Unit Hydrograph

Definition of Unit Hydrograph

This method was first suggested by Sherman in 1932

·         A unit hydrograph is defined as the hydrograph of direct runoff resulting from one unit depth (1 cm) of rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D hours).

·         The definition of a unit hydrograph implies the following:

·         The unit hydrograph represents the lumped response or the catchment to a limit rainfall excess of D-hduration to produce a direct-runoff hydrograph. It relates only the direct runoff to the rainfall excess. Hence the volume of water contained in the unit hydrograph must be equal to the rainfall excess. As 1 cm depth of rainfall excess is considered the area of the unit hydrograph is equal to a volume given by 1cm over the catchment.

·         The rainfall is considered to have an average intensity of excess rainfall (ER) of 1/D cm/h for the duration D-hof the storm.

·         The distribution of the storm is considered to be uniform all over the catchment.

 

Example 1

The ordinates of a hydrograph of surface runoff resulting from 4.5 cm of rainfall excess of duration 8 h in a catchment are as follows:

Time

(h)

0

5

13

21

28

32

35

41

Discharge

(m3/s)

0

40

210

400

600

820

1150

1440

Time

(h)

45

55

61

91

98

115

138

Discharge

(m3/s)

1510

1420

1190

650

520

290

0

 

Determine the ordinates of the 8-h unit hydrograph for this catchment.

Answer

C1

C2

C3

C4=C2/C3

Time

DRH

Excess Rainfall

8-h UH

h

m3/s

cm

m3/s

0

0

4.5

0.0

5

40

4.5

8.9

13

210

4.5

46.7

21

400

4.5

88.9

28

600

4.5

133.3

32

820

4.5

182.2

35

1150

4.5

255.6

41

1440

4.5

320.0

45

1510

4.5

335.6

55

1420

4.5

315.6

61

1190

4.5

264.4

91

650

4.5

144.4

98

520

4.5

115.6

115

290

4.5

64.4

138

0

4.5

0.0

 

Assumptions of Unit Hydrograph Theory

1.      The effective rainfall is uniformly distributed within its duration or specified period of time.

2.      The effective rainfall is uniformly distributed over the whole area of drainage basin

3.      The time base of the direct runoff hydrograph, i.e., the duration of the direct runoff hydrograph, depends only on the effective rainfall duration, and is independent of the effective rainfall intensity.

4.      The response of the drainage basin is linear. This implies that the principles of proportionality and superpositionare applicable.

5.      As per proportionality principle, the DRH ordinates are proportional to the effective rainfall intensity.

Similarly, as per superposition principle, DRH ordinates due to a complex storm, having varying effective rainfall intensities, can be obtained by superimposing the DRH due to each element of effective rainfall in succession.

5. The unit hydrograph reflects the basic effects of various physical characteristics of the basin, which do not change in time. This implies that the principle of time invarianceis valid.

 The definition of the UH together with these assumptions constitutes what is now called the unit hydrograph theory.

 Since in practice, assumption (1) and (2) are never satisfied, these forms the limitations of unit hydrograph theory.

 Unit hydrograph theory can be applied only for a basin having drainage area between 200 ha to 5, 00,000 ha

 Uses of Unit Hydrograph

1.      Development of flood hydrograph for extreme rainfall magnitudes for use in the design of hydraulic structures.

2.      Extension of flood-flow records based on rainfall records.

3.      Development of flood forecasting and warning systems based on rainfall.

 

 Application of Unit Hydrograph

Let it be assumed that a D-hunit-hydrograph and the storm hyetograph are available. The initial losses and infiltration losses arc estimated and deducted from the storm hydrograph to obtain the ERH. The ERH is then divided into M blocks of D-h duration each. The rainfall excess in each D-hduration is then operated upon the unit hydrograph successively to get the various DRH curves. The ordinates of these DRHs are suitably lagged to obtain the proper time sequence and are then collected and added at each time element to obtain the required net DRH due to the storm.

 

Consider Fig. 1 in which a sequence of M rainfall excess values R1, R2, R3… Rm each of duration D-h duration is shown. The line u[t]is the ordinate of a D-h unit hydrograph at t h from the beginning.

Description: Description: 241.webp

Fig.1.DRH due to an ERH.

The direct runoff' due to R1 at time t is

Description: Description: 242.webp

The direct runoff due to R1at time (t -D)is

Description: Description: 243.webp

Similarly,

Description: Description: 244.webp

and

 Description: Description: 245.webp

Thus at any time t, the total direct runoff is

After deriving the net DRH, the estimated base flow is then added to obtain the total flood hydrograph.

 

Example 2

The ordinates of a 6-h unit hydrograph area given:

Time

(h)

0

3

6

9

12

15

18

21

6-h UH Ordinates

(m3/s)

0

150

250

450

600

700

800

750

Time

(h)

24

30

36

42

48

54

60

66

6-h UH Ordinates

(m3/s)

700

600

450

320

200

100

50

0

 

A storm had three successive 6-h intervals of rainfall magnitude of 3.0, 5.0, and 4.0 cm, respectively. Assuming aindex of 0.20 cm/h and base flow of 30 m3/s, determine and plot the resulting hydrograph of flow.

Answer

 

(1)

(2)

(3)

Rainfall, (cm)

3

5

4

Ø index, (cm/h)

0.20

0.20

0.20

Time interval ,(h)

6

6

6

losses (Ø * Δt), (cm)

1.2

1.2

1.2

Excess rainfall (Rainfall-Initial losses), (cm)

1.8

3.8

2.8



C1

C2

C3=C2*1.8

C4=C2*3.8

C5=C2*2.8

C6= C3+C4+C5

C7

C8= C7+C6

Time

6-h UH

DRH due to

DRH due to

DRH due to

 

Base flow

Ordinates of flood

 

 

1.8 cm ER

3.8 cm ER

2.8 cm ER

 

 

hydrograph

 

 

 

lagged by 6-h

lagged by 12-h

 

 

 

h

m3/s

m3/s

m3/s

m3/s

m3/s

m3/s

m3/s

0

0

0

 

 

0

30

30

3

150

270

 

 

270

30

300

6

250

450

0

 

450

30

480

9

450

810

570

 

1380

30

1410

12

600

1080

950

0

2030

30

2060

15

700

1260

1710

420

3390

30

3420

18

800

1440

2280

700

4420

30

4450

21

750

1350

2660

1260

5270

30

5300

24

700

1260

3040

1680

5980

30

6010

30

600

1080

2660

2240

5980

30

6010

36

450

810

2280

1960

5050

30

5080

42

320

576

1710

1680

3966

30

3996

48

200

360

1216

1260

2836

30

2866

54

100

180

760

896

1836

30

1866

60

50

90

380

560

1030

30

1060

66

0

0

190

280

470

30

500

72

 

0

0

140

140

30

170

78

 

0

0

0

0

30

30

 

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