PATH REDUCTION FACTOR FOR
MICROWAVE TERRESTRIAL LINKS
DERIVED FROM THE MALAYSIAN
METEOROLOGICAL RADAR DATA
Nor Hisham bin Haji Khamis
Supervisors
Associate Professor Dr Jafri bin Din
Professor Dr Tharek bin Abdul Rahman
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
BAHAGIAN A - Pengesahan Kerjasama*
Adalah disahkan bahawa projek penyelidikan tesis ini telah dilaksanakan melalui kerjasama antara
dengan
Disahkan oleh:
Tandatangan
:
Tarikh :
:
Jawatan
:
(Cop rasmi)
* Jika penyediaan tesis/projek melibatkan kerjasama.
BAHAGIAN B - Untuk Kegunaan Pejabat Sekolah Pengajian Siswazah
Tesis ini telah diperiksa dan diakui oleh:
Nama dan Alamat
Pemeriksa Luar
:
Prof. Dr. Syed Idris bin Syed Hassan
School Of Electrical & Electronic Eng.,
Universiti Sains Malaysia,
14300 Nibong Tebal,
Penang
Nama dan Alamat
Pemeriksa Dalam I
:
Prof. Madya Dr. Norazan bin Mohd Kasim
Fakulti Kejuruteraan Elektrik UTM, Skudai
Pemeriksa Dalam II
:
Prof. Dr. Abu Bakar Mohamad
Fakulti Kejuruteraan Elektrik UTM, Skudai
Nama Penyelia lain
:
(j ika ada)
Disahkan oleh Penolong Pendaftar di Sekolah Pengajian Siswazah:
Tandatangan
:
Nama
:
Tarikh :
GANESAN A/L ANDIMUTHU
Nama
PATH REDUCTION FACTOR FOR MICROWAVE TERRESTRIAL LINKS DERIVED
FROM THE MALAYSIAN METEOROLOGICAL RADAR DATA
NOR HISHAM BIN HAJI KHAMIS
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Doctor of Philosophy
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
JUNE 2005
DEDICATIONS
To Almighty ALLAH, Most Gracious, Most Merciful
To my parents
Haji Khamis bin Haji Othman
Hajjah Esah binti Haji Md Sab
To my dearest wife
Hajjah Aisyah binti Che Mat
To my children
Muhammad Khalid
Nurul Iman
Luqman Hamdani
Izzatul Huda
Nasrul Azizi
Akmal Husaini
To all my teachers
To my brothers and sisters
For all the joy, love, understanding, and sacrifices.
Religion without science is lame, Science without religion is blind
ACKNOWLEDGMENTS
I would like to express my deepest gratitude and appreciation to both my supervisors, Assoc.
Professor Dr. Jafri bin Din and Professor Dr. Tharek Abd. Rahman. For their suggestions,
assistance, and support during the entire project. No doubt, without their constant help and
encouragement, this project would not be completed.
A special thanks to Mr Tan Boon Eng of Perkhidmatan Kajicuaca Malaysia for his assistance
in obtaining the radar data and during my practical training at Jabatan Kajicuaca Malaysia,
Petaling Jaya.
My deepest thanks to friends and colleagues, who helped me directly or indirectly. For their
continuing encouragement and support.
Finally, an acknowledgement to UTM, for providing me with the opportunity and facilities to
do and complete this project.
ABSTRACT
Attenuation due to rain is a major concern in transmission of microwave signals. The
effect of rain attenuation is more pronounce when signals are being transmitted at higher
frequencies. For tropical countries like Malaysia, rain occurs almost yearound and in most
instances, much heavier than temperate region. Even rain itself, does not distribute evenly in a
region experiencing precipitation. This gives rise to the need of a correction or reduction
factor when calculating attenuation due to rain. This topic has been the focus of many
researches. However, many of these researches were done in temperate regions, making it
necessary for a study using local data. This study utilized the local weather radar data
obtained from the Meteorological Department of Malaysia, and data from two rain gauge
networks installed in UTM, Skudai campus. From the analysis of the radar data, a reduction
factor is deduced. The reduction factor obtained in this study follows the same pattern as other
models but has a lower value as the path link increases. This shows that attenuation due to
rain is lower than as predicted using other models. Rain rate distribution and rain cell size
distribution is also formulated from radar data. R0.01 of 120.907 mm/hr agrees very well with
the ITU-R and the Meteorological Department of Malaysia values. Using data from the rain
gauge networks, the profile and the size of rain cells at different rain rates are determined.
This study finds that most rain cells in Malaysia are highly convective with an average cell
size of 1.2 to 1.5 km. All the information are important for attenuation predictions, link
budget estimation, microwave system planning, slant path rain attenuation modeling and
remote sensing of the earth’s surface, and have important applications in attenuation
mitigation techniques such as space diversity. Further study can be done with more precise,
elaborate, and sophisticated measuring systems such as Doppler or polarimetric radar,
complemented with microwave links and rain gauge networks.
ABSTRAK
Rosotan yang disebabkan oleh hujan adalah satu masalah yang besar di dalam
penghantaran isyarat gelombangmikro. Kesan rosotan hujan adalah lebih ketara pada
frekuensi yang lebih tinggi. Untuk negara-negara tropikal seperti Malaysia, hujan berlaku
hampir sepanjang tahun dan adalah lebih lebat dari kawasan berhawa sederhana. Taburan
hujan juga adalah tidak sekata di dalam kawasan hujan. Keadaan ini menjadikan keperluan
faktor pengurangan dalam pengiraan rosotan hujan. Topik ini telah menjadi fokus untuk
banyak penyelidikan. Walaubagaimanapun, kebanyakan penyelidikan adalah dalam kawasan
berhawa sederhana, menjadikan satu kajian yang menggunakan data tempatan satu
kepentingan. Kajian ini menggunakan data radar cuaca yang diperolehi daripada Jabatan
Kajicuaca Malaysia dan rangkaian tolok hujan yang dipasang di UTM, Skudai. Penganalisaan
data radar telah menghasilkan faktor pengurangan, taburan lebat hujan dan taburan saiz sel
hujan. Faktor pengurangan daripada kajian ini mempunyai bentuk yang serupa dengan lainlain model tetapi mempunyai nilai yang lebih rendah apabila jarak bertambah. Ini
menunjukkan bahawa ramalan rosotan daripada model lain adalah lebih tinggi dari nilai
sebenar. Nilai R0.01 sebanyak 120.907 mm/jam adalah setara dengan ITU-R dan Jabatan
Kajicuaca Malaysia. Daripada data tolok hujan, profil dan saiz sel hujan pada kelebatan hujan
yang berlainan telah ditentukan. Kajian juga menunjukkan bahawa hujan di Malaysia adalah
sangat konvektif dengan purata saiz sel hujan antara 1.2 hingga 1.5 km. Hasil kajian adalah
sangat penting untuk jangkaan pelemahan, anggaran bajet rangkaian, dan perangkaan sistem
gelombangmikro. Hasil kajian juga adalah berguna untuk teknik pengurangan seperti
kepelbagaian tapak. Kajian selanjutnya boleh dilakukan dengan menggunakan teknik
pengukuran yang lebih jitu dan canggih seperti penggunaan radar Doppler atau polarimetrik,
dilengkapi dengan laluan jalurmikro dan rangkain tolok hujan.
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
TITLE PAGE
i
DECLARATION
ii
DEDICATIONS
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF FIGURES
xi
LIST OF TABLES
xiii
LIST OF SYMBOLS
xv
LIST OF ABBREVIATIONS
xvii
LIST OF APPENDICES
xviii
INTRODUCTION
1
1.1
Overview
1
1.2
Problem Statement
2
1.3
Objectives
4
1.4
Scope of Study
4
1
viii
1.5
Outline of Thesis
5
Methodology
7
2.1
Introduction
7
2.2
Radar Data
7
2.3
Disadvantages of Radar Measurement
9
2.4
Radar Measurement Principle
10
2.5
Z-R Relationship
10
2.6
Selection of radar Data
12
2.7
Rain Gauge Data
15
2.8
Attenuation Measurements Using Microwave
16
2
Links
3
RAIN ATTENUATION, RAIN MODELS,
17
AND REDUCTION FACTORS
3.1
Background
17
3.2
Attenuation by Rain
18
3.3
Rainfall Rate, Rain Cell Size, and Rain Height
22
3.4
Rainfall Rate for 0.01 % of the time or R0.01
26
3.5
Rain Prediction Models
27
3.6
3.5.1 Crane’s Global Model
28
3.5.2 ITU-R Model
30
Reduction Factor
33
3.6.1 Lin Model
33
3.6.2 Moupfouma Model
34
3.6.3 CETUC Model
35
3.6.4 Improved CETUC Model
35
ix
3.6.5 Goddard and Thurai Model
36
3.6.6 ITU-R Model
37
3.6.7 Singapore Model
38
3.6.8 DAH Model
40
3.6.9 Comments on reduction Factor Models
40
3.7
Rain in Malaysia
41
3.8
Determination of Rain Cell Size
42
RAIN GAUGE AND RADAR DATA
44
4.1
Introduction
44
4.2
Rain Gauge and Rain Gauge Networks
45
4
4.2.1 Casella Rain Gauge
4.3
Radar Data Collection
4.3.1 Kluang Radar Data Format
48
50
58
DATA ANALYSIS AND RESULTS
61
5.0
Introduction
61
5.1
Rain Gauge Data Analysis
61
5.1.1 Preliminary Data Analysis
62
5.1.2 Selection of Rain Gauge Network
62
5
(RGN-UTM 1) Data
5.2
5.1.3 RGN-UTM 1 Data Analysis
62
5.1.4 Cell Size and Intensity Distribution
72
5.1.5 Rain Distribution Inside a Rain Cell
73
Radar Data Analysis
79
5.2.1 Rejection of Permanent Echo
80
5.2.2 Preliminary Results
80
x
5.2.3 Distribution of Rain Rate from Radar Data
82
5.2.4 Determination of Rain Cell Size from Radar
85
Data
5.2.5 Rain Attenuation Measurements in UTM
5.3
Deducing the Reduction Factor from Radar
88
89
Data
CONCLUSION AND FUTURE STUDIES
110
6.1
Conclusion
110
6.2
Future Studies
114
REFERENCES
116
APPENDICES
128
6
LIST OF FIGURES
TITLE
FIGURE
PAGE
2.1
Examples of virtual links
13
3.1
Rain formation through cold and warm air fronts
23
3.2
Rain cell diameter versus rainfall rate
23
3.3
Height of melting layer
25
3.4
Rain height
26
3.5
The global rain rate regions
28
3.6
Rain rate distribution curves for various regions
29
3.7
Rainfall climatic zones
30
3.8
Rainfall rate contours for 0.01% of the time for Asia
31
3.9
Revised rainfall rate contours for 0.01% of the time
32
4.1
RGN-UTM 1 Rain gauge network stations
46
4.2
RGN-UTM 2 Rain gauge network stations
47
4.3
Casella Tipping Bucket Rain Gauge with Integral
49
Logger
4.4
Tipping buckets of a Casella Rain Gauge
50
4.5
Merged PPI scan
51
4.6
A Kluang radar station PPI scan
53
4.7
A Kluang radar station RHI scan
54
4.8
A MATLAB radar plot
55
4.9
Top view of typical composite image
56
4.10
A cross-section of a typical composite image
56
xii
5.1
Graph of Rainfall Rate Recordings at all Rain Gauge
63
Stations
5.2
Rain Rate Distribution for 120 mm/hr at Civil Station
66
5.3
Rain Rate Distribution for 90 mm/hr at Civil Station
67
5.4
Rain Rate Distribution for 60 mm/hr at Civil Station
68
5.5
Rain Rate Distribution for 30 mm/hr at Civil Station
68
5.6
Averaged Rain Rate Distributions for RGN-UTM 1
69
54.7
Averaged Rain Rate Distribution for all stations
72
5.8
Rain rate distributions for RGN-UTM 2
74
5.9
Rain distributions assuming that TV Station is the
74
center of the rain cell
5.10
Rain distribution assuming the IVAT Station to be the
75
center of the rain cell
5.11
Averaged rain cell size
77
5.12
RGN-UTM 2 Rainfall rate distribution
78
5.13
Rain rate distribution
82
5.14
The plots of original data and the curve-fit line
84
5.15
Rain Cell Size Distribution
87
5.16
The best-fit curve for 1-km path links attenuation
92
distribution
5.17
Attenuation for 0.01% of the time at 7, 10, and 15
94
GHz
5.18
Reduction factor (r) plots for 1 to 10-km path lengths
95
at frequencies of 7, 10, and 15 GHz for 0.01% of the
time
5.19
Best fit line for coefficient a
97
5.20
Best fit line for coefficient b
97
5.21
Plots of all the reduction factor models at 7 GHz
100
5.22
Plots of all the reduction factor models at 10 GHz
101
5.23
Plots of all the reduction factor models at 15 GHz
102
6.1
Proposed reduction factor r
111
6.2
Predicted attenuation due to rain for 0.01 % of the
111
time
LIST OF TABLES
TABLE
3.1
TITLE
Point Rain Rate (RP) Distribution Values (mm/h)
PAGE
29
Versus Percent of Year Rain Rate is exceeded
3.2
Rainfall rates in the climatic zones
31
4.1
dBZ-R values for Kluang radar
52
4.2
Radar Scan Elevation Angles
57
4.3
Number of matrices in each data folders
59
4.4
The corresponding actual rain rate values in mm/hr to
60
the rain rate level
5.1
Rain events recorded at all rain gauges locations
62
5.2
Correlations for no. of readings at all stations
63
5.3
Equal Rainfall Rate At All Three Stations
65
5.4
The Rainfall Rates and their durations for all Rain
70
Gauge Stations RGN-UTM 1
5.5
The Rainfall Rate Percentages and the Averaged
71
Rainfall Rate Percentage for all Rain Gauge Stations
5.6
Simultaneous rain rate readings at all stations when
76
IVAT and TV Studio stations register 120 mm/hr rain
rate
5.7
Distribution of rainfall rate of RGN-UTM 2
78
5.8
R0.01 Values for RGN-UTM 2 Stations
79
5.9
Rainfall Intensity for averaged 1-km path
81
xiv
5.10
Rain rate distribution for range-bin size of 1-km from
83
radar data
5.11
Rain Cell Size Distributions
86
5.12
Specifications for Binariang system links
88
5.13
Specifications for Digi system links
89
5.14
Distribution of attenuation for 1-km links operating at 7
91
GHz
5.15
Attenuation (dB) for 0.01% of the time; at 7, 10, and 15
93
GHz for path lengths of 1 to 10-km
5.16
Reduction factor (r) values for 1 to 10-km path lengths
95
at frequencies of 7, 10, and 15 GHz for 0.01% of the
time
5.17
a & b values for best fit lines of reduction factors at 7,
96
10, and 15 GHz
5.18
a and b values at 7, 10, and 15 GHz
98
5.19
The reduction factor (r) for the proposed Malaysia
99
model
5.20
Comparison of r from various models at 7 GHz
100
5.21
Comparison of r from various models at 10 GHz
101
5.22
Comparison of r from various models at 15 GHz
102
5.23
Comparison of predicted attenuations (dB), with
105
measurements
LIST OF SYMBOLS
α
regression exponential for specific attenuation
β
exponential in Moupfouma’s model.
γs
specific attenuation due to rain (dB/km)
A
attenuation of radiowave propagating through free-space (dB)
a
excess attenuation due to water vapor
Ar
attenuation of radiowave due to rain (dB)
b
excess attenuation due to mist and fog; regression exponential for radar
reflectivity
c
excess attenuation due to oxygen
D
diameter of rain cell (km)
d
absorption losses due to other gasses
dB
decibels
e
excess attenuation due to rainfall
dBZ
radar reflectivity factor in dB
F
Frequency (GHz)
k
regression coefficient for specific attenuation
L
path length (km)
m
exponential in Moupfouma’s model.
n(r)
number of raindrops per unit volume per radius interval (m-3mm-1)
p
time percentage, percentage
Qt(r)
total extinction cross-section (cm2)
r
radius (cm), reduction factor
R
rainfall rate (mm/hr)
R0.01
rainfall rate (mm/hr) for 0.01 % of the time
xvi
Rt
threshold values of a specific rain rate
Z
radar reflectivity factor (dBZ or mm6/m3)
xvii
LIST OF ABBREVIATIONS
3D-RAPIC
3 dimensional software to process and handle weather radar data
CETUC
Center for Telecommunication Studies of the Catholic University of
Rio de Janeiro
CMOS
Complementary metal-oxide semiconductor
DAH
Dissanayake, Allnutt, Haidara
DSD, dsd
drop size distribution
EPROM
Erasable programmable read-only memory
ITU
International Telecommunication Union
ITU-R
International Telecommunication Union-Radio communication
Section
LOS
Line-of-sight
PPI
Pulse-Position Indicator
PPI
Pulse-position-indicator
r
Reduction factor
RGN-UTM 1 Rain Gauge Network in UTM no. 1
RGN-UTM 2 Rain Gauge Network in UTM no. 2
RHI
Rain Height Indicator
RHI
Rain height indicator
STC
Sensitivity Time Control
UTC
Universal Time Constant
UTM
Universiti Teknologi Malaysia
xviii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
1.1
Earth’s Climate and Raindrops
128
3.1
Specifications of the Casella Rain Gauge
137
3.2
Data Sample from RGN-UTM 1
138
3.3
Radar Measurement Theory
139
3.4
Radar Calibration Checklist
144
3.5
Kluang Radar Station Specifications
148
3.6
An Example of a Radar Data
149
3.7
Radar Data Encoding Format
153
4.1
MATLAB programs
157
4.2
Radar Rain Rate Distribution
162
4.3
173
4.4
Rain Cell Diameter from Radar Data
1 to 10-km path attenuations at 7, 10, and 15 GHz
174
4.5
Rec. ITU-R P.838-1
222
CHAPTER 1
INTRODUCTION
1.1
Overview
Radio link is very important in communication systems. Large number of
parameters must be considered and optimized to build an efficient radio link. That is,
radio signals must suffer minimum degradation possible. For reliable communication
link, selection of operating frequency and possible atmospheric attenuation must be
studied and understood. Since the governing body usually determines the operating
frequency, attenuation, especially due to rain, has become the subject of numerous
studies and researches. For good engineering and economic practice, it is always
desirable to reduce cost of a system and avoid interference to other radio systems.
Some factors which introduce attenuation to radio propagation are gaseous
absorption, absorption and scattering due to clouds, fogs, precipitation, atmospheric
turbulence and ionospheric effects. Since Malaysia is in the tropical region, studies
of attenuation due to hydrometers are very important. Rain, hail, ice, cloud and snow
are all types of hydrometers but raindrops cause the most attenuation by absorption
and scattering of radio waves. Eventhough the International Telecommunication
Union (ITU) recommends a technique to estimate rain attenuation, studies (Ajayi et
al, 1988; Juy et al, 1990; Yagasena et al, 1995) have shown that results using this
techniques does not agree with actual measurements done locally. This is
2
understandable as the recommendation is meant to be applicable to wide area as
possible and most studies were done using temperate region data. Thus, local studies
are needed and based on these studies; a model for rain attenuation in Malaysia can
be developed.
1.2
Problem Statement
Power budget and fade margin are important factors to be considered in
designing microwave transmission systems. The world of telecommunication is very
competitive such that when providing for a system, careful infrastructure planning is
needed to avoid unnecessary costs.
Microwave links are designed to meet specific reliability factor. Reliability,
or sometimes is known as availability of a system, is usually expressed as a
percentage. It represents the percentage of the time the link is expected to operate
without an outage caused by propagation conditions. It has been widely accepted that
a good communication system must provide at least 99.99% reliability (IEEE, 2004;
ITU-R SA 1414). In other words, the system can only be down for 0.01% of the
time, which is usually referenced to a year. This means that the system can be
unavailable for no less than 52.6 minutes per year [365.25*24*60*0.01/100]. (For
emergencies, call 999; for no emergency, it is 99.99%!)
A very important factor that affects path reliability is rain attenuation. It also
contributes in power budget and fade margin considerations. Thus, it is very
important to properly quantify rain attenuation. Due to the nature of rain events, a
reduction factor is needed in order to calculate rain attenuation.
A rain event occurring in an area is not constant. Rain does not distribute
evenly in a region experiencing precipitation. Even though specific attenuation due
3
to rain for a specific distance or per kilometer can be formulated; there arises a need
to find a reduction factor to account for the non-uniformity of rain for larger
distances. This is especially crucial in tropical regions as rain has been found to be
more convective in nature rather than widespread. Tropical region also suffers
heavier rainfall rates as compared to temperate regions.
To formulate the reduction factor, the experimental procedure would requires
several links with different path lengths to be set up in close proximity. However,
this would be very difficult to be constructed. An alternative approach is to use radar
data to obtain attenuation statistics for simulated links of various lengths.
In addition, even after a proposed microwave link has been evaluated with
regard to reliability, the calculations may show that it will not meet the required
standards. Or a designer may want to improve the reliability of the
telecommunication system. In this situation, mitigation techniques such as diversity
may be employed.
One such technique is space diversity where an additional receiver may be
constructed (Nor Hisham Khamis et al, 2000). By switching and/or combining the
signals received by the two receivers, the reliability of the communication link is
greatly increased. An important parameter to consider is site separation or the
distance between the two receivers. When spacing is adequate between the two
receivers, there should be little correlation between the two paths. Site separation or
distance is used to determine the diversity improvement factor and diversity gain
when employing diversity (ITU-R P.618-5, 1997). Knowing rain cell size
distribution will help to determine site separation.
Thus, the aim of this thesis is to find the reduction factor to be used in rain
attenuation calculation using radar data, and also to determine the rain cell size
distribution needed for site diversity application using rain gauge networks.
4
1.3
Objectives
The objectives ensure that the aim of this study is achieved. These objectives
are contributions accomplished during this study. The objective of this study are as
follows.
To formulate a suitable reduction factor (r), to be used in the calculation of
attenuation due to rain in the local Malaysian environment from the local weather
radar data obtained from the Meteorological Department of Malaysia.
To estimate the attenuation due to rain using the formulated r and other
models proposed by other researchers, and compare the results with measured values.
To find the profile of rain rate distribution inside a rain cell and to determine
the rain cell size distribution of local rain.
1.4
Scope of Study
The scope of study indicates the basic guidelines and techniques that this
study examined in achieving the objectives. It also ensures that the work done stays
within the intended study.
There are two types of data that are utilized in this study, radar data and rain
gauge network data.
5
Radar data gives the averaged rainfall rate for a range-bin size of 1-km each.
This rainfall data is used to calculate the rain attenuation for ‘virtual’ microwave
links of 1 to 10-km path lengths. Attenuation due to rain is then calculated using the
rainfall rate from the radar data. Reduction factor is then deduced from the rain
attenuation calculation. The radar data is obtained from the Kluang Radar Station of
the Meteorological Department of Malaysia.
Rain cell size distribution is also obtained from radar data. However, rain cell
size distribution from radar data is limited to 1-km integration size. This is due to the
fact that the radar uses a range bin size of 1 km.
To determine the profile of rain rate distribution inside a cell, rain gauge
networks were utilized. These rain gauge networks consisted of several rain gauges
that were fixed in almost a single line. Rain gauge gives point rainfall rate values.
Rain intensity profile inside a cell, and rain cell size are obtained from rain gauge
networks. Two rain gauge networks have been set up in UTM, Skudai campus.
1.5 Outline of Thesis
The outline of this thesis indicates the organization of this thesis. This thesis
is separated into 6 chapters.
Chapter One gives the introduction to this study, the problem statement,
objectives, and the scope of this study.
6
Chapter Two focuses on the methodology that was used in this study. It
discusses the feasibility of a study using radar data, some issues concerning radar,
rain gauge networks and rain cell size.
Chapter Three goes through the theory on attenuation due to rain, and
explained some parameters that important in propagation study. It also reviews a
couple of rain models and some reduction factors models.
Chapter Four explains the rain gauge networks that were set up in this study.
It also explains the data that were obtained from the Kluang radar, and how the data
were retrieved.
Chapter Five is an important part of this project. It analyses both data that
were utilized in this study. Results in this study are given in this chapter. The main
contribution of this study which the formulation of a reduction factor, is also given in
this chapter. Comparison with other models and actual measurement are also done.
Chapter Six concludes this study. It discusses the results of this study and
shows that the objectives of this study are achieved. Future studies are also briefly
given.
CHAPTER 2
METHODOLOGY
2.1
Introduction
The methodology will determined that the objectives are properly developed
and gives the steps and procedures involved in achieving them. The methodology
used in this study follows some works that have been published (Goddard, 1991;
Goddard et al, 1997; Goldhirsh, 1992; Sauvageot et al, 1999). In this study, two types
of measuring techniques are used. Radar data is used to deduce the reduction factor
for calculating rain attenuation, to formulate rainfall rate distribution and rain cell
size distribution, while rain gauge networks are used to obtain rain cell size and the
profile of rainfall rate inside a rain cell.
2.2
Radar Data
The ability of a radar to scan a wide area around the radar site and not just a
particular path made it a very attractive for many types of investigations. Radar can
be used to measure the rainfall rate indirectly. This is achieved by knowing the radar
8
reflectivity and then converting them into rainfall rate. The S-band frequency of the
meteorological radar ensures that propagation effects such as attenuation are
negligible (Goddard 1991).
Many studies have utilized meteorological radar data (Battan, 1973; Puhakka,
1974;.Goldhirsh, 1979; Wilson et al, 1979). A radar will actively probes a specific
region. The ability to scan a large area continuously makes radar measurement
technique very attractive. This enables a large amount of data to be collected in a
short period of time. A large database can be used to provide statistical information
by simulating particular systems. Compared to a rain gauge network, radar observes
larger variability of precipitation characteristics over a short period of time, and at a
faster rate (Olsen, 1982). Radar provides valuable information that is relevant in
modelling rain-induced propagation effects (Goddard, 1991). Radar also provides
spatially and temporally continuous measurements that are immediately available at
one location. Through technology and computer software advancement, radar can
scan 3-D space, seeks out region of rain, and acquire a quasi-photograph of the
precipitation structure. Goldhirsh (1979) has noted that researchers have
demonstrated that a summer’s database of radar reflectivity enabled the prediction of
rain rate distribution, which agreed in shape to the distribution acquired using 10
years of continuous rain gauge data. Lahaie et al (1993) suggested the use of 1000
virtual links to an attenuation model. (This study uses more than 5 millions virtual
links and that is just for the 1-km path lengths). Seed et al (1990), utilized a month of
radar data for his study. Wilson (Wilson, 1964) used radar data that covered a period
of 19 days, while Jatila et al (1973) used radar data taken during summer of 1969.
Thus, by using radar, adequate rain attenuation statistics can be obtained in a shorter
or limited period of time.
Techniques that utilize Doppler radar and polarimetric radar have also been
employed (Hornbostel et al, 1979; Meneghini et al, 1997; Zhang et al, 2001). Using
these kinds of radars, rain rate can be deduced, and hence attenuation can be
9
calculated. Also, drop size distribution (dsd) and rain height can be estimated.
However, these data are not readily available in Malaysia.
2.3
Disadvantages of Radar Measurement
In order to get reliable data; some disadvantages of radar measurement need
to be discussed. Steps must be taken to minimize these effects. Radar reading tends
to underestimate attenuation due to rain attenuation on the radar signal (Wilson et al,
1979). Other factors that affect radar measurements are radar domain cannot be
sampled at consistent elevations, with consistent bin volumes, or for precipitation
with similar stage of development or phase; beam elevation increases with distance
resulting in low-level precipitation not represented well; bin size increases with
distance, thus incomplete beam filling, smearing of small-scale structure; ground
clutter and terrain features may block low level information.
Some correction factor or technique has to be included in determining the
received or backscattered power from precipitation. This is known as the STC Sensitivity Time Control, which takes into account the time and distance of
precipitation. STC provides range normalization that eliminates the effect of range
attenuation. Thus target of equal reflective area regardless of their range will give
equal amplitude returns. The radar system also has to be calibrated regularly to
ensure reliable data collection.
The technology of radar for precipitation measurement is very stable and the
results of observations are highly accurate (Japan Meteorology Agency, 1979;
Goddard, 1991). Meteorological radar is also said to be a better tool to build a rain
attenuation prediction model for terrestrial microwave radiocommunication (Lahaie
et al, 1993).
10
2.4
Radar Measurement Principle
Radar will emit a pulse towards a target. If the pulse hit the target, some
energy will be scattered back to the radar. The backscattered or average power
received by the radar depends on the radar parameters, on the shape, size, number
and dielectric constant of raindrops. If these parameters are known, the radar
reflectivity factor Z can be calculated. An empirical relationship can be established
between Z and the rainfall rate R. By knowing R, specific attenuation can be
determined. A brief radar measurement theory is given in Appendix 3.3.
2.5
Z-R Relationship
Power received or returned from a scatterer depends on what is called the
radar reflectivity factor Z. The widely accepted empirical relationship of the radar
reflectivity factor Z, and rainfall rate R is given by eq. A22, in Appendix 3.3. A
method of obtaining this relationship is by using disdrometer measurement.
Disdrometer measures the drop size distribution of a falling rain. From time
integration of the drops sampled by the disdrometer, the rain rate can be determined.
This work has been carried out in UTM by Din (1997). From knowing the drop size
distribution (dsd), the radar reflectivity that would have been can be calculated. Z can
be plotted against R, and it is found that they have a “power law” relationship. This is
given by equation A22, and written again here,
Z = aRb
mm6/m3, (R in mm/hr)
(2.1)
11
Thus, if Z can be measured and thus known, then R can be found. However, a
and b varies for different types of rain, as given by eq. A23, in Appendix 3.3. The
constant a and b are related to the intercept and slope of the best-fit line through a
plot of R versus Z on a log-log plot. Puhakka (1974) has given that if b is fixed at
1.6, then for convective rain, a has an average of 360, 196 for continuous rain, and 56
in drizzle. Reported values of a varies between 100 to 600, while b varies between
1.3 to 1.8. Meanwhile, Battan (1973) reported that Cantaneo (1969) proposed that the
appropriate values of a and b can be predicted by using
a = 1.372 (TD) - 4.702 (RH) + 571
(2.2)
b = -0.00444 (RH) + 1.776
(2.3)
where TD is the mean annual percentage of rain days which are thunderstorm
days, and RH is the mean annual relative humidity at a level 500 m above the ground.
However, Battan and other researchers (Battan, 1973) have noted that these
parameters vary depending on geographic locality and types of rain. In addition, error
in measuring the average backscattered power also contributed to the uncertainty.
Notwithstanding, Wexler et al (1963) concludes that Z-R relationship is fairly
constant at low frequency (less than 3 GHz), but deviates considerably at high
frequency (more that 9 GHz). Hunter (1996) noted that the choice of Z-R relationship
has small outcome in determining R. Z-R relationship is mitigated by averaging rain
rate from radar data over large time and space scales. The most common values for a
and b are 200 and 1.6, respectively. These are also the values used by the radar
operator of the Malaysian Meteorological Department of Malaysia. Din (1997)
proposed values of 320 for a, and 1.4 for b.
12
Falling raindrops are found to be mostly oblate. However, in this study, the
radar uses vertical polarization. Thus, it is assumed that the raindrops are spherical,
and small enough compared to wavelength so that Rayleigh scattering is applicable.
This assumption is valid for detecting precipitation particles by meteorological data
(Japan Meteorology Agency, 1979). The wavelength of the meteorological radar is
107 mm while study in Malaysia (Din, 1997) showed that for rain rates of 226.33
mm/hr and 105.02 mm/hr, most raindrops have diameters of between 1 – 2 mm.
2.6
Selection of Radar Data
As it was mentioned before, the radar data is obtained from the
Meteorological Department of Malaysia. Thus, one of the earlier steps in this study is
the retrieval of radar data from the Meteorological Department. This is done through
visitation, personal communications, and practical training at the Meteorological
Department of Malaysia, Petaling Jaya during the course of this study.
One of the first data processing activities is the rejection of permanent echo or
permanent echo check. This is done by taking samples from the radar data and check
whether there are any instances where there is always a reading at a particular point.
This will indicates permanent echo. From this analysis, there is no permanent echo in
the radar data. The operator of the weather radar of the Meteorological Department of
Malaysia explained that they have included echo rejection in their data processing
routines.
Radial lines from radar data that are utilized in this study are selected. The
“virtual links” for the deduction of reduction factor and the formulation of rain cell
size distribution will be on these radial lines. This virtual links concept is as used by
13
Goddard et al (1997) and Jafri (1997). Since the rain rate along each radial lines are
known, then the attenuation due to rain can be calculated as if there is a link or a
microwave signal transmission along the path link. Figure 2.1 shows the virtual links
as used by Goddard.
Figure 2.1 Examples of virtual links (Goddard et al, 1997).
In their study, Goddard et al (1997) used both links along the radial lines and
orthogonal to the scanning radar. In this study, since the amount of data is very large,
it is decided to use virtual links along the radial lines only. Also, not all the radial
lines will be utilized. The range bin size for the Kluang radar is 1-km.
14
The total data that is available for this study is very large. It is unnecessary to
put a virtual link in every radial line of the radar data. Thus, several locations or
azimuthal angles were chosen in a quasi-random manner. Radial lines with the angles
of 3, 6, 12, 15, 238, 241, 244, 247, 250, 294, 297, 300, 303, 306, 334, 337, 340, 343
degrees were chosen in this study.
These angles for the “virtual paths” links were chosen by adopting similar
technique employed by ITU-R and other researches (ITU-R Rec. 581-2; Chebil,
1997; Yagasena et al, 2000) in which the concept of “worst month” is considered and
the highest exceedence probability were chosen. This is done so that “worst case
scenario” is taken into consideration.
In determining the suitable radial lines for the virtual links, results from the
permanent echo test were used. From the permanent echo test, several areas where
rain is likely to occur are determined. Bin ranges of 32 to 51 were chosen for
analysis. This means that the data chosen were rain events occurring 36 km away
from the Kluang Radar Station (readings for the Kluang radar station starts only after
4 km away from the station) and the virtual link has a maximum path length of 20
km. This range in adequate for deduction of reduction factor. It is also sufficient to
cover rain cell size of interest. The 20 km range would well cover the individual rain
cells that are likely to occur. This will also ensure that the problem of beam elevation
is minimized. In addition, this exercise reduces the raw data considered in this study.
The elevation angle chosen in this study is 0.5o, which is the lowest elevation
angle of the radar system. Readings from this elevation angle is much nearer to the
ground and thus giving the precipitation that occurs near the ground.
Rain cell size distribution of 1-km integration is obtained from radar data.
From this distribution and using curve fitting technique, the rain rate for 0.01% of the
15
time or R0.01 is determined. This value is used in the calculation of rain attenuation
along the virtual paths.
For reduction factor deduction, virtual links of 1-km to 10-km are constructed
in each radial line. Since, bin range of 32 to 51 are used, this means that there will be
two 10-km links in a radial line. Using the rainfall rate data in each bin, attenuation
due to rain is calculated using parameter values obtained from ITU-R.
Attenuation for 0.01 % of the time for 1 to 10-km path lengths are calculated
at frequencies of 7, 10 and 15 GHz. They were chosen as they represent the spectrum
that is usually used for terrestrial and satellite links. Moreover, frequencies of 7 and
15 GHz will enable comparison to be made with measurements done here in UTM.
Reduction factor is then deduced from these calculations.
2.7
Rain Gauge Data
Eventhough radar data is able to give the rain rate; it is averaged over 1-km
range bin. It is interesting to know the profile of rain rate inside a rain cell. Thus, data
from rain gauge networks are used to complement the radar data. However, there has
been no work published in using rain gauge networks specifically for the
determination of rain rate profile inside the rain cell. As a result, this will be the first
attempt of such work. Most works has been using radar data, beacon or satellite
signals. These are discussed in the next section.
Since high rainfall intensity is usually of short duration in nature, the
integration time for the recorded rain rate is a critical parameter. Studies (Ruthroff,
16
1970; Bodtmann et al, 1974; Watson et al, 1981) have shown that a 1-minute
integration time should be adequate for rain rate measurements using a rain gauge.
Two rain gauge networks were set up in this study. Details of these rain gauge
networks will be given in the next chapter. All the rain gauges used in this study uses
1-minute integration time. Rain intensity and cell size for a single cell are obtained
from these rain gauge networks.
2.8
Attenuation Measurements Using Microwave Links
Some measurements on rain attenuation have been in UTM (Chebil, 1997;
Md Rafiqul Islam, 2000; Karim, 2000). They concluded that available reduction
factor models did not represent the attenuation in Malaysia. Md Rafiqul proposed
modifications to a certain model to fit the measured attenuation data. This will be
discussed further in the proceeding chapters.
There was no work that has been done in UTM to obtain the reduction factor
through radar data or rain gauge network.
CHAPTER 3
RAIN ATTENUATION, RAIN MODELS, AND REDUCTION FACTORS
3.1
Background
Signal attenuation becomes more severe as the rain rate increases. When the
budget link is exceeded, communication ceased to exist. In a system design, the
highest rain rate and its duration are considered and a suitable mathematical model is
used.
The rain responsible for producing a rain attenuation event can occur
anywhere along the propagation path at heights where liquid precipitation is possible.
The specific attenuation at any point along the path is related to the intensity of the
rain at that point. However, rain rate along the propagation path is not constant.
In order to account for the spatial variability of a rain event, a reduction factor
r is applied to the specific attenuation to get the overall path attenuation due to rain.
The purpose of this study is to analyze data obtained from weather radar, and to
18
formulate a suitable reduction factor that can be used to predict rain attenuation
according to the Malaysian local conditions.
3.2
Attenuation by Rain
Attenuation of radio propagation through space is given by (Freeman, 1987)
A (dB) = 92.45 + 20 log F(GHz) + 20 log L(km) + a + b + c + d + e
(3.1)
where
F = operating frequency in GHz,
L = path length or distance in km,
a = excess attenuation due to water vapor,
b = excess attenuation due to mist and fog,
c = excess attenuation due to oxygen,
d = absorption losses due to other gases, and
e = excess attenuation due to rainfall.
Parameters b and d can often be neglected in calculation for propagation loss
with respect to excess attenuation due to rainfall. Parameters a and c are known as
atmospheric attenuation. For example, at 22 GHz for a 10-km line-of-sight (LOS)
link, attenuation due to atmospheric attenuation is 1.6 dB, where as the free-space
loss is 139.3 dB. This means that excess attenuation due to rainfall is more severe
compared to other factors (Freeman, 1987).
19
Attenuation of radio wave due to rain is caused by absorption and scattering
mechanism (Allnutt, 1989). Absorption occurs when the incident radiowave energy
heats the scatterer until its temperature is above the surroundings and the scatterer
reradiates the absorbed energy isotropically. Scattering occurs when energy is
reradiated in all directions. The scattering cross-section can be calculated for rain
attenuation studies. Frequency and temperature are included to find the scattering
cross-section. Other important parameters for rain attenuation studies are drop shape,
drop size distribution and rain rate (Freeman, 1987: Allnutt, 1989; Aydin et al, 2002).
Attenuation of radio waves through rain (Ar), over path length (L), is given by
(Rogers, 1976)
L
Ar =
∫ γs(l) dl
dB
(3.2)
0
where γs(l) is the specific attenuation of rain (dB/km).
Equation 3.2 can be modified to use constant specific attenuation value, As,
and include a reduction factor r, to account for the nonuniformity of rain (ITU-R
P.530-8; ITU-R P.618-5), giving
Ar = γs r L
dB
where
γs = specific attenuation of rain (dB/km).
r = reduction factor, and
L = path length (km).
(3.3)
20
Now, specific attenuation
γs, can be found directly by theoretical calculation
in which either measured drop size distribution or available drop size distribution
models are used, or by indirect method of measuring drop size distribution, rain rate,
radar reflectivity, or propagation of microwave through rain. The apparatus used for
measurements are disdrometer, rain gauge, radar, and radiometer, respectively.
Theoretical calculation of rain induced attenuation is a rather complex and tedious
process. Specific attenuation can be calculated using the equation (Rogers, 1976)
∞
γs = 0.4343 ∫
Qt(r) n(r) dr
dB/km
(3.4)
0
where
Qt(r) is the total attenuation cross-section (cm2), and n(r) dr is the number of
drops per unit volume of space with radius in the interval between r and r + dr (m-3)
or drop size distribution (dsd).
Equation 3.4 takes into account attenuation due to absorption and scattering.
Even then, some kind of statistics are needed to formulate the reduction factor r.
Attempts are being made to find solution so that attenuation due to rain can be
predicted and thus, reliable communication link can be designed. Reliable estimates
of rain attenuation can be obtained through measurements taken over several years at
frequency and elevation angle (for satellite link) of interest, or by using indirect
measurements using disdrometer, rain gauge, radar, and radiometer. However, it has
been shown that radar can provides data at a much shorter time period (Wilson, 1964;
Jatila et al, 1973; Olsen, 1982; Seed et al, 1990; Lahaie et al, 1993).
21
Although rain attenuation can be determined by measuring drop size
distribution, it is found out that specific attenuation due to rain is closely related to
rainfall rate (Rogers, 1976; Olsen et al, 1978). Thus, specific attenuation can also be
estimated by finding the rain rate percentage. And it is useful to relate rain induced
attenuation to the rainfall rate since the rainfall rate R data is available throughout the
world. An empirical equation that is much easier than the theoretical equation, has
been shown and widely used, to relate specific attenuation to the rainfall rate is given
by (Rogers, 1976; Olsen et al, 1978)
γs = k Rα
(3.5)
where k and α are parameters that depend on drop size distribution,
temperature and polarization. To produce k and α, a regression analysis was done by
Olsen et al, 1978.
Thus, drop size distribution is very important for rain attenuation prediction.
It can be use to predict excess rain attenuation, and relate rainfall rate to excess rain
attenuation. Drop size distribution is also used to relate radar reflectivity with rainfall
rate.
Some parameters that were usually used in propagation studies will be
discussed. Overview of several models for estimating rainfall rates will also be done
in the next chapter. A suitable rainfall rate to be used in this study is also determined.
In addition to all these, some models for reduction factor is reviewed and then
compared with the one formulated through this study.
22
3.3
Rainfall Rate, Rain Cell Size, and Rain Height
A brief discussion on atmospheric conditions, terminal velocity, shape and
drop size distribution of a raindrop is given in Appendix 1.1. Figure 3.1 shows how
rain can occur. When a cold front of air meets a warm front, condensation of water
vapor can occur. If the water vapor is heavy enough, precipitation, as manifested by
rain, will occur.
The intensity of rain is known as the rainfall rate, R, and measured in mm/hr.
It has also been noted that hot and cold fronts developed at high heights experience
significant microwave signal fade (Barbara et al, 1993). The heavier the rain rate, the
higher will be the attenuation (Ajayi et al, 1988; Allnutt, 1989; Juy et al, 1990;
Yagasena et al, 1995).
Statistically, the diameter of rain cell decreases as the intensity of rain
increases (Allnutt, 1989; Mitnik et al, 1998; Nor Hisham Khamis et al, 1999;
Konefal et al, 2002) as shown in Figure 3.2. From these studies, the rain cell size that
must be taken into account for measurements using radar or rain gauge network must
cover an area of at least 1 km.
For system planning, the rainfall structure such as horizontal and vertical
dimensions of rain cells, spatial and temporal variability of rain is very important.
With these information, rain attenuation and scattering can be determined and rain
attenuation mitigation technique such as site diversity can be applied.
23
Figure 3.1 Rain formation through cold and warm air fronts (Allnutt, 1989).
Figure 3.2 Rain cell diameter versus rainfall rate (Allnutt, 1989).
24
For slant-path propagation applications, such as satellite communications, the
height of the rain structure is important. A region known as the ‘melting layer’ or the
‘bright band’ must be identified. Below this region, rain occurs and microwave
propagation suffers attenuation due to rain. Losses in the ice region above the bright
band are negligible for the purposes of most calculations (Eastment et al, 1996).
Above this region, no rain occurs and the propagation suffers only spatial attenuation.
Studies (Pontes et al, 1995; ITU-R P.839-2) have shown that convective rain in
tropical region often has bright band above 10 km and also suffers from severe
updraft. However, the bright band region usually exists at the height of 4.5 – 5 km.
The ITU recommended that rain height for tropical region is 5 km (ITU-R P.839-2).
A more recent study (Ong et al, 2000) has shown that the variability of rain
height according to seasonal period and types of rain. Identification of the melting
layer can be done through radar reflectivity measurement. Figure 3.3 shows the
height of the melting layer. However, rain can sometimes occurs below the melting
layer. This is shown in Figure 3.4. This is especially true for heavy rainfall situations.
The uncertainty of the difference in height between rain event and the melting layer
need to be investigated so that a reliable prediction of attenuation can be made.
25
Figure 3.3 Height of melting layer (Allnutt, 1989).
26
Figure 3.4 Rain height (Allnutt, 1989).
3.4
Rainfall Rate for 0.01 % of the time or R0.01
An important characteristic of rainfall is known as the R0.01 rain rate. This is
the rainfall rate that will occur for 0.01% of the time. For a period of one year
(364.25 days) which is equivalent to 524,5200 minutes, 0.01% of the time will be for
52.45 minutes. The determination of the rain rate for 0.01 percent of the time or R0.01
comes from the fact that a good system must provide at least 99.99% reliability.
Design and system engineers use this value to construct communications system such
27
that the link is available for 99.99% of the time. I.e. the link can only be down for
only for a total time of 52.45 minutes for the entire year. Systems built with this
value ensure reliable microwave link and guarantee customer satisfaction. ITU-R has
recommended the use of this parameter for attenuation studies.
To determine rain rate for a specific percentage of time, rain prediction
models can be utilized. These rain models can be used to determine the rain rate for
0.01 % of the tome or R0.01.
3.5
Rain Prediction Models
Prediction models are used to provide the best possible estimates given the
available information. Using these models, the rain intensity can be known and thus,
the specific attenuation due to rain can be predicted.
There are several rain models that are available in the literature of which, two
of the often-used models will be discussed. These rain models can be used to
calculate the specific rain attenuation, especially rain rate for 0.01% of the time or
R0.01 where it usage is recommended by ITU-R. Values of R0.01 obtained from these
models will be compared to the values obtained in this study. Two of the widely used
models for rain intensity prediction, Crane’s Global Model and the ITU-R Model will
be discussed here.
28
3.5.1 Crane’s Global Model
Crane’s Global model (Crane, 1980) divides the world into eight regions, as
shown in Figure 3.5. It is based on total rain accumulation, and the number of
thunderstorm days from maps published by Landsberg (1974). Crane obtained
additional guidance from the Koppen world climate classification. Boundaries were
adjusted to accommodate variations in terrain, predominant storm type and motion,
general atmospheric circulation, and latitude. Satellite and precipitation frequency
data were used to extend the climate over the oceans. The measured 1-minute rain
rate distributions that were available for each of the regions were pooled to construct
the rain rate distributions as shown in Figure 3.6 and Table 3.1. Malaysia falls into
region H, and has a rain rate of 145 mm/hr for 0.01 percent of the time.
Figure 3.5 The global rain rate regions (Crane, 1980).
29
Figure 3.6 Rain rate distribution curves for various regions (Crane, 1980).
Table 3.1 Point Rain Rate (RP) Distribution Values (mm/h) Versus Percent of Year
Rain Rate is exceeded (Crane, 1980).
Percent
of Year
0.001
0.002
0.005
0.01
0.02
0.05
0.1
0.2
0.5
1.0
2.0
Number
of
Station
Years
of Data
Rain Climate Region
A
28
24
19
15
12
8.0
5.5
4.0
2.5
1.7
1.1
B
54
40
26
19
14
9.5
6.8
4.8
2.7
1.8
1.2
C
80
62
41
28
18
11
7.2
4.8
2.8
1.9
1.2
D1
90
72
50
37
27
16
11
7.5
4.0
2.2
1.3
D2
102
86
64
49
35
22
15
9.5
5.2
3.0
1.8
D3
127
107
81
63
48
31
22
14
7.0
4.0
2.0
E
164
144
117
98
77
52
35
21
8.5
4.0
0.4
F
66
51
34
23
14
8.0
5.5
1.2
1.2
0.8
0.4
G
129
109
85
67
51
33
22
14
7.0
3.7
1.6
H
251
220
178
147
115
77
51
31
13
6.4
2.8
0
25
44
15
99
18
12
20
2
11
30
3.5.2 ITU-R Model
The ITU-R (Allnutt, 1989) (formerly known as CCIR) divides the world into
a number of rainfall climatic zones as shown in Figure 3.7. Table 3.2 gives the
rainfall rates for the climatic zones. Figure 3.8 is the rainfall rate contours for 0.01%
of the time for Asia. From Table 3.2 and Figure 3.8, R0.01 for Malaysia is 145 mm/hr.
Figure 3.7 Rainfall climatic zones (Allnutt, 1989)
31
Table 3.2 Rainfall rates in the climatic zones (Allnutt, 1989)
Percentage of
time
1
0.3
0.1
0.03
0.01
0.003
0.001
A
B
C
D
E
F
G
H
J
K
L
M
N
P
Q
<0.1
0.8
2
5
8
14
22
0.5
2
3
6
12
21
32
0.7
2.8
5
9
15
26
42
2.1
4.5
8
13
19
29
42
0.6
2.4
6
12
22
41
70
1.7
4.5
8
15
28
54
78
3
7
12
20
30
45
65
2
4
10
18
32
55
81
8
13
20
28
35
45
55
1.5
4.2
12
23
42
70
100
2
7
15
33
60
105
150
4
11
22
40
63
95
120
5
15
35
65
95
140
180
12
34
65
105
145
200
250
24
49
72
96
115
132
180
Figure 3.8 Rainfall rate contours for 0.01% of the time for Asia (Allnutt, 1989)
32
Recent publication of the ITU-R shows a revised rainfall rate for 0.01% of the
time for Asia. Figure 3.9 shows the recommended rainfall rate for 0.01% of the time
for the Asian region (ITU-R P.837-4, 2003). The new R0.01 for Malaysia is 120
mm/hr.
Figure 3.9 Revised rainfall rate contours for 0.01% of the time (ITU-R P.837)
The new value for R0.01 of 120 mm/hr may had resulted from the fact that
newer and more accurate data are available. Eventhough long-term data are available,
most measurements have been carried out for meteorological or hydrological
purposes. These data are usually taken for intervals of one hour or longer, whereas it
has been proposed that a 1-minute integration time is better. These newer data also
enables methods of rain rate conversion to have better accuracy in converting a tminutes rain rate into an equivalent 1-minute integration time rain rate (Chebil,
33
1997). Newer measurement themselves uses a 1-minute integration time, giving more
accurate data in terms of rainfall rate.
3.6
Reduction Factor
The inhomogenuity of rain cell give rise for the need to compensate for rain
variability in rain induced attenuation calculation. One method of doing this is by
introducing the reduction factor in the calculation. By doing so, the specific
attenuation per distance can be employed and better value of rain attenuation on
specific microwave link can be estimated. The following sections will discuss some
of the reduction factors available in the literature. Even though they give the
reduction to be used in calculating rain attenuation, none of the available literature
describe in detail on how the reduction factor was obtained. A reduction factor is
function of length, rain rate, frequency, and polarization (Assis, 1990). Some models
are discussed here.
3.6.1 Lin Model
The Lin Model (Lin, 1977) is rather simple and easy to compute. Lin found
that the relationship between rain attenuation and path length is nonlinear. The Lin
Model proposed the reduction factor to be
34
r=
1
(3.6)
L
1+
L(R)
where L(R) ≈
2636
R P - 62
km.
L is a characteristic path length such that the nonlinear factor equals one-half
when L = L , and L related to the diameter of the rain cell.
3.6.2 Moupfouma Model
Moupfouma (Moupfouma, 1984) based his works from data gathered in
Congo, Europe, and the United States. He proposed the reduction factor to be
r=
1
(3.7)
−β
 p  m
1 + 0.03
 L
 0.01 
where m = 1 + 1.4 x 10-4 f 1.76 loge L
0.45
0.6
for
for
0.001 ≤ p ≤ 0.01

0.01 < p ≤ 0.1 
for L < 50 km
0.36
0.6
for
for
0.001 ≤ p ≤ 0.01

0.01 < p ≤ 0.1 
for L ≥ 50 km
β =
β =
35
3.6.3 CETUC Model
Pontes (Pontes et al, 1993), Silva Mello (Silva Mello et al, 1997) and their
colleagues did their research in Rio de Janeiro, Brazil, at the Center for
Telecommunication Studies of the Catholic University of Rio de Janeiro (CETUC).
Thus the climate is similar to Malaysia, which is also in the tropical region and near
the equator. From their works, they produced a reduction that is described below,
r=
1
1+
(3.8)
L
Lo
where Lo = µ {1 + Rp(ν - ωlogp)}-1
(3.9)
µ = 200, ν = 0.425, ω = 0.089
3.6.4 Improved CETUC Model
Perez Garcia and da Silva Mello (Perez Garcia et al, 2004) proposed new
CETUC model based on new research works, and additional data together with the
already available data from ITU-R. This model is developed with the assumption that
the nonuniformity of rainfall along the propagation path can be modelled by an
equivalent uniform cell with a rainfall rate that is dependant on length of the
terrestrial link, or specifically,
Ar = γs.r.L
(dB)
(3.10)
36
where
Ar = rain induced attenuation along a terrestrial link (dB),
γs = specific attenuation due to rain (dB/km),
r = reduction factor, and
L = actual path link (km).
The reduction factor is given as
r = 3.445 L-0.164 Rp(-0.369 + 0.115/L)
(3.11)
where Rp is the rainfall rate at the percentage time of interest.
3.6.5 Goddard and Thurai Model
Goddard and Thurai (Goddard et al, 1997) outlined several steps to calculate
rainfall attenuation for a particular microwave link. They are as follows: -
First, obtain rainfall rate, Rp that occurs for the time percentage p, of interest.
Usually, this would be R0.01.
Then compute specific attenuation As, for this rain rate, at the required
frequency using ITU-R 838.
Compute the path reduction factor r, from
37
s(L) = 2L-0.053 – 2.25
(3.12)
where L = path length (km)
r = 1.35 + s(L) log Rp
(3.13)
if r > 1, then r = 1
Compute the total path attenuation At using Equation 3.10.
3.6.6 ITU-R Model
The ITU-R model (ITU-R P.530-8) is the model that many researches
compared their results with. This is because ITU is the authoritative body governing
the world of communications. With its working committees around the world, and
results are always updated when new data are available. The ITU-R model can be
utilized by following the steps below,
Obtain R0.01 which is the rain intensity exceeded for 0.01% of the time (with
1-minute time integration).
Compute specific attenuation As, for R0.01 at the required frequency using
Recommendation 838.
Compute the reduction factor r, using
38
r0.01 =
1
1+
(3.14)
L
Lo
35 e -0.015 R 0.01
where L 0 = 
35 e -1.5
for R 0.01 ≤ 100 mm/hr
for R 0.01 > 100 mm/hr
Finally, compute A0.01 using Equation 3.10.
For other time percentages, ITU-R recommends the use of the following
equation
A s = 0.12 A 0.01 p -[0.546 + 0.043 log p ]
(3.15)
3.6.7 Singapore Model
Singapore is located just below the Malay Peninsula. Thus it shares many of
rain characteristics with Malaysia. The distance between UTM, Skudai and
Singapore is about 50 km. However, Singapore is a small island surrounded by water,
which might affect the local weather conditions. The reduction factor proposed by
Ong (Ong et al, 1995) has similar characteristics as compared to the ITU-R model. It
is described as follows,
r = 1/(1 + L0.9/L0)
(3.16)
39
where L0 = 35 exp (-0.015R0.01)
3.6.8 DAH Model
Asoka Dissanayake is a senior scientist at the COMSAT Laboratories,
Maryland, U.S.A. Dr Jeremy E. Allnutt is a professor and the Director of Masters in
Telecommunication program at the George Mason University. Fatim Haidara is a
senior engineer at Intelsat. They (Dissanayake et al, 1997) proposed a reduction
factor to be used in the calculation of rain attenuation for earth-satellite path that can
be also applied for terrestrial path. The reduction factor they proposed is
1
r=
(3.17)
LAs
1 + 0.78
− 0.38[1 − exp(−2 L)]
F
where
As = specific attenuation calculated using R0.01, or
= k R0.01
α
L = path length
(dB/km),
(km), and
F = frequency in GHz.
This model has been adopted by the ITU-R recently (ITU-R P.618-6, 1999).
40
3.6.9 Comments on Reduction Factor Models
Lin deduced his model from measurements done in Palmetto, Georgia, U.S.A.
Thus, the weather conditions are different from Malaysia. He obtained his data using
5-minutes integration time tipping bucket rain gauges, and an 11 GHz microwave
link with a path length of 42.5 km. The current accepted integration time as proposed
by ITU-R is 1-minute. The shorter time period would give a better reading of the
rainfall rate especially for climatic region such as Malaysia where the rainfall rate is
much heavier. Lin also included wet radomes effect in his calculations. Depending on
the structure of the radomes, he used the values of 4-8 dB. These values may be
different from the microwave systems that are employed in Malaysia. Thus, accurate
determination of the wet antenna effect is desirable.
The Moupfouma, ITU-R, and DAH models used data that were available
from several places. Some data are taken from temperate regions, while others are
obtained from tropical regions. These models tried to be as universal as possible.
However, studies (Ajayi et al, 1988; Juy et al, 1990; Yagasena et al, 1995) have
shown that rain events are rather localized and models need to be formulated using
local data. This has been the argument of carrying out this study.
The CETUC, Improved CETUC, and Singapore models are works that have
been done in tropical region. This means that the weather conditions are rather
similar. So, it interesting to compare such works with this study. However, there are
several differences in the local terrain conditions. Singapore is a small island. A body
of land surrounded by water. The CETUCs models are formulated in Brazil, near Rio
de Janeiro. Heavy rain forest and near the ocean.
Only the Goddard and Thurai used radar as their measurement instrument to
formulate the reduction factor, which the same as this study. However, their works
41
were done in Chibolton, UK. Thus the climate is different. The Singapore model
used rain gauge network and beacon data. The CETUCs models used rain gauge,
satellite and microwave links. The DAH model is formulated using beacon signal and
radiometer measurements.
No doubt there are many factors and differences in the formulation process of
these models. Investigations on reduction factor models have been done locally by
Chebil (1997) and Md Rafiqul Islam (2000). Md Rafiqul Islam concluded that the
ITU-R model does not reflect the measured attenuation done at seven sites in
Malaysia. The model underestimates rain attenuation. The Moupfouma and Lin
models are closer to the measured data, but the Moupfouma model overestimated
attenuation in some place where attenuation measurement were done. Md Rafiqul
Islam proposed modifications to the Moupfouma model to suit the attenuation
measurement data. However, there are some issues regarding the attenuation
measurement done. This will be discussed later in this thesis.
3.7
Rain in Malaysia
The monthly cumulative distribution of rainfall is influenced by the seasonal
monsoons, namely the Northeast monsoon from October to March, and the
Southwest monsoon from April to September. The Northeast monsoon is the primary
rainy season in Malaysia. Together with cold air rushing from Siberia this monsoon
produce heavy rainfall and usually causes floods in the east coast part of the Malay
Peninsular and Sarawak. The Southwest monsoon is relatively drier except in Sabah.
The rain events consist of convective and widespread rain. Convective rain is
characterised by intense rainfall over a short period and covers a limited area. The
widespread/stratiform rain is characterised by medium and low intensity rain over a
longer duration and covers a wider area (Yagasena et al, 1995).
42
Interesting parameters that are closely related to rain attenuation are rain cell
size or diameter (d) and the effective rain column height (he). In this study, rain cell
sizes were investigated through rain gauge data and radar data. Data for rain height
were available but due to the scope of this study, was not investigated. It will be
however, look into in future studies.
It is found out that most rainfall in tropical areas is ‘convective’ in nature
(Pan et al, 1994; Nor Hisham Khamis et al, 1999, Nor Hisham Khamis et al, 2004).
At lower rainfall rates, rain is rather widespread and uniform. The higher rainfall
rates exhibited rather random distribution, having multiple cells and also higher rain
height.
3.8
Determination of Rain Cell Size
Most studies (Kuhn, 1989; Pan et al, 1992) concluded that rain cell depends
on rain intensity. Kuhn (1989) found that for rain rate above 60 mm/hr, the mean
diameter of rain cell was less than 1.5 km. He did his research in Germany which is
of course, has different climate as compared to Malaysia. However, Pa et al (1992)
did their research in Papua New Guinea, which is in the tropical region. They
concluded that rainfalls are mainly convective with relatively small diameters. These
intense convective rains also usually occurred in relatively shorter period of time as
compared to widespread rain.
Goldhirsh et al (1992) and Sauvageot et al (1999) noted that there is no
generally accepted and preferred definition of a rain cell. A number of researchers
have employed their own definitions. One definition is the minimum detectable
contour values of rain rate (Goldhirsh et al, 1992). In his earlier work, Goldhirsh
43
(1983) defined rain cell diameter as “those distances over which the rain rate
continuously exceeds Rt,” where Rt is the threshold values of a specific rain rate. He
has selected Rt’s of 2, 5, 10, 20, 50, 100, and 150 mm/hr. This is also the definition
used by Sauvageout et al (1999). If Rt is equal to the minimum detectable rain rate,
then both definitions of rain cell are in agreement. Goldhirsh later defined rain cells
as having “core” values of rain intensities and nested families of rain rate isopleths
(Goldhirsh et al, 1992).
In this study, rain cell size distribution is of interest, regardless of the core
rain rate values. Previous study (Nor Hisham Khamis et al, 1999), has shown that
rain cell cores having intensities of 120, 90, 60, and 30 mm/hr have diameter between
0.95 to 1.2 km. The averaged cell size of core rain rate of 75 mm/hr is shown to be
1.2 km. Thus, it is felt that it is better to formulate the rain cell distribution against
the percentage of time. As a result, the definition of a rain cell size in this study is the
minimum detectable rain rate, which is 0.2 mm/hr from the radar data.
CHAPTER 4
RAIN GAUGE AND RADAR DATA
4.1
Introduction
An important parameter in calculating attenuation due to rain is the rainfall
rate. This is also the main parameter being measured in meteorology. The apparatus
widely used to measure rainfall rate is the rain gauge.
A rain gauge provides a fairly simple and accurate measure of point rainfall
rates. However, the measurement is only at certain points. Rainfall events vary
widely in both time and space. This means that an occurring rain event is not
constant. A rain event may start heavily but the rain rate may tapers off after a while.
Characteristics of rain events may also differ from one place to another. For example,
temperate region has significantly larger drop size compared to tropical region when
both experienced the same rain type. Even in tropical region, stratiform rains have
larger drop size than convective rains (Atlas et al, 1995). Thus, while rain gauge
gives good measurement of point rainfall rate; it is not adequate for most needs.
45
However, measurement done at a particular location will give some
indications of the characteristics of the rain events. This will enable comparison with
data obtained using the same technique.
The data gained from a network of rain gauges is accurate for a small area,
but not practical for large areas, remote land areas, and the ocean. In order to
overcome this problem, other types of measurements such as radar, remote sensing
and radiometer are used.
Rain gauge data for this study was obtained by setting up two rain gauge
networks in the Universiti Teknologi Malaysia, Skudai Campus. While radar data
was obtained from the Meteorological Department of Malaysia (Kluang Radar
Station).
4.2
Rain Gauge and Rain Gauge Networks
A preliminary rain gauge network was set up in the Skudai campus (RGNUTM 1). The network of rain gauges consisted of three rain gauges. One rain gauge
was placed in an open area in Kolej Merbau (Merbau), one on top of a Civil
Engineering Lab building (Civil), and the other one on top of a Mechanical
Engineering Lab building (Mechanical). The positions of the rain gauges were almost
on a straight line with distances of 0.41 km from Merbau to Civil, 0.55 km from
Civil to Mechanical, and 0.95 km from Merbau to Mechanical. Figure 4.1 shows the
locations of all the rain gauges.
46
Figure 4.1 RGN UTM 1 Rain Gauge Stations
The rain gauges were 0.5 mm Casella tipping-bucket type, which record the
number of tipping in a 1-minute integration time. No data is recorded if the bucket
does not tip which means there is no or very little rain (less than 0.5 mm/minute or
30 mm/hr). The specifications of the Casella rain gauge are given in Appendix 3.1.
Data were collected from 16 September until 28 November 1996. This
amounted to 74 days of data collection. However, rain events occurred only for 43
days, while there was 36 days where rain was recorded at all three rain gauge stations
simultaneously, giving valuable insight into the spread of rain events. A sample of
the collected data is given in Appendix 3.2.
A second network of rain gauge was installed in the UTM, Skudai campus
consisted four Casella Tipping Bucket with Integral Logger (RGN-UTM 2). Four
47
locations were chosen, the first one being near the Faculty of Chemical Engineering
(Chemical). Except for the Chemical site, which has a 0.2 mm tipping bucket, the
rest of the rain gauges have 0.5 mm tipping buckets. Other sites are Institut Voltan
dan Arus Tinggi (IVAT), TV Studio, and Kempas. The rain gauges were installed
such that the distances between them are about 250 meters. Figure 4.2 shows the
locations of all the rain gauges.
Figure 4.2 RGN-UTM 2 Rain gauge network stations.
48
This network of rain gauges was set-up around the campus in December
1998. RGN-UTM 2 was set-up for a year but unfortunately some data were lost
during transferring from the data logger into the computer notebook. Thus, available
data were from December 1998 until July 1999. The actual data collection ran until
December 1999.
4.2.1 Casella Rain Gauge
The Casella rain gauge is of tipping bucket type, which is fitted with a solidstate logger (Casella, 1996). It employs a lightweight plastic injection moulded
tipping bucket and support assembly. The construction of the rain gauge is quite
robust and has a very long life term. The Casella rain gauge is supplied readily
calibrated to indicate 0.1 mm, 0.2mm or 0.5 mm of rainfall with each bucket tip. In
this study, bucket sizes of 0.2 mm and 0.5 mm are used. The number of tips per
minute are counted and stored in the integral logger. Figure 4.3 shows the Casella
tipping bucket rain gauge with an integral logger.
49
Figure 4.3 Casella Tipping Bucket Rain Gauge with Integral Logger.
The integral logger operates on 9 V batteries. It contains a powerful CMOS
micro controller with 4K of EPROM program storage, 32K of solid-state data
storage, real time clock, battery backup and a serial communication interface.
Figure 4.4 shows the functional diagram of the tipping bucket rain gauge.
During rain fall, rainwater is funnelled into one of the two buckets, which is rest on a
stainless steel pivot pins in such a way that when a 0.2 mm (or 0.5 mm) of rain has
been collected in the buckets, it tips and momentarily closes a magnetic reed switch.
50
The tipping action discharges the water and at the same time causes the other bucket
to start collection. The number of tips per minute are counted and stored in integral
logger. Rainfall data is stored in the logger on a 1-minute time basis. Thus, the
integration rainfall rate stored will be 12, 24, 32, 64, 108, …, mm/hr for 1, 2, 3, 4, 5,
…, tips per minute of the bucket for the 0.2 mm bucket
Figure 4.4 Tipping buckets of a Casella Rain Gauge.
4.3
Radar Data Collection
The radar data was obtained from the Kluang Radar Station of The
Meteorology Department of Malaysia. The Kluang radar station is located about 61
km from the UTM, Skudai campus. For the Malay Peninsular, the Meteorology
Department has five radar stations located in Kluang, Subang, Kuantan, Butterworth,
and Kota Bharu. For system management and connectivity, the Meteorological
Department of Malaysia uses the 3D-RAPIC software produced by the Australian
51
Bureau of Meteorology, Observations and Engineering Branch, Radar Engineering
Section. Calibration of the Kluang radar system is done every 6 months. A partial
checklist for calibration is given in Appendix 3.4. Using this 3D-RAPIC system, data
from all radar stations were integrated to give a whole radar scan of the Malay
Peninsula. Figure 4.5 shows an example of a ‘merged’ PPI scan of a radar scan
produced by the 3D-RAPIC system.
Figure 4.5 Merged PPI scan.
52
The reflectivity color palette at the bottom of Figure 4.5 indicates the intensity
of the occurring rain events. The specifications of the radar system have 16 levels to
indicate the intensity of the falling rain. Every level corresponds to a particular
reflectivity value or reflectivity factor (Z), which in turns corresponds to a particular
rain rate. Table 4.1 gives the dBZ level (value of Z in dB), and the corresponding rain
rate R (mm/hr) for the Kluang radar station.
Table 4.1 dBZ-R values for Kluang radar.
Level
dBZ
R (mm/hr)
1
11.8
0.2
2
23.0
1.0
3
28.1
2.1
4
31.0
3.2
5
34.0
4.9
6
37.0
7.5
7
40.0
11.5
8
43.0
17.8
9
46.0
27.3
10
49.0
42.1
11
52.0
64.8
12
55.0
99.9
13
58.0
153.8
14
61.0
236.8
15
64.0
364.6
The radar scans can also be viewed individually for each radar station. Figure
4.6 shows a pulse-position-indicator (PPI) radar scan for the Kluang radar station.
53
The PPI gives the raining events as they occur. Figure 4.7 shows the rain height
indicator (RHI) scan, which is the product of volumetric scanning. The RHI scan
gives the vertical profile of the raining events. It indicates the height at which the rain
is falling. Both figures are shown simultaneously on the monitor screen of the 3DRAPIC system.
Figure 4.6 A Kluang radar station PPI scan.
54
Figure 4.7 A Kluang radar station RHI scan.
In this study, only the data from the Kluang radar station is utilized. The
specifications of the Kluang radar stations are as given in Appendix 3.5. The chief
controller of these radar stations is located at the Head Office of the Meteorological
Department in Petaling Jaya.
To operate the radar system, the Meteorology Department uses a Silicon
Graphics Indigo UNIX Station. As mentioned earlier, the RAPIC software,
developed by a company in Australia was used to process the radar data. After
processing and extracting the necessary information from the radar data, these data
are stored in DAT tapes. Thus, to obtain these data, a DAT tape system (HP
SureStore) was acquired. After copying the data in DAT tapes, these data are then
written on CDs for use with PCs. This is done in the campus using our own UNIX
55
station. The data consist of all the data from the five radar stations. Thus, using
MATLAB, a program was written to extract the Kluang radar data. Further analysis
and processing the data also uses MATLAB. Figure 4.8 shows an example of a radar
scan plot using MATLAB.
Figure 4.8 A MATLAB radar plot.
In its normal operational mode, the Kluang radar will do a composite PPI
scan every 10 minutes, and a volumetric scan every 30 minutes. The PPI scan will
lasts for a minute where the revolution or rotation of the antenna is 3 rpm. The
displayed composite PPI scan is a combination of 3 scan-angles 3.5o (0 – 30 km), 2o
(30 – 100 km), and 0.5o (100 – 500 km). The STC for Kluang radar station is up to
56
230 km. Figure 4.9 shows the top view of a typical composite image, while Figure
4.10 shows a cross-section of a typical composite image.
Figure 4.9Top view of typical composite image.
1
2
3
4
5
6
Legend
antenna beam
buildings
hills
rain below antenna beam
cloud formation
rain above antenna beam
Figure 4.10 A cross-section of a typical composite image.
57
For volumetric scan, the antenna beam will pass or rotates azimuthally 15
times in the duration of 5 minutes. After each pass or rotation, the antenna beam is
elevated to a higher elevation angle. These angles are also known as ‘volumetric
elevation angles’ as it is done in the volumetric scanning. Since the antenna does 15
rotations, there will be 15 volumetric elevation angles. Table 4.2 gives the volumetric
or scanning elevation angles for the Kluang radar station. The range of the Kluang
radar station is from 4 km up to 512 km in a radial direction. The range bin is 2 km
for the composite PPI scan and 1 km for the volumetric scan.
Scanning is done for every angle in the azimuthal plane. The mechanism of
the radar system is such that for a 1-km range bin resolution, it will send 8 pulses in
every 250-meter range. The reflected power is then averaged. Four averaged readings
will again be averaged for four 250-m ranges making a reading for 1-km range bin.
Thus, 32 pulses are averaged for a 1-km range bin.
Table 4.2 Radar Scan Elevation Angles.
Pass/Rotation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Volumetric Elevation Scanning angles
0.5 deg
1.2 deg
1.9 deg
2.7 deg
3.5 deg
4.6 deg
6.0 deg
7.5 deg
9.2 deg
11.0 deg
13.0 deg
16.0 deg
20.0 deg
25.0 deg
32.0 deg
58
For this study, the 1-km range bin is more useful and thus, the volumetric
scan. Operation of Kluang Radar Station was altered so that it will do volumetric
scan for every 10 minutes instead of every 30 minutes. This generated enough
amount of data that was used in this study. The period of the radar data is from 2
January 1998 at 4:23 (Universal Time Constant - UTC) up to 10 March 1998 at 1:03
(UTC). From 2 January to 8 January, the volumetric scanning was done at 30-minute
interval, and from 8 January (1:03 UTC), the volumetric scanning was done in a 10minute interval. Total scans where rain is detected are 7998 scans.
4.3.1 Kluang Radar Data Format
An example of the radar data is given in Appendix 3.6. It is stored in the
ASCII Asynchronous Format. This data format enables high data transfer rate since it
uses run length encoding and empty radials were not recorded. The format and
encoding algorithm for the radar data is as explained in Appendix 3.7. In order to
utilize the data, the encoded data is decoded. A MATLAB program was written for
this purpose. The program produces 360 x 101 matrices of the radar scans in which
the first column is the azimuthal scanning angles and the following columns are the
level of rain rate for each range bin. This gives a radial of 100 km that is sufficient as
it well covers the typical diameter of a rain cell.
The data is kept in 17 MATLAB file folders. These folders are called Data1
to Data17. The number of 360 x 101 matrices in each folders is as given in Table 4.3.
Since rain rate is the wanted parameter, the level of rain rate in all the matrices is
then converted into actual rain rate using Table 4.4. The values in this table are
supplied by the Meteorological Department of Malaysia.
59
Table 4.3 Number of 360 x 101 matrices in each data folders.
Data folders
Number of matrices in each data files
Data1
175
Data2
648
Data3.
949
Data4
906
Data5.
721
Data6
1041
Data7
955
Data8
792
Data9
869
Data10
777
Data11
785
Data12.
893
Data13
807
Data14
662
Data15
888
Data16
1049
Data17
996
Total no. of matrices
13913
60
Table 4.4 The corresponding actual rain rate values in mm/hr to the rain rate level.
Level
Rain rate in mm/hr
0
0
1
0.2
2
1.0
3
2.1
4
3.2
5
4.9
6
7.5
7
11.5
8
17.8
9
27.3
10
42.1
11
64.8
12
99.9
13
153.8
14
236.8
15
364.6
From Table 4.4, the actual number of individual data is 500,868,000. This is a
very large number. Not all the data are used in this study. Data are selected in a
quasi-random manner as will be explained in the next chapter.
CHAPTER 5
DATA ANALYSIS AND RESULTS
5.0
Introduction
Data analysis will be divided into two parts. Section 5.1 will be on the
analysis and results on the rain gauge data while the following Section 5.2 will be on
the radar data.
5.1
Rain Gauge Data Analysis
In this section, data from the two networks of rain gauge is discussed. The
important information extracted from the analysis are rain cell size and the
distribution of rainfall inside a rain cell.
62
5.1.1 Preliminary Data Analysis
Preliminary analysis was done on the data obtained from the network of 3
rain gauges set up in the Skudai campus (RGN-UTM 1). Table 5.1 shows the rain
events recorded at each station, and plotted as in Figure 5.1. The rain rate is obtained
from the 1-minute integration time for the Casella rain gauge. Amount of rain per
minute is then converted to per hour.
Table 5.1 Rain events recorded at all rain gauges locations.
No. of readings
Rain Rate (mm/hr)
Merbau
Civil
Mechanical
30
577
533
575
60
120
95
102
90
18
17
15
120
3
10
8
150
0
0
1
Total
718
655
701
Table 5.1 shows the individual readings of rainfall rate occurring at all the
rain gauge stations. It shows that most rain events occur at low rainfall rate, namely
30 and 60 mm/hr. High rainfall rates are few with 150 mm/hr occurs only once at the
Mechanical station. From the total time of the collection of data, which is 105,400
minutes; the 120 mm/hr rain rate is 0.0028 %, 0.0095 % and 0.0076 % for the
Merbau. Civil, and Mechanical station, respectively. From the ITU-R and radar data,
these values are very close to the value of 0.01 % for rainfall rate of 120 mm/hr. This
means that the data collected were good and reliable.
63
A closer examination of Table 5.1 indicates that rain events that have
occurred are rather distinctive. Eventhough the Civil station is located between the
other two stations; it recorded the lowest number of rain events. Considering the fact
that these rain gauges are rather close to one another, this means that the boundary
between raining and nonraining area is quite distinguishable. This may be due to the
highly convective nature of rain.
700
No. of readings
600
Merbau
500
Civil
400
Mechanical
300
200
100
0
0
20
40
60
80
100
120
140
Rain rate (mm/hr)
Figure 5.1 Graph of Rainfall Rate Recordings at all Rain Gauge Stations.
Table 5.2 Correlations for no. of readings at all stations.
Merbau
Civil
Merbau
1
Civil
0.999306
1
Mechanical
0.999379
0.999975
Mechanical
1
160
64
There is a high correlation of rain event at all three stations as can be seen
from Table 5.2 and Figure 5.1. The high correlation is for the cumulative collected
data after a period of time. Eventhough individual rain events might differ and vary
in both time and space; rain events recorded at two different places will produce
similar patterns if they experienced the same climatic weather conditions. This again
shows that the data collected were stable and sufficient.
5.1.2 Selection of Rain Gauge Network (RGN-UTM 1) Data
To get the distribution of rainfall rates inside a rain cell, rain events that occur
simultaneously at all rain gauge stations are considered. When this happens, the
rainfall rate recorded at all stations can be assumed to be from the same rain cell.
Since the Civil station is at the middle of the rain gauge stations arrangement, and to
get the profile of rainfall rate distribution inside a rain cell; of all the simultaneous
recordings; only when the readings at Civil station are equal or higher than the other
two stations are selected. Rain events that were recorded only at the Civil station are
also included for there is the possibility that the rain cell is very small that it only
covers the Civil station. Thus, of the rain events that occurred simultaneously; the
ones in which the Civil station have a rain rate of equal or greater value than the
other two stations, plus rain events that occurred only at the Civil station were
selected for analysis. This will give the conditional cumulative distribution function
for rain events in the Civil station to indicate the rainfall rate distribution inside a rain
cell.
65
5.1.3 RGN-UTM 1 Data Analysis
There are 360 times or events that is equivalent to 360 minutes of rainfall for
which the category of rain events as mentioned in the preceding section, occurred in
the selected rain gauge data. Out of the 360 recorded rain events, 205 times, rain was
detected only at Civil, and none or less than 0.5 mm/min at the other two stations.
This shows that 57 % of raining events considered, (205/360 * 100%) or a little more
than half of rain cells, are less than 1 km in diameter (assuming circular rain cells).
There are 113 times of rainfall rates that are equal at all stations (see Table
5.3). This phenomenon can be attributed to the widespread rain events. This is about
31.4 % (113/360 * 100%) of the total raining events being considered. Of these equal
rain intensity recorded at all three stations, none was detected at 120 mm/hr, 1 time
occurred at 90 mm/hr, 15 times occurred at 60 mm/hr, and 97 times occurred at 30
mm/hr. This showed that heavy, widespread rain events are low occurrence
phenomena and most rain cells are small and convective. These results are
summarized in Table 5.3.
Table 5.3 Equal Rainfall Rate At All Three Stations.
Rain Rate (mm/hr)
No of readings
120
0
90
1
60
15
30
97
Total
113
66
Further analysis of the data being considered shows that when a rainfall rate
of 120 mm/hr was recorded at the Civil Station, average rainfall rate at Merbau and
Mechanical Stations are 18 and 72 mm/hr, respectively. Total time for this event was
5 minutes. This is shown in Figure 5.2. From the curvefit line, the rain cell size is
about 1.2 km in diameter. The curvefit line also shows that the rain distribution
inside the rain cell is convective.
Rain Gauge
Stations
140
rain rate (mm/hr)
120
120
Curvefit Line
100
Civil
R2 = 1
80
72
60
Merbau
40
Mechanical
20
18
0
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
distance (km)
Figure 5.2 Rain Rate Distribution for 120 mm/hr at Civil Station.
For 90 mm/hr at Civil Station, 39 mm/hr was recorded at Merbau Station, and
42 mm/hr was recorded at Mechanical Station. This occurred for 10 minutes. For 60
mm/hr at Civil Station, 25.6 mm/hr ware recorded at both Merbau and Mechanical
stations, for 27 minutes. When 30 mm/hr was recorded at the Civil Station, no rain
event (or very light rain less than 30 mm/hr) was recorded at both Merbau and
67
Mechanical stations. This kind of rain event occurred for 205 minutes. These results
are given in Figure 5.3 to Figure 5.5. These figures also give the interpolation of
rainfall rate versus distance for the rain gauge network. This is shown by the curve fit
lines in the figures. Figure 5.6 gives the averaged rain cell size distribution and
averaged rain intensity distribution inside a rain cell.
100
Rain Gauge
Stations
90
rain rate (mm/hr)
80
Curvefit Line
60
Civil
40
42
39
R2 = 1
20
Merbau
Mechanical
0
-0.2
0
0.2
0.4
0.6
0.8
1
-20
distance (km)
Figure 5.3 Rain Rate Distribution for 90 mm/hr at Civil Station.
1.2
1.4
68
Rain Gauge
Stations
Curvefit Line
70
60
rain rate (mm/hr)
60
50
40
Civil
R2 = 1
Mechanical
30
25.6
25.6
20
Merbau
10
0
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
distance (km)
FIGURE 5.4 Rain Rate Distribution for 60 mm/hr at Civil Station.
35
Rain Gauge
Stations
30
30
Curvefit Line
rain rate (mm/hr)
25
Civil
20
R2 = 1
15
Mechanical
10
Merbau
5
0
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
distance (km)
FIGURE 5.5 Rain Rate Distribution for 30 mm/hr at Civil Station.
1.4
69
90
75
80
averaged rain rate (mm/hr)
Rain Gauge
Stations
Curvefit Line
70
60
50
R2 = 1
Civil
40
34.9
30
Mechanical
20.65
20
Merbau
10
0
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
distance (km)
FIGURE 5.6 Averaged Rain Rate Distributions for RGN-UTM 1.
Figure 5.2 to Figure 5.5 showed that most rain cells are convective. Except
for rain rate of 30 mm/hr at the center of a rain cell, which has cell size of 0.95 km or
maybe less; all other rain rates showed rain cell size of 1.2 km. From Figure 4.6, it
can be seen that the averaged rain rate cell size is also 1.2 km.
The total rain rates occurring at all rain gauge stations are given in Table 5.4.
The duration of the measurement taken is 74 days. The exact duration is 105,400
minutes.
70
Table 5.4 The Rainfall Rates and their durations for all Rain Gauge Stations RGNUTM 1.
Duration of events in minutes
Rain Rate
Merbau
Civil
Mechanical
0
104682
104745
104699
30
577
533
575
60
120
95
102
90
18
17
15
120
3
10
8
150
0
0
1
105400
105400
105400
(mm/hr)
Total time
duration (min)
The percentages of rain rates occurring at all rain gauge stations are given in
Table 5.5. This table also gives the averaged time percentage of all stations. The time
percentages are taken for the duration of a particular rain rate over the total duration
of the measurement taken.
71
Table 5.5 The Rainfall Rate Percentages and the Averaged Rainfall Rate Percentage
for all Rain Gauge Stations.
Rain Rate
(mm/hr)
Merbau
Civil
Mechanical
Averaged Rain Rate
(Percentage of time)
0
99.31879 99.37856
99.3349146
99.34409
30
0.547438 0.505693
0.5455408
0.532891
60
0.113852 0.090133
0.09677419
0.100253
90
0.017078 0.016129
0.0142315
0.015813
120
0.002846 0.009488
0.00759013
0.006641
0.00094877
0.000316
150
0
0
The values of the averaged rain rate are plotted in Figure 5.7. Best-fit
equation for averaged rain rate from Figure 5.7 gives R0.01, which is the percentage
of the rain rate for 0.01 % of the time as 119.031 mm/hr. This value is very close to
the one suggested by ITU-R (120 mm/hr), and the value that is extracted from the
radar data (120.907 mm/hr), as will be shown later in this thesis.
72
10
averaged rain rate (mm/hr)
10
10
10
50
Average R vs. percentage
curvefit line
0
-50
f(x) = 129.2*exp(-8.205*x)
R2 = 0.8845
-100
0.01% ==> 119.028
10
10
10
10
-150
-200
-250
-300
0
20
40
60
percentage of time
80
100
Figure 5.7 Averaged Rain Rate Distribution for all stations.
5.1.4 Cell Size and Intensity Distribution
From the analysis of the data, it can be said that the rain cell size is closely
related to the type of rain, either widespread or scattered. For widespread rain events,
the cell size is large (more than 1 km). The majority of this type of rain occurred at
30 mm/hr for about 97 minutes of the raining time being considered. The heaviest for
this type of rain is 90 mm/hr, which occurred for 1 minute. These results can be used
for rain attenuation considerations in microwave link design. For scattered rain, the
average rain cell size is 1.2 km. This is also true for higher rain rate, namely 120, 90,
and 60 mm/hr. There are indications that several cells may be present in a wider
73
scale of raining events. Not withstanding, the results given can be used for
microwave link design and site diversity applications.
The limitation of the equipment used for data recording enables only for the
rain rate to be recorded in 0.5 mm/minute integrations. This means that the recorded
rain rates are multiples of 0.5 mm/minute or 30 mm/hr. Interpolation has been used
to smooth out the data.
Preliminary results from the first rain gauge network set-up (RGN-UTM 1) in
the Skudai campus showed that Malaysia has a different rain cell distribution from
temperate region where available attenuation models are formulated. This
preliminary investigation has given an indication of rain cell size and distribution of
rain intensity inside a cell. For lower rain rate, the rain cell size tends to be
widespread and uniform. The larger rain rates, have narrower the rain cell size, as
can be deducted from the collected data. (Nor Hisham Khamis et al, 1999).
5.1.5 Rain Distribution Inside a Rain Cell
Figure 5.8 shows the rain rate distribution for RGN-UTM 2. The Chemical
Station uses 2 mm buckets and is able to measure lower rainfall rate. However,
readings at higher rainfall rate percentage are almost similar. Figure 5.9 shows the
rain distribution assuming the TV Station to be the center of the rain cell while
Figure 5.10 shows rain distribution assuming the IVAT Station to be the center of the
rain cell. From these figures, it can be seen that a rain cell with a center rainfall rate
of 120 mm/hr will have a diameter of about 1.2-1.5 km. Trend of high rainfall rates
have a smaller diameter when compared to low rainfall rates is also exhibited by data
from RGN-UTM 2.
74
2500
no of occurences
Kempas
2000
TV Lab
1500
IVAT
1000
Chemical
500
0
0
50
100
150
200
rain rate (mm/hr)
Figure 5.8 Rain rate distributions for RGN-UTM 2.
TV 120
140
rain rate (mm/hr)
TV 90
120
120
TV 60
100
100
80
78
64
60
70
54
57.6
51.7
40
20
Curvefit Line TV 120
90
R2 = 0.9295
60.0
37.7
31.1
Chem
IVAT
0.25
0.5
TV Studio
Kempas
0
0
0.75
1
1.25
distance (km)
Figure 5.9 Rain distributions assuming that TV Station is the center of the rain cell.
1.5
75
IVAT 150
160
150
IVAT 120
140
120
IVAT 90
rain rate (mm/hr)
120
105
IVAT 60
100
80
77
60
72
56.6
40
77.5
67.5 Curvefit Line IVAT
120
60
57.9
R2 = 0.5782
90.0
60.0
49.3
41.6
20
32.4
Chem
IVAT
0.25
0.5
30.0
TV Studio Kempas
0
-0.25
0
0.75
1
1.25
distance (km)
Figure 5.10 Rain distribution assuming the IVAT Station to be the center of the rain
cell.
Simultaneous readings at all stations in which the IVAT Station and the TV
Studio Station recorded readings of rain rate of 120 mm/hr are shown in Table 5.6.
Using these selected data, the assumption is that the center of the rain cell will be
either at the IVAT Station or TV Studio Station. All the readings are averaged and
these values are given in Table 5.6. The data are plotted in Figure 5.11.
1.5
76
Table 5.6. Simultaneous rain rate readings at all stations when IVAT and TV Studio
stations register 120 mm/hr rain rate.
Averaged Rain Rate (mm/hr) for each Rain Gauge
Stations
Chemical
IVAT
TV Studio
Kempas
77
120
77.5
67.5
64
100
120
70
70.5
110
98.75
68.75
120 mm/hr at IVAT
120 mm/hr at TV
Studio
Average
Table 5.6 shows the simultaneous recordings at all stations, assuming the
center of the rain events or rain cells to be at either IVAT or TV Studio. Whenever
IVAT station registers a rainfall rate of 120 mm/hr the simultaneously readings at
Chemical, TV Studio, and Kempas stations are 77, 77.5, and 67.5 mm/hr,
respectively. Similarly, whenever TV Studio station registers 120 mm/hr, the rainfall
rate readings at the respective stations are 64, 100, and 70 mm/hr.
From the curve fit lines in Figure 5.11, it can be seen that the rain events were
highly convective. The center of the rain cell experienced a heavy rainfall while the
rain rate tapers rather rapidly toward the edge. The averaged rain cell is about 1.25
km. It is determined here that the rain cell size is between 1.2 km to 1.5 km. (Nor
Hisham Khamis et al, 2004).
77
180
IVAT vs. distance
Curve fit IVAT
TV vs. distance
Curve fit TV LAB
AVERAGE vs. distance
Curve fit AVERAGE
160
140
120
100
80
60
40
20
0
-400
-200
0
200
400
600
800
1000
1200
distance (meters)
Figure 5.11. Averaged rain cell size.
Table 5.7 gives the percentages of the distribution of the rainfall rates at all
the rain gauge stations. Figure 5.12 shows the plots of the all rainfall rate
distributions and their respective curve fit lines. The equations for these curve fit
lines and values of R0.01 for all rain gauge stations are also shown in Figure 5.12.
78
Table 5.7 Distribution of rainfall rate of RGN UTM 2
Kempas
Rain
rate
Readings
%
(mm/hr)
0
12
24
30
36
48
60
72
84
90
96
108
120
132
144
150
180
Total
151494
0
0
967
0
0
131
0
0
37
0
0
7
0
0
4
0
152640
TV Studio
Readings
99.249
0
0
0.6335
0
0
0.0858
0
0
0.0242
0
0
0.0046
0
0
0.0026
0
100.00
273175
0
0
1527
0
0
223
0
0
82
0
0
27
0
0
5
1
275040
IVAT
%
Readings
99.321
0
0
0.5552
0
0
0.0811
0
0
0.0298
0
0
0.0098
0
0
0.0018
0.0004
100.00
234468
0
0
1388
0
0
203
0
0
76
0
0
21
0
0
4
0
236160
Chemical
%
99.283
0
0
0.5877
0
0
0.0860
0
0
0.0322
0
0
0.0089
0
0
0.0017
0
100.00
Readings
236058
2103
403
0
167
98
78
54
29
0
26
11
9
3
1
0
0
239040
%
98.752
0.8798
0.1686
0
0.0699
0.0410
0.0326
0.0226
0.0121
0
0.0109
0.0046
0.0038
0.0013
0.0004
0
0
100.00
1
0
20
40
60
80
100
120
140
160
Kempas
y = 1.7849e-0.0464x
R0.01 = 111.7 mm/hr
0.1
Kempas
TV
IVAT
percentage
2
0.01
TV
y = 1.7453e-0.0452x
R0.01 = 114.2 mm/hr
R = 0.9722
2
R = 0.9872
0.001
Chemical
IVAT
-0.0477x
y = 0.6745e
y = 1.9841e-0.0466x
R0.01 = 88.3 mm/hr R0.01 = 113.5 mm/hr
R2 = 0.9563
R2 = 0.9901
0.0001
rain rate (mm/hr)
Figure 5.12 RGN UTM 2 Rainfall rate distributions
Chemical
Chemical
Fit Line
Kempas
Fit Line
TV Fit
Line
IVAT Fit
Line
79
Table 5.8 shows the R0.01 values for all the gauge stations in RGN-UTM 2.
Also given in Table 5.8 are R0.01 values from the Meteorological Department in
Johor (S.K.A. Rahim, 2001) and ITU-R (ITU-R P.837-4, 2003). The lower value of
R0.01 for all stations may have resulted from the fact that data were taken during the
drier period of the season.
Table 5.8 R0.01 Values for RGN-UTM 2 Stations.
5.2
Location
Rain rate
Kempas Station
111.7 mm/hr
TV Lab Station
114.2 mm/hr
IVAT Station
113.5 mm/hr
Chemical Station
88.3 mm/hr
Johor Bahru
120 mm/hr
ITU-R
120 mm/hr
Radar Data Analysis
The analysis of radar data will follow steps to extract information from the
radar data. This will also include procedures to process the data to gather the needed
information. Most of the processing’s are done using programs in MATLAB and
EXCELL. Some MATLAB programs used in this study are enclosed in Appendix
4.1. Important information extracted from radar data are rain rate distribution, rain
cell size distribution, and the reduction factor.
80
5.2.1 Rejection of Permanent Echo
The first analysis done on the radar data is to check for permanent echo. This
is to ensure none of the data collected by the radar contained permanent echo, which
will affect the data. The elevation angles for volumetric scanning are 0.5, 1.2, 1.9,
2.7, 3.5, 4.6, 6.0, 7.5, 9.2, 11.0, 13.0, 16.0, 20.0, 25.0, and 32.0 degrees.
For permanent echo check, 150 scan of the lower elevation angles, namely
0.5, 1.2, 1.9, 2.7, and 3.5 degrees were checked. Permanent echo is checked by
looking for any spot in the radar scanning area that will return scattered energy at
each scan, which will indicate permanent echo. It is found that none of the selected
elevation angles contained permanent echo.
5.2.2 Preliminary Results
From the volumetric scanning of the radar, the data for the 1.20 and 3.50
elevation angles were chosen and the range selected was 65 km. Folders 1 to 10 were
selected for this exercise. The radar data gives the rain intensity for every kilometer
where there is rain. The rain intensity range is as given in Table 5.9 and is plotted in
Figure 5.13. From the data, it can be seen that for a 1-km path lengths, about 41.7%
for 1.20 elevation angle and almost 59.85% for 3.50 elevation angle, rain will be
occurring at 0.2 mm/hr rate. Very high intensity rainfall rate, which is above 364.6
mm/hr, occurs only 0.0022 % and 0.0002% of the 1-km path lengths for both
elevation angles respectively. For 0.01% of rain occurrences, the rain rate is about
192.778 mm/hr, by taking into account data for 1.20 elevation angle. For 3.50
elevation angle, the rain rate is about 78.183 mm/hr.
81
The result also showed that lower elevation angle was able to detect higher
rain rate reading. The higher elevation angle was able to detect very low rain rate,
which was not detected by the lower elevation angle eventhough these readings were
taken almost simultaneously. This is explained by the “updraft” phenomenon during
raining events where there is wind blowing upwards and causes small raindrops to
evaporate. It is decided that a lower elevation angle that is available (0.50) would be
utilized in this study because it will give better reading at high rainfall rate and nearer
to the ground giving ground level precipitation, comparable to rain gauge
measurement.
Table 5.9 Rainfall Intensity for averaged 1-km path.
Rain rate (mm/hr)
1.2 degrees
3.5 degrees
No. of readings
Percentage
0.2
5266864
41.7092
1051604
59.8502
1.0
2464238
19.5147
308820
17.5760
2.1
1687092
13.3604
139243
7.9248
3.2
1566119
12.4024
111385
6.3393
4.9
672429
5.3251
61789
3.5166
7.5
429690
3.4028
42213
2.4025
11.5
276478
2.1895
26017
1.4807
17.8
162252
1.2849
11977
0.6817
27.3
77966
0.6174
3032
0.1726
42.1
14143
0.1120
588
0.0335
64.8
5254
0.0416
227
0.0129
99.9
2419
0.0192
95
0.0054
153.8
1749
0.0139
53
0.0030
236.8
612
0.0048
14
0.0008
364.6
279
0.0022
3
0.0002
Total
12627584
100
No. of readings
1757060
Percentage
100
82
1.2 degrees
3.5 degrees
Power (1.2 degrees)
rain rate (mm/hr)
1000.0
100.0
10.0
1.0
Power (3.5 degrees)
Best-fit line for 1.2 degrees
y = 10.492x-0.6321
R2 = 0.9265
Best-fit line for 3.5 degrees
y = 7.0261x-0.5232
R2 = 0.9341
0.1
0.00
0.00
0.01
0.10
percentage
1.00
10.00
100.00
Figure 5.13 Rain rate distribution.
5.2.3 Distribution of Rain Rate from Radar Data
The first information extracted from radar data is the rain rate distribution.
The rain rate in the radar data is the averaged rain rate over a 1-km range-bin size.
The rain rate distribution for the 1-km range-bin size is as given in Table 5.9.
83
Table 5.10 Rain rate distribution for range-bin size of 1-km from radar data.
0.5 degrees elevation angle
Rain rate (mm/hr)
No. of readings
Percentage (%)
0
4743844
85.24121
0.2
236698
4.25318
1
124172
2.23122
2.1
114667
2.06043
3.2
125677
2.25827
4.9
65680
1.18019
7.5
54020
0.97068
11.5
44683
0.80290
17.8
33062
0.59409
27.3
17019
0.30581
42.1
2818
0.05064
64.8
1427
0.02564
99.9
727
0.01306
153.8
378
0.00679
236.8
203
0.00365
364.6
125
0.00225
Total
5565200
100
The percentage is calculated by, dividing the number of events for a
particular rain rate by the total number of events and then multiplying them by 100%.
Using the Curve Fitting Toolbox available in Matlab, the best-fit equation for
the data in Table 5.10 is obtained. This window is invoked using the “cftool”
command in Matlab’s Command Window. The procedure followed for curve fitting
84
in this study is given in Appendix 4.2. Figure 5.14 shows the plots data in Table 5.9
and the curvefit line for the rain rate distribution.
R vs. P
powerfit line
rain rate (mm/hr)
10
10
10
2
1
0
powerfit1(x) = a*xb
Coefficients (with 95% confidence bounds):
a=
4.382 (2.959, 5.806)
b = -0.7204 (-0.777, -0.6637)
R2 = 0.9950
10
-2
10
-1
10
percentage
0
10
1
Figure 5.14 The plots of original data and the curve-fit line.
From the analysis of the curvefit line, the rain rate for 0.01 % of the time is
120.907 mm/hr (as given in Appendix 4.2). This value will be used in the
mathematical model that is used to obtain the reduction factor.
The rain rate distribution Rp from radar data is given by (see Appendix 4.2)
85
Rp = 4.382 p –0.7204
(5.1)
where p is the percentage of time of interest. This rain rate distribution can be
used as a rain rate prediction model to predict the rain rate at the percentage of
interest.
5.2.4 Determination of Rain Cell Size from Radar Data
For the determination of rain cell size, only rain cells that occurred inside the
virtual links were considered. If a cell has a value in the 32nd range bin or in the 51st
range bin, it will not be considered. Thus, the maximum rain cell size considered is
18 km. The result of this analysis is shown in Table 5.11 and Figure 5.15. The
complete tabulation for rain cell size according to data files is given in Appendix 4.3.
86
Table 5.11 Rain Cell Size Distributions.
Rain cell diameter (km) Total # of rain cells
Percentage
1
146661
70.507
2
30604
14.713
3
14811
7.120
4
6745
3.243
5
4276
2.056
6
1585
0.762
7
1209
0.581
8
738
0.355
9
393
0.189
10
213
0.102
11
157
0.075
12
178
0.086
13
118
0.057
14
116
0.056
15
82
0.039
16
57
0.027
17
41
0.020
18
24
0.012
87
D vs. P
curve-fit line
1
diameter (km)
10
b
powerfit(x) = a*x
Coefficients (with 95% confidence bounds):
a=
5.803 (5.316, 6.291)
b = -0.2731 (-0.2987, -0.2474)
2
R = 0.9830
0
10
-1
10
0
10
1
10
percentage
Figure 5.15 Rain Cell Size Distribution.
From Table 5.10 and Figure 5.15, it can be seen that about 70% of rain cells
are of 1-km in diameter. This value is useful when mitigation technique such as site
diversity is to be employed.
In Figure 5.15, the formula for the rain cell size distribution is
D = 5.803 p – 0.2731
(5.2)
88
where D is the diameter of the rain cell in km, and p is the percentage of
interest. For example, the diameter of rain cell size for 99.99 % of the time would be
1.65 km. This means that eventhough the rain cell for R0.01 of 120 mm/hr (from rain
gauge data) is about 1.2 km; the rain cell size for 99.99 % of the time is 1.65 km
(from radar data). Thus, the rain cell size information from both types of data agreed
very well. This information is useful for some communication system that may have
the requirement of knowing rain cell size distribution.
5.2.5 Rain Attenuation Measurements in UTM
Two systems of microwave links operating at two different frequencies were
utilized for attenuation measurements in UTM (Karim, 2001). Binariang provided a
system operating at 7 GHz, and the other was provided by Digi Communications
operating at 15 GHz.
The Binariang system utilizes 4 ft radomeless parabolic
reflectors while the Digi system employs parabolic antenna of 0.6 meters in diameter
with radomes. The Binariang system consisted of three links and measurement
period was from 15 January, 1999 up to 14 January, 2000. The Digi system has six
links and measurement period was from 1 December 1998 to 30 November 1999.
Specifications for both systems are given in Table 5.12 and Table 5.13.
Table 5.12 Specifications for Binariang system links.
Hop
Frequency
Hop length
Polarization
Site A
Site B
(GHz)
(km)
UTM
Ulu Choh
7.807
11.87
Vertical
UTM
Tmn Perling
7.491
10.26
Vertical
UTM
Senai
7.491
5.57
Vertical
89
Table 5.13 Specifications for Digi system links.
Location
Frequency (GHz)
Hop length (km)
Polarization
Butterworth
14.81775
11.33
Vertical
Johor Bahru
14.83875
5.83
Vertical
Temerloh
14.83175
5.36
Vertical
Jitra
15.32525
4.85
Vertical
Kuala Lumpur
14.8195
3.96
Vertical
Taiping
14.83175
3.48
Vertical
5.3
Deducing the Reduction Factor from Radar Data
Formulation of the reduction factor from radar data followed the basis
adopted by Goddard and Thurai (Goddard et al, 1997). Attenuation of radio waves
through rain is given by Equation 3.3 in section 3.2.
Rearranging for the reduction factor,
r (t) =
A d (t)
γs L
(5.3)
where r(t) is the reduction factor for a given time percentage, Ad(t)is the radar
derived total attenuation at corresponding time percentage (dB),
γs
is the specific
attenuation at same time percentage from available rain gauge data (dB), and L is
total path length (km).
90
The next step is to find Ad(t). In this study, attenuation at three different
frequencies was considered. These frequencies are 7, 10, and 15 GHz. Using the
values recommended by ITU-R (ITU-R P.838-1) as in Appendix 4.5 for the k and α
coefficients at 7, 10, and 15 GHz and Equation 3.5; values for the specific
attenuation at the respective frequencies are calculated.
For 7 GHz,
γs = 0.00265 (120.907)1.312 = 1.4303 dB
(5.4a)
γs = 0.00887 (120.907)1.264 = 3.8031 dB
(5.4b)
For 10 GHz,
And for 15 GHz,
γs = 3.347e-2 (120.907)1.128 = 7.4758 dB
(5.4c)
Thus, the reduction factor will be derived using Equation 5.3 for all the
frequencies chosen.
The path lengths chosen are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 km. The same
radial lines as for the cell size distribution analysis are used. For a 1-km path length,
it is assumed that there will be 20 virtual path links within the range bins. For a 2-km
path link, the first one will be from range bin 31 to 32. The next link will be from 32
to 33, and so on. Thus, there will be 19 virtual links within the range chosen. This is
repeated for the rest of virtual links where there will be two 10-km path links for
each radial line. This will produce a reduction factor for path length of10 km and
91
using curve-fitting tool available in MATLAB and EXCELL, can be interpolated and
extended for other path lengths.
The distribution of the attenuation for 1-km path length for links operating at
7 GHz is given in Table 5.14.
Table 5.14 Distribution of attenuation for 1-km links operating at 7 GHz.
Attenuation (dB)
0
0.082323
Total
Number of readings for each
attenuation value
Percent
4743844
85.241
818496
14.707
0.631
1427
0.025641
1.1135
727
0.013063
1.9612
378
0.0067922
3.4549
203
0.0036477
6.0862
125
0.0022461
5565200
100
The values obtained in Table 5.14 uses the same data as in Table 5.9.
Attenuation values are calculated using Equation 3.5. Attenuation values are very
close to one another, so they were grouped in classes of 0.5 dB each. Values that fall
within each class are averaged and the number of occurrences or readings are taken.
Thus, the number of columns in Table 5.13 is less than Table 4.9 due to the grouping
of attenuation values into classes. The total data is still the same.
The best-fit curve for the data in Table 5.14 with attenuation values as the yaxis and percentage as the x-axis is as shown in Figure 5.16.
92
Attenuation vs. Percentage
Attenuation Distribution Fit Line
distribution of attenuation (dB)
10
10
10
10
0
-1
-2
-3
fittedmodel1(x) = a*xb
Coefficients (with 95% confidence bounds):
a = 0.02367 (-0.01339, 0.06072)
b = -0.8873 (-1.133, -0.6411)
0.01 ==> 1.40835
R2 = 0.9815
10
-2
10
-1
10
percentage
0
10
1
Figure 5.16 The best-fit curve for 1-km path links attenuation distribution.
The important information or parameter extracted from the best-fit curve of
Figure 5.16 is the attenuation value for 0.01% of the time for the 1-km path links
operating at 7 GHz. From the analysis, it is found out that the attenuation for 0.01%
of the time for a 1-km path link operating at 7 GHz is 1.40835 dB.
As a comparison, the specific attenuation calculated using ITU-R parameters
is 1.4163 dB (with R0.01 = 120 mm/hr).
% difference = [(1.4163 – 1.40835)/1.4163] * 100% = 0.55%
93
Thus the value deduced from radar data is very close to the value calculated
using ITU-R parameters.
The attenuation distribution tables and the best-fit curves for the attenuation
distributions of all 1 to 10-km path links operating at 7, 10, and 15 GHz are given in
Appendix 4.4. As can be seen from Appendix 4.4, this is a tedious and lengthy
procedure, which requires careful attention and determination when carrying out the
task. This is true not only when calculating the values and running the curve fitting
exercise, but also when compiling the results. The attenuation values for 0.01% of
the time for each path links of 1 to 10 km lengths; operating at 7, 10, and 15 GHz are
extracted from the best-fit lines. These values are summarized in Table 5.15 and
plotted as shown in Figure 5.17.
Table 5.15 Attenuation (dB) for 0.01% of the time; at 7, 10, and 15 GHz for path
lengths of 1 to 10-km.
Frequency
Path length
7 GHz
10 GHz
15 GHz
1-km
1.40835
3.7641
7.44543
2-km
2.62741
4.22063
6.4967
3-km
2.91245
5.13745
8.80735
4-km
3.17858
5.57111
9.04752
5-km
3.33466
5.84443
9.297
6-km
3.49907
5.95246
9.492
7-km
3.66776
6.18554
9.91478
8-km
3.84256
6.4482
10.3971
9-km
3.99616
7.23961
10.7589
10-km
4.14
6.74703
11.2355
94
16
14
attenuation (dB)
12
Attenuation at 7GHz
fit A7GHz
Attenuation at 10GHz
fit A10GHz
Attenuation at 15GHz
fit A15G
10
8
6
4
2
0
0
2
4
6
8
path length (km)
10
12
Figure 5.17 Attenuation for 0.01% of the time at 7, 10, and 15 GHz.
Using equation 4.3, the values obtained in equation 4.4, and the values in
Table 5.15; the reduction factors for path lengths of 1 to 10-km at frequencies of 7,
10, and 15 GHz are calculated. The reduction factor values are tabulated in Table
5.16 and plotted in Figure 5.18.
95
Table 5.16 Reduction factor (r) values for 1 to 10-km path lengths at frequencies of
7, 10, and 15 GHz for 0.01% of the time.
Frequency
Path length (km)
7 GHz
10 GHz
15 GHz
1
0.98465
0.98975
0.99594
2
0.91848
0.55489
0.43452
3
0.67875
0.45029
0.3927
4
0.55558
0.36622
0.30256
5
0.46629
0.30735
0.24872
6
0.40773
0.26086
0.21162
7
0.36633
0.23235
0.18946
8
0.33582
0.21194
0.17385
9
0.31044
0.21151
0.15991
10
0.28945
0.17741
0.15029
r7 vs. L
curvefit r7
r10 vs. L
curvefit r10
r15 vs. L
curvefit r15
reduction factor (r)
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
path length (km)
Figure 5.18 Reduction factor (r) plots for 1 to 10-km path lengths at frequencies of
7, 10, and 15 GHz for 0.01% of the time.
96
The best-fit lines for each reduction factor plots in Figure 5.18 follows the
power law relationship, given by
f(x) = a*xb
The a and b values for all the best fit lines are summarized in Table 5.17, and
are plotted in Figure 5.19 and Figure 5.20, respectively.
Table 5.17 a & b values for best fit lines of reduction factors at 7, 10, and 15 GHz.
Frequency
a
b
7 GHz
1.08
-0.5108
10 GHz
0.9798
-0.7319
15 GHz
0.9654
-0.8629
97
3
a vs. F
Curvefit line for a coefficients
2.5
b
afit(x) = a*x
Coefficients (with 95% confidence bounds):
a=
1.455 (-1.474, 4.384)
b = -0.1588 (-1.03, 0.7128)
coefficient a
2
1.5
2
R = 0.8237
1
0.5
2
4
6
8
10
12
14
16
18
20
Frequency (GHz)
Figure 5.19 Best fit line for coefficient a.
0.4
b vs. F
curvefit line for b coefficients
0.2
b coefficient
0
bfit(x) = a*xb
Coefficients (with 95% confidence bounds):
a=
-0.159 (-1.003, 0.6845)
b=
0.6322 (-1.527, 2.791)
-0.2
R2 = 0.9376
-0.4
-0.6
-0.8
-1
-1.2
2
4
6
8
10
12
14
16
Frequency (GHz)
Figure 5.20 Best fit line for coefficient b.
18
20
98
From Figure 5.18, Figure 5.19, and Figure 5.20, the reduction factor can be
formulated as follows:-
reduction factor, r = a L b
(5.5)
Where
a = 1.455 F –0.1588
b = –0.159 F 0.6322
L = path length (km), and
F = frequency (GHz).
The a and b values for the reduction factor r at 7, 10, and 15 GHz are given in
Table 5.18 below.
Table 5.18 a and b values at 7, 10, and 15 GHz.
Frequency
a
b
7 GHz
1.078
-0.544
10 GHz
1.009
-0.682
15 GHz
0.946
-0.881
99
The proposed Malaysia reduction factor is given in Table 5.19 for path
lengths of 1 to 10-km at 7, 10, and 15 GHz. The proposed reduction factor is
compared with other models in Table 5.20, Table 5.21, and Table 5.22 at 7, 10, and
15 GHz, respective. The graphs of all the tables for all the frequencies are plotted in
Figures 5.21, Figures 5.22 and Figure 5.23.
Table 5.19 The reduction factor (r) for the proposed Malaysia model.
path length (km)
value of r
7 GHz
10 GHz
15 GHz
1
1.078
1.009
0.946
2
0.739364
0.62891
0.513669
3
0.593014
0.476974
0.359375
4
0.507105
0.392
0.278918
5
0.449137
0.336662
0.229139
6
0.406728
0.297298
0.195137
7
0.374012
0.26763
0.170357
8
0.347807
0.244334
0.15145
9
0.32622
0.225475
0.136522
10
0.308048
0.209841
0.12442
100
path length
(km)
Lin
Moupfouma
CETUC
Improved
CETUC
Goddard
ITU-R
Singapore
DAH
Proposed
Model
Table 5.20 Comparison of r from various models at 7 GHz.
1
2
3
4
5
6
7
8
9
10
0.978
0.958
0.938
0.919
0.901
0.883
0.867
0.850
0.835
0.820
0.971
0.943
0.917
0.892
0.868
0.846
0.824
0.804
0.784
0.765
0.914
0.841
0.779
0.725
0.679
0.638
0.601
0.569
0.540
0.514
1.021
0.692
0.591
0.538
0.505
0.481
0.463
0.448
0.437
0.426
0.830
0.680
0.595
0.536
0.490
0.454
0.423
0.396
0.373
0.353
0.886
0.796
0.722
0.661
0.610
0.566
0.527
0.494
0.465
0.438
0.850
0.753
0.679
0.620
0.572
0.531
0.497
0.467
0.440
0.417
0.978
0.891
0.814
0.757
0.712
0.676
0.646
0.621
0.598
0.579
1.078
0.739
0.593
0.507
0.449
0.407
0.374
0.348
0.326
0.308
1.6
1.4
reduvtion factor, r
1.2
Lin
Moupfouma
1.0
CETUC
Improved CETUC
0.8
Goddard
ITU-R
Singapore
0.6
DAH
Proposed Model
0.4
0.2
0.0
1
2
3
4
5
6
7
8
9
10
path length (km)
Figure 5.21 Plots of all the reduction factor models at 7 GHz.
101
Path length
(km)
Lin
Moupfouma
CETUC
Improved
CETUC
Goddard
ITU-R
Singapore
DAH
Proposed
Model
Table 5.21 Comparison of r from various models at 10 GHz.
1
2
3
4
5
6
7
8
9
10
0.978
0.957
0.937
0.918
0.899
0.882
0.865
0.848
0.833
0.817
0.971
0.943
0.917
0.891
0.867
0.844
0.822
0.801
0.781
0.762
0.913
0.840
0.778
0.724
0.678
0.637
0.600
0.568
0.539
0.513
1.021
0.692
0.591
0.538
0.505
0.481
0.463
0.448
0.437
0.426
0.829
0.679
0.594
0.534
0.489
0.452
0.421
0.395
0.372
0.351
0.886
0.796
0.722
0.661
0.610
0.566
0.527
0.494
0.465
0.439
0.851
0.754
0.680
0.621
0.573
0.532
0.498
0.468
0.441
0.418
0.869
0.767
0.690
0.634
0.592
0.558
0.530
0.507
0.486
0.469
1.009
0.629
0.477
0.392
0.337
0.297
0.268
0.244
0.225
0.210
1.6
1.4
reduction factor, r
1.2
Lin
Moupfouma
1
CETUC
Improved CETUC
0.8
Goddard
ITU-R
Singapore
0.6
DAH
Proposed Model
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
path length (km)
Figure 5.22 Plots of all the reduction factor models at 10 GHz.
102
path length
(km)
Lin
Moupfouma
CETUC
Improved
CETUC
Goddard
ITU-R
Singapore
DAH
Proposed
Model
Table 5.22 Comparison of r from various models at 15 GHz.
1
2
3
4
5
6
7
8
9
10
0.978
0.958
0.938
0.919
0.901
0.883
0.867
0.850
0.835
0.820
0.971
0.943
0.916
0.890
0.865
0.841
0.817
0.795
0.774
0.753
0.914
0.841
0.779
0.725
0.679
0.638
0.601
0.569
0.540
0.514
1.021
0.692
0.591
0.538
0.505
0.481
0.463
0.448
0.437
0.426
0.830
0.680
0.595
0.536
0.490
0.454
0.423
0.396
0.373
0.353
0.886
0.796
0.722
0.661
0.610
0.566
0.527
0.494
0.465
0.438
0.850
0.753
0.679
0.620
0.572
0.531
0.497
0.467
0.440
0.417
1.098
1.035
0.965
0.910
0.865
0.828
0.797
0.771
0.747
0.726
0.946
0.514
0.359
0.279
0.229
0.195
0.170
0.151
0.137
0.124
1.6
1.4
reduction factor, r
1.2
Lin
Moupfouma
1.0
CETUC
Improved CETUC
0.8
Goddard
ITU-R
Singapore
0.6
DAH
Proposed Model
0.4
0.2
0.0
1
2
3
4
5
6
7
8
9
10
path length (km)
Figure 5.23 Plots of all the reduction factor models at 15 GHz.
103
At 7 GHz, the proposed reduction is similar to the Improved CETUC model
and generally follows the same trend as other models, namely the ITU-R, Singapore,
and Goddard models, as shown in Figure 5.21. The values for the proposed model
are nearer to the Goddard and Improved CETUC models, albeit a little lower. At
higher frequencies, especially at 15 GHz, the proposed model shows a much lower
reduction factor values. This means that the proposed model will predict a lower
attenuation value at higher frequencies. However, models that are dependant on
frequency are the Moupfouma and DAH models, beside the proposed model. It has
been shown in earlier sections that attenuation due to rain will increase with
frequency.
The Lin and Moupfouma models consistently exhibit higher values of r as
compared to other models. At higher frequency (15 GHz), the DAH models begin to
exhibits values that similar to Lin and Moupfouma models. Lin and DAH models
were developed using data from the US, while Moupfouma used data from several
places. The CETUC, ITU-R, Singapore, Improved CETUC, and Goddard models
tend to have values of r, which are close to one another. The proposed model values
are always close to the Goddard model in which both uses radar data. The Singapore,
Improved CETUC, and the proposed models have values that close to one another,
especially at lower frequency. All are done in tropical region, which may explain
this. The Improved CETUC has values that are always lower than the older CETUC
model. Thus an improvement to the CETUC model will give lower value in the
prediction of attenuation. Most models were developed using higher older value of
R0.01 from ITU-R, thus it is expected that most models will have lower r values that
approaches the values of the proposed model if they were developed using the new
value of R0.01 from ITU-R.
In some works that have been done in UTM, Islam et al (2000) concluded
that the ITU-R model does not reflect the measured attenuation done at several
locations in Malaysia. Moupfouma and Lin models were closer to the measured data,
but the Moupfouma model underestimated attenuation in some places where
104
measurements were done. Islam (2000) proposed some modifications to the
Moupfouma model to suit the measured attenuation data.
The Modified Moupfouma Model is as follows.
r = 1/[1 + 0.03 α (p/0.01)-βLm]
(5.6)
where m = 1 + 1.4 x 10-4 F1.76 logeL.
α = 2.6
β = 0.34
}
L < 3 km
}
0.001 ≤ p ≤ 0.01
0.001 ≤ p ≤ 0.02
α = 1.0
β = 0.45
β = 0.6
α = 2.8
β = 0.26
}
0.01 < p ≤ 0.02
}
3 km ≤ L ≤ 6 km
6 km < L ≤ 11.3 km
0.001 ≤ p ≤ 0.02
The performance of the proposed reduction factor is compared with the other
models. No actual measurements were done in this study. As a result, attenuation
measurement work done by other researcher (Karim, 2000), had to be used
eventhough some results from the attenuation measurement were rather questionable.
These results are shown in Table 5.23.
105
15
15
5.57 10.26 11.87
3.48
3.96
4.85
5.36
5.83
11.33
125
147
133
107
114
125
125
125
125
B'worth
15
Bahru
Temerloh
15
Johor
Jitra
15
7
Lumpur
15
7
Kuala
Taiping
Freq (GHz)
Path length
(km)
R0.01
(mm/hr)
Specific
attenuation
(dB/km)
Measured
attenuation
(dB)
Perling
Link
Tmn
7
Senai
Ulu Choh
Table 5.23 Comparison of predicted attenuations (dB), with measurements.
1.494 1.494 1.494 9.319 8.325 6.513 6.996 7.762 7.762
8.010 8.220 10.540 29.210 30.140 28.530 29.910 33.400 40.970
7.344 12.311 13.816 29.159 29.788 29.174 33.912 39.718 69.203
Lin
Moupfouma 7.118 11.657 12.987 29.331 29.417 27.506 32.201 38.371 64.834
Modified
7.115 8.139 8.76 29.284 29.373 27.418 32.099 38.238 43.004
Moupfouma
5.659 8.640 9.527 18.351 18.557 18.031 20.234 22.915 35.056
DAH
CETUC
5.405 7.686 8.247 23.670 23.586 22.088 25.118 28.914 41.915
S'pore
5.670 8.466 9.216 23.472 24.013 23.487 26.692 30.423 46.620
ITU-R
4.86 6.625 7.038 22.445 21.89
I-CETUC
4.024 6.407 7.184 17.030 17.187 16.732 18.912 21.620 35.976
Goddard
3.836 5.195 5.505 17.219 17.150 16.326 18.206 20.438 28.096
Proposed
Model
3.492 4.613 4.930 10.232 9.282 7.440 8.087 9.062 9.808
19.5
22.56 25.93 35.91
Table 5.23 shows that the proposed model predicts attenuation values that are
lower than other models. It also gives attenuation values that are much lower than the
measured attenuation. At 7 GHz, the proposed model is close to the Goddard,
Improved CETUC, and ITU-R models. At higher frequency, the proposed model
gives a much lower attenuation values than the other models. However, only the
Moupfouma and DAH models are dependant on frequency.
106
It must be mentioned here that the measurements done using both Binariang
and Digi systems suffers from wet antenna loss and actual attenuation due to rain
might be lower (S.K.A.Rahim, 2001). S.K.A.Rahim noted that available attenuation
prediction models underestimate the measured attenuation. Spray tests conducted on
a microwave system installed in UTM, Skudai campus (Md Rafiqul Islam, 2000)
showed that wet antenna loss can be as high as 8 dB at 38 GHz, and 5 dB at 23 GHz.
Wet antenna loss measurements cannot be done on the 7 and 15 GHz due to the
height of the communication towers. Study in Singapore has shown that wet antenna
loss can be as high as 20 dB, and is also affected by wind (Gang et al, 2000). This
wind effect is not taken into consideration in the attenuation measurement
experiment. Moreover, the wet antenna loss occurs not only during rainfall but also
several minutes after the rainfall. This adds more loss to the measured received
power. There are also other issues that may effects the measurements. These are
discussed here.
The path length of the Taman Perling link is almost twice the path length of
the Senai link but their measured attenuations have only 0.21 dB difference. Karim
suggested that this is due to an equal effective rain cell diameter, which is also to
suggest an equal effective path length for both links. This is in contradiction with all
the reduction models that have been discussed earlier. All of them have shown that
the effective path length is directly proportional to the actual path link as shown in
Figure 5.21 – Figure 5.23. In another instance, the length of the Ulu Choh link is
comparable to the Taman Perling link but their difference in measured attenuation is
2.32 dB.
These results do not tally with long-term measurements taken near each other.
For example, rain gauge networks data were collected at different time period. The
locations of both rain gauge networks were close to each other. Results from both
rain gauge networks however showed similar patterns in rain rate distributions, and
rain cell size distributions.
107
The measurement values of attenuation for 0.01 % of the time were rather
high for most links. For example, the measured attenuation for Senai link is 8.01 dB.
If rain is constant over the link then the total attenuation will be 8.32 dB, for constant
specific attenuation along the path. This inferred a large cell of diameter around 5 km
at R0.01. Analysis of rain gauge data in this study has shown that for R0.01; the rain
cell is about 1.2 km. Thus, it is very unlikely that heavy rain is constant over all the
links.
The prediction of attenuation values from the Lin and Moupfouma models are
very close to the measured values. These models were developed using data from the
temperate region. However, it has been widely accepted that tropical region suffers
heavier rain than temperate region. The closeness of the attenuation values seemed to
suggest otherwise. Thus, these two models are definitely not suitable for the tropical
region. They may not even applicable anymore, as newer, more accurate data are
available. These two models are discussed here because they can be considered as
“classical” models. Moupfouma himself suggested several models for rain
attenuation prediction (Chebil, 1997). In a later publication, Moupfouma even used a
reduction factor model that was developed by other researcher instead of using one
of his own (Moupfouma, 1997). Is not surprising that the Modified Moupfouma
model is also close to the measured attenuation values since it was modified
according to the measured values. However, due to the issues on the measured data;
which makes it questionable, the Modified Moupfouma model also is questionable.
The Modified Moupfouma model also suggested different parameters values for
different path lengths, which is uncommon with other models. This also points back
to the questionability of the measured attenuation values.
The DAH model is another model that utilized data from a temperate region.
Moreover, it was formulated for slant path attenuation prediction. At high frequency,
the predicted attenuation values seemed high since they were higher from models
developed in the tropics. Thus, this model is not suitable for terrestrial attenuation
prediction in the tropical region.
108
The CETUC and Improved CETUC models were selected because they were
developed in Brazil, a tropical region similar to Malaysia. The Improved CETUC
showed similar pattern to the proposed model, especially at lower frequency. The
Improved CETUC demonstrated that with a larger base and more accurate data, the
actual attenuation is lower than that was predicted from previous models. Both
CETUC models are, however, insensitive to frequency. This explains the departure
of predicted values from the proposed model at higher frequency. Both models also
used old data from the ITU-R. Using newer values from ITU-R and incorporating
dependence on frequency might make the Improved CETUC model to be much
closer to the proposed model.
The Singapore model was developed using rain gauge and satellite beacon
data. The rain gauges, however, were place quite far apart. The distances were 5.3,
4.9, and 7.1 km apart. It also assumed that rainfall rate is constant over 6 km. This
study has shown that rain cell diameters are much smaller than that. Thus, the
arrangement of the rain gauge does not give an accurate representation of rain cells
across a terrestrial link. As a result, the Singapore model does not predict the
attenuation accurately.
The ITU-R model was developed from data collected around the world.
Studies (Ajayi et al, 1988; Juy et al, 1990; Yagasena et al, 1995) have shown that the
model is not applicable everywhere. Characteristics of rain are rather localized and
local studies are needed to develop prediction models suitable for the local
environment. This has been a motivation for this study. Local studies (Karim, 2000;
Islam, 2000) also concluded that the ITU-R model is not suitable for Malaysia.
The Goddard and Thurai model is a model developed from radar data. In fact,
this study also used the virtual link concept as used by Goddard and Thurai. The
values predicted by the proposed model is very close to the values predicted by the
Goddard and Thurai model, especially at the lower frequencies. The Goddard and
109
Thurai model however, is insensitive to frequency. Thus, at higher frequencies, the
values differ. By incorporating frequency into the equation, the difference may be
minimized.
To really test the proposed model, measurements must be made for several
path lengths and at different frequencies. An elaborate scheme of rain gauge network
is also needed. The wet antenna loss must also be taken into consideration. No doubt,
this will be an enormous task. Notwithstanding, the proposed model can be used to
give an indication of attenuation due to rain, as it was developed using the local rain
data. The proposed model not only depends on the length of the link, but also on
frequency as well (Assis, 1990; Dissanayake et al, 1997).
CHAPTER 6
CONCLUSION AND FUTURE STUDIES
6.1
Conclusion
This work is done primarily using weather radar data obtained from the
Meteorological Department of Malaysia. Data from weather radar have been utilized
in many other studies. The biggest advantage of radar data is the large amount of
data that is available in a short period of time. Radar data is also capable of providing
areal precipitation where it is almost impossible to do using rain gauges.
The previous chapter discussed the inadequacies of available reduction factor
models. The proposed reduction model can calculated using Equation 5.5, and is as
shown in Figure 6.1 for 7, 10, and 15 GHz. The predicted attenuation due to rain for
0.01 % of the time using the proposed reduction factor is as shown in Figure 6.2
111
reduction factor, r
1.2
r (7 GH)
r (10 GHz)
r (15 GHz)
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
path length (km)
attenuation (dB)
Figure 6.1 Proposed reduction factor r.
10
9
8
7
6
5
4
3
2
1
0
A (7GHz)
A (10 GHz)
A (15 GHz)
1
2
3
4
5
6
7
path length (km)
8
9
10
Figure 6.2 Predicted attenuation due to rain for 0.01 % of the time.
Figure 6.2 shows that there will be higher attenuation at higher frequencies as
expected. It also shows that as the path link gets longer, the amount of attenuation
due to rain will increase at a slower rate. This is due to the fact that rain cells will not
cover the whole path link. Figure 6.2 also shows that multiple rain cells are taken
into consideration in the proposed reduction factor.
112
The proposed reduction factor can be used to calculate the attenuation due to
rain. The needed parameters are the length of the link (in km) and the frequency used
(in GHz). This is useful microwave link system planning and link budget estimation.
Below are the procedures for calculating attenuation due to rain using the proposed
reduction factor.
First the specific attenuation is calculated using the Equation 3.5. This
specific attenuation assumes that rain is constant over a link of 1-km.
Parameters k and α in Equation 3.5 are as recommended by ITU-R. The
reduction factor r is then calculated using the Equation 5.5.
The total attenuation is then calculated using Equation 3.3. This value
predicts the attenuation due to rain for 0.01 % of the time.
The reliability and the accuracy of the proposed reduction factor model
stemmed from the fact that meteorological radar data are highly accurate and
reliable. This is demonstrated by the fact that R0.01 extracted from the radar data is
similar to the ITU-R, and the long term rain gauge data of Johor Bahru.
From the distribution of the rain rate obtained from the radar data, a
prediction model for rain rate distribution is also suggested. Equation 5.1 gives the
rain rate model from radar data. This model will predict the rain rate, Rp for p
percentage of the time. The model for rain rate distribution is given in Figure 5.14.
Rain cell diameter will give a good indication for system planners doing
attenuation mitigation technique such as site diversity application. Mitigation
technique is important when high reliability of microwave link is needed. If
113
attenuation exceeds the link budget of a link, then an alternative technique is surely
required to overcome the attenuation problem. This is especially useful for satellite
link where it’s application has become more prominent as the communication
community moves into higher spectrum of available bandwidth.
A model for the distribution of rain cell size obtained from radar data is given
by the best-fit curve in Figure 5.15, and is given by Equation 5.2. From this equation,
most of the rain cells will have a diameter of 1.65 km. This agrees very well with the
rain gauge data.
This study also utilized two rain gauge networks that were set-up in UTM,
Skudai campus. Analysis of radar data produced the reduction factor; which is the
main intention of this study, and prediction models for rain rate distribution, and rain
cell size distribution. From rain gauge networks data, rain cell at several rain rates
and the profile of rain intensity inside a rain cell have been determined.
Results from RGN-UTM 1 and RGN-UTM 2 showed that most rain cells are
very convective. Plots of radar data shows that multiple rain cells may exist in a
raining region. Widespread rain has low intensity but the rate may be higher during
thunderstorms.
The rain cell diameter for 120, 90, and 60, mm/hr from RGN-UTM 1 is about
1.2 km. The averaged rain rate cell diameter is also about 1.2 km. For RGN-UTM 2,
the average cell diameter is about 1.5 km. From radar data, more than 70% of rain
cells have a diameter of about 1 km. Thus, it can be said that most rain cells in
Malaysia will have a diameter of around 1.5 km. These rain cells are very convective
in nature.
114
One of the most challenging tasks in this study is to determine the proper
procedure in formulating the reduction factor. Eventhough there are many reduction
factors that were proposed in the literature, none of them really give in detail how the
reduction factors were obtained. Also, due to the large amount of data, a very long
time is needed to process all the data. Eventhough a personal computer is adequate to
do the processing, care must be exercise not to overload the memory of the
computer. This means that the data have to be divided into several files and
processed separately. A more powerful computing facilities will surely expedite in
the processing of data and other works related to this study, such as larger data
storage.
6.2
Future Studies
Eventhough ground based weather radar is widely used in many studies;
Doppler radar and polarimetric radar have been developed and used (Hornbostel et
al, 1997). These types of radars allow the determination of the shape, distribution,
types of hydrometeors, and rain rate with more precision. Together with other types
of data measurements such as rain gauge and beacon receiver, these data can be
compared and checked out against each other (Hornbostel et al, 1995). This will raise
the degree of confidence in outcomes of researches.
Radars of these kinds are not readily available in Malaysia. It is hoped that as
a continuation to this study, using experience gained and expertise available, a radar
system can be built here in UTM that employs such techniques so that the results
found in this study can be refined. However, continuing studies are utilizing the
TRMM radar project (Oki et al, 2000; Rincon et al, 2001). Furthermore, due to
increasing popularity microwave communication using satellite, vertical path
reduction factor must also be studied (Bandera et al, 1999), as a continuation of this
115
study. Other factors that are to be considered are parametrization of dsd, and the
relationship between dsd and rain rate.
Another important aspect of future studies is to have a longer period of
measuring time. Also, different methods of measurements must be done concurrently
to enable cross checking of data obtained. As new instruments and systems are being
installed, greater accuracy and more reliable data will be available.
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Master's Thesis.
126
Silva Mello, L.A.R.; Pontes, M.S.; Souza, R.S.L. (1997). Rain attenuation prediction
for the design of site-diversity LEO/SMS Gateway configuration in the tropics.
Proceedings Microwave and Optoelectronics Conference, 1997. 'Linking to the
Next Century'. 1997 SBMO/IEEE MTT-S International, Volume: 2 , 11-14
Aug. 1997 Pages:729 - 733 vol.2
Watson, P.A, V. Sathiaseelan and B. Potter. (1981)Development of a climatic map of
rainfall attenuation for Europe," Interim Report for European Space Agency
under ESTEC contract No. 4162n9fNIJDG (SG), Report No. 300, 1981.
Wexler et al (1963) Radar Reflectivity and Attenuation of Rain. Journal of Applied
Meteorology. Vol. 2, April 1963, pp 276 – 280.
Wilson, J.W. (1964). Evaluation of Precipitation Measurements with the WSR-57
Weather Radar. Journal of Applied Meteorology, vol. 3, April 1964: 164-174.
Yagasena, A., Hassan, S.I.S., Yusoff, M.M.M. (1995) Rain Attenuation Prediction at
6.75 GHz in Malaysia Using Rain Gauge and Radiometer Measurements.
IEEE, 1995, pp. 596-599.
Yagasena, A., Hassan, S.I.S., Yusoff, M.M.M. (2000). Rain Attenuation Prediction at
6.75 GHz in Malaysia Using Rain Gauge and Radiometer Measurements.
Theme: 'Electrotechnology 2000: Communications and Networks'. [in
conjunction with the] International Conference on Information Engineering.,
Proceedings of IEEE Singapore International Conference on Networks, 2000:
pp. 596-599.
Zainal, A.R., Glover, I.A., Watson, P.A. (1993). Rain Rate and Drop Size
Distribution Measurements in Malaysia. Proceedings of the 1993 International
Geoscience
and
Remote
Sensing
Symposium
(IGARSS
’93),
Understanding of Earth Environment, Japan, vol. 1, 1993, pp. 309-311.
Better
127
Zhang, G.; Vivekanandan, J.; Brandes, E. (2001). A method for estimating rain rate
and drop size distribution from polarimetric radar measurements. IEEE
Transactions on Geoscience and Remote Sensing, April 2001. Volume: 39,
Issue: 4, pp. 830 – 841.
Zhang, G.; Vivekanandau, J.; Brandes, E. (2000). A method for estimating rain rate
and drop size distribution from polarimetric radar measurements. Geoscience
and Remote Sensing Symposium, 2000. Proceedings. IGARSS 2000. IEEE 2000
International, Volume: 1, 24-28 July 2000, pp. 180 –183.
128
Appendix 1.1 Earth’s Climate and Raindrops
1.
Atmospheric Conditions
A truly reliable wireless communication system such as satellite and
microwave links must take into account the effects of atmospheric conditions. The
earth’s atmospheric conditions are very important and must be considered for wireless
communication especially for satellite and microwave links. It has a direct effect on
frequencies and techniques used for transmission. For example, at 11 GHz,
electromagnetic energy will be absorbed by water molecules, resulting in high
attenuation. Also, the phenomenon of ‘bending’ or refraction of electromagnetic wave
at certain frequencies in earth’s atmosphere must be taken into account for reliable
communication link.
Figure A1.1.1 shows some division of earth’s atmosphere. For terrestrial
links, conditions in the troposphere must be considered while for satellite link,
conditions in the neutral and ionized sphere must be taken into account. In nonionized
atmosphere, the pressure, temperature, and water vapor content (humidity) all
decrease with increasing altitude. The dielectric constant also decreases with altitude.
Since electromagnetic waves travel faster in a medium of lower dielectric constant,
bending or refraction of the waves will occur (Freeman, 1987). This is a factor to be
considered in designing a microwave link. Changes in terrain also have strong effects
on ground waves. If the ground is highly conductive, attenuation will be reduced.
Ground wave propagation is much better over seawater than very dry desert terrain.
Diurnal changes must also be considered. In the ionized atmosphere, the thickness of
these layers varies during the day and nighttime. Electromagnetic waves traveling
through these layers will be refracted (Miller, 1999).
129
Figure A1.1.2 shows pressure and temperature distribution of the earth’s
atmosphere that can have an effect on microwave transmission. Another aspect of the
earth’s atmosphere that must be considered is that the potential energy distributed in
the atmosphere is not uniform. The difference in pressure, temperature, and energy
has an effect on the earth’s weather and the movement of air mass. Figure A1.1.3
shows the changes in the earth’s weather and climatic differences in various parts of
the world. This also has an effect on the earth’s weather. Thus, various part of the
world has different climatic experiences that give rise to the need for specific studies
of local weather conditions for wireless communication applications.
Figure A1.1.1 Earth’s atmosphere (Allnutt, 1989)
130
Figure A1.1.2 Pressure and temperature of earth’s atmosphere (Allnutt, 1989)
131
Figure A1.1.3a Mean temperature of the earth in July (Allnutt, 1989)
Figure A1.1.3b Mean temperature of the earth in December (Allnutt, 1989)
132
As Malaysia falls into a heavy rainfall region, attenuation of electromagnetic
wave propagation due to rain is of paramount concern rather than other atmospheric
conditions. This is especially true for terrestrial and satellite microwave links. Various
studies and analysis have been conducted to find a suitable model for prediction of
rain induced attenuation in the tropical region (Ajayi et al, 1988; Juy et al, 1990;
Yagasena et al, 1995; Aydin et al, 2002).
2.
Terminal Velocity and Drop Shapes
Terminal velocity of a raindrop depends on atmospheric pressure, humidity
and temperature. It increases with larger drop size but the rate of increase gradually
decreases before reaching its maximum of about 9 m/s (Gibbins, 1992). Figure
A1.1.4 shows the terminal velocity profiles of raindrops.
133
Figure A1.1.4 Terminal velocity of a rain drop (Allnutt, 1989)
The drop shape of a raindrop will cause depolarization of the electromagnetic
wave. An oblate drop with horizontal main axis will attenuate more in the horizontal
polarization. However, the difference of attenuation calculations using different drop
shapes show variations of less than 15% than using spherical shape (Crane, 1975).
The smallest drops are found in clouds and the largest will not exceed 4 mm in radius.
Larger drops are unstable and tend to break up. Figure A1.1.5 shows the shapes and
sizes of raindrops.
134
Figure A1.1.5 Rain drop shapes and sizes (Allnutt, 1989)
3.
Drop Size Distribution (DSD)
Drop size distribution (dsd) is very important for rain attenuation calculation.
Different region has different dsd while other rainfall microstructure parameters such
as terminal velocity, and the shape of the raindrops has less regional dependence
(Haddad et al, 1997; Meneghini et al, 1997; Aydin et al, 2002). It is usually expressed
as the number of drops per cubic meter of air per unit size interval. Dsd varies
considerably with time and locality, even for the same rain rate within the same rain
event. At low rain rates, raindrop spectra are about 2 to 3 mm. At the beginning of a
rain event, the drop spectrum (at ground level) is dominated by larger sizes because
larger drops fall faster and smaller drops easily evaporated. Since dsd is closely
related to the rainfall rate, models have been formulated to determine drop size
135
distribution. Common models for dsd are Marshall & Palmer, Gamma, Log-Normal,
and Laws & Parsons models.
4. Reference
1. Freeman, R.L. (1987) Radio System Design for Telecommunications (1-100
GHz), John Wiley & Sons, Inc., New York.
2. Miller, G.M. (1999). Modern Electronic Communication, 6th.ed. Prentice
Hall, Inc. New Jersey, USA.
3. Allnutt, J.E. (1989). Satellite-to-ground radiowave propagation, Theory,
practice and system impact at frequencies above 1 GHz, Peter Perigrinus Ltd.,
London, UK.
4. Ajayi, G.O., Ezekpo, S.U.B. (1988). Development of Climatic Maps of
Rainfall Rate and Attenuation for Microwave Applications in Nigeria. The
Nigerian Engineer, vol. 23, no. 4, 1988: 13-30.
5. Juy, M., Maurel, R., Rooryck, M., Nugroho, I.A., Hariman, T., “Rain Rate
Measurements in Indonesia,” Electronics Letters, vol. 29, no. 9, 26th April,
1990, pp. 595-598.
6. Yagasena, A., Hassan, S.I.S., Yusoff, M.M.M., “Rain Attenuation Prediction
at 6.75 GHz in Malaysia Using Rain Gauge and Radiometer Measurements,”
Theme: 'Electrotechnology 2000: Communications and Networks'. [in
conjunction with the] International Conference on Information Engineering.,
Proceedings of IEEE Singapore International Conference on Networks, 1995,
pp. 596-599.
136
7. Aydin, K.; Daisley, S.E.A. (2002). Relationships between rainfall rate and 35GHz attenuation and differential attenuation: modelling the effects of raindrop
size distribution, canting, and oscillation. Geoscience and Remote Sensing,
IEEE Transactions on, Volume: 40 Issue: 11 , Nov. 2002: 2343 –2352.
8. Gibbins, C.J. (1992). Studies of Millimetre-wave Propagation and Related
Meteorology Over a 500m Path. URSI Open Symposium, Wave Propagation
and Remote Sensing, Ravenscar, North Yorkshire, UK, 8-12 June,
1992:10.6.1-10.6.8.
9. Crane, R.K. (1975). Attenuation Due to Rain - A Mini-review. IEEE Trans.
On Antennas and Propagation, vol. AP-23, no. 5, September, 1975:750-752.
10. Haddad, Z.S.; Short, D.A.; Durden, S.L.; Im, E.; Hensley, S.; Grable, M.B.;
Black, R.A. (1997). A new parametrization of the rain drop size distribution.
Geoscience and Remote Sensing, IEEE Transactions on , Volume: 35 Issue: 3
, May 1997, pp. 532 –539.
137
Appendix 3.1 Specifications of the Casella Rain Gauge
138
Appendix 3.2 Data Sample from RGN-UTM 1
Date
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
08
08
08
08
08
08
08
08
08
08
08
08
08
08
10
10
10
12
12
13
13
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
09
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
Time
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
96
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
11
11
13
00
05
10
10
41
42
44
46
47
48
49
51
52
54
56
01
06
10
13
15
19
24
25
27
28
29
30
20
35
37
38
39
40
41
42
43
44
45
47
49
52
07
18
28
37
58
53
54
R
(mm/min)
000.5
000.5
000.5
000.5
001.0
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
001.0
001.0
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
13
13
13
13
13
13
13
13
10
10
10
10
10
10
10
10
96
96
96
96
96
96
96
96
10
10
10
10
11
16
17
17
55
56
57
59
08
52
09
30
000.5
000.5
000.5
000.5
000.5
000.5
000.5
000.5
139
Appendix 3.3 Radar Measurement Theory
Radar Measurement Theory
Amount of power intercepted by a particle is given by
Pσ =
Pt G A
4 π d 2
(A1)
t
where Pt = transmitted power,
G = gain of antenna,
At = cross-sectional area of target,
d = range or distance of target.
Assuming power is reradiated isotropically by the particle,
Pr =
Pσ
4 π d
2
A
(A2)
e
where Ae = effective area of antenna.
Thus,
Now,
Pr
=
Pt G A t
( 4 π )2 d 4
(A3)
A e
A e = ρ Ap
(A4)
where Ap = cross-section area of antenna
ρ = antenna efficiency.
Silver (1951) has shown that A
e
=
G λ2
4 π
(A5)
140
For circular parabolic antenna,
(A6)
 8 π A p 


 3 λ2

≈
G
Ae = 2/3 Ap
which gives
Then
Pr
(A7)
Pt G 2 λ2
=
(4
π
)
3
A t
d
4
P t A 2p
≈
9 π λ
A t
2
d
P σ = σ Pi
Now
(A8)
4
(A9)
where σ = backscattering cross-section of particle, and
Pi = power intercepted by the particle.
Thus
σ Pi = 4 π d2 S
(A10)
where S = backscattered power per unit area at receiving antenna.
Then for single scatterer,
Pr
=
Pt G 2 λ2
(4
π
)
3
σ i
d
(A11)
4
However, radar beam illuminates a large group of raindrops at the same time; and
the number is equal to that within a volume defined by the beamwidth and the pulse
length of the radar set. If the back-scattered power is averaged over a volume of n
numbers of randomly distributed scatterers, then the average received power can be
written [1] as
Pr
=
Pt G 2 λ2
(4
n
∑
π )3 d 4 i = 0
σ i
(A12)
Denoting the back-scattered power of m numbers of uniformly distributed scatterer
per unit volume,
141
σ i = Vm
m
(A13)
∑ σ iv
i= 0
where Vm = volume where particles are uniformly distributed, and
σiv = backscattering cross-section of a single scatterer per unit volume.
The volume Vm occupied by the radar beam of horizontal beamwidth θB and vertical
beamwidth φB, approximately can be written [1,3] as
Vm
=
π
4
θB  
φB 

d
 d


2  
2 
c τ
2
(A14)
where c = velocity of light (m/s), and
τ = pulse duration (sec).
Now, taking σ per unit volume and putting the expression of Vm in eq. A12 above,
we get
Pr
=
Pt G 2 λ2 θ B φ B h
512 π 2 d 2
∑ σ
(A15)
iv
vol
where h = c τ = pulse extent, and
= radar reflectivity.
∑ σ iv
vol
In deriving these equations, it is assumed that, across the radar beam between half
power points, the transmitted power per unit area has the same value. But, actually,
the transmitted power is maximum along the beam axis and decreases to half of the
value at the angles corresponding to the half of the beamwidth. So, by considering
the power per unit area as Gaussian function within the main lobe, the radar equation
can be written as [1,3](from Probert-Jones, 1962)
Pr
=
Pt G 2 λ2 θ B φ B h
5 1 2 (2 ln 2 ) π 2 d 2
∑
vol
σ iv
(A16)
142
Substituting for the Gaussian beam shape,
G
Pr
π2
θB φB
=
(A17)
Pt G λ2 c τ
=
1 0 2 4 ln 2 d
2
∑
(A18)
σ iv
vol
When the radar wavelength is large enough compared with the circumference of a
scattering particle of diameter D (Rayleigh scattering region), the radar cross-section
is [4,5]
σ iv
π5 D 6
=
where
λ4
K 2
(A19)
K 2
= (ε - 1)/(ε + 1), and
ε = permittivity of scattering particle.
The value of
K 2
for water varies with temperature and wavelength. At 100C and
10 cm wavelength, it is approximately 0.93 [5]. By substituting σ i v into eq. A16,
we get
Pr
=
π Pt G c τ
1 0 2 4 ( ln 2 ) d 2 λ 2
K 2
∑
D 6
(A20)
vol
The sum of the sixth power of diameter per unit volume is called Z, the radar
reflectivity factor or
Z = ∑ D6
(A21)
Experimental measurements showed that Z is related to rainfall rate R by [3,5,7]
143
Z = aRb
(A22)
Here, a and b are empirically determined constants. The choice of Z-R relationship
can be made on the basis of the type of rain. For different types of rain the Z-R
relationship can be given by [5]
Z = 200R1.6 (stratiform rain),
(A23a)
Z = 31R1.71 (orographic rain), and
(A23b)
Z = 486R1.37 (thunderstorm rain)
(A23c)
By considering stratiform rain, the average received power can be written as
Pr
=
2 .4 P t G τ R 1 .6
d
2
λ
2
x 1 0 -8
(A24)
where R in mm/hr, λ in meters, τ in sec, and Pt in watts.
Reference
[1]
Skolnik, M.I., Introduction to Radar Systems, McGraw-Hill Book Co., New
York, 1980.
[2]
Rogers, R.R , “Statistical rainstorm models, their theoretical and physical
foundations,” IEEE Trans. on Ant. and Prop., July 1976, pp 547 - 566.
[3]
Battan, L.J., Radar Observation of the Atmosphere, The University of
Chicago Press, 1973.
[4]
Allnutt, J.E., Satellite-to-ground radiowave propagation, Theory, practice
and system impact at frequencies above 1 GHz, Peter Perigrinus Ltd.,
London, UK, 1989.
[5]
Puhakka, T., “On the variability of the Z-R relationship in rainfall related to
radar echo pattern,” Geophysica, 13, pp 103 -119, 1974.
144
Appendix 3.4 Radar Calibration Checklist
145
146
147
148
Appendix 3.5 Kluang Radar Station Specifications
Meteorological Radar MR 781 S Stesen Kajicuaca, Kluang
with RAPIC Transmitter EH663 v. 8.00
Station ID
3 Kluang
Station position
latitude = 2.020o; longitude = 103.320o
Reflector
12 feet parabolic (3.66m)
Frequency
2800 MHz
Polarization
vertical
Gain
38 dB
Coverage
elevation: -2o to +90o; azimuth: 360o
Beamwidth
2.0o
Pulse duration
2.2 µs
PRF
278 pps
Peak power
389 kW
STC range
230 km
149
Appendix 3.6 An Example of a Radar Data
COUNTRY: 458 NAME: Kluang STNID: 03 DATE: 00798 TIME: 16.22 VERS:
8.04 RNGRES: 1000 ANGRES: 1.0 VIDRES: 16 STARTRNG: 2000 ENDRNG:
256000 PRODUCT: VOLUMETRIC [162200798] PASS: 01 of 15 IMGFMT: PPI
ELEV: 000.5 DBZLVL: 11.8 23.0 28.0 31.0 34.0 37.0 40.0 43.0 46.0 49.0 52.0 55.0
58.0 61.0 64.0 %041A10Epp20EA49VA15}IAEA %042A12h21VA48hEi2l11F-j
%043A11h4l17EFA47+1-+1-1l8+ %044A36E]o49+1-1l1ll13 %045A10\-24h52l2+1+ %046A3EA4@+-22h44l+-1@7+1 %047A11l13l54v2k2@8
%048A11l7l60lqk10l18 %049A11l69hm-10+ %051A5EA1EFA %052A6F1A38
%053A6EAEA37 %054A6EA@1l13h19 %055A8E %056A4EAFec+
%057A6FAxAl %058A6Eg(p %059A3EA3@m %060A8EAm %061A10 %063A10
%064A7E1 %067A3h %068A5 %069A4l2 %074A2 %093A2l+-1h+ %094A2l1+-1
%095A9hw %096A5h5\ %097A11@2 %098A9@3+ %099A13m2-3l
%100A7EA3E1A7 %101A8FA3Ep1k1l3l63vy %102A14@m-1@67Yg
%103A12F1j1kv1FA66}1 %104A13F[@2qFA67F %105A6EA3G-tA2qAFA67+
%106A10EAFAEFA1v2nA75 %107A10EA1FA1@+gE1A75
%108A13E+A1+1wA76 %109A5E1A4E2AEdvy %110A13Eha1+2+p52q
%111A13EAF-ou-56hm %112A14FEAFe1--51lEFA2 %113A2h2EA4@GAEqdt254G %114A4@7Em1A5l3l39l5@1EGA %115A12@6Eih2vp45YA1E1
%116A11E1A1GA3Eog+vo38l6hv %117A12E1AGA7l1}/45Y1j
%118A13FA1HAFA@vkvG[-43Y2 %119A14GA2Ee-EA1lFGA42+uAEk
%120A13GAGA2h2EA2BFA42V1i2+-40 %121A10GA6nt-h+AEA40UxCp46
%122A18E-AEAm1-42hFHDo25ll3ll1l4 %123A2@15EkFA@46@F/18l2+5u1l+4-1l2l %124A5h5FA1GAEFAEd1GCp36l1lllEd21+2u2u1u-ll+-l2l
%125A14FA3GAVAHEA34l+uWo1q1k19+1u2u1u3-l1l1+1uu1
%126A6@1FA4GAGA2@1IaA32+1U1A1ntgqp16+4u3u-+-+3u-2l25l
%127A9FA2FAFA1H1GAEAIAFA33l1hhEA2++p18+1u4uu1-l+7u-23
%128A19GgSAHA37l1+1-2+-15ll+3uuuu10u1u-8ll5l4+1 %129A22EFAFA36+17l17l1l+11uu2+--12+-1l+-4+ %130A21Gt+1A67+2-+1u6u3vs1-7+1-8+u-+3
%131A8FA12EA1GA69+5-3+3u+UB1g+-3+-1+u-ll2l2+u2uu3
%132A9FA10EAEqAl67l+3uuu2u3+g1u2-10ll1l1+u2u1uuu1-1+
%133A21ESvao68l1+9S1t1l5u1u2-ll+Spl+1uu-+u1-l+1
%134A20GA2G+Al68+6uu3-m2-+6u-2+Syt+k2l1+1u3u1-l+2
%135A19HkA2HA1l60l6+2Sp+1u3u2u7u5u2vo2qy-2S-2uu6-+
%136A21FAG1HAHA57l6llVp5-4u1uu8uu6+ukv1y1-3-3+u5u
%137A19H1A2GAGA\-54l7+W+-o+3u1-7l+u8-q-+2-g1m2lu3-1l2+2-67+1
%138A17FA2GlA3@65+-E+1jt1u1-3ll1+u3llu6llu1u3u10-+-3+-64+l2
%139A19G2A1Fg1j-64q1UA3hq-1-l2l4+2Skq-u3lg+uu3uuu4-6+1-64+
%140A10FA1GA3F1AGAG-jg-64lwAF1Ar$$kl4u1u4uu2+t1ll1u2-+5uu1-l8+
%141A20EA1GA1hm-65vvA1EAr+1p+(t8u5gqut+-2-1+1u3u-5+1u1
%142A2@9FEA2F1A4qu1p65+v$1AEAE1AEA2EA@+14+1k+u-+-2+2u1l1+u2uu-39+-10+ %143A23EA@3l45l19lr$AFu2[EA2Ep3-5u1uu4uu1-1ll+32l+u6-39+ %144A2h9GA5@1F/h1h45lm-17+W+2AE1-1++-1kt5u4u2-1l1l8+-4ll+2
%145A13Gdp5FAh50\1-18Yy1uar$orAE-1s4-+3-1+1uu1u1u-+-6+2u
%146A13FuEA7l50+-20mW$wAF-1AE-on1km-+12-l6l3l2+1
%147A13FEAEa1hFAmu-49l19+SAEv1-EAx2ancq6pl+5-6+2-l1l2+
%148A10EA2FgA1h@2l1+-17GA27h1ll12+1Slqv1FArg+4$uoq2-3u1u-7+1-1l6
150
%149A5h7Eha2hm-1+1-3h41l2l9+++u$1EA1r2-2{1(y2uk+4-+2-1+8u1
%150A7@FA3GAEtsSpl+-5FA5h32ll12+w3A@q4y2yucq2-7-+6-+3u6-24+
%151A14GEA@5l3l10ll30+u-l9v1q1kc1hl1h+gmv2e1+u6u1u4-+3u-27+2
%152A5h5GAGj-1p2l1+-11vc5l22l+-10lhxk-2uu-1l+u1Sphl1+-2+-3l5+
%153A14Gj$1oh18lGB-6l16l2+1-4+-2v2+k5S3t1l1ug3+1
%154A14GA@E1A3lm1-12hh4HA19l2+2u2u1-2vy2p2+gn2lu1tl+p
%155A9FA3GjoEA2lh2ll9l1l36+-5v3-1+AE1kcn1-ul1u1-35
%156A9FA4GAFAFA2l1vp47+-11l1Fk2(ycr1(t2u-39+-42
%157A12GA1FuAFA2m-65VFAGe(pE-+kk4 %158A11EGA2Fu2[+u-6l54+1FlEAEA@E2pk3 %159A10EAGA2F-lA1+2u-54+-3U+FA2EA1E1Aqt
%160A10@G1A1Gp1k-1ugl54+-3+FpFAE+-Ark %161A10EA4Gd1+o5l43+16mq$mFAEAF %162A4h2EA@1GA2Epc3qpl56l5vyywHA2FA@17m
%163A8FA)A2Fco5hh64vp1+1GA1l1n %164A9EA4F1Alx--pEA64we3m
%165A17\-@nc77 %166A9@2E1FAmwam1-1l63+-6 %167A13E2lAVa1q1kl63
%168A13ESEA1@rs-1 %169A5h2FAEA3FA1wh(pl
%170A5h4r+AEA3F[@1vk31+ %171A11@1E+A2xdEA38
%172A5qAFA1r1wA2@EaEAmgl31 %173A4\g2roE+EA1@2nt-1q1
%174A7@1@1@EA2xA2EA+EA2FA %175A10@5FploFBmrEA1HD
%176A6h3h4FAh6EAGlAHEA %177A6@1n1p5@EFA2FA1GA4GAl7+3
%178A9q1p3GAEGAFA5GA6EA7w
%179A10hh6G1FA1HA2H1A2Ew[p4vxFAE
%180A9qp1nAGA1FA1H1A1G1A5GHA8EA5
%181A9h2l3HA1HAHA2HA1GA8l3l2E
%182A10h3hEA1H1A4GA2FA1FA2h5l1GAh2
%183A11q1krUAHAHA2HAHAHAHA3@l7h2E
%184A10ll1hh2GA5HA1HIA4@1l7l1 %185A10l5h1HA1HA12EA10
%186A10l4mYEA2H1A7n1 %187A10l3+1-10EA1+2u
%188A12@+2g1EAGAFA2EAh4 %189A10l3+1SvAEA1+] %190A2@12+S{(
%191Aq1p17 %194B %195A2 %196A1h7 %199B %202B3 %205A11l+
%206A9l3 %207A8 %208A6h9 %209A12q %210A5l13 %212A13l1
%213A5h5l1l1 %214A13l %215A13+ %216A5l4hl %217A11 %218A11\2
%219A12 %220A5l5l4l85 %221A8l3+-4 %222A5h5l+-2+ %223A4l5Eo%224A4l9+-1 %225A11 %226A14v %227A3l8l %228A3 %229A11 %231A110l
%232A109+2u %233A37l69lh1EA %234A106ll@EAEe
%235A28l12l63+gx1AFEA+u1-l2 %236A110qw1AGA1qyupl3l+
%237A4l10l90l@EFAH1A1Fpoqt1-3 %238A14ll90vmqGA1HA1G1--al1+St2
%239A4h10l89+-V1AGlv-k1AEal1+-1+1
%240A16l23@53lll5l1woHAHA1IAI1p1eo5l+ %241A10l2m122l56l8UwS8yGA1l4+u %242A14ll27EA46l1hll8)+FAH-1-AFAFd %243A15+8l16h48lh+-6UUFA2FGA1FuGAh6+ %244A3m-4+-+-76v1p11EGA3EAEAE3kk4
%245A4h9+-22l54l10l@h1qkro %246A13+-24@66lm2-1+1Spn
%247A14l2l21GA68l1l4+AGAFAh6+ %248A4EA7l3l15l74l+-2l3F1Al5Y1+A2
%249A15l26@69+-2+Syp7G+1Ars %250A12ll19l6+-65l2l16CGAHGA@E
%251A12+1-98+-15Ul1 %252A12+1-18h63+2-32l1m %253A4h3l1lEA3h3+-72+1
%254A12BFA1FA6l23+ %255A12BGA1h1l26l+-109qp %256A23l23l+103l1vmuol2 %257A14EA1h4l12l4+1-4+1uu-h+1g90l1lmghllh34ll6l5
%258A14@2l10l5l11+1uu2g1xk1k95+Skv1k34+1-16 %259A14FA2l17h9h1+hqcEAEArj102l55+1 %260A17m2-23lhq2ykhEu1lal158+u %261A12EA3m17EA5+Sp1qcq1EA4@1h157+1 %262A10lEA3l24+2-4E1-(AEAFAEA3h76l77+1
%263A9+AFA3l4l19l1v1AEFAr1$1EA85 %264A23l18m-3VFA1EA4E
151
%265A23l20l3)A4EA3EA2 %266A17l26llh2GkA11 %267A5l2+-4l25Eo4H1A1FA3EA@hqk %268A9h3HA1l26l+-GA4E1A1@4 %269A17l26+1
%270A9h6ll10l8l2+1-EA4F1EA4h1l1 %271A43FA+g4Gt1AEA9
%272A8@8l11l8l2qy4FAGkFAEA4h2v %273A8wEA30vupqtVAGkA1@2@1qt-1
%274A4l3)GA5h22ll2FAwoF1-A6h1hh2l %275A9EA7h5@2ll6l1+2G(pvgAFA3l5qp %276A9@7h5EA2lvp4+u1-3h@@1Goo4l3l3
%277A14EA2h5h15vp3m+yVEA2h1qt1-hl
%278A14GAEA14l5ll6mScEg1u(p1h3+ %279A32+u-7h4l1E-e1@hh6+1
%280A32l1l8\-m1+pmg1hqph1+1u1 %281A12GA19+u1u-3FA4v2p3qu2yt1-l
%282A13EA2l12l1vk+-3HA2m1Slph1+2+2t-3 %283A3l5EA5h8h3Uk2l-6+1-q1{p5l+2 %284A12GA3l5l7rk1Sp7+1+pqkh+uu2u %285A19ll6l2v1-Sk4l2m1v-1ut32+u %286A16h2l5@4v1p1m-8+S2p1l+1 %287A16h9h1+-2l1h3HA6qut3u1
%288A16l12hl1+Sk6l2\l1u5-l %289A16l6lUFA2mu-l7h2hq-uu1u-l
%290A14HEA5EA+vm-s-3h6@l+u1-3+-1+ %291A26F1-A2m-2h9+Sk6+1u-+
%292A15FA6lh1EaF1i1-10l+u1-5l2 %293A20\-2FA@EA2+-10mg+-7l3+1
%294A16FA3ll2HA2Egj6xA4l+4-+1u-1+ %295A21l+gI-1Del6h6+2-l3l
%296A18h1hl1GAHAG/u-1l3l5+-7+u %297A21hl4GA+-8h6l9ll20
%298A21@5HC1p10@41 %299A17GAEAh1+AIFB1-10m1-38
%300A17EA3l3GAl12 %301A17EA2h+1Wj15FAh36E
%302A13GA5mu1ug18@G %303A18FAhm-+-17EA21 %304A6h12hll24
%305A27l13l6FA2l14+ %306A18EA1npl2l16FA5l15 %307A6h4FA2EA4n1g26l10+-+1 %308A14G1A5@1lhl22h11+-1q1 %309A21Ea1vg-35+-llm
%310A10GA4Ea1@@1h2l37l1qy1t %311A24qc+1-30l2l2m %312A23l1qt-4l25+l2 %313A15EA7l1qp5l29l+3S--69 %314A20@1lh1m-2ll27lll2l3l3h
%315A24l2h6l27lll2+2u1-2 %316A25l6l3l1l30+uu2Sh %317A14EA10lll3h4l32l+v2-u1 %318A35h1h+1-31lm1u2v %319A13@1@2qp1vp2l2h3+1-22+-5l+-ll@
%320A24h4l2h4+-32l+u2u1-2 %321A21qp2nt1-2lll+-32+5-2+u %322Cp36l2+329+u4-4 %323A19FA+-10ll3+2-34+2u %324A12FA8l13ll2l1+1-33l1+1
%325A18hEA12l1m2-l1m-l33+4 %326A15GA3@12+Sp7l26l8l1+2
%327A11GA7h11@5l47+ %328A19h14l46+ %329A12FA3v1p3@4F/nk5@38+112 %330A7EA2FA2EA2h3VA7@l3l4l34+ %331A11EA2EA1h2EA8E-1jh7h33+
%332A9FAFA2@l1@2@7Ep1yp6h30+1u-3
%333A10FEA6wo1F1A4EAEA1@9h28+-+-5 %334A17l6GA4h9h33+-l+3
%335A11EA2l25Edl2l26l6mS %336A11EA4l2h9U1o5FA2l1+-21+-6l+2
%337A10GA2EA1l7FA4l8IA4+2-21l6+1u1 %338A15lUo26+2-34
%339A20h20GAFA2 %340A20wo7h8GCp %341A13EA5h9l8GBg1m-9m%342A21h8l8E$a+-9mg1 %343A20+-7l8hF1Ah12vph4l1+1 %344A12@6+17l@15m-l6r1(3 %345A11G!5Eo1-14ll3GA7m-1l7lVaF[@m
%346A12ro4l5l12l12m-10+U3lA\1 %347A13@5l4l11lEA3l7l2l9h1Ekpqt
%348A11GAEA8l11+-l17l4l3++{e %349A13EA3l8lGA4l2h2@12l7m1-1vpmu1
%350A13EA1ll4l10h6+-1h5l7q{k1u2Sk+ %351A18+u-l10l8l1EA5lh6x1tk2U1AEk
%352A12h6+-+-3h10vp2FAl3l8EAFEA1+SqAGek %353A12@1\-+1u11l1@12Ea1@EA12@1FArp2W)dA %354A3wo5EA1\uugl20EA2lFA12w(-14GHAEo %355A17l1@+1-18m-17vp7vh %356A3h10h4l+1 %357A7EA7EA4+
%358A14GCmo1l7l7E %359A7EAFA5r1o31 %000A12FA1r2e1@h3
%001A7@6wo3@l3hl16l1 %002A7rEA4@2EA2\-2h12l5+g64
%003A4@1EyA2E1A3FA2h1l1lh10h6m %004A4h1EyA4Ecp1FAEill1l17q
%005A7EAEA2hxa5m-10l3@5 %006A7nwA1EA3G1HA2nt-11hFA2l6
%007A7nwA6EFA1EFAwo1l15hlv1 %008A4@1rAEFA3@ElAFA1qp+14h2EFAE %009A4h1n{o4E1AEA3lll16h1lGAE %010A7@h3lrvA1h2+1-
152
16@1UEA\ %011A6Edh@h1hG1A3mu-17lFB1- %012A6EA2wphHGA1l15l9m1S %013A7EA1wtp@GA2hh13h13
%014A3EA6hh2GAFAF/hl8h1EA7 %015A9qy1ph3FA2 %016A9hhmSpHA2h+30 %017A3@3qpvpCGA4+2 %018A11qp1@6l32 %019A3@5hq1pFA4ll14l15E
%020A11hh7l34 %021A10h1h6m-108 %022A5EA3h1h1qEA1l110
%023A8Ekpl2Y %024A1@EA4Edm-2EA1 %025A9n1--2 %026A9n1t-2
%027A7E1A1h2 %028A3EA3EA1h2 %029A3@3Ed4 %030A8ro3@75+-14l61
%031A4EA2Ekt-5EA11+-55m-8+2-63 %032A10ll20l54hh11 %033A9h21+150vSs %034A9qpl18l52m1+p17 %035A3EA4qp7l9vp2+-46+2-14l+1
%036A9@20h5h57l4+3S %037A4EA3rol5l13qyp49+1u-6vy2u
%038A9EA1h6l12GEA1l45l1v1--7lwom2 %039A10@8l12HGA50vl--7+v2(%040A5EA2re7l12GHAl47vms-10xAFkp END RADAR IMAGE
153
Appendix 3.7 Radar Data Encoding Format
154
155
156
157
Appendix 4.1 MATLAB programs
%filename : Radselec.m
%This program will select the Kluang Station radar data
filen='F:\13\02579803.220'; %filename of raw radar data in cd
fid=fopen(filen,'r');
select=[];testsc=0;
Nsize=1e6;kmax=50; %read the 1st 1Mb chars, 50x.
serN=1;
%read data
for k=1:kmax
data=fscanf(fid,'%c',Nsize);
sp=findstr(data,'PASS: 01 of 15'); %find loc/add of 1st char in string (of 0.5
deg)
sc=findstr(data,'COUNTRY');
if (testsc==1) %read more data if only part was read before
select=[select, data(1:sc(1)-1)];
testsc=0;
sklg=findstr(select,'Kluang');
if (isempty(sklg)==0)
eval(['klg',num2str(serN),'=select;']);
filen1=['C:\Radar Data 0.5
deg\12\klg',num2str(serN),'.txt'];
fid1=fopen(filen1,'w');
fprintf(fid1,'%c',select);
fclose(fid1);
serN=serN+1;
end
select=[];
end
for i=1:length(sp)
differ=abs(sc-sp(i));%find difference between "COUNTRY" and
"KLUANG"
n=find(differ< 200);
if (isempty(n)==0)%1(true) if empty and 0 if nonempty
if (length(sc)> n)
select=[select,data(sc(n):sc(n+1)-1)];
sklg=findstr(select,'Kluang');
if (isempty(sklg)==0)
eval(['klg',num2str(serN),'=select;']);
filen1=['C:\Radar Data 0.5
deg\12\klg',num2str(serN),'.txt'];
fid1=fopen(filen1,'w');
fprintf(fid1,'%c',select);
fclose(fid1);
serN=serN+1;
end
158
select=[];
else
select=[select,data(sc(n):length(data))];
testsc=1;
end
end
end
if(k<kmax),fseek(fid,k*Nsize,-1);end
end
fclose(fid);
clear fid filen testc
clear i k kmax n sp sc select differ fid1 filen1 Nsize testsc ans
clear data
159
%File name - Decoder. This program will decode the Kluang data into
corresponding numerical values
Code=['ABCDEFGHIJKLMNOP']; %Data code
level=[0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15]; %Corresponding absolute level
%Deviation encoding characters
Devencod=['![abc]@';'/defgh\';'ijk<lmn';'op.+qr';'stu>vwx';'(ySTUV)';'${WXY}&'];
rangbin1=[-3 -2 -1 0 1 2 3]; %Deviation values
rangbin2=[-3 -2 -1 0 1 2 3];
%read data from file
serN=1;
filen=['c:\Radar Data Samples\radar',num2str(serN),'.txt'];fid=fopen(filen,'r');
data=fscanf(fid,'%c');fclose(fid);
n=findstr(data,'%');
levklg=[];
for ind=1:length(n)
if (ind<length(n))
s0=data(n(ind)+1:n(ind+1)-2);
else
s0=data(n(ind)+1:length(data)-17);
% the array data contains one section only
end
deg=s0(1:3);
lev=[];
i=4;
while (i<=length(s0) )
Lr= s0(i);
mult=str2num(Lr);
if(isempty(mult)==1)
nc=find(Code==Lr);
if (isempty(nc)==0)
lev=[ lev level(nc)];
else
[Ic,Jc]=find(Devencod==Lr);
lev=[ lev lev(length(lev))+rangbin1(Jc)];
lev=[ lev lev(length(lev))+rangbin2(Ic)];
end
else
if(i<length(s0))
if (isempty(str2num(s0(i+1)))==0),
mult=str2num(s0(i:i+1));i=i+1;end
end
lev=[lev lev(length(lev))*ones(1,mult)];
end
i=i+1;
end
if (length(lev)>=100)
lev=[str2num(deg) lev(1:100)];
else
lev=[str2num(deg) lev zeros(1,100-length(lev))];
160
end
levklg=[levklg;lev];
end
temp=[];
for i=0:359
ni=find(levklg(:,1)==i);
if(isempty(ni)==1)
temp=[temp; i];
end
end
n=length(temp);
temp(1:n,2:101)=zeros(n,100);
levklg=[levklg;temp];
[Y,Isort] = sort(levklg(:,1));
eval(['levklg',num2str(serN),'=levklg(Isort,:);']);
clear Code Devencod Ic Jc Lr fid filen rangbin1 rangbin2 nc ind i level
clear s0 lev lev deg n mult ans Y Isort
clear data levklg temp n ni serN
161
%filename : DataSelect [Select data for virtual path links from specific area.]
% # of files in each data folder
d1=175;d2=648;d3=949;d4=906;d5=721;d6=1041;d7=955;d8=792;d9=869;
d10=777;d11=785;d12=893;d13=807;d14=662;d15=888;d16=1049;d17=996
;
for m=1:17
eval(['load data',num2str(m),';']);
% load data
eval(['p=d',num2str(m),';']);
% # of files in data
for j=1:p
eval(['A=levklg',num2str(j),';']);
B1=A([3 6 9 12 15],32:51);
B2=A([238 241 244 247 250],32:51);
B3=A([294 297 300 303 306],32:51);
B4=A([334 337 340 343 346],32:51);
eval(['D',num2str(j),'=[B1;B2;B3;B4];']);
clear B* A
end
eval(['save SD',num2str(m),' D*;']);
clear p levklg* D*
end
162
%Filename : CellSize - rain cell size for selected virtual paths data
% # of files in each data folder
d1=175;d2=648;d3=949;d4=906;d5=721;d6=1041;d7=955;d8=792;d9=869;
d10=777;d11=785;d12=893;d13=807;d14=662;d15=888;d16=1049;d17=996
;
clock
for ind=1:17
eval(['load SDR',num2str(ind),';']);
eval(['q=d',num2str(ind),';']);
% load data
% # of files in data
X1=[];X2=[];X3=[];X4=[];X5=[];X6=[];X7=[];X8=[];X9=[];X10=[];
X11=[];X12=[];X13=[];X14=[];X15=[];X16=[];X17=[];X18=[];X19=[];X20=[
];
C1=0;C2=0;C3=0;C4=0;C5=0;C6=0;C7=0;C8=0;C9=0;C10=0;
C11=0;C12=0;C13=0;C14=0;C15=0;C16=0;C17=0;C18=0;C19=0;C20=0;Cbi
g=0;
T=[];count=0;total=0;
for i=1:q
eval(['A=DR',num2str(i),';']);
for j=1:20
for k=1:20
temp=A(j,k);t1=A(j,1);t2=A(j,20);
if t1 + t2 == 0
if temp ~= 0
T=[T temp];
count=count + 1;
end
if temp == 0
if count==1
X1=[X1;T];C1=C1 + 1;T=[];count=0;total=total + 1;
elseif count==2
X2=[X2;T];C2=C2 + 1;T=[];count=0;total=total + 1;
elseif count==3
X3=[X3;T];C3=C3 + 1;T=[];count=0;total=total + 1;
elseif count==4
X4=[X4;T];C4=C4 + 1;T=[];count=0;total=total + 1;
elseif count==5
X5=[X5;T];C5=C5 + 1;T=[];count=0;total=total + 1;
elseif count==6
X6=[X6;T];C6=C6 + 1;T=[];count=0;total=total + 1;
elseif count==7
X7=[X7;T];C7=C7 + 1;T=[];count=0;total=total + 1;
elseif count==8
X8=[X8;T];C8=C8 + 1;T=[];count=0;total=total + 1;
elseif count==9
X9=[X9;T];C9=C9 + 1;T=[];count=0;total=total + 1;
elseif count==10
X10=[X10;T];C10=C10 + 1;T=[];count=0;total=total + 1;
elseif count==11
X11=[X11;T];C11=C11 + 1;T=[];count=0;total=total + 1;
elseif count==12
X12=[X12;T];C12=C12 + 1;T=[];count=0;total=total + 1;
163
elseif count==13
X13=[X13;T];C13=C13 + 1;T=[];count=0;total=total
elseif count==14
X14=[X14;T];C14=C14 + 1;T=[];count=0;total=total
elseif count==15
X15=[X15;T];C15=C15 + 1;T=[];count=0;total=total
elseif count==16
X16=[X16;T];C16=C16 + 1;T=[];count=0;total=total
elseif count==17
X17=[X17;T];C17=C17 + 1;T=[];count=0;total=total
elseif count==18
X18=[X18;T];C18=C18 + 1;T=[];count=0;total=total
elseif count==19
X19=[X19;T];C19=C19 + 1;T=[];count=0;total=total
elseif count==20
X20=[X20;T];C20=C20 + 1;T=[];count=0;total=total
elseif count > 20
Cbig=Cbig + 1;
eval(['Xbig',num2str(Cbig),'=[T];']);
T=[];count=0;total=total + 1;
end
end
end
end
end
end
eval(['save CSDR',num2str(ind),' X* C* total;']);
clear temp t1 t2 X* C* DR*
end
clock
+ 1;
+ 1;
+ 1;
+ 1;
+ 1;
+ 1;
+ 1;
+ 1;
164
%Filename : R1km - rain distribution for 1-km paths
%Get 1-km data
Onekm=[ ];OnekmNew=[ ];count=1;
for i=1:17
eval(['load CSDR',num2str(i),';']);
Onekm=[Onekm;X1];
clear X* C* total
end
%sort data
temp = sortrows(Onekm,1);
for j=1:(length(temp)-1)
a=temp(j,1);
if a==temp(j+1,1)
count=count+1;
else
OnekmNew=[OnekmNew;a count];
count=1;
end
if j==(length(temp)-1)
if a==temp(j+1,1)
OnekmNew=[OnekmNew;a count];
else
OnekmNew=[OnekmNew;temp(j+1,1) 1];
end
end
end
%save Onekm OnekmNew
save Onekm OnekmNew -ascii
clear all
165
%filename : Path1km7GAt [Total att dist for links of 1-km length]
clock
d1=175;d2=648;d3=949;d4=906;d5=721;d6=1041;d7=955;d8=792;d9=869;
d10=777;d11=785;d12=893;d13=807;d14=662;d15=888;d16=1049;d17=996
;
total=0;% total # of 1-km paths
count=0;% # of 1-km paths which have rain/attenuation
X=[];% temp to store att values
for m=1:17
eval(['load At7G',num2str(m),';']);
eval(['p=d',num2str(m),';']);
for j=1:p
eval(['B=At',num2str(j),';']);
for i=1:20
for k=1:20
Att=B(i,k);
total=total + 1;
if Att~=0
count=count + 1;
X=[X; Att];
end
end
end
end
end
clear d* m p i j B Att % count1 total
temp=sortrows(X,1);
T=temp(:,1);
clear temp X
countAt=1;% total count of each att value
Att1=[];% att dist for 1-km paths - [AttValue events]
for i=1:(length(T)-1)
t=T(i,1);
if t==T(i+1,1)
countAt=countAt + 1;
else
Att1=[Att1;t countAt];
countAt=1;
end
if i==(length(T)-1)
if t==T(i+1,1)
Att1=[Att1;t countAt];
else
Att1=[Att1;T(i+1,1) 1];
end
end
end
save P1km7GAttDist Att1 count total;
clear all;clock
166
Appendix 4.2 Radar Rain Rate Distribution
Table A4.2.1 Rain rate distribution for range-bin size of 1-km from radar data.
Rain rate (mm/hr)
0
0.2
1
2.1
3.2
4.9
7.5
11.5
17.8
27.3
42.1
64.8
99.9
153.8
236.8
364.6
Total
events/occurrence of rain rate value
4743844
236698
124172
114667
125677
65680
54020
44683
33062
17019
2818
1427
727
378
203
125
5565200
percentage (%)
85.24121
04.25318
02.231223
02.060429
02.258266
01.180191
00.970675
00.8029
00.594085
00.305811
00.050636
00.025641
00.013063
00.006792
00.003648
00.002246
100
The percentage is calculated by, dividing the number of events for a
particular rain rate by the total number of events and then multiplying them by
100%.
For example, for 11.5 mm/hr rain rate
percentage = 44683/5565200 * 100 % = 00.8029 %
(A4.2.1)
This is easily done using EXCEL or MATLAB.
Using the Curve Fitting Toolbox available in Matlab, the best-fit equation for
the data in Table A4.2.1 is obtained. The Curve Fitting Tool window is as shown in
Figure A4.2.1. This window is invoked using the “cftool” command in Matlab’s
Command Window.
167
Figure A4.2.1 Matlab’s Curve Fitting Tool window.
Data is chosen and put into the Curve Fitting Tool via the Data option. The
Data option window is shown in Figure A4.2.2. It shows the options for choosing
data sets for the x and y-axes. It also shows the preview of the data plot.
168
Figure A4.2.2 The window for inputting data in Curve Fitting Toolbox in Matlab.
The View Data Set window for curve fitting is as shown in Figure A4.2.3. It
shows the data sets for the y and x-axes. As in Figure A4.2.2, it also shows the
preview plot of the data. This window is opened by clicking the View button in the
Data window.
169
Figure A4.2.3 View Data Set window in Matlab.
Fitting is done using the Fitting option. Several fitting types are available in
Matlab. It has been found out that the Power fit fitting type gives the best result
based on the goodness-of-fit criterions. The Fitting window and its results are shown
Figure A4.2.4.
170
Figure A4.2.4 Fitting editor and the result of curve fitting.
Two important parameters from this curve fitting exercise is the R-square
value and the RMSE or the root mean square error value. These parameters indicate
the goodness-of-fit for the curve or equation found from the curve fitting exercise.
The R-square statistics measures how successful the fit is in explaining the
variation of the data. It is the square of the correlation between the response values
and the predicted response values. R-square has the value between 0 and 1. A value
of R-square closer to 1 indicates a good fit. In this case, the value of 0.99496 is the
best from any types of fit, and it is a good value.
The RMSE is the fit standard error or the standard error of regression. A low
value closer to 0 indicates a good fit. The result of 7.6482 for RMSE is rather good
for this fit.
The confidence bound defines the lower and upper values of the fitted
coefficients. The bounds define the level of certainty for the fitted coefficients.
Matlab has a default value of 95 % as this is the value that is often used.
The plot of the results is shown in Figure A4.2.5.
171
Figure A4.2.5 The plots of original data and the curve-fit line.
Using the Analysis option, several values or a range of values for the curvefit equation can be found. This is as shown in Figure A4.2.6.
172
Figure A4.2.6 Analysis from curve fitting.
The most important result from the analysis of the curve fitting exercise is
that the rain rate for 0.01 % of the time. It is shown here that from the radar data, the
rain rate for 0.01 % of the time is 120.907 mm/hr. This is very close to the value
that is obtained from rain gauge measurements and from ITU-R. This value will be
used in the mathematical model that is used to obtain the reduction factor. The
results are summarized below.
General model Power1:
powerfit1(x) = a*xb
Coefficients (with 95% confidence bounds):
a=
4.382 (2.959, 5.806)
b = -0.7204 (-0.777, -0.6637)
rsquare: 0.9950
rmse: 7.6482
Thus, the equation for the best curve-fit line is
y = 4.382 x -0.7204
(A4.2.2)
where y is the rain rate in mm/hr and x is the percentage of occurrence.
This procedure is followed for every curve fitting exercise in this study.
173
Appendix 4.3 Rain Cell Diameter from Radar Data
diameter SDR1 SDR2 SDR3 SDR4 SDR5 SDR6 SDR7 SDR8 SDR9 SDR10
1
3159 10987 14667 15016 8015 16193 12889 11838 5459 4247
2
371 1858 1755 4480 2676 2432 2978 3062 1063 912
3
134 692 548 1826 1020 831 1022 1270 830 810
4
56
305 216 978 603 297 507
730 316 360
5
22
190 171 693 399 206 333
445 193 185
6
11
75
61
259 262
95
141
172 37
58
7
5
47
25
118 126
34
82
96 82
88
8
2
27
39
149 110
43
62
83 31
32
9
1
4
6
15
19
2
5
28 45
44
10
0
3
1
16
12
3
7
25 18
22
11
2
3
4
1
4
1
1
8 13
26
12
2
3
0
7
5
2
3
14 24
14
13
0
0
1
5
6
0
2
6 10
16
14
0
0
0
11
7
1
0
8 6
9
15
0
1
1
20
3
0
3
10 3
6
16
0
1
0
0
1
0
0
1 2
7
17
0
0
0
0
0
0
0
3 5
6
18
0
0
0
0
2
0
0
1 2
8
total 3765 14196 17495 23594 13270 20140 18035 17800 8139 6850
SDR11
5235
1158
892
364
297
71
103
30
37
22
18
17
11
11
5
6
6
1
8284
SDR12 SDR13 SDR14 SDR15 SDR16
5576 5591 3743 3826 7243
1247
916
748
700
1291
1091
834
703
513
797
583
239
294
187
256
288
185
167
95
177
73
39
45
22
49
121
75
57
37
57
42
18
20
11
13
65
34
36
23
18
34
12
14
8
11
23
13
17
11
10
41
16
16
6
6
18
7
16
10
8
37
10
6
4
6
13
2
5
7
1
21
6
7
1
3
8
2
7
2
2
2
1
2
3
2
9283 8000 5903 5466 9950
SDR17 Total percentage
12977 146661 70.507
2957
30604 14.713
998
14811
7.120
454
6745
3.243
230
4276
2.056
115
1585
0.762
56
1209
0.581
26
738
0.355
11
393
0.189
5
213
0.102
2
157
0.075
2
178
0.086
2
118
0.057
0
116
0.056
2
82
0.039
1
57
0.027
0
41
0.020
0
24
0.012
17838 208008 100.000
174
Appendix 4.4 1 to 10-km path attenuations at 7, 10, and 15 GHz
Table A4.4.1a 1-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.0823
0.6310
1.1135
1.9612
3.4549
6.0862
No. of occurences
4743800
818500
1427
727
378
203
125
Total
Percentage
85.2410
14.7070
0.0256
0.0131
0.0068
0.0036
0.0022
5565160
99.9994
att1 vs. percent1
fit 1
0
attenuation (dB)
10
-1
10
b
-2
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 0.02367 (-0.01339, 0.06072)
b = -0.8873 (-1.133, -0.6411)
0.01==>1.40835
-3
10
2
R = 0.9815
-2
10
-1
10
0
10
percentage
Figure A4.4.1a 1-km path attenuation at 7 GHz
1
10
175
Table A4.4.2a 2-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.1365
0.6956
1.1944
1.9442
2.1629
2.5923
3.4175
3.6405
4.0859
4.5684
5.4161
6.1611
6.8135
7.1997
No. of occurences
3824100
1193700
2481
1213
526
94
10
267
47
2
2
1
190
3
2
Percentage
76.1380
23.7660
0.0494
0.0242
0.0105
0.0019
0.0002
0.0053
0.0009
0.0000
0.0000
0.0000
0.0038
0.0001
0.0000
Total
5022638
100.0003
0
10
Att2c vs. percentc
fit 1
attenuation (dB)
-100
10
-200
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 4.9 (3.769, 6.031)
b = -62.32 (-135.4, 10.76)
0.01==>2.62741
-300
10
0
2
R = 0.6576
2
4
6
percentage
Figure A4.4.2a 2-km path attenuation at 7 GHz
8
10
176
Table A4.4.3a 3-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.1822
0.7157
1.2134
1.8766
2.1725
2.6383
3.4139
3.6305
4.1182
4.5942
5.4175
6.1627
6.8052
7.2104
No. of occurences
3131400
1369800
3440
1594
591
232
21
295
109
6
3
2
250
5
5
Total
4507753
Percentage
69.4670
30.3880
0.0763
0.0354
0.0131
0.0051
0.0005
0.0065
0.0024
0.0001
0.0001
0.0000
0.0055
0.0001
0.0001
100.0004
0
10
atten3 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
-300
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.105 (3.941, 6.27)
b = -56.12 (-116.6, 4.334)
0.01==>2.91245
2
R = 0.6849
10
0
5
10
percentage
Figure A4.4.3a 3-km path attenuation at 7 GHz
15
177
Table A4.4.4a 4-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2135
0.7084
1.2174
1.8699
2.1394
2.6496
3.4502
3.6204
4.1653
4.5942
5.4501
6.1606
6.7334
7.2054
No. of occurences
2576600
1436900
3938
1707
598
306
27
300
134
9
3
3
283
7
10
Total
4020825
Percentage
64.0810
35.7370
0.0979
0.0425
0.0149
0.0076
0.0007
0.0075
0.0033
0.0002
0.0001
0.0001
0.0070
0.0002
0.0002
100.0002
0
10
Atten4 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
-300
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.166 (3.992, 6.341)
b = -48.57 (-98.78, 1.627)
0.01==>3.17858
2
R = 0.6922
0
2
4
6
8
10
12
percentage
Figure A4.4.4a 4-km path attenuation at 7 GHz
14
16
18
178
Table A4.4.5a 5-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2196
0.6928
1.2104
1.8797
2.1345
2.6507
3.4590
3.5928
4.1773
4.5943
5.4446
5.5973
6.1623
6.7234
7.2450
No. of occurences
2126700
1427300
4239
1741
577
350
28
276
153
11
3
3
1
286
6
12
Total
3561686
Percentage
59.7110
40.0730
0.1190
0.0489
0.0162
0.0098
0.0008
0.0077
0.0043
0.0003
0.0001
0.0001
0.0000
0.0080
0.0002
0.0003
99.9998
0
10
atten5 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.268 (4.215, 6.321)
b = -45.73 (-88.42, -3.044)
0.01==>3.33466
2
R = 0.7131
-300
10
0
5
10
15
percentage
Figure A4.4.5a 5-km path attenuation at 7 GHz
20
179
Table A4.4.6a 6-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2198
0.6832
1.2108
1.8934
2.1311
2.6638
3.4622
3.6023
4.1794
4.6068
5.4575
5.5999
6.1633
6.6890
7.2470
No. of occurences
1749900
1372700
4438
1734
536
391
27
242
179
11
3
3
1
283
5
13
Percentage
55.8990
43.8490
0.1418
0.0554
0.0171
0.0125
0.0009
0.0077
0.0057
0.0004
0.0001
0.0001
0.0000
0.0090
0.0002
0.0004
Total
3130466
99.9993
0
10
atten6 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
-300
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.293 (4.245, 6.34)
b = -41.38 (-79.1, -3.667)
0.01==>3.49907
2
R = 0.7191
0
5
10
15
percentage
Figure A4.4.6a 6-km path attenuation at 7 GHz
20
180
Table A4.4.7a 7-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2216
0.6780
1.2121
1.8926
2.1226
2.6745
3.4623
3.6081
4.1796
4.6132
5.4599
5.5999
6.1684
6.6869
7.2746
No. of occurences
1434300
1284600
4653
1712
487
439
28
202
202
11
3
3
1
279
6
13
Percentage
52.5960
47.1090
0.1706
0.0628
0.0179
0.0161
0.0010
0.0074
0.0074
0.0004
0.0001
0.0001
0.0000
0.0102
0.0002
0.0005
Total
2726939
99.9998
0
10
atten7 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
-300
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a =5.31 (4.261, 6.359)
b =-37 (-70.42, -3.584)
0.01==>3.66776
2
R = 0.7207
0
5
10
15
percentage
Figure A4.4.7a 7-km path attenuation at 7 GHz
20
181
Table A4.4.8a 8-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2245
0.6711
1.2117
1.8843
2.1224
2.6828
3.4683
3.6157
4.1872
4.6156
5.4743
5.6121
6.1756
6.6941
7.2785
No. of occurences
1163500
1179600
4910
1657
424
490
29
162
223
11
3
3
1
275
6
13
Percentage
49.4820
50.1690
0.2088
0.0705
0.0180
0.0208
0.0012
0.0069
0.0095
0.0005
0.0001
0.0001
0.0000
0.0117
0.0003
0.0006
Total
2351307
100.0000
0
10
atten8 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.307 (4.255, 6.359)
b = -32.29 (-61.67, -2.913)
0.01==>3.84259
2
R = 0.7185
-300
10
0
5
10
15
percentage
Figure A4.4.8a 8-km path attenuation at 7 GHz
20
182
Table A4.4.9a 9-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2281
0.6640
1.2151
1.8795
2.1256
2.6902
3.4694
3.6218
4.1676
4.6079
5.4523
5.5648
6.1813
6.7121
7.2866
No. of occurences
935230
1059900
5133
1602
363
522
30
139
229
9
4
2
2
264
6
13
Percentage
46.6810
52.9040
0.2562
0.0800
0.0181
0.0261
0.0015
0.0069
0.0114
0.0004
0.0002
0.0001
0.0001
0.0132
0.0003
0.0006
Total
2003448
100.0002
0
10
atten9 vs. percent
fit 1
attenuation (dB)
-100
10
-200
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.28 (4.221, 6.338)
b = -27.85 (-53.87, -1.83)
0.01==>3.99616
2
R = 0.7125
-300
10
0
5
10
15
percentage
Figure A4.4.9a 9-km path attenuation at 7 GHz
20
183
Table A4.4.10a 10-km path attenuation at 7 GHz
Attenuation (dB)
0.0000
0.2293
0.6603
1.2160
1.8651
2.1274
2.6917
3.4650
3.6249
4.1899
4.6326
5.4523
5.5755
6.1894
6.7328
7.2952
No. of occurences
738210
936980
5231
1529
318
530
32
123
234
9
4
2
2
248
6
13
Percentage
43.8500
55.6580
0.3107
0.0908
0.0189
0.0315
0.0019
0.0073
0.0139
0.0005
0.0002
0.0001
0.0001
0.0147
0.0004
0.0008
Total
1683471
99.9999
0
10
atten10 vs. percent
fit 1
attenuation (dB)
-100
10
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 5.285 (4.221, 6.349)
b = -24.42 (-47.44, -1.398)
-200
10
0.01==>4.14
2
R = 0.7108
-300
10
0
5
10
15
percentage
Figure A4.4.10a 10-km path attenuation at 7 GHz
20
184
Table A4.4.1b 1-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.0978
0.5797
1.0023
1.7288
2.9880
5.1551
8.8949
15.3480
Total
No. of occurences
4743800
798660
17019
2818
1427
727
378
203
125
Percentage
85.2410
14.3510
0.3058
0.0506
0.0256
0.0131
0.0068
0.0036
0.0022
5565157
99.9998
1
atten1 vs. percent
fit 1
10
attenuation (dB)
0
10
b
-1
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 0.07532 (0.009986, 0.1407)
b = -0.8494 (-0.9867, -0.7121)
-2
0.01==>3.7641
10
10
2
R = 0.9899
-2
10
-1
10
0
10
percentage
Table A4.4.1b 1-km path attenuation at 10 GHz
1
10
185
Table A4.4.2b 2-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.1576
0.6552
1.0963
1.7620
2.1266
2.9263
3.1654
3.7790
4.7168
5.2421
5.8554
6.1574
6.8839
8.1430
8.9178
9.2012
9.8973
10.6240
11.8830
14.0500
15.3840
15.7190
16.3510
17.0770
17.7900
18.3360
Total
No. of occurences
3824100
1155100
33465
5083
2256
201
609
568
60
10
577
20
13
10
4
247
58
5
2
2
1
171
17
2
2
1
2
5022586
Percentage
76.1380
22.9980
0.6663
0.1012
0.0449
0.0040
0.0121
0.0113
0.0012
0.0002
0.0115
0.0004
0.0003
0.0002
0.0001
0.0049
0.0012
0.0001
0.0000
0.0000
0.0000
0.0034
0.0003
0.0000
0.0000
0.0000
0.0000
99.9998
186
atten2 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 1.597 (0.1777, 3.016)
b = -0.212 (-0.3053, -0.1187)
0.01==>4.23897
2
R = 0.6513
-4
10
-2
10
0
percentage 10
Figure A4.4.2b 2-km path attenuation at 10 GHz
187
Table A4.4.3b 3-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2138
0.7081
1.1688
1.7855
2.1921
2.7955
3.1768
3.6812
4.1113
4.7732
5.2670
5.7212
6.2024
6.8719
7.2308
8.1972
8.9350
9.2036
9.8071
10.0110
10.7200
11.9020
12.0770
14.0540
15.4070
15.6640
16.3960
17.1100
17.8090
18.3690
Total
No. of occurences
3131400
1315800
46856
7320
2866
405
576
943
109
24
20
685
67
37
18
4
6
263
117
16
2
6
2
1
2
200
45
5
3
2
5
4507805
Percentage
69.4670
29.1890
1.0394
0.1624
0.0636
0.0090
0.0128
0.0209
0.0024
0.0005
0.0004
0.0152
0.0015
0.0008
0.0004
0.0001
0.0001
0.0058
0.0026
0.0004
0.0000
0.0001
0.0000
0.0000
0.0000
0.0044
0.0010
0.0001
0.0001
0.0000
0.0001
100.0004
188
atten3 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.232 (0.5273, 3.937)
b = -0.1804 (-0.2659, -0.09495)
0.01==>5.12344
2
R = 0.5620
-4
10
-2
10
0
percentage
10
Figure A4.4.3b 3-km path attenuation at 10 GHz
189
Table A4.4.4b 4-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2560
0.7290
1.2047
1.7800
2.2147
2.7699
3.1964
3.6746
4.1515
4.7544
5.2839
5.7127
6.2056
6.8689
7.1616
7.9089
8.3221
8.9294
9.1862
9.7559
10.1180
10.7380
11.8230
12.0770
14.1520
15.4110
15.6900
16.3680
16.6660
17.1290
17.8090
18.3420
18.7400
Total
No. of occurences
2576600
1372500
55652
8950
3140
528
491
1133
124
39
25
716
98
43
18
10
1
3
259
151
16
5
8
3
1
3
214
65
4
2
3
2
8
2
4020817
Percentage
64.0810
34.1350
1.3841
0.2226
0.0781
0.0131
0.0122
0.0282
0.0031
0.0010
0.0006
0.0178
0.0024
0.0011
0.0004
0.0002
0.0000
0.0001
0.0064
0.0038
0.0004
0.0001
0.0002
0.0001
0.0000
0.0001
0.0053
0.0016
0.0001
0.0000
0.0001
0.0000
0.0002
0.0000
99.9996
190
atten4 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.52 (0.7578, 4.281)
b = -0.1723 (-0.2506, -0.094)
0.01==>5.57111
2
R = 0.5590
-4
10
-2
10
0
percentage
10
Figure A4.4.4b 4-km path attenuation at 10 GHz
191
Table A4.4.5b 5-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2772
0.7334
1.2086
1.7694
2.2064
2.7675
3.1932
3.6504
4.1514
4.7520
5.2849
5.6854
6.2301
6.8415
7.1737
7.9101
8.3445
8.9419
9.1612
9.7659
10.0630
10.7770
11.3000
11.8230
12.0780
14.1370
14.5820
15.4150
15.6780
16.3200
16.8350
17.1290
17.8280
18.3600
18.6590
19.0780
Total
No. of occurences
2126700
1355700
61822
10043
3292
608
381
1260
144
46
26
715
112
44
19
12
1
3
230
174
18
4
9
1
3
1
3
1
206
73
7
2
3
1
8
3
1
3561676
Percentage
59.7110
38.0630
1.7357
0.2820
0.0924
0.0171
0.0107
0.0354
0.0040
0.0013
0.0007
0.0201
0.0031
0.0012
0.0005
0.0003
0.0000
0.0001
0.0065
0.0049
0.0005
0.0001
0.0003
0.0000
0.0001
0.0000
0.0001
0.0000
0.0058
0.0020
0.0002
0.0001
0.0001
0.0000
0.0002
0.0001
0.0000
99.9997
192
atten5 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.738 (1.037, 4.439)
b = -0.1646 (-0.2327, -0.09657)
0.01==>5.84443
2
R = 0.5783
-4
10
-2
10
0
percentage
10
Figure A4.4.5b 5-km path attenuation at 10 GHz
193
Table A4.4.6b 6-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2865
0.7303
1.2094
1.7694
2.2035
2.7571
3.2012
3.6605
4.1617
4.7479
5.2920
5.6765
6.2279
6.8271
7.1643
7.9412
8.2957
8.9372
9.1710
9.7061
10.0710
10.7850
11.3010
11.7740
12.0570
14.1750
14.5910
15.4160
15.6700
16.3080
16.8550
17.1440
18.3850
18.6600
19.0780
Total
No. of occurences
1749900
1296300
65715
11001
3348
665
322
1306
161
46
28
695
125
49
18
12
2
2
197
192
23
7
9
1
2
2
3
1
187
86
10
2
3
9
3
1
3130433
Percentage
55.8990
41.4100
2.0992
0.3514
0.1070
0.0212
0.0103
0.0417
0.0051
0.0015
0.0009
0.0222
0.0040
0.0016
0.0006
0.0004
0.0001
0.0001
0.0063
0.0061
0.0007
0.0002
0.0003
0.0000
0.0001
0.0001
0.0001
0.0000
0.0060
0.0027
0.0003
0.0001
0.0001
0.0003
0.0001
0.0000
99.9997
194
atten6 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.76 (1.029, 4.491)
b = -0.1669 (-0.2381, -0.09567)
0.01==>5.95246
2
R = 0.5666
-4
10
-2
10
0
percentage
10
Figure A4.4.6b 6-km path attenuation at 10 GHz
195
Table A4.4.7b 7-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2931
0.7322
1.2133
1.7679
2.1926
2.7385
3.2044
3.6688
4.1652
4.7664
5.2992
5.6692
6.2289
6.8065
7.1495
7.8735
8.3156
8.9434
9.1740
9.6867
10.1320
10.7730
11.3010
11.7740
12.0880
14.1840
14.5910
15.4190
15.6690
16.2940
16.8900
17.1720
18.4430
18.6600
19.0780
Total
No. of occurences
1434300
1203400
69428
12215
3411
731
308
1292
190
49
30
653
155
53
16
15
3
2
167
188
35
12
9
1
2
2
3
1
170
95
14
3
3
9
3
1
2726969
Percentage
52.5960
44.1300
2.5460
0.4479
0.1251
0.0268
0.0113
0.0474
0.0070
0.0018
0.0011
0.0239
0.0057
0.0019
0.0006
0.0006
0.0001
0.0001
0.0061
0.0069
0.0013
0.0004
0.0003
0.0000
0.0001
0.0001
0.0001
0.0000
0.0062
0.0035
0.0005
0.0001
0.0001
0.0003
0.0001
0.0000
99.9996
196
atten7 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.867 (1.138, 4.595)
b = -0.167 (-0.2372, -0.09685)
0.01==>6.18554
2
R = 0.5689
-4
10
-2
10
0
percentage
10
Figure A4.4.7b 7-km path attenuation at 10 GHz
197
Table A4.4.8b 8-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.2996
0.7353
1.2151
1.7604
2.1896
2.7316
3.2118
3.6827
4.1832
4.7924
5.3064
5.6804
6.2429
6.7782
7.1737
7.8393
8.1631
8.9463
9.1717
9.6861
10.1440
10.8080
11.3240
11.7930
12.0990
14.2280
14.6290
15.4220
15.6750
16.2480
16.9010
17.2070
18.4570
18.5960
19.0780
Total
No. of occurences
1163500
1094600
72089
13432
3501
821
289
1247
217
57
33
610
166
62
15
18
2
3
126
196
45
16
9
1
2
2
3
1
148
109
18
3
3
7
5
1
2351357
Percentage
49.4820
46.5520
3.0659
0.5713
0.1489
0.0349
0.0123
0.0530
0.0092
0.0024
0.0014
0.0259
0.0071
0.0026
0.0006
0.0008
0.0001
0.0001
0.0054
0.0083
0.0019
0.0007
0.0004
0.0000
0.0001
0.0001
0.0001
0.0000
0.0063
0.0046
0.0008
0.0001
0.0001
0.0003
0.0002
0.0000
100.0002
198
atten8 vs. percent
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 3.028 (1.266, 4.789)
b = -0.1642 (-0.2334, -0.09494)
0.01==>6.4482
2
R = 0.5635
-4
10
-2
10
0
percentage
10
Figure A4.4.8b 8-km path attenuation at 10 GHz
199
Table A4.4.9b 9-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.3059
0.7382
1.2149
1.7515
2.1902
2.7222
3.2194
3.6837
4.1738
4.8129
5.3117
5.6854
6.2674
6.7076
7.1784
7.7892
8.1675
8.9440
9.1774
9.6900
10.1740
10.8270
11.3250
11.8830
12.0800
14.2610
14.6290
15.4220
15.6730
16.2540
16.8350
17.2720
18.4490
18.6280
19.0870
Total
No. of occurences
935230
974180
72093
14198
3531
919
287
1187
239
66
31
558
185
64
14
20
3
3
95
203
49
19
8
1
1
3
3
1
121
122
19
5
3
7
5
1
2003474
Percentage
46.6810
48.6240
3.5984
0.7087
0.1762
0.0459
0.0143
0.0592
0.0119
0.0033
0.0015
0.0279
0.0092
0.0032
0.0007
0.0010
0.0001
0.0001
0.0047
0.0101
0.0024
0.0009
0.0004
0.0000
0.0000
0.0001
0.0001
0.0000
0.0060
0.0061
0.0009
0.0002
0.0001
0.0003
0.0002
0.0000
100.0000
200
0
10
atten9 vs. percent
fit 1
-100
attenuation (dB)
10
-200
fittedmodel1(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 12.71 (10.79, 14.62)
b = -56.25 (-99.77, -12.74)
0.01==>7.23961
-300
R = 0.5669
10
10
2
0
5
percentage
10
Figure A4.4.9b 9-km path attenuation at 10 GHz
15
201
Table A4.4.10b 10-km path attenuation at 10 GHz
Attenuation (dB)
0.0000
0.3085
0.7372
1.2137
1.7444
2.1851
2.7147
3.2223
3.6803
4.1980
4.8220
5.3119
5.6890
6.2554
6.7096
7.1986
7.7289
8.2178
8.9452
9.1855
9.7021
10.1940
10.8980
11.1870
11.9210
12.1670
14.2610
14.6960
15.4230
15.6860
16.2200
16.6680
17.1300
17.5380
18.4490
18.6760
19.1250
Total
No. of occurences
738210
853550
69554
14467
3498
989
289
1119
250
74
29
504
192
67
17
19
4
3
82
200
53
20
7
2
1
3
3
1
101
123
22
3
4
1
7
5
1
1683474
Percentage
43.8500
50.7020
4.1316
0.8594
0.2078
0.0587
0.0172
0.0665
0.0149
0.0044
0.0017
0.0299
0.0114
0.0040
0.0010
0.0011
0.0002
0.0002
0.0049
0.0119
0.0031
0.0012
0.0004
0.0001
0.0001
0.0002
0.0002
0.0001
0.0060
0.0073
0.0013
0.0002
0.0002
0.0001
0.0004
0.0003
0.0001
99.9999
202
atten10 vs. percent
fit 1
1
attenuation (dB)
10
b
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 3.031 (1.402, 4.661)
b = -0.1737 (-0.2395, -0.1079)
0
10
0.01==>6.74703
2
R = 0.6055
-4
10
-2
10
0
percentage
10
Figure A4.4.10b 10-km path attenuation at 10 GHz
203
Table A4.4.1c 1-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.1277
0.6937
1.3952
2.2743
3.6992
6.0279
9.8071
15.9570
25.9650
Total
No. of occurences
4743800
720910
77745
17019
2818
1427
727
378
203
125
5565152
atten1 vs. percent1
fit 1
1
10
attenuation (dB)
Percentage
85.2410
12.9540
1.3970
0.3058
0.0506
0.0256
0.0131
0.0068
0.0036
0.0022
99.9998
0
10
b
-1
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 0.235 (0.06574, 0.4043)
b = -0.7504 (-0.8666, -0.6342)
0.01==>7.44543
2
R = 0.9890
-2
10
-2
10
-1
10
0
10
percentage
1
10
Figure A4.4.1c 1-km path attenuation at 15 GHz
204
Table A4.4.2c 2-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.1982
0.7266
1.2982
1.6960
2.3348
2.7300
3.1355
3.7581
4.1248
4.5545
5.0945
5.9735
6.1374
6.7216
7.4108
8.3022
9.8339
10.1580
10.6680
11.2020
12.0690
13.5060
15.9360
16.2080
16.8190
17.3520
18.2320
19.6560
21.9850
25.9240
26.2160
26.8260
27.3600
28.2390
29.6640
31.9540
Total
No. of occurences
3824100
1021500
126470
32154
6905
5430
991
160
2000
256
143
58
24
1003
140
49
21
450
107
30
14
19
10
153
129
14
13
5
2
2
111
70
6
2
2
2
3
5022548
Percentage
76.1380
20.3390
2.5180
0.6402
0.1375
0.1081
0.0197
0.0032
0.0398
0.0051
0.0028
0.0012
0.0005
0.0200
0.0028
0.0010
0.0004
0.0090
0.0021
0.0006
0.0003
0.0004
0.0002
0.0030
0.0026
0.0003
0.0003
0.0001
0.0000
0.0000
0.0022
0.0014
0.0001
0.0000
0.0000
0.0000
0.0001
100.0000
205
atten2 vs. percent2
fit 1
1
attenuation (dB)
10
b
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a = 2.04 (0.5344, 3.545)
b = -0.2516 (-0.3336, -0.1695)
0
10
0.01==>6.4967
2
R = 0.6679
-4
10
-2
10
0
percentage
10
Figure A4.4.21c 2-km path attenuation at 15 GHz
206
Table A4.4.3c 3-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.2556
0.7554
1.2448
1.7141
2.3179
2.7383
3.2026
3.8073
4.2044
4.6493
5.2202
5.8675
6.2190
6.7507
7.3211
7.6662
8.3518
8.6942
9.1634
9.8582
10.1800
10.7240
11.2570
11.5950
12.1930
12.7160
13.4510
13.5800
14.2710
14.9020
15.9320
16.2160
16.7320
17.3130
17.7780
18.2800
18.5560
19.8020
20.5180
21.9850
22.1090
22.5110
25.9210
26.2300
26.7300
27.3130
No. of occurences
3131400
1143700
156650
43962
14440
8037
2388
668
2351
607
282
133
39
1172
240
114
40
31
11
5
443
216
73
23
11
39
4
1
16
4
1
118
203
41
28
2
10
2
5
1
1
1
1
92
124
21
10
Percentage
69.4670
25.3720
3.4751
0.9752
0.3203
0.1783
0.0530
0.0148
0.0522
0.0135
0.0063
0.0030
0.0009
0.0260
0.0053
0.0025
0.0009
0.0007
0.0002
0.0001
0.0098
0.0048
0.0016
0.0005
0.0002
0.0009
0.0001
0.0000
0.0004
0.0001
0.0000
0.0026
0.0045
0.0009
0.0006
0.0000
0.0002
0.0000
0.0001
0.0000
0.0000
0.0000
0.0000
0.0020
0.0028
0.0005
0.0002
207
28.3340
28.5640
29.7650
31.9540
32.1160
Total
4
1
3
4
3
4507776
0.0001
0.0000
0.0001
0.0001
0.0001
100.0006
atten3 vs. percent3
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
4.203 (1.898, 6.509)
b = -0.1606 (-0.2208, -0.1005)
0.01==>8.80735
2
R = 0.5157
-4
10
-2
0
10
10
percentage
Figure A4.4.3c 3-km path attenuation at 15 GHz
208
Table A4.4.4c 4-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.2992
0.7596
1.2424
1.7258
2.2887
2.7388
3.2302
3.8058
4.2133
4.6861
5.2578
5.7755
6.2404
6.7347
7.2631
7.6824
8.3353
8.7025
9.1938
9.8719
10.2130
10.7260
11.2790
11.6240
12.2430
12.5870
13.4840
13.6580
14.2950
14.7330
15.9590
16.2240
16.7480
17.2660
17.6600
18.2760
18.6650
19.8090
20.1820
20.5230
21.9850
22.0820
22.5110
25.9560
26.2250
26.6750
No. of occurences
2576600
1175900
173070
52139
20906
9970
3761
1152
2505
814
372
171
53
1195
301
123
64
34
18
9
417
272
95
29
19
46
5
1
17
8
2
97
227
54
37
5
10
4
6
1
2
1
2
1
78
152
33
Percentage
64.0810
29.2460
4.3044
1.2967
0.5199
0.2480
0.0935
0.0287
0.0623
0.0202
0.0093
0.0043
0.0013
0.0297
0.0075
0.0031
0.0016
0.0008
0.0004
0.0002
0.0104
0.0068
0.0024
0.0007
0.0005
0.0011
0.0001
0.0000
0.0004
0.0002
0.0000
0.0024
0.0056
0.0013
0.0009
0.0001
0.0002
0.0001
0.0001
0.0000
0.0000
0.0000
0.0000
0.0000
0.0019
0.0038
0.0008
209
27.2590
27.5430
28.3010
28.7650
29.4250
29.8240
31.9540
32.1130
32.9000
33.0550
Total
18
1
4
1
1
3
3
6
1
2
4020818
0.0004
0.0000
0.0001
0.0000
0.0000
0.0001
0.0001
0.0001
0.0000
0.0000
100.0002
atten4 vs. percent4
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
3.975 (2.011, 5.939)
b = -0.1786 (-0.2324, -0.1249)
0.01==>9.04752
2
R = 0.6012
-4
10
-2
10
0
percentage
10
Figure A4.4.4c 4-km path attenuation at 15 GHz
210
Table A4.4.5c 5-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3210
0.7597
1.2469
1.7297
2.2686
2.7395
3.2315
3.7865
4.2164
4.7129
5.2527
5.7175
6.2475
6.7180
7.2457
7.6962
8.2861
8.6820
9.1896
9.8769
10.1980
10.7320
11.2650
11.6290
12.2510
12.6450
13.2680
13.6740
14.3200
14.7880
15.9620
16.2510
16.7260
17.2310
17.6740
18.2790
18.6510
19.8410
20.1280
20.5370
21.3840
21.9850
22.0820
22.5170
25.9550
26.2360
No. of occurences
2126700
1145000
180270
58188
25928
11522
4841
1593
2511
1027
422
199
54
1152
344
149
82
35
24
12
359
324
105
35
23
44
8
1
18
9
3
66
241
63
38
6
11
5
3
3
3
1
1
2
1
45
175
Percentage
59.7110
32.1460
5.0613
1.6337
0.7280
0.3235
0.1359
0.0447
0.0705
0.0288
0.0118
0.0056
0.0015
0.0323
0.0097
0.0042
0.0023
0.0010
0.0007
0.0003
0.0101
0.0091
0.0029
0.0010
0.0006
0.0012
0.0002
0.0000
0.0005
0.0003
0.0001
0.0019
0.0068
0.0018
0.0011
0.0002
0.0003
0.0001
0.0001
0.0001
0.0001
0.0000
0.0000
0.0001
0.0000
0.0013
0.0049
211
26.6790
27.2770
27.7200
28.2940
29.4310
29.7740
31.9930
32.1940
32.7880
33.0550
33.9160
Total
43
19
2
6
1
4
2
6
2
2
1
3561734
0.0012
0.0005
0.0001
0.0002
0.0000
0.0001
0.0001
0.0002
0.0001
0.0001
0.0000
100.0001
atten5 vs. percent5
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
3.975 (2.061, 5.89)
b = -0.1845 (-0.238, -0.1309)
0.01==>9.297
2
R = 0.6182
-4
10
-2
10
0
percentage
10
Figure A4.4.5c 5-km path attenuation at 15 GHz
212
Table A4.4.6c 6-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3326
0.7616
1.2490
1.7361
2.2573
2.7401
3.2300
3.7715
4.2240
4.7167
5.2435
5.7143
6.2557
6.7269
7.2376
7.6821
8.2615
8.6793
9.2106
9.8862
10.2020
10.7490
11.2300
11.6560
12.2460
12.6690
13.2090
13.7260
14.2630
14.7030
15.9720
16.2540
16.7230
17.2250
17.6530
18.2980
18.7490
19.8420
20.1730
20.5740
21.3900
21.9850
22.2450
22.5220
25.9730
26.2280
No. of occurences
1749900
1080200
180850
61507
29476
12825
5817
2009
2448
1227
456
221
68
1064
390
165
98
43
24
13
301
351
123
40
30
42
11
2
17
6
5
40
236
75
41
12
12
7
3
3
3
1
1
2
1
29
170
Percentage
55.8990
34.5060
5.7770
1.9648
0.9416
0.4097
0.1858
0.0642
0.0782
0.0392
0.0146
0.0071
0.0022
0.0340
0.0125
0.0053
0.0031
0.0014
0.0008
0.0004
0.0096
0.0112
0.0039
0.0013
0.0010
0.0013
0.0004
0.0001
0.0005
0.0002
0.0002
0.0013
0.0075
0.0024
0.0013
0.0004
0.0004
0.0002
0.0001
0.0001
0.0001
0.0000
0.0000
0.0001
0.0000
0.0009
0.0054
213
26.6750
27.2740
27.8070
28.3060
28.5170
29.6980
30.0200
32.2590
32.7910
33.0550
33.9160
Total
56
21
3
7
1
4
1
8
2
2
1
3130471
0.0018
0.0007
0.0001
0.0002
0.0000
0.0001
0.0000
0.0003
0.0001
0.0001
0.0000
100.0000
atten6 vs. percent6
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
3.984 (2.179, 5.788)
b = -0.1885 (-0.2398, -0.1373)
0.01==>9.492
2
R = 0.6425
-4
10
-2
10
0
percentage
10
Figure A4.4.6c 6-km path attenuation at 15 GHz
214
Table A4.4.7c 7-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3400
0.7661
1.2492
1.7390
2.2529
2.7403
3.2351
3.7547
4.2321
4.7115
5.2366
5.7215
6.2723
6.7241
7.2266
7.7021
8.2741
8.6551
9.2110
9.8961
10.2070
10.7610
11.2450
11.6930
12.2590
12.6870
13.2130
13.7570
14.2420
14.6770
15.8960
16.2580
16.7070
17.2280
17.7050
18.3140
18.8240
19.3100
19.8840
20.2170
20.5990
21.3900
21.9850
22.0550
22.5790
25.9700
No. of occurences
1434300
986480
177220
64289
32618
14434
6959
2540
2423
1427
511
252
87
955
429
195
113
53
29
14
240
370
143
45
40
39
16
3
15
7
6
25
208
87
38
22
15
10
2
3
3
3
1
1
1
2
20
Percentage
52.5960
36.1750
6.4987
2.3575
1.1961
0.5293
0.2552
0.0931
0.0889
0.0523
0.0187
0.0092
0.0032
0.0350
0.0157
0.0072
0.0041
0.0019
0.0011
0.0005
0.0088
0.0136
0.0052
0.0017
0.0015
0.0014
0.0006
0.0001
0.0006
0.0003
0.0002
0.0009
0.0076
0.0032
0.0014
0.0008
0.0006
0.0004
0.0001
0.0001
0.0001
0.0001
0.0000
0.0000
0.0000
0.0001
0.0007
215
26.2390
26.7100
27.1990
27.7610
28.3340
28.6770
29.7750
30.0970
32.3270
32.6820
33.0550
33.9160
Total
166
51
31
5
7
3
5
1
9
1
2
1
2726975
0.0061
0.0019
0.0011
0.0002
0.0003
0.0001
0.0002
0.0000
0.0003
0.0000
0.0001
0.0000
99.9993
atten7 vs. percent7
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
4.188 (2.4, 5.976)
b = -0.1871 (-0.2365, -0.1378)
0.01==>9.91478
2
R = 0.6501
-4
10
-2
10
0
percentage
10
Figure A4.4.7c 7-km path attenuation at 15 GHz
216
Table A4.4.8c 8-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3447
0.7700
1.2484
1.7411
2.2473
2.7398
3.2337
3.7480
4.2375
4.7086
5.2276
5.7223
6.2849
6.7221
7.2149
7.7040
8.2392
8.6788
9.2542
9.8832
10.2280
10.7460
11.2270
11.7350
12.3050
12.7350
13.1570
13.7840
14.2190
14.7260
15.8970
16.2700
16.7290
17.2200
17.6780
18.3470
18.7610
19.2940
19.8290
20.1320
20.6010
21.4670
21.9850
22.1790
22.6180
25.9790
No. of occurences
1163500
883020
168460
65524
35256
15923
8079
3162
2453
1578
624
279
119
814
453
235
126
63
40
16
177
386
152
50
47
38
24
5
13
7
9
14
179
90
40
30
18
12
5
2
3
4
1
1
1
2
13
Percentage
49.4820
37.5540
7.1646
2.7867
1.4994
0.6772
0.3436
0.1345
0.1043
0.0671
0.0265
0.0119
0.0051
0.0346
0.0193
0.0100
0.0054
0.0027
0.0017
0.0007
0.0075
0.0164
0.0065
0.0021
0.0020
0.0016
0.0010
0.0002
0.0006
0.0003
0.0004
0.0006
0.0076
0.0038
0.0017
0.0013
0.0008
0.0005
0.0002
0.0001
0.0001
0.0002
0.0000
0.0000
0.0000
0.0001
0.0006
217
26.2480
26.7330
27.2130
27.6910
28.2570
28.7010
29.7610
30.1820
32.3700
32.6250
33.0880
33.9160
Total
152
56
36
10
8
4
4
2
7
3
2
1
2351332
0.0065
0.0024
0.0015
0.0004
0.0003
0.0002
0.0002
0.0001
0.0003
0.0001
0.0001
0.0000
99.9996
atten8 vs. percent8
fit 1
1
attenuation (dB)
10
b
0
10
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
4.337 (2.528, 6.146)
b = -0.1899 (-0.2399, -0.1398)
0.01==>10.3971
2
R = 0.6535
-4
10
-2
10
0
percentage
10
Figure A4.4.8c 8-km path attenuation at 15 GHz
218
Table A4.4.9c 9-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3485
0.7732
1.2508
1.7417
2.2474
2.7393
3.2347
3.7440
4.2366
4.7191
5.2191
5.7266
6.2876
6.7310
7.2277
7.7093
8.2615
8.7040
9.2449
9.8820
10.2460
10.7450
11.2010
11.7530
12.3200
12.7280
13.1230
13.7700
14.2140
14.7620
15.2650
15.9620
16.2690
16.7420
17.1910
17.6730
18.3110
18.7740
19.2470
19.7100
20.0430
20.6100
21.4730
21.9850
No. of occurences
935230
773440
156130
64729
35992
16744
8907
3655
2543
1657
720
308
164
694
470
267
135
71
51
16
136
363
157
69
53
30
33
9
7
12
7
3
9
150
89
48
31
23
13
6
3
2
5
1
1
Percentage
46.6810
38.6050
7.7928
3.2308
1.7965
0.8358
0.4446
0.1824
0.1269
0.0827
0.0359
0.0154
0.0082
0.0346
0.0235
0.0133
0.0067
0.0035
0.0025
0.0008
0.0068
0.0181
0.0078
0.0034
0.0026
0.0015
0.0016
0.0004
0.0003
0.0006
0.0003
0.0001
0.0004
0.0075
0.0044
0.0024
0.0015
0.0011
0.0006
0.0003
0.0001
0.0001
0.0002
0.0000
0.0000
219
22.6200
23.0410
25.9790
26.2470
26.7310
27.2210
27.7280
28.2110
28.7550
29.8590
30.0670
30.8240
32.3450
32.7180
33.2130
33.9500
Total
2
1
11
127
64
42
9
10
5
4
1
1
7
3
2
1
2003473
0.0001
0.0000
0.0005
0.0063
0.0032
0.0021
0.0004
0.0005
0.0002
0.0002
0.0000
0.0000
0.0003
0.0001
0.0001
0.0000
100.0004
atten9 vs. percent9
fit 1
1
attenuation (dB)
10
b
0
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
4.538 (2.769, 6.307)
b = -0.1874 (-0.2344, -0.1405)
10
0.01==>10.7589
2
R = 0.6649
-4
10
-2
10
0
percentage
10
Figure A4.4.9c 9-km path attenuation at 15 GHz
220
Table A4.4.10c 10-km path attenuation at 15 GHz
Attenuation (dB)
0.0000
0.3531
0.7747
1.2546
1.7446
2.2479
2.7388
3.2332
3.7439
4.2351
4.7204
5.2035
5.7344
6.2956
6.7276
7.2137
7.7116
8.2581
8.7183
9.2250
9.8600
10.2450
10.7370
11.2150
11.7480
12.3090
12.6970
13.1740
13.6670
14.2920
14.8090
15.2200
15.9020
16.2760
16.7480
17.1920
17.6920
18.3000
18.6930
19.2370
19.6900
20.2050
20.6210
21.4730
21.5640
22.1090
22.5170
23.2460
No. of occurences
738210
666800
142230
61850
35375
16976
9275
4021
2588
1698
785
330
204
602
464
273
159
71
53
21
103
341
155
81
53
32
35
11
7
12
7
3
8
134
83
53
34
23
16
7
3
2
5
1
1
1
1
2
Percentage
43.8500
39.6090
8.4488
3.6740
2.1013
1.0084
0.5509
0.2389
0.1537
0.1009
0.0466
0.0196
0.0121
0.0358
0.0276
0.0162
0.0094
0.0042
0.0031
0.0012
0.0061
0.0203
0.0092
0.0048
0.0031
0.0019
0.0021
0.0007
0.0004
0.0007
0.0004
0.0002
0.0005
0.0080
0.0049
0.0031
0.0020
0.0014
0.0010
0.0004
0.0002
0.0001
0.0003
0.0001
0.0001
0.0001
0.0001
0.0001
221
25.9800
26.2490
26.7260
27.2330
27.6640
28.1280
28.7690
29.8920
30.1910
31.0250
32.3450
32.6610
33.2880
34.0740
Total
8
106
65
45
10
12
6
2
3
1
7
2
3
1
1683470
0.0005
0.0063
0.0039
0.0027
0.0006
0.0007
0.0004
0.0001
0.0002
0.0001
0.0004
0.0001
0.0002
0.0001
100.0000
atten10 vs. percent10
fit 1
1
attenuation (dB)
10
b
fittedmodel1(x) = a*x
Coefficients (with 95% confidence bounds):
a=
4.829 (3.016, 6.643)
b = -0.1834 (-0.2295, -0.1372)
0.01==>11.2355
2
R = 0.6607
0
10
-4
10
-2
10
0
percentage
10
Figure A4.4.10c 10-km path attenuation at 15 GHz
222
Appendix 4.5 Rec. ITU-R P.838-1
Regression coefficients for estimating specific attenuation
Frequency (GHz)
1
2
4
6
7
8
10
12
15
20
25
30
35
40
45
50
60
70
80
90
100
120
150
200
300
400
k
0.0000352
0.000138
0.000591
0.00155
0.00265
0.00395
0.00887
0.0168
0.0335
0.0691
0.113
0.167
0.233
0.310
0.393
0.479
0.642
0.784
0.906
0.999
1.06
1.13
1.27
1.42
1.35
1.31
α
0.880
0.923
1.075
1.265
1.312
1.310
1.264
1.200
1.128
1.065
1.030
1.000
0.963
0.929
0.897
0.868
0.824
0.793
0.769
0.754
0.744
0.732
0.711
0.690
0.689
0.684