Rainfall Runoff Relationships - 2 Notes | EduRev

Engineering Hydrology

Civil Engineering (CE) : Rainfall Runoff Relationships - 2 Notes | EduRev

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Direct runoff calculations using unit hydrograph

Assume that a 6-hour unit hydrograph (UH) of a catchment has been derived, whose ordinates are given in the following table and a corresponding graphical representation is shown in Figure 8.

Time (hours) 

Discharge (m3/s) 

0

0

6

5

12

15

18

50

24

120

30

201

36

173

42

130

48

97

54

66

60

40

66

21

72

9

78

3.5

84

2


Rainfall Runoff Relationships - 2 Notes | EduRev

FIGURE 8. A 6-hour unit hydrograph

Assume further that the effective rainfall hyetograph (ERH) for a given storm on the region has been given as in the following table:  

Time (hours)

Effective Rainfall (cm) 

0

0

6

2

12

4

18

3

 

This means that in the first 6 hours, 2cm excess rainfall has been recorded, 4cm in the next 6 hours, and 3cm in the next.

The direct runoff hydrograph can then be calculated by the three separate hyetographs for the three excess rainfalls by multiplying the ordinates of the hydrograph by the corresponding rainfall amounts. Since the rainfalls of 2cm, 4cm and 3cm occur in successive 6-hour intervals, the derived DRH corresponding to each rainfall is delayed by 6 hours appropriately.

These have been shown in the figures indicated. 

Rainfall Runoff Relationships - 2 Notes | EduRev

Rainfall Runoff Relationships - 2 Notes | EduRev

Rainfall Runoff Relationships - 2 Notes | EduRev

The final hydrograph is found out by adding the three individual hydrographs, as shown in Figure 12. 

Rainfall Runoff Relationships - 2 Notes | EduRev

FIGURE 12. Final direct runoff hydrograph derived from summation of individual DRHs

The calculations to generate the direct runoff hydrograph (DRH) from a given UH and ERH can be conveniently done using a spreadsheet program, like the Microsoft XL. 

A sample calculation for the example solved graphically is given in the following table. Note the 6 hour shift of the DRHs in the second and subsequent hours. 

Time

(hours)

Unit

Hydrograp h ordinates (m3/s)

Direct runoff due to 2 cm excess rainfall in first 6 hours (m3/s)

(I)

Direct runoff due to 4 cm excess rainfall in second 6 hours (m3/s)

(II)

Direct runoff due to 3 cm excess rainfall in third 6 hours (m3/s)

(III)

Direct

runoff

Hydrograph

(m3/s)

(I)+(II)+(III)

0

0

0

0

0

0

6

5

10

0

0

10

12

15

30

20

0

50

18

50

100

60

15

175

24

120

240

200

45

485

30

201

402

480

150

1032

36

173

346

804

360

1510

42

130

260

692

603

1555

48

97

194

520

519

1233

54

66

132

388

390

910

60

40

80

264

291

635

66

21

42

160

198

400

72

9

18

84

120

222

78

3.5

7

36

63

106

84

2

4

14

27

45

90

 

0

8

10.5

18.5

96

 

0

0

6

6

 

The last column in the above table gives the ordinates of the DRH produced by the ERH.  If the base flow is known or estimated (Lesson 2.2), then this should be added to the DRH to obtain the 6-houly ordinates of the flood hydrograph. 

The S – curve

This is a concept of the application of a hypothetical storm of 1 cm ERH of infinite duration spread over the entire catchment uniformly.  This may be done by shifting the UH by the T-duration for a large number of periods. The resulting hydrograph (a typical one is shown in Figure 13) is called the S – hydrograph, or the S – curve due to the summation of an infinite series of Thour unit hydrographs spaced T – hour apart. For the example of the UH given in the earlier section, the table below provides the necessary calculations.

Rainfall Runoff Relationships - 2 Notes | EduRev

FIGURE 13. S - Curve, or Summed up Unit Hydrographs

Time
(hr)
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
96

UH
Ordi-Nates
0
5
15
50
120
201
173
130
97
66
40
21
9
3.5
2
0
0

UH Ordinates shifted by 6 hr

0
0
5
15
50
120
201
173
130
97
66
40
21
9
3.5
2
0

UH
Ordi-nates shifted  by12 hr '
0
0
0
5
15
50
120
201
173
130
97
66
40
21
9
3.5
2

UH
Ordi-nates
shifted
by
18 hr
0
0
0
0
5
15
50
120
201
173
130
97
66
40
21
9
3.5

UH
Ordi-nates
shifted
by
24 hr
0
0
0
0
0
5
15
50
120
201
173
130
97
66
40
21
9

 0
0
0
0
0
0
5
15
50
120
201
173
130
97
66
40
21

  0
0
0
0
0
0
0
5
15
50
120
201
173
130
97
66
40

  0
0
0
0
0
0
0
0
5
15
50
120
201
173
130
97
66

  0
0
0
0
0
0
0
0
0
5
15
50
120
201
173
130
97

  0
0
0
0
0
0
0
0
0
0
5
15
50
120
201
173
130

 0
0
0
0
0
0
0
0
0
0
0
5
15
50
120
201
173

  0
0
0
0
0
0
0
0
0
0
0
0
5
15
50
120
201

 0
0
0
0
0
0
0
0
0
0
0
0
0
5
15
50
120

  0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
15
50

  0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
15

  0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5

Sum
of
all the UH ordinates
0
5
20
70
190
391
564
694
791
857
897
918
927
930.5
932.5
932.5
932.5

 

The average intensity of the effective rainfall producing the S – curve is 1/T (mm/h) and the equilibrium discharge is given as A/TX104m/ h where, A is the area of the catchment in Km2 and T is the unit hydrograph duration in hours. 


Application of the S – curve  

Though the S – curve is a theoretical concept, it is an effective tool to derive a t – hour UH from a T – hour UH, when t is smaller that T or t is lager than T but not an exact multiple of T. In case t is a multiple of T, the corresponding UH can be obtained without the aid of a S – hydrograph by summing up the required number of UH, lagged behind by consecutive T – hours.  

For all other cases shift the original S – hydrograph as derived for the T – hour UH by t hours to obtain a lagged S- hydrograph. Subtract the ordinates of the second curve from the first to obtain the t – hour graph. Next, scale the ordinates of the discharge hydrograph by a factor t/T, to obtain the actual t – hour UH which would result due to a total 1 cm of rainfall over the catchment. This is illustrated by the S-curve derived in the previous section.

Recall that the S-curve was obtained from a 6-hour UH. Let us derive the UH for a 3-hour duration. Since we do not know the ordinates of the S-curve at every 3-hour interval, we interpolate and write them in a tabular form as given in the table below: 

Time

S-curve ordinates as derived from 6-hr UH (I)

S-curve ordinates as derived from 6-hr UH but with interpolated values (II)

S-curve ordinates as derived from 6-hr UH lagged by 3 hrs. (III)

Difference of the two S- curves (II) - (III) (IV)

3-hr UH ordinates Col. (IV) divided by (3hr/6hr) (IV)*2

(hours)

(m3/s)

(m3/s)

(m3/s)

(m3/s)

(m3/s)

 

 

 

 

 

 

0

0

0

 

0

 

3

 

2.5

0

2.5

 

6

5

5

2.5

2.5

 

9

 

12.5

5

7.5

 

12

20

20

12.5

7.5

 

15

 

45

20

25

 

18

70

70

45

25

 

21

 

130

70

60

 

24

190

190

130

60

 

27

 

290.5

190

100.5

 

30

391

391

290.5

100.5

 

33

 

477.5

391

86.5

 

36

564

564

477.5

86.5

 

39

 

629

564

65

 

42

694

694

629

65

 

45

 

742.5

694

48.5

 

48

791

791

742.5

48.5

 

51

 

824

791

33

 

54

857

857

824

33

 

57

 

877

857

20

 

60

897

897

877

20

 

63

 

907.5

897

10.5

 

66

918

918

907.5

10.5

 

69

 

922.5

918

4.5

 

72

927

927

922.5

4.5

 

75

 

928.75

927

1.75

 

78

930.5

930.5

928.75

1.75

 

81

 

931.35

930.5

0.85

 

84

932.5

932.5

931.35

1.15

 

87

 

932.5

932.5

0

 

90

932.5

932.5

932.5

0

 

93

 

932.5

932.5

0

 

96

932.5

932.5

932.5

0

 

 

Derivation of unit hydrograph 

 An observed flood hydrograph at a streamflow gauging station could be a hydrograph resulting from an isolated intense short – duration storm of nearly uniform distribution in time and space, or it could be due to a complex rainfall event of varying intensities.  In the former case, the observed hydrograph would mostly be single peaked whereas for the latter, the hydrograph could be multi peaked depending on the variation in the rainfall intensities.  For the purpose of this course, we shall only consider rainfall to be more or less uniformly distributed in time and space for the purpose of demonstrating the derivation of unit hydrograph.  The procedure may be broadly divided into the following steps:

  1. Obtain as many rainfall records as possible for the study area to ensure that the amount and distribution of rainfall over the watershed is accurately known.  Only those storms which are isolated events and with uniform spatial and temporal distribution are selected along with the observed hydrograph at the watershed outlet point.
  2. Storms meeting the following criteria are generally preferred and selected out of the uniform storms data collected in Step 1.
  3. Storms with rainfall duration of around 20 to 30 % of basin lag,  
  4. Storms having rainfall excess between 1 cm and 4.5 cm.
  5. From the observed total flood hydrograph for each storm separate the base flow (discussed in lecture 2.2) and plot the direct runoff hydrograph.
  6. Measure the total volume of water that has passed the flow measuring point by finding the area under the DRH curve.  Since area of the watershed under consideration is known, calculate the average uniform rainfall depth that produced the DRH by dividing the volume of flow (step 3) by the catchment area.  This gives the effective rainfall (ER) corresponding to the storm.  This procedure has to be repeated for each selected storm to obtain the respective ERs.
  7. Express the hydrograph ordinate for each storm at T – hour is the duration of rainfall even.  Divide each ordinate of the hydrograph by the respective storm ER to obtain the UH corresponding to each storm.
  8. All UHs obtained from different storm events should be brought to the same duration by the S – curve method.
  9. The final UH of specific duration is obtained by averaging the ordinates of he different UH obtained from step 6.

Unit hydrograph for ungauged catchments

For catchments with insufficient rainfall or corresponding concurrent runoff data, it is necessary to develop synthetic unit hydrograph.  These are unit hydrographs constructed form basin characteristics.  A number of methods like that of Snyder’s had been used for the derivation of the Synthetic hydrographs.  However, the present recommendations of the Central Water Commission discourage the use of the Snyder’s method.

Instead, the Commission recommends the use of the Flood Estimation Reports brought out for the various sub–zones in deriving the unit hydrograph for the region.  These sub–zones have been demarcated on the basis of similar hydro – meteorological conditions and a list of the basins may be found.  The design flood is estimated by application of the design storm rainfall to the synthetic hydrograph developed by the methods outlined in the reports. 

Catchment modelling 

With the availability of personal computer high processing speed within easy reach of all, it is natural that efforts have been directed towards numerical modeling the catchment dynamics and its simulation.  It is not possible to outline each model in detail, but the general concept followed is to represent each physical process by a conceptual mathematical model which can be represented by an equivalent differential or ordinary equation.  These equations are solved by changing the equations to solvable form and writing algorithms in suitable computer language.  However, the user of the programs generally input data through a Graphical User Interface (GUI) since there is a lot of spatial information to be included like land-use, land-cover, soil property, etc.  Now a day, this information interaction between the user and the computer is through Geographic Information System (GIS) software.  Once the information is processed, the output results are also displayed graphically. 

Examples of catchment models

Though many of these models are sold commercially, there are quite a few developed by academic institutions and government agencies worldwide which are free and can be downloaded for non – commercial purposes through the internet.  A few examples are given below.

  • US Army corps of Engineers’ HEC-HMS and HEC-GeoHMS 
  • US Army corps of Engineers’ GRASS
  • US Army corps of Engineers’ TOPMODEL 

Water resources section of the Department of Civil Engineering, IIT Kharagpur has developed a watershed simulation model based on deterministic theory.  A copy of the same may be made available on request for educational purposes.

Important terms 

  1. Linearity: A linear relation between rainfall and runoff form a catchment suggests that variations in rainfall over a catchment is related to the variations in runoff from the outlet of the catchment by a linear function.
  2. Basin lag: Basin lag is the time between the peak flow and the centroid of rainfall. 
  3. Graphical User Interface (GUI): An interface that represents programs, files, and options with graphical images is called GUI. These images can include icons, menus, and dialog boxes. The user selects and activates these options by pointing and clicking with a mouse or with the keyboard. A particular GUI item (for example, a scroll bar) works the same way in all applications.
  4. Geographic Information System (GIS):  A system, usually computer based, for the input, storage, retrieval, analysis and display of interpreted geographic data.  The database is typically composed of map-like spatial representations, often called coverages or layers.  These layers may involve a three dimensional matrix of time, location, and attribute or activity.  A GIS may include digital line graph (DLG) data, Digital Elevation Models (DEM), geographic names, land-use characterizations, land ownership, land cover, registered satellite and/or areal photography along with any other associated or derived geographic data.
  5. HEC-HMS: The Hydrologic Modeling System (HEC-HMS) is designed to simulate the precipitation-runoff processes of dendritic watershed systems. It is designed to be applicable in a wide range of geographic areas for solving the widest possible range of problems. This includes large river basin water supply and flood hydrology, and small urban or natural watershed runoff. Hydrographs produced by the program are used directly or in conjunction with other software for studies of water availability, urban drainage, flow forecasting, future urbanization impact, reservoir spillway design, flood damage reduction, floodplain regulation, and systems operation.
  6. HEC-GeoHMS: The Geospatial Hydrologic Modeling Extension (HECGeoHMS) is a public-domain software package for use with the ArcView Geographic Information System. GeoHMS uses ArcView and Spatial Analyst to develop a number of hydrologic modeling inputs. Analyzing the digital terrain information, HEC-GeoHMS transforms the drainage paths and watershed boundaries into a hydrologic data structure that represents the watershed response to precipitation. In addition to the hydrologic data structure, capabilities include the development of grid-based data for linear quasi-distributed runoff transformation (ModClark), HEC-HMS basin model, physical watershed and stream characteristics, and background map file.
  7. GRASS: GRASS is an integrated set of programs designed to provide digitizing, image processing, map production, and geographic information system capabilities to its users.  GRASS is open software with freely available source code written in C.
  8. Topmodel: TOPMODEL predicts catchment water discharge and spatial soil water saturation pattern based on precipitation and evapotranspiration time series and topographic information.
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