniques, the equation of continuity and some linear or curvilinear relation between storage and discharge within the river or reservoir is used.
Applications of routing techniques:
Flood predictions
Evaluation of flood control measures
Assessment of effects of urbanization
Flood warning
Spillway design for dams

5. Hydrologic Routing Continuity Equation: Where I = Inflow O= Outflow
DS/Dt = Rate of change of storage
Problem:
You have a hydrograph at one location (I)
You have river characteristics (S=f(I,O))
Need:
A hydrograph at different location (O)

6. Hydrologic Routing Hydrograph at point A Hydrograph at point B
The hydrograph at B is attenuated due to storage characteristics of the stream reach.
Assumption: no seepage, leakage, evaporation, or inflow from the sides.

7. Hydrologic Channel Routing
Muskingum Method:
Flow in a channel
wedge
prism
wedge
prism
prism
Storage in wedge: KX(I-O)
Storage in prism: KO
So, Storage S=KX(I-O)+KO

8. Muskingum Method Storage S=KO+KX(I-O) rewritten as S=K[XI+(1-X)O]
Where
S = Storage in the river reach
K = Storage time constant (T)
X = A weighting factor that varies between 0 and 0.5 (defines relative importance of inflow and outflow on storage)
If X=0.5 pure translation, if X=0 max attenuation

9. Muskingum Method How it works: Write continuity equation as Where
I = Average inflow during Dt
O= Average outflow during Dt or

10. Muskingum Method Combine and rearrange
Simplified into the routing equation:
Subscript 1 refers to t1and 2 to t2 = (t+Dt)

11. Muskingum Method
Need K and Dt in the same units

12. Estimation of K, X and Dt K=0.6L/vavg Where L = Length of river reach
Vavg = Average velocity in reach
Constraint K<tp/5 (divide reach up if needed)
X = 0.2 for most cases
X = 0.4 for steep channels with narrow flood plains
X = 0.1 for mild channels with broad flood plains
2KX<Dt<2K(1-X) and ideally Dt<tp/5. Choose Dt in numbers that divide into 24 (Daily data)

13. Example 1 Tp = 4 hr, L = 2 mi, vavg = 2.5 ft/s, wide flat floodplain
Solution:
K = 0.6L/vavg = 0.6(2x5280)/2.5=2,534 sec = 0.7 hr
X = 0.1
Dt:
2KX = 2(0.7)0.1 = 0.14
2K(1-X) = 2(0.7)0.9 = 1.26
0.14<Dt<1.26 and Dt<tp/5 or Dt<0.8 hr,
so Dt = 0.5 hr is most accurate.

14. Channel Routing in spreadsheet
Example 2
Channel Routing in spreadsheet

15. Reservoir Routing Storage-Indication Method:
Apply the storage-indication method for reservoirs that have a spillway.
Assume that storage (S)=0 when no overflow occurs (surcharge storage).
Apply this to an ungated spillway like a weir, outlet discharge pipe, or gated spillway with fixed position.

16. Reservoir Routing
Use a relationship between outflow (O) and elevation head (H). For example, for a broad crested weir:
Q=CLH3/2
Where
O = Discharge at the outlet (cfs)
C = Discharge coefficient of weir (cfs)
L = Length of crest (ft)
H = Depth above spillway (ft)

17. Reservoir Routing Two relationships specific for reservoir:
Storage-Head Relationship
Outflow-Head Relationship
Need:
An inflow hydrograph
A starting elevation above spillway

18. Reservoir Routing Use the continuity equation as: Where
I = Average inflow during Dt
O = Average outflow during Dt Or
Where subscripts denote the time interval

19. Reservoir Routing
For i=1, we know Ii and Ii+1 (Initially) and Si (Initially)
We do not know Oi+1 and Si+1
So, we rewrite “Knowns = Unknowns”

20. Reservoir Routing
We can find Oi+1, if we have a relationship between term on RHS and O. This is possible using the so-called Storage-Indication Curve.

21. Routing Steps Set i=1, obtain initial head and inflow hydrograph.
Find initial outflow O1 corresponding to initial head above spillway.
Find 2S/Dt for S(H) relationship.
From the continuity equation, calculate
Enter storage-indication curve to find O2.
Calculate
Change i=2
From continuity equation, calculate
Repeat steps 4-7, and so on…..

22. Reservoir Routing in spreadsheet
Example 3
Reservoir Routing in spreadsheet