1. FLOOD ROUTING Topic 5 River/Stream Routing Muskingum Method.
CONCEPT OF FLOOD ROUTING
CHANNEL ROUTING
River/Stream Routing Muskingum Method.
Muskingum Formula.
Calculate Channel Routing From Runoff Hydrograph.
RESERVOIR ROUTING
The elevation-Storage (S-H) Graph
The Storage-outflow (S-O) Relationship

2. FLOOD ROUTING

3. CONCEPT OF FLOOD ROUTING
 Flood routing is a process used to predict the temporal and spatial variations of a flood hydrograph as it moves through a river reach or reservoir  Flood routing is used to predict the magnitudes, volumes, and temporal patterns of a flood hydrograph as it translates down a river reach or reservoir  The effects of storage and flow resistance within a river reach are reflected by changes in hydrograph shape and timing as the floodwave moves from upstream to downstream  In general, routing methods are classified as hydrologic and hydraulic, depending, respectively, on whether the methods are based on empirical or physical process equations of motion

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

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

6. River/ Channel vs. Reservoir Routing
 River routing differs from reservoir routing in that storage in a river reach of length L depends on more than just outflow  The peak of the outflow hydrograph from a reach is usually attenuated and delayed compared with that inflow hydrograph River vs. Reservoir Routing  Because storage in a river reach is a function of whether stages rising or falling, storage in this case is a function of both outflow and inflow for the routing reach  Reservoir routing is generally easier to perform than river routing because storage-discharge relations for pipes, weirs, and spillways are single-valued functions independent of inflow

7. River/ Channel vs. Reservoir Routing

8. 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 )

9. Muskingum Method S = K[xI + (1-x)O], where
 The Muskingum method was developed by McCarthy (1938) and utilizes the continuity equation and a storage relationship that depends on both inflow and outflow
 In natural channels the exact relationship between inflow, outflow, and storage is usually quite complicated, but Muskingum channel routing procedure makes use of the simplifying assumption that the relationship can be approximated as:
S = K[xI + (1-x)O], where
 K is a constant, whose units are those of time and the value of K approximates the travel time of the flood wave through the reach
 x is a factor that weighs the relative influences of inflow and outflow upon the storage. For most river channels, x lies between 0.1 and 0.3, indicating both attenuation and translation. The modal value is about 0.2

10. 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

11. 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

12. 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

13. 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

15. Muskingum Method

16. Calculate Channel Routing From Runoff Hydrograph
Example: Route the inflow hydrograph tabulated in the following table through a river reach for which x = 0.20 and K = 8 hours . Assume that inflow equals outflow for the first day.
TIME (HOUR)
INFLOW DISCHARGE (M3/S)
100 4
250 8
680 12
520 16
300 20
280 24
150

17. Inflow Discharge (m3/s)
SOLUTION:
Time (Hour)
Inflow Discharge (m3/s)
C0I2
C1I1
C2O1
Outflow
(m3/s)
100 4
250 8
680 12
520 16
300 20
280 24
150

18. The Reservoir Storage Concept

19. The Reservoir Storage Concept
At time t1, inflow and outflow are equal and the maximum storage is reached
For times exceeding t1, outflow exceeds inflow and the reservoir empties
Area C represents the volume of water that flows out of the reservoir and must equal area A if the reservoir begins The Reservoir Storage Concept and ends at the same level
The peak of the outflow from reservoir should intersect the inflow hydrograph, since, in general, outflow is uniquely determined by reservoir storage or level
Storage routing through a reservoir will generally attenuate the peak outflow and lag the time to peak for the outflow hydrograph

20. The Reservoir Storage Concept
The rate of change of storage can be written as the continuity equation
I – O =
Where
I = inflow
O = outflow
ΔS = change in storage
Δt = change in time

21. 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

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

23. 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

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

25. 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

26. 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

27. 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.

28. 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

30. 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

32. 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

34. 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

35. 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

36. 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