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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.