CHARACTERIZATION OF CONVECTIVE RAIN IN KLANG VALLEY,
MALAYSIA
NORDILA BINTI AHMAD
UNIVERSITI TEKNOLOGI MALAYSIA
CHARACTERIZATION OF CONVECTIVE RAIN IN KLANG VALLEY,
MALAYSIA
NORDILA BINTI AHMAD
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Master of Engineering (Hydrology and Water Resources)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
DECEMBER 2008
iii
“Dedicated to my beloved father,
Ahmad B. Yunus and mother, Ramlah Bt. Salleh,
my sisters, Marsilah, Norliza, Aspalela, Norli, Roslaili, and Norsheeda,
my brothers, Kamarul Azman and Mohd Fauzi, and also to
my beloved fiancé, Herman for their love, understanding and support to me”
“My deepest appreciation to all my colleagues,
Chong Meng Hui, Goh Yee Chai, Geoffery, Chow, Zulkifli, Nordiana,
Norhidayah, Masyitah and Mariyana Aida for their assistance and encouragements towards the
success of this study. May God shower them
with health and happiness”
iv
ACKNOWLEDGEMENT
In the name of Allah S.W.T, I’m most grateful to Him for giving me strength
to finish my project entitled ‘Characterization of Convective Rain in Klang Valley,
Malaysia’.
First of all I would like to thank my supervisor, Professor Dr. Zulkifli Yusop
and my co-supervisor who is also my project leader, Associate Professor Dr. Zalina
Md Daud for their helpful advices, consistent guidances and times. Without their
assistance, it is impossible to complete this study and project report.
Thanks are due to the Department of Irrigation and Drainage (DID) for
providing valuable rainfall data for Klang Valley region, without which my research
project would not have been possible to start. Special thanks are due to Mr Azmi, Ir
Mohd Zaki, Mr Azlan and Mrs Norhayati (officers of JPS Ampang) for their help. I
am indebted to Mr Nazri and staffs at KLIA Meteorological Department. The radar
images for the Klang Valley were provided by KLIA Meteorological Department.
Many thanks are extended to Prof Dr Ahris for allowing me the use GIS Laboratory
at the Faculty of Geoinformation, Science and Engineering. I will not forget the
kindly help from Mohamad Ediwan Ahmad on GIS matters. Without his assistance,
the spatial analysis is impossible to complete. Each discussion with him made me
understand the GIS concept more deeply. To Huda, a research assistant of this
project, thanks a lot for all your help.
Last but not least, I would like to convey my appreciations to my family and
friends who had given me moral supports and encouragement. I wish you all the best
and may GOD bless you all.
This study was funded by the Ministry of Science, Technology and
Innovation (MOSTI) under Vot 74280.
v
ABSTRACT
Storms of convective origin are generally known to be responsible for
most of flash flood events in Malaysia. Flood problems are aggravated by rapid
urbanization which modified the hydrological processes of a catchment. This study
is aimed to evaluate the characteristic of convective rain in Klang Valley. The
characteristics are based on short rainfall interval data between years 2000 and 2004.
The convective events were analysed in terms of timing and spatial distribution. The
spatial distributions of convective rainfall, derived from meteorological radar data
and those observed on the ground are compared. Convective storm occurred most
frequently during intermonsoon months which made up about 44%. A variety of
storm shape is evident. Most of the convective events occurred over short durations.
The convective storms were further classified into slightly convective, moderately
convective and strongly convective by using β parameter values.
A 35 mm/hr
threshold intensity is used for separating convective from non convective storms for
local conditions. The areal distributions derived from radar and those from raingauge
are poorly correlated. Each storm is unique in term of the movement of its storm
centre. Some have long paths while others are circling within a limited area. The
Aerial Reduction Factor (ARF) obtained from this study is comparable with ARF
values obtained earlier by other researchers. A new Intensity Duration Frequency
(IDF) curve is plotted based only on convective storms. For a given duration and
return period, the new IDF generally results in higher storm intensity compared to the
existing IDF curve.
However, the new IDF curves are more appropriate for
determining design storms for areas experiencing high occurrence of convective
events. It is found that, a threshold value of 35 mm/hr could be used in developing
IDF of Peak Over Threshold (POT) series.
vi
ABSTRAK
Ribut perolakan boleh menyebabkan pelbagai kejadian banjir kilat di
Malaysia. Masalah banjir diburukkan lagi dengan proses perbandaran yang pantas
dan telah mengubah proses hidrologi bagi suatu kawasan tadahan.
Kajian ini
bertujuan untuk menilai ciri-ciri ribut perolakan di Lembah Klang. Ciri-ciri tersebut
adalah berdasarkan kepada data sela hujan yang pendek di antara tahun 2000 hingga
2004. Peristiwa ribut perolakan telah dianalisis untuk aspek masa dan taburan ruang.
Taburan ruang hujan perolakan yang diperoleh dari data radar meteorologi dan semua
data yang dicerap di permukaan bumi (tolok hujan) telah dibandingkan.
Ribut
perolakan yang paling kerap berlaku dalam bulan perantaraan monsun iaitu kira-kira
44% daripada keseluruhan hujan perolakan. Pelbagai bentuk taburan hujan boleh
diamati. Kebanyakan hujan perolakan berlaku dalam tempoh yang pendek. Ribut
perolakan seterusnya diklasifikasikan kepada perolakan sedikit, perolakan sederhana
dan perolakan kuat dengan menggunakan nilai parameter β. Nilai ambang keamatan
hujan, 35mm/jam digunakan untuk mengasingkan ribut perolakan daripada ribut
bukan perolakan untuk keadaan tempatan. Taburan ruang yang diterbit daripada
radar dan tolok hujan mempamerkan perbezaan yang sangat ketara. Setiap ribut
adalah unik dalam aspek pergerakan titik pusat ribut. Sebilangannya mempunyai
laluan yang panjang sementara yang lain bergerak secara berkitar dalam laluan yang
terhad. Lengkung ‘Areal Reduction Factor’ (ARF) yang diperoleh daripada kajian
ini boleh dibanding dengan nilai ARF yang diperoleh daripada pengkaji terdahulu.
Lengkung Keamatan-Tempoh-Frekuensi (IDF) baru telah diplot berdasarkan ribut
perolakan sahaja. Bagi tempoh dan kala kembali diberi, lengkung IDF yang baru
berupaya menghasilkan keamatan ribut yang lebih tinggi berbanding lengkung IDF
sedia ada. Didapati, nilai ambang 35 mm/hr boleh diguna dalam membina IDF dari
siri ‘Peak Over Threshold’ (POT).
vii
TABLE OF CONTENTS
CHAPTER
I
II
TITLE
PAGE
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xi
LIST OF FIGURES
xiii
LIST OF SYMBOLS AND ABBREVIATIONS
xvi
LIST OF APPENDICES
xvii
INTRODUCTION
1.1
Research Background
1
1.2
Problem Statement
2
1.3
Objectives
2
1.4
Scope of Study
2
1.5
Significance of Study
3
LITERATURE REVIEW
2.1
Introduction
5
2.2
Type of Rain
6
viii
2.3
2.4
2.5
2.6
2.7
2.8
III
2.2.1 Forntal Activity
6
2.2.2 Convection
6
2.2.3 Orographic Effect
9
2.2.4 Tropical Activity
9
Measurement of Rainfall
10
2.3.1 Raingauge
10
2.3.2 Radar Measurement of Rainfall
10
2.3.3 Satellite Estimates of Rainfall
11
Convective Rain
12
2.4.1 Identification of Convective Rain
12
2.4.1.1 Rainfall Intensity
12
2.4.1.2 Rainfall Duration
13
2.4.1.3 Analyses of Convective Rain
13
Probability of Flash Flood due to Convective
Storm
16
Spatial Interpolation
17
2.6.1 Inverse Distance Weighted
18
2.6.2 Kriging Method
19
2.6.3 Spline Method
21
2.6.4 Spatial Distribution of Rainfall
22
Rainfall Intensity-Duration-Frequency (IDF)
Relationship
23
Conclusion
27
METHODOLOGY
3.1
Introduction
28
3.2
Research Design and Procedure
28
3.3
Study Area
29
3.4
Terminal Doppler Radar
31
3.5
Data Source and Collection
35
3.6
Data Analysis
35
3.6.1 Separation of Rainfall Events
35
ix
3.6.2 Analysis of Convective Rain
37
3.6.2.1 Temporal
37
3.6.2.2 Spatial Distribution
38
3.6.2.3 Procedure To Derive Rainfall
Contour from Radar and
Raingauge Data Using GIS
41
3.6.2.4 Storm Movements and
Depth Area Relationship
43
3.6.3 Intensity-Duration-Frequency (IDF)
Relationship
3.7
IV
44
3.6.3.1 L-Moments and Their Estimators
45
3.6.3.2 Generalized Pareto Distribution (GPA)
47
3.6.3.3 One-step Least square Method
49
Limitations
49
RESULTS AND DISCUSSION
4.1
Introduction
50
4.2
Diurnal and Monthly Distribution
50
4.3
Minimum Interevent Time (MIT)
51
4.4
Characterization of Convective Rain
4.5
Based on Short Duration Rainfall
52
4.4.1 Preliminary Analysis
52
4.4.2 Characterization of 5-minute Rainfall
53
4.4.3 Classification of Convective Events
57
Spatial Distribution
59
4.5.1 Digitized Radar Image
59
4.5.2 Comparison on Intensity
60
4.5.3 Comparison of Area Rainfall between
Radar and Surface Rainfall
4.6
71
4.5.4 Storm Movement
74
4.5.5 Depth-Area Relationship
78
IDF Relationship
83
x
V
CONCLUSION AND RECOMMENDATION
5.1
Introduction
87
5.2
Assessment of Objectives
87
5.2.1 Characteristics of Convective Rain
Based on Short Rainfall Duration Data
5.2.2 Classification of Convective Events
88
88
5.2.3 Comparison of Spatial Distribution
of Convective Rainfall between
Radar and Ground Rainfall
5.3
89
5.2.4 Depth Area Relationship and IDF Curve
89
Research Recommendations
90
REFERENCES
92
APPENDICES
99
xi
LIST OF TABLES
TABLE NO.
3.1
TITLE
PAGE
Main characteristics of KLIA Terminal Doppler radar
used in this study
32
3.2
Sources of data for achieving the various objectives of the study
36
3.3
Times during which the digitized images were captured
by TDR
40
Summary statistics of monthly convective and nonconvective rainfalls between 2000 and 2004 at Ampang
station
54
Frequency of convective storm events during monsoon
and inter-monsoon periods
54
Summary statistics of 5 minutes rainfall between years
2000 and 2004
55
Characteristics of storms with the highest 5-minutes
intensity (I5)
55
Number of convective and non convective events
Between 2000 and 2004
57
Comparison of rainfall intensity (mm/hr) between
surface and radar rainfalls on January 6, 2006
62
Comparison of rainfall intensity (mm/hr) between
surface and radar rainfalls on February 26, 2006
63
Comparison of rainfall intensity (mm/hr) between
surface and radar rainfalls on April 6, 2006
64
Comparison of rainfall intensity (mm/hr) between
surface and radar rainfalls on May 10, 2006
65
Areal distribution of storm intensity obtained from radar
and raingauge
73
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
xii
4.11
Correlation of areal distribution of storm intensity
between radar and raingauge
73
The coordinates and intensity of storm centres on
6.01.2006 and 6.02.2006
76
The coordinates and intensity of storm centres on
6.04.2006 and 10.05.2006
77
4.14
Areal reduction factors (ARF) values for each event
81
4.15
Summary of the design rainfall intensity for convective
storm at station 3117070 JPS Ampang
84
Summary of the design rainfall intensity for station
3117070 taken from DID (using POT series)
85
Summary of the design rainfall intensity for convective
storms and POT series (DID’s curve) at station 3117070
86
4.12
4.13
4.16
4.17
xiii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
The formation of warm and cold fronts
7
2.2
The formation of convective rainfall
8
2.3
Orographic effects
9
2.4
Schematic diagram of water vapor input and
precipitation output
17
The interpolated value at the unmeasured yellow point
is a function of the neighbouring red points
18
Example of semivariogram depicting range, sill, partial
sill and nugget
20
2.7
Rainfall contours derived from inverse distance weighted
23
2.8
Rainfall contours derived from Kriging
24
2.9
Radar derived rainfall contours
24
3.1
Flow chart of research design and procedure
30
3.2
The study area in Klang Valley
31
3.3
Terminal Doppler Radar at KLIA
32
3.4
Radar image
34
3.5
Various level of reflectivity colour derived from radar
image (a) and simplified rainfall intensity colour after
digitization
34
Separation of rainfall events based on minimum
interevent time (MIT)
37
Example of radar image in JPEG format
39
2.5
2.6
3.6
3.7
xiv
3.8
The locations of twenty rain gauge stations selected
in this study
40
3.9
Flow chart of plotting rainfall contours derived from radar
42
3.10
Flow chart of plotting rainfall contours derived from
ground data
43
3.11
Flow chart to produce IDF relationships
46
4.1
Diurnal and monthly distributions of rainfall (greater than
5 mm) in 2004 at station JPS Ampang
51
4.2
Annual number of rainfall events as a function of MIT
52
4.3
Convective storms with the highest 5 –minutes intensity
for each year
56
Percentage of occurrence of convective and non-convective
storms in 2004 at station JPS Ampang
58
4.5
Monthly number of event for each class of convective storm
58
4.6
Yearly percentage of occurrence of convective storm
59
4.7
Digitized image using ArcGIS 9.1
60
4.8
Comparison of spatial rainfall distributions derived from
raingauge and radar for event on January 6, 2006
67
4.9
Legends
67
4.10
Comparison of spatial rainfall distributions derived from
raingauge and radar for event on February 26, 2006
68
Comparison of patial rainfall distributions derived from
raingauge and radar for event on April 6, 2006
69
Comparison of spatial rainfall distributions derived from
raingauge and radar for event on May 10, 2006
70
Comparison of areal distribution of intensity between
surface rainfall and radar
73
4.14
Storm movement on January 6, 2006
75
4.15
Storm movement on February 26, 2006
76
4.16
Storm movement on April 6, 2006
77
4.4
4.11
4.12
4.13
xv
4.17
Storm movement on May 10, 2006
78
4.18
Spatial variation of rainfall depth (mm) for six selected
storms
79
4.19
Depth-area relationships for six selected storms
82
4.20
Comparison of depth-area curves obtained in this study
and at other location
82
The new IDF curve for station 3117070- JPS Ampang
developed from convective storm data
84
DID’s curve for station 3117070
85
4.21
4.22
xvi
LIST OF SYMBOLS AND ABBREVIATIONS
β
-
Beta parameter for classifying convective rain
ΔT
-
Time interval of accumulation of the precipitation
L
-
Intensity threshold
N
-
total number of ΔT
dBZ
-
decibels of z
z
-
Reflectivity factor
ARF
-
Areal Reduction Factor
IDF
-
Intensity Duration frequency
POT
-
Peak Over Threshold
XT
-
Quantile value
IDF
-
Intensity Frequency Duration
TDR
-
Terminal Doppler Radar
KLIA
-
Kuala Lumpur International Airport
xvii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Process of digitizing radar image
B
Steps to derive rainfall contours by Kriging
Method using Geostatistical Analyst
105
C
Steps for developing areal reduction curve
109
D
Steps to summarize diurnal and monthly
E
99
distribution of rainfall
124
Steps to develop IDF relationship
139
CHAPTER 1
INTRODUCTION
1.1
Research Background
A detailed understanding of rainfall processes is a key requirement for
efficient solutions of many water related problems in urban areas. The heterogeneity
of rainfall means that a systematic study is necessary, especially in the tropical
region where abundant rainfall often causes severe urban flash floods. Such data is
crucial for the derivation of rainfall input for proper designs of drainage network,
particularly in small urban catchments.
In Malaysia, flash flood events occur frequently in urban areas such as the
Klang Valley. These events occur mainly during inter monsoon periods. Damages
and losses caused by flash floods have been mounting. The storms of convective
origin are generally known to be responsible for much of flash flood events in
Malaysia. A convective storm is characterized by a sudden burst of heavy rainfall
over a short period of time. Studies on the origin and physics of convective storms
have been reported worldwide (Doswell et. al., 1996; Dong and Hyung 2000; Llasat,
2001; Pascual et al., 2004). Methods of classifying rainfall into convective and nonconvective events are useful for estimating rainfall amount and improve prediction
capability.
Despite the apparently strong association between convective rain and major
flash flood, the linkages have yet to be sufficiently established. The main reason is
due to the difficulty in getting reliable data of convective rain which is not readily
identified in meteorological records.
2
1.2
Problem Statement
Rapid urbanization, which modified the hydrological processes of a
catchment is responsible for many water related problems in urban areas, especially
in the tropical regions. Urban drainage systems, often cannot cope with intense
convective rainfall events. It is also difficult to forecast convective rain in terms of
timing and spatial distribution. This is because convective rain develops over a short
period and can happen any time, during day or night and can cause much disruption
to the livelihood of the people. Thus far, no specific guideline for characterizing
convective rainfalls have been established in the tropics. For that reason, an in-depth
study on the temporal and spatial characteristics along with the characterization of
local rainfall processes is deemed vital.
1.3
Objectives
The main objectives of this study are as follows:i)
to characterize rain properties based on short rainfall duration data;
ii)
to establish criteria for separating convective from non convective
storms;
iii)
to determine and compare spatial distribution of convective rainfall
between meteorological radar data and observed surface data
(raingauge); and
iv)
to determine the frequency of convective events of different duration
for low return period.
1.4
Scope of Study
The scope of this research includes characterization of convective rain and
comparison of spatial distribution between meteorological radar and observed
surface rainfall.
The study area is Klang Valley.
The convective rain was
3
characterised in terms of intensity, rainfall duration and total rainfall.
In this
analysis, five years rainfall data with 5 minutes interval from JPS Ampang (3117070
station) was used to characterize convective rain.
All data was extracted from
hydrological data bank managed by the Department of Irrigation and Drainage
(DID).
In the next stage, four large storm events were selected to compare the spatial
distribution between radar and surface rainfall data. These events coincided with
major flood events. Radar data for Klang Valley area were taken from Meteorology
Malaysia (MM), KLIA in Sepang. All data were digitized first using Geographical
Information System (GIS) software (ArcGIS 9.1) before comparison is made. For
ground data, 20 raingauge stations in Klang Valley were selected to produce rainfall
contours derived by Kriging Method. Subsequently, by matching data set for the
same location and similar recording time, line rainfall contour from surface rainfall
data (Kriging) were compared with rainfall contour derived from radar image
(digitized image). Finally, a relationship between the observed areal rainfall derived
from Kriging and their rainfall depth was examined.
Storm movements for four selected storms were also illustrated.
The
movements of rainfall pattern were observed. In order to get relationship between
area and rainfall depth, surface rainfall data from eleven raingauge stations were
used. The rainfall depth pattern and the area for every color code of rainfall contours
were presented in six selected storms. Finally, the areal reduction curves for all
storms were plotted.
1.5
Significance of Study
A major reason for the water related problems encountered in urban areas of
Malaysia is the dynamic change of the land use associated with rapid urbanization.
Expectedly, this would modify the hydrological processes involved. Urban drainage
systems, particularly in the tropical region, often suffer from frequent flash floods as
4
a result of intense short convective rainfall events.
For that reason, a deep
understanding of local rainfall processes is necessary.
Knowledge of rainfall characteristics in the humid tropics can contribute
toward better theoretical understanding of rainfall processes. This study strengthen
understanding of convective rainfall characteristics especially for heavy storms. In
addition, relationship between surface rainfall and meteorological radar data through
the true spatial distribution of rainfall is also established. The movement of short
term rainfall storms is crucial especially in an urbanized area. Relationships between
area and rainfall depth through the spatial distribution of rainfall is important for
understanding the areal properties of short term rainfall. It can also helps improve
the design of urban water related systems.
CHAPTER II
LITERATURE REVIEW
2.1
Introduction
Forecasting of convective initiation is important for flood modelling. It has
been widely known that storms of convective origins are responsible for major flash
flood events that have caused significant loss of life, property damages, disruption to
ecological habitats and other socio-economic problems.
Unfortunately, the
behaviour of convective storms especially their spatial distribution and storm
movements are still poorly understood. This study examines the characteristics of
convective rain and their coverage using both surface rainfall data and radar data.
A convective storm is formed when warm moist air mass is trapped beneath
cold air, with a layer of warmer air in between, which act as a lid. Eventually the
warm air breaks through the lid. It rises like a hot air balloon through a deep layer of
cold air above, and as water vapour condenses and freezes, the air gains latent heat.
The lid varies in strength in space and time and there may be multiple lids (Keith,
Alan and Peter, 2004).
This chapter reviews the characteristics and analysis of convective rain with
special highlights on the application of radar data in tracking the development of
convective storm. The probability of flood occurrence due to convective storm is
also discussed. Finally this chapter assesses various methods for spatial interpolation
of radar and ground data.
6
2.2
Types of Rain
There are four major types of rain, namely frontal activity, convection,
orographic effects and tropical activity.
Each rainfall type has quite different
characteristics.
2.2.1
Frontal Activity
Frontal activity usually occurs from stratiform clouds as a consequence of
slow ascent of air in large systems, such as along cold fronts, and in the advance of
warm fronts in stable atmosphere. Cold fronts are defined as the leading edge of a
cooler and drier mass of air whilst warm fronts are the leading edge of a mass of
warm air (Wikipedia, 2008). Both processes are attributed to the forced lifting of air
which cause low level convergence (coming closer) and upper level divergence
(moving away in different directions). As unsaturated air rises, the relative humidity
of the air is increased. When the air saturates, continued lifting will produce clouds
and eventually precipitation (Haby, 2003). Stratiform precipitation is also known as
dynamic precipitation.
It tends to have a less intense rain than convective
precipitation and also tends to last longer. Figure 2.1 shows the formation of warm
and cold fronts that causes stratiform clouds.
2.2.2
Convection
Unlike stratiform precipitation which is formed in a stable atmosphere,
convective precipitation is formed in an unstable atmosphere. Convective rain is a
sudden short outburst of rain that brings heavy rainfall over a short period of time.
Usually, this short outburst of rain is heavier than normal rainfall. This precipitation
occurs from convective clouds e.g., cumulonimbus or cumulus congestus. It falls as
showers or a sudden downpour with rapidly changing intensity. Besides, this rain
7
Figure 2.1 : The formation of warm and cold fronts
falls only over a small area at a time, as convective clouds have limited horizontal
extent (WikiAnswers, 2007). Convective precipitation is the most important in the
tropics especially in midlatitudes due to active convection process. Convection is the
vertical transport of heat and moisture in the atmosphere, especially by updrafts and
downdrafts in an unstable atmosphere. The atmosphere is classified as unstable
when the temperature of displaced surface air is warmer than its surrounding air.
This difference in temperature causes the displaced air to rise up into the atmosphere
until the air mass is cooler than its surrounding air. At this time, the air begins to fall
back towards its original location. This happens because warm air has a smaller
density than cold air at equal pressure (PennState, 2001). Figure 2.2 shows the
process of convective rainfall.
8
(a) warm air rises
(b) Air from surrounding regions move in to replace the warm air as it moves up. The air that
moves in to take the place of the rising air has to come from the north or the south
because the air to east and west is also hot and rising.
(c) As the warm air rises it expands and cools. Since cool air cannot hold as much moisture,
this often results in rainfall. The cooled air is then drawn back towards the poles,
dropping towards the earth to replace the air moving along the surface near the equator.
This cycle of air movement is called convention and causes convective rainfall.
Figure 2.2 : The formation of convective rainfall (After Hogue, 2007)
9
2.2.3
Orographic Effect
Orographic effect is also a form of precipitation which occurs when wind
blows towards mountains. The rising air motion of a large-scale flow of moist air
across the mountain ridge will undergo adiabatic cooling and condensation
(WikiAnswers, 2007).
Figure 2.3 shows the occurrence of orographic effects.
Orographic precipitation is common on oceanic islands which produce more rain on
the windward side and is usually much drier on the leeward side.
Figure 2.3 : Orographic effects
2.2.4
Tropical Activity
Tropical rainfall involves large air masses of several hundred miles across
with low pressure at the centre of the earth. At this moment, wind blows around the
centre in either a clockwise direction (Southern hemisphere) or anticlockwise
(Northern hemisphere). Tropical rainfall occurs when a warm front is formed by
moving on mass of warm air. As the warm air is lifted up, it becomes cool and form
rainfall (Manning et al., 1996).
10
2.3
Measurement of Rainfall
A variety of instruments and techniques have been developed to get
information on rainfall intensity and the amount. All forms of rainfall are measured
based on the vertical depth of water over a level surface (Linsey et al., 1988).
2.3.1
Raingauge
Raingauge is the most commonly used instrument for measuring liquid
rainfall.
The major types of raingauges include graduated cylinders, weighing
raingauges and tipping bucket raingauges.
Each type has its advantages and
disadvantages during collecting rainfall data. Raingauge have their limitations and
only show rainfall in the area where the raingauge is located.
2.3.2
Radar Measurement of Rainfall
Radar transmits a pulse of electromagnetic energy as a beam in a direction
determined by a movable antenna. Energy that is returned to the radar is called
target signal and the amount is termed returned power. When it is displayed on the
radarscope, it is known as echo.
The brightness of an echo or echo intensity
indicates the magnitude of returned power. The magnitude is measured in radar
reflectivity. The reflectivity depends on (1) drop-size distribution, (2) number of
particles per unit volume, (3) physical state, i.e. solid or liquid, (4) shape of the
individual elements, and (5) if asymmetrical, their aspect with respect of the radar.
Generally speaking, a more intense precipitation has a greater reflectivity and wise
versa.
Many studies had described the relationships between raindrop-size
distribution and rainfall intensity. The radar measurement of precipitation is based
on empirical relationships between ∑d6 (d is the diameter of the individual
11
precipitation particles), usually represented by Z, and rainfall rate R in the following
form
Z = aRb
Equation 2.1
where values of a and b can be obtained by direct measurement of raindrop-size
distribution or comparison of radar and raingauge measurements (Linsey et al.,
1988).
Discrepancies in the Z-R relationship arise because a radar measures rainfall
in the atmosphere while gauges measure rainfall at the ground. The magnitude of the
discrepancy varies with the angle of the beam elevation, beam’s width and range.
Another factor that contributes to error is evaporation of rainfall, before it reach the
ground, especially when the raindrop pass through dry air masses before striking the
earth surface. Beside, winds may blow rain-drops away from their original location
at the time when the radar recorded the cloud.
2.3.3
Satellite Estimates of Rainfall
Satellites cannot measure rainfall directly.
Instead a rainfall estimate is
measured based on the relationship between brightness of cloud photographs and
rainfall intensities. The degree of brightness increases with the height of the cloud
top. The tallest and the highest density of clouds produce the heaviest intensity. The
relationship between brightness and rainfall intensity can be determined by
calibrating with gauge measurements (Oliver and Scofield, 1976) and radar estimates
(Follansbee, 1973; Griffith et al., 1978).
A major problem in estimating rainfall from satellite is that the images
photographs often do not reveal precipitation-producing clouds. This is because of
overlaying cloud layers (Linsey et al., 1988). However, future developments in
instrumentation and techniques would be able to improve estimate of rainfall from
satellite images.
12
2.4
Convective Rain
A summary of important studies of convective rain is provided in the
following sections. The summary focuses on the convective rainfall characteristics
such as intensity, rainfall duration and analysis of convective rain in terms of areal
rainfall, size and shape, and storm movements.
2.4.1
Identification of Convective Rain
2.4.1.1 Rainfall Intensity
The intensity of rainfall is dependent on the rate at which a storm processes
the water vapor. In this case, a distinction could be made between precipitation of
convective origin and stratiform precipitation. Many researchers used intensity as a
method to differentiate between convective and stratiform rainfall.
Dutton and
Dougherty (1979) and Watson et al., (1982) set a threshold rainfall of 50 mm/hr to
separate convective from non-convective storms.
Llasat and Puigcerver (1997)
divided rainfall events into four categories: (1) non-convective (2) convective with
rain ≤ 0.8 mm/min (3) convective with rain ≥ 0.8 mm/min; and (4) thunderstorms.
Llasat (2001) used 35 mm/hr as a threshold intensity and a parameter β for the
characterization of convective rain.
Nevertheless, Houze (1993) distinguished stratiform from convective
precipitation on the basis of vertical air velocity, w. If w is less than the terminal fall
velocity of ice crystals and snow, it is a stratiform storm. Nowadays, radar can
differentiate these two types of rainfall. Using 4-D radar imagery, the ‘bright band’
near the melting level is a signature that helps to distinguish convective mode from
stratiform mode (Llasat, 2001). Steiner et al. (1995) proposed two methods for
distinguishing stratiform from convective precipitations in radar echo patterns.
Radar used reflectivity to measure the intensity of rain which is usually expressed in
dBZ.
Dong and Hyung (2000) used 35 dBZ to determine convective rainfall.
Pascual et al. (2004) in Spain used four reflectivity thresholds, i.e. 30 dBZ, 35 dBZ,
13
40 dBZ and 45 dBZ in identifying convective cells origin. On the other hand, Rigo
and Llasat (2002) used 43 dBZ to analyse convective event which is derived from
meteorological radar.
2.4.1.2 Rainfall Duration
As already mentioned, convective rain is a sudden short outburst of rain that
brings heavy rainfall in a short period of time. In the tropics, high intensity storms
tend to have short duration whereas low intensity storms have longer durations.
Brooks et al. (1992) noted that convective cell typically has a lifetime of about 20
minutes. It follows then that any convective storm lasting more than about 20
minutes constitutes of more than one cell. A convection cell is a phenomenon of
fluid dynamics which occurs in situations where there are temperature differences
within a body of liquid or gas (Wikipedia, 2007).
Ronal and Andrew (1981) studied about duration of convective events related
to visible cloud, convergence, radar and rain gage parameters in South Florida. The
highly variable response could be understood better by taking into account the time
span of the cloud, which is defined as the time from first surface convergence until
its complete dissipation.
2.4.1.3 Analysis of Convective Rain
Despite great improvements over recent years on general weather forecasting
techniques, the ability to forecast the occurrence of convective rains is still poor.
Predicting where a storm will break out or start abruptly is still one of the major
challenges faced by meteorologists today. This situation motivates many researchers
to study convective rain.
14
Llasat and Puigcerver (1997) studied the relationship between total rainfall
and convective rainfall in north-east Spain.
Events were classified into four
categories: non-convective, convective with low rainfall rates, convective with
moderate to high rates and thunderstorm events. Convective rains made up between
70 and 80% of the total rainfall but reduce to less than 30% in winter. Llasat (2001)
characterized convective rain for developing intensity-duration-frequency curves and
design hyetographs. She defined a parameter related to greater or lesser convective
character of the precipitation, β.
Intensity value of 35 mm/hr was taken as a
threshold intensity and β parameter was classified into four categories; nonconvective, slightly convective, moderately convective and strongly convective.
Rigo and Llasat (2002) then compared convective structures between meteorological
radar data and surface rainfall data. Recently, Llasat and Barnolas (2007) used
geodatabase and its climatological applications to study convective rain in Spain. In
their study, convective rain was divided into three types based on their duration and
intensity, i.e. (1) very convective rainfall events: episodes of very short duration (less
than 6 h) but very high rainfall intensity, (2) very convective and moderate rainfall
events: episodes of short duration (between 6 and 72 h) with heavy rain sustained for
several hours, and (3) episodes of long duration (approximately 1 week) with weak
raingauge intensity values. It was found that fall season floods are mainly associated
with convective episodes with heavy rain sustained for several hours. The inland
region is mainly affected by episodes of types 2 and 3, whereas episodes of type 1
were mainly detected in urban area and responsible for most flood events.
There are increasing interests in using meteorological radar to detect
convective areas and perform related analyses. Using radar data, Johnson et al.
(1998) applied an algorithm, to identify convective cells as a region of maximum
reflectivity in 3D. Another algorithm was proposed by Steiner et al. (1995) for
detecting convective structures at the lowest 2D level. Both algorithms classify
pixels from radar image as rainfall or non-rainfall, and subsequently identify rainfalls
which satisfy criteria as being ‘convective’ or ‘stratiform’. These two algorithms
were also applied by Rigo and Llasat (2002) to improve the tracking and nowcasting
of convective structures in Catalonia, Spain, using both radar and surface data. They
used a 35 mm/hr threshold intensity for separating convective from stratiform
storms. In addition, a reflectivity threshold of 43dBZ was chosen as a first
15
identification of convective rainfall. A comparison of the daily β parameter for
raingauges and radar charts allows identification of areas that are most prone to
convective precipitation for different seasons.
Studies of convective rain using meteorological radar were also carried out by
Pascual et al., (2002) and Callado et al., (2002).
They analyzed the origin of
convection identified in radar data with low levels convergence zones.
Later,
Pascual et al., (2004) studied convective activities during summer and relate it with
convergence areas associated with terrain characteristics and the interaction between
different flows at low levels. They used 15 C-band Doppler radar. The results were
presented in term of relative frequency of radar reflectivity echo values. Higher
relative frequencies for all thresholds (30 dBZ, 35 dBZ, 40 dBZ and 45 dBZ) appear
in mountainous terrain and most of the frequencies were detected between 12:00 and
18:00 hours.
The diurnal cycles of convective activity are not always the same and depend
on the location and weather. If the location is near the sea, the convective activity
may due to wind and water vapour from the sea. The duration can also vary with
location. Hara et al. (2006) conducted a cloud-resolved simulation using regional
climate model to clarify the mechanism of diurnal cycle of convective activity
around Borneo Island. The convective activities on top of mountain tend to decay in
the evening. The diurnal cycle of convective activity in Borneo Island is maintained
by sea breeze and upslope wind and it depends on the distance from the coast to the
centre of mountain.
Dong and Hyung (2000) studied heavy rainfall with Mesoscale Convective
Systems (MCSs) over the Korean Peninsula using WSR-88D radar data. MCSs are
complex thunderstorms which become organized on a scale larger than individual
thunderstorms, and normally persist for several hours. The evolution and movement
of convective storms which result in heavy rainfall were investigated. They found
that heavy rainfalls are formed by well-organized multi-cell type convective storms
in MCSs. The storms started abruptly near the sea and land, and then merged into
large convective storm within less than 2 hours. The movement of the convective
16
storms was investigated by tracking the edges of the storms. It is found that the
storm boundaries changed into a very complex shape.
2.5
Probability of Flash Flood due to Convective Storm
Convective storms are constantly related to flash floods because they process
and precipitate large amounts of water vapor in a short period. In Oklahoma, Charles
(1993) noted that precipitation rate of about 25 mmhr-1 is not sufficient to cause flash
floods. Rainfall intensities greater than 25 mmhr-1 are likely to be associated with
convective storms. Charles also highlighted the concept of precipitation efficiency
which is defined as the ratio of the water vapour absorbed into the storm to the water
dropped as rainfall. This ratio is not meaningfully evaluated in an instantaneous
value. At the on-set of a convective storm, no raindrop has reached the ground, so
the ratio is zero, but at the end of the storm, rain continue to fall after the updraft has
dissipated. Figure 2.4 shows a schematic diagram of precipitation efficiency. This
quantity only makes sense as a time integral over the lifetime of the convective
system (Fankhauser, 1988).
In Spain, Llasat and Barnolas (2007) classified flash flood into three types
based on the convective character of the rainfall events.
Type 1 is for very
convective rainfall events, very short duration (less than 6 h) but with very high
intensity. The resultant floods are usually ordinary or extraordinary, following the
classification developed by Llasat et al., (2005). Type 2 is very convective and
moderate rainfall events of short duration (between 6 and 72 h) with heavy rain (200500 mm) sustained for several hours. Type 3 is for long duration (approximately 1
week) storms but with weak intensity and possible peaks of high intensity. The
accumulated rainfall can be over 200 mm and contribute to ordinary or extraordinary
floods.
From the literatures, it can be concluded that heavy rainfalls that produce
flash floods are the result of high rainfall rates.
The high rainfall rates are
contributed by high water vapour mass flow through convection, coupled with high
17
precipitation efficiency. Convective events are often associated with flash flood
especially in developed and highly populated areas. Such information is useful in
minimising risk of flash flood
Figure 2.4: Schematic diagram showing the time history (in arbitrary time units) of
water vapor input and precipitation output (hatching) for a convective
storm system. The ratio of the areas under the two curves is the
precipitation efficiency (after Charles, 1993)
2.6
Spatial Interpolation
A very basic problem in spatial analysis is interpolating a spatially continuous
variable from point samples. In hydrology, rainfall is always measured as point
measurement by raingauges. Nevertheless, engineers are interested to estimate the
total rainfall in a watershed. One of the most common issues in the interpolation
18
process is how to assign weightage to the individual rain measurements to obtain the
best estimate of rainfall at an unmeasured location. Figure 2.5 shows the basic
interpolation process in some area.
Figure 2.5 : The interpolated value at the unmeasured yellow point (circle) is a
function of the neighbouring red points (From ArcGIS Help Menu)
There are a number of techniques for interpolation such as the Thiessen
Polygon, Polynomial Regression, Kriging, Inverse Distance Weighted (IDW) and
Spline Method (Keckler, 1995; Curtis, 1999). Three of these techniques namely the
Inverse Distance Weighted (IDW), Kriging and Spline Method will be discussed
here.
2.6.1
Inverse Distance Weighted (IDW)
One of the most commonly used techniques for interpolating scattered points
is inverse distance weighted (IDW) interpolation. This method is based on the
assumption that the surface which want to be interpolated should be influenced most
by the nearest point and the least by the most distant points (Curtis, 1999). The
interpolating surface is a weighted average of the scattered points. The weightage
assigned to each point decreases as the distance from the interpolation point to the
scattered point increases.
IDW allows a number of neighboring stations to be
19
included in the estimation of interpolated value. Generally speaking, the closer the
station, the higher the weightage. The equation of IDW is:
n
∑
Rj =
1
2
d
1
∑
d
i =1
ri
ij
Equation 2.2
n
i =1
2
ij
where,
2.6.2
Rj
=
rainfall estimate for the jth grid point;
ri
=
observation at gauge i;
dij
=
distance from gauge i to the jth grid point; and
n
=
the number of gauges.
Kriging Method
Interpolation by Kriging is a geostatistical method based on statistical models
that predict spatial correlation of sampled data points (Dille et al., 2002). Kriging
was developed in 1960s by a French mathematician, Georges Matheron. Originally,
it was proposed by Krige, a South African mining geologist, who is the first to
introduce the use of moving averages to avoid overestimation of gold reserves. After
that, it become similar with the variety of geological statistics (Matheron, 1963).
Today, Kriging finds its way in the earth science and other disciplines. In spatial
interpolation, it is an improvement from IDW method because prediction estimates
tend to be less bias and predictions are accompanied by prediction standard errors
(quantification of the uncertainty in the predicted values) (Jon and David, 2002).
The objective of Kriging is to estimate values of a field (or linear functions of
the field) at a point (or points) from a limited set of observed values (Bras and
Rodriguez-Iturbe, 1985).
Spatial correlation is a statistical relationship among
measured points in one data set. Kriging can also provide some measure of certainty
or accuracy of the prediction models based on correlation. Kriging models use
semivariogram or covariance to depict the spatial correlation between measured
20
sample points and to make optimum predictions.
The model assumes that
measurements that are geographically close together are more similar than ones that
are farther apart (Donald, 1994).
Semivariograms are described by the parameters of range, sill, and nugget.
These elements are needed to interpolate data with the Kriging method (Figure 2.6).
A range is the distance from a measurement (known sample) point to the point where
the semivariance stops increasing with distance from the sample point. Sill is known
as the value at which the semivariogram model attains the range. This means that the
change in semivariance is no longer increasing with increasing distance from the
sample point. The nugget is created by measurement errors or spatial sources of
variation at distances smaller than the sampling interval. Nugget is also recognized
as the value of semivariance when the distance from the sample point equals zero
(Main et al., 2004). Another element needed for Kriging interpolation is partial sill
which is the sill minus the nugget. Figure 2.6 shows an example of semivariogram.
Figure 2.6 : Example of semivariogram depicting range, sill, partial sill and nugget
(after Main et al., 2004)
As noted earlier, Kriging model uses semivariogram or covariance to depict
spatial correlation.
Estimation of covariance is similar to the estimation of
semivariogram but the covariance requires mean data. However, the mean is usually
determined by an estimation which introduce some bias. This situation compelled
most geostatistical softwares to use semivariogram as a default function tool to
21
characterize spatial data structure (Konstantin, 2006). The empirical semivariogram
and empirical covariance are given in equations 2.3 and 2.4, respectively.
Semivariogram (distance,h) =
½ average [(value at location i – value at location j)2]
Equation 2.3
Covariance (distance, h) =
average [(value at location i – mean)*(value at location j – mean)]
Equation 2.4
where, for all pairs of locations i and j are separated by distance h
Kriging is considered the best predictor of non-sampled locations because its mean
residual error is minimized (Isaaks and Srivastava, 1989). The main principle in
Kriging interpolation is similar to IDW where it uses the surrounding data points to
predict an unknown value for an unmeasured location. However, the difference with
Kriging is that the predicted point depends on a fitted model to the measured points,
the distance from the unknown point to measured points, and the spatial relationship
among the measured points around the predicted point.
In this study, Kriging
Method is chosen to show the spatial distribution of rainfall derived from surface
rainfall data.
2.6.3
Spline Method
Another method in spatial interpolation is thin plate spline (TPS) which was
initially introduced to geometric design by Duchon (1976). The name thin plate
spline refers to a physical analogy that involved the bending of a thin sheet of metal
(Wahba, 1990).
This method needs the estimation of smoothing parameter to
determine an optimal balance between reliability to the data and smoothness of the
fitted spline function. The thin plate smoothing spline is easier to use because it can
be computed automatically by minimizing the GCV (Generalized Cross Validation).
22
The process of minimizing is called "bending energy" which is defined here as the
integral over R2 of the squares of the second derivatives (Wahba, 1990);
[ f (x, y )] = ∫∫ ( f 2 xx + 2 f 2 xy + f 2 yy )dxdy
Equation 2.5
R2
where,
2.6.4
f ( x, y )
=
energy function
{xi } and {yi }
=
point-sets
R2
=
2 dimensional vector space over the field of real numbers
Spatial Distributions of Rainfall
Comparison of spatial distribution of rainfall derived by the raingauge
methods discussed above has been studied by many researchers (eg: Matheron, 1963;
Duchon, 1976; Bras and Rodriguez-Iturbe, 1985; Isaaks and Srivastava, 1989;
Wahba, 1990; Curtis, 1999; Keckler, 1995; Jon and David, 2002 and Main et al.,
2004). One of them is Curtis (1999), studied spatial distribution of rainfall derived
from raingauges and radar in Florida. The results shown in Figures 2.7 are derived
using IDW and in Figure 2.8 derived using Kriging. Both methods show rainfall
features that are smoothly circular.
Radar-derived contours however are very
detailed (Figure 2.9), indicating a far more complex storm structure. In addition, the
maximum storm amounts obtained from radar is also much higher compared the
amount derived from the contours via the IDW and Kriging methods.
This is
because with resolutions on rectilinear grids down to 2-km x 2-km, radar can
determine characteristics of surface rainfall in much more detail. Raingauge network
densities on the other hand are rarely better than 1 gage per 26 km2 and 1 gage per
259 km2 (Curtis, 1999). Thus, the radar can provide accurate estimate of actual
rainfall over a watershed.
23
2.7
Rainfall Intensity-Duration-Frequency (IDF) Relationship
The rainfall intensity-duration-frequency (IDF) relationship is one of the tools
commonly used in water resources engineering. Basically, it is used for planning,
designing and operating of water resource projects or protection of various
engineering structures (e.g. highways, drainage system, etc) against floods. The
Figure 2.7 : Rainfall contours derived from inverse distance weighted in Florida
(values are raingauge measurements in inches) (after Curtis, 1999)
24
Figure 2.8 : Rainfall contours derived from Kriging (values are raingauge
measurements in inches) (after Curtis, 1999)
Figure 2.9 : Radar derived rainfall contours (values are raingauge measurements in
inches) (after Curtis, 1999)
25
establishment of such relationships was firstly proposed in the thirty’s (Bernard,
1932). Since then, many sets of relationship have been developed in several parts
of the world. IDF formula is an empirical equation representing a relationship
among maximum rainfall intensity (as dependant variable) and other parameters of
interest such as rainfall duration and frequency (as independent variables). An IDF
curve contained the following information: I(d), the average rainfall intensities in a
generic interval of duration d, Imax (d), the annual maximum of I(d), and imax (d,T),
the value exceeded by Imax(d) on average every T years. The IDF curves are plots
of imax against d for different values of T (Daniele et al., 2007).
There are several commonly used functions found in the literature of
hydrologic applications (Chow et al., 1988). Four basic equations used to describe
the rainfall intensity duration relationship are:
Talbot equation:
i=
a
b+d
Equation 2.6
Bernard equation:
i=
a
de
Equation 2.7
Kimijima equation:
i=
a
d +b
e
Equation 2.8
Sherman equation:
i=
a
( d + b) e
Equation 2.9
where i is the rainfall intensity (mm/hour); d is the duration (minutes), whilst a, b and
e are the constant parameters related to the meteorological conditions. All of these
empirical equations show that rainfall intensity decreases with rainfall duration for a
given return period.
Rainfall intensity-duration-frequency (IDF) relationship is normally required
for designing water resource projects. Hershfield (1961) developed many rainfall
contour maps to provide design rain depths for various return periods and durations.
26
Bell (1969) proposed a generalized IDF formula using one hour, 10 years rainfall
depths; P110 (Pik, i refers to rain aggregation and k is the return period) as an index.
Chen (1983) further developed a generalized IDF formula for any location in the
United States using three base rainfall depths: P110, P2410, P1100, which describe the
geographical variation of rainfall.
Kouthyari and Garde (1992) presented a
relationship between rainfall intensity and P242 for India.
Recently, some other approaches which are mathematically more consistent
have been proposed. Koutsoyiannis et al., (1998) noted that IDF relationship is a
mathematical relationship between the rainfall intensity i, the duration d, and the
return period T. They proposed two methods for a reliable parameter estimation of
IDF relationships. The proposed formulation of IDF relationships constitutes an
efficient parameterisation, facilitating the description of the geographical variability
and regionalisation of IDF curves. In addition, the method allow integrating data
from non-recording station. Therefore, it solve the problem of establishing IDF
curves in places with a sparse network of rain-recording stations, by using data of the
denser network of non-recording stations. The equation of generalized IDF
relationship that they used is,
i=
λT κ
( d + θ )η
Equation 2.10
where,
λ, κ, θ and η =
parameters to be estimated (non-negative), (θ > 0, 0 <
η < 1)
d
=
duration
T
=
return period
This is a simplified version of the equation derived by Bernard (1932).
According to Koutsoyiannis (1998), studies had been done on estimating
maximum expected short-duration rainfall intensities from extreme convective
storms. The study found that the 3-parameter function together with the Talbot
function provide satisfactory goodness-of-fit, although in most cases underestimation
of maximum rainfall intensities for very short durations is observed.
27
Desa et al., (2006) developed low return period regional IDF relationship
using Generalized Pareto (GPA) distribution in an urban catchment, in Klang Valley.
The 2P-GPA distribution using Partial Duration data series was used with the IDF
formulation by Koutsoyiannis (1998).
2.8
Conclusion
The characteristics of convective rain and the process of convection that
causes convective rainfall have been discussed in detailed.
Methods for analysing spatial rainfall were compared.
However, these
comparisons concentrate only on the pattern of rainfall contours and the highest
amount of rainfall.
Other important characteristics such as area between the
simulated isohyetal line, intensity, storm movements and depth-area relationships
have yet to be explored.
Finally, IDF relationship has been the main input of engineering decisions on
hydraulic designs. However, more rigorous mathematical equations have been used
to produce these relationships. In recent studies, no matter how they produce the
IDF curves, all of the IDF relationships are very useful especially in planning,
designing and operating of water resource projects.
In the following chapter, the methodologies used in this study are described
and the sources of data are presented.
CHAPTER III
METHODOLOGY
3.1
Introduction
To analyse and characterize convective rain in the Klang Valley, the temporal
pattern and the spatial distribution between meteorological radar data and surface
rainfall (rain gauge) need to be explored. This chapter presents the methodologies
used in this research with focus on the characterization of rain properties,
establishment of criteria for separating convective from non-convective storms and
checking discrepancies or similarities between meteorological radar data and
observed surface data (rain gauge). The source of data and data limitations are also
described.
3.2
Research Design and Procedure
The first step to analyse the characteristics of convective rain is selection of
an appropriate region. Next is the selection of raingauge stations in the study area.
Rainfall data were obtained from the Department Irrigation and Drainage (DID). To
separate rainfall events, Minimum Interevent Time (MIT) method is used. After that,
the first objective of this study was carried out where it is to characterize convective
rain based on short rainfall duration data. The characterization were analysed in term
of intensity, duration and total rainfall. Next, for the second objective is to establish
criteria for separating convective from non convective storms. In this stage, the
convective events will be classified into slightly convective, moderately convective
29
and strongly convective. For the third objective, the analysis is to compare observed
areal rainfall with those derived from radar. Both data is shown in rainfall contours
where the contours from raingauge is derived from Kriging method whilst rainfall
contours from radar were made by digitizing the image. The comparison was shown in
term of spatial distribution, the movement of rainfall and developed relationships
between rainfall depth and area of rainfall contour. Lastly, the fourth objective is to
determine the frequencies of convective rain through Intensity Duration Frequency
(IDF) curves. The IDF curves were developed in different duration at low return
period. Then, all the results were analysed. The research procedure of this study is
summarised in Figure 3.1.
3.3
Study Area
The study area covers the whole Klang Valley, comprises Kuala Lumpur and
its surroundings and suburbs. Klang Valley is surrounded by hilly areas especially to
the east and northeast and the Port Klang coastline to the west. Based on the most
recent census, the population in the Klang Valley has increased to 7.2 million (World
Gazetteer, 2008), and it has an area of about 3200 Km2 (Norhan and Mazian, 1997).
The climate of the area is tropical with average monthly temperature ranging from
220C to 330C throughout the year and the relative humidity as high as 90%. Being
located in the equatorial zone, the climate is governed by the northeast and southwest
monsoons.
The northeast monsoon usually commences in early November and
ended in March and the southwest monsoon usually starts in the later half of May or
early June and ended in September. These two monsoon seasons are separated by
two relatively short inter-monsoon seasons which usually recorded heavy rainfall.
The annual rainfalls vary between 2,000 mm and 2,500 mm and the mean monthly
rainfall between 133 mm and 259 mm (Desa et al., 2005). Figure 3.2 shows the area
of Klang Valley magnified from the map of Peninsular Malaysia as well as rainfall
station 3117070-JPS Ampang from where data for analysis of convective rain was
obtained.
30
Selection of an appropriate region
Selection of rain gage stations
Determination of Minimum Interevent Time (MIT)
1st objective
To characterize
convective rain
based on short
rainfall duration
data
2nd objective
To establish criteria
for separating
convective from non
convective storms
3rd objective
To compare
observed
areal rainfall with
those derived from
radar
Rain gages
- Intensity
- Duration
- Total rainfall
- slightly convective
-moderately convective
- strongly convective
4th objective
To determine the
frequencies of
convective rain
through IDF curves
Radar
Rainfall contours
derive from radar
Rainfall contours
derive from
kriging method
-
-
to compare and evaluate
the spatial distribution
between rain gages and
radar
to see the movement of
rainfall
to make relationships
between rainfall depth and
area of rainfall contour
Analyse the results
Report writing
Figure 3.1 : Flow chart of research design and procedure
Duration
(min): 5, 15, 30
and 60 min
Return Period,
T (month): 0.5,
1, 2, 3, 6 and
12
31
3117070
Klang Valley
Peninsular Malaysia
Figure 3.2 : The study area in Klang Valley
3.4
Terminal Doppler Radar
The radar images were derived from the Terminal Doppler Weather Radar
(TDR) located at Bukit Tampoi, about 10 km north of KLIA. The station is used for
the detection and warning of wind shear and micro bursts in the vicinity of KLIA.
RADAR stands for Radio Detection and Ranging which is used for detecting the
position, velocity and characteristic of target (bearing, range, and altitude). The
difference between a conventional weather radar and Doppler weather radar is that
the former can only detect the characteristic, size, direction and distance of
precipitations while the latter, in addition to the above parameters can also measure
radial wind speed, wind shear and microburst. Figure 3.3 shows the TDR at KLIA
while Table 3.1 summarizes the principle characteristics of this radar.
32
Figure 3.3 : Terminal Doppler Radar at KLIA
Table 3.1 : Main characteristics of KLIA Terminal Doppler radar used in this study
______________________________________________________________
Radome
- 12 m. diameter
Parabolic Reflector
- 8.5 m. diameter
Wavelength
- 10 cm
Frequency
- 2874.5 MHz
Peak power
- 750 KW
Pulse Width
- 1.0 µs /3.0 µs
Pulse Repetition
- 1000Hz (1.0 µs pulse width)
Frequency
- 300 Hz (3.0 µs pulse width)
Azimuth Resolution
- 0.7º
Range Resolution
- 125m
Doppler Velocity
- 1.0m/s
______________________________________________________________
The colours of radar represent the values of energy reflected toward the radar.
The reflected intensities or echoes are measured in (decibles of z) dBZ. The scale of
dBZ values is also related to the intensity of rainfall. Typically, light rains have dBZ
value of less than 20. The higher the dBZ, the stronger the rain intensity. The
Doppler radar does not determine where rain is located but only areas of returned
energy (National Weather Service, 2006). The “dB” in the dBZ is logarithmic and
has no numerical value, but is used only to express a ratio. The “z” is the ratio of the
33
density of water drops (measured in unit mm6) in each cubic meter (mm6/m3).
Mathematically:
dBZ = 10*log (z/z0)
Equation 3.1
where,
z
=
reflectivity factor
z0
=
1 mm6/m3
When the “z” is large (many drops in a cubic meter), the reflected power is large. A
small “z” means little returned energy. In fact, “z” can be less than 1 mm6/m3 and
since it is in logarithmic form, dBZ values will become negative when the radar is in
clear air mode and indicated by earthtone colours (National Weather Service, 2006).
Figure 3.4 shows a rainfall image from Doppler radar at KLIA. The intensity was
measured in two units. On the left side, the scale is in dBZ and on the right in
mm/hr. In this study, rainfall intensity in mm/hr was used to show the rainfall rate in
digitized image. The Doppler radar image has too many colours for various intensity
scales. As the image is provided in JPEG file, the intensity was determined manually
by ‘eye’ or visual interpolation rather than using special computer program. To
simplify the data analysis, the colour scales were reduced to seven by redigitizing the
radar image. The new intensity scales and the corresponding radar intensity values
are shown in Figure 3.5. These scales were used in determining and constructing
rainfall contours. Note that the range of rainfall intensity is not the same for every
colour. For low intensity, the ranges are small but high for high intensity band. Due
to the wide range of colour representation, it is difficult to differentiate those colours
during digitizing process. To simplify the data analysis, the colour scales were
reduced to seven by redigitizing the radar image
34
Figure 3.4 : Radar image
(a)
(b)
80.0-100.0 mm/hr
dBZ
35.0-80.0 mm/hr
8.0-35.0 mm/hr
3.0-8.0 mm/hr
0.9-3.0 mm/hr
0.5-0.9 mm/hr
0.3-0.5 mm/hr
Figure 3.5 : Various level of reflectivity colour derived from radar image (a) and
simplified rainfall intensity colour after digitization
35
3.5
Source of Data
In order to analyse convective rain of the study area, several different data
sources are used. In the first stage, a five year (2000-2004) rainfall data from the
hydrological data bank of the Department of Irrigation and Drainage (DID) for
station 3117070-JPS Ampang was used. All data from this station were used to
satisfy the first and second objectives. In the second stage, rainfall data from 20
raingauges (9 raingauges in Wilayah Persekutuan and 11 raingauges in Selangor)
were selected to achieve the third objective, which is to determine the spatial
distribution between meteorological radar data and observed surface data
(raingauge). Ground data was obtained from DID while radar data were taken from
the Meteorological Station at KLIA in Sepang. Heavier rainfalls were selected for
this analysis. These events coincided with major flood events on June 10, 2003; Nov
5, 2004; Jan 6 Feb 26, Apr 6, and May 10, 2006. Table 3.2 lists the various data
sources for achieving the study objectives.
3.6
Data Analysis
3.6.1
Separation of Rainfall Events
Rainfall events must be isolated before they can be analysed. The period
without rainfall or interevent time is a typical criterion used to isolate an individual
rainfall event from continuous rainfall. The criterion is also known as minimum
interevent time (MIT) (Figure 3.6). Many researchers used MIT values between 0
and 50 hours to separate rainfall events (e.g. Hydroscience, 1979; Bedient and
Huber, 2002) while Adams et. al., (1986) suggested MIT values between 1 and 6
hours for urban applications. In this study, a rainfall event is defined from the
minimum interevent time (MIT). To determine an appropriate MIT, annual number
of rainfall events were plotted against different MIT values. A value was selected
from the graph at the point after which increases in the MIT do not result in
significant changes in the number of event.
36
Table 3.2 : Sources of data for achieving the various objectives of the study
Method of
Data Description
Year/Date
Sources
data
collection
1st and 2nd Rain
objectives gauge
3117070 – JPS Ampang
2000-2004
WILAYAH PERSEKUTUAN
3116003 – Ibu Pejabat JPS
3116006 – Ldg Edinburgh Site 2
3216001 – Kg. Sg Tua
3217001 – KM 16, Gombak
3217002 – Emp. Genting Klang
3217003 – KM 11, Gombak
3217004 – Kg Kuala Sleh
3317001 – Air Terjun Sg Batu
3317004 – Genting Sempah
Rain
gauges
10th Jun 2003
Irrigation &
SELANGOR
05th Nov 2004
Drainage (DID),
2917001 – JPS Kajang
06th Jan 2006
Malaysia
Hydrological
data bank
3014084 – JPS Klang
3rd objective
Department of
3014091 – UiTM Shah Alam
26th Feb 2006
3018101 – Emp. Semenyih
06th Apr 2006
3115079 – Pt Penyelidikn Sg
10th May 2006
Buloh
3117070 – JPS Ampang
3118102 – SK Kg Lui
3119104 – Jln Genting Peres
3216004 – SMJK Kepong
3315037 – Tmn Bukit Rawang
3315038 – Country Home
Malaysian
Meteorological
Radar
The whole Klang Valley
Department
Radar data
(MMD), KLIA,
Sepang
th
4 objective
Rain
gauge
3117070 – JPS Ampang
2000-2004
Department of
Durations: 5,
Irrigation &
15, 30 & 60
Drainage (DID),
minutes
Malaysia
37
Since the lag time, td
between event i and
event j is greater than
the MIT, the rainfalls
belong to different
storm events
MIT
td < MIT thus the two
storms belong to the
same event
td
td
MIT
Figure 3.6 : Separation of rainfall events based on minimum interevent time (MIT)
3.6.2
Analysis of Convective Rain
3.6.2.1 Temporal
One of the aims of this study is to characterize convective rain in the Klang
Valley. Initially rainfall data was analysed in terms of intensity, rainfall duration and
total rainfall. Short interval rainfall data recorded between years 2000 and 2004
were used. In year 2000, DID had installed automatic raingauges that can record
short intervals of 1-minute or 5-minutes rather than 15-minutes intervals as
previously recorded. Shorter rainfall aggregation can give more accurate information
about the duration of a storm and thus short intervals data is more appropriate for
analysing convective rain. This is because convective storms usually lasted over a
short period of time.
The temporal analysis used five years rainfall data recorded at station number
3117070 JPS Ampang. Firstly, the diurnal and monthly rainfall patterns at Ampang
station were studied. The separation between non-convective from convective events
38
was carried out based on a 35mm/hr threshold for each 5 minute interval. This
threshold is often used in precipitation models for engineering applications to set
apart non-convective from convective precipitation (Llasat, 2001).
Five minute
intensity is used because rainfall data are already collected in 5 minutes interval. The
convective characteristics were clearly shown by the shape of 10 heavy storms.
Next, convective events were divided into four classes based on the β parameter.
This classification is according to their greater or lesser convective character (Llasat,
2001). The β parameter was determined using equation (3.2):
β L ,ΔT
⎡N
⎤
⎢∑ I (t i , t i + ΔT ) > L ⎥
⎦
= ⎣ i =1 N
∑ I (t i , t i + ΔT )
Equation 3.2
i −1
where,
ΔT
=
time interval of accumulation of the precipitation
I(ti,ti+ΔT)
=
precipitation measured between ti and ti+ΔT
L
=
is set at 35 mm/hr
N
=
total number of ΔT integration steps into which the
episode is divided
Llasat (2001) further divided the storms into four categories based on the β values as
follows:
β
=
0 non-convective
0 < β≤ 0.3
=
slightly convective
0.3 < β≤ 0.8
=
moderately convective
0.8 < β≤ 1.0
=
strongly convective
3.6.2.2 Spatial Distribution
The spatial distribution of rainfall derived from meteorological radar data was
compared with surface rainfall data (rain gauge) using Geographical Information
System (GIS). There are a number of softwares available in GIS, for example
ArcView, ArcInfo and ArcGIS. All of these softwares were developed by ESRI,
39
which is one of the most analytically developed GIS products. In this study, ArcGIS
9.1 was used to digitize radar data and displaying the image in rainfall contour.
Radar data need to be digitized first because the image which is taken from KLIA
Meteorological Station is in JPEG format.
This format is the end product of
Interactive Radar Information System (IRIS), the radar software used at
Meteorological Station at KLIA IRIS cannot give rainfall image in GIS format.
Figure 3.7 shows a radar image taken from KLIA Meteorological Station.
The digitized images using ArcGIS can give the area between isohyetal
interval (coded in colours) and the corresponding rainfall intensity. On the other
hand, the isohyetal line for surface rainfall was constructed using TIDEDA database.
TIDEDA is a computer program for processing time-dependent data, particularly
hydrological data. Comparison was made based on 5-minutes rainfall aggregations.
For comparison purposes, 4 events which coincided with major flood events were
selected. These events occurred on 06th Jan, 26th Feb, 06th Apr, and 10th May 2006.
For every event, several images at different time were selected and digitized. By
matching the same occurrence time, rainfall contour from surface data (Kriging)
were compared with rainfall contour from radar image (digitized image). Finally, a
relationship between areas of rainfall contour (derived from Kriging) with rainfall
depth was examined. Table 3.3 shows the time when the images were captured by
TDR for analysis of spatial comparison and correlation with ground data.
Figure 3.7 : Example of radar image in JPEG format
40
During the above four events, twenty rain gauge stations in Klang Valley
which exhibited relatively good continuity of rainfall data were chosen to provide
data. Figure 3.8 shows the location of the rainfall stations used in this study.
Table 3.3 : Times during which the digitized images were captured by TDR
Date of events
Jan 6, 2006
Feb 26, 2006
Apr 6, 2006
May 10, 2006
18:19
03:23
15:08
15:01
18:25
04:55
15:13
15:12
Capturing Time
18:30
06:21
15:19
15:28
(hh:mm)
18:36
06:32
15:29
15:33
06:38
15:35
15:39
06:43
15:41
Figure 3.8 : The locations of twenty rain gauge stations selected in this study
3.6.2.3 Procedure to Derive Rainfall Contour from Radar and Raingauge Data
Using GIS
As already noted in section 3.6.2.2, the radar images from KLIA
Meteorological Station is in JPEG format. All images need to be digitized before
41
rainfall contours is created.
Radar images need to be digitized layer by layer
according to the intensity represented by the colours in that image. Due to the wide
range of colour representation, it is difficult to differentiate those colours by eye. To
simplify the data analysis, the colour scales were reduced to seven by redigitizing the
radar image (see Figure 3.5). The new intensity scales and the corresponding radar
intensity values were used in the radar’s contour. Figure 3.9 shows the flow chart to
produce rainfall contour derived from radar. The process of digitizing radar image is
shown in Appendix A. Rainfall contours from surface rainfall were derived by
Kriging Method in ArcGIS 9.1. As noted in Chapter 2, Kriging produces an estimate
of the underlying (usually assumed to be smooth) surface by a weighted average of
the data, with weights declining with distance between the point at which the surface
is being estimated and the locations of the data points. The selected rainfall station
in Klang Valley is shown as point features in GIS. Rainfall intensities were the input
for the analysis. In ArcGIS, Kriging Method compute the rainfall contour in two
ways, that is either Spatial Analyst or Geostatistical Analyst. In this study,
Raw data from radar
(JPEG image)
Digitize radar image
using GIS - ArcGIS 9.1
(digitize layer by layer)
Layer 1
Red
80 – 100
mm/hr
Layer 2
Orange
35 – 80
mm/hr
Layer 3
Yellow
8 – 35
mm/hr
Layer 4
Green
3–8
mm/hr
Layer 5
Dark
Green
0.9 – 3
mm/hr
Layer 6
Dark
Blue
0.5 – 0.9
mm/hr
Layer 7
Blue
0.3 – 0.6
mm/hr
Union
(merge all layers)
Rainfall contours
Figure 3.9 : Flow chart of plotting rainfall contours derived from radar
42
Geostatistical Analyst is chosen because the Matern model (now it is recognized as
K-Bessel) tends to produce surfaces that are smoother locally (on a very fine scale)
than some other models (such as the exponential or spherical). Besides that, among
the advantages of the implementation of kriging in Geostatistical Analyst relative to
that in Spatial Analyst are the ability to directly handle the data and the ability to
make plots of prediction errors as a way of assessing uncertainty. There are four
steps to execute kriging in Geostatistical Analyst. Figure 3.10 shows the flow chart
of producing rainfall contours by ground data. The four steps used for interpolating
the rainfall contour in ArcGIS is given in Appendix B. After rainfall contours (both
radar and ground data) were created, the spatial distributions of rainfall were
compared in term of intensity and area. The area of rainfall contours was also
determined by GIS.
Key-in ground data in ArcGIS
(from 20 raingauge stations)
Choose Geostatistical Analyst
1st
Geostatistical
Method
Selection
(Ordinary
Kriging)
2nd
Semivariogram /
Covariance
Modeling
(Matern model /
K-Bessel)
3rd
Searching
Neighborhood
4th
Cross
Validation
Rainfall contours
Figure 3.10 : Flow chart of plotting rainfall contours derived from ground data
3.6.2.4 Storm Movements and Depth Area Relationship
To study storm movement, four flash flood events that occurred in the Klang
Valley were chosen. The storms that led to the flash floods had exhibited convective
43
characters. These events also are a good example of unusually strong convective
events responsible for heavy rainfall. To identify convective rainfall in radar images,
a value of 35 dBZ was taken as the reflectivity threshold. This technique was
developed by Dong and Hyung (2000) in identifying heavy rainfalls with mesoscale
convective systems over the Korean Peninsular. Moreover, this value coincides with
the radar’s scale, so it is easy to read the reflectivity according to radar’s colour code.
The highest reflectivity, which is greater than 35 dBZ is chosen as centre of the
storm for convective events. The centre of the storm is used as a reference point to
track the movement of the storm. The coordinates of every movement of the storm
centre were plotted in Rectified Skew Ortomorphic (RSO) Malaysia, which is a
coordinate system widely used in GIS (ArcGIS 9.1).
To get the relationship between areal coverage and rainfall depth, surface
rainfall data from eleven raingauge stations were used. In this analysis, two more
events were included, which occurred on 10th Jun 2003, 05th Nov 2004. These events
also coincided with major flood events. The rainfall depth pattern and the area for
every color code of rainfall contours in small catchment were presented in six
selected storms. The catchment area is about 241.34 km2. The areas between all
pairs of neighbouring isohyets of the six selected storms were computed by ArcGIS
9.1. These rainfall contours were also derived by Kriging Method as stated in
section 3.6.2.3. After the area of every colour code was calculated, mean area
precipitation (MAP) were computed. MAP is the mean areas between all pairs of
neighboring isohyets. The MAP was determined using equation (3.3). Then, the
percentage reduction of storm depth was determined and lastly, areal reduction
curves for all storms were plotted. Calculations to produce the areal reduction curve
are shown in Appendix C.
P=
1 J ∧
∑ P(x j )A j
A j =1
Equation 3.3
where,
P (x j )
= average between isohyet
Aj
= amount of the averaging area contained in cell j or between
∧
isohyet
44
3.6.3
A
=
total areas between all pairs of neighbouring isohyets
J
=
number of cells that contain a portion of the averaging area
Intensity-Duration-Frequency (IDF) Relationship
Rainfall intensity-duration-frequency (IDF) relationship comprises the
estimate of rainfall intensities of different duration and recurrence interval. The IDF
analysis is one of the most commonly used tools in water resources engineering.
Certain hydrological applications require estimates of maximum rainfall intensity for
short durations especially for urban hydrological design. Short duration rainfall
intensities are affected by large uncertainties when durations less than 10 or 5
minutes are considered.
This happens when they are produced during extreme
convective rainfall events.
This study proposes an approach to derive design rainfall depth at low ARI
using rainfall data in an urban catchment. Five years rainfall data were collected
from the Department of Irrigation and Drainage (DID). Again the station 31117070Pusat Penyelidikan JPS Ampang was chosen to develop the IDF curve. This study
applied the Peak Over Threshold (POT) approach to analyze IDF relationship. The
POT approach enables the analyst to use all the data exceeding a sufficiently high
threshold in contrast with the classical extreme value analysis which typically uses
annual extreme values. But in this study, all intensity values which exceed the
threshold value are used. A value of 35 mm/hr was chosen as threshold intensity
value in this analysis. This threshold is very often used in precipitation models for
engineering applications to set apart non-convective from convective precipitation
(Llasat, 2001). Next, the method of parameter estimation (L-moments) is defined for
the Generalized Pareto Distribution.
Subsequently the quantile estimates were
obtained. Then, one step least square method is used to estimate parameters of both
functions a(T) and b(d) in one step, minimising the total square error of the fitted IDF
relationship to the data in equation 2.10. Figure 3.11 shows the flow chart to
produce IDF relationship in this study.
procedure in detail.
The next section will describe each
45
3.6.3.1 L-Moments and Their Estimators
The method of parameter estimation in this study is L-moments. The theory
of L-moment has been discussed in many literatures. L-moments are another way to
summarize the statistical properties of hydrological data based on linear
combinations of the original observations (Hosking, 1990). Sample L-moment
Data Collection
5 years (2000-2004) rainfall data with different durations
(5, 15, 30 & 60 minutes) from 1 raingauge station
Peak Over Threshold (POT) approach
35 mm/hr is chosen as a threshold intensity value
Distribution of the POT Model
The Generalized Pareto Distribution (GPA)
Method of parameter estimation
L-Moments Parameter Estimator
Quantile estimation
Quantile estimation analysis for low return period
One-Step Least Square Method
Gringorten plotting formula, mean square error and
optimization process
Developing IDF curve
Figure 3.11 : Flow chart to produce IDF relationships
estimates are often computed using intermediate statistics called probability weighted
moments (PWMs). The rth probability weighted moment is defined as:
βr= E{X[F(X)]r}
Equation 3.4
46
where F(X) is the cumulative distribution function of X.
The unbiased PWM
estimators, br, (estimators of βr) are computed according to Landwehr et al., (1979)
and Hosking and Wallis, (1995):
N
bo =
1
N
b1 =
N
1
∑ (i − 1) xi
N ( N − 1) i =2
b2 =
N
1
(i − 1)(i − 2) xi
∑
N ( N − 1)( N − 2) i =3
b3 =
N
1
∑ (i − 1)(i − 2)(i − 3) xi
N ( N − 1)( N − 2)( N − 3) i = 4
∑x
i =1
i
Equation 3.5
The general formula become
βr =
r
+∞
∫ x[Fx( x)]
fx( x)dx
Equation 3.6
−∞
where Fx and fx are the cumulative distribution function and probability density
function of x, respectively.
The L-moments λ r , are linear combinations of the
probability-weighted moments, βr, and the first four L-moments are computed from
the Probability Weighted Moments (PWMs) using the relationship
λ1 = β ο
λ2 = 2β1 − β ο
λ3 = 6 β 2 − 6 β 1 + β ο
λ4 = 20β 3 − 30β 2 + 12β1 − β ο
Equation 3.7
This, in general, can be expressed as
r
⎛ r ⎞⎛ r + k ⎞
⎟⎟
⎝ k ⎠⎝ k ⎠
λr +1 = ∑ β k (−1) r − k ⎜⎜ ⎟⎟⎜⎜
k =0
Equation 3.8
L-moment ratios are defined as (Hosking, 1990)
τ2 =
λ
λ2
λ
,τ 3 = 3 ,τ 4 = 4
λ3
λ2
λ2
Equation 3.9
47
where τ2 is the L-coefficient variation, τ3 is the L-skewness and τ4 is the L-kurtosis.
λ1 is the mean.
3.6.3.2 Generalized Pareto Distribution (GPA)
Fitting a distribution to data sets provides a compact and smoothed
representation of the frequency distribution revealed by the available data (Jery et al.,
1993). The GPA distribution was introduced by Pickards in 1975 (Vogel et al.,
1993). The GPA distribution’s cumulative distribution functions (cdf) is given by:
⎡1
⎛ κ ( X − X ο ) ⎞⎤
F ( x) = 1 − exp ⎢ log⎜1 −
⎟⎥
α
⎝
⎠⎦
⎣κ
for κ ≠ 0
Equation 3.10
where Xο is the threshold value, α and κ are the scale and shape parameter
respectively. For positive κ this cdf has upper bound xmax = Xο + α/κ; for κ < 0, an
unbounded and thick-tailed distribution results; κ=0 yields a two parameter
exponential distribution (2P-GPA) in the form of
⎡ 1
⎤
F ( x) = 1 − exp ⎢− ( x − X ο )⎥
⎣ α
⎦
for κ = 0
Equation 3.11
The parameters of the GPA distribution in terms of L-moments:
κ=
4 β 1 + 3β ο + X ο
β ο − 2β1
Equation 3.12
α = ( β ο − X ο )(1 + κ )
for κ ≠ 0
Equation 3.13
α = βο − X ο
for κ = 0
Equation 3.14
where in the case of κ=0, resolve to the 2P- Exponential distribution.
In this study κ is assumed as 0, so 2P-GPA is used to get all the parameters. The
quantiles of the GPA distribution can be calculated from:
XT = Xο +
α
[1 − (1 − F )κ ]
κ
X T = X ο + α [− ln(1 − F )]
for κ ≠ 0
Equation 3.15
for κ = 0
Equation 3.16
48
where F = 1- 1/ψT, where ψ is the average number of events per year larger than a
threshold Xο. From the literature, it is suggested to use ψ > 1.8 or 1.9 to ensure
greater
efficiency
of
(Koutsoyiannis, 1998).
partial
duration
estimates
of
quantiles
estimation
However, this study adopted ψ = 2 because this value
produces better quantile estimates (Desa et al., 2006).
3.6.3.3 One-step Least square Method
After all the quantile values (XT) have been obtained, one-step least square
method estimates all the parameters of both functions a(T) and b(d) in one step,
minimising the total square error of the fitted IDF relationship to the data. To do
this, an empirical return period can be assigned using the Gringorten plotting formula
T jl =
n j + 0.12
l − 0.44
to each data value ijl (j refer to a particular duration d, j=1,….k; l
denoting the rank, l = 1,….nj where nj is the length of the group j). Each data will
have a triplet of values (ijl, Tij, dj) with the intensity model as iˆjl =
a (T jl )
b( d j )
. The
⎛i
⎞
corresponding error could be measured as e jl = ln i jl − ln i jl = ln⎜⎜ jl ˆ ⎟⎟ . The overall
⎝ i jl ⎠
mean square error is e 2 =
1 k 1 n
2
∑ ∑ e jl which lead into an optimization procedure
k j =1 n j l =1
to minimize e = f 2 (η , θ , κ , λ ) (see equation 2.10) (Koutsoyiannis et al., 1998).
All of these calculations were performed using the MS-EXCEL spreadsheet
and Excel Solver was used for optimization process.
49
3.7
Limitations
The above sections have described the research methodologies especially on
to be used in the data analysis. However, several limitations are foreseen as follows:
(a)
Several rainfall stations in Klang Valley are no longer in operation and some
stations have missing data. This limits the numbers of rainfall stations used
in this study.
(b)
Although a number of flash flood events had occurred between years 2001
and 2006, complete sets of rainfall data for both surface rainfall and radar
rainfall are not always available.
(c)
Due to the small numbers of rainfall stations, rainfall contours derived by
Kriging Method cannot give a smooth contour. This is because Kriging
works best with large input data and prediction errors are larger in areas with
small number of samples.
CHAPTER IV
RESULTS AND DISCUSSION
4.1
Introduction
In this analysis, the research flowchart described in section 3.2 was applied.
In general, three main analyses are included in this chapter.
The first,
characterization of convective rain based on short rainfall duration; second, the
separation between convective and non convective storms and establishment of their
criteria; and third, comparison between spatial distribution of rainfall derived from
radar and surface rainfall.
4.2
Diurnal and Monthly Distribution
In order to characterize the convective storms, historical rainfall of 5-min
intervals was extracted from the hydrological data bank of the Department of
Irrigation and Drainage of Malaysia. Station 3117070 – JPS Ampang was chosen
because the data sets have the least missing records. Only about 0.66% of the data
was missing. The rainfall station is located at 3° 9’ 20” North and 101° 45’ 00” East.
Figure 4.1 shows the diurnal and monthly distributions of rainfall (greater
than 5 mm) in 2004 at the Ampang station. About 79% of the total rainfall occurred
during the daytime (07:00h – 19:00h). Approximately 75% of the rains fall between
51
13:00h and 19:00h and 12.5% fall between 19:00h and 22:00h. It means that most of
the rainfall occurred in the afternoon. Convective storms are caused by differential
solar heating of the ground and lower air layers, which typically occur during
afternoons when warm moist air covers an area (Hewlett, 1969). In this regard, most
afternoon rainstorms at Ampang can be classified as convectional storms. Appendix
D shows the data used to summarize diurnal and monthly distributions of rainfall at
station 311707- JPS Ampang.
550
500
Precipitation (mm)
450
400
350
300
250
200
150
100
50
0
> 45
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
J
F
40 - 45
M
35 - 40
A
30 - 35
25 - 30
M
J
20 - 25
J
15 - 20
A
S
10 - 15
5 -10
O
N
<5
D
0
3
6
9
12
Local Time (h)
15
18
21
24
0
50
100 150 200 250 300 350 400 450 500 550 600
Pr eci pi tati on (mm)
Figure 4.1 : Diurnal and monthly distributions of rainfall (greater than 5 mm)
in 2004 at station JPS Ampang
4.3
Minimum Interevent Time (MIT)
In this analysis, a rainfall event is defined based on the Minimum Interevent
Time (MIT). One year rainfall data was used to define the MIT. The annual number
of rainfall events were plotted against different MIT values and an appropriate MIT
value was selected from the graph at a point after which increases in the MIT do not
52
result in significant changes in the number of event. An MIT value of three hours is
chosen. As can be seen from Figure 4.2, after an MIT value of 3, changes in the
numbers of events with respect to MIT values become insignificant. Therefore, two
storms which have separation time less than 3 hours is considered as a single event.
Likewise two storm events which have time lapse of more than 3 hours were
considered as two separate events. This value is acceptable as Adams et al., (1986)
suggested MIT values between 1 and 6 hours for urban applications.
300
250
200
150
100
50
0
0
1
2
3
4
5
6
7
M IT ( hr )
Figure 4.2 : Annual number of rainfall events as a function of MIT
4.4
Characterization of Convective Rain Based on Short Duration Rainfall
4.4.1
Preliminary Analysis
The preliminary results on the characteristics of convective and nonconvective storms are presented in terms of total rainfall, intensity and duration.
Table 4.1 presents the statistical summary of the rainfalls between year 2000 and
2004 with a total 988 events. The separation between convective and non-convective
storms is based on the 35 mm/hr threshold intensity as described by Llasat (2001).
Convective rain occurred most frequently in November (45 times). Of the total 297
convective storm events which exceeded 35 mm/hr, 130 storms or 44% occurred
during inter-monsoon months (Oct – Nov and Apr – May). The southwest and
northeast monsoons recorded 27% and 30% of the events respectively.
This
phenomenon is influenced by inter-monsoon process where the atmosphere is quite
stable in the morning with strong convective clouds developing in the late morning
53
and early afternoon (Billa et al., 2004). Besides, the wind direction during this
period is often variable and the wind speeds seldom exceed 10 knots.
The
frequencies of storms event in different monsoon periods are shown in Table 4.2.
4.4.2
Characterization of 5-minute Rainfall
The characteristics of 5-minutes rainfall, presented in Table 4.3 are different
from Table 4.1.
In Table 4.3 the means, medians, standard deviations and
coefficients of variation were computed from the 5 minute data for every event
whereas in Table 4.1, the values were computed from cumulative monthly amounts.
The purpose of this analysis is to observe the characteristics of convective rain on the
basis of 5 min series for each rainfall event. Again the 35 mm/hr threshold intensity
was used to separate convective from non-convective storms. It was found that the
mean, median and standard deviation are very low. These are expected as the 5
minutes rainfall data have smaller values compare to monthly total values.
In
addition, the 5 minute intervals have many zero values especially when another
storm occur within less than 3 hours (the MIT used in this analysis).
The details of ten convective events with the highest intensity are given in
Table 4.4. Eight of these events occurred in the afternoon with duration ranging
from 15 to 215 minutes and averaged at 90 minutes. However, the highest intensity
of 384 mm/hr was observed during a morning storm in year 2003.
The
characteristics of these storms are shown in Figure 4.3. A great variety of storm
shape is evident but the more intense sections of the events occurred over short
durations. The convective storms often occurred in the afternoon. This situation
could be associated with the process of convective storm whereby hot air rises, cools
and condenses, forming water droplets. If the air is hot enough, it can rise very
quickly to form thunderstorms and intense precipitation.
54
Table 4.1 : Summary statistics of monthly convective and non-convective rainfalls
between 2000 and 2004 at Ampang station
Intermonsoon
Northwest
Precipitation
class
and totals
Month
Dec
Jan
Feb
Mar
Apr
May
Southwest
Jun
Jul
Aug
Inter-monsoon
Sep
Oct
Nov
Nonconvective
Total rainfall amounts (mm)
696.2
405.6 529.5
686.8
902.1
360.6 409.3 419.1 450.9
834.6
824.1
1312.6
precipitation
Mean (mm)
139.2
81.1
105.9
137.4
180.4
72.1
81.9
83.8
90.2
166.9
164.8
262.5
(mm) with rate
Median (mm)
99.9
66.4
66.2
114.8
164.4
80.5
86.0
61.8
50.6
146.6
163.0
263.8
< 35 mm/hr
Standard Deviation
121.2
71.1
123.1
88.0
68.3
31.0
60.0
66.4
90.9
92.3
51.3
97.4
Coefficient of variation (%)
87.0
87.6
116.2
64.1
37.8
42.9
73.3
79.2
100.8
55.3
31.1
37.1
Number of event
65
44
39
60
79
38
34
47
46
74
63
99
Precipitation per event
10.7
9.2
13.6
11.4
11.4
9.5
12.0
8.9
9.8
11.3
13.1
13.3
Convective
Total rainfall amounts (mm)
483.1
200.1 331.2
809.0
716.5
396.9 454.6 317.6 309.0
632.1
917.9
883.5
precipitation
Mean (mm)
96.6
40.0
66.2
161.8
143.3
79.4
90.9
63.5
61.8
126.4
183.6
176.7
(mm) with rate
Median (mm)
92.7
27.4
61.3
118.8
139.1
52.8
15.7
79.1
27.2
95.9
192.2
239.2
> 35 mm/hr
Standard Deviation
51.0
36.1
24.8
150.9
50.2
60.6
129.3
61.3
70.7
69.9
102.4
121.1
Coefficient of variation (%)
52.8
90.3
37.5
93.3
35.0
76.4
142.2
96.6
114.5
55.3
55.8
68.6
Number of event
Precipitation per event
Bulk all kinds
(mm)
Total rainfall amounts (mm)
18
15
22
33
33
16
18
14
17
30
36
45
26.8
13.3
15.1
24.5
21.7
24.8
25.3
22.7
18.2
21.1
25.5
19.6
1179.3 605.7 860.7 1495.8 1618.6 757.5 863.9 764.5 759.9 1466.7 1742.0 2196.1
Mean (mm)
235.9
121.1 172.1
299.2
323.7
151.5 172.8 152.9 152.0
293.3
348.4
439.2
Median (mm)
183.9
93.8
129.0
295.0
351.7
143.9 190.1 140.9 172.1
324.5
359.9
470.5
Standard Deviation
143.4
102.5 119.7
176.9
90.4
81.3
148.5 111.6
97.7
107.7
77.1
136.3
Coefficient of variation (%)
60.8
84.6
69.5
59.1
27.9
53.7
85.9
73.0
64.3
36.7
22.1
31.0
83
59
61
93
112
54
52
64
63
104
99
144
13.4
9.0
16.2
15.9
14.6
13.7
14.3
11.6
11.6
14.0
18.1
15.7
Number of event
Precipitation per event
Table 4.2 : Frequency of convective storm events during monsoon and intermonsoon periods
Monsoon
Southwest
Northeast
Intermonsoon
Frequency
79
88
130
%Frequency
27
30
43
55
Table 4.3 : Summary statistics of 5 minutes rainfall between years 2000 and 2004
Intermonsoon
Northwest
Precipitation
class
and totals
Month
Dec
Jan
Southwest
Inter-monsoon
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
0.4
Nonconvective Mean (mm)
0.4
0.3
0.5
0.4
0.5
0.4
0.4
0.4
0.4
0.5
0.4
precipitation
0.1
0.1
0.3
0.1
0.2
0.1
0.2
0.2
0.2
0.2
0.2
0.2
(mm) with rate Standard Deviation
0.6
0.5
0.5
0.6
0.6
0.5
0.5
0.6
0.5
0.6
0.5
0.6
Median (mm)
< 35 mm/hr
Coefficient of variation
1.6
1.5
1.1
1.6
1.4
1.4
1.3
1.4
1.3
1.2
1.4
1.4
Convective
Mean (mm)
0.4
0.5
0.7
0.5
0.5
0.4
0.4
0.4
0.4
0.5
0.5
0.4
precipitation
Median (mm)
0.1
0.1
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
(mm)with rate Standard Deviation
0.9
0.8
1.7
1.1
1.0
1.3
0.7
0.6
0.7
1.0
1.1
0.6
> 35 mm/hr
Coefficient of variation
2.4
1.8
2.5
2.4
1.9
3.0
1.9
1.5
1.7
2.0
2.4
1.6
Bulk all kinds
Mean (mm)
0.6
0.5
0.7
0.8
0.8
0.8
0.7
0.7
0.63
0.7
0.8
0.7
(mm)
Median (mm)
0.1
0.1
0.4
0.1
0.2
0.2
0.2
0.2
0.20
0.2
0.2
0.2
Standard Deviation
1.3
1.0
1.5
1.8
1.5
1.8
1.6
1.3
1.70
1.4
1.8
1.2
Coefficient of variation
2.2
2.0
2.0
2.3
2.0
2.3
2.2
1.9
2.68
1.9
2.3
1.9
Note : The rainfall amount and number of events are similar with Table 4.1
Table 4.4 : Details of storms with the highest 5-minutes intensity (I5)
Date
28.02.2000
23.02.2000
26.05.2000
16.09.2000
03.10.2000
09.04.2001
14.12.2001
14.04.2002
21.08.2003
12.10.2004
Max
Intensity
(mm/hr)
249.6
164.4
366.0
271.2
225.6
244.8
220.8
229.2
384.0
147.6
Storm
Depth
(mm)
20.8
13.7
30.5
22.6
18.8
20.4
18.4
19.1
32.0
12.3
Start
time
15:30:00
16:20:00
14:55:00
15:55:00
18:05:00
1:50:00
16:50:00
15:20:00
10:35:00
16:25:00
End
time
19:05:00
16:50:00
15:15:00
18:05:00
20:25:00
4:00:00
17:35:00
16:10:00
10:50:00
17:30:00
Duration
min
215
30
80
130
140
130
45
50
15
65
56
Storm on 28.02.2000
Storm on 26.05.2000
Storm on 16.9.2000
Storm on 23.02.2000
400
400
400
400
350
350
350
350
300
300
300
intensity (mm/hr)
300
250
200
150
100
250
250
250
200
200
200
150
150
150
100
100
100
50
50
50
50
0
0
0
30
60
90
120
150
180
210
240
270
0
300
30
60
90
120
150
180
210
240
270
300
0
0
0
30
60
90
tim e (m in)
t im e ( m in)
Storm on 3.10.2000
400
350
350
300
150
180
210
240
270
0
300
30
60
90
t im e ( m in)
120
150
180
210
240
270
300
240
270
300
time (min)
Storm on 14.04.2002
Storm on 14.12.2001
Storm on 9.4.2001
400
120
400
400
350
350
300
300
300
250
250
250
200
200
150
150
100
100
50
50
250
200
200
150
150
100
100
50
50
0
0
30
60
90
120
150
180
210
240
270
300
330
0
0
t im e ( m in)
0
0
30
60
90
120
150
180
210
240
270
0
300
30
60
90
120
150
180
210
240
270
300
0
30
60
Storm on 21.08.2003
Storm on 12.10.2004
400
400
350
350
300
300
250
250
200
200
150
150
100
100
50
50
0
0
0
30
60
90
120
150
180
t im e ( m in)
210
240
270
300
0
30
60
90
120
150
180
90
120
150
180
t im e ( m in)
t ime ( m in)
time (min)
210
240
270
300
t im e ( m in)
Figure 4.3 : Convective storms with the highest 5 –minutes intensity for each year
210
57
4.4.3
Classification of Convective Events
In order to classify convective events, it is useful to have a parameter for each
one of them. As noted in Chapter III, an intensity of 35 mm/hr is taken as the 5
minute mean intensity threshold (Llasat, 2001). This threshold is useful in order to
derive convective storm properties. Table 4.5 shows the number of non-convective
and convective events between 2000 and 2004. In this analysis, it is found that,
convective and non-convective events contributed 30.1% and 69.9% of total yearly
event, respectively.
The highest number of convective event occurred in inter-
monsoon months where 45 convective events were recorded in November. Figure
4.4 shows the percentage of occurrence of convective and non-convective storms in
2004. Most of the convective storms occurred in the afternoon. Approximately 24%
of the convective rains fall between 18:00h and 19:00h. While, non-convective
storms occurred anytime of the day, the rain falls mostly in the afternoon. On the
whole there is a higher occurrence of convective storms in the afternoons..
Table 4.5 : Number of convective and non convective events between 2000 and
2004
Season
Month
Non-convective
events (< 35
mm/hr)
Convective
events
(> 35 mm/hr)
InterInterSouthwest
monsoon
monsoon
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
Northwest
65
44
39
60
79
38
34 47
46
74
63
99
18
15
22
33
33
16
18 14
17
30
36
45
58
Percentage of Occurrence of Convective & Non-convective Storm
Percentage of Non-convective
and Convective Storm (%)
25
20
15
10
5
0
6
3
12
9
18
15
21
24
Time (hour)
Non-convective
Convective
Figure 4.4 : Percentage of occurrence of convective and non-convective storms in
2004 at station JPS Ampang
A classification of episodes based on the β parameter is shown in Figures 4.5
and 4.6.
This classification is according to their greater or lesser convective
character (Llasat, 2001).
The number of event which fall under moderately
convective class is the highest in all months (Figure 4.4). On a yearly basis, the
percentages of event that fall under moderately convective storm range from 51.5%
to 69.3% (Figure 4.5).
Frequency of occurrence convective storm between year 2000-2004
35
30
No of events
25
20
15
10
5
0
Jan
Feb
Mar
Apr
slightly convective
May
Jun
Jul
Month
moderately convective
Aug
Sep
Oct
Nov
Dec
strongly convective
Figure 4.5 : Monthly number of event for each class of convective storm
59
Percentage for classification of Convective Rain
2004
Year
2003
2002
2001
2000
0
20
slightly convective
40
60
Percentage (%)
moderately convective
80
100
strongly convective
Figure 4.6 : Yearly percentage of occurrence of convective storm
4.5
Spatial Distribution
In this analysis, the spatial distributions between meteorological radar data
and surface rainfall were compared in terms of intensity and the area between
isohyetal lines. In addition, the movements of storm centre for selected convective
events were observed. Finally, the depth-area relationship was plotted for six single
events.
4.5.1
Digitized Radar Image
In order to analyse storm areal coverage, the radar images were digitized to
get layers of isohyetal contour in GIS format. The original images (JPEG image)
from KLIA Meteorological Station were matched with Klang Valley Map. Then, the
colours of rainfall image were digitized one by one until a rainfall contour is
produced. Figure 4.7 shows the digitized images of rainfall contour for events on
January 6, February 26, April 6, and May 10, 2006 using GIS (ArcGIS 9.1).
60
Figure 4.7 : Digitized image using ArcGIS 9.1
4.5.2
Comparison on Intensity
A temporal comparison on intensity values between surface rainfall data and
meteorological radar data was carried out for selected events. Tables 4.7, 4.8, 4.9
and 4.10 show the rainfall intensity between radar rainfall and surface rainfall. For
event on January 6, 2006, the rainfall intensity was compared at four different times,
i.e. 18:19, 18:25, 18:30 and 18:36 (Table 4.6). The selected times represent high
rainfall intensity. Unfortunately, rainfall data for stations R4, R5, R12 and R13 were
missing.
The comparison showed large differences between radar and ground
rainfall intensity. Table 4.7 shows event on February 26, 2006 and the rainfall
intensities at 06:21, 06:32, 06:38, 06:43, 04:55 and 03:23 hr. Despite no missing
ground rainfall data, the differences in intensity value between raingauge and radar
are still too large. Two more events on April 6 and May 10, 2006 (Tables 4.8 and
4.9) also show poor agreement between raingauge and radar data.
Overall, it is observed that both radar and surface rainfall produced marked
difference in intensity. For a given storm, the radar data can both overestimate or
underestimate the surface rainfall. The main challenge in narrowing the differences
61
between radar rainfall and surface rainfall is to establish a good relationship between
decibel of Z-R in unit mm6/m3 and rainfall, R in unit mm/hr (Linsey et al., 1988).
Another factor that could contribute error is evaporation of precipitation before
reaching the ground, which might be more intense in the tropics. Also, winds may
carry precipitation away from beneath the rain producing cloud.
Besides, the
discontinuities in the vertical distribution of precipitation in the cloud affect radar
reflectivity and add another source of error (Linsey et al., 1988). For this particular
study, the most difficult part is to manually estimate the rainfall from the JPEG
image especially rainfall intensity greater than 35 mm/hr as the range is so wide.
Radar images can be difficult to interpret.
It can possibly be solved by using
algorithm to analyze convective storms. Two algorithms had been tested before.
The first (Steiner et al., 1995) identified convective structures at the lowest 2D level
and the second (Johnson et al., 1998) identified convective cells as a region of
maximum reflectivity in 3D. But these algorithms could not be performed in this
study because IRIS Software at KLIA Meteorological Station could not give two or
three-dimensional Cartesian-gridded radar echo.
62
Table 4.6 : Comparison of rainfall intensity (mm/hr) between surface and radar rainfalls on January 6, 2006
Time
Raingages
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
R19
R20
3217001-KM16 Gombak
3116006-Ldg Edinburgh Site 2
3217003-KM11 Gombak
3216001-Kg Sg Tua
3116003-JPS Msia
3018101-Emp. Semenyih
3118102-SK Kg Lui
311104-Jln Genting Peres
2917001-JPS Kajang
3117070-JPS Ampang
3115079-Pusat Penyldkn Sg Buloh
3315037-Tmn Bkt Rawang
3315038-Country Homes
3217004-Kg Kuala Sleh
3217002-Emp. Genting Klang
3216004-SMJK Kepong
3317001-Air Terjun Sg Batu
3317004-Genting Sempah
3014091-UiTM Shah Alam
3014084-JPS Klang
?
=
missing data
RG
= rain gauge
RDR = radar
Latitude
Longitude
3.2680
3.1833
3.2361
3.2722
3.1514
3.0856
3.1736
3.1403
2.9917
3.1556
3.1583
3.3014
3.0167
3.2583
3.2361
3.2319
3.3347
3.3681
3.0022
3.0389
101.7291
101.6333
101.7139
101.6861
101.6847
101.8892
101.8722
101.9297
101.7972
101.7500
101.5597
101.5008
101.5022
101.7903
101.7528
101.6361
101.7042
101.7708
101.4019
101.4444
RG
0
0
0
?
?
0
21
4.8
0
0
22.8
?
?
6
0
0
6
0
15.6
0
18:19
RDR
0.6
no rain
0.5
0.5
no rain
4
0.5
1
0.9
no rain
20
35
0.9
1
no rain
15
3
2
2
no rain
18:25
18:30
RDR
RG
RDR
Intensity (mm/hr)
0
0.5
0
0.8
5
1.5
0
10
0
0.7
0
1
?
no rain
?
0.6
?
no rain
?
2
0
0.8
0
1.5
21
0.9
4
3
4.8
2
8.4
4
0
0.3
0
no rain
7.2
0.3
7.2
3
22.8
20
52.8
35
?
20
?
20
?
no rain
?
no rain
6
0.3
0
0.7
0
0.6
6
0.5
0
20
0
10
0
3
0
1.5
0
2
0
3
10.8
1
8.4
1.5
0
no rain 1.2
0.4
RG
18:36
RG
RDR
6
0
6
?
?
0
1
3.6
0
8.4
50.4
?
?
0
0
0
0
0
79.2
1.2
2.0
20.0
0.8
0.7
8.0
1.5
2.0
9.0
0.7
7.0
25.0
5.0
0.7
0.8
2.0
0.8
2.0
0.7
6.0
0.3
63
Table 4.7 : Comparison of rainfall intensity (mm/hr) between surface and radar rainfalls on February 26, 2006
Time
Raingages
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
R19
R20
RG
3217001-KM16 Gombak
3116006-Ldg Edinburgh Site 2
3217003-KM11 Gombak
3216001-Kg Sg Tua
3116003-JPS Msia
3018101-Emp. Semenyih
3118102-SK Kg Lui
311104-Jln Genting Peres
2917001-JPS Kajang
3117070-JPS Ampang
3115079-Pt Penyldkn Sg Buloh
3315037-Tmn Bkt Rawang
3315038-Country Homes
3217004-Kg Kuala Sleh
3217002-Emp. Genting Klang
3216004-SMJK Kepong
3317001-Air Terjun Sg Batu
3317004-Genting Sempah
3014091-UiTM Shah Alam
3014084-JPS Klang
= rain gauge
RDR = radar
Latitude Longitude
3.2680
3.1833
3.2361
3.2722
3.1514
3.0856
3.1736
3.1403
2.9917
3.1556
3.1583
3.3014
3.0167
3.2583
3.2361
3.2319
3.3347
3.3681
3.0022
3.0389
101.7291
101.6333
101.7139
101.6861
101.6847
101.8892
101.8722
101.9297
101.7972
101.7500
101.5597
101.5008
101.5022
101.7903
101.7528
101.6361
101.7042
101.7708
101.4019
101.4444
RG
12
0
0
6
0
0
0
0
0
50.4
0
4
1
30
30
6
18
12
0
0
6:21
RDR
9
no rain
9
6
2
no rain
no rain
no rain
no rain
20
no rain
0.8
0.9
4
6
0.4
2
0.8
no rain
0.7
RG
18
0
0
24
6
0
33
0
0
19.2
0
0
0
6
18
6
6
6
0
0
6:32
RDR
6
no rain
2
6
0.8
no rain
0.9
0.5
no rain
5
no rain
0.5
0.8
1.5
1.5
1
6
0.8
no rain
no rain
RG
18
0
0
24
0
0
28
0
0
6
0
0
0
6
6
6
48
6
0
0
6:38
6:43
RDR
RG
RDR
Intensity (mm/hr)
4
18
6
0.3
0
0.4
1.5
6
3
15
12
15
0.3
0
no rain
0.8
0
4
10
28
8
no rain 21.6 no rain
no rain
0
no rain
3
3.6
4
no rain
0
no rain
0.3
0
0.3
0.6
0
0.5
0.7
12
1.5
9
6
20
1
6
0.4
5
42
5
1.5
6
1
no rain
0
no rain
no rain
0
no rain
RG
48
20
12
0
6
0
0
0
0
1.2
0
0
0
0
0
6
0
6
7.2
0
4:55
RDR
RG
0.4
6
0.6
0.6
1.5
4
no rain
no rain
5
0.5
4
no rain
0.3
0.6
1.5
15
0.4
no rain
0.8
0.5
0
5
0
48
6
0
0
0
0
1.2
18
25
6
0
0
6
0
0
16.8
0
3:23
RDR
0.3
20
3
65
0.9
no rain
no rain
no rain
no rain
no rain
2
50
1.5
7
0.6
50
no rain
no rain
2
no rain
64
Table 4.8 : Comparison of rainfall intensity (mm/hr) between surface and radar rainfalls on April 6, 2006
Time
Raingages
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
R19
R20
3217001-KM16 Gombak
3116006-Ldg Edinburgh Site
2
3217003-KM11 Gombak
3216001-Kg Sg Tua
3116003-JPS Msia
3018101-Emp. Semenyih
3118102-SK Kg Lui
311104-Jln Genting Peres
2917001-JPS Kajang
3117070-JPS Ampang
3115079-Pt Penyldkn Sg
Buloh
3315037-Tmn Bkt Rawang
3315038-Country Homes
3217004-Kg Kuala Sleh
3217002-Emp. Genting Klang
3216004-SMJK Kepong
3317001-Air Terjun Sg Batu
3317004-Genting Sempah
3014091-UiTM Shah Alam
3014084-JPS Klang
?
=
missing data
RG
= rain gauge
RDR = radar
Latitude Longitude
RG
15:08
RDR
3.2680
101.7291
72
65
3.1833
3.2361
3.2722
3.1514
3.0856
3.1736
3.1403
2.9917
3.1556
101.6333
101.7139
101.6861
101.6847
101.8892
101.8722
101.9297
101.7972
101.7500
5
0
108
0
0
0
1.2
?
2.4
0.5
0.4
50
0.9
0.5
0.6
1
no rain
15
3.1583
3.3014
3.0167
3.2583
3.2361
3.2319
3.3347
3.3681
3.0022
3.0389
101.5597
101.5008
101.5022
101.7903
101.7528
101.6361
101.7042
101.7708
101.4019
101.4444
0
0
0
0
?
0
12
0
0
0
0.4
no rain
no rain
no rain
65
no rain
6
0.5
no rain
no rain
15:13
RG RDR
42
7
15
0.8
0
0.3
54
65
6
6
0
2
11 no rain
1.2
1
? no rain
3.6
35
0
0
0
0
?
0
6
6
0
0
0.3
no rain
no rain
no rain
50
0.4
3
no rain
no rain
no rain
15:19
15:29
RG RDR RG RDR
Intensity (mm/hr)
12
6
6
0.3
5
0
30
6
0
1
4.8
?
7.2
0
0
0
0
?
0
0
0
0
0
RG
15:35
RDR
6
0.3
no rain 5 no rain 5
0.4
12
3
90
35
24
50
18
15
24
35
24
20
0
15
0
no rain
1
0.7
0
0.7
25.2
1.5
20.4
4
?
50
?
20
10.8
35
8.4
no rain
15
50
6
15
0.4
2
7
35
no rain
no rain
no rain
0.6
20
no rain
1.5
no rain
no rain
no rain
no rain
no rain
no rain
35
1
no rain
0.4
no rain
no rain
no rain
0
0
0
0
?
0
0
0
0
0
no rain
no rain
no rain
50
1
0.4
0.5
0.6
no rain
no rain
0
0
0
0
?
0
0
0
0
0
RG
0
15:41
RDR
0.3
0
no rain
48
9
12
10
12
9
0
7
0
0.6
6
0.9
?
1.5
14.4
35
0
5
0
0
?
0
0
0
0
0
no rain
no rain
0.3
65
0.9
no rain
0.5
no rain
no rain
no rain
65
Table 4.9 : Comparison of rainfall intensity (mm/hr) between surface and radar rainfalls on May 10, 2006
Time
Raingages
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
R19
R20
3217001-KM16 Gombak
3116006-Ldg Edinburgh Site 2
3217003-KM11 Gombak
3216001-Kg Sg Tua
3116003-JPS Msia
3018101-Emp. Semenyih
3118102-SK Kg Lui
311104-Jln Genting Peres
2917001-JPS Kajang
3117070-JPS Ampang
3115079-Pusat Penyldkn Sg Buloh
3315037-Tmn Bkt Rawang
3315038-Country Homes
3217004-Kg Kuala Sleh
3217002-Emp. Genting Klang
3216004-SMJK Kepong
3317001-Air Terjun Sg Batu
3317004-Genting Sempah
3014091-UiTM Shah Alam
3014084-JPS Klang
?
=
missing data
RG
= rain gauge
RDR = radar
Latitude Longitude
3.2680
3.1833
3.2361
3.2722
3.1514
3.0856
3.1736
3.1403
2.9917
3.1556
3.1583
3.3014
3.0167
3.2583
3.2361
3.2319
3.3347
3.3681
3.0022
3.0389
101.7291
101.6333
101.7139
101.6861
101.6847
101.8892
101.8722
101.9297
101.7972
101.7500
101.5597
101.5008
101.5022
101.7903
101.7528
101.6361
101.7042
101.7708
101.4019
101.4444
RG
?
45
?
102
90
?
0
0
15
21.6
0
25
0
0
0
?
0
0
0
0
15:01
RDR
0.8
20
no rain
6
65
50
no rain
1
15
15
no rain
no rain
15
80
20
20
0.3
no rain
no rain
no rain
RG
?
20
?
66
20
0
0
10
42
0
5
0
0
0
?
0
0
0
0
15:12
RDR
15:28
15:33
15:39
RG
RDR RG RDR RG RDR
Intensity (mm/hr)
80
?
35
?
65
?
50
35
0
50
0
35
0
50
6
?
35
?
15
?
7
9
6
2
0
4
6
7
65
10
50
10
15
10
7
20
?
2
?
2
?
0.9
0.5
0
35
0
5
0
5
35
0
6
0
0.8
0
3
9
0
1.5
0
0.7
0
no rain
0.4
0
0.3
0 no rain 0
0.3
0.3
23
0.3
5
1
11
2
no rain
5
no rain
5 no rain 7
no rain
4
1
no rain
3 no rain
2
no rain
20
0
65
0
10
0
7
80
0
35
6
35
24
50
7
?
0.3
?
0.3
?
0.3
20
12
65
18
50
36
50
0.3
0
20
6
7
12
9
no rain
0
no rain
0 no rain
0
no rain
no rain
0
no rain
0 no rain
0
no rain
66
The spatial distributions of rainfall were derived by Kriging for every
raingauge.
However, out of four storms, only one event on January 6, 2006
produced smooth circular isohyetal lines. The rainfall contour patterns for this event
exhibit very similar patterns with radar data. This storm started at 18:10hr and lasted
for about two hours. Figure 4.8 compares the spatial distribution derived by Kriging
Method with that of observed rainfall radar data for January 6, 2006 as the storm
progress. In this figure both rainfall contour from radar and ground data used similar
legends.
This storm also shows increasing intensity as its centre moves from
northeast to southwest. However, the other three storms (February 26, April 6 and
May 10), failed to show good agreements between radar and raingauge data. Most of
the isohyetal lines derived from the raingauge data are not smooth compared to those
derived from digitized images. Moreover, the spatial distributions of the radar and
surface rainfall are remarkably different. This might be due to the small number of
raingauge station employed in the study and further complicated by the occurrence of
missing data for some of the events. Kriging method requires a large number of
rainfall stations to produce smooth curves. Prediction errors tend to be larger in
areas with small number of rainfall station. Besides, the discrepancies arise from the
way Doppler radar estimate rainfall intensity. Doppler radar does not determine
actual rainfall intensity, but measure the returned energy which is reflected back
toward the radar (National Weather Service, 2006).
The more intense the
precipitation, the greater the reflectivity (Linsey et al., 1988). Figures 4.10, 4.11 and
4.12 show the spatial distribution of rainfall on February 26, April 6, and May 10,
2006.
67
Derived from raingauge using Kriging
Derived from raingauge using Kriging
1819
1825
1830
1836
Derived from Radar
1819
1825
1830
1836
Figure 4.8 : Comparison of spatial rainfall distributions derived from raingauge and
radar for event on January 6, 2006
Figure 4.9 : Legends
68
Derived from raingauge using Kriging
0323
0455
0621
0632
0638
0643
Derived from radar
0323
0455
0632
0638
0638
0621
0643
0632
Figure 4.10 : Comparison of spatial rainfall distributions derived from raingauge and
radar for event on February 26,2006 (using similar legends as in Figure 4.9)
69
Derived from raingauge using Kriging
1508
1513
1529
1535
1519
1541
Derived from radar
1519
1508
1513
1529
1535
1541
Figure 4.11 : Comparison of spatial rainfall distributions derived from raingauge and
radar for event on April 6, 2006 (using similar legends as in Figure 4.9)
70
Derived from raingauge using Kriging
1501
1528
1512
1533
1539
Derived from radar
1501
1512
1533
1528
1539
Figure 4.12 : Comparison of spatial rainfall distributions derived from raingauge and
radar for event on May 10, 2006 (using similar legends as in Figure 4.9)
71
4.5.3
Comparison of Areal Rainfall between Radar and Surface Rainfall
Comparison of the areal rainfall derived from radar and surface rainfall was
carried out using GIS software (ArcGIS 9.1). The colour represents the intensity
level. The analysis used four selected storms. Three of the storms analysed occurred
in the afternoon. Table 4.11 compares the areal coverage of rainfall intensity derived
from radar against those from raingauges. For event on January 6, 2006, the heaviest
rainfall was detected at 18:36 h. For both ground and radar data, the storms centres
were observed on the west of Klang Valley. The areal distribution between radar and
surface rainfall is different. The storm centre derived from raingauge is bigger than
those derived from radar (red colour). Based on twenty raingauges, the highest
intensity of 79.2 mm/hr was recorded at station R19 (red colour) while the highest
intensity from radar, between 80 – 100 mm/hr, were observed at stations R5 and
R11. The interpolation process using Kriging did not produce smooth isohyetal lines
as those derived from digitized images (radar). As a result, the centre of the storm
was not accurately captured by the ground data.
Comparison of areal distribution for event on February 26, 2006 was taken at
04:55 h. The highest intensity from radar was between 35 and 80 mm/hr which was
detected above station R2. The highest ground intensity at this time was 48 mm/hr
and the corresponding total rainfall was 8.9 mm. These were observed at station R1.
Ground rainfalls were available only from 8 stations. Again the spatial distribution
differ between ground data and radar data. In general, the area between rainfall
contours from ground data is larger than those derived from radar.
For event on April 6, 2006 there were two storm centres (red colour) with
intensity between 80 and 100 mm/hr at 15:29 h. From Table 4.10, it is found that
low intensity rainfalls cover a bigger area compared to high intensity rainfalls. This
might be influenced by ground data where no high intensity value was recorded at
that time.
The surface rainfall produced three storm centres (Figure 4.12) at
raingauges number R4, R5 and R8 with intensities of 24, 24 and 25.2 mm/hr,
respectively.
The spatial distributions derived from raingauge and radar gave
different results.
The colours of radar images represent the values of energy
reflected toward the radar. The higher the dBZ, the stronger the rain intensity. In
72
addition, only nine raingauges had recorded rainfall intensity. This results in poor
contour of the ground rainfall. Besides the small number of raingauge that produce
poor interpolation of areal rainfall, strong wind can push rain far from the original
location where it start to fall.
The event on May 10, 2006 is quite similar with event on April 6, 2006.
There was only one storm centre for the ground rainfall but the radar contour
produced two storm centres at 15:12 h. The areal coverage by low rainfall intensity
is bigger than high rainfall intensity. The locations of storm centre for both surface
and radar data are also different. For this event, only six raingauges had recorded
rainfall. This complicates the interpolation process and resulted in unsmooth rainfall
contours. Table 4.11 shows the correlation of coefficient (R) of areal coverage for
different intensity between radar and raingauge data for four selected storms. The R
values are very small with a maximum of 0.49 for event on 26 February 2006. All
correlations are not significant as the P values are all greater than 0.05. These
suggest that the correlation between radar and raingauge were very poor. Figure 4.13
compared the areal distributions between radar and surface rainfalls for the four
selected storms.
On the whole, it is evident that the two analyses produced remarkably
different results. Such discrepancies could be attributed to the interpolation process
in the Kriging Method. The spatial interpolation requires an estimate of unknown
values of a variable at unsampled points by using measured values from other points
(Weise, 2001). Moreover, a few raingauges had missing data. This has worsened
the interpolation process in Kriging compared to the digitized images (radar).
Besides that, it can possibly be solved by using some algorithm to analyze
convective storms. Two algorithms had been applied which is by Steiner et al.,
(1995) and Johnson et al., (1998).
However, these algorithms could not be
performed in this study because the IRIS Software at KLIA Meteorological Station
could not give two or three-dimensional Cartesian-gridded radar echo.
raingauge density also contributes to this error.
The
There are very few raingauge
stations available for this study. If the number of raingauges could be increased, the
contours might be smoother than the results shown in this thesis. Another source of
73
error is wind that may carry precipitation away from beneath the rain producing
cloud.
Table 4.10 : Areal distribution of storm intensity obtained from radar and raingauge
Date
Time
Intensity
(mm/hr)
0.3-0.5
0.5-0.9
0.9-3.0
3.0-8.0
8.0-35
35-80
80-100
6-Jan-06
18:36
Area (km2)
Radar Raingauge
309.86
767.68
277.37
560.18
457.4
425.49
555.11
206.00
234.24
285.05
186.24
549.19
5.76
62.24
26-Feb-06
04:55
Area (km2)
Radar Raingauge
463.11
893.28
408.87
331.33
539.74
306.71
370.48
411.08
202.63
500.26
94.90
413.16
0.00
0.00
6-Apr-06
15:29
Area (km2)
Radar Raingauge
303.83
765.27
159.15
223.4
167.55
1423.71
128.86
408.68
240.51
29.07
362.60
5.42
3.03
0.28
10-May-06
15:12
Area (km2)
Radar Raingauge
213.81
1270.45
189.88
375.71
237.34
999.32
239.36
151.87
303.98
44.42
284.56
11.11
2.38
2.95
Table 4.11 : Correlation of coefficient (R) of areal distribution of storm intensity
between radar and raingauge
Correlation of Coefficient (R)
Significance
Date of Event
Between Radar and Raingauge
level, P
6-Jan-06
0.1737
0.71
26-Feb-06
0.4947
0.26
6-Apr-06
0.0295
0.95
10-May-06
0.1062
0.82
**Note: P > 0.05 is not significance
6th January
18:36
26th February
04:55
6th April
15:29
10th May
15:12
Derived from raingauge using Kriging
18:36
04:55
18
15:29
15:12
Derived from radar
Figure 4.13 : Comparison of areal distribution of intensity between surface rainfall
and radar (using similar legends as in Figure 4.9)
74
4.5.4
Storm Movement
It is interesting to investigate the movement pattern of convective storms by
tracking its storm centre. It is known that an area situated in the tropics experiences
predominantly convective precipitation which is an active component of the tropical
weather system (Hastenrath, 1991). Two features of storm which receive wide
attention from researchers are the velocity and direction of storm cells movement. It
was found that storm velocities and directions may change seasonally
(Niemczynowicz and Dahlblom 1984; Chaudry et. al., 1994). The movement and
intensity of convective storm are important for predicting the magnitude and location
of flash flood (Doswell et. al., 1996). This section attempts to find out indicators or
predictors that govern the movement of convective storms. In this analysis, four
flash flood events that occurred in the Klang Valley were chosen. The corresponding
storms that caused flash floods exhibited strong convective characters. Radar images
were used to perform this analysis. Figures 4.14, 4.15, 4.16 and 4.17 illustrate the
storm movement for these events.
Pascual et al., (2004) used 30 to 45 dBZ to differentiate convective from
stratiform precipitation. On the other hand, Rigo and Llasat (2002) used 43 dBZ to
analyse convective event derived from meteorological radar. In Korean Peninsular,
Dong and Hyung (2000) used 35 dBZ in their study on heavy rainfall with mesoscale
convective systems. In this study a value of 35 dBZ was taken as reflectivity
threshold to identify convective rainfall from radar images.
This value also
corresponds with the radar’s scale, thus ease the reading of reflectivity according to
radar’s colour code. The highest reflectivity (> 35 dBZ) was chosen as the centre of
storm. The storm centre was used to track the movement of the storms (Figures 4.14,
4.15, 4.16 and 4.17). The coordinates of storm movement were then plotted in
Malaysia’s RSO (Rectified Skew Ortomorphic) which is a coordinate system in GIS
(ArcGIS 9.1). Tables 4.12 and 4.13 present the coordinates of the storm centre and
the corresponding reflectivity values. For storm on January 6, 2006, the storm centre
developed at 18:03 hr with reflectivity of 65 dBZ (90 mm/hr). This storm exhibited
decreasing reflectivity as it move from northeast to southwest (Figure 4.14). It took
65 minutes to travel 32.14 km. The storm on February 26, 2006 moved from
northwest to southeast and the storm centre at 03:39 hr is shown in Figure 4.15. The
75
storm duration was 1 hour and 16 minutes and it travelled for 46 km. Initially, the
reflectivity was 65 dBZ and decreased to 35 dBZ when the storm ceased.
Storm on January 6, 2006
N
50
200
100
Rainfall rate in mm/hr
80
50
20
10
8
6
4
Legend
2
1
0.
0.
= centre of the storm
= arrow of storm
movement
0.
Figure 4.14 : Storm movement on January 6, 2006
For the other two storms, their durations were very short, only 20 to 30
minutes and over short paths. As such it is difficult to determine the centre of these
storms. Both storms travelled for about 17.7 km and 14 km, respectively. Figures
4.16 and 4.17 show the movement of very strong convective storms on April 6 and
May 10, 2006. The storm centre coordinates and their reflectivity are presented in
Table 4.13.
In short the analysis suggests that a storm can move on a single path or
multiple paths. The duration of this movement range from 20 minutes to 1 hour
when the centres of the storms disappeared. Sometime, the evolution of the storm
centre is difficult to predict especially for short duration storms. This is because the
centre of the storm can immerge and disappeared almost abruptly. At the same time
new strong convective storms can be formed. Beside that, it is observed that the
storm movement for short duration was very limited. The highest intensity at the
storm centre was 80 dBZ (100 mm/hr) for events on April 6, and May 10, 2006.
76
Storm on February 26, 2006
50
N
200
100
80
Rainfall rate in mm/hr
50
Figure 4.12 : Storm movement on January 6, 2006
20
10
8
6
4
2
Legend
1
= centre of the storm
= arrow of storm
movement
0.
0.
0.
Figure 4.15 : Storm movement on February 26, 2006
Table 4.12 : The coordinates and intensity of storm centres on 6.01.2006 and
6.02.2006
No
Time
1
2
3
4
5
6
7
8
9
10
11
12
13
18:03
18:09
18:14
18:30
18:36
18:47
18:52
19:08
6-Jan-06
Coordinate Coordinate
dBZ mm/hr Time
x
y
403611.86 366344.86 65
90
3:39
395780.33 364193.73 65
90
3:50
394085.73 363303.39 50
80
3:55
393554.94 359183.38 50
80
4:06
392603.98 356918.98 35
65
4:11
391620.26 346201.21 35
65
4:17
387676.04 340387.28 35
65
4:22
381964.49 332887.73 35
65
4:28
4:33
4:38
4:44
4:49
4:55
26-Feb-06
Coordinate Coordinate
dBZ mm/hr
x
y
363432.7 371967.6
65
90
366902.1 367303.8
65
90
370233.0 364128.4
65
90
371106.8 360999.8
65
90
372464.8 358668.4
35
65
374450.8 357020.6
35
65
379764.0 355024.8
35
65
383585.9 353876.2
35
65
387431.4 351956.7
35
65
395388.3 349947.7
35
65
398607.4 348651.6
35
65
400997.3 347367.0
35
65
405145.4 343049.8
35
65
77
Table 4.13 : The coordinates and intensity of storm centres on 6.04.2006 and
10.05.2006
No Time
1
2
3
4
5
6
15:46
15:51
15:57
16:02
16:08
16:13
6-Apr-06
10-May-06
Coordinate Coordinate
Coordinate Coordinate
dBZ mm/hr Time
dBZ mm/hr
x
y
x
y
408014.4 354555.7 80
100 14:39 407001.2 357150.4 80
100
403815.7 351078.0 65
90
14:45 406613.6 357002.2 80
100
403583.0 350619.2 65
90
14:50 406296.3 349207.7 65
90
405663.6 349146.6 35
65
15:01 403297.0 349818.1 65
90
409915.8 345370.8 50
80
409608.4 343723.8 35
65
Storm on April 6, 2006
N
500
200
100
80
Rainfall rate in mm/hr
50
20
10
8
6
4
Legend
2
1
0.8
0.6
= centre of the storm
= arrow of storm
movement
0.4
Figure 4.16 : Storm movement on April 6, 2006
Overall, there is no specific pattern on the four storm movements studied in
this section. There are possibilities that wind direction influenced the movement of
the rain bearing clouds, hence resulting in ambiguous patterns.
78
Storm on May 10, 2006
N
50
200
100
80
Rainfall rate in mm/hr
50
20
10
8
6
4
Legend
2
1
0.
1501
0.6
= centre of the storm
= arrow of storm movement
= time
0.4
Figure 4.17 : Storm movement on May 10, 2006
4.5.5
Depth-Area Relationship
In order to obtain information on the size of rainfall cell and areal volume
distribution during a single event, depth-area relationships were derived.
This
analysis focused on a smaller area using eleven raingauges which cover 241.34 km2.
The areas between isohyet intervals of the six selected storms were computed by
ArcGIS 9.1 (Figure 4.18). As shown, four of the storms, i.e. on January 6, 2006,
February 26, 2006, May 10, 2006 and November 5, 2004 have the highest rainfall
depth at the southwest and decrease as the storm move to northeast. However, the
storms on April 6, 2006 and June 10, 2003 have no clear direction of rainfall depth.
Only 11 raingauges have rainfall values. Table 4.14 depicts the values of areal
reduction factor (ARF) for each event. The percentages reduction of rainfall depth
are plotted against the cumulative area from
79
06.04.2006
06.01.2006
26.02.2006
10.05.2006
05.11.2004
10.06.2003
Rainfall depth increase
Figure 4.18 : Spatial variation of rainfall depth (mm) for six selected storms
the storm centre (Figure 4.19).
The shapes of the areal reduction curves were
different between storms. An average curve for all the six storms was also drawn.
Despite the large differences in the depth area curve patterns, the graph generally
80
show that total rainfall depth decreases as the area increases.
This finding is
consistent with the property of convective events in section 4.5.1 where the highest
intensity covers a small fraction of the area.
From the curves plotted, it seems that the ARF values are quite consistent.
The average curve found from this study was superimposed with ARF curves derived
by Desa (1997), Niemczynowicz (1984) for Lund in Sweden and by Shaw (1989) in
the United Kingdom. In a small urban area (23 km2) in Kuala Lumpur region, Desa
(1997) found a lower average of ARF curve than the average ARF curve of this
study. This might be due to different catchment size (23 km2). From Figure 4.20, it
can be noticed that the area reduction curve derived from this study is quite similar
with those derived for Malaysia by Yan and Lin (1986) for 1 hour event.
Nevertheless, Yan and Lin (1986) used data with poorer resolution: 0.5 mm per
tipping bucket with on a weekly chart recorder. But the raingauge density was
better, 23 raingauges over 200km2 compared 11 raingauges over 241.34 km2 for this
study.
81
Table 4.14 : Areal reduction factors (ARF) values for each event
10-Jun-03
05-Nov-04
6-Jan-06
26-Feb-06
6-Apr-06
10-May-06
Catchment
Area (km2)
ARF
values
Catchment
Area (km2)
ARF
values
Catchment
Area (km2)
ARF
values
Catchment
Area (km2)
ARF
values
Catchment
Area (km2)
ARF
values
Catchment
Area (km2)
ARF
values
0.02
0.02
1.27
25.62
102.97
183.56
219.9
239.31
241.34
241.34
0.95
0.95
0.76
0.66
0.58
0.52
0.49
0.48
0.47
0.47
0.02
11.03
24.81
46.44
88.02
124.23
156.27
191.11
236.86
241.34
0.98
0.88
0.82
0.75
0.66
0.61
0.56
0.50
0.44
0.43
6.32
12.87
20.01
33.82
55.52
81.74
110.37
141.97
176.35
241.34
0.96
0.91
0.86
0.78
0.69
0.62
0.55
0.48
0.42
0.32
19.7
56.19
81.05
101.97
133.79
174.18
218.03
238.63
241.06
241.34
0.98
0.92
0.87
0.83
0.77
0.70
0.63
0.60
0.59
0.59
0.02
1.52
15.22
51.02
90.81
164.29
221.67
240.14
241.33
241.34
0.96
0.86
0.77
0.69
0.63
0.55
0.50
0.48
0.48
0.48
19.22
34.28
77.90
112.99
138.70
163.76
188.37
203.47
214.84
241.34
0.95
0.91
0.82
0.77
0.73
0.68
0.64
0.61
0.59
0.53
82
Percentage reduction (%) of storm depth
100
90
equation for average curve,
y = -6.46x + 100
80
06.1.06
70
26.02.06
60
06.04.06
50
10.05.06
40
10.06.03
05.11.04
30
average
20
10
0
0
25
50
75
100
125
150
175
2
Cumulative catchment area (km )
200
225
250
Figure 4.19 : Depth-area relationships for six selected storms
Average ARF for this study
Figure 4.20 : Comparison of depth-area curves obtained in this study and at other
location
83
4.6 IDF Relationship
In this section, the frequencies of short duration convective rain for low return
period are analysed. The purpose of this analysis is to determine the frequency of
convective events with different duration for low return period and compare the result
with the existing IDF curve developed by the Department of Irrigation and Drainage,
(DID) Malaysia. Again the 5 years rainfall data from station 3117070 was used to assess
the IDF relationship for low return period. The selected durations dj ranges from 5
minutes to 60 minutes (i.e. j = 5 min, 15 min, 30 min and 60 min). The highest intensity
for every rainfall event is selected for each duration, where 35 mm/hr is chosen as a
threshold value to differentiate between convective and non-convective events. The
three parameter Generalized Pareto (3P-GPA) distribution was selected as probability
distribution for the frequency analysis.
The method of L-moments was used for
estimating parameters of the GPA probability distribution.
The one step least square method, discussed in Chapter 3 is aimed at solving
Equation 2.10 by means of minimising the total error (e) used in the embedded
optimization procedure in MS Excel. Using the derived design rainfall intensity of the
raingauge, and the Gringorten plotting position; the functions of a(T) and b(d) in
Equation 2.10 were simultaneously calculated which resulted in a minimum error e of
0.5728.
The IDF relationship is in the form of Equation 4.1 below and this
generalization of IDF parameters is relatively simple to apply to estimate the design
rainstorm (Koutsoyiannis et al., 1998).
69.1698T 0.0660
I=
(d + 0.6022) 0.6833
Equation 4.1
The design rainfall intensity at low ARI corresponding to T = 0.5, 1, 2, 3, 6 and 12
month is tabulated in Table 4.15. Figure 4.21 shows the IDF relationship for station
3117070- JPS Ampang. From the graph, it can be seen that short duration storms have
84
higher intensities for all return periods. For example the intensities for the 5 minute
storm exceed 100mm/hr for return periods of more than one month.
Table 4.15 : Summary of the design rainfall intensity for convective storm at station
3117070 JPS Ampang
Duration
(hr)
0.083
0.25
0.5
1
Design rainfall intensity (mm/hr) corresponding to return
period, T (month)
0.5
1
2
3
6
12
89.70
106.60
123.40
133.00
150.00
166.90
65.00
79.40
93.00
101.70
115.80
129.88
50.28
61.44
72.60
79.14
90.30
101.46
33.04
40.78
48.53
53.06
60.80
68.54
Rainfall Intensity Duration Frequency Curve Station
3117070 JPS Am pang, Selangor
Rainfall Intensity (mm/hr)
1000.00
Re turn
Pe riod
(month)
100.00
0.5
1
2
10.00
3
6
12
1.00
0.083
0.25
0.5
1
Duration (hr)
Figure 4.21 : The new IDF curve for station 3117070- JPS Ampang developed from
convective storm data
Figure 4.22 gives the IDF relationship produced by the Department of Irrigation and
Drainage Malaysia (DID) for the same station (JPS Ampang). Peak over threshold
(POT) series was used in the building of these IDF curves using arbitrary threshold
values. A visual comparison of the curves in Figure 4.21 and Figure 4.22 reveals very
close resemblance of the shape of the curves as well as the intensity values for all return
periods. As mentioned earlier, the curves derived in this study used threshold values
>35mm to denote convective processes whilst the curves by DID used some arbitrary
85
threshold values of POT series. Due to this, the similarity is fitting. A more detailed
look at the intensity values in Table 4.17 reveals slightly higher intensities from the
convective storms compared to the POT series for all return periods. The outcome could
have been different had DID used extreme value series for its IDF curves. However, at
this juncture it could be concluded that IDF curves obtained using POT series would
account for convective processes and are appropriate for estimating design storms for
areas experiencing high occurrence of convective events. A more comprehensive study
is warranted to further verify these findings. All calculations are shown in Appendix E.
Rainfall Intensity Duration Frequency Curve
S tation 3117070 - JPS Ampang
1000.00
Rainfall intensity (mm/hr)
Return
Period
(month)
100.00
1
2
3
6
12
10.00
I=
69.1727T 0.2488
(d + 0.1918) 0.8374
1.00
0.25
0.5
1
Duration (hr)
Figure 4.22 : DID’s curve for station 3117070
86
Table 4.16 : Summary of the design rainfall intensity for station 3117070 taken from
DID (using POT series)
Duration
(hr)
0.25
0.5
1
Design rainfall intensity (mm/hr) corresponding to
return period, T (month)
1
2
3
6
12
73.90
87.80
97.10
115.40
137.10
50.80
60.30
66.70
79.30
94.20
32.20
38.20
42.30
50.30
59.70
Table 4.17 : Summary of the design rainfall intensity for convective storms and POT
series (DID’s curve) at station 3117070
Design rainfall intensity (mm/hr) corresponding to return period, T (month)
Duration
1
2
3
6
12
(hr) POT Conv. POT Conv. POT Conv. POT Conv. POT Conv.
0.25 73.90 79.40 87.80 93.00 97.10 101.70 115.40 115.80 137.10 129.88
0.5
50.80
61.44
60.30
72.60
66.70
79.14
79.30
90.30
94.20
101.46
1
32.20
40.78
38.20
48.53
42.30
53.06
50.30
60.80
59.70
68.54
CHAPTER V
CONCLUSION AND RECOMMENDATION
5.1
Introduction
This chapter emphasises the important findings of the study. Management
implications that arise from the analysis are also highlighted. Research
recommendations to improve the present study are discussed towards the end of this
chapter.
5.2
Assessment of Objectives
Knowledge of temporal and spatial characteristics of tropical storms is still
lacking for effective engineering design and planning. This is so especially for
convective storm which has been associated with the occurrences of major flash
floods in many urban areas. It is imminent that extreme weather events such as more
intense rain, longer dry spells and rapid changes in global temperature make tropical
weather more difficult to predict.
Of particular importance is properties of
convective storms which have strong influence on flash flood. This study makes a
contribution to these needs by providing a greater understanding of convective rain
behaviors. By integrating results of temporal and spatial distribution in term of
intensity, rainfall depth and area of rainfall, the characteristics of convective rain
were examined.
88
5.2.1
Characteristics of Convective Rain Based on Short Rainfall Duration
Data
The diurnal and monthly distribution of rainfall (greater than 5mm) at a
selected station was discussed in Chapter IV. The results show that the bulk of the
rains fall in the afternoon, between 13:00 and 19:00hr which makes up about 75% of
the total rainfall.
A Minimum Interevent Time (MIT) of 3 hours was used to
separate storm events.
Convective rain occurred most frequently in the
intermonsoon months (especially in November) which made up about 44% of the
storms. This is due to light variable winds and unstable atmosphere which favor
strong convective activity. This results in thunderstorms and heavy rains especially
in the late afternoons and early evenings.
Over five years, the highest 5 minutes rainfall intensity was 384 mm/hr
recorded in 2003. These characteristics were discussed in Chapter IV where a great
variety of storm shape is evident and the patterns show that most of the convective
events occurred over short durations, ranging from 15 to 90 minutes.
5.2.2
Classification of Convective Events
A classification of episodes based on β parameter was discussed in Chapter
IV. This classification is according to their greater or lesser convective character
(Llasat, 2001). The classification of the convective storm into slightly, moderately
and strongly convective indicates that the highest proportion is for the moderately
convective class, which makes up 63.8% of the total convective events. It seems that
a 35 mm/hr threshold intensity is appropriate for separating convective from non
convective storms for local conditions. However, this analysis needs to be replicated
to cover more rainfall stations.
89
5.2.3
Comparison between Radar and Ground Rainfall
Comparison of spatial distribution between radar and surface rainfall was
carried out in terms of intensity, areal coverage, storm movements and depth-area
relationship.
The intensity values between raingauge and radar show large
differences. The main difficulty in determining the Z-R (with Z in mm6/m3 and R in
mm/hr) relationship arises from the fact that radar measures precipitation in the
atmosphere while gauges measure it at the ground.
Winds may also carry
precipitation away from beneath the producing cloud.
As for the storm intensity, out of four storms, only one showed reasonably
good match in the contour patterns between radar and raingauge. This might be due
to inadequate number of raingauge and also missing data which limit the ability of
Kriging method.
The areal rainfall for each interval of isohyets between radar and surface
rainfall was compared using ArcGIS software. The ground rainfall data produced
remarkably different areal rainfall for various intervals of isohyets.
The areal
distributions derived from radar and those from raingauge are poorly correlated.
Overall, the areas of each interval derived from raingauge are bigger than those
derived from radar.
5.2.4
Depth Area Relationship and IDF Curve
Each storm is unique in term of the movement of the storm cell. Some have
long paths while others are circling within a limited path.
Depth-area relationships of six storms were examined. Each storm display
quite different areal reduction curve.
However, in general the rainfall depth
decreases with increasing catchment area. The ARF curve was compared with the
ARFs from other areas. The present study found quite similar ARF values with those
90
obtained by Yan and Lin (1986). The ARF values derived from smaller areas are
different from this study. Therefore, the shapes of such curves can only be compared
if the temporal and spatial resolutions of the measurements are similar.
The
agreement between the relationships derived for convective storms cells in Klang
Valley and the entire Peninsular Malaysia (Yan and Lin, 1986) can be explained in
term of similarity in the climatic conditions.
The frequencies of short duration convective storms and short duration of all
storms for low return period were analysed and their IDF curves were plotted. The
new IDF curve (greater than 35 mm/hr) generally produces higher rainfall intensity
for storms having similar duration and return period. But the IDF curve developed
using all data produces lower rainfall intensity when compared with the existing
DID’s IDF curve. Overall, a visual comparison of the curves reveals very close
resemblance of the shape of the curves as well as the intensity values for all return
periods. It could be concluded that the IDF curves obtained using POT series would
account for convective processes and are more appropriate as design storms for areas
experiencing high occurrence of convective events.
5.3 Research Recommendations
This research focused on two major aspects: 1) characterization of convective
rain and 2) spatial variation of convective rainfall derived from radar data and
surface data. Prior to this study, the approach used to characterize and compare
spatial variations between radar and surface rainfall data has not been tested in the
tropics.
In order to improve future studies, the following research areas are
suggested:
i)
this study used one station to characterize convective rain. Future studies
shall use more rainfall stations to examine whether such characteristic vary
with space;
ii)
the density of rainfall stations need to be increased to give a better
interpolation in Kriging Method. This is because kriging works best when
the input point is large and vice versa when the number of point is small;
91
iii)
the influence of wind direction and wind velocity need to be checked in
evaluating the storm movement;
iv)
most of the storm movements have no clear storm path. In the future, more
images need to be analysed (say 30 pictures) to give a better tracking of storm
movement; and
v)
the difficulties to interpret radar rainfall intensity from JPEG file need to be
checked to prevent overestimation or underestimation of rainfall intensity
values. This might be solved using a program to interpret the coding output
from radar software or execute a projection using GIS method.
92
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APPENDIX A
PROCESS OF DIGITIZING RADAR IMAGE
Radar image
Klang Valley map
Figure A1 : Radar images were first rectified with Klang Valley map
100
Figure A2 : Digitizing radar image for intensity 80 – 100 mm/hr (red layer)
Figure A3 : Digitizing radar image for intensity 35 – 80 mm/hr (orange layer)
101
Figure A4 : Digitizing radar image for intensity 8 – 35 mm/hr (yellow layer)
Figure A5 : Digitizing radar image for intensity 3 – 8 mm/hr (green layer)
102
Figure A6 : Digitizing radar image for intensity 0.9 – 3 mm/hr (dark green layer)
Figure A7 : Digitizing radar image for intensity 0.5 – 0.9 mm/hr (dark blue layer)
103
Figure A8 : Digitizing radar image for intensity 0.3 – 0.5 mm/hr (blue layer)
Figure A9 : Union process (merged all layers)
104
Figure A10 : Digitized image
105
APPENDIX B
STEPS TO DERIVE RAINFALL CONTOURS BY KRIGING METHOD
USING GEOSTATISTICAL ANALYST
Figure B1 : Choose input data and method
106
Figure B2 : Geostatistical method selection
Figure B3 : Semivariogram / Covariance modeling
107
Figure B4 : Searching neighborhood
Figure B5 : Cross validation
108
Figure B6 : Output layer information
Figure B7 : Rainfall contour derived from Kriging
109
APPENDIX C
STEPS FOR DEVELOPING AREAL REDUCTION CURVE
Event on January 6, 2006
110
Percentage reduction (%) of storm depth (event on January 6, 2006)
1
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighboring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(32 + 36)/2 = 34
6.32 + 6.55 = 12.87
[(38 x 6.32) + (34 x 12.87)] / 12.87 = 36
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(28 + 32) /2 = 30
6.32 + 6.55 + 7.14 = 20.01
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01)] / 20.01 = 33.8
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(24 + 28 ) /2 = 26
6.32 + 6.55 + 7.14 + 13.81 = 33.82
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82)] / 33.82 = 30.6
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(20 + 24) /2 = 22
6.32 + 6.55 + 7.14 + 13.81 + 21.7 = 55.52
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52)] / 55.52 = 27.3
6
Average between isohyet
Total Areas between isohyet
(16 + 20 )/2 = 18
6.32 + 6.55 + 7.14 + 13.81 + 1.7 + 26.22 = 81.74
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52) + (18 x 81.74)] /
81.74 = 24.3
2
Mean Area Precipitation, (MAP)
(36 + 40 ) / 2= 38
6.32+ 0 = 6.32
(38 x 6.32)/6.32 = 38
111
7
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(12 + 16 )/2 = 14
6.32 + 6.55 + 7.14 + 13.81 + 21.7 + 26.22 + 28.63 = 110.37
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52) + (18 x 81.74) +
(14 x 110.37)] / 110.37 = 21.6
(8 + 12 ) /2= 10
6.32 + 6.55 + 7.14 + 13.81 + 21.7 + 26.22 + 28.63 + 31.6 = 141.97
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52) + (18 x 81.74) +
(14 x 110.37) + (10 x 141.97)] / 141.97 = 19.0
(4 + 8) /2 = 6
6.32 + 6.55 + 7.14 + 13.81 + 21.7 + 26.22 + 28.63 + 31.6 + 34.38 = 176.35
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52) + (18 x 81.74) +
(14 x 110.37) + (10 x 141.97) + (6 x 176.35)] / 176.35 = 16.5
(0 + 4 ) /2= 2
6.32 + 6.55 + 7.14 + 13.81 + 21.7 + 26.22 + 28.63 + 31.6 + 34.38 + 64.99 =
241.34
[(38 x 6.32) + (34 x 12.87) + (30 x 20.01) + (26x33.82) + (22x 55.52) + (18 x 81.74) +
(14 x 110.37) + (10 x 141.97) + (6 x 176.35) + (2 x 241.34)] / 241.34 = 12.6
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
38 / 39.5 * 100
36 / 39.5 * 100
33.8 / 39.5 * 100
30.6 / 39.5 * 100
27.3 / 39.5 * 100
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 39.5 mm
Percentage reduction (%) of storm depth
= 96.2 %
6 24.3 / 39.5 * 100
= 91 %
7 21.6 / 39.5 * 100
= 85.7 %
8 19.0 / 39.5 * 100
= 77.6 %
9 16.5 / 39.5 * 100
= 69 %
10 12.6 / 39.5 * 100
=
=
=
=
=
61.5%
54.7 %
48.2 %
41.8 %
31.9 %
112
Event on April 6, 2006
113
Percentage reduction (%) of storm depth (event on April 6, 2006
1
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighbouring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(28.8 + 32.4) / 2 = 30.6
0.02 + 1.50 = 1.52
[(34.2 x 0.02) + (30.6 x 1.52)] / 1.52 = 30.6
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(25.2 + 28.8 ) / 2 = 27
0.02 + 1.50 + 13.7 = 15.22
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22)] / 15.22 = 27.4
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(21.6 + 25.2) / 2 = 23.4
0.02 + 1.50 + 13.7 + 35.8 = 51.02
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02)] / 51.02 = 24.6
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
6
Average between isohyet
Total Areas between isohyet
(18 + 21.6) /2 = 19.8
0.02 + 1.50 + 13.7 + 35.8 + 39.79 = 90.81
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)] / 90.81 =
22.5
(14.4 + 18) / 2 = 16.2
0.02 + 1.50 + 13.7 + 35.8 + 39.79 + 73.48 = 164.29
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)+ (16.2 x
164.29)] / 164.29 = 19.7
2
Mean Area Precipitation, (MAP)
(32.4 + 36) /2 = 34.2
0.02 + 0 = 0.02
(34.2 x 0.02)/0.02 = 34.2
114
7
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(10.8 + 14.4 )/2 = 12.6
0.02 + 1.50 + 13.7 + 35.8 + 39.79 + 73.48 + 57.38 = 221.67
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)+ (16.2 x
164.29) + (12.6 x 221.67)]/ 221.67 = 17.8
(7.2 + 10.8 ) /2 = 9
0.02 + 1.50 + 13.7 + 35.8 + 39.79 + 73.48 + 57.38 + 18.47 = 240.14
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)+ (16.2 x
164.29) + (12.6 x 221.67) + (9 x 240.14)] / 240.14 = 17.2
(3.6 + 7.2) /2 = 5.4
0.02 + 1.50 + 13.7 + 35.8 + 39.79 + 73.48 + 57.38 + 18.47 + 1.19 = 241.33
[(34.2 x 0.02) + (30.6 x 1.52+ (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)+ (16.2 x
164.29) + (12.6 x 221.67) + (9 x 240.14) + (5.4 x 241.33)] / 241.33 = 17.1
(0 + 3.6) /2 = 1.8
0.02 + 1.50 + 13.7 + 35.8 + 39.79 + 73.48 + 57.38 + 18.47 + 1.19 + 0 =
241.33
[(34.2 x 0.02) + (30.6 x 1.52) + (27 x 15.22) + (23.4 x 51.02) + (19.8 x 90.81)+ (16.2 x
164.29) + (12.6 x 221.67) + (9 x 240.14) + (5.4 x 241.33) + (1.8 x 241.34)] / 241.33 =
17.1
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
34.2 / 35.5 * 100
30.6 / 35.5 * 100
27.4 / 35.5 * 100
24.6 / 35.5 * 100
22.5 / 35.5 * 100
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 35.5 mm
Percentage reduction (%) of storm depth
= 96.3 %
6
19.7 / 35.5 * 100
= 86.3 %
7
17.8 / 35.5 * 100
= 77.1 %
8
17.2 / 35.5 * 100
= 69.2 %
9
17.1 / 35.5 * 100
= 63.3 %
10 17.1 / 35.5 * 100
=
=
=
=
=
55.4%
50.3 %
48.3 %
48.2 %
48.2 %
115
Event on May 10, 2006
116
Percentage reduction (%) of storm depth (event on May 10, 2006)
1
2
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighbouring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(72.9 + 81 )/2 = 76.95
19.22 + 0 = 19.22
(76.95 x 19.22)/ 19.22 = 76.95
(64.8 + 72.9)/2 = 68.85
19.22 + 15.06 = 34.28
[(76.95 x 19.22) + (68.85 x 34.28)] / 34.28 = 73.4
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(56.7 + 64.8) /2 = 60.75
19.22 + 15.06+ 43.62 = 77.9
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9)] / 77.9 = 66.3
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(48.6 + 56.7 )/2 = 52.65
19.22 + 15.06+ 43.62 + 35.09 = 112.99
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99)] / 112.99 = 62.1
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
6
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
7
Average between isohyet
(40.5 + 48.6)/2 = 44.55
19.22 + 15.06+ 43.62 + 35.09 + 25.71 = 138.7
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7)] /
138.7 = 58.8
(32.4 + 40.5)/2 = 36.45
19.22 + 15.06+ 43.62 + 35.09 + 25.71 + 25.06 = 163.76
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7))+
(36.45 x 163.76)] / 163.76 = 55.4
(24.3 + 32.4)/2 = 28.35
117
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
19.22 + 15.06+ 43.62 + 35.09 + 25.71 + 25.06+ 24.61 = 188.37
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7))+
(36.45 x 163.76) + (28.35 x 188.37)]/ 188.37 = 51.9
(16.2 + 24.3 )/2 = 20.25
19.22 + 15.06+ 43.62 + 35.09 + 25.71 + 25.06+ 24.61 + 15.1 = 203.47
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7))+
(36.45 x 163.76) + (28.35 x 188.37) + (20.25 x 203.47)] / 203.47 = 49.5
(8.1 + 16.2 )/2 = 12.15
19.22 + 15.06+ 43.62 + 35.09 + 25.71 + 25.06+ 24.61 + 15.1 + 11.37 = 214.84
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7))+
(36.45 x 163.76) + (28.35 x 188.37) + (20.25 x 203.47) + (12.15 x 214.84)] / 214.84 =
47.5
(0 + 8.1)/2 = 8.1
19.22 + 15.06+ 43.62 + 35.09 + 25.71 + 25.06+ 24.61 + 15.1 + 11.37 + 26.51 =
241.35
[(76.95 x 19.22) + (68.85 x 34.28) + (60.75 x 77.9) + (52.65 x 112.99) + (44.55 x 138.7))+
(36.45 x 163.76) + (28.35 x 188.37) + (20.25 x 203.47) + (12.15 x 214.84+ (8.1 x 241.35)]
/ 241.35 = 42.8
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 81.0 mm
Percentage reduction (%) of storm depth
76.95 / 81.0 * 100 = 95.0 %
6
55.4 / 81.0 * 100
73.4 / 81.0 * 100 = 90.6 %
7
51.9 / 81.0 * 100
66.3 / 81.0 * 100 = 81.9 %
8
49.5 / 81.0 * 100
62.1 / 81.0 * 100 = 76.6 %
9
47.5 / 81.0 * 100
58.8 / 81.0 * 100 = 72.6 %
10 42.8 / 81.0 * 100
=
=
=
=
=
68.4%
64.0 %
61.1 %
58.7 %
52.8 %
118
Percentage reduction (%) of storm depth (event on June 10, 2003)
1
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighbouring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(104 + 117)/2 = 110.5
0.02 + 0 = 0.02
[(123.5 x 0.02) + (110.5 x 0.02)] / 0.02 = 123.5
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(91 + 106)/2 = 98.5
0.02 + 0 + 1.25 = 1.27
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27)] / 1.27 = 98.9
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(78 + 91 ) /2 = 84.5
0.02 + 0 + 1.25+ 24.35 = 25.62
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62)] / 25.62 = 85.2
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
6
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
7
Average between isohyet
(65 + 78 ) /2 = 71.5
0.02 + 0 + 1.25+ 24.35 + 77.35 = 102.97
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)] / 102.97
= 74.9
(52 + 65 )/2 = 58.5
0.02 + 0 + 1.25+ 24.35 + 77.35 + 80.59 = 183.56
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56)] / 183.56 = 67.7
(39 + 52)/2 = 45.5
2
(117 + 130)/2 = 123.5
0.02
(123.5 x 0.02) / 0.02 = 123.5
119
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
0.02 + 0 + 1.25+ 24.35 + 77.35 + 80.59 + 36.34 = 219.9
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)]/ 219.9 = 64.0
(26 + 39)/2 = 32.5
0.02 + 0 + 1.25+ 24.35 + 77.35 + 80.59 + 36.34 + 19.41 = 239.31
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (32.5 x 239.31)] / 239.31 = 61.5
(13 + 26) /2 = 19.5
0.02 + 0 + 1.25+ 24.35 + 77.35 + 80.59 + 36.34 + 19.41 + 2.06 = 241.37
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (32.5 x 239.31) + (19.5x 241.37)] / 241.37= 61.1
(0 + 13)/2 = 6.5
0.02 + 0 + 1.25+ 24.35 + 77.35 + 80.59 + 36.34 + 19.41 + 2.06 + 0 = 241.37
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (32.5 x 239.31) + (19.5x 241.37) + (6.5 x 241.37)] / 241.37 =
61.1
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 129.5 mm
Percentage reduction (%) of storm depth
123.5 / 129.5 * 100 = 95.4 %
6
67.7 / 129.5 * 100
123.5 / 129.5 * 100 = 95.4 %
7
64.0 / 129.5 * 100
98.9 / 129.5 * 100 = 76.4 %
8
61.5 / 129.5 * 100
85.2 / 129.5 * 100 = 65.8 %
9
61.1 / 129.5 * 100
74.9 / 129.5 * 100 = 57.8 %
10 61.1 / 129.5 * 100
=
=
=
=
=
52.3 %
49.4 %
47.5 %
47.2 %
47.2 %
120
Percentage reduction (%) of storm depth (event on February, 26 2006)
1
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighbouring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(60 + 67.5)/2 = 110.5
19.7 + 36.49 = 56.19
[(71.25 x 19.7)) + (110.5 x 56.19)] / 56.19 = 66.4
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(52.5 + 60)/2 = 56.25
19.7 + 36.49 + 24.86 = 81.05
[(71.25 x 19.7)) + (110.5 x 56.19)+ (56.25 x 81.05)] / 81.05 = 63.3
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(45 + 52.5 ) /2 = 48.75
19.7 + 36.49 + 24.86 + 20.92 = 101.97
[(71.25 x 19.7)) + (110.5 x 56.19)+ (56.25 x 81.05) + (48.75 x 101.97)] / 101.97 = 60.3
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
6
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
7
Average between isohyet
(37.5 + 45 ) /2 = 41.25
19.7 + 36.49 + 24.86 + 20.92 + 31.82 = 133.79
[(71.25 x 19.7)) + (110.5 x 56.19)+ (56.25 x 81.05) + (48.75 x 101.97)+ (41.25 x 133.79)] /
133.79 = 55.8
(30 + 37.5 )/2 = 33.75
19.7 + 36.49 + 24.86 + 20.92 + 31.82 + 40.39 = 174.18
[(71.25 x 19.7)) + (110.5 x 56.19)+ (56.25 x 81.05) + (48.75 x 101.97)+ (41.25 x 133.79)+
(33.75 x 174.18)] / 174.18 = 50.7
(22.5 + 30)/2 = 26.25
2
(67.5 + 75)/2 = 71.25
19.7
(71.25 x 19.7) / 19.7 = 71.25
121
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
19.7 + 36.49 + 24.86 + 20.92 + 31.82 + 40.39 + 43.85 = 218.03
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)]/ 219.9 = 64.0
(15 + 22.5)/2 = 18.75
19.7 + 36.49 + 24.86 + 20.92 + 31.82 + 40.39 + 43.85 + 20.6 = 238.63
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (18.75 x 238.63)] / 238.63 = 43.4
(7.5 + 15) /2 = 11.25
19.7 + 36.49 + 24.86 + 20.92 + 31.82 + 40.39 + 43.85 + 20.6 + 2.43 = 241.06
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (18.75 x 238.63)+ (11.25x 241.06)] / 241.06 = 43.1
(0 + 7.5) / 2 = 3.75
19.7 + 36.49 + 24.86 + 20.92 + 31.82 + 40.39 + 43.85 + 20.6 + 2.43 + 0.28 =
241.34
[(123.5 x 0.02) + (110.5 x 0.02) + (98.5 x 1.27) + (84.5 x 25.62) + (71.5 x 102.97)+ (58.5 x
183.56) + (219.9 x 45.5)+ (18.75 x 238.63)+ (11.25x 241.06)+ (3.75 x 241.34)] / 241.34 =
43.0
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 72.5 mm
Percentage reduction (%) of storm depth
71.25 / 72.5 * 100 = 98.3 %
6
50.7 / 72.5 * 100 = 69.9 %
66.4 / 72.5 * 100 = 91.6 %
7
45.8 / 72.5 * 100 = 63.1 %
63.3 / 72.5 * 100 = 87.3 %
8
43.4 / 72.5 * 100 = 59.9 %
60.3 / 72.5 * 100 = 83.2 %
9
43.1 / 72.5 * 100 = 59.4 %
55.8 / 72.5 * 100 = 76.9 %
10 43 / 72.5 * 100 = 59.4 %
122
Percentage reduction (%) of storm depth (event on November 5, 2004)
1
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation,
( MAP) = (average between
isohyet x area between isohyet) /
total areas between all pairs of
neighbouring isohyets
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(85.5 + 95)/2 = 90.25
0.02
3
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(66.5 + 76)/2 = 71.25
0.02 + 11.01 + 13.78 = 24.81
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81)] / 24.81 = 75.5
4
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
(57 + 66.5 ) /2 = 61.75
0.02 + 11.01 + 13.78 + 21.63 = 46.44
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)] / 46.44 = 69.1
5
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
6
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
7
Average between isohyet
(47.5 + 57 ) /2 = 52.25
0.02 + 11.01 + 13.78 + 21.63 + 41.58 = 88.02
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)] /
88.02 = 61.1
(38 + 47.5 )/2 = 42.75
0.02 + 11.01 + 13.78 + 21.63 + 41.58 + 36.41 = 124.23
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)+
(22.75 x 124.23)] / 124.23 = 55.8
(28.5 + 38)/2 = 33.25
2
(85.5 x 0.02) / 0.02 = 90.25
(76 + 85.5)/2 = 80.75
0.02 + 11.01 = 11.03
[(85.5 x 0.02) + (80.75 x 11.03)] / 11.03 = 80.8
123
Total Areas between isohyet
Mean Area Precipitation, (MAP)
8
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
9
Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
10 Average between isohyet
Total Areas between isohyet
Mean Area Precipitation, (MAP)
0.02 + 11.01 + 13.78 + 21.63 + 41.58 + 36.41 + 32.04 = 156.27
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)+
(22.75 x 124.23) + (33.25 x 156.27)]/ 156.27 = 51.2
(19 + 28.5)/2 = 23.75
0.02 + 11.01 + 13.78 + 21.63 + 41.58 + 36.41 + 32.04 + 34.84 = 191.11
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)+
(22.75 x 124.23) + (33.25 x 156.27)+ (23.75 x 191.11)] / 191.11 = 46.2
(9.5 + 19) /2 = 12.25
0.02 + 11.01 + 13.78 + 21.63 + 41.58 + 36.41 + 32.04 + 34.84 + 45.75 = 236.86
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)+
(22.75 x 124.23) + (33.25 x 156.27)+ (23.75 x 191.11)+ (12.25x 236.86)] / 236.86 = 40.0
(0 + 9.5) / 2 = 4.75
0.02 + 11.01 + 13.78 + 21.63 + 41.58 + 36.41 + 32.04 + 34.84 + 45.75 + 4.5 =
241.36
[(85.5 x 0.02) + (80.75 x 11.03)+ (71.25 x 24.81) + (61.75 x 46.44)+ (52.25x 88.02)+
(22.75 x 124.23) + (33.25 x 156.27)+ (23.75 x 191.11)+ (12.25x 236.86)+ (4.75 x 241.36)]
/ 241.36 = 39.3
Percentage reduction (%) of storm depth
storm maximum (reference gauge)
No.
1
2
3
4
5
= (Mean Area Precipitation, (MAP) / storm maximum)* 100
= 92 mm
Percentage reduction (%) of storm depth
90.25 / 92* 100 = 98.1 %
6
55.8 / 92* 100 =
80.8 / 92* 100 = 87.8 %
7
51.2 / 92* 100 =
75.5 / 92* 100 = 82.0 %
8
46.2 / 92* 100 =
69.1 / 92* 100 = 75.1 %
9
40.0 / 92* 100 =
61.1 / 92* 100 = 66.4 %
10 39.3 / 92* 100 =
60.6 %
55.6 %
50.2 %
43.5 %
42.8 %
124
APPENDIX D
STEPS TO SUMMARIZE DIURNAL AND MONTHLY DISTRIBUTIONS OF
RAINFALL
125
Jan 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time(hr)
Total
Rainfall
14.4
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0
0
0
0
0
14.4
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
126
Feb 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Time
(hr)
Total
Rainfall
5.6
2
12.5
27
14
5.4
19.2
0.4
2.9
9.5
10.5
20.2
39.8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25.8
59.7
66.2
14
2.9
0
0
0
0
127
Mac 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time (hr)
Total
Rainfall
17.7
1.3
1.8
11
1.5
0.3
0.3
3.5
3.2
1
1.3
4.2
0.9
1
0.5
0.6
0.4
0.3
17.6
1.1
0.7
1
2.4
1.2
9.2
15
18
6.3
19
33.7
20
21
29.9
38
35.5
0
0.3
4.5
0.2
1
2
3
4
5
6
7
8
5.1
9
0
1
0
0
1
1.3
7.4
1
6.4
10
11
12
13
14
15
16
5
17
0
0
0
0
1.3
0.8
1.2
28.9
22
0.8
1
23
24
0.2
1.8
0
128
April 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
16
24
24
6.5
35
8.5
1.1
2.6
1.9
16.8
1.8
9.6
10.7
3.5
18.3
1.8
23.1
0.2
6.3
0.2
0.9
2.4
0.5
39
11
25.4
2.4
6.5
0.1
1.1
5.4
5.9
1.8
2.9
4.7
0.7
2.7
1.1
4.2
3.1
1
2.5
0.1
5.3
9
14.3
7
1.6
1.2
0.9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0
0
0
0
0
0
0
0
0
12.5
8.8
76.2
27
67.1
44
104
17.7
5.2
7.8
4.2
1
129
May 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
5
14
0.7
3.6
1.5
3.4
0.4
0.5
1.6
0.1
0.4
0.4
17.7
13.6
11
5
1.5
0.9
2.2
0.5
0.5
9.6
0.7
0.3
1.6
6.5
0.8
23.4
65.9
12.1
23.5
1.7
44
3.8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1.6
2.2
0.5
0
0
0.5
0
0
0
0
0
5
0.8
23.4
66.6
16
19
31.4
60
6.4
17.2
26.9
0.5
0
130
Jun 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
0.5
1.1
2.8
2.8
0.1
0.6
3
2.8
0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0
0
0
0
0
0
3.9
2.9
0
0
0
0
3.6
2.8
0.9
0
0
0
0
0
0
131
July 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
1.1
2.9
0.3
2
1.2
2.1
0.4
8.1
0.4
0.9
7.1
2.4
0.8
4.5
2.5
1.6
1.2
4.1
1.2
2.9
14.7
6
8.9
2.4
0.9
3.7
0.1
13
0.7
31
25.4
2
1.2
0.5
33.3
3.5
11.4
0.5
0.4
1.4
8
0.5
7
6.8
2.2
8
4.1
12.1
0.3
2.1
1.5
5.7
0.3
15.4
2.7
4.7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1.9
5.3
16
8.1
16.9
21.2
9.4
5.7
5.5
1.5
0
0
8.9
14.7
23.5
37
67.7
28.9
3.9
0.5
0.4
7.1
3.3
2.8
132
August 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
1.5
33
0.1
7.9
2.3
0.3
2.9
7.5
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0.1
2.9
0
1.5
0
0
0
0
0
0
2
33
15.4
2.3
0.3
0
0
0
0
0
0
133
Sept 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
11.5
0.9
1.1
0.5
0.4
2.1
0.7
0.1
30.6
1.1
31.1
2
2.9
5.7
0.3
17.9
0.4
48
4.6
1.8
28.1
1.4
1
9.8
5.4
18.2
16.1
3
7.2
0.3
0.1
2.1
1.2
0.2
1
0.8
2.4
0.4
0.6
11.3
0.5
0.1
9.9
6.1
0.5
8.8
0.6
4
0.5
0.5
8.6
3.2
1.5
0.6
17
0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0.5
0
1.8
0
0
8.6
8.8
0
1
0
0
0
28.4
25
47.2
15.6
79.4
28.5
70
14.9
4.7
2
0
0.1
134
Oct 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
0.4
0.6
1.3
3.5
45.8
15.1
26.9
0.3
49.4
1.9
0.7
41
0.8
4.2
13
19.8
1.6
0.5
0.5
2.4
18.3
9.6
0.7
13.4
26.6
0.8
6
25
1.9
5.2
2.2
3.1
2.1
2
0.8
6
0.6
1
4.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0.5
0
0
0
0
0
0
0.5
0.8
0
0
0.7
13.4
1
28.5
49
92
69.6
61
27.3
8
5.2
2
0.8
135
Nov 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
2.9
25
10
9.8
0.7
3
0.3
0.5
5.9
12.9
5.3
0.8
0.2
6.1
11.3
0.2
6.6
0.4
6
0.6
0.2
1.6
0.5
0.7
0.6
54
0.4
5
0.6
2.8
1.6
15.6
0.5
3.8
0.2
26.5
30.3
4.1
3.2
30
4.2
31
4.7
0.4
7.4
3.3
11
12.4
13.7
4.7
10.8
0.9
3
28
0.1
1
2.9
3.3
2.5
1.6
1.2
1
54.1
0.7
13.6
1.1
10.1
10.5
6.6
0.4
3
28.4
0.5
8
1.9
0.2
0.4
6
0.5
0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0.7
52
10
9.8
3.7
0.3
0
0
0.5
0
0.5
0.5
5.9
86.7
52.5
33.8
34.4
44.8
132
67.7
28.4
9.5
8.3
3.7
136
Dec 2004
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Time
(hr)
Total
Rainfall
(mm)
3.6
1.5
1.7
0.8
12
2
1.6
4
2.4
0.2
4.6
3.2
0.9
0.5
46.5
0.5
0.5
1.3
3.5
0.5
0.2
0.4
0.6
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
0
0
0
0
5.1
1.7
0.8
0
0
0
0
0
0
0
0
2.7
9.7
7.7
16
46.9
0.5
1.3
0
0.6
137
Table D1 : Diurnal and monthly distributions of rainfall (greater than 5 mm) in 2004 at station JPS Ampang
Total rainfall at each time of day in each month (2004)
J
0
0
0
0
0
0
0
0
14.4
0
0
0
0
F
0
0
0
0
0
0
0
0
0
0
0
0
0
M
0
1
0
0
1
1.3
7.4
1
6.4
0
0
0
0
0
0
0
0
0
0
0
25.8
59.7
66.2
1.3
0.8
1.2
28.9
29.9
16
0
0
14
2.9
0
38
35.5
0
0
0
0
0
0
0
0.2
1.8
0
A
0
0
0
0
0
0
0
0
0
0
0
0
12.5
8.8
76.2
27
67.1
44
104
17.7
5.2
7.8
4.2
1
M
1.6
2.2
0.5
0
0
0.5
0
0
0
0
0
5
0.8
23.4
66.6
16
19
31.4
60
6.4
17.2
26.9
0.5
0
J
0
0
0
0
0
0
0
0
0
3.9
2.9
0
0
0
0
3.6
2.8
0.9
0
0
0
0
0
0
J
1.9
5.3
16
8.1
16.9
21.2
9.4
5.7
5.5
1.5
0
0
8.9
14.7
23.5
37
67.7
28.9
3.9
0.5
0.4
7.1
3.3
2.8
A
0
0
0
0.1
2.9
0
1.5
0
0
0
0
0
0
2
33
15.4
2.3
0.3
0
0
0
0
0
0
S
0.5
0
1.8
0
0
8.6
8.8
0
1
0
0
0
28.4
25
47.2
15.6
79.4
28.5
70
14.9
4.7
2
0
0.1
O
0.5
0
0
0
0
0
0
0.5
0.8
0
0
0.7
13.4
1
28.5
49
92
69.6
61
27.3
8
5.2
2
0.8
N
0.7
52
10
9.8
3.7
0.3
0
0
0.5
0
0.5
0.5
5.9
86.7
52.5
33.8
34.4
44.8
132
67.7
28.4
9.5
8.3
3.7
D
0
0
0
0
5.1
1.7
0.8
0
0
0
0
0
0
0
0
2.7
9.7
7.7
16
46.9
0.5
1.3
0
0.6
Time
(hr)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
138
550
500
Precipitation (mm)
450
400
350
300
250
200
150
100
50
0
> 45
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
J
F
40 - 45
M
35 - 40
A
30 - 35
25 - 30
M
J
20 - 25
J
15 - 20
A
S
10 - 15
5 -10
O
N
<5
D
0
3
6
9
12
Local Time (h)
15
18
21
24
0
50
100 150 200 250 300 350 400 450 500 550 600
Pr eci pi tati on (mm)
Figure D1: Summary of diurnal and monthly distributions of rainfall at station JPS Ampang
139
APPENDIX E
STEPS TO DEVELOP IDF RELATIONSHIP
140
Generalized Pareto Distribution (GPD) in IDF Relationship Using Probability
Weighted Moments (PWM’s) at Station 3117070 – JPS Ampang
5 minutes data
Rank
i
1
2
3
PD
Rainfall
Xi (mm)
6.1
6.3
6.3
Fi=(i0.44)/
N+0.12
0.0037
0.0104
0.0171
Yi = -ln(1Fi)
Fi=(i0.35)/N
XiFi
XiFi2
0.0037
0.0104
0.0172
0.0043
0.0110
0.0177
0.0264
0.0693
0.1113
0.000115
0.000762
0.001966
4
6.3
0.0237
0.0240
0.0243
0.1533
0.003730
5
6.4
0.0304
0.0308
0.0310
0.1984
0.006150
6
7
8
9
10
11
6.4
6.4
6.4
6.4
6.4
6.4
0.0370
0.0437
0.0504
0.0570
0.0637
0.0703
0.0377
0.0447
0.0517
0.0587
0.0658
0.0729
0.0377
0.0443
0.0510
0.0577
0.0643
0.0710
0.2411
0.2837
0.3264
0.3691
0.4117
0.4544
0.009080
0.012579
0.016646
0.021283
0.026488
0.032262
12
6.4
0.0770
0.0801
0.0777
0.4971
0.038606
13
6.5
0.0837
0.0874
0.0843
0.5482
0.046229
14
15
6.5
6.6
0.0903
0.0970
0.0947
0.1020
0.0910
0.0977
0.5915
0.6446
0.053827
0.062956
16
6.6
0.1037
0.1094
0.1043
0.6886
0.071844
17
18
19
20
21
22
23
24
25
26
27
28
29
30
6.7
6.7
6.8
6.8
6.8
6.8
6.9
7
7
7
7
7
7
7
0.1103
0.1170
0.1236
0.1303
0.1370
0.1436
0.1503
0.1569
0.1636
0.1703
0.1769
0.1836
0.1902
0.1969
0.1169
0.1244
0.1320
0.1396
0.1473
0.1550
0.1628
0.1707
0.1787
0.1866
0.1947
0.2028
0.2110
0.2193
0.1110
0.1177
0.1243
0.1310
0.1377
0.1443
0.1510
0.1577
0.1643
0.1710
0.1777
0.1843
0.1910
0.1977
0.7437
0.7884
0.8455
0.8908
0.9361
0.9815
1.0419
1.1037
1.1503
1.1970
1.2437
1.2903
1.3370
1.3837
0.082551
0.092764
0.105120
0.116695
0.128874
0.141658
0.157327
0.174011
0.189038
0.204687
0.220958
0.237851
0.255367
0.273505
31
7.1
0.2036
0.2276
0.2043
1.4508
0.296440
32
7.1
0.2102
0.2360
0.2110
1.4981
0.316099
33
34
35
36
37
38
39
7.2
7.2
7.2
7.3
7.3
7.3
7.3
0.2169
0.2236
0.2302
0.2369
0.2435
0.2502
0.2569
0.2445
0.2530
0.2616
0.2703
0.2791
0.2879
0.2969
0.2177
0.2243
0.2310
0.2377
0.2443
0.2510
0.2577
1.5672
1.6152
1.6632
1.7350
1.7836
1.8323
1.8810
0.341127
0.362343
0.384199
0.412344
0.435801
0.459907
0.484662
40
7.3
0.2635
0.3059
0.2643
1.9296
0.510066
41
42
7.4
7.4
0.2702
0.2768
0.3150
0.3241
0.2710
0.2777
2.0054
2.0547
0.543463
0.570531
141
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
7.4
7.4
7.4
7.4
7.4
7.4
7.5
7.5
7.7
7.7
7.8
7.9
7.9
7.9
7.9
7.9
8
8.1
8.2
8.2
8.2
8.4
8.5
8.5
8.8
8.9
9
9
9.2
9.3
9.3
9.4
9.4
9.5
9.5
9.5
9.6
9.6
9.7
9.9
10
10
10
10
10
10
10.1
10.1
10.2
10.3
10.3
10.3
10.3
10.3
0.2835
0.2902
0.2968
0.3035
0.3102
0.3168
0.3235
0.3301
0.3368
0.3435
0.3501
0.3568
0.3634
0.3701
0.3768
0.3834
0.3901
0.3967
0.4034
0.4101
0.4167
0.4234
0.4301
0.4367
0.4434
0.4500
0.4567
0.4634
0.4700
0.4767
0.4833
0.4900
0.4967
0.5033
0.5100
0.5167
0.5233
0.5300
0.5366
0.5433
0.5500
0.5566
0.5633
0.5699
0.5766
0.5833
0.5899
0.5966
0.6033
0.6099
0.6166
0.6232
0.6299
0.6366
0.3334
0.3427
0.3522
0.3617
0.3713
0.3810
0.3908
0.4007
0.4107
0.4208
0.4310
0.4413
0.4517
0.4622
0.4728
0.4836
0.4944
0.5054
0.5165
0.5278
0.5391
0.5506
0.5622
0.5740
0.5859
0.5979
0.6101
0.6224
0.6349
0.6476
0.6604
0.6734
0.6865
0.6998
0.7133
0.7270
0.7409
0.7550
0.7692
0.7837
0.7984
0.8133
0.8285
0.8438
0.8595
0.8753
0.8914
0.9078
0.9245
0.9414
0.9586
0.9761
0.9940
1.0121
0.2843
0.2910
0.2977
0.3043
0.3110
0.3177
0.3243
0.3310
0.3377
0.3443
0.3510
0.3577
0.3643
0.3710
0.3777
0.3843
0.3910
0.3977
0.4043
0.4110
0.4177
0.4243
0.4310
0.4377
0.4443
0.4510
0.4577
0.4643
0.4710
0.4777
0.4843
0.4910
0.4977
0.5043
0.5110
0.5177
0.5243
0.5310
0.5377
0.5443
0.5510
0.5577
0.5643
0.5710
0.5777
0.5843
0.5910
0.5977
0.6043
0.6110
0.6177
0.6243
0.6310
0.6377
2.1041
2.1534
2.2027
2.2521
2.3014
2.3507
2.4325
2.4825
2.6000
2.6514
2.7378
2.8256
2.8782
2.9309
2.9836
3.0362
3.1280
3.2211
3.3155
3.3702
3.4249
3.5644
3.6635
3.7202
3.9101
4.0139
4.1190
4.1790
4.3332
4.4423
4.5043
4.6154
4.6781
4.7912
4.8545
4.9178
5.0336
5.0976
5.2154
5.3889
5.5100
5.5767
5.6433
5.7100
5.7767
5.8433
5.9691
6.0364
6.1642
6.2933
6.3620
6.4306
6.4993
6.5680
0.598256
0.626639
0.655680
0.685379
0.715735
0.746750
0.788941
0.821708
0.877945
0.912954
0.960968
1.010611
1.048636
1.087364
1.126794
1.166926
1.223048
1.280924
1.340581
1.385152
1.430453
1.512494
1.578969
1.628193
1.737403
1.810269
1.885129
1.940449
2.040937
2.121939
2.181583
2.266161
2.328118
2.416345
2.480650
2.545798
2.639284
2.706826
2.804129
2.933358
3.036010
3.109921
3.184721
3.260410
3.336988
3.414454
3.527738
3.607775
3.725232
3.845206
3.929575
4.014859
4.101058
4.188173
142
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
10.3
10.4
10.5
10.6
10.6
10.6
10.7
10.8
10.9
11.1
11.1
11.2
11.4
11.5
11.5
11.5
11.6
11.6
11.6
11.7
11.7
11.8
11.9
11.9
12
12.1
12.3
12.3
12.3
12.4
12.4
12.4
12.4
12.6
13.4
13.5
13.7
13.8
13.9
14.7
14.7
15.1
15.2
18.4
18.8
19
19.1
19.1
20.4
20.8
22.6
24.1
30.5
32
0.6432
0.6499
0.6565
0.6632
0.6699
0.6765
0.6832
0.6898
0.6965
0.7032
0.7098
0.7165
0.7232
0.7298
0.7365
0.7431
0.7498
0.7565
0.7631
0.7698
0.7764
0.7831
0.7898
0.7964
0.8031
0.8098
0.8164
0.8231
0.8297
0.8364
0.8431
0.8497
0.8564
0.8630
0.8697
0.8764
0.8830
0.8897
0.8963
0.9030
0.9097
0.9163
0.9230
0.9297
0.9363
0.9430
0.9496
0.9563
0.9630
0.9696
0.9763
0.9829
0.9896
0.9963
1.0306
1.0495
1.0687
1.0883
1.1083
1.1286
1.1494
1.1707
1.1924
1.2146
1.2373
1.2605
1.2843
1.3087
1.3336
1.3592
1.3855
1.4125
1.4402
1.4687
1.4981
1.5284
1.5595
1.5917
1.6250
1.6594
1.6951
1.7320
1.7704
1.8103
1.8519
1.8953
1.9406
1.9881
2.0379
2.0904
2.1458
2.2044
2.2667
2.3332
2.4043
2.4809
2.5639
2.6544
2.7538
2.8643
2.9886
3.1304
3.2958
3.4941
3.7417
4.0714
4.5667
5.5913
0.6443
0.6510
0.6577
0.6643
0.6710
0.6777
0.6843
0.6910
0.6977
0.7043
0.7110
0.7177
0.7243
0.7310
0.7377
0.7443
0.7510
0.7577
0.7643
0.7710
0.7777
0.7843
0.7910
0.7977
0.8043
0.8110
0.8177
0.8243
0.8310
0.8377
0.8443
0.8510
0.8577
0.8643
0.8710
0.8777
0.8843
0.8910
0.8977
0.9043
0.9110
0.9177
0.9243
0.9310
0.9377
0.9443
0.9510
0.9577
0.9643
0.9710
0.9777
0.9843
0.9910
0.9977
6.6366
6.7704
6.9055
7.0419
7.1126
7.1833
7.3224
7.4628
7.6046
7.8181
7.8921
8.0379
8.2574
8.4065
8.4832
8.5598
8.7116
8.7889
8.8663
9.0207
9.0987
9.2551
9.4129
9.4922
9.6520
9.8131
10.0573
10.1393
10.2213
10.3871
10.4697
10.5524
10.6351
10.8906
11.6714
11.8485
12.1154
12.2958
12.4776
13.2937
13.3917
13.8568
14.0499
17.1304
17.6281
17.9423
18.1641
18.2914
19.6724
20.1968
22.0953
23.7224
30.2255
31.9253
4.276204
4.407530
4.541517
4.678191
4.772555
4.867860
5.010940
5.156795
5.305453
5.506548
5.611283
5.768509
5.981110
6.145152
6.257749
6.371369
6.542412
6.659082
6.776783
6.954960
7.075756
7.259110
7.445604
7.571638
7.763425
7.958424
8.223519
8.358163
8.493900
8.700900
8.839945
8.980092
9.121342
9.413109
10.165789
10.399034
10.714023
10.955558
11.200696
12.021936
12.199839
12.715893
12.986760
15.948402
16.529313
16.943543
17.274059
17.517096
18.970751
19.611093
21.601806
23.350782
29.953471
31.850841
143
M100
M110
10.5
6.1000
4.532941
M120
Generalized Pareto Distribution
Generalized Pareto Distribution
(GPA)
κ
(9M120-10M110+2M100)/(2M110-3M120)
-0.56938
β
(2M110-M100)(K+1)(K+2)
1.047278
Xο
λ
M100 - [β/(1+K)]
8.067953
1.89
XT
XT
Xo + β [1-exp(-KYT]/K
Xo + β [1-(1-F)K]/K
Cumulative Distribution Function (cdf) and Quantile
T
(month)
0.5
1
2
3
6
12
T(AM)
year
T(POT)
year
0.041667
0.083333
0.166667
0.25
0.5
1
CDF
Fi
-11.6984127
-5.349206349
-2.174603175
-1.116402116
-0.058201058
0.470899471
Std. Exp
Yi
-2.54148
-1.84833
-1.15518
-0.74972
-0.05657
0.636577
Xi
(mm)
6.661348
6.870733
7.181438
7.428871
8.009652
8.871468
Design rainfall intensity (mm/hr) for 5 minutes
data
Duration
(hr)
0.083
Design rainfall intensity (mm/hr) corresponding to return period, T
(month)
0.5
1
2
3
6
12
79.97
82.48
86.21
89.18
96.15
106.50
144
15 minutes data
Rank
i
1
2
3
PD
Rainfall
Xi (mm)
12.5
12.5
12.5
Fi=(i0.44)/
N+0.12
0.0037
0.0104
0.0171
Yi = -ln(1Fi)
Fi=(i0.35)/N
XiFi
XiFi2
0.0037
0.0104
0.0172
0.0043
0.0110
0.0177
0.0542
0.1375
0.2208
0.000235
0.001513
0.003901
4
12.5
0.0237
0.0240
0.0243
0.3042
0.007401
5
12.8
0.0304
0.0308
0.0310
0.3968
0.012301
6
7
8
9
10
11
12.8
12.8
12.9
13
13.3
13.4
0.0370
0.0437
0.0504
0.0570
0.0637
0.0703
0.0377
0.0447
0.0517
0.0587
0.0658
0.0729
0.0377
0.0443
0.0510
0.0577
0.0643
0.0710
0.4821
0.5675
0.6579
0.7497
0.8556
0.9514
0.018160
0.025158
0.033553
0.043231
0.055046
0.067549
12
13.4
0.0770
0.0801
0.0777
1.0407
0.080830
13
13.5
0.0837
0.0874
0.0843
1.1385
0.096014
14
15
13.5
13.5
0.0903
0.0970
0.0947
0.1020
0.0910
0.0977
1.2285
1.3185
0.111794
0.128774
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
13.5
13.7
13.9
13.9
13.9
14
14
14.1
14.1
14.1
14.1
14.3
14.4
14.6
14.8
14.8
0.1037
0.1103
0.1170
0.1236
0.1303
0.1370
0.1436
0.1503
0.1569
0.1636
0.1703
0.1769
0.1836
0.1902
0.1969
0.2036
0.1094
0.1169
0.1244
0.1320
0.1396
0.1473
0.1550
0.1628
0.1707
0.1787
0.1866
0.1947
0.2028
0.2110
0.2193
0.2276
0.1043
0.1110
0.1177
0.1243
0.1310
0.1377
0.1443
0.1510
0.1577
0.1643
0.1710
0.1777
0.1843
0.1910
0.1977
0.2043
1.4085
1.5207
1.6356
1.7282
1.8209
1.9273
2.0207
2.1291
2.2231
2.3171
2.4111
2.5406
2.6544
2.7886
2.9255
3.0241
0.146954
0.168798
0.192452
0.214877
0.238538
0.265330
0.291650
0.321494
0.350509
0.380777
0.412298
0.451386
0.489294
0.532623
0.578267
0.617931
32
14.8
0.2102
0.2360
0.2110
3.1228
0.658911
33
14.9
0.2169
0.2445
0.2177
3.2432
0.705944
34
35
36
37
38
39
15.3
15.5
15.5
15.5
15.6
15.6
0.2236
0.2302
0.2369
0.2435
0.2502
0.2569
0.2530
0.2616
0.2703
0.2791
0.2879
0.2969
0.2243
0.2310
0.2377
0.2443
0.2510
0.2577
3.4323
3.5805
3.6838
3.7872
3.9156
4.0196
0.769979
0.827096
0.875524
0.925331
0.982816
1.035717
40
15.7
0.2635
0.3059
0.2643
4.1500
1.096992
41
42
43
16
16
16
0.2702
0.2768
0.2835
0.3150
0.3241
0.3334
0.2710
0.2777
0.2843
4.3360
4.4427
4.5493
1.175056
1.233580
1.293527
44
45
16.1
16.1
0.2902
0.2968
0.3427
0.3522
0.2910
0.2977
4.6851
4.7924
1.363364
1.426548
145
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
16.3
16.3
16.4
16.4
16.4
16.5
16.5
16.7
16.7
16.8
16.8
16.9
17
17.2
17.3
17.3
17.4
17.5
17.6
17.7
17.8
17.8
18
18.1
18.2
18.3
18.5
18.7
18.7
18.9
19.4
19.7
20.1
20.2
20.5
20.6
20.7
20.7
21.2
21.4
21.5
21.6
21.6
21.7
21.7
21.7
21.7
21.8
21.8
22.3
22.4
22.6
22.6
22.8
0.3035
0.3102
0.3168
0.3235
0.3301
0.3368
0.3435
0.3501
0.3568
0.3634
0.3701
0.3768
0.3834
0.3901
0.3967
0.4034
0.4101
0.4167
0.4234
0.4301
0.4367
0.4434
0.4500
0.4567
0.4634
0.4700
0.4767
0.4833
0.4900
0.4967
0.5033
0.5100
0.5167
0.5233
0.5300
0.5366
0.5433
0.5500
0.5566
0.5633
0.5699
0.5766
0.5833
0.5899
0.5966
0.6033
0.6099
0.6166
0.6232
0.6299
0.6366
0.6432
0.6499
0.6565
0.3617
0.3713
0.3810
0.3908
0.4007
0.4107
0.4208
0.4310
0.4413
0.4517
0.4622
0.4728
0.4836
0.4944
0.5054
0.5165
0.5278
0.5391
0.5506
0.5622
0.5740
0.5859
0.5979
0.6101
0.6224
0.6349
0.6476
0.6604
0.6734
0.6865
0.6998
0.7133
0.7270
0.7409
0.7550
0.7692
0.7837
0.7984
0.8133
0.8285
0.8438
0.8595
0.8753
0.8914
0.9078
0.9245
0.9414
0.9586
0.9761
0.9940
1.0121
1.0306
1.0495
1.0687
0.3043
0.3110
0.3177
0.3243
0.3310
0.3377
0.3443
0.3510
0.3577
0.3643
0.3710
0.3777
0.3843
0.3910
0.3977
0.4043
0.4110
0.4177
0.4243
0.4310
0.4377
0.4443
0.4510
0.4577
0.4643
0.4710
0.4777
0.4843
0.4910
0.4977
0.5043
0.5110
0.5177
0.5243
0.5310
0.5377
0.5443
0.5510
0.5577
0.5643
0.5710
0.5777
0.5843
0.5910
0.5977
0.6043
0.6110
0.6177
0.6243
0.6310
0.6377
0.6443
0.6510
0.6577
4.9606
5.0693
5.2097
5.3191
5.4284
5.5715
5.6815
5.8617
5.9730
6.1208
6.2328
6.3826
6.5337
6.7252
6.8796
6.9950
7.1514
7.3092
7.4683
7.6287
7.7905
7.9091
8.1180
8.2838
8.4509
8.6193
8.8368
9.0570
9.1817
9.4059
9.7841
10.0667
10.4051
10.5915
10.8855
11.0759
11.2677
11.4057
11.8225
12.0767
12.2765
12.4776
12.6216
12.8247
12.9694
13.1140
13.2587
13.4651
13.6105
14.0713
14.2837
14.5619
14.7126
14.9948
1.509686
1.576552
1.654959
1.725151
1.796800
1.881310
1.956330
2.057457
2.136355
2.230011
2.312369
2.410483
2.511106
2.629553
2.735801
2.828298
2.939225
3.052795
3.169034
3.287970
3.409628
3.514292
3.661218
3.791204
3.924019
4.059690
4.221061
4.386623
4.508215
4.681003
4.934431
5.144084
5.386373
5.553494
5.780201
5.955160
6.133385
6.284541
6.593033
6.815303
7.009882
7.207894
7.375222
7.579398
7.751358
7.925247
8.101066
8.316964
8.497468
8.878990
9.108261
9.382739
9.577903
9.861580
146
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
M100
M110
M120
23
23
23
23.1
23.3
23.5
23.7
23.8
23.9
23.9
24
24.2
24.6
24.7
24.7
25
25
25.3
25.4
25.7
25.8
26
26
26.2
26.5
26.5
26.8
26.9
26.9
27.1
28.9
29.4
29.4
29.5
29.6
29.7
29.7
30.1
30.2
30.3
30.4
31.2
31.7
32.4
32.8
33.3
33.3
33.7
35.7
37.1
58.5
21.5
0.6632
0.6699
0.6765
0.6832
0.6898
0.6965
0.7032
0.7098
0.7165
0.7232
0.7298
0.7365
0.7431
0.7498
0.7565
0.7631
0.7698
0.7764
0.7831
0.7898
0.7964
0.8031
0.8098
0.8164
0.8231
0.8297
0.8364
0.8431
0.8497
0.8564
0.8630
0.8697
0.8764
0.8830
0.8897
0.8963
0.9030
0.9097
0.9163
0.9230
0.9297
0.9363
0.9430
0.9496
0.9563
0.9630
0.9696
0.9763
0.9829
0.9896
0.9963
1.0883
1.1083
1.1286
1.1494
1.1707
1.1924
1.2146
1.2373
1.2605
1.2843
1.3087
1.3336
1.3592
1.3855
1.4125
1.4402
1.4687
1.4981
1.5284
1.5595
1.5917
1.6250
1.6594
1.6951
1.7320
1.7704
1.8103
1.8519
1.8953
1.9406
1.9881
2.0379
2.0904
2.1458
2.2044
2.2667
2.3332
2.4043
2.4809
2.5639
2.6544
2.7538
2.8643
2.9886
3.1304
3.2958
3.4941
3.7417
4.0714
4.5667
5.5913
0.6643
0.6710
0.6777
0.6843
0.6910
0.6977
0.7043
0.7110
0.7177
0.7243
0.7310
0.7377
0.7443
0.7510
0.7577
0.7643
0.7710
0.7777
0.7843
0.7910
0.7977
0.8043
0.8110
0.8177
0.8243
0.8310
0.8377
0.8443
0.8510
0.8577
0.8643
0.8710
0.8777
0.8843
0.8910
0.8977
0.9043
0.9110
0.9177
0.9243
0.9310
0.9377
0.9443
0.9510
0.9577
0.9643
0.9710
0.9777
0.9843
0.9910
0.9977
15.2797
15.4330
15.5863
15.8081
16.1003
16.3952
16.6927
16.9218
17.1522
17.3116
17.5440
17.8515
18.3106
18.5497
18.7144
19.1083
19.2750
19.6750
19.9221
20.3287
20.5798
20.9127
21.0860
21.4229
21.8448
22.0215
22.4495
22.7126
22.8919
23.2428
24.9792
25.6074
25.8034
26.0878
26.3736
26.6607
26.8587
27.4211
27.7135
28.0073
28.3024
29.2552
29.9354
30.8124
31.4115
32.1123
32.3343
32.9474
35.1407
36.7661
58.3635
10.150792
10.355543
10.562339
10.818010
11.125307
11.438361
11.757225
12.031400
12.309586
12.539345
12.824664
13.168481
13.629190
13.930825
14.179252
14.605136
14.861025
15.300566
15.625541
16.080002
16.415820
16.820755
17.100746
17.516764
18.007424
18.299867
18.805170
19.176977
19.481007
19.934546
21.590384
22.304045
22.646784
23.070341
23.498878
23.932422
24.289218
24.980622
25.431786
25.888081
26.349534
27.431626
28.268965
29.302592
30.081715
30.966961
31.396605
32.211542
34.590162
36.435205
58.227319
12.1581
8.827784
147
Generalized Pareto Distribution
Generalized Pareto Distribution
(GPA)
κ
(9M120-10M110+2M100)/(2M110-3M120)
β
(2M110-M100)(K+1)(K+2)
Xο
λ
M100 - [β/(1+K)]
XT
XT
Xo + β [1-exp(-KYT]/K
Xo + β [1-(1-F)K]/K
-0.40095
2.69773
16.99669
1.89
Cumulative Distribution Function (cdf) and Quantile
T
(month)
0.5
1
2
3
6
12
T(AM)
year
T(POT)
year
0.041667
0.083333
0.166667
0.25
0.5
1
CDF
Fi
-11.6984127
-5.349206349
-2.174603175
-1.116402116
-0.058201058
0.470899471
Std. Exp
Yi
-2.54148
-1.84833
-1.15518
-0.74972
-0.05657
0.636577
Xi
(mm)
12.69694
13.47503
14.50239
15.24984
16.8458
18.95306
Design rainfall intensity (mm/hr) for15 minutes data
Duration
(hr)
0.25
Design rainfall intensity (mm/hr) corresponding to return period, T
(month)
0.5
50.79
1
53.90
2
58.01
3
61.00
6
67.38
12
75.81
148
30 minutes data
Rank
i
1
2
3
PD
Rainfall
Xi (mm)
17.6
17.7
17.7
Fi=(i0.44)/
N+0.12
0.0037
0.0104
0.0171
Yi = -ln(1Fi)
Fi=(i0.35)/N
XiFi
XiFi2
0.0037
0.0104
0.0172
0.0043
0.0110
0.0177
0.0763
0.1947
0.3127
0.000330
0.002142
0.005524
4
17.7
0.0237
0.0240
0.0243
0.4307
0.010480
5
18
0.0304
0.0308
0.0310
0.5580
0.017298
6
7
8
9
10
11
18
18
18.5
18.5
18.5
18.5
0.0370
0.0437
0.0504
0.0570
0.0637
0.0703
0.0377
0.0447
0.0517
0.0587
0.0658
0.0729
0.0377
0.0443
0.0510
0.0577
0.0643
0.0710
0.6780
0.7980
0.9435
1.0668
1.1902
1.3135
0.025538
0.035378
0.048119
0.061521
0.076567
0.093259
12
18.6
0.0770
0.0801
0.0777
1.4446
0.112197
13
18.8
0.0837
0.0874
0.0843
1.5855
0.133708
14
15
19.2
19.4
0.0903
0.0970
0.0947
0.1020
0.0910
0.0977
1.7472
1.8947
0.158995
0.185052
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
19.5
19.8
20
20.3
20.6
20.7
21
21.1
21.1
21.3
21.3
21.5
21.5
21.6
21.7
21.8
0.1037
0.1103
0.1170
0.1236
0.1303
0.1370
0.1436
0.1503
0.1569
0.1636
0.1703
0.1769
0.1836
0.1902
0.1969
0.2036
0.1094
0.1169
0.1244
0.1320
0.1396
0.1473
0.1550
0.1628
0.1707
0.1787
0.1866
0.1947
0.2028
0.2110
0.2193
0.2276
0.1043
0.1110
0.1177
0.1243
0.1310
0.1377
0.1443
0.1510
0.1577
0.1643
0.1710
0.1777
0.1843
0.1910
0.1977
0.2043
2.0345
2.1978
2.3533
2.5240
2.6986
2.8497
3.0310
3.1861
3.3268
3.5003
3.6423
3.8198
3.9632
4.1256
4.2894
4.4545
0.212266
0.243956
0.276909
0.313813
0.353517
0.392309
0.437474
0.481101
0.524520
0.575216
0.622833
0.678657
0.730544
0.787990
0.847865
0.910196
32
22
0.2102
0.2360
0.2110
4.6420
0.979462
33
22.3
0.2169
0.2445
0.2177
4.8540
1.056547
34
35
36
37
38
39
22.4
22.8
22.8
22.9
22.9
23.2
0.2236
0.2302
0.2369
0.2435
0.2502
0.2569
0.2530
0.2616
0.2703
0.2791
0.2879
0.2969
0.2243
0.2310
0.2377
0.2443
0.2510
0.2577
5.0251
5.2668
5.4188
5.5952
5.7479
5.9779
1.127290
1.216631
1.287868
1.367102
1.442723
1.540297
40
23.2
0.2635
0.3059
0.2643
6.1325
1.621033
41
42
43
23.4
23.4
23.5
0.2702
0.2768
0.2835
0.3150
0.3241
0.3334
0.2710
0.2777
0.2843
6.3414
6.4974
6.6818
1.718519
1.804111
1.899868
44
45
23.5
23.6
0.2902
0.2968
0.3427
0.3522
0.2910
0.2977
6.8385
7.0249
1.990004
2.091088
149
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
23.7
23.9
23.9
24
24
24.2
24.2
24.2
24.4
24.5
25
25.5
25.9
25.9
26.1
26.2
26.3
26.7
26.9
27
27
27.4
27.5
27.5
27.5
27.5
27.6
27.6
27.7
28
28
28.1
28.1
28.1
28.1
28.4
28.5
28.7
28.9
30
30.4
30.5
30.5
30.8
31.5
31.7
31.8
31.9
32.2
32.4
32.5
32.6
33.1
33.2
0.3035
0.3102
0.3168
0.3235
0.3301
0.3368
0.3435
0.3501
0.3568
0.3634
0.3701
0.3768
0.3834
0.3901
0.3967
0.4034
0.4101
0.4167
0.4234
0.4301
0.4367
0.4434
0.4500
0.4567
0.4634
0.4700
0.4767
0.4833
0.4900
0.4967
0.5033
0.5100
0.5167
0.5233
0.5300
0.5366
0.5433
0.5500
0.5566
0.5633
0.5699
0.5766
0.5833
0.5899
0.5966
0.6033
0.6099
0.6166
0.6232
0.6299
0.6366
0.6432
0.6499
0.6565
0.3617
0.3713
0.3810
0.3908
0.4007
0.4107
0.4208
0.4310
0.4413
0.4517
0.4622
0.4728
0.4836
0.4944
0.5054
0.5165
0.5278
0.5391
0.5506
0.5622
0.5740
0.5859
0.5979
0.6101
0.6224
0.6349
0.6476
0.6604
0.6734
0.6865
0.6998
0.7133
0.7270
0.7409
0.7550
0.7692
0.7837
0.7984
0.8133
0.8285
0.8438
0.8595
0.8753
0.8914
0.9078
0.9245
0.9414
0.9586
0.9761
0.9940
1.0121
1.0306
1.0495
1.0687
0.3043
0.3110
0.3177
0.3243
0.3310
0.3377
0.3443
0.3510
0.3577
0.3643
0.3710
0.3777
0.3843
0.3910
0.3977
0.4043
0.4110
0.4177
0.4243
0.4310
0.4377
0.4443
0.4510
0.4577
0.4643
0.4710
0.4777
0.4843
0.4910
0.4977
0.5043
0.5110
0.5177
0.5243
0.5310
0.5377
0.5443
0.5510
0.5577
0.5643
0.5710
0.5777
0.5843
0.5910
0.5977
0.6043
0.6110
0.6177
0.6243
0.6310
0.6377
0.6443
0.6510
0.6577
7.2127
7.4329
7.5922
7.7840
7.9440
8.1715
8.3329
8.4942
8.7271
8.9262
9.2750
9.6305
9.9542
10.1269
10.3791
10.5935
10.8093
11.1517
11.4146
11.6370
11.8170
12.1747
12.4025
12.5858
12.7692
12.9525
13.1836
13.3676
13.6007
13.9347
14.1213
14.3591
14.5464
14.7338
14.9211
15.2697
15.5135
15.8137
16.1166
16.9300
17.3584
17.6188
17.8222
18.2028
18.8265
19.1574
19.4298
19.7036
20.1035
20.4444
20.7242
21.0053
21.5481
21.8345
2.195065
2.311632
2.411799
2.524611
2.629464
2.759254
2.869284
2.981464
3.121381
3.252100
3.441025
3.637119
3.825744
3.959618
4.127422
4.283319
4.442622
4.657693
4.843581
5.015547
5.171907
5.409640
5.593528
5.760116
5.929150
6.100628
6.297366
6.474374
6.677944
6.934819
7.121859
7.337500
7.530204
7.725405
7.923104
8.210027
8.444515
8.713349
8.987672
9.554163
9.911646
10.177813
10.414086
10.757855
11.251972
11.577435
11.871608
12.170236
12.551306
12.900416
13.215110
13.534393
14.027813
14.359845
150
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
33.4
33.5
33.5
33.8
34
34.5
35.4
35.8
35.9
36.3
36.7
36.8
37.1
37.3
37.8
38.3
38.7
38.9
39
39.2
39.9
40.3
40.6
42
42.6
42.7
42.8
43.2
43.6
45.2
45.3
45.4
45.5
47.6
49
50.9
52.3
53.9
54.5
58.5
58.6
61.1
62
M100
31.75
M110
M120
0.6632
0.6699
0.6765
0.6832
0.6898
0.6965
0.7032
0.7098
0.7165
0.7232
0.7298
0.7365
0.7431
0.7498
0.7565
0.7631
0.7698
0.7764
0.7831
0.7898
0.7964
0.8031
0.8098
0.8164
0.8231
0.8297
0.8364
0.8431
0.8497
0.8564
0.8630
0.8697
0.8764
0.8830
0.8897
0.8963
0.9030
0.9097
0.9163
0.9230
0.9297
0.9363
0.9430
1.0883
1.1083
1.1286
1.1494
1.1707
1.1924
1.2146
1.2373
1.2605
1.2843
1.3087
1.3336
1.3592
1.3855
1.4125
1.4402
1.4687
1.4981
1.5284
1.5595
1.5917
1.6250
1.6594
1.6951
1.7320
1.7704
1.8103
1.8519
1.8953
1.9406
1.9881
2.0379
2.0904
2.1458
2.2044
2.2667
2.3332
2.4043
2.4809
2.5639
2.6544
2.7538
2.8643
0.6643
0.6710
0.6777
0.6843
0.6910
0.6977
0.7043
0.7110
0.7177
0.7243
0.7310
0.7377
0.7443
0.7510
0.7577
0.7643
0.7710
0.7777
0.7843
0.7910
0.7977
0.8043
0.8110
0.8177
0.8243
0.8310
0.8377
0.8443
0.8510
0.8577
0.8643
0.8710
0.8777
0.8843
0.8910
0.8977
0.9043
0.9110
0.9177
0.9243
0.9310
0.9377
0.9443
22.1887
22.4785
22.7018
23.1305
23.4940
24.0695
24.9334
25.4538
25.7642
26.2933
26.8277
27.1461
27.6148
28.0123
28.6398
29.2740
29.8377
30.2512
30.5890
31.0072
31.8269
32.4146
32.9266
34.3420
35.1166
35.4837
35.8521
36.4752
37.1036
38.7665
39.1543
39.5434
39.9338
42.0943
43.6590
45.6912
47.2966
49.1029
50.0128
54.0735
54.5566
57.2914
58.5487
14.740715
15.083074
15.384276
15.828949
16.234354
16.792488
17.561425
18.097652
18.490131
19.045114
19.611049
20.024798
20.554591
21.037237
21.699422
22.375069
23.004867
23.525376
23.991972
24.526695
25.387257
26.072170
26.703473
28.080309
28.947784
29.486955
30.032137
30.797227
31.575164
33.248763
33.842367
34.442301
35.048594
37.225363
38.900169
41.015497
42.771922
44.732742
45.895110
49.981939
50.792195
53.720267
55.289458
16.8291
11.633836
151
Generalized Pareto Distribution
Generalized Pareto Distribution
(GPA)
κ
(9M120-10M110+2M100)/(2M110-3M120)
0.069534
β
(2M110-M100)(K+1)(K+2)
4.223674
Xο
λ
M100 - [β/(1+K)]
27.80092
1.89
XT
Xo + β [1-exp(-KYT]/K
XT
Xo + β [1-(1-F)K]/K
Cumulative Distribution Function (cdf) and Quantile
T
(month)
0.5
1
2
3
6
12
T(AM)
year
T(POT)
year
0.041667
0.083333
0.166667
0.25
0.5
1
CDF
Fi
-11.6984127
-5.349206349
-2.174603175
-1.116402116
-0.058201058
0.470899471
Std. Exp
Yi
-2.541477
-1.84833
-1.155183
-0.749718
-0.05657
0.636577
Xi
(mm)
16.05963
19.47031
22.7205
24.55037
27.56152
30.43098
Design rainfall intensity (mm/hr) for30 minutes data
Duration
(hr)
0.5
Design rainfall intensity (mm/hr) corresponding to return period, T
(month)
0.5
32.12
1
38.94
2
45.44
3
49.10
6
55.12
12
60.86
152
60 minutes data
Rank
i
1
2
3
PD
Rainfall
Xi (mm)
34.8
35
35.7
Fi=(i0.44)/
N+0.12
0.0037
0.0104
0.0171
Yi = -ln(1Fi)
Fi=(i0.35)/N
XiFi
XiFi2
0.0037
0.0104
0.0172
0.0043
0.0110
0.0177
0.1508
0.3850
0.6307
0.000653
0.004235
0.011142
4
36
0.0237
0.0240
0.0243
0.8760
0.021316
5
36
0.0304
0.0308
0.0310
1.1160
0.034596
6
7
8
9
10
11
37.5
37.6
38.1
38.1
38.1
38.9
0.0370
0.0437
0.0504
0.0570
0.0637
0.0703
0.0377
0.0447
0.0517
0.0587
0.0658
0.0729
0.0377
0.0443
0.0510
0.0577
0.0643
0.0710
1.4125
1.6669
1.9431
2.1971
2.4511
2.7619
0.053204
0.073901
0.099098
0.126699
0.157687
0.196095
12
39.2
0.0770
0.0801
0.0777
3.0445
0.236459
13
39.3
0.0837
0.0874
0.0843
3.3143
0.279506
14
15
39.3
39.5
0.0903
0.0970
0.0947
0.1020
0.0910
0.0977
3.5763
3.8578
0.325443
0.376782
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
39.7
39.9
40.5
40.6
42
42
42.7
43.6
44
44.2
44.7
44.8
45
45
45.3
45.9
0.1037
0.1103
0.1170
0.1236
0.1303
0.1370
0.1436
0.1503
0.1569
0.1636
0.1703
0.1769
0.1836
0.1902
0.1969
0.2036
0.1094
0.1169
0.1244
0.1320
0.1396
0.1473
0.1550
0.1628
0.1707
0.1787
0.1866
0.1947
0.2028
0.2110
0.2193
0.2276
0.1043
0.1110
0.1177
0.1243
0.1310
0.1377
0.1443
0.1510
0.1577
0.1643
0.1710
0.1777
0.1843
0.1910
0.1977
0.2043
4.1420
4.4289
4.7655
5.0479
5.5020
5.7820
6.1630
6.5836
6.9373
7.2635
7.6437
7.9595
8.2950
8.5950
8.9543
9.3789
0.432152
0.491608
0.560741
0.627626
0.720762
0.795989
0.889531
0.994124
1.093786
1.193641
1.307073
1.414132
1.529045
1.641645
1.769967
1.916422
32
46.1
0.2102
0.2360
0.2110
9.7271
2.052418
33
46.3
0.2169
0.2445
0.2177
10.0780
2.193637
34
35
36
37
38
39
46.4
46.8
48.1
48.2
48.4
48.5
0.2236
0.2302
0.2369
0.2435
0.2502
0.2569
0.2530
0.2616
0.2703
0.2791
0.2879
0.2969
0.2243
0.2310
0.2377
0.2443
0.2510
0.2577
10.4091
10.8108
11.4318
11.7769
12.1484
12.4968
2.335101
2.497295
2.716950
2.877481
3.049248
3.220017
40
48.6
0.2635
0.3059
0.2643
12.8466
3.395785
41
42
43
48.7
48.8
48.9
0.2702
0.2768
0.2835
0.3150
0.3241
0.3334
0.2710
0.2777
0.2843
13.1977
13.5501
13.9039
3.576577
3.762420
3.953342
44
45
49.4
49.4
0.2902
0.2968
0.3427
0.3522
0.2910
0.2977
14.3754
14.7047
4.183241
4.377109
153
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
50.9
54.1
54.2
54.2
54.5
55.9
56.9
58.5
60.2
60.4
62.1
65.8
66.2
67.6
68.2
70.6
78.5
87.8
88.9
100.2
M100
33.0
0.3035
0.3102
0.3168
0.3235
0.3301
0.3368
0.3435
0.3501
0.3568
0.3634
0.3701
0.3768
0.3834
0.3901
0.3967
0.4034
0.4101
0.4167
0.4234
0.4301
0.3617
0.3713
0.3810
0.3908
0.4007
0.4107
0.4208
0.4310
0.4413
0.4517
0.4622
0.4728
0.4836
0.4944
0.5054
0.5165
0.5278
0.5391
0.5506
0.5622
M110
0.3043
0.3110
0.3177
0.3243
0.3310
0.3377
0.3443
0.3510
0.3577
0.3643
0.3710
0.3777
0.3843
0.3910
0.3977
0.4043
0.4110
0.4177
0.4243
0.4310
15.4906
16.8251
17.2175
17.5789
18.0395
18.8756
19.5926
20.5335
21.5315
22.0057
23.0391
24.8505
25.4429
26.4316
27.1209
28.5459
32.2635
36.6711
37.7232
43.1862
4.714296
5.232606
5.469436
5.701412
5.971075
6.373650
6.746374
7.207259
7.701112
8.017422
8.547506
9.385193
9.778542
10.334756
10.785065
11.542072
13.260299
15.316310
16.007225
18.613252
11.6000
3.5000
M120
Generalized Pareto Distribution
Generalized Pareto Distribution
(GPA)
κ
(9M120-10M110+2M100)/(2M110-3M120)
β
(2M110-M100)(K+1)(K+2)
Xο
λ
M100 - [β/(1+K)]
XT
Xo + β [1-exp(-KYT]/K
XT
Xo + β [1-(1-F)K]/K
-1.456693
2.43162
38.32441
1.89
154
Cumulative Distribution Function (cdf) and Quantile
T
(month)
0.5
1
2
3
6
12
T(AM)
year
T(POT)
year
0.041667
0.083333
0.166667
0.25
0.5
1
CDF
Fi
-11.6984127
-5.349206349
-2.174603175
-1.116402116
-0.058201058
0.470899471
Std. Exp
Yi
-2.541477
-1.84833
-1.155183
-0.749718
-0.05657
0.636577
Xi
(mm)
36.69632
36.76817
36.96539
37.21519
38.19237
40.87451
Design rainfall intensity (mm/hr) for30 minutes data
Duration
(hr)
1
Design rainfall intensity (mm/hr) corresponding to return period, T
(month)
0.5
36.70
1
36.77
2
36.97
3
37.22
6
38.19
12
40.87
155
Optimization Process
λT κ
I=
(d + θ )η
l
5 min
15 min
30 min
60 min
λ
κ
θ
η
25
0.1424
0.159
0.8454
I
(mm/hr)
T
d (hr)
I∧ e = ln(I /I∧)
79.97
0.5
0.083
75.07416
0.063152
82.48
1
0.083
82.86233
-0.004603
86.21
2
0.083
91.45844
-0.059078
-0.082942
89.18
3
0.083
96.89451
96.15
6
0.083
106.9463
-0.106373
106.50
12
0.083
118.0409
-0.102884
0.051663
50.79
0.5
0.250
48.23058
53.90
1
0.250
53.234
0.012435
58.01
2
0.250
58.75648
-0.012794
-0.020277
61.00
3
0.250
62.24883
67.38
6
0.250
68.70651
-0.019448
75.81
12
0.250
75.8341
-0.000288
-0.003274
32.12
0.5
0.500
32.22461
38.94
1
0.500
35.56758
0.090603
45.44
2
0.500
39.25735
0.146276
0.165997
0.182987
49.10
3
0.500
41.59071
55.12
6
0.500
45.90532
60.86
12
0.500
50.66752
0.183323
0.607250
36.70
0.5
1.000
19.99389
36.77
1
1.000
22.06805
0.510502
36.97
2
1.000
24.35738
0.417147
37.22
3
1.000
25.80512
0.366144
38.19
6
1.000
28.48214
0.293358
1.000
31.43687
0.262525
40.87
12
2.941401
0.432592
√ε
0.657717
156
Design rainfall intensity (mm/hr) and IDF curve before optimization process
Duration
(hr)
0.083
0.25
0.5
1
Design rainfall intensity (mm/hr) corresponding
to return period, T (month)
0.5
1
2
3
6
12
79.97
50.79
32.12
36.70
82.48
53.90
38.94
36.77
86.21
58.01
45.44
36.97
89.18
61.00
49.10
37.22
96.15
67.38
55.12
38.19
106.50
75.81
60.86
40.87
Rainfall Intensity Duration Frequency (IDF) Curve For All
Storms at Station 3117070-JPS Ampang
Rainfall intensity (mm/hr)
1000.00
100.00
12
6
3
2
10.00
1
0.5
1.00
0.083
0.25
0.5
Duration (hr)
1
157
Design rainfall intensity (mm/hr) and IDF curve after optimization process
Duration
(hr)
Design rainfall intensity (mm/hr) corresponding
to return period, T (month)
0.083
0.25
0.5
75.07
48.23
1
82.86
53.23
2
91.46
58.76
3
96.89
62.25
6
106.95
68.71
12
118.04
75.83
0.5
1
32.22
19.99
35.57
22.07
39.26
24.36
41.59
25.81
45.91
28.48
50.67
31.44
Rainfall Intensity Duration Frequency (IDF) Curve For All
Storms at Station 3117070-JPS Ampang
Rainfall intensity (mm/hr)
1000.00
12
100.00
6
3
2
10.00
1
0.5
1.00
0.083
0.25
0.5
Duration (hr)
1