Design Methods: Peak Discharge or Hydrograph Methods?
• Watershed size is a very important criterion for
selection of a design method,
The Unit Hydrograph
Design Method
• Peak discharge equations are appropriate for
small watersheds
• Hydrograph methods preferred for moderate
and large watersheds
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Hydrographs
From rainfall to runoff
Hydrographs show the response of a catchment to precipitation events
 Not all of the amount of precipitation of a storm
event contribute directly to the flow at the outlet
Initial abstraction
 Initial precipitation is stored or absorbed in the
catchment. This is termed the initial abstraction
 Losses represent storage of precipitation
upstream after the storm hydrograph begins
losses
P
storm hydrograph
eff. P
Effective rainfall is that part of rainfall which
contributes directly to runoff
 Direct runoff is the portion of the precipitation
that contributes directly to the hydrograph
(effective precipitation)
 Discharge not associated with the storm (i.e.
groundwater) is termed base flow
Runoff generation is the process of partitioning the
effective rainfall from the losses and infiltration
Peff= effective
rainfall
Peff  QD
runoff hydrogr.
Q
direct runoff
base flow
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QD = direct runoff
time
Determination of the effective rainfall:
Losses
• Losses reflect the ability of the watershed to
retain water.
For the partitioning of total precipitation P to
effective precipitation Peff and losses:
• Losses consist of water intercepted by vegetation
(interception storage), water stored in small
surface depressions (depression storage), and
water that infiltrates into the soil (soil storage).
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Runoff coefficients and Loss-ratio approaches
could be used.
ψ = runoff
Runoff coefficient (ψ)
Ratio of runoff depth to
precipitation depth
Simple method to
determine Peff

Peff
P

QD
P
coefficient
Peff= effective
rainfall
P = rainfall
QD = direct runoff 6
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Determining Effective Rainfall
The Φ Index
But: Parameters which control runoff are changing over time
 Runoff coefficient is not constant!
• The Φ index is a constant rate of abstraction
(cm/h) that will yield an excess rainfall hyetograph
with a total depth equal to the depth of runoff over
the watershed
loss ratio - approach
% - approach
Peff (t )  P(t )  If (t )
Peff (t )  P(t )  (t )
P
Φ-Index
Peff
Horton
I f   f c   f 0  f c   e  k t   P
I f    const.
L
If
P
• Trial and error method.
P
(with initial losses L), Ψ=const.
f0
Losses: urban: 1-1.5 mm
If
f
If(t)
agriculture: 1-5 mm
exponential approach
forest: 4-12 mm
reducing infiltration rate
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Φ Index Method
• The phi index (Φ index) equals
the average rainfall depth above
which the volume of rainfall
excess equals the volume of
direct runoff.
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Procedure for computing the phi index
P
1. Compute the depths of rainfall (Vp) and direct runoff (Vd).
2. Make an initial estimate of the phi index:
𝜙=
If
• Thus the value of ϕ is adjusted such
that the volumes of rainfall excess
and direct runoff are equal.
•
𝑉𝑝 − 𝑉𝑑
𝐷
D is the duration of rainfall (excluding that part separated as
initial abstraction) and ϕ is an intensity, with dimension of
length per unit time such as mm per hour.
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Example: 𝜙 =
𝑉𝑝 −𝑉𝑑
𝐷
Consider the rainfall hyetograph
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What is a Unit Hydrograph?
Assuming that the depth of direct
runoff is 0.4 in
• A unit hydrograph is the hydrograph that results from 1 cm of
rainfall excess generated uniformly over the watershed at a
uniform rate during a specified period of time.
Total rainfall depth =
(0.1+0.25+0.15+0.2) = 0.7in
Rainfall duration = 4 hours
𝜙=
(0.7 − 0.4)𝑖𝑛
4 ℎ𝑟
=0.075 in / hr
Check: time distribution of rainfall
excess = (0.025, 0.175, 0.075, 0.125)
in/hr.
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• Four aspects of this definition:
(1) 1 cm of rainfall excess,
(2) Uniform spatial distribution of rainfall over the watershed,
(3) A rainfall excess rate that is constant with time,
(4) Specific duration of rainfall excess.
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The unit hydrograph method
Assumptions for a UH
Assumptions:
•a unit of effective rainfall generates a
characteristic direct runoff response at the
catchment outlet
• the transfer of excess rainfall into runoff is
independent of antecedent conditions within the
catchment
Conditions of application:
•effective rainfall has a constant intensity and is
uniformly distributed within the catchment
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Implications of the UH Assumptions
1. The effective rainfall has a constant intensity within the
effective duration.
2. Effective rainfall is uniformly distributed over the whole
watershed.
3. The catchment behaves as a linear time-invariant system,
such that the principle of superposition applies
4. The ordinates of all DRH’s of a common time base are
directly proportional to the total amount of direct runoff.
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Implications of the UH Assumptions
• Assumption 1: The effective rainfall has a
constant intensity within the effective duration.
• The storms selected for analysis should be of short
duration. Short storms are most likely to produce
an intense and nearly constant excess rainfall rate
• Assumption 2: Effective rainfall is uniformly
distributed over the whole watershed.
• When the drainage are is too large, it is unlikely to
be covered by a uniform distribution of rainfall
• Assumption 3: The catchment behaves as a linear
time-invariant system, such that the principle of
superposition applies
• The principles of superposition and proportionality are
assumed. Actual hydrologic data are not truly linear, the
resulting hydrograph is an approximation
• Time invariance (the unit hydrograph is unique for a
given watershed and does not vary with time). Unit
hydrographs are applicable when channel conditions
remain unchanged and watersheds do not have
appreciable storage
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UH Principle of equal duration
Application of the UH
• The unit hydrograph is prepared from a known
hydrograph
• It is then used to compute a hydrograph of runoff
for this area for any particular storm or
sequence of storms of any duration or intensity
over any period of time.
• The resulting runoff hydrograph could then be
used for design purposes.
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• Different rainstorms with the same duration but with different
intensities produce runoff for the same period of time.
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UH: Principle of proportionality
• The 1 hour unit hydrograph for a watershed is given below.
Determine the runoff from this watershed for the storm
pattern given. The abstractions have a constant rate of 0.3
mm/h
• Different rainstorms with the
same duration but with different
intensities produce different
volumes of runoff.
• The ratio between this runoff is
the same as the ratio between
the intensities.
• That is to say, that ‘n’ times as
much rain in a given time will
give a hydrograph with ordinates
‘n’ times as large.
Time (h)
1
Unit hydrograph (m3s-1) 10
Time (h)
Precipitation (mm)
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1
0.5
2
100
2
1.0
3
200
4
150
3
1.5
5
100
6
50
4
0.5
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UH: Principle of superposition. Convolution
• The time distribution of direct
runoff from a given storm is
independent of runoff from
earlier storms.
• The total hydrograph of runoff
due to three separate storms
is the sum of the three
separate hydrographs.
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