The document discusses unit hydrographs, which are used to model the response of a watershed's streamflow to rainfall. It covers topics such as: - Defining a unit hydrograph and explaining its use in predicting streamflow from rainfall amounts. - Describing the assumptions and terminology used in unit hydrograph models, such as uniform rainfall distribution and the components of a hydrograph. - Explaining how to create a unit hydrograph from streamflow data or synthetically, and how to apply it to calculate a direct runoff hydrograph from rainfall inputs.

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UNIT HYDROGRAPH
By Engineer Mr. Anwar Marwat
.

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Flood pictorial views
Hydrograph - Review
Unit Hydrograph
Unit Hydrograph. Why ?
Assumptions For UH
Terminology for UH
Creating Unit Hydrograph
Applications of Unit H

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FLOOD PICTORIAL VIEWS

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26. Prediction
The only hydrograph that predicts the behavior
of a flood from a storm of any duration

27. Why
Construct & Analyse
Hydrographs ?
To find out discharge patterns of
a particular drainage basin
Help predict flooding events,
therefore influence implementation
of flood prevention measures

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Hydrograph Theory

29. Hydrograph
Graphical representation of time
(hours) versus discharge (cfs or
cms) at a particular point on a
stream or channel which drains
the watershed area

30. Peak Discharge
?

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-------------------------YES
?
Then we will be able to
1. Manage the Storm water.
2. Identify the Flood Plans on downstream side.
3. To place the Hydraulic structures at safe level.
4. Efficient Urban Storm water management plan.
5. Design the Different types of Hydraulic structures.
6. Minimize the effects of Floods.

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Micro Hydro Projects

33. Unit Hydrograph
A conceptual direct runoff
hydrograph resulting from a
rainfall excess of unit depth and
constant intensity for a particular
watershed is called a unit
hydrograph

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 The unit hydrograph method is employed to
calculate the direct runoff hydrograph at the
watershed outlet given the rainfall excess
produced by a storm event.
 This method is categorized as a lumped model
in which the hydrologic characteristics of the
entire watershed are combined and typified by
one or more parameters, simple mathematical
expressions, or graphs.

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 The Unit hydrograph is a useful tool in the process of
predicting the impact of precipitation on stream flow.
 The Unit depth is 1cm in the SI unit system and 1inch
in the U.S. system.
 It is usually abbreviate as a Uhc.
 The subscript “c” indicate the Duration of the rainfall
excess.

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For instance, the direct runoff hydrograph
produced by a rainfall excess that has a
duration of 3 hr and constant intensity of 1/3
in./hr is denoted by UH3 and depth of the
rainfall excess is (1/3 in./hr)(3 hr) = 1 in

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 We can develop a unit hydrograph for a gaged
watershed by analyzing the simultaneous
rainfall and runoff records.
 Unfortunately, most small, urban/rural
watersheds are ungaged. However, there are
several synthetic unit hydrograph methods
available to develop a unit hydrograph for
ungaged watersheds e.g. Espey Ten-Minute
Unit Hydrograph.

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UNIT HYDROGRAPH—WHY ?
Simplifying our task / work / procedures.
Gives us a base line for a specified watershed.
Standardize the hydrograph for different watersheds.
Gives us information that how the flow of a stream will
be affected over time by the addition of one unit of
runoff.

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The role of Unit Hydrograph theory in the flood prediction
process is to provide an estimate of stream flow given
and amount precipitation.
Once we know how much rainfall or snowmelt has
occurred, or is likely to occur, and we have an idea of
how much of this will turn into runoff, we still need to
know how the flow of a stream will be affected over time
by that runoff. The unit hydrograph provide us with a way
to estimate this, and is an integral part of many
hydrological modeling systems.

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ASSUMPTIONS
 The primary assumption of unit hydrograph theory is
that the rainfall has uniform distribution, both in space-
with minimal variations across the basin-and in time; in
other words, the rainfall rate did not vary much during
the event.
 In reality, precipitation events are rarely uniform in
space and time. Often, one portion of the basin
experiences higher intensity precipitation than another
portion.

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 The base duration of direct runoff hydrograph due to an effective
rainfall of unit duration is constant.
 The ordinates of DRH are directly proportional to the total amount
of DR of each hydrograph (principles of linearity, superposition,
and proportionality)
 For a given basin, the runoff hydrograph due to a given period of
rainfall reflects all the combined physical characteristics of basin
(time-invariant)

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BASIN-AVERAGED RAINFALL
In typical non-snow situations, we begin the hydrologic process with
rainfall. In particular, we start with a basin-averaged rainfall. This simply
tells us how much rain fell, or is forecast to fall, on a given basin and
typically takes the form of a rainfall depth per time. In unit hydrograph
theory, we assume that this rainfall has fallen uniformly across the
basin

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BASIN-AVERAGED EXCESS
RAINFALL
From averaged rainfall, we need to know how much of the basin-
averaged rainfall will become runoff. In unit hydrograph theory, runoff is
often referred to as “excess precipitation” or “excess rainfall.” Rainfall
runoff models will typically provide an estimate of what becomes
excess rainfall.
So, for example, if 25% of our 4.00 cm basin-averaged rainfall
becomes excess rainfall, then we have a basin averaged excess
rainfall of 1.00 cm

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Direct Runoff
The unit hydrograph represents the excess
precipitation or quick – response runoff

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TERMINOLOGY - UH
 Duration
 Rising Limb
 Recession Limb (falling
limb)
 Peak Flow
 Time to Peak (rise time)
 Time of Concentration
 Recession Curve
 Base flow Separation line
 Base flow
 Quick Response Run off
 Point of inflection

50. UH Components / Terminology

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CREATING U.HYDROGRAPH
 From Stream flow Data
 Synthetically
 Espey Ten-Minute Unit Hydrograph
 Snyder
 SCS Unit Hydrograph
 Time-Area Unit Hydrograph(Clark, 1945)
 Gamma Function Unit Hydrograph
 “Fitted” Distributions
 Geomorphologic
My Concern

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A unit hydrograph can be derived from a total stream
flow hydrograph at a given stream gauge location
along with the following information:
• The Basin Area
• The Basin-averaged rainfall depth
• The duration over which the excess precipitation
occurred.
STEPS FOR DERIVING THE UNIT HYDROGRAPH

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When deriving a unit hydrograph it is important to
start with an archived hydrograph in which the
quick-response runoff portion is from one single
storm event. In addition, that storm should have
produced its excess precipitation with nearly
uniform coverage in space and time over the basin
Select Appropriate Precipitation EventStep-1

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Remove Base flow ContributionStep-2

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The total volume of water from the quick-response runoff needs
to be calculated. This is done by summing the areas under the
QRR Hydrograph for each time step, in this case, hourly.
Calculate Quick – Response VolumeStep-3

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Determine Excess PPT Depth from BasinStep-4

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Determine Excess PPT Depth from BasinStep-4
For example, assume we have a basin area of 100 square km,
which is 100,000,000 sq.m and calculated volume of quick-
response to be 2,000,000 cum-then the depth will be

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Adjust the Quick-Response HydrographStep-5
The excess ppt depth probably won`t be exactly one unit as unit
hydrograph requires. So, we have to adjust the QRR
hydrograph to show what the response from one unit would be.

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Adjust the Quick-Response HydrographStep-5
Once we multiply each point on the hydrograph by our
adjustment factor of 0.5, our resulting unit hydrograph is for
exactly 1 cm of excess precipitation

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Determine Duration of UHStep-6
The duration of a unit hydrograph refers to a continuous
time period during which one unit of excess ppt occurred.
If it took 6 hours for the one unit of excess to occur, we
have a 6-hr unit hydrograph. Remember, the unit
hydrograph duration does not refer to the duration of the
stream flow response.

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 The difficult part of determining the duration of a unit
hydrograph is estimating which portion of the entire
precipitation event actually contributes to excess ppt.
 Recall that the water that infiltrates & percolates into
deeper storage and base flow is not part of excess ppt.
 We can estimate this portion of the ppt. by applying a
constant loss function to the rainfall.
 Recall that we have already calculated the depth of the
excess ppt to be 2.0 cm. Now, we need to know how
long it took for that excess to occur.

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 So we move this loss function line such that the
amount of ppt. above the line is equal to the depth
of excess ppt. that we already calculated for the
basin.
 Below that line the ppt. goes to long-term storage.
Above the line is the excess ppt.

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 Now we have an excess precipitation bar graph of 6-hr.
 Notice that the amounts from hour to hour on this
graph are not truly uniform. This is typical.
 For purposes of calculating a unit hydrograph duration,
however, we assume that all excess ppt occurred
uniformly in time.

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Final Unit Hydrograph
At the end of these steps, we have a 6-hr unit hydrograph.
It show the stream flow response to 6 hrs of excess ppt
that produced one unit of depth.

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Application of Unit Hydrograph

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 The UH method is based on the assumption of a linear
relationship between the rainfall excess and the DR
rates. More specifically, the method assumes that
 The base time of the DRH resulting from a rainfall
excess of a given duration is constant regardless of
the amount of the rainfall excess, and
 The ordinates of a DRH resulting from a rainfall
excess of a given duration are directly proportional
to the total amount of rainfall excess

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 In other words, the base of the DRH resulting from a
rainfall excess of, say, 1.5 in. produced over af 2-hr
duration is the same as that of the 2-hr UH. Also the
ordinate of this DRH are 1.5 times the ordinates of the
UH2 at respective times. We can simply state that
DRH = cUH2
DRH = 1.5 UH2
General Form

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73. Example:
Two storm each of 6-hr duration and having rainfall
excess values of 3.0cm and 2.0 cm respectively
occur successively. The 2-cm ER rain follows the
3-cm rain. The 6-hr UH for the catchment is the
same as given in previous example. Calculate the
resulting DRH.

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77. Unit Hydrograph of Different Durations
 Under condition where lack of adequate data in
developement of unit hydrograph
 D-hour unit hydrograph is used to develop unit
hydrographs of differing durations nD
 Two method available:
1. Method of superposition
2. The S-Curve

78. If a D-h unit hydrograph is available, and its desired to
develop unit hydrograph of nD, its is easily
accomplished by superposing n unit hydrographs with
each graph separated from the previous on by D-h.
Method of Superpositions

79. D = 2-Hr Unit Hydrograph
Adjusted Net Rainfall
one inch over basin
Qp

80. Change UH Duration
Consider 1 hr UH
Add and Lag two UH
by one hour
Sum and divide by 2
Results in 2 hr UH

81. Example
Given the ordinates of a 4-hr unit hydrograph as
below derive the ordinates of a 12-hr unit
hydrograph for the same catchment
Time (hr) 0 4 8 12 16 20 24 28 32 36 40 44
Ordinates of
4-hr UH
0 20 80 130 150 130 90 52 27 15 5 0

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84. S-Curve
 Also known as S-hydrograph
 Hydrograph produced by continous effective
rainfall at a constant rate for infinite period.
 Curve obtained by summation of an infinite series
of D-h UH spaced D-h apart.

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86. S-Curves for UH

87. S-Curves
• Convert 2 hr UH to 3-hr
• Lag each 2-hr UH by
Duration D
• Add to produce S-curve
S-curve

88. Example
Solve previous example with S-curve method:
Given the ordinates of a 4-hr unit hydrograph as below
derive the ordinates of a 12-hr unit hydrograph for the
same catchment
Time (hr) 0 4 8 12 16 20 24 28 32 36 40 44
Ordinates of
4-hr UH
0 20 80 130 150 130 90 52 27 15 5 0

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90. Hydrograph Convolution
1
2
3
31 2
Add up the ordinates of all three to produce storm hydrograph
STORM
HYDRO
Add and Lag Method

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