notes for bachelor civil engineering and construction
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About This Presentation
notes for bachelor civil engineering engineering hydrology
Slide Content
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 5
Flood, its Effects & Important Characteristics
•What is flood?
–Flood is an unusually high stage (or water level) in a river, in which, normally,
river overflows its banks and inundates the adjoining area.
•Effects/impacts of floods
–It causes losses of life, property, physical infrastructure, and economy
–It also costs significant amount of money for post-flood management activities
•Hydrologic design of water infrastructure projects ensures the structure can
survive for the floods less than or equal to design flood.
•What aspects of floods are important for hydrologic design?
–Hydrograph of extreme floods and corresponding stage data
–Flood peak is the most important & widely used characteristics of flood
hydrograph
–Flood peak at a location varies from year to year, its time-series is valuable
information.
Flood, its Effects & Important Characteristics
•What is flood?
–Flood is an unusually high stage (or water level) in a river, in which, normally,
river overflows its banks and inundates the adjoining area.
•Effects/impacts of floods
–It causes losses of life, property, physical infrastructure, and economy
–It also costs significant amount of money for post-flood management activities
•Hydrologic design of water infrastructure projects ensures the structure can
survive for the floods less than or equal to design flood.
•What aspects of floods are important for hydrologic design?
–Hydrograph of extreme floods and corresponding stage data
–Flood peak is the most important & widely used characteristics of flood
hydrograph
–Flood peak at a location varies from year to year, its time-series is valuable
information.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 6
Design Flood & its Frequency
•A flood used for the design of structure on
considerations of its safety, economy, life
expectancy and probable damage considerations
is called as “design flood”.
•Small structures such as culverts and storm-
drainages can be designed for less severe floods
as the consequence of higher than design flood
will not be very serious.
•Larger structures such as dams demands greater
attention to the magnitude of floods used in the
design, because of failure of these structures
causes large loss of life and property on the
downstream of structures
•Choosing appropriate magnitude of flood as
“design flood” depends upon;
–Types of structure
–Importance of the structure
–Economic development in the surrounding area
Design Flood & its Frequency
•A flood used for the design of structure on
considerations of its safety, economy, life
expectancy and probable damage considerations
is called as “design flood”.
•Small structures such as culverts and storm-
drainages can be designed for less severe floods
as the consequence of higher than design flood
will not be very serious.
•Larger structures such as dams demands greater
attention to the magnitude of floods used in the
design, because of failure of these structures
causes large loss of life and property on the
downstream of structures
•Choosing appropriate magnitude of flood as
“design flood” depends upon;
–Types of structure
–Importance of the structure
–Economic development in the surrounding area
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 7
Design Flood & its Frequency
•Different types of design floods are;
–Frequency-based flood (FBF): mostly used for designing spillways (also called as Spillway
design flood).
▪design flood estimated using flood frequency analysis (e.g., 10 yr, 20 yr, 50 yr, 100 yrfloods)
–Probable maximum flood (PMF):
▪the extreme flood that is physically possible in a region as a severe-most combinations. It is
estimated based on unit hydrograph & PMP (probable maximum precipitation)
–Standard project flood (SPF):
▪flood computed from standard project storm occurredover the project area or on the adjoining
areas with similar hydro-meteorological and basin characteristics
▪Generally 40-60% of PMF for the same drainage basin.
•Frequency refers to the number of occurrences of a variate (i.e., an individual
observation or the value of any variable)
–A plot of frequency against the variate is called as frequency distribution.
Design Flood & its Frequency
•Different types of design floods are;
–Frequency-based flood (FBF): mostly used for designing spillways (also called as Spillway
design flood).
▪design flood estimated using flood frequency analysis (e.g., 10 yr, 20 yr, 50 yr, 100 yrfloods)
–Probable maximum flood (PMF):
▪the extreme flood that is physically possible in a region as a severe-most combinations. It is
estimated based on unit hydrograph & PMP (probable maximum precipitation)
–Standard project flood (SPF):
▪flood computed from standard project storm occurredover the project area or on the adjoining
areas with similar hydro-meteorological and basin characteristics
▪Generally 40-60% of PMF for the same drainage basin.
•Frequency refers to the number of occurrences of a variate (i.e., an individual
observation or the value of any variable)
–A plot of frequency against the variate is called as frequency distribution.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 8
Return Period, Frequency & Risk
•Frequency analysis of storm events provides information on probability of occurrence of
extreme events. And,
–Structures are built to be safe against the extreme events of certain return period.
•Frequency analysis is based on historical records of hydrological data
•For frequency analysis, the data of the given series is 1
st
arranged in descending order
of magnitude and then the probability of each event being equalled to or exceeded is
calculated by,
–Where, P is probability of each event, m = order (or rank) number of the event; N = total
number of events in the data series
•The return period (T) or recurrence interval is calculated by
–T = 1/P = (N + 1) / m.1+
=
N
m
P
Return Period, Frequency & Risk
•Frequency analysis of storm events provides information on probability of occurrence of
extreme events. And,
–Structures are built to be safe against the extreme events of certain return period.
•Frequency analysis is based on historical records of hydrological data
•For frequency analysis, the data of the given series is 1
st
arranged in descending order
of magnitude and then the probability of each event being equalled to or exceeded is
calculated by,
–Where, P is probability of each event, m = order (or rank) number of the event; N = total
number of events in the data series
•The return period (T) or recurrence interval is calculated by
–T = 1/P = (N + 1) / m.1+
=
N
m
P
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 9
Return Period, Frequency & Risk
•Return period (or recurrence interval), T:
–It is defined as the averageinterval of time (T) within which an event of given magnitude will be
equalled or exceeded at least once.
–It is the average interval between the occurrence of flood equal to or greater thana given magnitude.
The return period is widely used in hydrologic frequency analysis.
•Risk (R): It represents probability of failure of a structure.
–It is the probability of occurrence of event (x ≥ x
T, where T is the return period) at least onceover a
period of n successive years (or design life of structure); ??????=??????−??????−
??????
??????
??????
•Other relevant terminologies
–Probability of occurring an event in any year (P) with return period T is given by ??????=
1
??????
.
–Probability of non-occurrence of event = 1-P = 1−
1
??????
–Probability of non-occurrence in n years (P
n) = (1 –P)
n
= 1−
1
??????
??????
–Probability of occurrence of event at least once in nyear (i.e., Risk!) = 1 –P
n= 1−1−
1
??????
??????
Return Period, Frequency & Risk
•Return period (or recurrence interval), T:
–It is defined as the averageinterval of time (T) within which an event of given magnitude will be
equalled or exceeded at least once.
–It is the average interval between the occurrence of flood equal to or greater thana given magnitude.
The return period is widely used in hydrologic frequency analysis.
•Risk (R): It represents probability of failure of a structure.
–It is the probability of occurrence of event (x ≥ x
T, where T is the return period) at least onceover a
period of n successive years (or design life of structure); ??????=??????−??????−
??????
??????
??????
•Other relevant terminologies
–Probability of occurring an event in any year (P) with return period T is given by ??????=
1
??????
.
–Probability of non-occurrence of event = 1-P = 1−
1
??????
–Probability of non-occurrence in n years (P
n) = (1 –P)
n
= 1−
1
??????
??????
–Probability of occurrence of event at least once in nyear (i.e., Risk!) = 1 –P
n= 1−1−
1
??????
??????
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 10
Return Period, Frequency & Risk
•Question#09: A flood of 4000 m
3
/s in a certain river has a return period of 40 years.
–(a) What is its probability of exceedance?
–(b) What is the probability that a flood of 4000 m
3
/s or greater magnitude may occur in
the next 20 years?
–(c) What is the probability of occurrence of a flood of magnitude less than 4000 m
3
/s?
•Solution;
–Here, Flood (X) = 4000 m
3
/s; Return period (T) = 40 years
–(a) Probability of exceedance, P
▪(P) =
1
??????
=
1
40
= 0.025
–(b) P(X>=4000) in next 20 years =? (n=20 years)
▪P(X>4000) = 1−(1−??????)
??????
=1−(1−0.025)
20
= 0.397
–(c) P(X<4000) = ?
▪P(X<4000) = 1 –P = 1 –0.025 = 0.975
Probability of
exceedance is for
a specific value &
Risk is for a range
of values
Return Period, Frequency & Risk
•Question#09: A flood of 4000 m
3
/s in a certain river has a return period of 40 years.
–(a) What is its probability of exceedance?
–(b) What is the probability that a flood of 4000 m
3
/s or greater magnitude may occur in
the next 20 years?
–(c) What is the probability of occurrence of a flood of magnitude less than 4000 m
3
/s?
•Solution;
–Here, Flood (X) = 4000 m
3
/s; Return period (T) = 40 years
–(a) Probability of exceedance, P
▪(P) =
1
??????
=
1
40
= 0.025
–(b) P(X>=4000) in next 20 years =? (n=20 years)
▪P(X>4000) = 1−(1−??????)
??????
=1−(1−0.025)
20
= 0.397
–(c) P(X<4000) = ?
▪P(X<4000) = 1 –P = 1 –0.025 = 0.975
Probability of
exceedance is for
a specific value &
Risk is for a range
of values
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 11
Return Period, Frequency & Risk
•Question#10: Compute the probability of a flood equal to or greater than the 50-
year flood occurring next year, and the next 3 years.
•Solution;
–Return period (T) = 50 year;
–a) Probability (P) of a flood > = 50-year occurring next year (i.e., n =1) is;
▪??????=1−1−
1
??????
??????
=1−1−
1
50
1
= 0.02
–B) Probability (P) of a flood > = 50-year occurring next 3 years (i.e., n =3) is;
▪??????=1−1−
1
??????
??????
=1−1−
1
50
3
= 0.0588
Return Period, Frequency & Risk
•Question#10: Compute the probability of a flood equal to or greater than the 50-
year flood occurring next year, and the next 3 years.
•Solution;
–Return period (T) = 50 year;
–a) Probability (P) of a flood > = 50-year occurring next year (i.e., n =1) is;
▪??????=1−1−
1
??????
??????
=1−1−
1
50
1
= 0.02
–B) Probability (P) of a flood > = 50-year occurring next 3 years (i.e., n =3) is;
▪??????=1−1−
1
??????
??????
=1−1−
1
50
3
= 0.0588
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 12
Plotting Positions & Frequency Factors
•The purpose of frequency analysis of an annual series is,
–To obtain a relation between magnitude of the event & its probability of exceedance
•Probability analysis is made either by empirical or by analytical methods
•A simple empirical technique is Probability Plotting, using following steps;
–Arrange the given annual extreme series in descending order of magnitude and assign an
order number “m”.
▪Thus for the first entry, m = 1, for the second entry, m = 2, and so on till the last event for which
m = N = number of years of record.
–Compute plotting position (i.e., probability (P) of an event equalled or exceeded), using
Weibull Formula; and Return period, T = 1/P = (N+1)/m.
–When there are two or more magnitudes are same (but with different m), P is calculated for
the largest m value of the set.
–Plot given data versus P or T in semi-log or log-log paper; & Fit a straight line.1+
=
N
m
P
Plotting Positions & Frequency Factors
•The purpose of frequency analysis of an annual series is,
–To obtain a relation between magnitude of the event & its probability of exceedance
•Probability analysis is made either by empirical or by analytical methods
•A simple empirical technique is Probability Plotting, using following steps;
–Arrange the given annual extreme series in descending order of magnitude and assign an
order number “m”.
▪Thus for the first entry, m = 1, for the second entry, m = 2, and so on till the last event for which
m = N = number of years of record.
–Compute plotting position (i.e., probability (P) of an event equalled or exceeded), using
Weibull Formula; and Return period, T = 1/P = (N+1)/m.
–When there are two or more magnitudes are same (but with different m), P is calculated for
the largest m value of the set.
–Plot given data versus P or T in semi-log or log-log paper; & Fit a straight line.1+
=
N
m
P
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 13
Plotting Positions & Frequency Factors
•A sample of
Probability Plot for a
Flood time series
Plotting Positions & Frequency Factors
•A sample of
Probability Plot for a
Flood time series
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 14
Plotting Positions & Frequency Factors
•Plotting position
–It refers to the probability value assigned to each piece of data to be plotted, most of
which are empirical
–There are several equations available for assigning plotting position. Among them,
Weibull’s one is widely used.
•Probability Plotting:
–Having calculated P (and hence T) for all the events in the time series, variation of flood
magnitudes is plotted against the corresponding T on a semi-log or log-log paper. The plot
is called as Probability Plotting.
–By suitable extrapolation of this curve, the flood magnitude of specific duration for any
recurrence interval can be estimated.
•Various analytical calculation procedures using frequency factorsare available.
Examples, used in this course, include;
–Log Pearson Type III (LP III) Method
–Gumbel (or Extreme Value Type I) Method
Plotting Positions & Frequency Factors
•Plotting position
–It refers to the probability value assigned to each piece of data to be plotted, most of
which are empirical
–There are several equations available for assigning plotting position. Among them,
Weibull’s one is widely used.
•Probability Plotting:
–Having calculated P (and hence T) for all the events in the time series, variation of flood
magnitudes is plotted against the corresponding T on a semi-log or log-log paper. The plot
is called as Probability Plotting.
–By suitable extrapolation of this curve, the flood magnitude of specific duration for any
recurrence interval can be estimated.
•Various analytical calculation procedures using frequency factorsare available.
Examples, used in this course, include;
–Log Pearson Type III (LP III) Method
–Gumbel (or Extreme Value Type I) Method
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 15
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 16
Continuous Probability Distribution –Terminologies
•Frequency:
–Number of occurrence of a variate
•Relative frequency (or probability of a function!)
–Number of observations (n
i) in interval “i” divided by total number of observations
•Cumulative frequency function
–Sum of values of relative frequencies up to a given point
•Cumulative distribution function (CDF): its value ranges between 0 & 1 (0 ≤ CDF ≤ 1)
–For a discrete random variable: CDF is the sum up of the probabilities
–For a continuous random variable: CDF is integral of its probability density function (PDF)
•Probability density function (PDF):
–PDF is derivate of the CDF.
–It’s representation of randomness of continuous random variable
Continuous Probability Distribution –Terminologies
•Frequency:
–Number of occurrence of a variate
•Relative frequency (or probability of a function!)
–Number of observations (n
i) in interval “i” divided by total number of observations
•Cumulative frequency function
–Sum of values of relative frequencies up to a given point
•Cumulative distribution function (CDF): its value ranges between 0 & 1 (0 ≤ CDF ≤ 1)
–For a discrete random variable: CDF is the sum up of the probabilities
–For a continuous random variable: CDF is integral of its probability density function (PDF)
•Probability density function (PDF):
–PDF is derivate of the CDF.
–It’s representation of randomness of continuous random variable
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 17
Continuous Probability Distribution
•Continuous Probability Distributions commonly used in
Hydrology are;
–Normal (or Gaussian) distribution
–Lognormal distribution
–Exponential distribution
–Gamma distribution
–Pearson Type III (or three parameter gamma) distribution
–Gumbel (Extreme Value Type I) distribution
•The curves of each probability distribution are plotted using
PDF equation of each distribution.
–There are Excel functions too for different distributions (e.g.
NORMDIST for normal distribution).
Continuous Probability Distribution
•Continuous Probability Distributions commonly used in
Hydrology are;
–Normal (or Gaussian) distribution
–Lognormal distribution
–Exponential distribution
–Gamma distribution
–Pearson Type III (or three parameter gamma) distribution
–Gumbel (Extreme Value Type I) distribution
•The curves of each probability distribution are plotted using
PDF equation of each distribution.
–There are Excel functions too for different distributions (e.g.
NORMDIST for normal distribution).
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 18
Continuous Probability Distribution –Normal distribution
•The Normal Distribution arises from the central limit theorem, which states that if a
sequence of random variables “Xi” are independently & identically distributedwith
mean µand variance σ
2
, then the distribution of the sum of nsuch random variables,
tends towards the Normal Distribution with mean nµand variance nσ
2
as
n becomes large.
•The PDF of normal distribution, for
–Where: µand σare population mean & standard deviation, and are parameters of the
distribution.
•The parameters of the Normal Distribution are, , where is sample
mean and S
xis sample standard deviation.
•If and Z →N (0, 1), it is called standard normal distribution.
=
=
=
ni
i
i
Xy
1 ()
( )
−
−=
2
2
2
exp
2
1
x
xf − x x
Sx==, x
−
=
x
z
Continuous Probability Distribution –Normal distribution
•The Normal Distribution arises from the central limit theorem, which states that if a
sequence of random variables “Xi” are independently & identically distributedwith
mean µand variance σ
2
, then the distribution of the sum of nsuch random variables,
tends towards the Normal Distribution with mean nµand variance nσ
2
as
n becomes large.
•The PDF of normal distribution, for
–Where: µand σare population mean & standard deviation, and are parameters of the
distribution.
•The parameters of the Normal Distribution are, , where is sample
mean and S
xis sample standard deviation.
•If and Z →N (0, 1), it is called standard normal distribution.
=
=
=
ni
i
i
Xy
1 ()
( )
−
−=
2
2
2
exp
2
1
x
xf − x x
Sx==, x
−
=
x
z
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 19
Continuous Probability Distribution –Normal distribution
•Properties of Normal Distribution;
–Bell shaped
–Symmetric about mean
–Unbounded
•The curve in which mean, median and the model value coincide is the normal curve.
•The normal or Gaussian frequency distribution is the most important in statistical theory
•Most hydrological data are NOTnormally distributed, but they can sometimes be
normalized by various methods like, using
–Logarithms of the sample data
–Cube root of the sample data
•Hydrological variables such as annual precipitation, calculated as the sum of effects of
many independent events tends to follow Normal Distribution.
Continuous Probability Distribution –Normal distribution
•Properties of Normal Distribution;
–Bell shaped
–Symmetric about mean
–Unbounded
•The curve in which mean, median and the model value coincide is the normal curve.
•The normal or Gaussian frequency distribution is the most important in statistical theory
•Most hydrological data are NOTnormally distributed, but they can sometimes be
normalized by various methods like, using
–Logarithms of the sample data
–Cube root of the sample data
•Hydrological variables such as annual precipitation, calculated as the sum of effects of
many independent events tends to follow Normal Distribution.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 20
Continuous Probability Distribution –Lognormal distribution
•If a random variable Y = logXis normally distributed, then X is said to be Log-Normally
distributed.
•The PDF of Lognormal distribution is; ; where: y= logX, X>0
•The parameters of the distribution are, ; where: is sample mean and
S
yis sample standard deviation.
•Properties of Lognormal distribution;
–X ranges from 0 to (lower bound)
–X is positively skewed
–Distribution tends to be symmetric as σdecreases()
( )
−
−=
2
2
2
exp
2
1
y
y
y
x
xf
x
Sy==, y
Continuous Probability Distribution –Lognormal distribution
•If a random variable Y = logXis normally distributed, then X is said to be Log-Normally
distributed.
•The PDF of Lognormal distribution is; ; where: y= logX, X>0
•The parameters of the distribution are, ; where: is sample mean and
S
yis sample standard deviation.
•Properties of Lognormal distribution;
–X ranges from 0 to (lower bound)
–X is positively skewed
–Distribution tends to be symmetric as σdecreases()
( )
−
−=
2
2
2
exp
2
1
y
y
y
x
xf
x
Sy==, y
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 21
Continuous Probability Distribution –Exponential distribution
•Exponential distribution is useful for instantaneously and independently occurring events,
e.g. occurrence of precipitation, occurrence of flood.
•The PDF of exponential distribution is given by; , for x ≥ 0.
•The parameter of the distribution is given by, ()
x
exf
−
= x
1
=
Continuous Probability Distribution –Exponential distribution
•Exponential distribution is useful for instantaneously and independently occurring events,
e.g. occurrence of precipitation, occurrence of flood.
•The PDF of exponential distribution is given by; , for x ≥ 0.
•The parameter of the distribution is given by, ()
x
exf
−
= x
1
=
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 22
Continuous Probability Distribution –Gamma distribution
•Gamma distribution (symbol: ??????) is useful to find the time taken for a
particular event to occur in a Poisson process (instantaneously and
independently occurring event).
•The gamma distribution has a smoothly varying form and is useful for
describing skewed hydrological variableswithout log transformation.
–Example: distribution of depth of precipitation in storms.
•This distribution has lower bound as zero, which is disadvantage for
application to hydrological variables that have lower bound > 0.
•PDF of Gamm Distribution is given by; �??????=
??????
??????
??????
??????−1
Γ??????
�
−????????????
; for x ≥0
•Parameters of Gamma Distribution are: ??????and ??????are parameters. They
are given by; ??????=
ҧ??????
??????
2
, ??????=
1
??????
??????
2, Γ??????=??????−1!
Continuous Probability Distribution –Gamma distribution
•Gamma distribution (symbol: ??????) is useful to find the time taken for a
particular event to occur in a Poisson process (instantaneously and
independently occurring event).
•The gamma distribution has a smoothly varying form and is useful for
describing skewed hydrological variableswithout log transformation.
–Example: distribution of depth of precipitation in storms.
•This distribution has lower bound as zero, which is disadvantage for
application to hydrological variables that have lower bound > 0.
•PDF of Gamm Distribution is given by; �??????=
??????
??????
??????
??????−1
Γ??????
�
−????????????
; for x ≥0
•Parameters of Gamma Distribution are: ??????and ??????are parameters. They
are given by; ??????=
ҧ??????
??????
2
, ??????=
1
??????
??????
2, Γ??????=??????−1!
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 23
Continuous Probability Distribution –Log Pearson III distribution
•Pearson Type III distribution is also called 3-parameter gamma distribution, as it
includes one more parameters parameter ??????in the gamma distribution.
•This distribution can be used to describe distribution of the annual maximum flood.
•The PDF for Pearson Type III distribution is given by;
–Where,
•Parameters of Pearson Type III Distribution are; ??????,??????and ??????; which are given by;
•By the method of moments, three sample moments (mean, standard deviation, &
coefficient of skewness) can be transferred to ??????,??????, and ??????()
()
()
()
−
=
−−
−
x
ex
xf
1 x
x
s
x
Sx
C
S
−=
== ,
2
,
2
Continuous Probability Distribution –Log Pearson III distribution
•Pearson Type III distribution is also called 3-parameter gamma distribution, as it
includes one more parameters parameter ??????in the gamma distribution.
•This distribution can be used to describe distribution of the annual maximum flood.
•The PDF for Pearson Type III distribution is given by;
–Where,
•Parameters of Pearson Type III Distribution are; ??????,??????and ??????; which are given by;
•By the method of moments, three sample moments (mean, standard deviation, &
coefficient of skewness) can be transferred to ??????,??????, and ??????()
()
()
()
−
=
−−
−
x
ex
xf
1 x
x
s
x
Sx
C
S
−=
== ,
2
,
2
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 24
Continuous Probability Distribution –Log Pearson III distribution
•If logXfollows a Pearson Type III (LP III) distribution, then X is said to follow Log
Pearson Type III distribution.
•The log transformation reduces the skewness of the transformed data.
•It is widely used for frequency analysis of the annual maximum flood.
•The PDF of LP III distribution is given by;
–where: y = log X;
•Parameters of LP III distribution are given by;()
y
s
y
Sy
yC
S
−=
== ,
2
,
2 logx ()
()
()
()
−
=
−−
−
x
ey
xf
y
1
Continuous Probability Distribution –Log Pearson III distribution
•If logXfollows a Pearson Type III (LP III) distribution, then X is said to follow Log
Pearson Type III distribution.
•The log transformation reduces the skewness of the transformed data.
•It is widely used for frequency analysis of the annual maximum flood.
•The PDF of LP III distribution is given by;
–where: y = log X;
•Parameters of LP III distribution are given by;()
y
s
y
Sy
yC
S
−=
== ,
2
,
2 logx ()
()
()
()
−
=
−−
−
x
ey
xf
y
1
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_1 25
Continuous Probability Distribution –Gumbel (EV I) distribution
•Gumbel distribution is also called as Extreme Value Type I (EV I) distribution
•The PDF of Gumbel Distribution for is given by;
•Parameters of Gumbel Distribution are given by;()
−
−−
−
−=
uxux
xf expexp
1 − x
5772.0,
6
−== xu
S
x
Continuous Probability Distribution –Gumbel (EV I) distribution
•Gumbel distribution is also called as Extreme Value Type I (EV I) distribution
•The PDF of Gumbel Distribution for is given by;
•Parameters of Gumbel Distribution are given by;()
−
−−
−
−=
uxux
xf expexp
1 − x
5772.0,
6
−== xu
S
x
Vishnu Prasad Pandey, PhD
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#6_1: Flood Hydrology (2)
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#6_1: Flood Hydrology (2)
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 3
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 4
Statistical Techniques for Flood Frequency Analysis
•What are hydrological extremes?
–Floods, Droughts, and Severe Storms (heavy rainfall)
–Their annual time series (e.g. annual maximum flood series) is used for frequency analysis
•Flood frequency analysis aims at
–Relating the magnitude of extreme events to their frequency of occurrencethrough the use
of probability distribution.
•Various applications of results of flood frequency analysis are;
–For the design of dams, bridge, culverts, and flood control structures
–To determine the economic value of flood control works
–To delineate flood plains
•Commonly used statistical techniques for flood frequency analysis are;
–Gumbel’s Method
–Log Pearson Type III (LP III) Method
Statistical Techniques for Flood Frequency Analysis
•What are hydrological extremes?
–Floods, Droughts, and Severe Storms (heavy rainfall)
–Their annual time series (e.g. annual maximum flood series) is used for frequency analysis
•Flood frequency analysis aims at
–Relating the magnitude of extreme events to their frequency of occurrencethrough the use
of probability distribution.
•Various applications of results of flood frequency analysis are;
–For the design of dams, bridge, culverts, and flood control structures
–To determine the economic value of flood control works
–To delineate flood plains
•Commonly used statistical techniques for flood frequency analysis are;
–Gumbel’s Method
–Log Pearson Type III (LP III) Method
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 5
Estimating Flood Peak –Various Methods
•Rational Method
•Empirical Methods,
–Dicken’s Method (1865)
–R. D. Richard’s Method
–Fuller’s Method
–Horton’s Method
–WECS/DHM method (or HYDEST method)
•Statistical Methods (or Flood Frequency Analysis)
–Gumbel’s Extreme Value Type I Method;
–Log Pearson Type Methods –Type II (2 parameters), Type III (3 parameters)
–Log-Normal Distribution-based Method
•Unit-hydrograph method
Selection of a suitable
method depends upon;
1)Desired objectives
2)Availability of data
3)Importance of the
objectives
Estimating Flood Peak –Various Methods
•Rational Method
•Empirical Methods,
–Dicken’s Method (1865)
–R. D. Richard’s Method
–Fuller’s Method
–Horton’s Method
–WECS/DHM method (or HYDEST method)
•Statistical Methods (or Flood Frequency Analysis)
–Gumbel’s Extreme Value Type I Method;
–Log Pearson Type Methods –Type II (2 parameters), Type III (3 parameters)
–Log-Normal Distribution-based Method
•Unit-hydrograph method
Selection of a suitable
method depends upon;
1)Desired objectives
2)Availability of data
3)Importance of the
objectives
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 6
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Gumbel (1941)’s method is one of the most widely used method for extreme values in
Hydrological & Meteorological Studies for prediction of,
–Flood peaks;
–Maximum rainfalls;
–Maximum wind speed, etc.
•Gumbel defined a floodas the largest of the 365 daily flowsand the annual series
of flood flowsconstitute a series of the largest values of flows.
•According to Gumbel’s theory of extreme events, the probability of occurrence of an
event equal to or larger than a value x
0is;
–????????????≥??????
0=
1
�
=1−??????
−??????
−??????
??????
; Where: P is probability of occurrence; x is event of
hydrologic series; x
0is the desired value of the event; y
Tis reduced variate.
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Gumbel (1941)’s method is one of the most widely used method for extreme values in
Hydrological & Meteorological Studies for prediction of,
–Flood peaks;
–Maximum rainfalls;
–Maximum wind speed, etc.
•Gumbel defined a floodas the largest of the 365 daily flowsand the annual series
of flood flowsconstitute a series of the largest values of flows.
•According to Gumbel’s theory of extreme events, the probability of occurrence of an
event equal to or larger than a value x
0is;
–????????????≥??????
0=
1
�
=1−??????
−??????
−??????
??????
; Where: P is probability of occurrence; x is event of
hydrologic series; x
0is the desired value of the event; y
Tis reduced variate.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 7
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•From, ????????????≥??????
0=1−??????
−??????
−??????
??????
, where, �
�is reduced variate, �
�=
�
??????−??????
??????
–Where;
–Taking natural log (ln) both sides; ln1−??????=−??????
−��
–Taking natural log (ln) again both sides; �??????(�??????1−??????)=−�
�
–Therefore, �
�=−�??????(�??????1−??????); or Y
T= -[0.834+2.303 log logT/(T-1)]
–If we replace P with return period T (i.e., P = 1/T), then, �
�=−�??????�??????
�
�−1
•Value of variate x for return period T, �
�can be estimated based on reduced variate
�
�with following relation; ??????
??????=ഥ??????+????????????
??????; where, �=
�??????−�??????
????????????
; k=
�??????−0.577
1.2825
–Where: k is frequency factor; �
??????is reduced mean, a function of sample size N, for N →∞ ,
�
??????→0.577;??????
??????is reduced standard deviation, a function of sample size N, for N →∞ ,
??????
??????→1.2825. For other sample size, refer Tables in next slide.xxx
x
SxSxxuS
S
45.078.0*577.0577.0,78.0
6
−=−=−===
For N →∞
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•From, ????????????≥??????
0=1−??????
−??????
−??????
??????
, where, �
�is reduced variate, �
�=
�
??????−??????
??????
–Where;
–Taking natural log (ln) both sides; ln1−??????=−??????
−��
–Taking natural log (ln) again both sides; �??????(�??????1−??????)=−�
�
–Therefore, �
�=−�??????(�??????1−??????); or Y
T= -[0.834+2.303 log logT/(T-1)]
–If we replace P with return period T (i.e., P = 1/T), then, �
�=−�??????�??????
�
�−1
•Value of variate x for return period T, �
�can be estimated based on reduced variate
�
�with following relation; ??????
??????=ഥ??????+????????????
??????; where, �=
�??????−�??????
????????????
; k=
�??????−0.577
1.2825
–Where: k is frequency factor; �
??????is reduced mean, a function of sample size N, for N →∞ ,
�
??????→0.577;??????
??????is reduced standard deviation, a function of sample size N, for N →∞ ,
??????
??????→1.2825. For other sample size, refer Tables in next slide.xxx
x
SxSxxuS
S
45.078.0*577.0577.0,78.0
6
−=−=−===
For N →∞
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 8
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Values of reduced mean and reduced standard deviation for different sample size (N);
•for N →∞ ,
�
??????→0.577
•for N →∞ ,
??????
??????→1.2825
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Values of reduced mean and reduced standard deviation for different sample size (N);
•for N →∞ ,
�
??????→0.577
•for N →∞ ,
??????
??????→1.2825
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 9
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Second methodfor computing K: from K-T relationship for large samples(N > 100). The
relation based on Chow’s formula is;
–??????=−
6
??????
0.5772+�??????�??????
�
�−1
; OR, ??????=−0.45+0.78�??????�??????
�
�−1
–This method can also be used if table or values of �
??????and S
nisnot given (assuming large
samples)
•Alternatively, as n →, �
??????→0.577, Sn →1.2825.
–So for n →, K can also be computed from; ??????=
�
??????−0.577
1.2825
•Procedures/Steps for estimating flood magnitude of given return period using Gumbel;
–Compute mean, ҧ�and standard deviation, σof the given data or variate (x).
–Compute frequency factor (K) using formula in previous slide, for small size or second method
for large sample size
–Compute X
T; ??????
??????=ഥ??????+????????????
??????1
)(
2
1
−
−
=
−
N
XX
n
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Second methodfor computing K: from K-T relationship for large samples(N > 100). The
relation based on Chow’s formula is;
–??????=−
6
??????
0.5772+�??????�??????
�
�−1
; OR, ??????=−0.45+0.78�??????�??????
�
�−1
–This method can also be used if table or values of �
??????and S
nisnot given (assuming large
samples)
•Alternatively, as n →, �
??????→0.577, Sn →1.2825.
–So for n →, K can also be computed from; ??????=
�
??????−0.577
1.2825
•Procedures/Steps for estimating flood magnitude of given return period using Gumbel;
–Compute mean, ҧ�and standard deviation, σof the given data or variate (x).
–Compute frequency factor (K) using formula in previous slide, for small size or second method
for large sample size
–Compute X
T; ??????
??????=ഥ??????+????????????
??????1
)(
2
1
−
−
=
−
N
XX
n
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 10
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•How to verify whether given data follow the assumed Gumbel’s distribution?
–Plot value of x
Tfor different values of return period in semi-log or log-log or Gumbel’s
probability paper and see whether the plot is straight line.
•Gumbel’s probability paper;
–It’s an aid for convenient graphical representation of Gumbel’s distribution
–It consists of Abscissa (X-axis) specially marked for various convenient values of the return
period (T) (e.g., 2, 10, 50, 100, 500 and 1000 years).
–Find the value of y
Tusing equation for y
T. Then mark-off those positions on the abscissa.
–Then, plot discharge versus T (and y
T).
•Gumbel’s distribution has the property which gives T = 2.33 yrsfor the average of
annual series, when N is very large.
–Thus, the value of a flood with T = 2.33 years is called the mean annual flood (or normal
flood).
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•How to verify whether given data follow the assumed Gumbel’s distribution?
–Plot value of x
Tfor different values of return period in semi-log or log-log or Gumbel’s
probability paper and see whether the plot is straight line.
•Gumbel’s probability paper;
–It’s an aid for convenient graphical representation of Gumbel’s distribution
–It consists of Abscissa (X-axis) specially marked for various convenient values of the return
period (T) (e.g., 2, 10, 50, 100, 500 and 1000 years).
–Find the value of y
Tusing equation for y
T. Then mark-off those positions on the abscissa.
–Then, plot discharge versus T (and y
T).
•Gumbel’s distribution has the property which gives T = 2.33 yrsfor the average of
annual series, when N is very large.
–Thus, the value of a flood with T = 2.33 years is called the mean annual flood (or normal
flood).
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 11
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Question#11: 10-years annual flood at a hydrological station is provided below. If
values of reduced mean and reduced standard deviation in Gumbel’s Extreme value
distribution as 0.4952 and 0.9496, respectively, find out the frequency of a flood of
magnitude 2000 m
3
/s.
Year 2000200120022003200420052006200720082009
Q
P(m
3
/s)300700 200 400 1000900 800 500 100 600
•Here, after processing the annual flood time-series, we can get,
–Mean (ҧ�)=
σ??????
??????
??????
=
5500
10
=550; &
–Standard deviation, ??????=
σ??????
??????−ҧ�
2
??????−1
=
825000
9
=302.765
•For X = 2,000 m
3
/s, from ??????
�=ҧ�+??????
�??????; we will get, K
T= 4.789.
•Again, from ??????
�=
�??????−�??????
�??????
; Y
T= 5.043.
•And from �
�=−�??????�??????
�
�−1
; T = 155.4 years.
Estimating Flood Peak –Gumbel Extreme Value Type I Method
•Question#11: 10-years annual flood at a hydrological station is provided below. If
values of reduced mean and reduced standard deviation in Gumbel’s Extreme value
distribution as 0.4952 and 0.9496, respectively, find out the frequency of a flood of
magnitude 2000 m
3
/s.
Year 2000200120022003200420052006200720082009
Q
P(m
3
/s)300700 200 400 1000900 800 500 100 600
•Here, after processing the annual flood time-series, we can get,
–Mean (ҧ�)=
σ??????
??????
??????
=
5500
10
=550; &
–Standard deviation, ??????=
σ??????
??????−ҧ�
2
??????−1
=
825000
9
=302.765
•For X = 2,000 m
3
/s, from ??????
�=ҧ�+??????
�??????; we will get, K
T= 4.789.
•Again, from ??????
�=
�??????−�??????
�??????
; Y
T= 5.043.
•And from �
�=−�??????�??????
�
�−1
; T = 155.4 years.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 12
Log Pearson III Method
•This method is used for approximation of frequency characteristics of measured annual
flood peak data.
•In this method, the variate is transferred into logarithmic form (base 10, i.e. log) & then
transformed data is analysed.
•If X is a variate of a random hydrologic series them, Z = log (X)
•For this Z-series, for any return period T, Z
T= log (X
T).
•Then, ??????
�=ҧ??????+??????
????????????; where: K
Zis a frequency factor& is a function of return period
(T) and skewness coefficient (Cs).
Log Pearson III Method
•This method is used for approximation of frequency characteristics of measured annual
flood peak data.
•In this method, the variate is transferred into logarithmic form (base 10, i.e. log) & then
transformed data is analysed.
•If X is a variate of a random hydrologic series them, Z = log (X)
•For this Z-series, for any return period T, Z
T= log (X
T).
•Then, ??????
�=ҧ??????+??????
????????????; where: K
Zis a frequency factor& is a function of return period
(T) and skewness coefficient (Cs).
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 13
Log Pearson III Method
•Steps for computing floods of various return periods using Log-Pearson III method,
–First, transform peak discharge (X) to logarithm of base 10 ( Z = log
10X)
–Compute mean (ҧ??????), standard deviation (??????), and coefficient of skewness (Cs) of Z
▪ҧ�=
σ�
??????
▪??????=
σ�
??????−ҧ�
2
??????−1
▪??????
??????=
??????
??????−1(??????−2)
�
??????−ҧ�
3
??????
3
–Obtain the value of K
Tfor Cs and selected/required return period (T) from the Table for
Log Pearson Type III distribution (slide#15) (or by using formulae, slide#14).
–Compute; ??????
�=ҧ??????+??????
????????????
–Flood of return period T →X
T= antilog (Z
T).
•For Coefficient of Skewness (Cs) = 0, LP III method
–reduces to →Lognormal Distribution.
Log Pearson III Method
•Steps for computing floods of various return periods using Log-Pearson III method,
–First, transform peak discharge (X) to logarithm of base 10 ( Z = log
10X)
–Compute mean (ҧ??????), standard deviation (??????), and coefficient of skewness (Cs) of Z
▪ҧ�=
σ�
??????
▪??????=
σ�
??????−ҧ�
2
??????−1
▪??????
??????=
??????
??????−1(??????−2)
�
??????−ҧ�
3
??????
3
–Obtain the value of K
Tfor Cs and selected/required return period (T) from the Table for
Log Pearson Type III distribution (slide#15) (or by using formulae, slide#14).
–Compute; ??????
�=ҧ??????+??????
????????????
–Flood of return period T →X
T= antilog (Z
T).
•For Coefficient of Skewness (Cs) = 0, LP III method
–reduces to →Lognormal Distribution.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 14
Log Pearson III Method
•Formula to compute K
T;
–??????
�=�+�
2
−1�+
1
3
�
3
−6��
2
−�
2
−1�
3
+��
4
+
1
3
�
5
–k = C
S/6
–�=�−
2.515517+0.802853�+0.010328�
2
1+1.432788�+0.189269�
2
+0.001308�
3
–�=�??????
1
??????
2
1/2
–p = 1/T
Log Pearson III Method
•Formula to compute K
T;
–??????
�=�+�
2
−1�+
1
3
�
3
−6��
2
−�
2
−1�
3
+��
4
+
1
3
�
5
–k = C
S/6
–�=�−
2.515517+0.802853�+0.010328�
2
1+1.432788�+0.189269�
2
+0.001308�
3
–�=�??????
1
??????
2
1/2
–p = 1/T
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 15
Log Pearson III Method
Log Pearson III Method
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 16
Log Pearson III Method
•Question#12: A 20-year annual peak flow (m
3
/s) time series is transformed into log
10.
The log
10transformed time-series has mean of 3.632, standard deviation of 0.202,
and coefficient of skewness of 1.2. Compute flood magnitude of 25 year return period
using Log-Pearson Type III method using two methods: i) Taking values from Table; and
ii) calculating values using formula.
•Solution:
•i) Taking values from Table –
–For T = 25 years and Cs = 1.20, from Table,
▪K
T= 2.087.
–??????
�=ҧ??????+??????
�??????= 3.632+2.087x0.201
▪Z
T= 4.05
–And, flood of 25 year return period (X
25) = Antilog (Z
T)
▪= 10
4.05
= 11,220 m
3
/s
Log Pearson III Method
•Question#12: A 20-year annual peak flow (m
3
/s) time series is transformed into log
10.
The log
10transformed time-series has mean of 3.632, standard deviation of 0.202,
and coefficient of skewness of 1.2. Compute flood magnitude of 25 year return period
using Log-Pearson Type III method using two methods: i) Taking values from Table; and
ii) calculating values using formula.
•Solution:
•i) Taking values from Table –
–For T = 25 years and Cs = 1.20, from Table,
▪K
T= 2.087.
–??????
�=ҧ??????+??????
�??????= 3.632+2.087x0.201
▪Z
T= 4.05
–And, flood of 25 year return period (X
25) = Antilog (Z
T)
▪= 10
4.05
= 11,220 m
3
/s
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_2 17
Log Pearson III Method
•ii) Calculating values using Formula –
–p = 1/T
▪= 1/25 = 0.04
–�=�??????
1
??????
2
1/2
▪= 2.537
–�=�−
2.515517+0.802853�+0.010328�
2
1+1.432788�+0.189269�
2
+0.001308�
3
▪= 1.751
–k = C
S/6 = 1.2/6 = 0.2
–??????
�=�+�
2
−1�+
1
3
�
3
−6��
2
−�
2
−1�
3
+��
4
+
1
3
�
5
▪= 2.08
–??????
�=ҧ??????+??????
�??????= 3.632+2.09x0.201 = 4.05
–Flood of 25 year return period (X
25) = Antilog (Z
T) = 10
4.05
= 11,220 m
3
/s.
Log Pearson III Method
•ii) Calculating values using Formula –
–p = 1/T
▪= 1/25 = 0.04
–�=�??????
1
??????
2
1/2
▪= 2.537
–�=�−
2.515517+0.802853�+0.010328�
2
1+1.432788�+0.189269�
2
+0.001308�
3
▪= 1.751
–k = C
S/6 = 1.2/6 = 0.2
–??????
�=�+�
2
−1�+
1
3
�
3
−6��
2
−�
2
−1�
3
+��
4
+
1
3
�
5
▪= 2.08
–??????
�=ҧ??????+??????
�??????= 3.632+2.09x0.201 = 4.05
–Flood of 25 year return period (X
25) = Antilog (Z
T) = 10
4.05
= 11,220 m
3
/s.
Vishnu Prasad Pandey, PhD
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#6_1: Flood Hydrology (3)
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#6_1: Flood Hydrology (3)
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 3
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
6. Flood Hydrology
6.1 Design flood and its frequency
6.2 Statistical methods of flood prediction
6.2.1 Continuous Probability distribution
6.2.2 Return period, Frequency and risk
6.2.3 Plotting positions, frequency factors
6.2.4 Log Pearson III Method
6.2.5 Gumbel’s Extreme Value Type I Method
6.3 Flood prediction by Rational and Empirical methods
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 4
Estimating Flood Peak –Rational Method
•It’s the most widely used method for the analysis of runoff response from small
catchments
•Though it’s simple, a reasonable care is necessary to apply it effectively.
•It’s particular application is in urban storm drainage →to estimate peak runoff rates
for the design of storm sewers and small drainage facilities.
•The hydrologic characteristics or processes that Rational method accounts for are;
–Rainfall intensity
–Rainfall duration
–Rainfall frequency
–Catchment area
–Hydrologic abstractions
–Runoff concentration,
–Runoff diffusion: a measure of the catchment’s ability to attenuate the flood peaks.
Estimating Flood Peak –Rational Method
•It’s the most widely used method for the analysis of runoff response from small
catchments
•Though it’s simple, a reasonable care is necessary to apply it effectively.
•It’s particular application is in urban storm drainage →to estimate peak runoff rates
for the design of storm sewers and small drainage facilities.
•The hydrologic characteristics or processes that Rational method accounts for are;
–Rainfall intensity
–Rainfall duration
–Rainfall frequency
–Catchment area
–Hydrologic abstractions
–Runoff concentration,
–Runoff diffusion: a measure of the catchment’s ability to attenuate the flood peaks.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 5
Estimating Flood Peak –Rational Method
•If a rainfall of uniform intensity and very long duration is
occurring over a catchment, the runoff rate gradually increases
from zero to a constant value (see figure), then the peak value
of runoff at the outlet, a per Rational Method, is given by;
–Q
P= C * i* A (for t ≥ t
c) ; where, C is the coefficient of runoff (=
runoff/ rainfall), i= intensity of rainfall, A = catchment area; t
c=
time of concentration.
–In SI unit, with Q in m
3
/s, “i” in mm/hr, and “A” in km
2
, the equation
is modified as; Q
P= 1/3.6 * C * i* A .
•Limitations of Rationale Method
–Applicable for small-sized catchments (< 50 km
2
)
–Rainfall intensity must be of constant over the entire basin during
tc. And, duration of rainfall intensity > tc
–Gives only peak, but not a complete hydrograph
–C assumed to be small for all storms
Q
P
t
c
Estimating Flood Peak –Rational Method
•If a rainfall of uniform intensity and very long duration is
occurring over a catchment, the runoff rate gradually increases
from zero to a constant value (see figure), then the peak value
of runoff at the outlet, a per Rational Method, is given by;
–Q
P= C * i* A (for t ≥ t
c) ; where, C is the coefficient of runoff (=
runoff/ rainfall), i= intensity of rainfall, A = catchment area; t
c=
time of concentration.
–In SI unit, with Q in m
3
/s, “i” in mm/hr, and “A” in km
2
, the equation
is modified as; Q
P= 1/3.6 * C * i* A .
•Limitations of Rationale Method
–Applicable for small-sized catchments (< 50 km
2
)
–Rainfall intensity must be of constant over the entire basin during
tc. And, duration of rainfall intensity > tc
–Gives only peak, but not a complete hydrograph
–C assumed to be small for all storms
Q
P
t
c
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 6
Estimating Flood Peak –Rational Method
•The rational method does NOTtake into account these characteristics or processes;
–Spatial or temporal variations in either total or effective rainfall
–Time of concentration much greater than storm duration
–A significant portion of runoff occurring in the form of streamflow
•The Rational Method also does NOT explicitly account for the catchment’s antecedent
moisture content, however it may be implicitly accounted for by varying the runoff
coefficient.
•Limit of catchment area:
–Upper limit: There is no consensus on upper limit of catchment area to apply Rational
Method. However, current trend is to use area <=2.5 km
2
as upper limit.
–Lower limit: There is no theoretical lower limit. Catchments as small as 1 ha or less can be
analysed using rational method.
Estimating Flood Peak –Rational Method
•The rational method does NOTtake into account these characteristics or processes;
–Spatial or temporal variations in either total or effective rainfall
–Time of concentration much greater than storm duration
–A significant portion of runoff occurring in the form of streamflow
•The Rational Method also does NOT explicitly account for the catchment’s antecedent
moisture content, however it may be implicitly accounted for by varying the runoff
coefficient.
•Limit of catchment area:
–Upper limit: There is no consensus on upper limit of catchment area to apply Rational
Method. However, current trend is to use area <=2.5 km
2
as upper limit.
–Lower limit: There is no theoretical lower limit. Catchments as small as 1 ha or less can be
analysed using rational method.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 7
Estimating Flood Peak –Rational Method
•Time of Concentration (t
c):
–Time required to a drop of water to flow from the farthest part of the catchment to reach
the outlet. If rainfall continues beyond t
c, the runoff will be constant.
–Number of empirical equations are available for the estimation of tc.
–The most commonly used method is, KirpichEquation (1940), t
c= 0.01947 * L
0.77
* S
–
0.385
; where, t
cis the time of concentration (in minutes), L is the maximum length of travel of
water or the longest flow path (in meters), S is slope of the catchment = ΔH/L, in which, ΔH
is the difference in elevation between the most remote point on the catchment and the
outlet.
Estimating Flood Peak –Rational Method
•Time of Concentration (t
c):
–Time required to a drop of water to flow from the farthest part of the catchment to reach
the outlet. If rainfall continues beyond t
c, the runoff will be constant.
–Number of empirical equations are available for the estimation of tc.
–The most commonly used method is, KirpichEquation (1940), t
c= 0.01947 * L
0.77
* S
–
0.385
; where, t
cis the time of concentration (in minutes), L is the maximum length of travel of
water or the longest flow path (in meters), S is slope of the catchment = ΔH/L, in which, ΔH
is the difference in elevation between the most remote point on the catchment and the
outlet.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 8
Estimating Flood Peak –Rational Method
•Rainfall intensity (i):
–Rainfall intensity depends upon various factors. First determine time of concentration. Then
compare time of concentration (tc) and rainfall duration (t)
▪If Tc ≥ t →i=(total rainfall amount)/t.
▪If T
c< t →i= (total rainfall until Tc)/T
c.
–Rainfall intensify corresponding to duration tcand the desired probability of exceedance P
(i.e. return period, T = 1/P) can also be calculated from rainfall-frequency-duration
relationship for a given catchment; ??????
??????
??????,??????=
??????∗??????
??????
??????
??????+??????
??????
; where: K, a, x and m are constants.
Values of those constants generally used in Nepal can be assumed same as in Northern
India, and they are, K = 5.92, x = 0.162, a = 0.5, n = 1.013.
Estimating Flood Peak –Rational Method
•Rainfall intensity (i):
–Rainfall intensity depends upon various factors. First determine time of concentration. Then
compare time of concentration (tc) and rainfall duration (t)
▪If Tc ≥ t →i=(total rainfall amount)/t.
▪If T
c< t →i= (total rainfall until Tc)/T
c.
–Rainfall intensify corresponding to duration tcand the desired probability of exceedance P
(i.e. return period, T = 1/P) can also be calculated from rainfall-frequency-duration
relationship for a given catchment; ??????
??????
??????,??????=
??????∗??????
??????
??????
??????+??????
??????
; where: K, a, x and m are constants.
Values of those constants generally used in Nepal can be assumed same as in Northern
India, and they are, K = 5.92, x = 0.162, a = 0.5, n = 1.013.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 9
Estimating Flood Peak –Rational Method
•Runoff Coefficient (C):
–Value of C depends upon integrated effects of the catchment losses, therefore, depends on
▪Nature of surface
▪Surface slope
▪Rainfall intensity
–Value of C ranges from 0.1 (heavy forest) to 1.0 (rocky and permeable soil). Please refer
Table 7.1 in K. Subramanyabook for value of C for various types of areas
–If the catchment is non-homogenous (which is usually the case!), value of C for each sub-
basin can be calculated using weighted average C, where C
i, A
iare runoff coefficient and
catchment area of i
TH
sub-basin.( )
..
..
321
332211
+++
+++
=
AAA
ACACAC
C
Estimating Flood Peak –Rational Method
•Runoff Coefficient (C):
–Value of C depends upon integrated effects of the catchment losses, therefore, depends on
▪Nature of surface
▪Surface slope
▪Rainfall intensity
–Value of C ranges from 0.1 (heavy forest) to 1.0 (rocky and permeable soil). Please refer
Table 7.1 in K. Subramanyabook for value of C for various types of areas
–If the catchment is non-homogenous (which is usually the case!), value of C for each sub-
basin can be calculated using weighted average C, where C
i, A
iare runoff coefficient and
catchment area of i
TH
sub-basin.( )
..
..
321
332211
+++
+++
=
AAA
ACACAC
C
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 10
Rational Method
•Rainfall frequencyversus Flood (Peak Q) frequency: Are they equivalent?
–Peak Discharge frequency (for different return periods) can be estimated based on flood
frequency analysis techniques (e.g., Gumbel) [Probabilistic Approach]
–Rainfall frequency can also be estimated using same approach. Then the rainfall of desired
frequency (T yrs) is fed to a Unit Hydrographto estimate Flood Discharge of T yrsReturn
Period [Deterministic Approach]
•In practice, frequencies of storms and floods are NOT necessarily the same, largely due
to factors like …;
–Antecedent moisture condition
–Variability in channel transmission losses
–Overbank storage, etc.
•In practice →take higher among the two (deterministic & probabilistic) estimates.
Rational Method
•Rainfall frequencyversus Flood (Peak Q) frequency: Are they equivalent?
–Peak Discharge frequency (for different return periods) can be estimated based on flood
frequency analysis techniques (e.g., Gumbel) [Probabilistic Approach]
–Rainfall frequency can also be estimated using same approach. Then the rainfall of desired
frequency (T yrs) is fed to a Unit Hydrographto estimate Flood Discharge of T yrsReturn
Period [Deterministic Approach]
•In practice, frequencies of storms and floods are NOT necessarily the same, largely due
to factors like …;
–Antecedent moisture condition
–Variability in channel transmission losses
–Overbank storage, etc.
•In practice →take higher among the two (deterministic & probabilistic) estimates.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 11
Estimating Flood Peak –Rational Method
•Question#13: Distribution of rainfall storm for a period of 180 minutes is given below.
The catchment has area of 400 ha of land with a maximum length of travel of 1250 m.
The general slope of the catchment is 0.001 and its runoff coefficient is 0.4. Estimate
the peak flow by rational method.
Duration(min) 20 40 60 180
Rainfall(mm) 50 80 100 120
•Solution:
–A = 400 ha = 4 km
2
, C = 0.4, L = 1250 m, S = 0.001, Qp= ?
–Using Kirpichequation, Time of concentration ??????
??????=0.01947??????
0.77
??????
−0.385
= 67.45 mins.
–Rainfall at 67.45 min (i.e., time of concentration) from given data, by linear interpolation,
▪Rainfall = 100+
120−100
180−60
??????7.45= 101.24mm
–Rainfall intensity (i) at t
c=
101.24
67.45
??????60= 90 mm/hr.
–Peak flood (Qp), using rational method: ??????
??????=
??????????????????
3.6
=
0.4??????90??????4
3.6
= 40 m
3
/s.
Estimating Flood Peak –Rational Method
•Question#13: Distribution of rainfall storm for a period of 180 minutes is given below.
The catchment has area of 400 ha of land with a maximum length of travel of 1250 m.
The general slope of the catchment is 0.001 and its runoff coefficient is 0.4. Estimate
the peak flow by rational method.
Duration(min) 20 40 60 180
Rainfall(mm) 50 80 100 120
•Solution:
–A = 400 ha = 4 km
2
, C = 0.4, L = 1250 m, S = 0.001, Qp= ?
–Using Kirpichequation, Time of concentration ??????
??????=0.01947??????
0.77
??????
−0.385
= 67.45 mins.
–Rainfall at 67.45 min (i.e., time of concentration) from given data, by linear interpolation,
▪Rainfall = 100+
120−100
180−60
??????7.45= 101.24mm
–Rainfall intensity (i) at t
c=
101.24
67.45
??????60= 90 mm/hr.
–Peak flood (Qp), using rational method: ??????
??????=
??????????????????
3.6
=
0.4??????90??????4
3.6
= 40 m
3
/s.
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 12
Estimating Flood Peak –Empirical Methods
•Dicken’s Method (1865);
–Where, Q
Pis maximum flood discharge (m
3
/s); A is catchment area (km
2
); C
Dis Dicken’s
constant with value of 6 to 30.
–The value of C
Dfor Nepal can be adopted as in Northern India (6 for plains and 11-14 for
hilly regions)
•R. D. Richard’s Method;
–Q = 0.222 * A * I * F, where, A = basin area (km
2
), I is rainfall intensity corresponding to
the time of concentration; F is Aerial reduction factor ( = 1.09352 –0.6628*ln (A)).
–This method is used in MahakaliIrrigation Project.
•Horton’s Method:
–where, q
tris the flood equalled or exceeded in T year return period (m
3
/s/km
2
); A is
drainage area (km
2
)4
3
ACQ
Dp= 5.0
25.0
2.71
A
T
q
tr=
Estimating Flood Peak –Empirical Methods
•Dicken’s Method (1865);
–Where, Q
Pis maximum flood discharge (m
3
/s); A is catchment area (km
2
); C
Dis Dicken’s
constant with value of 6 to 30.
–The value of C
Dfor Nepal can be adopted as in Northern India (6 for plains and 11-14 for
hilly regions)
•R. D. Richard’s Method;
–Q = 0.222 * A * I * F, where, A = basin area (km
2
), I is rainfall intensity corresponding to
the time of concentration; F is Aerial reduction factor ( = 1.09352 –0.6628*ln (A)).
–This method is used in MahakaliIrrigation Project.
•Horton’s Method:
–where, q
tris the flood equalled or exceeded in T year return period (m
3
/s/km
2
); A is
drainage area (km
2
)4
3
ACQ
Dp= 5.0
25.0
2.71
A
T
q
tr=
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 13
Estimating Flood Peak –Empirical Methods
•Fuller’s Method
–This method was developed in basins of USA and may be used to estimate flood discharges
in the ungauged basins of Nepal for comparison purpose
–The maximum instantaneous flood discharge as per Fuller’s Method is given by;
– ; where, Q
Tis the maximum 24 hr flood.
–With frequency once in T years in m
3
/s and A as basin area in km
2
, Q
Tis given by
Q
T= Q
av(1 + 0.8 log (T)),
▪where Q
avis yearly average 24 hour flood over a number of years, and given by,
▪Q
av= C
f* A
0.8
, where C
fis Fuller’s Coefficient (= 0.18 to 1.88), with value of 1.03 in an
average for Nepal.
+=
−3.0
max
59.2
21
A
QQ
T
Estimating Flood Peak –Empirical Methods
•Fuller’s Method
–This method was developed in basins of USA and may be used to estimate flood discharges
in the ungauged basins of Nepal for comparison purpose
–The maximum instantaneous flood discharge as per Fuller’s Method is given by;
– ; where, Q
Tis the maximum 24 hr flood.
–With frequency once in T years in m
3
/s and A as basin area in km
2
, Q
Tis given by
Q
T= Q
av(1 + 0.8 log (T)),
▪where Q
avis yearly average 24 hour flood over a number of years, and given by,
▪Q
av= C
f* A
0.8
, where C
fis Fuller’s Coefficient (= 0.18 to 1.88), with value of 1.03 in an
average for Nepal.
+=
−3.0
max
59.2
21
A
T
Prof. Vishnu Prasad Pandey | BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L6_3 14
Estimating Flood Peak –Empirical Methods
•WECS/DHM Method: Water and Energy Commission Secretariat (WECS) & DHM has
developed empirical relationships for analysing flood of different return periods;
Where: Q
2and Q
100are floods of 2 and 100 year return periods; A
3000is basin area
(km
2
) below 3,000 m elevation
•For other return periods, 8783.0
30002 )1(8767.1 += AQ 7342.0
3000100 )1(63.14 += AQ )(lnexp
2SQQ
T +=
Where: Q
Tis flood of T year return period (m
3
/s),
S= standard normal variate, σ=
ln(Q
100/Q
2)/2.326
T (Years) S
2 0
5 0.842
10 1.282
25 1.645
50 2.054
100 2.326
Estimating Flood Peak –Empirical Methods
•WECS/DHM Method: Water and Energy Commission Secretariat (WECS) & DHM has
developed empirical relationships for analysing flood of different return periods;
Where: Q
2and Q
100are floods of 2 and 100 year return periods; A
3000is basin area
(km
2
) below 3,000 m elevation
•For other return periods, 8783.0
30002 )1(8767.1 += AQ 7342.0
3000100 )1(63.14 += AQ )(lnexp
2SQQ
T +=
Where: Q
Tis flood of T year return period (m
3
/s),
S= standard normal variate, σ=
ln(Q
100/Q
2)/2.326
T (Years) S
2 0
5 0.842
10 1.282
25 1.645
50 2.054
100 2.326
Vishnu Prasad Pandey, PhD
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#7_1: Flood Routing (1)
Professor –Civil Engineering (Water Resources)
Institute of Engineering, TribhuvanUniversity, Nepal
E: [email protected]
Engineering Hydrology (CE 606)
Lecture#7_1: Flood Routing (1)
BE (Civil) | IOE/TU -Nepal | Engineering Hydrology Course | L7_1 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
Course Delivery Plan [Vishnu Pandey’s Part]
Chapter Contents LectureHrs
3
3.1, 3.2
(partly)
Initial losses; Evaporation processes L#3_1 2
3
3.2 (partly),
3.3
Actual evapotranspiration and Lysimeters; Potential
evapotranspiration (Penamn’sequation)
L#3_2 2
3 3.4
Infiltration–Horton’s equation; infiltration indices;
infiltrometers
L#3_3 2
6
6.1, 6.2.1 –
6.2.3
Design flood and its frequency; continuous probability
distribution; return period; frequency, and risk; Plotting
position and frequency factors.
L#6_1 2
66.2.4, 6.2.5
Log Pearson III method; Gumbel’s Extreme Value Type I
method
L#6_2 2
6 6.3Flood frequency by Rational and Empirical methodsL#6_3 2
7 7.1Linear reservoir routing L#7_1 2
7 7.2Time areamethod L#7_2 2
7 7.3Clark Unit Hydrograph L#7_3 2
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