3. Submitted to
Dr. Ahmad Hasan Nury
Associate Professor
Department of Civil and Environmental Engineering
Shahjalal University of Science and Technology, Sylhet
4. Introduction
In the realm of hydrology, routing stands as a crucial technique employed to anticipate the dynamic
alterations in a hydrograph's form as water traverses through a river channel or reservoir. At the heart
of this hydrological process lies flood routing, a method designed to ascertain the timing and intensity
of a flood wave at a specific point along a stream. This determination is derived from the available or
assumed data at one or more upstream points. Flood routing becomes indispensable in addressing
various challenges, including flood forecasting, reservoir and spillway design, and flood protection
measures.Two broad categories encapsulate flood routing methods: hydrologic and hydraulic
approaches. These methods find applications in reservoir routing and channel routing, each playing a
pivotal role in different facets of water management. The nuanced formulations and techniques
associated with these methods are explored in detail below.
5. Basic Equations
Continuity equation, used in all hydrologic routing as the primary equation states that the difference
between the inflow and outflow rate is equal to the rate of change of storage.
π =
ππ
ππ‘
(1)
Where, I = inflow rate, Q = outflow rate and S = storage. Alternatively, in a small-time interval Dt the
difference between the total inflow volume and total outflow volume in a reach is equal to the change
in storage in that reach.
πΌβπ‘ β ππ₯π‘ = βπ (2)
Where I = average inflow in time Dt, Q = average outflow in time Dt and DS = change in storage. By
taking πΌ = (I1 + I2)/2, Q = (Q1 + Q2)/2 and βπ = S2 β S1 with suffixes 1 and 2 to denote the beginning
and end of time interval βt, Eq. (2) is written as
πΌ1+πΌ2
2
βπ‘ β
π1+π2
2
βπ‘ = π2 β π1 (3)
6. Basic Equations
The time interval Dt should be sufficiently short so that the inflow and outflow hydrographs can be
assumed to be straight lines in that time interval.
In the differential form the equation of continuity for unsteady flow in a reach with no lateral flow is
given by,
ππ
ππ₯
+ π
ππ¦
ππ‘
= 0 (4)
where T = top width of the section and y = depth of flow.
The equation of motion for a flood wave is derived from the application of the momentum equation
as,
ππ¦
ππ₯
+
π
π
ππ
ππ₯
+
1
π
ππ
ππ‘
= π 0 β π π (5)
where V = velocity of flow at any section, S0= channel bed slope and Sf = slope of the energy line.
7. Hydrologic Storage Routing
Hydrologic routing emerges as a methodology rooted in the principles of mass conservation and the
interplay between storage and discharge within a defined stretch of a stream or reservoir. This method
comes into play when a flood wave, denoted as I(t), enters a reservoir equipped with an outlet,
typically a spillway. The outlet's behavior is contingent solely upon the reservoir's elevation,
expressed as Q = Q(h). Simultaneously, the reservoir's storage is intricately tied to its elevation,
denoted as S = S(h)
Figure 8.1: Storage Routing (Schematic)
t
q
h
t
S
t
outflow
Q = Q(h)
Reservoir
S = S(h)
Inflow
I = I (t)
I
t
8. Hydrologic Storage Routing
If an uncontrolled spillway is provided in a reservoir, typically
π =
2
3
Cd 2π
Leπ»
3
2
= π(β)
Where, H = head over the spillway
Le = Effective length of the spillway crest, and
Cd = Coefficient of discharge
Similarly, for other forms of outlets, such as gated spillways, sluice gates, etc. other relation for Q(h) will be available.
For reservoir routing, the following data have to be known. Graphs or tables showing
β’ Storage volume vs elevation for the reservoir.
β’ Water-surface elevation vs outflow and hence storage vs outflow discharge
β’ Inflow hydrograph, I = I(t), and
β’ Initial Values of S, I and Q at time t=0.
9. Methods available for routing of floods
There are a variety of methods available for routing of floods through a reservoir. All of
them is based of basic equation of inflow and outflow.
There are two commonly used semi-graphical methods and a numerical method available
for routing the flood.
β’ Modified Pulβs Method.
β’ Goodrich Method.
10. Fig. 8.2 Modified Pul's method of storage routing
Equation (8.3) is rearranged as
πΌ1+πΌ2
2
βπ‘ + π1 β
π1βπ‘
2
= π2 +
π2βπ‘
2
(8.6)
At the starting of flood routing, the initial storage and outflow discharges are
known. In Eq. (8.6) all the terms in the left-hand side arc known at the
beginning of a time step βt. Hence, the value of the function π2 +
π2βπ‘
2
at
the end of the time step is calculated by Eq. (8.6). Since the relation S=S(h)
and Q =Q(h) are known, π +
πβπ‘
2 2
will enable one to determine the
reservoir elevation and hence the discharge at the end of the time step. The
procedure is repeated to cover the full inflow hydrograph.
Modified Pulβs Method
11. Modified Pulβs Method
For practical use in hand computation, the following semi graphical method is very convenient.
1. From the known storage-elevation and discharge-elevation data, prepare a curve of π +
πβπ‘
2
vs
elevation (Fig. 8.2). Here βπ‘ is any chosen interval, approximately 20 to 40% of the time of rise of the
inflow hydrograph.
2. On the same plot prepare a curve of outflow discharge vs elevation (Fig. 8.2).
3. The storage, elevation and outflow discharge at the starting of routing are known. For the first time
interval βπ‘,
πΌ1+πΌ2
2
βπ‘ and π1 +
π1βπ‘
2
are known and hence by Eq. (8.6) the term π2 +
π2βπ‘
2
is
determined.
4. the water-surface elevation corresponding to π2 +
π2βπ‘
2
is found by using the plot of step (1). The
outflow discharge π2, at the end of the time step βπ‘ is found from plot of step (2).
5. Deducting π2βπ‘, from π2 +
π2βπ‘
2
gives for the beginning of the next time step.
6. The procedure is repeated till the entire inflow hydrograph is routed.
12. Problem
Example 8.1
A reservoir has the following elevation
discharge and storage relationships:
Elevation
(m)
Storage
(106 m3)
Outflow
discharge (m3/s)
100.00 3.350 0
100.50 3.472 10
101.00 3.380 26
101.50 4.383 46
102.00 4.882 72
102.50 5.370 100
102.75 5.527 116
103.00 5.856 130
Time(h) 0 6 12 18 24 30 36 42 48 54 60 66 72
Discharge
(m3/s)
10 20 55 80 73 58 46 36 55 20 15 13 11
When the reservoir level was at 100.50 m, the following
hydrograph entered the reservoir
Route the flood and obtain (i) the outflow hydrograph, and (ii)
the reservoir elevation vs time curve during the passage of the
flood wave.
13. Solution
β’ A time interval βt =6 h is chosen from the available data elevation-discharge β
π +
ππ₯π‘
2
table is prepared.
Elevation (m) 100 10050 101 10150 102 10250 10275 103
Discharge Q
(m3/s)
0 10 26 46 72 100 116 130
π +
ππ₯π‘
2
(Mm3)
3.35 3.58 4.16 4.88 5.66 6.45 6.78 7.26
14. Solution
Graph of Q vs elevation and π +
ππ₯π‘
2
vs elevation is prepared. At the start of routing elevation =
100.50 m, Q = 10 m3/s and π β
ππ₯π‘
2
=3.362 Mm3. Starting from this value of π +
ππ₯π‘
2
equation of
modified Pul's method is used to get π +
ππ₯π‘
2
at the end of first-time step of 6 h as
π +
ππ₯π‘
2 2
= πΌ1 + πΌ2
π₯π‘
2
+ π +
ππ₯π‘
2 1
= (10+20) Γ
0.0216
2
+ (3.362)
= 3.686 Mm3
15. Solution
Looking up in the figure the water surface elevation
corresponding to π +
ππ₯π‘
2
= 3.686 Mm3 is 100.62 m and
the corresponding outflow discharge Q is 13 m3/s. For the next
step, initial value of
π β
ππ₯π‘
2
= π +
ππ₯π‘
2
of the previous step - Q βt
= 3.686-13Γ0.0216
= 3.405Mm3
The process is repeated for the entire duration of the inflow
hydrograph in a tabular form. Using the data in columns 1, 8
and 7, the outflow hydrograph and a graph showing the
variation of reservoir elevation with time are prepared.
Sometimes a graph of π β
ππ₯π‘
2
vs elevation prepared from
known data is plotted
Figure 8.3: Variation of Inflow and Outflow Discharges-Example-8.1
18. Goodrich Method
This method is used for hydrologic reservoir routing, known as Goodrich method.
πΌ1 + πΌ2 β π1 β π2 =
2π2
βπ‘
β
2π1
π₯π‘
where suffixes 1 and 2 stand for the values at the beginning and end of a time step βt respectively.
Collecting the known and initial values together,
(πΌ1+πΌ2) +
2π1
π₯π‘
β π1 =
2π2
βπ‘
+ π2 (1)
For a given time step, the left-hand side of Eq. (1) is known and the term (
2π2
βπ‘
+ π2)is determined by
using Eq. (1). From the known storage-elevation-discharge data, the function (
2π2
βπ‘
+ π2)is established as a
function of elevation. Hence, the discharge, elevation and storage at the end of the time step are
obtained. For the next time step,
[(
2π2
βπ‘
+ π2 β 2π2)] of the previous time step =
2π1
π₯π‘
β π1 for use as the initial values.
19. Attenuation
Illustrations provided in Figures 3 and 8.6 (Refer to Page 350 of the recommended book) offer a
glimpse into the outcomes of routing a flood hydrograph through a reservoir. The storage effect
manifests itself, influencing the dynamics of the outflow hydrograph, notably diminishing its peak in
comparison to the inflow hydrograph. This reduction in peak value is formally termed "attenuation."
Moreover, a temporal shift unfolds in the timing of the peaksβ the peak of the outflow follows that
of the inflow, and this temporal gap is recognized as "lag." The interplay of attenuation and lag
assumes paramount significance when a reservoir operates under a flood-control criterion. Strategic
management of the initial reservoir level during the arrival of a critical flood can lead to significant
attenuation of the floods. The reservoir's storage capacity, coupled with the characteristics of
spillways and other outlets, exerts control over both the lag and attenuation observed in an inflow
hydrograph. Within the rising segment of the outflow curve, where the inflow surpasses the outflow,
the area between the curves signifies flow accumulation as storage. Conversely, in the declining
portion of the outflow curve, where the outflow exceeds the inflow, the area between the curves
denotes depletion from storage. In instances where the outflow from a storage reservoir is
uncontrolled, as observed in freely operating spillways, the peak of the outflow hydrograph aligns
with the intersection point of the inflow and outflow curves in Figures 3 and 8.6 (Refer to Page 350
of the recommended book).
20. Hydrologic channel
routing
In reservoir routing presented in the previous sections, the storage
Was a unique function of the outflow discharge, S =f(Q). However,
in channel routing the storage is a function of both outflow and
inflow discharges and hence a different routing method is needed.
The flow in a river during a flood belongs to the category of
gradually varied unsteady flow. The water surface in a channel reach
is not only not parallel to the channel bottom but also varies with
time (Fig. 8.7). Considering a channel reach having a flood flow, the
total volume in storage can be considered under two categories as-
β’ Prism storage
β’ Wedge storage
Figure: Storage in a channel reach
21. Hydrologic Channel Routing (cont.)
PRISM STORAGE
It is the volume that would exist if the uniform flow occurred at the downstream depth, i.e., the volume formed
by an imaginary plane parallel t0 the channel bottom drawn at the outflow section water surface.
WEDGE STORAGE
It is the wedge -like volume formed between the actual water surface profile and the top surface of the prism
storage.
At a fixed depth at a downstream section of a river reach, the prism storage is constant while the wedge storage
changes from a positive value at an advancing flood to a negative value during a receding flood. The prism
storage SP is like a reservoir and can be expressed as a function of the outflow discharge, SP = f(Q). The wedge
storage can be accounted for by expressing it as SW = f(I). The total storage in the channel reach can then be
expressed as
S = K [xIm +(1 - x)ππ]
where K and x arc coefficients and m = a constant exponent. It has been found that the value of m varies from
0.6 for rectangular channels to a value of about 1.0 for natural channels.
22. Muskingum Equation
Using m = 1.0, the previous equation reduces to a linear relationship for S in terms of I and Q as,
S = K [xI +(1-x) Q]
This relationship is known as Muskingum Equation.
x = weighting factor. (Takes values between 0 and 0.5)
If x = 0, the storage is a function of discharge only.
S = KQ
This type of storage is a linear storage or linear reservoir.
If x = 0.5, Both inflow and outflow are equally important is determining the storage.
The co-efficient of K is known as storage-time constant and has the dimensions of time. It is
approximately equal to the time of travel of a flood wave through the channel reach.
23. Estimation of K and x
The figure shows a typical inflow and outflow hydrograph through a
channel reach. The outflow peak doesnβt occur tat the point of intersection.
From the continuity equation:
πΌ1 + πΌ2
βπ‘
2
β π1 + π2
βπ‘
2
= βπ
The increment in storage at any time t and time element βπ‘ can be
calculated. Summation of the various incremental storage values give us the
channel storage S vs. time t relationship graph.
With the set of inflow and outflow hydrographs available for a given reach,
values of S at various time intervals can be determined. For any trial value
of x, value of S at any time t are plotted again the corresponding values.
If the chosen x value is correct, it will give a straight-line relationship.
Where if the chosen x value is incorrect, then it will give a looping curve. So,
by trial and error, the correct value of x is chosen. The inverse slope of the
straight line gives the value of K.
24. Problem
Example-8.4
The following inflow and outflow hydrographs were observed in a river reach. Estimate the values of
K an x applicable to this reach for use in Muskinghum equation
Time (h) 0 6 12 18 24 30 36 42 48 54 60 66
Inflow
(m3/s)
5 20 50 50 32 22 15 10 7 5 5 5
Outflow
(m3/s)
5 6 12 29 38 35 29 23 17 13 9 7
25. Solution
Using a time increment of 6 hr (βπ‘ = 6) the
calculations are performed in a table.
Three values of x were used for trial. For x= 30 a
looped curve is obtained. Hence another trial is
done with x = 35 and lastly x=25. For x = 25, the
graph become nearly a straight line. So, x = 25 is
taken as the appropriate value for the reach.
So, K = 13.3 h
27. Muskingum Method of Routing
For a given channel reach by selecting a routing interval Ξt and using the Muskingum equation, the change in storage is
π2 β π1 = πΎ π₯ πΌ2 β πΌ1 + (1 β π₯)(π2 β π1) β¦β¦β¦(i)
Where suffixes 1 and 2 refer to the conditions before and after the time interval Ξt. The continuity equation for the reach is
π2 β π1 =
πΌ2+πΌ1
2
βπ‘ β (
π2+π1
2
)βπ‘β¦β¦β¦(ii)
From equation (i) and (ii), Q2 is evaluated as
π2 = πΆ0πΌ2 + πΆ1πΌ1 + πΆ2π1β¦β¦..(iii)
Where,
πΆ0 =
βπΎπ₯+0.5βπ‘
πΎβπΎπ₯+0.5βπ‘
β¦β¦β¦(iii-a)
πΆ1 =
πΎπ₯+0.5βπ‘
πΎβπΎπ₯+0.5βπ‘
β¦β¦β¦(iii-b)
πΆ2 =
πΎβπΎπ₯β0.5βπ‘
πΎβπΎπ₯+0.5βπ‘
β¦β¦β¦(iii-c)
Note that πΆ0 + πΆ1 + πΆ2 = 1.0, equation (iii) can be written in a general form for the nth time step as
ππ = πΆ0πΌπ + πΆ1πΌπβ1 + πΆ2ππβ1
28. Muskingum Method of Routing
To use the Muskingum equation to route a given inflow hydrograph through a reach, the
values of K and x for the reach and the value of outflow, Q1, from the reach at the start are
needed. The procedure is indeed simple.
β’ Knowing K and x, select appropriate value of Ξt
β’ Calculate C0, C1 and C2
β’ Starting from the initial conditions I1, Q1 and known I2 at the end of the first-time step Ξt
calculate Q2 by equation (iii).
β’ The outflow calculated in step-c becomes the known initial outflow for the next time step.
Repeat the calculations for the entire inflow hydrograph.
The calculations are best done row by row in a tabular form. Example-8.5 illustrates the
computation procedure. Spread sheet (such as MS Excel) is ideally suited to perform the
routing calculations and to view the inflow and outflow hydrographs.
29. Problem
Example-8.5
Route the following flood hydrograph through a river reach for which K = 12.0 h and x =
0.20. At the start of the inflow flood, the outflow discharge is 10 m3/s.
Time
(h)
0 6 12 18 24 30 36 42 48 54
Inflow
(m3/s)
10 20 50 60 55 45 35 27 20 15
30. Solution
Since K = 12 h and 2πΎπ₯ = 2 Γ 12 Γ 0.2 = 4.8 β, Ξt should be such that 12 β > βπ‘ > 4.8 β. In the present case, Ξt =
6 h is selected to suit the given inflow hydrograph ordinate interval.
Using equations (iii-a, b & c) the coefficients C0, C1 and C2 are calculated as
πΆ0 =
β12Γ0.20+0.5Γ6
12β12Γ0.2+0.5Γ6
=
0.6
12.6
= 0.048
πΆ1 =
12Γ0.20+0.5Γ6
12.6
= 0.429
πΆ2 =
12β12Γ0.20β0.5Γ6
12.6
= 0.523
For the first time interval, 0 to 6 h,
I1 = 10.0 C1I1 = 4.29
I2 = 20.0 C0I2 = 0.96
Q1 = 10.0 C2Q1 = 5.23
From equation (iii),
π2 = πΆ0πΌ2 + πΆ1πΌ1 + πΆ2π1 = 10.48 π3
/π
31. Solution
For the next time step, 6 to 12 h, Q1 = 10.48 m3/s. The procedure is repeated for the entire duration of the inflow
hydrograph. The computations are done in a tabular form as shown in Table 8.4. By plotting the inflow and outflow
hydrographs the attenuation and peak lag are found to be 10 m3/s and 12 h respectively.
Alternative form of equation (iii) is,
π2 = π1 + π΅1 πΌ1 β π1 + π΅2(πΌ2 β πΌ1)β¦β¦(iv)
Where,
π΅1 =
βπ‘
πΎ 1 β π₯ + 0.5βπ‘
π΅2 =
0.5βπ‘ β πΎπ₯
πΎ 1 β π₯ + 0.5βπ‘
The use of equation (iv) is essentially the same as that of equation (iii).
33. Flood Control
Definition
The term flood control is commonly used to denote all the measures adopted to reduce damages to
life and property by floods. Currently, many people prefer to use the term flood management instead
of flood control as it reflects the activity more realistically. The flood control measures that are in use
can be classified as follows:
1. Structural Measures
β’ Storage and detention reservoirs
β’ Levees (flood embankments)
β’ Flood ways (new channels)
β’ Channel improvement
β’ Watershed management
2. Non-structural Methods
β’ Flood plain zoning
β’ Flood forecast/warning
β’ Evacuation and relocation
β’ Flood insurance
34. Structural Methods
Storage reservoirs
Storage reservoirs serve as a reliable flood
control method by reserving a portion of
their capacity to absorb incoming floods.
The controlled release of stored water over
time prevents downstream flooding. An
ideal flood control reservoir operates with
a strategic plan, effectively mitigating the
impact of surges. This approach acts as a
proactive defense mechanism against
uncontrolled flooding. It offers an efficient
and systematic solution to manage
floodwaters.
Fig.1: Flood Control Operation of a Reservoir
35. Structural Methods
Detention reservoirs: A detention reservoir consists of an obstruction to a river with an uncontrolled
outlet. These are essentially small structures and operate to reduce the flood peak by providing
temporary storage and by restriction of the outflow rate.
Levees: Levees, also known as dikes or flood
embankments, are earthen banks constructed
parallel to the course of the river to confine it
to a fixed course and limited cross-sectional
width. The heights of levees will be higher
than the design flood level with sufficient free
board. The confinement of the river to a fixed
path frees large tracts of land from inundation
and consequent damage.
Fig.2: A Typical Levee
36. Structural Methods
Floodways: Floodways are natural channels into which a part of the flood will be diverted during
high stages. A floodway can be a natural or human-made channel and its location is controlled
essentially by the topography. Generally, wherever they are feasible, floodwaysβ offer an economical
alternative to other structural flood-control measures.
Channel Improvement: The works under this category involve:
β’ Widening or deepening of the channel to increase the cross-sectional area.
β’ Reduction of the channel roughness, by clearing of vegetation from the channel perimeter.
β’ Short circuiting of meander loops by cut off channels, leading to increased slopes.
All these three methods are essentially short-term measures and require continued maintenance.
37. Structural Methods
Watershed Management: Watershed management and land treatment in the catchment aims at
cutting down and delaying the runoff before it gets into the river. Watershed management measures
include developing the vegetative and soil cover in conjunction with land treatment works like Nala
bunds, check dams, contour bunding, zing terraces, etc. These measures are towards improvement of
water infiltration capacity of the soil and reduction of soil erosion. These treatments cause increased
infiltration, greater evapotranspiration, and reduction in soil erosion; all leading to moderation of the
peak flows and increasing of dry weather flows.
38. Non-Structural Methods
Nonstructural flood risk management measures are proven methods and techniques for reducing
flood risk and flood damages incurred within floodplains. The following non-structural measures
encompass the philosophy of living with floods.
Flood Plain Zoning: When the river discharges are very high, it is to be expected that the river will
overflow its banks and spill into flood plains. In view of the increasing pressure of population, these
basic aspects of the river are disregarded and there is greater encroachment of flood plains by humans
leading to distress. The following figure shows a conceptual zoning of a flood-prone area.
Zone Flood Return Period Example of uses
1 100 Years Residential houses, Offices, Factories etc.
2 25 Years Parks
3 Frequent No Construction/Encroachments
40. Flood Forecasting & Warning
The process of flood forecasting involves the examination of storm runoff data, reservoir levels, and
river level increases, enabling flood control managers to anticipate local flooding with a high degree
of precision. A robust flood forecasting system is essential, offering ample lead time for effective
response to minimize damage and potential loss of life. Accuracy and reliability are paramount
qualities that such a system must possess to ensure its effectiveness in safeguarding communities
from the impacts of flooding.
Flood forecasting techniques:
41. Flood Forecasting Techniques
1. Short-range forecast: This method gives advanced warning of 12-40 hours for floods.
This is done by correlating river stages at successive stations with hydrological
parameters such as rainfall over local area, variation of stage at the upstream base point
during the travel time of flood.
2. Medium-range forecast: This method predicts flood level with warning of 2-5 days
using rainfall-runoff relationships. Other parameters like the time of the year, storm
duration are used along with rainfall for correlations with runoff.
3. Long-ranged forecast: This method is for advanced information about critical storm-
producing weather system. Radars and meteorological satellites are used for data
collection.
42. Some Terminology
β’ Evacuation and relocation are two very important measures of flood
management. During flood times, communities along with their live
stocks and other valuables are evacuated from chronic flood affected
areas. Then they are relocated at nearby safer locations. This is called
non-structural measures. Structural measures include permanent
shifting of communities, raising the elevations of buildings etc.
Evacuation
& Relocation
β’ Flood insurance is a type of property insurance that covers for a
dwelling for losses sustained by water damage specifically due to
flooding. It also covers flood plain zoning, flood forcasting and disaster
preparedness activities.
Flood
Insurance