Chapter Two
S-curve method
UH Lagging
A UH has a particular duration, D. Unit hydrographs are linear, they can be added,
for example, to generate a hydrograph for a storm 2x, 3x, 4x, etc. … longer
1–hr UH
2–hr UH
The linear property of a UH can be used to generate a UH of a larger
duration. Here two copies of a 1-hour UH are lagged by 1-hr and added,
then the ordinates are divided by 2, to make a 2-hour UH (1 inch over
two hours).
However this lagging method is restricted to integer multiples of the
original duration.
S –curve method
S –curve method works for any duration. The first step is to add a series
of UH’s of duration D, each lagged by time period D, This corresponds to
the runoff hydrograph from a continuous rainfall excess intensity of 1/D
inches/hour.
S –curve method works for any duration, D’
By shifting a copy of the S-curve by D’ hours, and subtracting the ordinates, the
resulting hydrograph (dashed line - - - - - - ) must be due to rainfall of intensity 1/D
inches/hour that lasts for a duration of D’ hours.
To convert the hydrograph (dashed line - - - - -) to a UH, multiply ordinates by D/D’
,resulting in a UH of duration D’. D’ need NOT be an integral multiple of D.
Example 2-4
• Convert the following 2-hr UH to a 3-hr UH
using the S-curve Method
____________________________________________________
TIME (hr)
2-hr UH Ordinate (cfs)________
.
0
0
1
75
2
250
3
300
4
275
5
200
6
100
7
75
8
50
9
25
10
0
• Make a spreadsheet with the 2-hr UH
ordinates, then copy them in the next column
lagged by D=2 hours. Keep adding columns
until the row sums are fairly constant. The
sums are the ordinates of your S-curve.
Draw your S-curve, it looks like the upper curve.
Figure E2-4
• Copy your S-curve ordinates into a new
spreadsheet, then copy the same ordinates
D’=3 time units down. Calculate the
difference, then multiply by D/D’ ,here = 2/3,
to get your 3 hour UH.
Why multiply by a correction factor?
• Here the original UH was for a 2-hour storm, and
we need a UH for a 3-hour storm.
• A 2-hour UH is for a storm with 1/2 in/hr for 2 hours
• A 3-hour UH is for a storm with 1/3 in/hr for 3 hours
• 1/2 x 2/3 = 1/3
• For each s-curves difference of lagged UHs ,
multiply the ordinates by D /D’ to get the correct
UH
Review of this method
• Let’s look at the example again.
• Here are the two copies of your S-curve based
on a sum of 2-hr UHs. The second copy is
lagged by D’=3 hours.
• Calculate the difference, and re-scale the
difference by D/D’
• Plot the new ordinates, and here is your new 3
hour UH, or whatever D’ you need
Prediction
• This method provides a hydrograph that
predicts the behavior of a flood from a storm
of any duration