Chapter 5_Hydrograph Analysis, Unit Hydrograph.pdf

Hydrograph, base flow separation, direct runoff, infiltration, flood hydrograph, stream hydrograph, excess rainfall, unit hydrograph, method of superposition, summation curve, synthetic unit hydrograph, distribution hydrograph, Snyder method, limitations of unit hydrograph

1. Engineering Hydrology
Chapter 5: Hydrograph Analysis (6 hr)
Prof. Dr. Hari Krishna Shrestha
[email protected]
9851006010
January 31, 2024
1.Storm hydrograph, factors affecting hydrograph (shape, size
and slope of basin, drainage density, and land use
2.Components of a flood hydrograph
3.Base flow separation, excess rainfall
4.Application and limitations of unit hydrograph (UH)
5.Derivation of UH from flood hydrograph, method of
superposition and S-curve

2. 5.1.a Characteristics of storm hydrograph
•Storm Hydrograph: time (in x-axis) versus discharge (in y-axis)
•Hydrograph of an isolated storm event: single picked
•Hydrograph of a complex storm event: single or multiple peaked
•Hydrograph shape as a function of basin bio-physical
characteristics, including basin shape
•Hydrograph shape as a function of climatic parameters
•Gentle negative slope just before increase in ordinate value
•Sharper rise, gentler fall
•No base flow in hydrograph of intermittent river
•Base flow value slightly higher at end point than at starting
point
*
, due to lingering effect of higher groundwater flow
(storage) component, again, depends on aquifer properties

3. 5.1.a Storm Hydrograph River discharge versus time
I ma g e result for a nnua l g a ug e

4. Single peaked hydrograph with no
base flow
Approximation of a single peaked
hydrograph with no base flow by
a triangle

5. 5.1.b Factors Affecting Hydrograph
•Catchment factors
•Basin size, shape, slope
•Nature of the valley: wide, narrow
•Elevation
•Drainage density
•Infiltration factors
•Land-use and land-cover
•Soil type & geological conditions
•Depression storages
•Channel characteristics
•Cross section
•Roughness:
–river bed, river banks
•Storage capacity
Meteorological Factors:
•Storm Characteristics
•Initial loss
•Evapotranspiration
CatchmentBasin
Same slide as 4.2

6. 5.2 Components of a Hydrograph0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80 100 120
time (hours)
Discharge (m
3
/s)
◼Flood/Storm Hydrograph
◼Concentration curve
(Rising Limb)
▪Crest Segment
◼Depletion curve
(Recession limb/Falling limb)
◼Lag time
◼Time to peak
◼Time of concentration
◼Time base
◼Peak discharge
◼Centroid
◼Base flow
◼Direct Runoff Hydrograph
Crest
Qp

7. Components of flood hydrograph
Points of inflection
Concentration curve/rising curve/rising limb
Depletion curve/falling curve/falling limb
Crest
Peak Flow or peak discharge
Base flow: flow in river when there is no
rainfall
Time of concentration: time difference
between centroid of rainfall and peak flow
time, time lag (t
l)
Time to peak: time from inflection point to
peak flow time (t
p)
Time base: from initial to final inflection
point (t
b)
DRH: net effect of rainfall
FH: FH – baseflow = DRH0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80 100 120
time (hours)
Discharge (m
3
/s)
Crest
Qp

8. Stream flow recessions0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80 100 120
time (hours)
Discharge (m
3
/s)
•Extends from point of inflection at
the end of crest segment to the
commencement of natural
groundwater flow.
•Represents the withdrawal of water
from the storage built up in the
basin during the earlier phase of
hydrograph
•Shape independent of rainfall,
depends on basin geology, aquifer
characteristics
•Surface storage (surface
detention and channel storage)
•Interflow storage
•Groundwater storage
Slope and shape of the
recession curve is a function
of geological parameters.

9. 5.3.a Base Flow separation
•Separation of hydrograph into rainfall (surface water)
component and base flow (groundwater) components
•Base flow separation from hydrograph
 Straight line from initial inflection point to peak time, and
then another straight line to end point of recession limb (for
low permeability, no (or disconnected) fractures)
 Straight line joining initial and final inflection points, not
necessary horizontal (for medium permeability)
 Back extend straight line from final inflection point to time of
crest end, join with initial inflection point using smooth curve
(for high permeability, and/or interconnected fractures)
•Choice of base flow separation method depends on past
data

10. 0
10
20
30
40
50
60
0 5 10 15 20 25
Time
(hr)
FH
(m
3
/s)
Base
flow 1
(m
3
/s)
Base
flow 2
(m
3
/s)
Base
flow 3
(m
3
/s)
DRH1
(m
3
/s)
DRH2
(m
3
/s)
DRH3
(m
3
/s)
0 4.44.44.44.4 0 0 0
14.014.014.014.01 0 0 0
2 4 3.4 4 4 0.6 0 0
3 9 3 4.04.5 6 5.04.5
4 18 2.64.1 515.413.9 13
5 33 2.24.15.530.828.927.5
6 54 1.84.2 652.249.8 48
7 54 2.04.26.752.049.847.3
8 50 2.24.27.847.845.842.2
9 45 2.34.3 942.740.736.0
10 41 2.54.38.738.536.732.3
11 37 2.74.38.434.332.728.6
12 33 2.94.48.130.128.624.9
13 29 3.04.47.826.024.621.2
14 25 3.24.57.521.820.517.5
15 21 3.44.57.217.616.513.8
16 17 3.64.56.913.412.510.1
17 14 3.74.66.610.39.47.4
18 11 3.94.66.37.16.44.7
19 9 4.14.6 6 4.94.43.0
20 7 4.34.75.72.72.31.3
21 6 4.44.75.41.61.30.6
22 5.14.64.85.10.50.30.0
23 4.84.84.84.8 0 0 0
FH = Flood (Storm) hydrograph,
DRH = Direct Runoff Hydrograph = FH – Base flow
Base flow separation example
Note:
● FH ≥ BF
● Starting and ending value of FH and BF same.
● DRH and UH always start and end in zero
ordinate value. Why?
Base flow 1: green dashed line
Base flow 2: blue dotted line
Base flow 3: red dash-dot line

11. 5.3.b Excess Rainfall and Direct Runoff Hydrograph (DRH)
•DRH represents the net effect of the rainfall by
excluding the effect of the river flow prior to the
rainfall event i.e., by excluding the base-flow
•DRH = Flood Hydrograph – Base-flow
•Excess Rainfall = Total rainfall - infiltration
Example: Total rainfall duration = 4 hr
Effective rainfall duration = 3 hr
(∵rainfall rate < average infiltration rate during 1 hr)
Total rainfall depth = 2.5 cm
Effective rainfall depth = Excess rainfall = 1.4 cm (i.e., 1.1 cm infiltrated)
FH – base-flow = DRH (3 hr DRH, with ER = 1.4 cm)
DRH/ER = Unit Hydrograph (3 hr UH)
UH is always associated with 1 cm ER
DRH and UH always start and end in 0 ordinate value

12. 5.4 Unit Hydrograph Concept,
application and limitations
•Hydrograph resulting from a rainfall event of Excess
Rainfall (ER) of unit depth (normally 1 cm) in a specific
duration (normally in hours)
•For example, a 1.4-hr. unit hydrograph (1.4-hr UH)
means a hydrograph resulting from excess (or effective)
rainfall duration (ERD) of 1.4 hours that produce 1 cm
excess rainfall (ER).
•ER obtained by deducting infiltration from total rainfall.
Infiltration depends on rate of rainfall and -index
•ERD is duration of rainfall during which rainfall rate is
higher than average infiltration rate.

13. 5.4.a Application and Limitations of unit hydrographs
Once we know the size and shape of a unit hydrograph of a particular river
basin, the UH can be used to estimate various hydrological parameters needed
for the design of different water projects.
•Estimate runoff from rainfall data: compared to measurement of river runoff,
the measurement of rainfall data is easier, less hazardous, less expensive,
and more accurate. Once a UH of a particular catchment is developed, the
hydrograph, time to peak, and Qp, can estimated for various rainfall values.
•Estimate flood discharge of particular return period: UH facilitates flood
discharge estimate of different return period based on the return period of
rainfall event; PMP can be converted to PMF, which are required for design
of water resources projects, like HPP, WASH, Water Supply, Irrigation, …
•Flood plane delineation: The Qp at the catchment outlet can be used to
delineate flood plane using Manning’s equation.
•Early warning of floods: The rainfall value can be used to get time to peak,
and Qp, from UH. This, in turn, can be used for flood early warning.
Link to effect of check dams:
https://www.facebook.com/byMapScaping/videos/1205963856222647/

14. 5.4.b Limitations of unit hydrographs (UH)
•Need site specific data.
•Need continuous rainfall and associated hydrograph data
•Assumes uniform rainfall over the entire catchment
•Assumes uniform infiltration over the entire catchment
•Assumes a linear relation between UH of different
magnitude of Excess Rainfall (i.e., assumes that linearity
concept is valid regardless the rainfall intensity)
•Assumes that the antecedent soil moisture has no effect
on the Excess Rainfall and Direct Runoff (Time
invariance)
•Assumes that previous episode of hydrograph has no
effect on the following episode of hydrograph and UH.

15. 5.5.a Derivation of Unit Hydrograph (UH) from storm hydrograph
Rainfall Event causing hydrograph
Clock Time 6810121416
Accumulated rainfall (cm)022.558.58.9
Incremental Rainfall (cm)020.52.53.50.4
-index (cm/hr) 00.50.50.50.50.5
Potential Infiltration (cm)011111
Actual Infiltration (cm)010.5110.4
Excess Rainfall (cm)0101.52.505
Total Rainfall Duration (hr)2222210
Effective Rainfall Duration
(hr) 202206
Total Rainfall Depth (cm)8.9
Effective Rainfall Depth
(cm) 5Catchment area = 770km
2
rainfall duration =6hrs
Assume suitable base flow values 6-hr Unit Hydrograph = ?
Time from storm beginning (h)0 61218243036424854606672
Discharge (m
3
/s) 4065215360400350270205145100705042
Time
(h)
Discharge
(m
3
/s)
Base flow
(assumed)
Direct Runoff
Hydrograph
6-hr UH
(m
3
/s)
0 40 40 0 0.0
6 65 40 25 5.0
12215 40 175 35.0
18360 40 320 64.0
24400 40 360 72.0
30350 40 310 62.0
36270 41 229 45.8
42205 41 164 32.8
48145 41 104 20.8
54100 41 59 11.8
60 70 42 28 5.6
66 50 42 8 1.6
72 42 42 0 0.0
1782
1782 m
3
/s * 6 hrs * 3600 s/hr / 770 km
2
* km
2
/ 1000000 m
2
* 100 cm /m = 5 cm. Note: in the calculation,
6 hrs came from the data spacing of hydrograph, not due to 6-hr UH. The DRH resulted from 5 cm of
effective rainfall (ER). Divide the DRH by 5 to obtain 6-hr UH.

16. 5.5.a Unit Hydrograph (UH) Concept
Rainfall Event causing hydrograph
Clock Time 6810121416
Accumulated rainfall (cm)022.558.58.9
Incremental Rainfall (cm)020.52.53.50.4
-index (cm/hr) 00.50.50.50.50.5
Potential Infiltration (cm)011111
Actual Infiltration (cm)010.5110.4
Excess Rainfall (cm)0101.52.505
Total Rainfall Duration (hr)2222210
Effective Rainfall Duration
(hr) 202206
Total Rainfall Depth (cm)8.9
Effective Rainfall Depth
(cm) 5Catchment area = 770km
2
rainfall duration =6hrs
Assume suitable base flow values 6-hr Unit Hydrograph = ?
Time from storm beginning (h)0 61218243036424854606672
Discharge (m
3
/s) 4065215360400350270205145100705042
Time
(h)
Discharge
(m
3
/s)
Base flow
(assumed)
Direct Runoff
Hydrograph
6-hr UH
(m
3
/s)
0 40 40 0 0.0
6 65 40 25 5.0
12215 40 175 35.0
18360 40 320 64.0
24400 40 360 72.0
30350 40 310 62.0
36270 41 229 45.8
42205 41 164 32.8
48145 41 104 20.8
54100 41 59 11.8
60 70 42 28 5.6
66 50 42 8 1.6
72 42 42 0 0.0
1782
1782 m
3
/s * 6 hrs * 3600 s/hr / 770 km
2
* km
2
/ 1000000 m
2
* 100 cm /m = 5 cm. Note: in the calculation,
6 hrs came from the data spacing of hydrograph, not due to 6-hr UH. The DRH resulted from 5 cm of
effective rainfall (ER). Divide the DRH by 5 to obtain 6-hr UH.

17. 5.5.b Conversion of unit hydrograph duration
[from D-hr UH to (n*D)- hr UH; e.g.: from 2hr UH to 6hr UH, n = 3]
Method of Superposition (MoS): when n is an integer
Steps of MoS:
1. Copy given D-hr UH (n-1) times, each time lagged by D-hr
2. Add given and copied UH to get superposed flow
3. Divide superposed flow by n to get (n*D)-hr UH
Method of Summation Curve (S-curve): when n is (or not) not an integer
Steps of S-Curve:
1.Generate S-curve from given D-hr UH by adding all previous
ordinate values preceded by D hrs.
2.Copy generated S-curve, lagged by (n*D) hr
3.Calculate Ordinate Difference between original and lagged S-curves
4.Divide OD by n to get (n*D)-hr UH
•Graphical concept
•Practical aspect of UH duration conversion (why convert?)
•Numerical Examples

18. Graphical representation of the
Superposition and the S-Curve methods

19. 5.5.b Superposition Curve (S-Curve)
•Curve resulting from addition of an infinite
number of unit hydrographs
•Useful tool to convert unit hydrographs from
one duration to another duration of integer
and non-integer multiple duration

20. Note: The first two columns are the given values, all values in all other columns are calculated.
In the S-Curve column, the first two values (0 and 10) are directly copied from the 12-hr UH because there
is no data of “previous 12 hours”. The third value (i.e., 37) in the S-curve is the addition of 0 and 37 in 12-
UH. Similarly, the value of 148 in the S-curve column came from the addition of 111+37+0; note that these
values came directly from 12-hr UH. However, once we know the trend, the previous values from S-curve
column can be used.
UH starts in ends in 0 ordinate values; when UH duration decreases Q
p increases and T
b decreases.

21. (d) The 6-hour unit hydrograph (UH) of a river catchment is given below. Derive flood
hydrograph (in m
3
/s) of the catchment resulting from following rainfall events. Take -
index = 1/12 (cm/h) and base flow = 5% of the direct runoff hydrograph.
(e) The ordinates of a 2-hour unit hydrograph (UH) are given. Find 4-hour UH (in m
3
/s)
from superposition method, and then use the 4 hour UH to find 2-hour UH using
summation (S-Curve) method.
Time (h) 0612 18
Accumulated rainfall (cm) 066.112.1
Time (hr.) 036 912182430364248546066
6-hr UH(m
3
/s) 0150250450600800700600450320200100500
Time (hr) 0246810121416182022
2-hr. UH Ordinate (m
3
/s)02510016019017011070302060
(f) Discuss the use of unit hydrograph for flood risk management and gate operation of a
hydropower project.