HYDROGRAPH ANALYSIS
Hydrograph

Hydrographs are graphical representations of “flow parameters
against time”. When a storm falls in a catchment, after initial
losses and loss due infiltration, rainfall excess eventually flows to
the main stream.

“If the discharge ‘Q’, average velocity ’V’ and depth or stage ‘Y’ at
outlet point of the stream is measured from beginning of the
storm to the end of storm in the catchment and if they are plotted
against time, they may be called Hydrograph”.
i)
If ‘Q’ is plotted against time ‘t’, it is called flow or “flood
Hydrograph”
ii) If ‘V’ is plotted against ‘t’, it is known as “Velocity
Hydrograph”
iii) If depth ‘Y’ or stage ‘H’ is plotted against time ‘t’, it is called
depth or “Stage Hydrograph”.
“But most commonly in Hydrology, Hydrograph means the
1
graph of flow rate ‘Q’ against time ‘t’”
HYDROGRAPH ANALYSIS
Hydrograph of Single and Complex Storms (Picture-I)
2
HYDROGRAPH ANALYSIS
Hydrograph of Single and Complex Storms (Picture-II)
3
HYDROGRAPH ANALYSIS
Components of Hydrograph of Isolated Storm
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
AB is approach segment
BC is rising limp or concentration curve
CPD is crest segment or peak limb
DE is falling limb
Lower portion DE is called “Ground Water Depletion” curve
P is the point of crest or peak
tB is time of rise
Tp is the time of peak
Area under ABE is the volume of base flow (shown by shaded
line). This volume is assumed to have no contribution of storm.
x. Area between BPE and BE is the volume of direct surface runoff
(DSR) shown by dots.
xi. OA is the value of discharge at initial time t=0 and this OA may
be assumed to be the base flow.
xii. ‘C’ is the first point of inflexion and ‘D’ is the second point of
inflexion.
4
xiii. OE1 is the base period ‘T’ of the hydrograph
HYDROGRAPH ANALYSIS
Hydrograph Components
5
HYDROGRAPH ANALYSIS
Hydrograph Segment
6
HYDROGRAPH ANALYSIS
Segments of Hydrograph of an Isolated Storm
Hydrograph is broadly divided into following three segments;

Rising Limb/ Segment
In the initial time of rainfall, losses cause the discharge to rise
slowly. Building up of storage is evidently gradual.
However, if the storm is continuous, a accumulative discharge
from upstream reaches the outlet (as infiltration and absorption
loss decreases with time). “Of course, shape of basin and storm
characteristics affect the rising limp”.

Peak Limb/ Crest Segment
It is the most important part of Hydrograph. Peak outflow is
essential for design of Hydraulic Structures. When runoffs from
all sources reach the outlet, peak flow occurs.
In large catchment, peak flow may even occur after the storm.
“Estimation of peak flow and its time of occurrence are very
7
important in Hydrology”.
HYDROGRAPH ANALYSIS
Segments of Hydrograph of an Isolated Storm

Recession Limb/ Depletion Curve
The recession limb represents the “withdrawal of water from
storage after all inflows to the channel have ceased. “Therefore, it
is time independent of rainfall or infiltration and is essentially
dependent on channel features alone”.
8
HYDROGRAPH ANALYSIS
Factors Affecting Flood Hydrograph
i.
“Climatic factors” are movement, infiltration, intensity and
duration of rainfall.
ii. “Physiographic factors depend on”;
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Shape of Basin
Size of Basin
Slope of Basin
Nature of Basin
Drainage Density
Elevation of Catchment
Land use and Cover
Soil type and Geological Condition
Lakes, Storages, Swamps
Channel Characteristics
9
HYDROGRAPH ANALYSIS
Base Flow Separation

Base flow is the initial flow of the stream before the rain comes.
“It is the sustained or dry weather flow of the stream resulting
from the outflow of perennial or almost permanent ground water
flow that reaches the channel”. This base flow of such channel is
more or less assumed to be constant.

Following are the methods of separating this base flow from the
total recorded flows of the Hydrograph;
i)
Straight Line Method
ii) Fixed Base Method
iii) Variable Slop Method
10
HYDROGRAPH ANALYSIS
Separation of Base Flow
11
HYDROGRAPH ANALYSIS
i) Straight Line Method
In this method, base flow separation is achieved by a straight line
joining from a point ‘A’ figure below to a point ‘B’ on the recession
limb representing the end of surface runoff. “This method is
approximate, but very easy to separate. Error is not much”.
12
HYDROGRAPH ANALYSIS
ii) Fixed Base Method

Time base of Direct Surface Hydrograph (DSR) should remain
relatively constant for storm to storm. In using method of
separation, this point should be kept in mind.

“This is usually provided by terminating the direct runoff at a
fixed time after the peak of the Hydrograph. As a rule of thumb,
time in days ‘N’ may be approximated by”
N = 0.8A0.2

Where ‘A’ is area of catchment (km2) and ‘N’ is the time in days
the figure below shows the reasonable and un-reasonable value
of ‘N’.
13
HYDROGRAPH ANALYSIS
Fixed Base Method
14
HYDROGRAPH ANALYSIS
Variable Slope Method

Here base flow curve existing prior to the commencement of
surface runoff is extended till it intersects the ordinate drawn at
point ‘D’. This point ‘D’ is joined with a straight line DB.

The volume below ADB is volume of base flow (figure-’a’ & ‘b’
enclosed). In figure-’b’, base flow recession curve after depletion
of the floodwater at ‘B’ is extended backward till it intersects the
ordinate DB at point of inflection. The points ‘A’ and ‘D’ are joined
by straight line.

“The volume under ADB represents the volume of base flow”.
15
HYDROGRAPH ANALYSIS
Variable Slope Method
16
HYDROGRAPH ANALYSIS
Computation of Direct Surface Runoff (DSR) from a Storm
Enclosed figure shows the flood hydrograph of a storm with flood
ordinates at different time interval Δt. “From the flood hydrograph,
separate the base flow by any one of the methods described earlier”.
Let the “Base Flow” is separated by simple straight line method and
Direct Surface Runoff (DSR) Hydrograph is drawn (figure enclosed).
Let Q1, Q2, Q3, Q4, …., Qn-2, Qn-1, Qn are the ordinates of Direct Surface
Runoff (DSR) Hydrograph at different time interval Δt.
Find the area under the (DSR) Hydrograph, which will represent the
volume of (DSR);
Area under the curve APB = Volume of DSR
= A1+A2+A3+A4+….. + An-2 + An-1 + An
= 1Q1Δt + [Q1+Q2]Δt + [Q2+Q3]Δt + [Q3+Q4] Δt+ … + [Qn+2+ Qn+1]Δt
2
2
2
2
2
+ [Qn-1+ Qn]Δt + 1 Δt
2
2
17
HYDROGRAPH ANALYSIS
= [1Q Δt+Q1 Δt]+[Q2Δt+Q2 Δt]+[Q3Δt] + [Q4Δt+Q4 Δt] +…+ [Qn-2Δt+Qn-2 Δt]
2
2
2
2
2
2
2
2
2
+ [Qn-1Δt+Q1Δt] + [QnΔt+Qn Δt]
2
2
2
2
= [(Q1 + Q2 + Q3 + Q4 + …. Qn-2 + Qn-1 + Qn)] Δt
= ∑QΔt
Q = Total volume of Direct Surface Runoff. If ‘Q’ in m3/sec, & Δt in hr.
Volume of DSR = ∑QΔt m3 x (60 x 60) sec
sec
= ∑QΔt m3 x (60 x 60) m3
If ‘A’ is the area of the catchment in km2, A = A x 106 m3
DSR in cm = {[(60 x 60) ∑QΔt] x 100} cm
A x 106
DSR = 0.36 ∑Q x t (cms)
A
Thus, DSR volume (depth in cm) = Rainfall excess or net rainfall
18
HYDROGRAPH ANALYSIS
Flood Hydrograph of a Single Storm
19
HYDROGRAPH ANALYSIS
Calculation of Direct Surface Runoff (DSR) Hydrograph (Depth)
20
HYDROGRAPH ANALYSIS
Example:Calculate Direct Surface Run-off for Rainfall excess from a Storm
Hydrograph from the following data. Assume Area of Catchment as
30 km2
Date and Time
Ordinate of Hydrograph
Total Q (Cumecs)
Base Flow
(Cumecs)
Direct Runoff
(Cms)
1
2
3
4
0500
14
14
0
0800
25
12
13
1100
51
11
40
1400
65
10
55
1700
54
11
43
2000
28
13
15
2300
14
14
0
14.08.2012
∑Q = 166
21
HYDROGRAPH ANALYSIS
Solution

Find the “ordinates of storm Hydrograph”, representing total
discharge Q at a given time interval, say ‘t’ hours.

Separate the “Base Flow” by any of the methods. Find the
ordinates of the base flow at the same time interval.

Find the ordinates of “Direct Run-off” by subtracting the
ordinates of base flow from total discharge ordinates.

The Direct Surface Run-off (depth in cm) is found from the
expression.
22
HYDROGRAPH ANALYSIS
23
HYDROGRAPH ANALYSIS
Unit Hydrograph

Unit Hydrograph (UH) is “defined as the Hydrograph of surface
runoff of a catchment area resulting from unit depth
(usually 1 cm) of rainfall excess or net rainfall occurring uniformly
over the basin and at uniform rate for a specified duration”.

Unit Hydrograph is a linear model of the catchment which is used
to find out the volume of DSR due to 1 cm of direct surface runoff
or 1 cm of rainfall excess. This is always constant for the
catchment since area of the catchment is constant.

If rainfall comes to the catchment producing 2 cm of rainfall
excess, “the ordinates of the DSR will be twice as great of the
Unit Hydrograph (UH) ordinates and volume of DSR will be two
time the volume of DSR of unit hydrograph”.
HYDROGRAPH ANALYSIS
Assumptions in Derivation of UH Theory
i.
The rainfall is of “uniform intensity” within its specified duration.
ii. The effective rainfall is “uniformly distributed” throughout the
whole area of drainage basin.
iii. “The base of time duration of Hydrograph of direct runoff due to
effective rainfalls of unit duration is constant”. Base period of
Hydrograph of different rainfall intensities remain approximately
same. As represented in enclosed figure.
iv. The ordinates of DSR Hydrograph “due to net rains of different
intensities but same duration are proportional”.
v. A Unit Hydrograph reflects
characteristics of the basin.
all
the
combined
physical
HYDROGRAPH ANALYSIS
Derivation of UH from a simple Flood Hydrograph –
(Isolated Storm)
Step 1 From the given flood Hydrograph, “separate the base flow” by
any one of the methods. Most commonly used method to
draw a straight line without much error for simplicity (Figure
enclosed)
Step 2 Determine the volume of DSR Hydrograph by the formula;
“Volume of DSR = ∑QΔt”
Step 3 Divide this volume by “known Area of Catchment” to get DSR
volume (depth in cm) i.e., “net rainfall or rainfall excess”.
Step 4 Divide the ordinates of DSR by the depth of DSR Hydrograph
to obtain ordinates of UH.
Step 5 Plot the ordinates of UH of the catchment as per enclosed
figure.
HYDROGRAPH ANALYSIS
Unit Hydrograph Derivation
HYDROGRAPH ANALYSIS
Example-I
Calculate and Draw a “Unit Hydrograph” from a Storm Hydrograph, resulting
from a Catchment Area of 25 km2. The data is shown in the following table:
HYDROGRAPH ANALYSIS
Direct Runoff = 0.36 (∑Q x t) = 0.36 x 822 x 2
A
25
= 23.7 cm
HYDROGRAPH ANALYSIS
Unit Hydrograph from a Single Flood Hydrograph
HYDROGRAPH ANALYSIS
Example-II:-(UH) from a Single Flood Hydrograph (Isolated)
HYDROGRAPH ANALYSIS
Limitations and Uses of UH Theory
Limitations
i. Similar rainfall distribution from storm over a large area is rare.
Hence UH theory is suited to catchment area under about 500 km3
(=2000 sq. miles)
ii. Odd shaped basins particularly those which are long and narrow,
commonly have very uneven rainfall distribution and hence UH
theory for such basins is not much suitable.
iii. In mountainous regions, subject to orographic rainfall, aerial
distribution is very uneven, but the pattern tends to remain the
same from storm to storm, and UH theory may not be
successfully applied.
iv. The unit hydrograph method cannot be applied when an
appreciable portion of the storm precipitation falls as snow.
v. The catchment having large storage like reservoir, lake, low areas,
etc. affect the linear relationship and hence theory cannot be
applied.
vi. If the variation of base period and peak flow vary more than +/10%, theory applied is not generally accepted.
HYDROGRAPH ANALYSIS
Limitations and Uses of UH Theory
Uses
i.
As the UH is a “linear model of the catchment”, it is used to
determine runoff Hydrograph of the Catchment even for
extreme magnitude for “the calculation of peak discharge to
design the Hydraulic Structures”.
ii. It can also be used for flood forecasting and warning.
iii. Based on rainfall records, “it is used for extension of flood
records”.
HYDROGRAPH ANALYSIS
CALCULATION OF STORM
HYDROGRAPH
FROM
THE GIVEN UNIT HYDROGRAPHS
OF VARIOUS RAINFALL
INTENSITIES
HYDROGRAPH ANALYSIS
Case-I
Application of the (UH) Theory for the “Construction of a Flood
Hydrograph Resulting from Rainfall of Single Duration”





The Unit Hydrograph can be used to construct a “Flood Hydrograph“
resulting from rainfall of the “same unit duration for which the Unit
Hydrograph is available”.
The number of Unit Hydrographs for a given drainage basin is
theoretically infinite since there may be one for every possible
duration of rainfall and every possible distribution pattern in a basin.
Practically only a limited number of Unit Hydrographs can be used
for a given basin. “The Unit Hydrograph selected for computing the
flood Hydrograph should be corresponding to the storm of like
duration and pattern”.
However, a tolerance of as much as 25% of the Unit Hydrograph
duration can ordinarily be accepted without much serious error. Thus
a 6-hours Unit Hydrograph must be applied for storms of 4.5 to 7.5
hours duration.
Alternatively, Unit Hydrograph having a similar range in duration may
be averaged to obtain an average Unit Hydrograph.
HYDROGRAPH ANALYSIS
Procedure
The calculations for the storm Hydrograph corresponding to ‘n’ cm of
rainfall-excess are done in the tabular form as per enclosed table;
Direct runoff ordinates=(ordinates of Unit Hydrograph) x‘n’ cm
Step-I
: Write down the “given hourly ordinates” (Discharge) of
Unit Hydrograph.
Step-II
: Multiply the ordinates of Unit Hydrograph with ‘n’ cm of
Rainfall.
Step-III : List out the given hourly “base flow (m3/sec)”
Step-IV :
Find out the total storm ordinates i.e. = Step-II + Step-III
The above procedure is elaborated by the enclosed table. Through an
example (Calculation of Storm Hydrograph Resulting from 8 cm
Rainfall.
HYDROGRAPH ANALYSIS
Example:- Calculate Storm Hydrograph of 8 cm Rainfall
4
5
HYDROGRAPH ANALYSIS
Case-II
Application of Unit Hydrograph Theory “for the Construction of a
Flood Hydrograph Resulting from two or more Periods of
Rainfall (Multi Duration Rainfall)” from a Single UH

A Unit Hydrograph of some specific unit duration can also be
utilized for construction of flood Hydrograph resulting from the
“rainfall lasting for a longer duration”.

The essential condition, however, is that the storm pattern should
be the same as that for the Unit Hydrograph.

As an example, let a 3-hours Unit Hydrograph is available, and it
is required “to compute the flood Hydrograph resulting from a
rainfall lasting for 9-hours with variable intensities of rainfall”.

The intensity rates having “n1 cm/3-hours” for the first period of
3-hours, “n2 cm/3-hours” for the second 3-hours, and that of
“n3 cm/3-hours” for the last 3-hours.
HYDROGRAPH ANALYSIS
Procedure
Step-I

The storm is divided into 3 parts, and the flood Hydrograph of
each part is computed separately and added.
Step-II

The Hydrographs for the second part of the storm starts 3 hours
later than that for the first part.
Step-III

Similarly, the Hydrograph for the third part of the storm starts 6
hours later than that for the first, or 3 hours later than that for the
second part.

The above procedure is illustrated through the enclosed example.
HYDROGRAPH ANALYSIS
Example:Find the ordinates of a “storm Hydrograph resulting from a 3 hours
storm with rainfall of 2.0, 6.75 and 3.75 cms during subsequent 3
hours intervals”. The ordinates of Unit Hydrograph are given in the
following table. Assume an initial loss of 5 mm, infiltration index of
2.5 mm/hour and base flow of 10 cumecs.
Ordinates of given Unit Hydrograph
Hours
03
06
09
12
15
18
21
24
03
06
09
12
15
18
21
24
Ordinate of
UH
0
110
365
500
390
310
250
235 175 130
95
65
40
22
10
0
HYDROGRAPH ANALYSIS
Solution:i)
Rainfall excess during the first three hours
= 20 – (2.5 x 3) – 5 = 7.5 mm = 0.75 cm
ii)
Rainfall excess during the second three hours
= 67.5 – (3 x 2.5) = 60 mm = 6 cm.
iii)
Rainfall excess during the last three hours.
= 37.5 – (3 x 2.5) = 30 mm = 3 cm

The Rainfall excess as ratio of the unit Rainfall of 1 cm during the
subsequent 3 hours intervals are 0.75, 6 and 3.

The computations of Runoff due to 0.75 cm rainfall excess will
start from 03 hours. The computations of runoff due to 6 cm
rainfall excess will start from 6 hours. Lastly, the computations of
runoff due to 3 cm rainfall excess will start from 9 hours.

“The above procedure is illustrated in the enclosed table”.
HYDROGRAPH ANALYSIS
Table:-
HYDROGRAPH ANALYSIS
Flood Hydrograph Resulting from a Storm of Longer Duration
HYDROGRAPH ANALYSIS
Example:Calculation of Storm Hydrograph Resulting from Single
Unit Hydrograph of Various Rainfall Intensities
Contd…..
HYDROGRAPH ANALYSIS
HYDROGRAPH ANALYSIS
Case-III
S-Hydrograph (S-Curve)



S-Hydrograph or S-Curve is a Hydrograph which is produced by a
“continuous effective rainfall at a constant rate for indefinite
period”.
It is a “continuous rising curve”, in the form of letter ‘S’, till
equilibrium is reached. At the time of equilibrium, “it will
represent a constant rate of continuous effective rainfall, say Ro
cm per hour”.
At the time of equilibrium, “the S-Curve will represent a runoff
discharge as under”;
Qo = (A x 100 x 100) Ro
100 x 3600
= A Ro cumec
36
(Where A is the catchment area in hectares)
Contd…
HYDROGRAPH ANALYSIS

If the catchment area ‘A’ is in “square kilometers”, the discharge
represented by S-Curve, at the time of equilibrium is given by;
Qo = (A x 1000 x 1000) Ro
100 x 3600
=(AR0) x 100 (cms)
36
= 2.778 A Ro (cms)
(‘A’ = Area of catchment in km2 and Ro = Constant rate of
continues effective Rainfall.)

The S-Hydrograph or S-Curve is constructed by “adding together
number of Unit Hydrographs of unit time duration (T0) spaced at a
unit time duration (T0) (i.e., duration of effective rainfall).

“This is illustrated in the enclosed example were in S-Curve has
been drawn for 6 hours Unit Hydrograph. Area of basin is 311
km2”.
HYDROGRAPH ANALYSIS
Computation of S-Hydrograph from Successive Unit Hydrograph
Contd…
HYDROGRAPH ANALYSIS
This discharge of 144 cumecs will be achieved in the above table at 36
hours (which is equal to base period – T0 hours.)
HYDROGRAPH ANALYSIS
Derivation of S-Hydrograph from Series of Unit Hydrograph
HYDROGRAPH ANALYSIS
CALCULATION OF UNIT
HYDROGRAPH
FROM
THE GIVEN UNIT HYDROGRAPHS
OF VARIOUS INTENSITIES
HYDROGRAPH ANALYSIS
Case-I
Construction of Unit Hydrograph of Different Unit Duration
from the a Unit Hydrograph of given Unit Duration


Unit Hydrograph may be of different duration ‘D’. If a unit
hydrograph of 2 hrs. duration available, unit hydrograph of 4 hrs.
duration, 6 hrs. duration, 8 hrs. duration, etc. may be obtained i.e.,
the unit hydrograph to be derived is an integral multiple. In such
cases, durations from 2 hrs. to 4 hrs., 6 hrs. etc. can be done by
method of superposition.
However, if the Duration of Unit Hydrograph to be derived is less
than duration of known Unit Hydrograph, “this method of
superposition will not hold good”. Thus, Unit Hydrograph of
different duration may be derived by the following two methods.
i)
Method of superposition when duration of UH to be derived is
2 times, 3 times or 4 times of the duration of known UH.
ii) S-Curve method (Summation hydrograph method) when
duration of UH to be derived is less than the duration of the
known UH.
HYDROGRAPH ANALYSIS
Unit Hydrograph of Different Durations
Phase-A:Construction of Longer period Unit Hydrograph from a given
Unit Hydrograph of Shorter Unit Period/ Duration.
Method of Superposition
i)
As shown (figure enclosed) D-hr UH is plotted (Curve-1)
ii)
Also plot the UH lagged by D hrs. (Curve-2)
iii)
Add the two Unit Hydrographs and plot it (Curve-3)
iv)
Divide Curve-III, i.e. DSR Hydrograph by 2D duration to get
the curve shown by dotted line, i.e. (Curve-4)
It is noted that base period of 2-D-hr UH shown by dotted line
increases by D-hrs from the given UH of T hrs base period.
Therefore, the peak of 2-D-hrs UH will decrease as the base
period is increased from T to (T + D hrs)
HYDROGRAPH ANALYSIS
Example – Unit Hydrograph of Different Durations
A 4-hr UH of different durations is shown in the following table. Derive
the 8 hr Unit Hydrograph.
Column (5) gives the ordinates of 8-hr unit Hydrograph derived from
column (4) and unit UH in column (2). The peak of the 8-hr UH is
reduced to 16m3/sec from 20m3/sec as the base period is increased
from 20 to 24 hrs.
HYDROGRAPH ANALYSIS
Method of Superposition
HYDROGRAPH ANALYSIS
Example-II:- Method of Superposition
HYDROGRAPH ANALYSIS
Case-II
Unit Hydrograph of Different Durations - S- Curve Method

S-Curve (Summation Curve), also known as S-Hydrograph is a
Hydrograph produced by a “continuous effective rainfall of unit
depth at a constant rate for indefinite period”. It is a curve
obtained by summation of an infinite series of Unit Hydrographs
each lagged by D-hrs with respect to preceding one.

It is shown that when a UH of ‘n’ ‘D’ duration is required where ‘n’
is whole number like 2,3,4 etc., method of superposition serves
the purpose. If ‘n’ is in-fraction, then S-Curve method is required.

As an example, from UH of 4 hrs. duration, to develop UH of 2 hrs.
duration cannot be developed by the pervious method of
superposition. In such situation, “S-Hydrograph is constructed.
Which is used to find the UH of desired duration”.

As shown (figure enclosed), S-Hydrograph is continuously a
rising curve which ultimately attains a constant value when
equilibrium discharge is reached.
HYDROGRAPH ANALYSIS
Unit Hydrograph of Different Durations
Unit Hydrograph can be derived as under;
Step 1 “Construct the S-Curve” from the given Unit Hydrograph of
known time duration D-hrs.
Step 2 “Then advance or offset” the position of all the ordinates of
“S-Hydrograph” for a period equal to the desired duration of
D0 hrs. of unknown UH. “Name this S-Hydrograph as offset
Hydrograph”.
Step 3 Find the “Difference” of the ordinates of Original S-Curve and
“Offset Hydrograph”.
Step 4 “Divide this each difference” by (D0/D) to get the ordinates of
new UH of D0 hrs. duration.
HYDROGRAPH ANALYSIS
S-Hydrograph or S-Curve
HYDROGRAPH ANALYSIS
Phase-B:
Construction of Shorter or
from a given Unit Hydrograph
Longer
Period
Unit
Hydrograph

Let it be required to obtain a “Unit Hydrograph” of unit period t0 from a
given Unit Hydrograph of unit period. T0, “where t0 can be either greater
or smaller than T0”. For this, the S-Hydrograph method will be used.

From the given Unit Hydrograph of unit period T0, “S-Curve is derived”.
This S-Curve will represent a constant effective rainfall of R0 = 1/ T0
cm/hour.

“An offset curve is then drawn by advancing or offsetting the position of
original S-Curve” for a period equal to the desired unit period to hours.

“The difference between the ordinates of original S-Curve and the offset
S-Curve divide by the R0 t0“ will give the ordinate of the desired Unit
Hydrograph.

Thus, for any time period t, if the difference ordinates of the two SCurves is Δy, then the ordinate of the desired Unit Hydrograph of t0 unit
period.
Δy
R 0t 0
= Δy
(1/T0)t0
=
Δy. T0
t0
HYDROGRAPH ANALYSIS
Example-I
Derivation of Unit Hydrograph of t0 (= 3 hours) unit duration from the
given Unit Hydrograph of duration T0 (= 6 hours)
HYDROGRAPH ANALYSIS
Construction of Shorter or Longer Period of Unit Hydrograph
from a given Unit Hydrograph
HYDROGRAPH ANALYSIS
Example-II:- of S-Curve Method
Given below are the ordinates of 4 hrs UH of a basin.
Derive 2 hrs UH from it using S-Curve Method.
HYDROGRAPH ANALYSIS
HYDROGRAPH ANALYSIS
HYDROGRAPH ANALYSIS
Case-III
Derivation of UH from Complex Storm

Practically, “it is not always possible “to have such isolated
storms”. Storms having different rainfall excess like R1, R2 and R3
may occur. “Such storms of different rainfall excess are called
complex storm”.

Assume 3 storms which can produce rainfall excess R1, R2 and
R3. The Hydrograph of these 3 storms (after deducting base flow)
is shown in figure enclosed.

Let Q1, Q2, Q3,….. Qn are the known ordinates of complex storm as
per figure enclosed and U1, U2, U3, ….. Un are ordinates of Unit
Hydrograph which are to be determined. R1, R2 and R3 are known
rainfall excesses due to complex storm, which are also known.
Then;
HYDROGRAPH ANALYSIS
Derivation of UH from Complex Storm
Qn = RnU1 + Rn-1U2 + Rn-2U3 + ….,
When
n = 1,
Q1 = R1U1
(i.e. Q1 and R1 are known, U1 is determined)
n = 2,
Q2 = R 2 U 1 + R 1 U 2
(i.e. Q2,R2,U1,R1 are known, U2 is determined)
n=3,
Q3=R3U1+R2U2+R1U3
(i.e. Q3,R3,U1,U2,R1,R2 are known, U3 is determined)
n=4,
Q4=R4U1+R3U2+R2U3+R1U4,
R4U1 is zero, since no 4th rainfall is considered
Since Q4, R3, R2, R1, U2, U3 are known, U4 can be determined
Thus, all ordinate of Unit Hydrograph U1, U2, U3, U4, …… Un can be
determined and resulting Unit Hydrograph (UH) can be obtained.
HYDROGRAPH ANALYSIS
Derivation of UH from Complex Storm
HYDROGRAPH ANALYSIS
Derivation (UH) from Complex Storm
Example
Draw the Unit Hydrograph from the complex storm having the data
given below;
Time (Hrs)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
UH Ordinates
m3/sec
0
58
110
96
53
26
14
8
5
4
3
1.5
1
0
Compute the storm Hydrograph resulting from three hour storm rainfall
as under:Time
1st hr
2nd hr
3rd hr
Rainfall depth (cm)
4
3
2.5
Take Φ-index as 2 cm/hr and assume a base flow of 2 m3/sec.
Solution
Net Rainfall are DSR in depth 1st hr = 4 – 5 Φ Index = 4 – 2 x 1 = 2 cm
2nd hr = 3 – 2 x 1 = 1 cm
3rd hr = 2.5 – 2 x 1 = 0.5 cm
HYDROGRAPH ANALYSIS
Example of Derivation (UH) from Complex Storm