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Flood Frequency Analysis Using Gumbel and Lognormal Distribution in Buaya River
In partial fulfillment for the requirement in Water Resources Engineering
Presented to:
Engr. Ricardo Fornis
Presented by:
Agrabio, Thomas John
Alcala, Charllote
Gonzales, Vivianne Rose
Kapuno, Alan Jr.
AY: 2012- 2013
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ACKNOWLEDGEMENT
We would like to express our profound gratitude to these generous people who
assisted and shared their knowledge to us in the long process of making this project:
Firstly, to the Lord Almighty for providing us the knowledge we needed to in order
for us to make this project a success.
To our adviser, Engr. Ricardo Fornis, for the unending guidance, patience and
consideration all throughout the creation of this project.
To our loving parents who gave us their love and support, financially and morally,
upon the ardent creation of this project.
And to the researchers, ourselves, for the effort each and every one of us has given
for the completion of this project.
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Table of Contents
Introduction, Objectives and Description of the Problem 1
Literature Review 4
Frequency Analysis 4
Return Period 4
Gringorten Plotting Position 7
Gumbel Distribution 7
Lognormal Distribution 8
Data Presentation 9
Table 1.1 Annual Peak Flow of Buaya River 9
Table 1.2 Sorted Discharge and Plotting Distribution 9
Table 1.3 Gumbel Distribution 10
Table 1.4 Lognormal Distribution 12
Graph 1.1 Graph using Gumbel Distribution 13
Graph 1.2 Graph using Lognormal Distribution 13
Sample Computation 14
Analysis and Interpretation of Results 16
Conclusion 17
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Introduction, Objectives and Description of the Problem
Ever since before, flood control seems to be the hardest problem to solve and one of
the deadliest catastrophes the society can encounter. Different projects were done like
drainage systems, dams and pumping stations, building barriers, control of land use and many
more methods to prevent flood increase and from further destruction of properties. But these
methods would not be possible without precisely predicting extreme precipitation events and
flood levels.
Future floods cannot be predicted with certainty. Therefore, their magnitude and
frequency are treated using probability distributions.
Frequency Analysis is done to determine the return periods of recorded events of
known magnitudes or to estimate the magnitudes of events for design return periods beyond
the recorded range. It involves the fitting of a probability model to the sample of annual flood
peaks recorded over a period of observation, for a catchment of a given region. The model
parameters established can then be used to predict the extreme events of large recurrence
interval. Flood is termed as a hydrologic extreme since it occur relatively rarely comparing to
moderated events. The magnitude of these hydrologic extremes events is inversely
proportional to their frequency or probability of occurrence, which means that more severe
events or large discharges occur less frequently and vice versa. This information on
magnitude and frequency relationship is used in the design of dams, culverts, highways,
water supply systems, bridges and flood control systems. Reliable flood frequency estimates
are vital for floodplain management; to protect the public, minimize flood related costs to
government and private enterprises, for designing and locating hydraulic structures and
assessing hazards related to the development of flood plains.
This study aims to analyze the flood frequency of Buaya River. The Specific
objectives of the study are:
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To use the best probability distribution for the discharge data. To relate the magnitude of events to their frequency of occurrence through probability
distribution.
To predict probable flooding of Buaya River using flood frequency analysis.The map presented below shows the location of the Buaya River in Galimuyod, Ilocos
Sur region (288.481875 degrees from North clockwise.)
The pictures shown below shows what the river looks like during non-flooding and
flooding seasons.
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As can be seen in the picture, the Buaya River really overflows and gets the Kampung
Sungai Buaya flooded. An article written byStuart Michael from The Star Online just last
March 1, 2013 reveals that Residents in Kampung Sungai Buaya, were facing frequent floods
because the river in the area was not deep enough to hold the volume of water whenever there
was a downpour. Many residents have placed concrete slabs at the entrance to their houses to
keep floodwaters out but sometimes this does not work. Resident S. Viran, 53, said when
there was a downpour, his house would be flooded and household items damaged. This is
because Sungai Buaya or Buaya River has not been deepened. Instead, it overflows and
floods the village. I have been living here for 14 years and have experienced floods many
times. I am the most affected as my house is located beside the river. I hope the authorities
can deepen the river and resolve the problem, he said. Another resident R. Parasuraman, 60,
said flooding occurred every time it rained heavily and that the villagers had to move their
belongings to higher ground when the river swelled. Also, the cement wall along the Sungai
Buaya riverbank is cracking. We are afraid that the houses nearby will be badly affected, he
said. Housewife G. Mariayaee, 41, who only moved into the village a few months ago, said
she was unaware about the floodingproblem. If I had known, I would not have come here. I
am renting this house and floodwaters have entered my house twice. My furniture has all
been damaged. If the situation is not resolved soon, I will move out, he said.
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Literature Review
Frequency AnalysisFlood frequency analysis involves the fitting of a probability model to the sample of
annual flood peaks recorded over a period of observation, for a catchment of a given region.
The model parameters established can then be used to predict the extreme events of large
recurrence interval (Pegram and Parak, 2004) Reliable flood frequency estimates are vital for
floodplain management; to protect the public, minimize flood related costs to government
and private enterprises, for designing and locating hydraulic structures and assessing hazards
related to the development of flood plains (Tumbare, 2000). Nevertheless, to determine flood
flows at different recurrence intervals for a site or group of sites is a common challenge in
hydrology. Although studies have employed several statistical distributions to quantify the
likelihood and intensity of floods, none had gained worldwide acceptance and is specific to
any country (Law and Tasker, 2003). Analysis of consecutive days maximum rainfall of
different return periods is a basic tool for safe and economical planning and design of small
dams, bridges, culverts, irrigation and drainage work etc. Though the nature of rainfall is
erratic and varies with time and space, yet it is possible to predict design rainfall fairly
accurately for certain return periods using various probability distributions (Upadhaya and
Singh, 1998).
Return PeriodA general concept for estimating return periods and risks of different types of
hydrologic events is presented here. Return period has been customarily defined as the
average number of trials required to the first occurrence of an event D $D0, or an event that
is greater or equal than a particular critical event or design event D0 (Bras 1990). For
instance, such critical eventD0 may be the so-called design flood (flood of a given return
period T or T-year flood) when designing flood-related hydraulic structures, or it may be the
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critical drought (a drought of a given return period) in the case of designing water supply
storage systems. The foregoing definition assumes that an event D $D0 occurred in the past,
a finite-time t has elapsed since then, and the interest is in the residual or remaining waiting
timeN for the next occurrence ofD $D0. An alternative definition of return period has been
the expected value of the number of trials between any two successive occurrences of
eventsD $D0 or recurrence interval (Lloyd 1970; Kite 1988; Loaiciga and Marino 1991).
The recurrence interval conveys information about the mean elapsed time between
occurrences of geophysical events. This definition assumes that an event D $ D0 has just
occurred and the interest is in the time of arrival of the next event D $ D0. Also, this
definition can be considered to be equivalent to the former definition when the time past t,
after the occurrence of D $ D0, is equal to zero. In practice, both definitions have been
accepted as being equivalent because, in simple cases such as those related to independent
annual flood events, they lead to the same result. However, a further examination will show
that these two definitions are essentially different and lead to different results when applied to
complex hydrological events.
The standard procedure to determine probabilities of flood flows consists of fitting the
observed stream flow record to specific probability distributions. However, this procedure
only works for basins;
that have stream flow records, where stream flow records are 'long enough' to warrantstatistical analysis;
where flood flows are not appreciably altered by reservoir regulation, channelimprovements (levees) or land use change.
Continuous hydrologic simulation is a valuable tool to determine flood frequencies in
gaged watersheds that have short stream flow records or are heavily regulated.
Meteorological data for most watersheds in the United States extend 40 to 80 years. Stream
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flow records, if available at all, are often shorter. Continuous hydrologic simulation can use
the observed meteorological data available to extend the existing stream flow record from a
few years to 40 or 80 years. The extended record can then be fitted to a probability
distribution.
Hydrologic simulation can also be used to determine flood frequencies in ungaged
streams. In this case the model is calibrated to a near-by, hydrologically similar, gaged
stream. The model parameters are then adjusted to reflect the physical changes between the
calibration watershed and the ungaged watershed. Finally, all the available observed
meteorological data are used to create a long stream flow record for the ungaged stream,
which can then be fitted to a statistical distribution. This method produces much better results
than alternative simplified approaches such as comparison to similar watersheds, or indirect
approaches that equate runoff frequency to precipitation frequency (such as unit hydrographs
or the rational formula).
Land use changes can have a significant effect on flood flow frequencies. Historic
stream flow records may be non-stationary for basins in which widespread urbanization is
taking place. Hydrologic simulation uses historic flow records to calibrate to the historic
conditions and it then incorporates the effects of future urbanization.
Similarly, in basins where reservoir regulation significantly affects flood flows,
continuous hydrologic simulation can isolate the effect of the reservoir. The model makes it
possible to compare flood levels with and without the reservoir and for various reservoir
operations. When the possibility of a dam failure is considered, the results from hydrologic
simulation can be used together with a full equations routing model.
In addition to generating or extending stream flow records, hydrologic simulation can
be used to study the validity of an assumed probabilistic distribution for peak flows. The U.S.
Water Resources Council recommends the use of the Log-Pearson Type III frequency
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distribution. However, it has been Hydrocomp's experience that this distribution can produce
unreasonable results in semi-arid areas: The calculated runoff intensity above certain return
periods greatly exceeds the precipitation for the same return period. Since continuous
hydrologic simulation maintains a continuous accounting of soil moistures, it provides a
unique tool to analyze the complex relationship between frequencies of precipitation, soil
moisture and runoff.
Gringorten Plotting PositionThe Gringorten plotting position was used in this project to plot the data obtained
and computed to a graph. The formula to use this plotting position is
0.440.12 where m is the rank of trhe ordered data from lowest to highest and n is the number of data.
Gumbel DistributionGumbel distribution is a statistical method often used for predicting extreme
hydrological events such as floods (Zelenhasic, 1970; Haan, 1977; Shaw, 1983).
Inprobability theory andstatistics, the Gumbel distribution is used to model the distribution
of the maximum (or the minimum) of a number of samples of various distributions. Such a
distribution might be used to represent the distribution of the maximum level of a river in a
particular year if there was a list of maximum values for the past ten years. It is useful in
predicting the chance that an extreme earthquake, flood or other natural disaster will occur.
The potential applicability of the Gumbel distribution to represent the distribution of
maxima relates toextreme value theory which indicates that it is likely to be useful if the
distribution of the underlying sample data is of the normal or exponential type.
The Gumbel distribution is a particular case of thegeneralized extreme value
distribution (also known as the Fisher-Tippett distribution). It is also known as thelog-
http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Extreme_value_theoryhttp://en.wikipedia.org/wiki/Generalized_extreme_value_distributionhttp://en.wikipedia.org/wiki/Generalized_extreme_value_distributionhttp://en.wikipedia.org/wiki/Weibull_distributionhttp://en.wikipedia.org/wiki/Weibull_distributionhttp://en.wikipedia.org/wiki/Generalized_extreme_value_distributionhttp://en.wikipedia.org/wiki/Generalized_extreme_value_distributionhttp://en.wikipedia.org/wiki/Extreme_value_theoryhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Probability_theory -
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Weibull distribution and the double exponentialdistribution (which is sometimes used to
refer to theLaplace distribution). It is often incorrectly labelled asGompertz distribution.
In thelatent variable formulation of themultinomial logit model common
indiscrete choice theory the errors of the latent variables follow a Gumbel distribution.
This is useful because the difference of two Gumbel-distributedrandom variables has
a logistic distribution. The Gumbel distribution is named afterEmil Julius Gumbel (1891
1966). Thecumulative distribution function of the Gumbel distribution is
:
and the mean is given by
0.5772 and the standard deviation is given by
6 Lognormal Distribution
Inprobability theory, a log-normal distribution is a continuousprobability
distribution of arandom variable whoselogarithm isnormally distributed. IfXis a random
variable with a normal distribution, then Y= exp(X) has a log-normal distribution; likewise,
if Yis log-normally distributed, thenX= log(Y) has a normal distribution. A random variable
which is log-normally distributed takes only positive real values.
http://en.wikipedia.org/wiki/Weibull_distributionhttp://en.wikipedia.org/wiki/Laplace_distributionhttp://en.wikipedia.org/wiki/Gompertz_distributionhttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Multinomial_logithttp://en.wikipedia.org/wiki/Discrete_choicehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Logistic_distributionhttp://en.wikipedia.org/wiki/Emil_Julius_Gumbelhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Logarithmhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Logarithmhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Emil_Julius_Gumbelhttp://en.wikipedia.org/wiki/Logistic_distributionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Discrete_choicehttp://en.wikipedia.org/wiki/Multinomial_logithttp://en.wikipedia.org/wiki/Latent_variablehttp://en.wikipedia.org/wiki/Gompertz_distributionhttp://en.wikipedia.org/wiki/Laplace_distributionhttp://en.wikipedia.org/wiki/Weibull_distribution -
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Data Presentation
Table 1.1 Annual Peak Flow in cu.m/s Table 1.2 Sorted Discharge
and of Buaya River Plotting Position
Year Rank (m) Plotting
Position
using
Gringorten (P)
Sorted
Discharge (Q)
1978 1 0.01743 0.47
1961 2 0.04857 31.50
1973 3 0.07970 50.00
1958 4 0.11083 110.40
1975 5 0.14197 145.00
1952 6 0.17310 148.40
1965 7 0.20423 211.00
1955 8 0.23537 221.00
1966 9 0.26650 239.00
1959 10 0.29763 243.80
1979 11 0.32877 246.00
1970 12 0.35990 267.00
1976 13 0.39103 268.80
1960 14 0.42217 274.001969 15 0.45330 281.80
1974 16 0.48443 308.00
1972 17 0.51557 346.28
1980 18 0.54670 364.00
1963 19 0.57783 398.60
1948 20 0.60897 404.80
1971 21 0.64010 470.91
1951 22 0.67123 483.00
1957 23 0.70237 483.00
1954 24 0.73350 511.20
1968 25 0.76463 530.00
1953 26 0.79577 583.00
1967 27 0.82690 637.00
1977 28 0.85803 693.00
1949 29 0.88917 775.00
1964 30 0.92030 1070.00
1950 31 0.95143 1106.00
1956 32 0.98257 1950.00
Year Annual
Peak
Flow in
cu.m/s
Year Annual
Peak
Flow
in
cu.m/s
1948 404.80 1965 211.00
1949 775.00 1966 239.00
1950 1106.00 1967 637.00
1951 483.00 1968 530.001952 148.40 1969 281.80
1953 583.00 1970 267.00
1954 511.20 1971 470.91
1955 221.00 1972 346.28
1956 1950.00 1973 50.00
1957 483.00 1974 308.00
1958 110.40 1975 145.00
1959 243.80 1976 268.80
1960 274.00 1977 693.00
1961 31.50 1978 0.471963 398.60 1979 246.00
1964 1070.00 1980 364.00
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Table 1.3 Gumbel Distribution
sample SD = 382.22
sample mean = 432.87
= 298.01
= 260.86
Year
Annual
Peak
Flow in
cu.m/s
Rank(m)
Plotting
Position
using
Gringorten
(P)
sorted
Discharge
(Q)
Return
Period
(T)
1956 1950.00 1 0.01743 1950.00 57.36
1950 1106.00 2 0.04857 1106.00 20.59
1964 1070.00 3 0.07970 1070.00 12.55
1949 775.00 4 0.11083 775.00 9.02
1977 693.00 5 0.14197 693.00 7.04
1967 637.00 6 0.17310 637.00 5.78
1953 583.00 7 0.20423 583.00 4.90
1968 530.00 8 0.23537 530.00 4.25
1954 511.20 9 0.26650 511.20 3.75
1951 483.00 10 0.29763 483.00 3.36
1957 483.00 11 0.32877 483.00 3.04
1971 470.91 12 0.35990 470.91 2.781948 404.80 13 0.39103 404.80 2.56
1963 398.60 14 0.42217 398.60 2.37
1980 364.00 15 0.45330 364.00 2.21
1972 346.28 16 0.48443 346.28 2.06
1974 308.00 17 0.51557 308.00 1.94
1969 281.80 18 0.54670 281.80 1.83
1960 274.00 19 0.57783 274.00 1.73
1976 268.80 20 0.60897 268.80 1.64
1970 267.00 21 0.64010 267.00 1.56
1979 246.00 22 0.67123 246.00 1.49
1959 243.80 23 0.70237 243.80 1.42
1966 239.00 24 0.73350 239.00 1.36
1955 221.00 25 0.76463 221.00 1.31
1965 211.00 26 0.79577 211.00 1.26
1952 148.40 27 0.82690 148.40 1.21
1975 145.00 28 0.85803 145.00 1.17
1958 110.40 29 0.88917 110.40 1.12
1973 50.00 30 0.92030 50.00 1.09
1961 31.50 31 0.95143 31.50 1.051978 0.47 32 0.98257 0.47 1.02
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Return
Period
(T)
Probability
of
Exceedance
p=1/T
Probability of
non-
exceedance
F(x) = 1-1/T
Estimated
Discharge
(Qest)
1 1.000 0.00000 NA
2 0.500 0.50000 370.09
3 0.333 0.66667 529.88
4 0.250 0.75000 632.16
5 0.200 0.80000 707.86
6 0.167 0.83333 768.07
7 0.143 0.85714 818.09
8 0.125 0.87500 860.899 0.111 0.88889 898.28
10 0.100 0.90000 931.50
11 0.091 0.90909 961.38
12 0.083 0.91667 988.52
13 0.077 0.92308 1013.40
14 0.071 0.92857 1036.36
15 0.067 0.93333 1057.67
16 0.063 0.93750 1077.56
17 0.059 0.94118 1096.21
18 0.056 0.94444 1113.7519 0.053 0.94737 1130.32
20 0.050 0.95000 1146.02
21 0.048 0.95238 1160.93
22 0.045 0.95455 1175.13
23 0.043 0.95652 1188.68
24 0.042 0.95833 1201.64
25 0.040 0.96000 1214.07
26 0.038 0.96154 1225.99
27 0.037 0.96296 1237.46
28 0.036 0.96429 1248.50
29 0.034 0.96552 1259.15
30 0.033 0.96667 1269.43
31 0.032 0.96774 1279.36
32 0.031 0.96875 1288.98
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Table 1.4 Lognormal Distribution
SampleSD(s)=
382.22 pop SD()=
0.76
sample
mean(x)=
432.87 pop mean
()=
5.78
Return
Period
(T)
Probability
of
Exceedance
p=1/T
Probability
of non-
exceedance
F(x) = 1-
1/T
Estimated
Discharge
(Qest)
1 1.000 0.00000 NA
2 0.500 0.50000 324.483 0.333 0.66667 450.00
4 0.250 0.75000 541.49
5 0.200 0.80000 614.75
6 0.167 0.83333 676.36
7 0.143 0.85714 729.79
8 0.125 0.87500 777.13
9 0.111 0.88889 819.73
10 0.100 0.90000 858.53
11 0.091 0.90909 894.20
12 0.083 0.91667 927.26
13 0.077 0.92308 958.09
14 0.071 0.92857 987.00
15 0.067 0.93333 1014.24
16 0.063 0.93750 1040.00
17 0.059 0.94118 1064.45
18 0.056 0.94444 1087.72
19 0.053 0.94737 1109.95
20 0.050 0.95000 1131.21
21 0.048 0.95238 1151.6122 0.045 0.95455 1171.21
23 0.043 0.95652 1190.08
24 0.042 0.95833 1208.28
25 0.040 0.96000 1225.86
26 0.038 0.96154 1242.85
27 0.037 0.96296 1259.32
28 0.036 0.96429 1275.27
29 0.034 0.96552 1290.77
30 0.033 0.96667 1305.82
31 0.032 0.96774 1320.4532 0.031 0.96875 1334.70
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Graph 1.1 Graph using Gumbel Distribution
Graph 1.2 Graph using Lognormal Distribution
0100200
300400500600700800900
100011001200130014001500160017001800190020002100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
DischargeQ(cu.m
/s)
F(x) = 1-1/T
Gumbel Distribution fitted to the data
Gumbel Distribution Buaya River Annual Peak FLow
0100200
300400500600700800900
100011001200130014001500160017001800190020002100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
x(cu.m
/s)
F(x) = 1-1/T
Lognormal distribution fitted to the data
Buaya River Annual Peak Flow Lognormal Distribution
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Sample Computations
Sample Mean
=
.+++
. ./
Sample Standard Deviation
1 132 404.8432.87 364432.87 .Scale Parameter,
6
382.22(6)
.
Location Parameter,
0.5772432.870.5772298.01 .Plotting Position Using Gringorten
0.440.12 10.44320.12 . Probability of Non-Exceedance
1 1 1 12 . FOR GUMBEL DISTRIBUTION
Estimated Discharge
[ln1 1]260.86 298.01[1 12]
.
Correlation
10:41,10:41 Where 10 41
10 41 .
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FOR LOGNORMAL DISTRIBUTION
Standard Deviation for Population
1 382.22432.87 1 .
Mean for Population
2 432.87 0.76
2 .
Estimated Discharge
.11, $$3, $$2 Where11
3 2
. /
Correlation
.
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Analysis and Interpretation of Results
From two flood frequency analysis distribution employed, Gumbel Distribution and
Lognormal Distribution does not seem to capture accurately the given data with the basis of
correlating the distribution analysis with the given actual discharge.
The magnitude of discharge for a specific flood event is inversely proportional to the
frequency or probability of occurance. This means that for a sooner return period, the
magnitude of the discharge is higher. Therefore a storm with the highest discharge has a
longer return period. Take for example from table 1.3, the return period for a 1950 cu.m/s
discharge is 57.36 years and for a 0.42 cu.m/s discharge is 1.02 years.
The correlation value for Gumbel distribution is 0.688237 while for the Lognormal
distribution is 0.724861. It can be inferred that lognormal distribution is more suited to our
given data sample than the Gumbel distribution because it has a correlation value closer to 1
from the two distributions.
Based from Graphs 1.1 and 1.2, the plot for the given discharges showed an outlier
value which might have caused the difficulty of fitting the given distributions. But it can be
proved from the graph that the lognormal distribution is more suitable for this project. As can
be seen in the graph, the points in the lognormal distribution graph are closer to the best fit
line than the points in graph of the Gumbel distribution.
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Conclusion
The Buaya River located in Ilocos Sur seems to always overflow because the river is
shallow and even a short period of rain would allow water to overflow from the river. Using
the lognormal and Gumbel distribution, we are able to relate the magnitude of events to their
frequency of occurrence through probability distribution. For the Gumbel distribution, the
maximum discharge of 1288.98cu.m/s for a single storm occurrence can occur over a return
period of 32 years. But it doesnt mean that this particular storm will return exactly after 32
years. This simple means that this particular storm will occur once every 32 years but the
exact date of its return cant be easily determined. On the other hand, for the lognormal
distribution, the maximum discharge of 1334.70 cu.m/s for a single storm occurrence can
occur over a return period of 32 years. From these findings, we can conclude that for this
study, the lognormal distribution can describe the data better than the Gumbel distribution.
This can be inferred because a more conservative value is to consider when describing the
discharge and return period of a particular storm.
Another basis that we have considered in our conclusion that the lognormal
distribution is better is the correlation obtained from both distribution methods. We have
computed the correlation of both methods and found out that the correlation of the lognormal
distribution is nearer to one, therefore the values obtained from the lognormal distribution is
nearer to the values from the best fit curve of the graph.
With these conclusion, we can recommend that the residents residing near the Buaya
River should prepare for flow levels as indicated in this report for a certain return period.
Though the exact reoccurrence of a particular storm (like a 32-year return period storm) cant
be determined, at least preparations can be made because the maximum flood levels can be
estimated using the maximum discharge.