Hydrographs Hydrograph River Discharge Storm Hydrographs · Hydrographs Response of a given catchment to rainfall input. A hydrograph is a graph showing discharge versus time. Hydrograph

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Hydrographs

Response of a given catchment to rainfall input.

A hydrograph is a graph showing discharge versus time.

Hydrograph

Record of River Discharge over a period of time

River Discharge

= cross sectional area rivers mean (average) velocity

X

(at a particular point in its course)

Storm Hydrographs

Show the change in discharge caused by a period of rainfall

Hydrograph :applications

To find out discharge patterns of a particular drainage basin

Help predict flooding events, therefore used for flood prevention measures

0 12 24 36 48 30 72

Hours from start of rain storm

3

2

1

Dis

char

ge (

m3/s

)

Base flow

Through flow

Overland flow

Basin lag time

mm

4

3

2

Peak flow

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

2

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

mm

4

3

2

Rainfall shown in mm, as a bar graph

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

mm

4

3

2

Discharge in m3/s, as a line graph

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

mm

4

3

2

The rising flood water in

the river

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

mm

4

3

2

Peak flow

Peak flow

Maximum discharge in the river

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

mm

4

3

2

Peak flow Falling flood water in the

river

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

Basin lag time

mm

4

3

2

Peak flow

Basin lag time

Time difference

between the peak of the rain storm

and the peak flow of the

river

3

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

Base flow

Basin lag time

mm

4

3

2

Peak flow

Base flow

Normal discharge of the river

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

Base flow

Through flow

Overland flow

Basin lag time

mm

4

3

2

Peak flow

Overland flow

Through flow

+

= Storm Flow

Volume of water reaching the river from surface run off

Overland flow Through flow

Volume of water reaching the river

through the soil and underlying rock

layers

Storm Hydrographs

•Rainfall Intensity

•Rising Limb

•Recession Limb

•Lag time

•Peak flow compared to Base flow •Recovery rate, back to Base flow

Basin lag time

0 12 24 36 48 30 72


3

2

1

Dis

char

ge (

m3/s

)

Base flow

Through flow

Overland flow

mm

4

3

2

Peak flow

Time Characteristics of hydrograph

1. Time to peak

– • From beginning of rising limb to peak discharge

– • Function of basin characteristics

– • Drainage density, slope channel size, roughness and soil

infiltration characteristics

2. Time of concentration

– • Time required for the farthermost rain to reach the outlet

3. Lag time or Basin lag time

– • Between centre of mass of rainfall and runoff hydrograph mass

– • Since it is very difficult to find the centre then it is the time

between centre of mass of effective rainfall to peak discharge

4. Duration of rainfall

5. Base time of hydrographs

Storm rainfall:

Hydrograph :

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9

Series1

14 15 16 17 18 19 20 21 22

?

Precipitation and river response

4

Understanding hydrological

responses

Peak discharge?

Lag time?

Rate of recession?

Factors affecting flood hydrographs

Channel characteristics

– Cross section,

– roughness

– Storage capacity.

Infiltration characteristic

– (a) Land use and cover

– (b) Soil type and geological condition

– (c) Lakes, swamps and other storage

Climatic factors

– (a) Shape

– (b) Size

– ( c) slope

– (d) Nature of the valley

– (e) Elevation

– (f) Drainage density

Physiographic Factors

Factors affecting flood hydrographs

Storm characteristics

– precipitation,

– Intensity,

– duration,

– magnitude and

– movement of storm.

Initial loss

Evapotranspiration

Climatic Factors

Factors influencing Storm Hydrographs

• Area

• Shape

• Slope

• Rock Type

• Soil

• Land Use

• Drainage Density

• Precipitation / Temp

• Tidal Conditions

Stream order and flood response Regional

climate

and flood

response

5

Geological substrate and flood

response Basin geometry and flood

response

circular

elonga

ted

effect of

storm

path?

Land use and flood response

Area

Large basins receive more precipitation than small therefore have larger runoff

Larger size means longer lag time as water has a longer distance to travel to reach the trunk river

Area Rock Type Drainage Density

Shape Soil Precipitation / Temp

Slope Land Use Tidal Conditions

Shape

Elongated basin will produce a lower peak flow and longer lag time than a circular one of the same size




Slope

Channel flow can be faster down a steep slope therefore steeper rising limb and shorter lag time




6

Rock Type

Permeable rocks mean rapid infiltration and little overland flow therefore shallow rising limb




Soil

Infiltration is generally greater on thick soil, although less porous soils eg. clay act as impermeable layers

The more infiltration occurs the longer the lag time and shallower the rising limb




Land Use

Urbanisation - concrete and tarmac form impermeable surfaces, creating a steep rising limb and shortening the time lag

Afforestation - intercepts the precipitation, creating a shallow rising limb and lengthening the time lag




Drainage Density

A higher density will allow rapid overland flow




Precipitation & Temperature

Short intense rainstorms can produce rapid overland flow and steep rising limb

If there have been extreme temperatures, the ground can be hard (either baked or frozen) causing rapid surface run off

Snow on the ground can act as a store producing a long lag time and shallow rising limb. Once a thaw sets in the rising limb will become steep




Tidal Conditions

High spring tides can block the normal exit for the water, therefore extending the length of time the river basin takes to return to base flow




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Base flow separation

To draw surface runoff hydrograph, it is

required to separate base flow

Methods

1. Straight line method

N=0.83A0.2 Line AB

2. Line ACB

3. Line AFE

Effective rainfall or Rainfall Excess

The direct runoff,

(initial losses and

infiltration losses are

separated).

Called as effective

rainfall hyetograph or

hyetograph of rainfall

excess

It is the rainfall which

contributed for direct

runoff

Example

A storm over a catchment of area 15 sq.km had a 12

hrs duration. The mass curve of rainfall is given. If φ

index is 0.3 cm/h, determine the effective rainfall

hyetograph and the volume of direct runoff from the

catchment.

Time from

start of the

storm

0 2 4 6 8 10 12

Accumulated

rainfall

(cm)

0 0.7 2.5 5.8 7.2 9.0 9.9

Solution Time from start of

the storm 0 2 4 6 8 10 12

Accumulated

0 0.7 2.5 5.8 7.2 9 9.9 rainfall

(cm)

φ index 0.6 0.6 0.6 0.6 0.6 0.6

depth of rainfall in cm 0.7 1.8 3.3 1.4 1.8 0.9

Effective rainfall (cm) 0.1 1.2 2.7 0.8 1.2 0.3

Rainfall intensity cm/hr 0.05 0.6 1.35 0.4 0.6 0.15 3.15

47250000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6

Ra

infa

ll In

ten

sit

y (

cm

/hr)

Time from start of storm (hr)

Unit hydrograph

The measurement of runoff works out to be a costly and

more time consuming process

Hence various methods has been used like RR models,

empirical, rational, soft computing etc…

UNIT HYDROGRAPH METHOD – Introduced by

Sherman (1932)

The unit hydrograph represents the lumped response

of the catchment to a unit rainfall excess of D-h

duration 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 volume of rainfall

excess.

As 1 cm depth of rainfall excess is considered, the area

of the unit hydrograph is equal to a volume given by 1

cm over the catchment for that duration.

The rainfall is considered to have an average intensity of

excess rainfall (ER) of 1 cm/h for the D hr duration of the

storm.

The distribution of the storm is considered to be uniform

all over the catchment.

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Basic assumptions of unit hydrograph

Time invariance

– First basic assumption is that direct-runoff response in a

catchment is time-invariant.

Linear Response

– The direct-runoff response to the rainfall excess is assumed

to be linear.

– This is the most important assumption of the unit-

hydrograph theory.

– The Rainfall –runoff obeys the principles of superposition

Application of unit hydrograph

It is useful in calculating DRH (flood as well as storm hydrograph) of a given storm occurred for D hr.

If a D hr duration UH is available, it is possible to derive multiples of D hr duration unit hydrograph

Unit hydrograph of different

durations

Method of superposition

– Suitable when m is an integer

Method of S- curve

– Suitable when m is a fraction

Method of superposition

suitable when m is an

integer

D hr Unit hydrograph

is available

Super impose m unit

hydrographs with

each hydrograph

lagged by D hr from

the previous unit

hydrograph

Method of S- curve Also suitable when m is a fraction

Develop a hydrograph produced by a continuous

effective rainfall of D hr for a infinite period.

Then get the summation hydrograph (S curve

ordinates)

Lag this S curve by mD hrs (SB) take the difference

between the two S curves, (SA-SB)

Example

Rainfall of magnitude 3.8 cm and 2.8 cm

occurring on two consecutive 4-h

durations on a catchment area 27km2

produced the following hydrograph of flow

at the outlet of the catchment. Estimate

the rainfall excess and φ-index

Time from start of rainfall -6 0 6 12 18 24 30 36 42 48 54 60 66

Observed flow (m3/s) 6 5 13 26 21 16 12 9 7 5 5 4.5 4.5

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Solution

Time from start of rainfall -6 0 6 12 18 24 30 36 42 48 54 60 66

Observed flow (m3/s) 6 5 13 26 21 16 12 9 7 5 5 4.5 4.5

DRH ordinates 1 0 8 21 16 11 7 4 2 0 0 -0.5 -0.5

Example

The following are

ordinates of 4hr unit

hydrograph.

Determine ordinates of

12 hr unit hydrograph by

S-curve method.

Time 4hr. UH

0 0 4 50 8 100 12 110 16 140 20 90 24 80 28 60 32 40 36 20 40 0

time 4hr. UH

S-curve addition

S-

Curve

Ordina

tes

S-Curve

lagged

by 12 hr. Diff. (Y) Y*T/t

0 0 0 0 0 0.00

4 50 0 50 0 50 16.67

8 100 50 0 150 0 150 50.00

12 110 100 50 0 260 0 260 86.67

16 140 110 100 50 0 400 50 350 116.67

20 90 140 110 100 50 0 490 150 340 113.33

24 80 90 140 110 100 50 0 570 260 310 103.33

28 60 80 90 140 110 100 50 0 630 400 230 76.67

32 40 60 80 90 140 110 100 50 0 670 490 180 60.00

36 20 40 60 80 90 140 110 100 50 0 690 570 120 40.00

40 0 20 40 60 80 90 140 110 100 50 0 690 630 60 20.00

690 670 20 6.67

690 690 0 0

690 690 0 0

Solution :

10

Hydrograph

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

0 10 20 30 40 50 60

Dis

cha

rge

Q (

cum

ec)

Time (Hours)

Example

Re-gernerate the ordinates of 4hr

UH by the 12 hr UH ordinates.

Solution :

time 12hr. UH S-Curve Addition

S-Curve

Ordinate

s

S-Curve

lagged

by 4 hr. Diff. (Y) Y*T/t

0 0 0 0 0

4 16.66 16.66 0 16.66 49.98

8 50 50 16.66 33.34 100.02

12 86.66 0 86.66 50 36.66 109.98

16 116.66 16.66 133.32 86.66 46.66 139.98

20 113.33 50 163.33 133.32 30.01 90.03

24 103.33 86.66 0 189.99 163.33 26.66 79.98

28 76.66 116.66 16.66 209.98 189.99 19.99 59.97

32 60 113.33 50 223.33 209.98 13.35 40.05

36 40 103.33 86.66 0 229.99 223.33 6.66 19.98

40 20 76.66 116.66 16.66 229.98 229.99 -0.01 -0.03

44 6.66 60 113.33 50 229.99 229.98 0.01 0.03

48 0 40 103.33 86.66 229.99 229.98 0.01 0.03

229.99

Hydrograph

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50

Dis

charg

e Q

(cu

mec

)

Time (Hours)

Example

For the given

ordinates of 8hr unit

hydrograph

Obtain the ordinates

of 24 hr unit

hydrograph

time 8hr. UH

0 0

4 5

8 13

12 26

16 45

20 82

24 162

28 240

32 231

36 165

40 112

44 79

48 57

52 42

56 31

60 32

64 14

68 9.5

72 6.6

76 4

80 2

84 1

88 0

Solution :

time 8hr. UH

8hr UH

lagged by 8

hr

8hr UH

lagged by 16

hr Addirion 24 hr. UH

col. 1 col. 2 col. 3 col. 4 col5 = 2+3+4 col5/3

0 0 0 0.0

4 5 5 1.7

8 13 0 13 4.3

12 26 5 31 10.3

16 45 13 0 58 19.3

20 82 26 5 113 37.7

24 162 45 13 220 73.3

28 240 82 26 348 116.0

32 231 162 45 438 146.0

36 165 240 82 487 162.3

40 112 231 162 505 168.3

44 79 165 240 484 161.3

48 57 112 231 400 133.3

52 42 79 165 286 95.3

56 31 57 112 200 66.7

60 32 42 79 153 51.0

64 14 31 57 102 34.0

68 9.5 32 42 83.5 27.8

72 6.6 14 31 51.6 17.2

76 4 9.5 32 45.5 15.2

80 2 6.6 14 22.6 7.5

84 1 4 9.5 14.5 4.8

88 0 2 6.6 8.6 2.9

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Hydrograph

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0 20 40 60 80 100

Dis

cha

rge

Q (

cum

ec)

Time (Hours)

Time(min) Rainfall

(cm/hr) Rainfall

(cm) ϕ Index

(cm/hr) ϕ Index (cm) Effective

rainfall

0-20 2.5 0.83 3.20 1.07 0.00 20-40 2.5 0.83 3.20 1.07 0.00 40-60 10 3.33 3.20 1.07 2.27 60-80 7.5 2.50 3.20 1.07 1.43

80-100 1.25 0.42 3.20 1.07 0.00 100-120 1.25 0.42 3.20 1.07 0.00 120-140 5 1.67 3.20 1.07 0.60

Total Rainfall 10 Total Runoff 4.30

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Documents

Hydrographs Hydrograph River Discharge Storm Hydrographs · Hydrographs Response of a given catchment to rainfall input. A hydrograph is a graph showing discharge versus time. Hydrograph