1. HYDROLOGY Lecture 10 Unit Hydrograph
Assoc.Prof. dr.tarkan erdik

2. What’s hydrograph? (just a reminder)
A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point

3. Why Construct & Analyse Hydrographs ?
1-To find out discharge patterns of a particular drainage basin
2-To help predict flooding events.

4. What is the main source of Direct flow?
t(hrs)
Hours from start of rain storm
___ Components of Streamflow
___ Elements of Hydrograph 3 2 1
Discharge (m3/s)
Base flow
Direct flow
Rising limb
Recession limb
Basin lag time mm 4
Peak flow (crest)
Flood Hydrograph
Direct runoff
(Surface flow + undelayed subsurface flow)
Base flow
(Groundwater flow + delayed subsurface flow)
What is the main source of Direct flow?
Runoff
What is the main source of Base flow?
Groundwater

5. 3 2 1
Discharge (m3/s)
Hours from start of rain storm

6. Rainfall shown in mm, as a bar graph3 2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

7. Discharge in m3/s, as a line graph2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

8. The rising flood water in the river
Rising limb
The rising flood water in the river 3
Rising limb 2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

9. Maximum discharge in the river
Peak flow
Peak flow
Maximum discharge in the river 3
Rising limb 2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

10. Falling flood water in the river
Recession limb
Peak flow
Falling flood water in the river 3
Rising limb
Recession limb 2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

11. Hours from start of rain storm
Basin lag time
Basin lag time
Peak flow
Time difference between the peak of the rain storm and the peak flow of the river 3
Rising limb
Recession limb 2 mm
Discharge (m3/s) 4 1 3 2
Hours from start of rain storm

12. Normal discharge of the river
Base flow
Basin lag time
Peak flow
Normal discharge of the river 3
Rising limb
Recession limb 2
Direct flow mm
Discharge (m3/s) 4 1 3 2
Base flow
Hours from start of rain storm

13. Direct Flow: Volume of water reaching the river from surface run off (Source: rainfall
Baseflow: Volume of water reaching the river from surface run off (Source: Groundwater flow)

14. Unit hydrograph assumptions
Excess rainfall has constant intensity during duration
Excess rainfall is uniformly distributed on watershed
Base time of runoff is constant
Ordinates of unit hydrograph are proportional to total runoff (linearity)
Unit hydrograph represents all characteristics of watershed and is time invariant (stationarity)

15. Area Area Drainage Density Shape Soil Precipitation / Temp
Large basins receive more precipitation than small therefore have larger runoff
Larger size means longer lagtime as water has a longer distance to travel to reach the outlet
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

16. Shape Area Drainage Density Shape Soil Precipitation / Temp
Elongated basin will produce a lower peak flow and longer lag time than a circular one of the same size
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

17. Slope Area Drainage Density Shape Soil Precipitation / Temp
Channel flow can be faster down a steep slope therefore steeper rising limb and shorter lag time
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

18. Soil Area Drainage Density Shape Soil Precipitation / Temp
The more infiltration occurs the longer the lag time and shallower the rising limb
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

19. Land Use Area Drainage Density Shape Soil Precipitation / Temp
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
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

20. Drainage Density Area Drainage Density Shape Soil Precipitation / Temp
A higher density will allow rapid overland flow
Area Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

21. Precipitation & Temperature
Short intense rainstorms can produce rapid overland flow and steep rising limb
If the ground is frozen rapid surface run off occurs
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
Area Rock Type Drainage Density
Shape Soil Precipitation / Temp
Slope Land Use

22. Unit Hydrograph Theory (Transforming the Runoff from Rainfall)
A mathematical concept (based on linearity)
A unit hydrograph is defined as the hydrograph of direct runoff resulting from one unit depth (1cm) of rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D hours)
total amount of rainfall minus all abstractions including interception, depression storage, and infiltration.

23. Unit Hydrograph Components
Duration of excess precip.
Duration
Lag Time
Time of Concentration
Rising Limb
Recession Limb (falling limb)
Peak Flow
Time to Peak (rise time)
Recession Curve
Separation
Base flow
Lag time
Time of concentration
Base flow
Time Base

24. Derived Unit Hydrograph

25. Derived Unit Hydrograph

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

27. EXAMPLE Given below are the ordinates of a 6-h unit hydrograph for a catchment. Calculate the ordinates of the DRH due to a rainfall excess of 3.5 cm occurring in 6 hr.

28. EXAMPLE Given below are the ordinates of a 6-h unit hydrograph for a catchment. Calculate the ordinates of the DRH due to a rainfall excess of 3.5 cm occurring in 6 hr.

29. Exercise2:Two storms each of 6-h duration and having rainfall excess values of 3.0 and 2.0 cm, respectively occur successively. The 6-h unit hydrograph for the catchment is the same as given in tha table below. Please calculate the resulting DRH

30. Ordinate of 3-cm DRH (col.2) 1 2 3 4 5
Time (h)
Ordinate of 6-h UH (m3/s)
Ordinate of 3-cm DRH (col.2)
Ordinate of 2-cm DRH (col.2 lagged by 6 h)
Ordinate of 5-cm DRH (col. 3 + col.4) (m3/s) 25 6 50 9 85 12
125 15
160 18
185 21
172.5 24 30
110 36 60 42 48 54 16 8 66
2.7 69 75

31. No lag 6-hr lag 1 2 3 4 5 Time (h) Ordinate of 6-h UH (m3/s)
Ordinate of 3-cm DRH (col.2) x 3
Ordinate of 2-cm DRH (col.2 lagged by 6 h) x 2
Ordinate of 5-cm DRH (col. 3 + col.4) (m3/s) 25 75 6 50
150 9 85
255
305 12
125
375
100
475 15
160
480
170
650 18
185
555
250
805 21
172.5
517.5
320
837.5 24
370
850 30
110
330 36 60
180
220
400 42
108
120
228 48 72
147 54 16 98 8 32 56 66
2.7
8.1
24.1 69
10.6
No lag
6-hr lag

33. Exercise 3: The ordinates of a 6-hour unit hydrograph of a catchment is given below. The variation of accumulated rainfall is given. The baseflow can be assumed to be 15m3/s at the begining and increasing by 2m3/s for every 12 hours. The storm loss rate is estimated as 0.25cm/h. Calculate DRH.
Interval
1st 6 hours
2nd 6 hours
3rd 6 hours
Rainfall depth (cm)
3.5
7.5
5.5

34. Effective rainfall (cm)
Interval
1st 6 hours
2nd 6 hours
3rd 6 hours
Rainfall depth (cm)
3.5
7.5
5.5
Total loss (cm)
1.5 (0.25×6)
Effective rainfall (cm) 2 6 4

35. DRH due to 6 cm ER x 6.0 (Advanced by 6 h)
Time
Ordinaters of U.H.
DRH due to 2 cm ER
DRH due to 6 cm ER x 6.0 (Advanced by 6 h)
DRH due to 4 cm ER (Advanced by 12 h)
Ordinates of final DRH (Col )
Base flow (m3/s)
Ordinates of flood hydrograph (m'Vs) (Col ) 3 25 6 50 9 85 12
125 15
160 18
185 21
172.5 24 27
135 30
110 33 60 36 39 42 16 45 8 48
2.7 51 54 57 63 66

36. DRH due to 6 cm ER x 6.0 (Advanced by 6 h)
Time
Ordinaters of U.H.
DRH due to 2 cm ER
DRH due to 6 cm ER x 6.0 (Advanced by 6 h)
DRH due to 4 cm ER (Advanced by 12 h)
Ordinates of final DRH (Col )
Base flow (m3/s)
Ordinates of flood hydrograph (m'Vs) (Col ) 15 3 25 50 65 6
100
115 9 85
170
150
320
335 12
125
250
300
550 17
567
160
510
930
947 18
185
370
750
200
1320
1337 21
172.5
345
960
340
1645
1662 24
1110
500
1930 19
1949 27
135
270
1035
640
1945
1964 30
110
220
740
1920
1939 33 60
120
810
690
1620
1639 36 72
660
1372
1393 39
360
540
950
971 42 16 32
216
440
688
709 45 8
240
406
427 48
2.7
5.4 96
144
245.4 23
268.4 51
148
171 54
16.2 64
80.2
103.2 57 55
10.8
35.8 63 66

37. Exercise 4: Given the ordinates of a 4-h unit hydrograph as below derive the ordinates of a 12-h unit hydrograph for the same catchment.
Time (h) 4 8 12 16 20 24 28 32 36 40 44
Ordinate of 4-h UH (m3/s) 80
130
150 90 52 27 15 5
Pay attention: desired duration (12-h unit hydrograph) is multiple of given unit hydrograph (4-h unit hydrograph).

38. Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h
Time (h)
Ordinates of 4-h UH (m3/s)
Ordinates of 4-h UH (m3/s) lagged by 4 h
Ordinates of 4-h UH (m3/s) lagged by 8 h
DRH of 3 cm in 12 hours
DRH of 1 cm in 12 hours 4 20 8 80 12
130 16
150 24 90 28 52 32 27 36 15 40 5 44 48

39. Ordinates of 4-h UH (m3/s) Ordinates of 4-h UH (m3/s) lagged by 4 h
Time (h)
Ordinates of 4-h UH (m3/s)
Ordinates of 4-h UH (m3/s) lagged by 4 h
Ordinates of 4-h UH (m3/s) lagged by 8 h
DRH of 3 cm in 12 hours
DRH of 1 cm in 12 hours
0.00 4 20
6.67 8 80
100
33.33 12
130
230
76.67 16
150
360
120.00
410
136.67 24 90
370
123.33 28 52
272
90.67 32 27
169
56.33 36 15 94
31.33 40 5 47
15.67 44 48
1.67

40. S hydrograph
An S-hydrograph (summation) is the hydrograph that results from continuous rainfall excess at a constant rate for an indefinite (long) time
An S-hydrograph (summation) is the hydrograph that results from continuous rainfall excess at a constant rate for an indefinite (long) time

41. S hydrograph is obtained by translating UH of duration tr by many times

42. S-hydrograph
Example:Please compute the 3-hr unit hydrograph from the given 2-hour unit hydrograph by using S-hydrograph method.
Time (hr)
2hr UH
2nd 2 hr UH
3rd 2 hr UH
4th 2 hr UH
5th 2 hr UH
6th 2 hr UH
7th 2 hr UH
S hydrograph UH 1 20 2 45 3 60 4 46 5 34 6 21 7 14 8 9 10 11 12 13

43. Time (hr)
1st 2 hr
2nd 2 hr
3rd 2 hr
4th 2 hr
5th 2 hr
6th 2 hr
7th 2 hr
S hydrograph 1 20 2 45 3 60 80 4 46 91 5 34
114 6 21
112 7 14
128 8 9
121
132 10 11 12 13
S hydrograph becomes horizontal after a while

44. Time (hr)
S hydrograph
Lagged S hydrograph
Difference
3hr UH
0.00 1 20
13.33 2 45
30.00 3 80
53.33 4 91 71
47.33 5
114 69
46.00 6
112 32
21.33 7
128 37
24.67 8
121
4.67 9
132
20 *2 /3 where 2 is UH duration given and 3 is UH duration asked

45. Exercise: Please derive UH. intensity=50mm/hr, theta=10mm/hr, A=162km2

46. 900*120*60/2=3.24×106 m3
RD=3.24×106 m3/162×106 m2=0.02m=2cm

47. UH
Ordinates should be divided by 2cm
RD =20mm
The duration of unit hydrograph is 20𝑚𝑚 40𝑚𝑚/ℎ𝑟 =0.5 hr
(50mm/hr-10mm/hr)