FLOOD ROUTING
Siti Kamariah Md Sa’at
School of Bioprocess Engineering,
UniMAP
Flow Routing
Q
t


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
Q
t
Q
t
Q
t
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
Types of flow routing

Lumped/hydrologic



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
Lumped flow routing

Three types
1.
Level pool method (Modified Puls)

2.
Muskingum method

3.
Storage is nonlinear function of Q
Storage is linear function of I and Q
Series of reservoir models

Storage is linear function of Q and its time
derivatives
S and Q relationships
Level pool routing

Procedure for calculating outflow
hydrograph Q(t) from a reservoir with
horizontal water surface, given its
inflow hydrograph I(t) and storageoutflow relationship
Wedge and
Prism Storage
• Positive wedge
I>Q
• Maximum S when I = Q
• Negative wedge
I<Q
Hydrologic River Flood
Routing
Basic Equation
dS
t I O
t
t
dt
Hydrologic river routing
(Muskingum Method)
Wedge storage in
reach
S Prism  KQ
S Wedge  KX ( I  Q)
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 = 0.0 - 0.3  Natural stream
S  KQ  KX ( I  Q)
Receding
Flood
Wave
Q>I
I
Q
I Q
Q
Q
I
Q
QI
S  K [ XI  (1  X )Q]
I
I
Continuity Equation in
Difference Form

Referring to figure, the continuity
equation in difference form can be
expressed as DS  S2  S1  _I  O_  (I1  I2 )  (O1  O2 )
Dt
t t
2 1
2
2
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, …
KX  0.5Dt

KX

0.5
D
t
C

where C 
;
; C2 = 1 – Co – C1
o K  KX  0.5Dt 1 K  KX  0.5Dt
Note: K and Dt must have the same unit.
Routing
Muskingum Routing
Equation
Q2  C0 I 2  C1 I1  C2Q1
Qt 1  C0 I t 1  C1 I t  C2Qt
where C’s are functions of x, K, Dt and sum to 1.0
Muskingum Equations
where
C0 = (– Kx + 0.5Dt) / D
C1 = (Kx + 0.5Dt) / D
C2 = (K – Kx – 0.5Dt) / D
D = (K – Kx + 0.5Dt)
Repeat for Q3, Q4, Q5 and so on.
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.
Example 8.4: Estimating the
value of x and K.

Try and error to get the nearly straight
line graph.
Muskingum Routing
Procedure


Given (knowns): O1; I1, I2, …; Dt; 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.

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)
Solution:

Time
(hr)
0
Inflow 10
(m3/s)
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.
6
12
18
24
30
36
42
48
54
20
50
60
55
45
35
27
20
15
Reservoir Routing
• Reservoir acts to store water
and release through control
structure later.
•
Max Storage
Inflow hydrograph
• Outflow hydrograph
• S - Q Relationship
• Outflow peaks are reduced
• Outflow timing is delayed
Inflow and Outflow
dS
I Q
dt
Inflow and Outflow
I1 + I2 – Q1 + Q2
2
2
=
S2 – S1
Dt
Inflow & Outflow Day 3
= change in storage / time
S3  S2
I 2  I 3 / 2  Q2  Q3 / 2  dt
Repeat for each day in progression
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
Q  CA 2gH for orifice flow
Q  CLH
3/2
for weir flow
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
Comparisons:
River vs.
Reservoir
Routing
Level pool reservoir
River Reach
Flood Control


Structural Measures
Non-structural Methods
Structural Measures




Storage and detention reservoir
Flood ways (new channel)
Levees (flood embankment)
Channel Improvement
Reservoirs



Reservoirs reduce flooding by temporarily
storing flood waters behind dams or in
storage or detention basins.
Reservoirs lower flood heights by holding
back, or detaining, runoff before it can flow
downstream.
Flood waters are detained until the flood has
subsided, then the water in the reservoir or
detention basin is released or pumped out
slowly at a rate that the river can
accommodate downstream.
Timah Tasoh Dam
Reservoirs


Flood control reservoirs are most commonly
built for one of two purposes. Large
reservoirs are constructed to protect property
from existing flood problems.
Smaller reservoirs, or detention basins are
built to protect property from the impacts of
new development (i.e., more runoff).
Think!
Many dams have a function for flood
management, but in some cases dams
actually make floods worse!
Flood way diversion




A diversion is a new channel that sends floodwaters
to a different location, thereby reducing flooding
along an existing watercourse.
Diversions can be surface channels, overflow weirs,
or tunnels.
During normal flows, the water stays in the old
channel.
During flood flows, the floodwaters spill over to the
diversion channel or tunnel, which carries the excess
water to a receiving lake or river.
Flood levees




Also known as dikes or flood embankments.
Probably the best known flood control
measure is a barrier of earth (levee) or
concrete (floodwall) erected between the
watercourse and the property to be protected.
Levees and floodwalls confine water to the
stream channel by raising its banks.
They must be well designed to account for
large floods, underground seepage, pumping
of internal drainage, and erosion and scour.
Flood levees
Channel/Drainage
Improvement

There are three types of drainage
improvements that are usually pursued to
reduce storm water flooding:



Channelization- straightening, deepening and/or
widening a ditch or drainage way to remedy local
drainage or flooding problems.
removing obstructions caused by stream crossings,
such as culverts and bridges with small openings constricts flows and causes localized backwater
flooding.
Drainage system maintenance to clean out blockages
caused by debris, sediment or vegetation and repair
stream bank erosion
Clearing the drainage/channel
Non-structural measures

Flood plain zoning


Flood forecast/warning



Flood forecasting system by DID and MMD, Malaysia.
Flood warning is meaningful if given in sufficient time.
Evacuation and relocation


Normal level, alert level and danger level
Evacuation of communities along their livestocks and other
valuables in the flood affected areas and relocate them to
the safer locations.
Flood insurance

Provide a mechanism for spreading the loss over large
numbers of individuals and modifies the impact of loss
burden.
Flood control in Malaysia.



In 5 month interval, 2 flood event happen
at Perlis in 2011. From your opinion, how
to control the flood from happen again.
Write your proposal.
Submit next week