1. CHANGE IN UNIT HYDROGRAPH DURATION

1.01
A unit hydrograph is defined for a certain storm duration.

1.02
In unit hydrograph convolution, the duration of the unit hydrograph must match the interval of definition of the effective storm hyetograph.

1.03
Thus, in certain cases it may be necessary to change the duration of the unit hydrograph to match the interval of the hyetograph.

1.04
Once a unit hydrograph has been derived, a unit hydrograph of another duration can be calculated.

1.05
There are two methods to change the duration of a unit hydrograph:

(1) superposition method, and

(2) S-hydrograph method.

2. SUPERPOSITION METHOD

2.01
The superposition method enables the conversion of an X-hr unit hydrograph into an nX-hr unit hydrograph, in which n is an integer.

2.02
The procedure consists of lagging n X-hr unit hydrographs in time, each for an interval equal to X hours, summing up the ordinates of all hydrographs, and dividing the summed ordinates by n to obtain the nX-hr unit hydrograph.

2.03
The conversion of a 1-hr unit hydrograph to a 2-hr and 3-hr unit hydrographs is illustrated in this table.

2.04

2.05
Column 1 shows the time in hours.

2.06
Column 2 shows the ordinates of the 1-hr unit hydrograph.

2.07
Column 3 shows the ordinates of the 1-hr unit hydrograph, lagged 1 hour.

2.08
Column 4 shows the ordinates of the 1-hr unit hydrograph, lagged 2 hours.

2.09
Column 5 shows the ordinates of the 2-hr unit hydrograph, obtained by summing up the ordinates of Columns 2 and 3, and dividing the sum by 2.

2.10
Column 6 shows the ordinates of the 3-hr unit hydrograph, obtained by summing up the ordinates of Columns 2, 3, and 4, and dividing the sum by 3.

2.11
The sum of Columns 2, 5, and 6 is the same, indicating that the volume under the unit hydrographs, corresponding to 1 unit of runoff, has been conserved.

3. S-HYDROGRAPH METHOD

3.01
The S-hydrograph method enables the conversion of an X-hr unit hydrograph into a Y-hr unit hydrograph, regardless of the ratio between X and Y.

3.02
The procedure consists of the following steps:

3.03
1. Determine the X-hr S-hydrograph, by accumulating the unit hydrograph ordinates at intervals equal to X.

3.04

3.05
2. Lag the X-hr S-hydrograph by a time equal to Y hours.

3.06
3. Subtract the ordinates of the two previous S-hydrographs.

3.07
4. Multiply the resulting hydrograph ordinates by the ratio X/Y to obtain the Y-hr unit hydrograph.

3.08
The conversion of a 2-hr to a 3-hr unit hydrograph, followed by the conversion of the 3-hr to a 1-hr unit hydrograph, is illustrated in this table.

3.09

3.10
Column 1 shows the time in hours.

3.11
Column 2 shows the 2-hr unit hydrograph. This is the same unit hydrograph calculated in the previous example.

3.12
Column 3 is the 2-hr S-hydrograph, obtained by accumulating the ordinates of Column 2 at intervals of X = 2 hr.

3.13
Column 4 is the S-hydrograph of Column 3 lagged Y = 3 hours.

3.14
Column 5 is Column 3 minus Column 4.

3.15
Column 6 is the product of Column 5 times X/Y = 2/3. This Column is the 3-hr unit hydrograph.

3.16
Column 7 is the 3-hr S-hydrograph, obtained by accumulating the intervals of Column 6 at intervals of X = 3 hours.

3.17
Column 8 is the S-hydrograph of Column 7, lagged Y = 2 hours.

3.18
Column 9 is Column 7 minus Column 8.

3.19
Column 10 is the product of Column 9 times X/Y = 3/2. This Column is the 2-hr unit hydrograph.

3.20
It is confirmed that Column 10 is the same as Column 2.

3.21
The sum of Columns 2, 6, and 10 is the same, indicating that the volume under the unit hydrographs, corresponding to 1 unit of runoff, has been conserved.

3.22
Note that the S-hydrograph is defined only at intervals equal to the unit hydrograph duration.

4. CONVOLUTION

4.01
The procedure to calculate a composite or flood hydrograph based on a unit hydrograph and an effective storm hyetograph is referred to as hydrograph convolution.

4.02
This technique is based on the principles of linearity and superposition.

4.03
Appropriate multiples of the unit hydrograph are lagged and correspondingly added to calculate the storm hydrograph corresponding to the effective storm hyetograph.

4.04

4.05
The procedure is illustrated by this table.

4.06

4.07
Column 1 shows the time in hours.

4.08
Column 2 shows the unit hydrograph ordinates.

4.08
The headings of Columns 3 to 8 show the hourly values of the effective storm hyetograph.

4.09
Column 3 shows the product of the first-hour rainfall depth times the unit hydrograph ordinates of Column 2.

4.10
Column 4 shows the product of the second-hour rainfall depth times the unit hydrograph ordinates of Column 2, lagged 1 hour with respect to Column 3.

4.11
The computational pattern established for Columns 3 and 4 is repeated for Columns 5 to 8.

4.12
Column 9 is obtained by summing across Columns 3 to 8.

4.13
Column 9 is the composite hydrograph for the specified storm pattern.

4.14
Unit hydrograph convolution is effectively a rainfall-runoff transform method, that is, a way of converting effective storm rainfall into flood runoff.

Narrator: Victor M. Ponce

Music: Fernando Oñate

Editor: Flor Pérez

Copyright © 2011

Visualab Productions

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