1. FLOOD ROUTING

2. Flood Routing
We may have to find the magnitude of flood and flood hydrograph parameters at a particular space due to flood at another space or at same space
Of course both the spaces are hydrologically connected
The space may be very nearer also
Upstream to downstream of a reservoir – storage is large
One section of the river to another section of the river – long distance
This way of finding the hydrologic route of flood from one space to another space is called flood routing

3. Flood Routing (contd…)
The flood hydrograph is in fact a wave
The Stage-discharge relationship represent the passage of waves
As this waves moves down the river
The shape of wave gets modified
Channel storage
Resistance
Lateral addition/withdrawal
When the flood passes through a reservoir
The peak is attenuated
Time base is enlarge
Due to effect of storage

4. Flood Routing (Contd…)
Thus the main purpose of reservoir flood routing is to safely dispose the flood magnitude by reducing the peak and increasing the base time.
Determination of flood hydrograph at a river section
By utilizing the data of flood flow at one or more upstream sections
Flood routing is more useful in:
Flood forecasting
Flood protection
Reservoir design
Spillway design

5. Applications (Types of flood routing)
Reservoir Routing
Channel Routing

6. Reservoir Routing
To predict the variations of reservoir elevation and outflow discharge with time
Study the effect of a flood wave entering a reservoir
Volume-elevation characteristic of reservoir
Outflow-elevation relationship for the spillways and other outlets
Reservoir Routing is Essential
Design of the capacity of spillway/other reservoir outlets
Location and sizing of the capacity of reservoirs to meet specific requirements

7. Channel Routing
Change in shape of Hydrograph as it travels down a channel is studied
To predict the flood hydrograph at various sections of the reach
Information on the flood-peak attenuation and the duration of high-water levels
Flood forecasting
Flood protection
Flood operations

8. Classification of Routing
Hydrologic Routing – employs the continuity equation
Hydraulic Routing - employs the continuity equation together with the momentum equation of unsteady flow
St. Venant Equations

9. Flood Routing Hydrologic Routing Hydraulic Routing
(Based on Continuity Equation) Based on Momentum equation
Reservoir Routing Channel Routing

10. Basic equations used in hydrologic routing
The change in storage is the difference between the inflow and outflow
I is Inflow, Q is outflow and S is the storage
In a small time interval (Δt)
I is average Inflow, Q is average outflow during the time interval
If storage at beginning is S1 and at end is S2 during time Δt
In this time interval the hydrograph is linear and is smaller than the transit of the flood wave through the reach.
…..1
…..2
…..3

11. St. Venant equation (based on application of momentum equation (used in hydraulic routing)
Differential form of Continuity Equation
Equation of motion for a flood wave
…..4
…..5

12. Hydrologic Storage Routing (Level Pool Routing) horizontal water surface is assumed in the reservoir
Uncontrolled spillway provided
…..6

13. Data required for reservoir routing
Storage volume vs elevation for the reservoir
Water-surface elevation vs outflow and hence storage vs outflow discharge
Inflow hydrograph, I = I (t)
Initial values of S, I and Q at time t = 0

14. Methods for Flood Routing Through a Reservoir
Modified Pul’s Method
Goodrich Method
Standard Fourth – Order Runge-Kutta Method (SRK)

15. Goodrich Method Semi-graphical Method
On rearranging equation 3
On collecting known and initial values
In the above equation the starting inflow and end inflow at time period t is known (read it from the inflow hydrograph), and the initial storage and discharge is also known
Then estimate the value remember both are unknown quantities
…..7
…..8

16. Is flood routing is too confusing
Contd….
To know the discharge, we need a graph between elevation Vs
Thus called as semi graphical method
This quantity is called storage-elevation-discharge data
The graph gives the relationship between discharge and elevation
From graph estimate the elevation
From elevation estimate the discharge
Is flood routing is too confusing
The following problem will help to understand this method

17. Outflow discharge (m3/s)
? Route the following flood hydrograph through the reservoir by Goodrich method:
Inflow hydrograph
Time (h) 6 12 18 24 30 36 42 48 54 60 66
Inflow (m3/s) 10 85
140
125 96 75 46 35 25 20
The storage-elevation-discharge data is as follows:
Elevation
Storage (106 m3)
Outflow discharge (m3/s)
100.00
3.350
100.50
3.472 10
101.00
3.880 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
The initial conditions are when t = 0, the reservoir elevation is m.

18. Step 1: Construct the storage-elevation-discharge curve
Assume a time period of 6 hr (t )
Equal to time of discharge measurement in the inflow hydrograph
Estimate the values of
Plot a graph
elevation-Vs-discharge
Elevation-Vs-
For initial time period t=0 find the Q2 and
From the graph
Elevation
Storage (106 m3)
Outflow discharge (m3/s)
(m3/s)  
100
3.35
310.19
100.5
3.472 10
331.48
101
3.88 26
385.26
101.5
4.383 46
451.83
102
4.882 72
524.04
102.5
5.37
597.22
102.75
5.527
116
627.76
103
5.856
130
672.22

20. Solution 356 =(40+316) Find this from graph Time (h) (m3/s)
Elevation (m)
Discharge Q 10
340
100.6 12 6 30 40
316 =(340-2*12)
356 =(40+316)
Find this from graph 85
115 18
140
225 24
125
265 96
221 36 75
171 42 60
135 48 46
106 54 35 81 25 66 20 45

22. Solution 100.74 17 356-2*17=322 322+115 =437 From graph find this
Time
(h)
(m3/s)
Elevation (m)
Discharge Q 10
340
100.6 12 6 30 40
340-2*12=316
=356
100.74 17 85
115
356-2*17=322
=437
From graph find this 18
140
225 24
125
265 96
221 36 75
171 42 60
135 48 46
106 54 35 81 25 66 20 45

24. Solution
Time
(h)
(m3/s)
Elevation (m)
Discharge Q 10
340
100.6 12 6 30 40
340-2*12=316
=356
100.74 17 85
115
356-2*17=322
=437
101.38 18
140
225
437-2*40 = 357
= 582 … 24
125
265 96
221 36 75
171 42 60
135 48 46
106 54 35 81 25 66 20 45

25. Solution Time (h) (m3/s) Elevation (m) Discharge Q 10 340 100.6 12 610
340
100.6 12 6 30 40
316 =(340-2*12)
356
100.74 17 85
115
322
437
101.38 18
140
225
357
582
102.50 95 24
125
265
392
657
102.92
127 96
221
403
624
102.70
112 36 75
171
400
571
102.32 90 42 60
135
391
526
102.02 73 48 46
106
380
486
101.74 57 54 35 81
372
453
101.51 25
361
421
101.28 37 66 20 45
347
101.02 27
335

26. What we achieved through this flood routing
The peak discharge magnitude is reduced, this is called attenuation.
2. The peak of outflow gets shifted and is called as lag
3. The difference in rising limb shows the reservoir is storing the water
4. The difference in receding limb shows the reservoir is depleted.
5. When the outflow is through uncontrolled spillway, the peak of outflow always occurs at point of inflection of inflow hydrograph and also is the point at which the inflow and outflow hydrograph intersect.
Lag
Attenuation
Reservoir storing
Reservoir Depleting

27. Hydrologic Channel Routing
In reservoir routing storage was a unique function of the outflow discharge, S = f(Q)
Here, Storage is a function of both outflow and inflow discharges
Therefore different routing method needed
River flow during floods belongs to the category of gradually varied unsteady flow
Water is not only parallel to the channel bottom, but also varies with time

28. Total Volume of Storage in a channel during flood
Prism Storage: vol. that would exist if uniform flow occurred at the downstream depth
= function (outflow)
Wedge storage: wedge like vol. formed between the actual water surface profile and the top surface of the prism storage
= function (inflow)
The total storage in the channel is given by:
…..9
K, and x are coefficients and m-is a constant

29. Muskingum Equation One of the most popular channel routing
Uses the hydrologic spatially lumped form of the continuity equation
First applied to Muskingum river in Ohio state, USA
Tributary of Ohio river
Length 179 km (111 mi )
Basin area 20,852 km² (8,051 mi² )

30. Muskingum Equation (Contd…)
Using m =1.0, equation 9. reduces to a linear relationship for S in terms of I and Q as
x – weighting factor varies bet. 0 to 0.5
When x = 0, storage function is discharge only
Linear storage or linear reservoir
x = 0.5 both inflow and outflow are equally imp. In determining storage
K – storage-time constant ~ time of travel of a flood wave through the channel reach
…..10
…..11

31. Estimation of K and x
Like reservoir routing in channel routing also we can draw inflow-outflow hydrograph through a channel reach
The increment in storage at any time t due to a small time period t can be calculated.
The summation of the various incremental storage gives us the channel storage Vs time relationship

32. Estimation of K and x (contd…)
Once this storage Vs time is known for a reach
Assume a value of x and estimate
for various time intervals
Draw the graph between the storage and
if the assumed x is correct we will get a linear line, else a loop will be formed
By trial and error find the value of x until a straight line is formed
Inverse slope of the line will give the value of K
Let us see how to estimate this using an example

33. ? The following inflow and outflow hydrographs were observed in a river reach. Estimate the values of K and x applicable to this reach for use in the Muskingum equation.
Time (h) 6 12 18 24 30 36 42 48 54 60 66
Inflow (m3/s) 5 20 50 32 22 15 10 7
Outflow (m3/s) 29 38 35 23 17 13 9
Time I Q
(I-Q)
Avg.
ΔS=
S = ΣΔS
[xI + (1-x) Q] (m3/s)
(h)
(m3/s)
Col. 5 x Δt
(m3/s.h)
x = 0.35
x = 0.3
x = 0.25 5 6 20 14 7 42
10.9
10.2
9.5 12 50 38 26
156
198
25.3
23.4
21.5 18 29 21
29.5
177
375
36.35
35.3
34.25 24 32 -6
7.5 45
420
35.9
36.2
36.5 30 22 35
-13
-9.5
-57
363
30.45
31.1
31.75 36 15
-14
-13.5
-81
282
24.1
24.8
25.5 10 23
201
18.45
19.1
19.75 48 17
-10
-11.5
-69
132
13.5
14.5 54 13 -8 -9
-54 78
10.6 11 60 9 -4
-36
7.6
7.8 8 66 -2 -3
-18
6.3
6.4
6.5

35. Muskingum Method of Routing
For a given channel reach
K and x are assumed to be constant
will not change with respect to time
But changes when the shape of channel changes in the reach
For a given channel reach by selecting a routing interval Δt and using the Muskingum equation the change in storage is
The continuity eqn. for the reach is
…..12
…..13

36. On simplifying the equations 12 and 13
where
…..14

37. In general form for the n th time step
This equation is known as Muskingum Routing Equation
It provides a simple linear equation for channel routing
…..15

38. Procedure to use Muskingum Equation to route a given inflow hydrograph through a reach
Knowing K and x, select an appropriate value of Δt
Calculate C1, C2 and C3
Starting from the initial conditions I1, Q1 and known I2 at the end of the first time step Δt calculate Q2 by Muskingum equation (14 or 15)
The outflow calculated in above step becomes the known initial outflow for the next time step. Repeat the calculations for the entire inflow hydrograph

39. Route the following hydrograph through a river reach for which K = 12
? Route the following hydrograph through a river reach for which K = 12.0 h and x = At the start of the inflow flood, the outflow discharge is 10 m3/s.
Time (h) 6 12 18 24 30 36 42 48 54
Inflow (m3/s) 10 20 50 60 55 45 35 27 15
Time (h)
I (m3/s)
0.429 I1
0.048 I2
0.523 Q1
Q (m3/s) 10 6 20
4.29
0.96
5.23
10.48 12 50
8.58
2.40
5.48
16.46 18 60
21.45
2.88
8.61
32.94 24 55
25.74
2.64
17.23
45.61 30 45
23.60
2.16
23.85
49.61 36 35
19.31
1.68
25.94
46.93 42 27
15.02
1.30
24.54
40.86 48
11.58
21.37
33.91 54 15
0.72
17.74
27.04

40. Flood Control
All the measures adopted to reduce damages to life and property by floods
Flood control measures
Structural Methods
Storage and detention reservoirs
Levees (flood embankments)
Channel improvement
Flood ways (new channels)
Soil conservation
Non-structural methods
Flood plain zoning
Flood warning evacuation and relocation

41. Self Study Hydrologic routing –other famous methods Hydraulic routing
Flood forecasting
Solve all the problems in this section

42. Current research in this area
Suitable methods for flood forecasting
Estimation of Muskingum parameters using AI (mostly using Genetic Algorithms and Genetic Programming).
Use of Nash IUH model for flood forecasting
Use of AI for estimation of Nash parameters