Flood Routing
Applied Hydrology
Flow Routing
Channel Routing
Reservoir Routing
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
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
Hydrologic Routing
Continuity Equation:
Where
IO 
DS
Dt
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)
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.
Hydrologic Channel Routing
Muskingum Method:
wedge
Flow in a channel
prism
wedge
prism
prism
Storage in wedge:
KX(I-O)
Storage in prism:
KO
So, Storage
S=KX(I-O)+KO
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
Muskingum Method
How it works:
Write continuity equation as
Where
I = Average inflow during Dt
O= Average outflow during Dt
or
I1  I2 O1  O2 S2  S1


2
2
Dt
I O 
DS
Dt
Muskingum Method
I1  I2 O1  O2 S2  S1


2
2
Dt
S  k[XI  (1 X)O]
Combine and rearrange
I1  I2 O1  O2 K

 [X(I2  I1)  (1 X)(O2  O1)]
2
2
Dt
Simplified into the routing equation:
O2  C0I2  C11
I  C2I0
Subscript 1 refers to t1and 2 to t2 = (t+Dt)
Muskingum Method
C0  C1  C2  1
Need K and Dt in the
same units
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)
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.
Example 2
Channel Routing in spreadsheet
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.
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)
Reservoir Routing
Two relationships specific for reservoir:
• Storage-Head Relationship
• Outflow-Head Relationship
Need:
• An inflow hydrograph
• A starting elevation above spillway
Reservoir Routing
Use the continuity equation as:
I O 
DS
Dt
Where
I = Average inflow during Dt
O = Average outflow during Dt
Or
Ii  Ii 1 Oi  Oi 1 Si 1  Si


2
2
Dt
Where subscripts denote the time interval
Reservoir Routing
Ii  Ii 1 Oi  Oi 1 Si 1  Si


2
2
Dt
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”
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.
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
2S2
 O2
Dt
Enter storage-indication curve to find O2.
Calculate
2S2
2S
 O2  [ 2  O2 ]  2O2
Dt
Dt
Change i=2
From continuity equation, calculate
Repeat steps 4-7, and so on…..
2S3
 O3
Dt
Example 3
Reservoir Routing in spreadsheet