NUR ASMA’ BINTI SUHAIMEEumpir.ump.edu.my/id/eprint/12211/1/FKASA - NUR ASMA... · IDF, proses yang terlibat adalah mencari data yang hilang dari stesen terdekat, min, standard penyimpangan,

THE DEVELOPMENT OF INTENSITY-DURATION-FREQUENCY CURVES FOR

PAHANG

NUR ASMA’ BINTI SUHAIMEE

Report submitted in partial fulfilment of requirements

for the award of the degree of

B. Eng. (Hons) Civil Engineering

Faculty of Civil Engineering & Earth Resources

UNIVERSITI MALAYSIA PAHANG

JUNE 2015

v

ABSTRACT

In past few years, Pahang was experienced flooding in certain area and it getting worse

by year with heavy rainfall especially at low level area cause of clog drain, design

failing, wrong estimation and other natural causes. IDF curve use to design rainfall data

by estimate peak discharge from IDF curve for engineering design such drainage, flood

elevation, and other hydraulic design. This study purpose to develop intensity-duration-

frequency (IDF) curve for all 12 district in Pahang based on this past year data and

compare it with Log-Person Type III method than Gumbel method that use in Urban

Storm Water Management (MSMA) to compare the differences value of IDF curve

using both method. IDF curve requires rainfall data from the Department of Irrigation

and Drainage (DID) for period of 5 minutes to 72 hour starting on year 1990 to year

2014. To designing IDF curve, process involved are find the missing data from nearest

station, mean, standard deviation, frequency factor, and intensity value for 2, 5, 10 ,20,

50 and 100 years return period for both methods Gumbel and Log-Pearson Type III.

Both methods, Gumbel and Log-Pearson Type III is compared to see the different value

given by both methods. To test the accuracy of both methods, Komogorov Smirnov

(KS) was constructed for fitting distribution. Based on the result, Gumbel method give

clear trend than Log-Pearson Type III with 26.92% test accepted from 78 tests while

Log-Pearson Type III almost all test was rejected.

vi

ABSTRAK

Dalam tahun-tahun kebelakangan ini, Pahang telah mengalami banjir di kawasan

tertentu dan ia semakin teruk setiap tahun dengan hujan lebat terutama di kawasan

rendah menyebabkan tahap longkang tersumbat, reka bentuk gagal, anggaran yang salah

dan lain-lain sebab-sebab semula jadi. IDF menggunakan keluk untuk mereka bentuk

data hujan dengan anggaran pelepasan puncak dari lengkung IDF untuk reka bentuk

kejuruteraan saliran, ketinggian banjir, dan reka bentuk hidraulik lain. Tujuan kajian ini

adalah membangunkan keamatan-tempoh-frekuensi (IDF) lengkung untuk semua 12

daerah di Pahang ini berdasarkan data tahun-tahun lepas dan membandingkannya

dengan kaedah Log-Pearson Jenis III dengan kaedah Gumbel yang digunakan oleh

Pengurusan Air Ribut Bandar (MSMA) dengan membandingkan nilai perbezaan

lengkung IDF menggunakan kedua-dua kaedah tersebut. Lengkung IDF memerlukan

data hujan daripada Jabatan Pengairan dan Saliran (JPS) untuk tempoh 5 minit hingga

72 jam bermula pada tahun 1990 hingga tahun 2014. Untuk mereka bentuk lengkung

IDF, proses yang terlibat adalah mencari data yang hilang dari stesen terdekat, min,

standard penyimpangan, faktor kekerapan dan nilai keamatan untuk 2, 5, 10, 20, 50 dan

100 tahun kembali tempoh untuk kedua-dua kaedah Gumbel dan Log Pearson Jenis III.

Kedua-dua kaedah, Gumbel dan Log-Pearson Type III dibandingkan dengan melihat

nilai yang berbeza yang diberikan oleh kedua-dua kaedah. Untuk menguji ketepatan

kedua-dua kaedah, Komogorov Smirnov (KS) telah dibina untuk diagihkan sesuai.

Berdasarkan keputusan, kaedah Gumbel memberikan trend jelas daripada Log-Pearson

Type III dengan ujian 26,92% diterima daripada 78 ujian manakala Log-Pearson jenis

III hampir semua ujian telah ditolak.

vii

TABLE OF CONTENT

Page

SUPERVISOR'S DECLARATION i

STUDENT'S DECLARATION ii

DEDICATION iii

ACKNOLEWDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xiii

LIST OF SYMBOLS xvi

LIST OF ABBREVIATION xviii

CHAPTER 1 INTRODUCTION

1.1 Background 1

1.2 Problem Statement 2

1.3 Objectives 3

1.4 Scope of Study 3

1.5 Significant of Study 3

CHAPTER 2 LITERATURE RIVIEW

2.1 Introduction 5

2.2 Intensity-Duration-Frequency (IDF) Curve 6

2.3 Mass Curve 9

2.4 Missing Data Method 12

2.4.1 Normal Ratio Method 12

viii

2.4.2 Arithmetic Mean Method 12

2.5 Distribution for IDF Curve Development 13

2.5.1 Log-Normal Distribution 13

2.5.2 Normal Distribution 16

2.5.3 Gamma Distribution 17

2.5.4 Gumbel Distribution 18

2.5.5 Log-Pearson Type III Distribution 20

2.6 Goodness of Fit 21

2.6.1 Kolmogorov-Smirnov test (KS test) 21

2.6.2 Chi-square test 22

2.6.3 Anderson-Darling test 23

CHAPTER 3 METHODOLOGY

3.1 Introduction 25

3.2 Flow Chart 26

3.3 Study Area 27

3.4 Data Collection 27

3.5 Analysis Method 29

3.5.1 Missing Data 29

3.5.2 Frequent Factor 30

3.5.3 Mean and Standard Deviation 31


3.5.4.1 Frequency Factor 31

3.5.4.2 Flood of Specific Probability 32


3.5.5.1 Frequency Factor 33

3.5.5.2 Flood of Specific Probability 35

3.6 Graphical Method 35

3.7 Confidence Limits 38

3.8 Percentage of Differences 39

CHAPTER 4 RESULT AND DISCUSSION

4.1 Introduction 40

ix

4.2 Missing Data 42

4.3 Mean and Standard Deviation 43



4.4 Frequency Factor 44



4.5 Intensity 46



4.6 IDF Curve for Gumbel Distribution 50

4.6.1 Bentong 50

4.6.2 Bera 54

4.6.3 Cameron Highland 57

4.6.4 Jerantut 59

4.6.5 Kuala Lipis 62

4.6.6 Kuantan 66

4.6.7 Maran 68

4.6.8 Pulau Tioman 70

4.6.9 Pekan 71

4.6.10 Raub 74

4.6.11 Rompin 75

4.6.12 Temerloh 79

4.6.13 Conclusion 80

4.7 IDF Curve for Log-Pearson Type III Distribution 81

4.7.1 Bentong 81

4.7.2 Bera 85

4.7.3 Cameron Highland 88

4.7.4 Jerantut 89

4.7.5 Kuala Lipis 93

4.7.6 Kuantan 98

4.7.7 Maran 100

4.7.8 Pulau Tioman 102

4.7.9 Pekan 103

4.7.10 Raub 106

4.7.11 Rompin 107

4.7.12 Temerloh 111

4.7.13 Conclusion 112

4.8 Comparison between Constructed IDF Curve and

Existing IDF Curve in MSMA

113

x

4.9 Comparison between IDF Curve for Gumbel

Distribution and Log-Pearson Type III Distribution

119

4.10 Comparison of Kolmogorov-Smirnov for Gumbel and

Log-Pearson Type III Distribution

131

4.10.1 Emperical Calculation for Gumbel Distribution 131

4.10.2 Emperical Calculation for Log-Pearson Type

III Distribution

136

4.10.3 Comparison of Probability Value between both

Method

139

4.11 Summary 141

CHAPTER 5 CONCLUSION

5.1 Background 143

5.2 Conclusion 143

5.3 Recommendation 145

REFERENCE 147

APPENDICES 150

A Rainfall Data in mm 151

B Rainfall Depth in mm 177

C Rainfall Intensity for Log-Pearson Type III Distribution in

mm/hr 191

D Rainfall Intensity for Gumbel Distribution in mm/hr 198

E Gumbel’s Distribution with 90% Confidence Intervals 205

xi

LIST OF TABLES

Table No. Title Page

3.1 Selected Rainfall Station 28

3.2 Frequency Factors K for Gamma and log-Pearson Type III Distributions 33

3.3 Various Plotting Positions Formula 36

3.4 Value of Kolmogorov Smirnov, ∆0 39

4.1 Rainfall Data for Rompin (Stn 3228174) 41

4.2 Rainfall Data for Pulau Tioman (Stn. 2841001) 42

4.3 Descriptive Statistic for Rompin (Stn. 3228174) for Gumbel Distribution 43

4.4 Descriptive Statistic for Rompin (Stn. 3228174) for Log-Pearson Type

III Distribution 44

4.5 Frequency Factor based on Return Period 45

4.6 Value Cs for Rompin (Stn 3228174) 46

4.7 Frequency Factor based on Return Period 46

4.8 Rainfall Depth for Rompin (Stn 3228174) in mm 47

4.9 Intensity for Rompin (Stn 3228174) in mm/hr 48

4.10 Rainfall Depth for Rompin (Stn 3228174) in mm before anti-log 49

4.11 Rainfall Depth for Rompin (Stn 3228174) in mm after anti-log 49

4.12 Intensity for Rompin (Stn 3228174) in mm/hr for Log-Pearson Type III 50

4.13 Coefficient IDF equation for Pahang in MSMA 114

4.14 Intensity from Coefficient in MSMA 115

4.15 Percentage of Difference for Rompin, Bera, Temerloh, Maran, Raub,

Jerantut, Kuantan and Cameron Highland 117

xii

4.16 Intensity of District in Pahang using Gumbel Distribution 119

4.17 Intensity of District in Pahang using Log-Pearson Type III Distribution 123

4.18 Percentage different between Gumbel and Log-Pearson Type III 127

4.19 Summary Calculation for Plotting Position Formula for Gumbel

Distribution 132

4.20 Summary Calculation for Plotting Position Formula for Log-Pearson

Type III Distribution 137

4.21 Maximum Probability Different between Gumbel and Log-Pearson Type

III Distribution 139

5.1 Maximum Value of the Intensity 144

5.2 Minimum Value of the Intensity 144

xiii

LIST OF FIGURES

Table No. Title Page

2.1 IDF curve 7

2.2 Mass curve (Cumulative Rainfall of Stations in The Period 2002-2010) 10

2.3 Cumulative Log-Normal Distribution of Rainfall 14

2.4 Normal Distribution of Precipitation 16

3.1 Flow Chart of Study 26

3.2 Maps of District at Pahang 27

3.3 Pahang Rainfall Station 29

4.1 IDF curve for Bentong (Stn. 3122142) 51



4.4 IDF curve for Bera (Stn. 3026156) 54



4.7 IDF curve for Cameron Higland (Stn.. 4513033) 58

4.8 IDF curve for Jerantut (Stn. 3924072) 59



4.11 IDF curve for Kuala Lipis (Stn. 4019001) 62




xiv

4.15 IDF curve for Kuantan (Stn. 3833002) 66


4.17 IDF curve for Maran (Stn. 3628001) 69

4.18 IDF curve for Pulau Tioman (Stn. 2841001) 70

4.19 IDF curve for Pekan (Stn.3034168) 71

4.20 IDF curve for Pekan (Stn. 3330109) 72


4.22 IDF curve for Raub (Stn.3818054) 74

4.23 IDF curve for Rompin (Stn. 3228174) 76










4.33 IDF curve for Cameron Highland (Stn. 4513033) 88





xv






4.43 IDF curve for Maran (Stn. 368001) 101

4.44 IDF curve for Pulau Tioman (Stn. 2841001) 102




4.48 IDF curve for Raub (Stn. 3818054) 106




4.52 IDF curve for Temerloh (Stn. 3424081) 111

4.53 Plotting Gumbel ( 15 minutes) in Jerantut (Stn.4324001) for 95%

Confidence Intervals 135

xvi

LIST OF SYMBOL

Pi The rainfall at neighbor stations

Nx Annual rainfall at missing data station

Ni Annual rainfall at neighbor station

n The number neighbor station whose data are used

Px The missing precipitation

Pn The precipitation value at n station

𝜎 Standard Deviation

µ Mean

Xi The variate i.e record used in the computation

N The total number of record

𝑥 𝑖 Mean of the sample

𝛼𝑧 The scale

𝜆𝑧 Shape parameters of the gamma distribution

PT The frequency precipitation

K Gumbel frequency

S Standard deviation of P value

Pave The average of the maximum precipitation in a specific duration

Td Duration in hours

P*T The frequency precipitation

S* Standard deviation of P* value

KT The Pearson frequency factor which depends on return period (T)

and skewness coefficient (Cs).

v Degree of freedom

xvii

s Number of parameter using fitting distribution

A2 Anderson-Darling statistic

Fn(x(i)) Empirical Distribution (PDF)

x(i) The ordered data

T Return period (years)

xviii

LIST OF ABBREVIATION

MSMA Manual Saliran Mesra Alam

CDF Cumulative Density Function

PDF Probability Density Function

KS Kolmogorov-Smirnov Test

LP3 Log-Pearson Type III

LN Log-Normal

IDF Intensity-Duration-Frequency

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

Malaysia is one of the countries located at Southeast Asia, near the equator which

is humid and hot all the year. The location of Malaysia at equator zone gives Malaysia

experience tropical climate with two type of monsoon season which are the northeast

and southwest through the year. Northeast occur during November to May bring

moisture and more rainfall. Where southwest give wind blowing monsoon within May

to September. These results give average rainfall in Malaysia in 2500mm with average

temperature 27oC a year.

Seasonal variation give effect on rainfall pattern depend on geography of

Malaysia that surrounded by mountain. This condition give two different climate which

is depend on highland and lowland region. As a result, both condition cause temperature

raging between 23oC to 32

oC through the year with humidity between 75% and 80%

and annually receive rainfall between 2000mm to 4000mm with 150 to 200 rainy days.

From this rainfall pattern, the data will be used to construct temporal pattern using

rainfall intensity-duration-frequency (IDF) curves. Rainfall intensity –duration-

frequency (IDF) should be up to date in line with the changes of rainfall pattern due to

global warming effect and temperature changes. Rainfall intensity-duration-frequency

(IDF) is one of the most important tools in hydrology and hydraulic design use by

engineer in planning, designing, and operate rainwater infrastructure like drainage

2

structure and flood elevation in urban and rural area (Le Minh Nhat,etc,2007). Failing in

implant the IDF estimation in design can cause public safety or fund at risk.

Those data from rainfall data was use in frequency analysis method to develop

intensity-duration-frequency (IDF) curve. To use this method, local history data was

needed to get maximum annual rainfall depth corresponding to various duration. Latest

duration data will be taken within period of 5 minutes to 120 hours with different return

periods 2, 5, 10, 20, 50 and 100 years. The IDF curve will show the infinite number of

rainfall event with different average intensity and duration with same return period. For

a specific return period, the average intensity will decrease as the duration increase. As

the result, for same duration, the average intensity is higher for longer return periods

than the shorter one (Akan et al., 2003).

1.2 PROBLEM STATEMENT

All rainwater design in Malaysia must refer to the Urban Storm Water

Management Manual 2nd

edition (MSMA 2) to follow standard. Based on observation in

MSMA 2, the data of IDF curve for Pahang was updated until 2009. The climate change

in Malaysia in storm rainfall intensity may affect the data by change of latest addition

data (MSMA, 2012).

To get more accurate analysis, it necessary to estimate reliable rainfall intensity

by comparing the IDF curve by using different theoretical distribution function in

developing rainfall intensity and return period from rainfall data. Method being use for

IDF graph in MSMA only Gumbel distribution using data until 2009 and never be

compared before. Gumbel may suitable for condition in Malaysia but not been approved

until it compared with other method. Beside data given in MSMA is updated to 2009,

while until 2014 lot of change happen during that period of time.

New MSMA 2 has covered limited location which provided the parameter for

intensity calculation. Average location provided in MSMA is 2 locations for each

district while rainfall station for each district average in 10 stations each district.

Department Irrigation and Drainage (DID) should provide more location area for value

3

of intensity. For district not covered in MSMA need to use nearest district intensity

parameter to calculate intensity for design drainage. That way may affect the value of

intensity should be use for that location area and design drainage for that location.

1.3 OBJECTIVES

The objectives of this study are;

i. To calculate missing data for each station.

ii. To develop IDF curve for every district in Pahang.

iii. To compare differences values of IDF curves using Gumbel distribution and

Log-Pearson Type III distribution.

1.4 SCOPE OF STUDY

This study was conducted in Pahang area using rainfall data from 1990-2014 to

develop IDF curves. The duration of IDF curve from 5, 15, 60, 180, 360, 720, 1440

minutes until 72 hours and the return period including 2, 5, 10, 20, 50 and 100 years.

The data collections are from Department of Irrigation and Drainage (DID).

In this study, arithmetic formula was used to find the missing data for each

station. The best station was selected based on number of missing data which the lesser

missing data, the best station was selected. Few stations were selected to represent each

district. To calculate missing data, station within area 100 km radiuses was considered

to use in formula arithmetic. To ensure data fit, the Komolgorov Smirnov (KS) was

done.

1.5 SIGNIFICANT OF STUDY

All the water rain design in Malaysia use MSMA as reference for engineer to

design. Method use in MSMA to determine the intensity of rainfall is Gumbel

distribution and never be compared with other method. To test the reliable of this curve

to be used as reference, it needs to be compare with other method to see the reliability

of the IDF curve in MSMA. By developing new IDF curve can plant awareness to

4

MSMA user about the changes in MSMA due to the climate change in Malaysia. With

this development the risk for damaging hydrology design can be reduced while using

MSMA for designing material.

By developing new IDF curve, new location for new IDF curve was developed

and it can be used as designing material based on value of intensity for that location

area. Limited location for IDF curve use in MSMA can be covered with new location.

Thus nearest design location can refer to new IDF curve in new location to predict

intensity value which more reliable than more nearest then provided in MSMA as now.

CHAPTER 2

LITERATURE RIVIEW

2.1 INTRODUCTION

Inadequate hydrologic data and the need for proper planning of water resources

development have forced engineer to analyze available data more critically. This is

particularly so in developing countries. The Intensity-Duration-Frequency (IDF)

relationship is one of the most commonly use basis for water resources planning and

development.

Break-point, short duration, rainfall data are not generally available in the

historical records at the locations. Generalized accumulated rainfall patterns developed

by Department of Irrigation and Drainage (DID) were matched with rainfall data for the

locations of study, and the advanced pattern had the best fit with the observed

characteristics was used to break down recorded daily totals into shorter duration

rainfall data. The method of annual maxima series was used to select data sets for the

rainfall analysis.

In the statistical method, the Type I extreme-value distribution (Gumbel) was

applied to the annual maximum series for each of stations to estimate the relevant

parameters of the IDF model. The non-parametric Kolmogorov-Smimov test and the

test were used to confirm the appropriateness of the fitted distributions for the locations.

6

2.2 INTENSITY-DURATIOM FREQUENCY (IDF) CURVE

Extreme environmental events, such as floods, droughts, rainstorms, and high

winds, have severe consequences for human society. Planning for weather-related

emergencies, design of engineering structures, reservoir management, pollution control,

and insurance risk calculations, all rely on knowledge of the frequency of these extreme

events (Hosking and Wallis, 1997). The assessment of extreme precipitation is an

important problem in hydrologic risk analysis and design. This is why the evaluation of

rainfall extremes, as embodied in the intensity-duration frequency (IDF) relationship,

has been a major focus of both theoretical and applied hydrology (Andreas and

Veneziano, 2006). Dupont et al. (2000) defined rainfall IDF relationships as graphical

representations of the amount of water that falls within a given period of time.

Intensity-Duration-Frequency is representing amount of water rainfall that fall in

certain period of time in catchment area. This relationship was done since 1932 and still

being constructed for other country but it may not accurately construct in many

developing country.

Based on Koutyoyiannis , 2003, the IDF curves is a mathematical relationship

between the duration, d the rainfall intensity and the return period. This is allow the

estimation of return period in rainfall event corresponding to amount of rainfall at given

period for different aggregation times. These graphs are used to determine when an area

will be flooded, and when a certain rainfall rate or a specific volume of flow will

reoccur in the future. Below in Figure 2.1 show example of IDF curve for station at

Pulau Pinang.

7

Figure 2.1: IDF curve

Source: MSMA, 2011

According to Brian (2006), rainfall frequency analyses are used extensively in the

design of systems to handle storm runoff, including roads, culverts and drainage

systems. Smith (1993) states that the “the precipitation frequency analysis problem is to

compute the amount of precipitation y falling over a given area in a duration of x min

with a given probability of occurrence in any given year.” For engineering design

applications, it is necessary to specify the temporal distribution of rainfall for a given

frequency, or return interval. According to Stedinger (1993), IDF curves “allow

calculation of the average design rainfall intensity [or depth] for a given exceedance

probability over a range of durations” and is the result of the rainfall frequency analysis.

IDF estimates are important statistical summaries of precipitation records used for

hydrologic engineering design (Gerold and Watkins, 2005).

IDF curves received considerable attention in engineering hydrology over the past

decades. Approaches based on statistical analysis of data were developed,. Bell (1969)

and Chen (1983) derived the IDF formulae for the United States, Baghirathan and Shaw

(1978), Gert (1987) and Niemczynowicz (1982) developed IDF formulas for ungauged

8

sites, Sivapalan and Bloeschl (1998) proposed a method of constructing IDF curves

based on the spatial correlation structure of rainfall, Koutsoyiannis (1998) proposed a

new generalizing approach to the formulation of IDF curves using efficient

parameterization.

The first attempts to construct regional IDF curves were made by Dub (1950).

„Samaj and Valovi„c (1973) presented a comprehensive IDF study based on 68 stations

covering the area of Slovakia using data mostly from the period 11931-1960. Their

results were re-evaluated by Urcik'an and Horv'ath (in Urcik'an and Imri„ska, 1986);

however, the analysis mostly concentrated on the different formal presentations of IDF

curves. They also proposed a method for the spatial interpolation of IDF curves for sites

with no direct observations. These procedures were data and time demanding, therefore

it seemed advantageous to develop models which would describe rainfall characteristics

through a number of timescales including interpolation or extrapolation at time

resolutions that may not have been observed and start from there, IDF curve was widely

use in drainage system design.

The IDF curve is commonly use in water resource engineering for designing and

operating of water resources project. These methods usually use to estimate runoff

during storm, Empirical method, Rational method, Unit-Hydrograph method and Flood

frequency studies. To use those methods need to match with the purpose of study and

depend to available data use based on importance of the project.

The use of IDF was widely use and being standard practice for many years in

designing sewerage system and other hydraulics structure. IDF give idea about

frequency and return period for mean and volume rainfall intensity that can be expected

in certain period of storm duration. In this situation, storm duration is parameter can be

compromise as part of rainfall event. Even now, IDF can provide a lot information for

rainfall and can be used as base for determination of design storm ( A.S.Wayal, 2014).

9

2.3 MASS CURVE

During high flows, water flowing in river has to be stored so that a uniform supply

of water can be assured, for water resources utilization lake irrigation, water supply,

power generation during period of low flow rivers.

A mass curve is graphical representation of cumulative inflow or outflow of water

versus time which may be monthly or yearly. A mass curve shown in Fgure 2.2 is

example of mass curve. The slope of the mass at any point is a measure of the inflow

rate at that time. Mass curve or double mass curve is a commonly used data analysis

approach for investigating the behavior of records made of rainfall data at a number of

locations. It is used to determine whether there is a need for corrections to the data to

account for changes in data collection procedures or other local conditions. Such

changes may result from a variety of things including changes in instrumentation,

changes in observation procedures, or changes in gauge location or surrounding

conditions.

Mass analysis use for checking consistency of a rainfall record is considered to be

an essential tool before taking it for analysis purpose. This method is based on the

hypothesis that each item of the recorded data of a precipitation consistency (H. M.

Raghunath, 2006).

Documents

NUR ASMA’ BINTI SUHAIMEEumpir.ump.edu.my/id/eprint/12211/1/FKASA - NUR ASMA... · IDF, proses yang terlibat adalah mencari data yang hilang dari stesen terdekat, min, standard penyimpangan,