S-hydrograph
The next important concept is that of S-hydrograph. In the above example, we learned
to use the given D-hr unit hydrograph to compute the discharge hydrograph for any n*D hour
rainfall, where 'n' is an integer. But what if our rainfall is not a multiple of D hour. In that case,
we'll need some other unit hydrograph which corresponds to given duration rainfall. In such cases,
S-hydrograph method can help overcome the limitations.
Example:Our rainfall is for 3 hour duration. Our job is to compute the 3-hr unit hydrograph
from the given 2-hour unit hydrograph. We'll use S-hydrograph method.
Solution:Here's how it goes...First we add several 2-hour unit hydrographs, each lagged by
2 additional hours of time. Following table shows the resulting S-hydrograph.
Time 1st 2nd 3rd 4th 5th 6th 7th S-hydrograph
(hr) -2hr -2hr -2hr -2hr -2hr -2hr -2hr
0 0 0
1 20 20
2 45 0 45
3 60 20 80
4 46 45 0 91
5 34 60 20 114
6 21 46 45 0 112
7 14 34 60 20 128
8 9 21 46 45 0 121
9 4 14 34 60 20 132
10 0 9 21 46 45 0 121
11 0 4 14 34 60 20 132
12 0 0 9 21 46 45 0 121
13 0 0 4 14 34 60 20 132
Once, we get S-hydrograph, we lag it by 3 hours (as that's what we want - Remember ! 3 hour unit hydrograph).
We'll obtain the difference and then multiply it by 2/3;
2 for using 2-hr duration UH and 3 for computing 3-hr UH.
See table below.
Time S Lagged Difference 3 hour
(hr) hydrograph S-hydrograph unit hydrograph
0 0 0 0 (0)
1 20 20 13.3 (13.3)
2 45 45 30 (30)
3 80 0 80 53.3 (53.3)
4 91 20 71 47.3 (47.3)
5 114 45 69 46 (46)
6 112 80 32 21.3 (21.3)
7 128 91 37 24.7 (24.7)
8 121 114 7 4.7 (4.7)
9 132 112 20 13.3 (0)
