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STUDY OF THE EFFECT OF ATMOSPHERIC PRESSURE ON RADIO
REFRACTIVITY VARIATION IN TROPICAL REGION USING NIGERIA
AS A CASE STUDY.
BY
ONAOLAPO, OLAYINKA S.
(011911)
BEING A PROJECT REPORT SUBMITTED
TO
THE DEPARTMENT OF ELECTRONIC/ELECTRICAL ENGINEERING
FACULTY OF ENGINEERING AND TECHNOLOGY
LADOKE AKINTOLA UNIVERSITY OF TECHNOLOGY,
OGBOMOSO, OYO STATE, NIGERIA.
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR
THE AWARD OF BACHELOR OF TECHNOLOGY (B.TECH.HONS) IN
ELECTRONIC/ELECTRICAL ENGINEEERING.
NOVEMBER, 2007.
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CERTIFICATION
I certify that this work was carried out by Onaolapo, Olayinka S. of the
department of Electronic and Electrical Engineering, Faculty of Engineering and
Technology, Ladoke Akintola University of Technology, Ogbomosho.
_______________________ ___________
Mrs O. AGUNLEJIKA Date
(supervisor)
_______________________ ___________
Engr. G.O AJENIKOKO Date
(Head of Department)
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ACKNOWLEDGEMENT
My immense appreciation goes to the almighty God, for sparing my life through
ups and downs and for the successful completion of my project work. I acknowledge his
presence in my life and forever thankful for his guidance towards my success in life.
My profound gratitude goes to my supervisor Mrs. Agunlejika O., for her
encouragement and useful suggestions. I am grateful to all those that have assisted me in
the execution of my project; Shola, Yomi, Femi, Deji, Bukola, Mr Godswill, Mr
Adewale, Aunty Amoke and to my fellow course mate.My deep appreciation goes to my rare gem of inestimable value; Mr and Mrs
Onaolapo- my parents for their support, morally and financially. My love goes to all
members of the family for their immense contribution and I pray that we will always be
bonded in unity.
Onaolapo, Olayinka S.
November, 2007.
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TABLE OF CONTENTS
CONTENT PAGE
Title page i
Certification ii
Dedication iii
Acknowledgement iv
Table of content v-vii
List of Tables viii
List of Figures ix
Abstract x
CHAPTER ONE
Introduction 1
1.1 Preamble 1
1.2 Aims and Objectives 4
1.3 Significance of study 4
1.4 Scope of the project 5
1.5 Methodology 6
CHAPTER TWO
Literature Review 8
2.0 Introduction 8
2.1 Refraction 9
2.1.1 Ducting 11
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2.1.2 Factors responsible for ducting 14
2.1.2.1 Evaporation Ducts 14
2.1.2.2 Temperature Inversion 14
2.1.2.3 Subsidence 15
2.2 Atmospheric Boundary Layer 15
2.3 Measurement of Radio Refractivity 16
2.4 Multipath Propagation 17
2.5 Review of work done on Radio refractivity 19
CHAPTER THREE
METHODOLOGY 21
3.1 Data Collection 21
3.2 Method of Analysis 22
3.3 Sample of Analysed Parameters 23
CHAPTER FOUR
RESULTS AND DISCUSSION 26
4.1 Introduction 26
4.2 Estimating the value of Atmospheric Parameter 26
4.3 Effect of Pressure on Surface Refractivity 30
4.4 Seasonal Variation of Surface Refractivity 30
4.5 Regional Variation of Surface Refractivity 32
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS 33
5.1 Suggestion for Future Work 34
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REFERENCE 36
APPENDIX A 37-42
APPENDIX B 43-58
APPENDIX C 59-66
GLOSSARY 67
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LIST OF TABLES
PAGE
TABLE4.1 Table of Refractivity, keeping Temperature, Relative Humidity
constant and varying pressure. 27
TABLE4.2 Table of Refractivity, keeping Temperature, Pressure constant
and varying Relative Humidity.
28
TABLE4.3 Table of Refractivity, keeping Relative Humidity, Pressure constant
and varying Temperature.
29
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LIST OF FIGURES
PAGE
FIGURE 2.1 Four basic category of Refraction. 12
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ABSTRACT
This project work investigated the effect(s) of atmospheric variables on radio
refractivity and its input on radio and radar performance. Atmospheric variables of
pressure, temperature and humidity were obtained from radiosonde stations in three
regions i.e Ikeja, Minna, and Kano.
By using Microsoft Excel software, the statistical analysis of values obtained for
pressure, temperature and relative humidity is carried out. The monthly mean values of
radiosonde data- pressure, temperature and relative humidity- collected from threemeteorological stations in Nigeria were estimated. The surface refractivity was calculated
by using an equation that relates temperature, pressure and water vapour pressure. The
seasonal and regional variation of refractivity and the effect of pressure on these
variations were determined.
It was observed that refractivity is directly proportional to the pressure.
Comparing the value of refractivity at the selected centers it was also observed that
refractivity varies both seasonally and regionally.
This research work can be used as tool in proper planning and design of
telecommunication links.
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CHAPTER ONE
INTRODUCTION
1.1 PREAMBLE
The speed of propagation of an electromagnetic wave may be considered to be
constant and equal to the speed of light in free space, 3 x 10 8 ms-. However, the
troposphere as an inhomogeneous medium with changing refractive index is significantlydifferent from free space; it is sufficiently different to produce observable changes in the
speed and in direction of propagation of radio waves [1] . Therefore, electromagnetic
waves propagating within the troposphere do not travel in straight lines but are generally
refracted.
In a standard atmospheric condition, refractivity decreases with height. There are
two situations, however, that can change this standard condition. The first is an abrupt
decrease of water vapour pressure with height, which occurs mostly in narrow layer over
water surface and results in the so called evaporation duct. The other is an inverse
increase of temperature with height causing surface or elevated duct in various ranges of
heights [3] . Depending on the refractivity profile, various well known and described
effects such as sub-refraction, super-refraction, or ducting can occur causing shortening
or extending radio horizon and possibly resulting in interference effects. When
characterizing the radio propagation environment, it is usual to consider the vertical
refractivity gradient of the air of the first kilometer above ground level to estimate
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propagation effects such as ducting, surface reflection and multi-path on terrestrial line-
of-sight links.
Effects of refraction include the introduction of errors in the radar measurements,
bending of radio waves and others. Some of these effects are as explained below:
(1) Extension of the radio horizon
The quantity of the refractive index n, depends on temperature, pressure and of
water vapour, and decreases with height in the troposphere. Since its height gradient
(dn/dz) is negative, radio waves in the troposphere are bent downwards. The effect of
tropospheric refraction is to extend the distance to the horizon, thus increasing theweather radio coverage. Bending of radio waves in the troposphere is caused by the
variation with altitude of the velocity of propagation [2] .
(2) Angular Error caused by Refraction
Another effect is the introduction of error in the measurement of elevation angle.
Tropospheric refraction is troublesome primarily at low angles of elevation, especially
near the horizon. Refraction causes the radio rays to bend, resulting in an apparent
elevation angle different from the true one. Therefore, it is necessary to make corrections
to the radar data due to atmospheric refraction in order to obtain a better estimate of
elevation angle or range. In general, surface observation of radio refractivity seems to
suffice for overcoming the effects of tropospheric refraction.
(3) Anomalous Propagation of Radio Waves
In the lower troposphere, water vapour differences are most important in
accounting for differences the refractive index, n, but at higher altitudes where water
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vapour pressure are low, changes in the refractive index are mostly a result of changes in
temperature.
The abnormal propagation of electromagnetic waves is called ducting or super-
refraction. A duct is produced when the index of refraction decreases with altitude at
rapid rate. A temperature inversion is very pronounced in order to produce super-
refraction. The duct acts as a guide directing energy to great distance. A super-refracting
duct which lies close to the ground is called a ground - based duct, while one lying above
the surface is called an elevated duct.
There are several meteorological conditions which may lead to the formation of super-refracting ducts, such as:
(i) Nocturnal radiation, which occurs on clear night when the ground is moist, leads to a
temperature inversion at the ground and a sharp decrease in moisture with height. These
conditions frequently produce abnormal propagation of radio waves.
(ii) The movement of warm dry air from land, over cooler bodies of water produces a
temperature inversion. In this way strong ducts and extreme anomalous propagation of
radio waves are produced. In general, low - sited radio transmitters are more susceptible
to super-refraction than are high - sited ones.
The term anomalous propagation includes both super-refraction and sub-refraction. The
Refractive index gradient may bend radar rays upward rather than downward, leading to a
decrease in range as compared with standard conditions. This is called sub-refraction.
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1.2 AIM AND OBJECTIVES
To determine the effect of pressure on the variation of refractivity in tropical region.
To collect data of pressure, relative humidity and temperature from three
meteorological centres Lagos (ikeja) - a coastal area, Minna- a savannah region and
Kano- a sub sahelian region.
To calculate the refractivity from the average values of pressure, relative humidity
and temperature obtained. To carry out the statistical analysis of values gotten above and determine the regional
and seasonal characteristics of radio refractivity.
To determine the effect(s) of pressure on refractivity
1.3 SIGNIFICANCE OF STUDY
As a result of changing refractive index of the medium between the transmitting
and the receiving antenna, microwave signal may be loss. Effects such as signal
variations i.e. slow variations which are due to major changes in refractive index are
weather dependent. They are not strongly dependent on frequency. This study will
provide information that will be of help in the design of communication links. It will also
help in understanding the effect(s) of atmospheric variables on radio refractivity and its
impact on radio and radar performance radio and radar performance.
This work will help in providing reasonable information for design of
communication link in that the result obtained after computing and analyzing the required
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data i.e. pressure, temperature and relative humidity will help determine when ducting,
super-refraction, sub-refraction and multi-path fading will occur. Therefore the result will
aid communication engineer to know the frequency and power at which to transmit
information and also to determine the best region and season that will yield the best result
for location of communication link.
By relating the radiosonde data of temperature, humidity and pressure to
refractivity, it will be seen that variation of temperature, humidity and pressure result to
changes in refractivity. In an atmosphere of constant refractivity, no bending of
electromagnetic wave occurs regardless of the value of refractivity. Therefore the effectsof atmospheric variable on radio performance can be seen as electromagnetic wave bends
with changes in value of atmospheric variable such as temperature, pressure and relative
humidity.
1.4 SCOPE OF THE PROJECT
The radiosonde data of temperature, humidity and air pressure are obtained from
three geographical regions in Nigeria, which are: Lagos (Oshodi) (62"N, 345"E), Minna
(930"N, 615"E) and Kano (122"N, 830"E). The analysis of these data was carried out
for a period of eight years (1998-2005). Although, the initial aim was to get the data for a
period of ten years (1997-2006) which could not be obtained due to logistic problems.
Since Nigeria was used as a case study, the data gotten are only peculiar to that of
a tropical region which means the values gotten will be definitely different from those
gotten from temperate and artic region.
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The values pressure and refractivity obtained are used in analysing the effect of
pressure on the variation of refractivity in tropical region.
1.5 METHODOLOGY
Meteorological factors such as pressure P, temperature T and relative humidity
(Pv) measured directly by means of radiosonde are collected. By using Microsoft Excel
software, the statistical analysis of values obtained for pressure, temperature and relative
humidity is carried out. The sum and mean value of radiosonde data obtained i.e.
pressure, temperature and relative humidity was calculated respectively on monthly basisfor the region of Lagos, Kano and Minna.
The surface refractivity was calculated by using an equation that relates
temperature, pressure and water vapour pressure which will be seen in chapter two. The
graph of refractivity is plotted against each month of the year to determine the variation
of refractivity on each month. The graph of pressure against each month of the year is
also plotted to determine the variation of pressure on each month. By comparing the
refractivity to the pressure for each month of the year, the effect of pressure on
refractivity will be determined. The seasonal variation is determined from the fluctuations
of refractivity with each season of the year. The regional variation will be seen by
comparing and relating the analysis of the three regions. The value of sea level
refractivity No is calculated by:
hbso N N
= exp 1.1
Since for tropical region, the scale height b = 7km (Kolawole & Owolabi, 1982) [4]
Where,
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h = the vertical height in kilometers
N s = the surface refractivity
b = the scale height for the three stations
NO= sea level refractivity
The surface height for the three selected stations are as listed below:
Ikeja = 128.55m
Minna = 259.59m
kano = 475.8m.
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CHAPTER TWO
LITERATURE REVIEW
2.0 INTRODUCTION
All electromagnetic radiation (EM) propagation through the atmosphere is
affected by the atmosphere. EM energy can be reflected, refracted, scattered, and
absorbed by different atmospheric constituents. The extent of these atmospheric effects
depends upon both the frequency and power of the EM source and on the state of the
atmosphere through which the EM energy must propagate.
The refractivity (N) of the neutral atmosphere can be related to pressure and
temperature through the following formula (Bean and Dutton, 1968) [5] :
(2.1)
(2.2)Where n is the refractive index, T is the air temperature (K), P is the atmospheric pressure
(hPa) and P V is the water vapour pressure (hPa).
There are two terms, the 'dry term' which covering dry gases, mainly Nitrogen and
Oxygen and the 'wet term' governed by water vapour. The first part of equation (2.1) is
the dry term and the second part after the addition sign is the wet term.
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Furthermore, Willoughby (1997) expressed equation 2.1 as the dry (N dry) and wet
(N wet) components of refractivity. The first term can be called the N dry which comprises
of pressure and temperature and the second term be called N wet which comprises of water
vapour pressure and square of temperature. He further reiterated that the first term
contributes about 70% to the total value of N and the wet term is responsible for 30%.
Willoughby further reiterated that at low temperature N wet reduces to a very small value
even for saturated air and this makes refractivity N almost independent of relative
humidity. An increase in temperature will force N dry to decrease but, at the same time,
cause a rapid increase in the saturated value N wet-max . At high temperatures Ns wet-max may become greater than N dry so that N will vary with the relative humidity when both
temperature and relative humidity are high; N becomes very sensitive to small changes in
both variables.
2.1 REFRACTION
Refraction is the bending of light rays due to refractive index (density) changes in
the atmosphere. For visible and Infra-red (IR) propagation, refraction can cause image
distortion, image inversion, and path length changes important for laser ranging.
Refractive conditions are characterized by comparison to the refraction expected from a
standard atmosphere. Differences from standard conditions are due to temperature and
water vapour density fluctuations. Large gradients of these parameters near the ocean
surface can seriously affect surface horizontal propagation paths. Propagation over slant
paths is usually not seriously affected by refraction.
The index of refraction of a medium, n is defined by:
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refractivity must also exist. Battan (1973) showed that when the gradient of refractivity
(i.e., dN/dZ) is equal to 157 km -1, a propagating electromagnetic wave will bend with a
curvature exactly equal to that of the Earth. Bending would cause a horizontally
propagating electromagnetic wave to remain constantly parallel to the Earth's surface,
always at the same height. Any value of dN/dZ less than -157 km -1 would cause an
electromagnetic wave to bend with greater curvature than the Earth's surface; therefore, -
157 km -1 is the threshold for "trapping" of an electromagnetic wave.
2.1.1 DUCTING
Trapping, or ducting, occurs when the microwave energy is trapped in layers and
propagates to greater ranges than normal because of the lack of vertical spreading of the
rays. Ducting regions can be elevated or surface based. Electromagnetic wave is affected
by the refractive nature of the atmosphere. Nonstandard refractive conditions lead to
anomalous propagation and can cause microwaves to be refracted less than normal (sub-
refraction), refracted more than normal (super-refraction), or trapped in wave-guide
modes (ducted) as in Fig. 2-1.
Over the oceans, a persistent surface ducting mechanism is the rapid, near-surface
decrease in moisture due to evaporation, which creates evaporation ducts. The relation for
the vertical gradient of refractivity as a function of temperature , pressure , and specific
humidity (q) is given by Equation (2.4).
(2.4)
Where, P is the pressure, q the specific humidity and T is the temperature
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Figure 2.1 Four basic categories of Refraction
It is sometimes convenient to think of the Earth's surface as flat and to represent
the EM wave refraction in this frame of reference. A modified refractivity M has been
developed to take into account the Earth's curvature and to allow for easy identification
of ducting. The relationship of M to N is as follows (Battan, 1973):
M = N + 157Z (Z in km) (2.3)
Where,
Z = height in km
M = modified refractivity
N = refractivity
The radio waves can become trapped between a layer in the troposphere and the
surface or even between layers in the troposphere depending on the refractivity profile.
This is generally called a duct and is a waveguide like mode of propagation. As a result,
energy is constrained into two dimensions as it can spread out horizontally but not
vertically. This means the path loss increases directly with range rather than with range
squared, resulting in much lower path losses and very high signal levels at long ranges.
Ducting is caused by strong low level inversions (temperature increases with height),
ducting can also occur when a strong cap of warm and dry air exists in the lower
troposphere above very moist air. Ducting is more common in the morning hours since
this time of the day experiences the strongest low-level inversions (due to cooling of
earth's surface through long wave radiation emission) but ducting can also occur anytime
a strong cap exists in the lower troposphere.
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When trapped between an elevated layer and the surface in a surface duct,
extended propagation will occur if the reflection from the ground is low loss. The angles
are small and low loss reflections can occur, especially where the roughness of the terrain
is small compared to the wavelength. When trapped between layers within the
troposphere in an elevated duct is formed and the refraction loss depends on the
roughness of the layers. The major cause of ducting is humidity and temperature
inversion.
2.1.2 Factors responsible for ducting
2.1.2.1 Evaporation Ducts
There is usually a region for a few metres above the surface of the sea where the
water vapour pressure is high due to evaporation. This also occurs over large bodies of
water, for example the great lakes [6] . The thickness of the duct varies with temperature of
the location, typically 5m in the North Sea, 10-15m in the Mediterranean and often much
more over warm seas as in the Caribbean and Gulf. Naturally, these ducts have a
significant effect on Shipping and have been extensively researched. It is the reason that
VHF/UHF propagation over sea can extend to great distances causing all sorts of
international frequency co-ordination problems.
2.1.2.2 Temperature Inversions
Usually, temperature falls with height by about 1Kelvin per 100m. On clear nights
the ground cools quickly and this can result in a temperature inversion, where the air
temperature rises with height. If it is dry, the temperature term is dominant and super
refraction and ducting can occur. This is particularly common in desert regions.
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If there is significant water vapour the relative humidity can quickly rise to 100%
and vapour condenses out as fog. This condensation reduces the water vapour density
near the ground leading to cold dry air near the ground, warmer moister air above and
results in sub-refraction. This can lead to multi-path on otherwise apparently perfectly
good line of sight links.
2.1.3.3 Subsidence
This is a mechanism that can lead to elevated ducts and is associated with high
pressure weather systems - anticyclones. Descending cold air forced downwards by the
anticyclone heats up as it is compressed and becomes warmer than the air nearer the
ground leading to an elevated temperature inversion. (Atmospheric pressure always
increases closer to the ground). This all happens around 1-2km above the ground far too
high to cause ducting except for very highly elevated stations as the coupling angle into
the duct is too great for a ground based station. As the anticyclone evolves the air at the
edges subsides and this brings the inversion layer closer to the ground. A similar descending effect happens at night. In general, the inversion layer is lowest close to the
edge of the anticyclone and highest in the middle. Anticyclones and subsequent
inversions often exist over large continents for long periods.
2.2 ATMOSPHERIC BOUNDARY LAYER
Propagating electromagnetic waves, unless in a completely homogeneous
medium, will experience some degree of bending due to changes in the index of
refraction. The Earth's atmosphere is normally a very inhomogeneous fluid. Certain
regions, such as the Atmospheric Boundary Layer (ABL), characteristically have large
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mean gradients in temperature and/or humidity. Rapid vertical changes in both
temperature and humidity create layers that significantly refract propagating
electromagnetic signals.
This phenomenon is readily apparent, for example, in the evaporation duct at the base of
the Marine Atmospheric Boundary Layer (MABL) and in the elevated trapping layer
associated with the inversion layer at the top of the ABL.
The ABL is defined by Stewart (1979) as the portion of the lower atmosphere that
has turbulent flow and is in direct contact with the Earth's surface. The ABL extends
from the surface to a height of a few meters in conditions of strongly stable stratificationand to thousands of meters in highly convective conditions. On the average, the ABL
extends through the lowest 3,300 ft (~1Km) of the atmosphere and contains 10 percent of
the mass of the atmosphere. The boundary layer is very important to the dynamics and
thermodynamics of the atmosphere because it is in this layer that all momentum, water
vapor, and thermal energy exchanges between the atmosphere and the Earth's surface
takes place.
2.3 MEASUREMENT OF RADIO REFRACTIVITY
(a) Direct method : The microwave refractometer is used. It is capable of measuring
rapid fluctuations in refractivity. The refractometer measures the change in the resonant
frequency of a cylindrical cavity with ends open to the atmosphere and compares with the
resonant frequency of a standard cavity sealed from the atmosphere. The refractometer is
usually mounted on an aircraft for obtaining N-height profile; hence it is an expensive
technique [7] .
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(b) Indirect method : refractivity can be computed from measured pressure, temperature
and water vapour pressure. The various methods of indirect method are listed below:
(i) Tethered balloon system can be used for height profile in the first km of the
troposphere. It has poor time resolution because each profile can take up to one hour.
(ii) Meteorological sensors can be installed at intervals on a, tower for measurement of
the three parameters pressure, temperature and relative humidity. It is only applicable to
the lowest 200 m part of the atmosphere.
(iii) Upper air meteorological data measurements using radiosondes are carried out at
some hundreds of stations all over the world, with launches at 0000 hrs GMT and 1200hrs GMT. This system provides a large volume of data for statistical analysis, but the
spatial and temporal resolutions of the data are poor for radio communication
applications.
(c) Sodar : This is an acoustic sounding system, which is very useful for studying
temperature inversions which cause radio ducts.
2.4 Multipath Propagation
Multipath fading occurs primarily at night, but can occur during the day or
whenever the lower atmosphere is thoroughly mixed by rising convection current and
winds. On clear night with little or no wind, sizable irregularities or layer can collect at
random elevations and these irregularities in refraction result in multipath transmission
on path lengths of the order of million wavelength or longer. It tends to build up during
the night with a peak in the morning hours and then disappear as the layer is broken by
convection caused by heat of the early morning sun [7] .
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The presence of distinct propagation paths give rise to variations in the received
signal (amplitude and phase) in accordance with the mutual relationship between the
amplitudes and phases of the separate signal contributions. The main effect is the
generation of fades, which includes variations of the amplitude, the phase and the
polarization of the received signal. multipath fading (MPF) is a principal cause of outage
in medium and high capacity microwave digital r adio systems. The diurnal and seasonal
variations of multipath propagation are closely related to the occurrence of the
meteorological conditions causing multipath propagation.
In cases, where strong surface reflection has been prevented, the fading can be dividedinto 3 types:
(i) Rapid Scintillation - these are usually small amplitude fluctuations, which may not be
significant and they are more noticeable at frequencies above 10 GHz.
(ii) Slow non-selective fading due to single path propagation effects. It occurs during
stratified atmospheric conditions and is less severe than multipath fading.
(iii) Rapid frequency - selective fading due to multipath propagation. It is the most severe
and governs the outage of analogue and digital radio links. Because the fading is
frequency selective, the distortion induced at all amplitude levels in a wideband digital
link can be a major source of outage. Multipath propagation reduces the cross-
polarization isolation in a dual-polarized link.
Conditions for fade types (ii) and (iii) occur during the night and early morning
hours of summer days in the temperate climates. In the tropics (especially at the costal
locations), the fades have a higher incidence of occurrence.
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2.5 Review of work done on Radio refractivity
Various researchers have one way or the other done various work on refractivity which
helps in the determination of information use in he design of communication link. Listed
below are some of the early researchers:
Kolawole and Owolabi (1982) have computed the vales of surface refractivity for
Africa, using meteorological data for 202 stations for 1978 1979. To remove the
dependence on elevation, surface values were reduced to sea level values No. A
refractivity scale height value of H = 7km obtained for tropical conditions by
Kolawole (1980) was adopted. Bean Thayer (1963) showed that the surface radio refractivity could be used to
estimate both radio range errors and elevation angle errors between radio links.
Willoughby (1997) made statistical analysis of regional and seasonal characteristics
of radio refractive index gradients in the first kilometer of a tropical atmosphere over
four meteorological stations in the West African sub-region, namely, Oshodi, a
coastal area, Minna, a savannah area, Kano and Niamey, both sub-sahelian regions.
He utilized data obtained from daily ascents made at noon. Based on these data, daily
values of refractivity gradient, their monthly means, standard deviations and
frequency distributions were computed to ascertain seasonal mean values. He also
analyzed the correlation coefficients between monthly means of refractivity at the
surface level, Ns, and the monthly means of refractivity decrease in the first kilometer
above ground. He also examined the seasonal behaviour of the dry and wet
components of the gradients.
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CHAPTER THREE
METHODOLOGY
3.1 Data Collection
The data needed for this research work are pressure, temperature and relative
humidity. Three regions are selected and they are; Lagos (Oshodi) - a coastal area ,
Minna - a savannah region and Kano- a sub-sahelian region. The daily measurement of
pressure, temperature and relative humidity for the three regions were obtained from the
Nigeria Meteorological Centre in Oshodi (NIMET) which is the headquarter providing
meteorological services in Nigeria. The data gotten were for a period of eight years(1998-2005), though the initial aim was to get the data for a period of ten years (1997-
2006) which could not be obtained due to logistic problems. The parameters gotten were
each converted to the appropriate units for the calculation and analysis involved.
For the pressure which is defined as force per unit area, the unit of the pressure
variable collected is in percentage (%). The temperature, which is the degree of coldness
or hotness of a medium, is measured, in degree Celsius (C). This can be converted to
absolute temperature which is in degree Kelvin. The relationship between the absolute
temperature and the measured one is as follow:
Temperature (K) = Temperature (C) + 273 (3.1)
Relative humidity can be defined as the amount of water content in the atmosphere. The
value of water vapour used in the calculation from obtained from the equation given
below [8] :
Pv = 0.01 x 8 x 5854/T 6 x 10 (20 2050/T) (3.2)
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Its unit is in hecto-pascal (hpa). Where,
Pv = water vapour pressure
T = temperature
3.2 METHOD OF ANALYSIS
The sum and mean values of pressure, temperature and relative humidity for each of the
three radiosonde stations (lagos oshodi , Kano and Minna) are analysed using Microsoft
excel software package. The values of the monthly and yearly surface refractivity was
also derived using the Microsoft excel statistical application. By using equation 2.1.
In Microsoft excel the command line for the following parameters were gotten:
A. Product of A and B (A*B) = PRODUCT (A, B)
B. Sum of A and B (A+B) = SUM (A, B)
C. Power of A and 2 (A) = POWER (A, 2)
D. Power of A and -2 (A (POWER (A,-2 = (
E. Division of A and B (A/B) = A x B 1 = PRODUCT (A, POWER (B, -1))
Therefore, the equation 2.1 can be written as:
N=SUM(PRODUCT(77.6,B4,POWER(B3,1)),PRODUCT(373000,PRODUCT(0.01,B5,
5854,POWER(B3,-6),POWER(10,SUM(20,PRODUCT(-2050,POWER(B3,-
1))))),POWER(B3,-2))). (3.3 )
Where B1-B5 represent the columns and rows on the excel sheet where the values for
pressure, temperature and relative humidity is located.
The graph of the surface refractivity against the corresponding month of the year
was plotted in order to determine the seasonal and the regional variations.
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To derive the effect of pressure on surface refractivity, the graph of surface
refractivity was then plotted against pressure for the whole year using the values obtained
from the three radiosonde stations. From the graph, the seasonal, regional and yearly
variation of surface refractivity is estimated for the three radiosonde stations. To get the
regional variation of refractivity, we compare the analysed value of refractivity for Lagos,
Kano and Minna region. Sea level refractivity value was also obtained from equation
(1.1) which relates surface refractivity to height obtained at the three regions.
In conclusion, the effect of pressure on surface refractivity will be determined by
relating the value of surface refractivity to the monthly mean value of pressure obtainedfor Lagos, Kano and Minna region.
3.3 SAMPLE OF ANALYSED PARAMETERS
By taking Kano region, which is a sub-sahelian region as a case study. The following
values were measured:
For the month of January 2005,
Pressure (P) = 60.3 hpa
Temperature ( C) = 25.5
Applying equation 3.1, temperature in degree celcius was converted to an
absolute temperature (K).
Temperature (K) = 25.5 + 273
T (K) = 298.8 Kelvin
Relative humidity (H in %) is converted to water vapour pressure ( Pv) using the equation
(3.2) :
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These calculations are repeated until monthly values of refractivity for the eight years
considered at the three selected regions had been calculated. Tables for the calculated
value of surface refractivity are presented in the Appendix A.
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TABLE 4:1 Table of refractivity; keeping temperature, relative humidity constant and
varying pressure.
Number Temperature Humidity Pressure Refractivity
1 302 61 6 251.0
2 302 61 12 252.6
3 302 61 18 254.1
4 302 61 24 255.6
5 302 61 30 257.2
6 302 61 36 258.7
7 302 61 42 260.3
8 302 61 48 261.8
9 302 61 54 263.3
10 302 61 60 264.9
11 302 61 66 266.4
12 302 61 72 267.9
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TABLE 4.2 : Table of refractivity, keeping temperature, pressure constant and varying
relative humidity.
Number Temperature Humidity Pressure Refractivity
1 302 7 55 42.76
2 302 14 55 71.39
3 302 2155
100.0
4 302 28 55 128.6
5 302 35 55 157.3
6 302 42 55 185.9
7 302 49 55 214.5
8 302 56 55 243.2
9 302 63 55 271.8
10 302 70 55 300.4
11 302 77 55 329.0
12 302 84 55 357.7
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TABLE 4.3 Table of refractivity; keeping relative humidity, pressure constant and
varying temperature.
Number Temperature Humidity Pressure Refractivity
1 294 61 55 277.8
2 296 61 55 274.1
3 298 61 55 270.5
4 300 61 55 267.0
5 302 61 55 263.6
6 304 61 55 260.2
7 306 61 55 256.9
8 308 61 55 253.7
9 310 61 55 250.5
10 312 61 55 247.4
11 314 61 55 244.4
12 316 61 55 241.4
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4.3 EFFECT OF PRESSURE ON SURFACE REFRACTIVITY
Since pressure increases directly with height, the pressure in Ikeja is the lowest
because the surface height is low. The surface height of Ikeja is 128.55m. This is low
when compared to that of Minna, which is 259.59m and Kano which has the highest
surface level height of 475.8m.
It was observed that, though Ikeja had a very low pressure compared to Kano and
Minna, the effect of change in pressure relatively in the three regions is small. Therefore,
the effect of pressure on surface refractivity is relatively low as shown by table (4.1). The
graph comparing the variation of pressure, temperature and humidity with refractivity areshown in Appendix C.
4.4 SEASONAL VARIATION OF SURFACE REFRACTIVITY
With various season we have in Nigeria such as rainy and harmattan (wet and dry)
season, there is variation in seasonal refractivity in the three regions which is as a result
of difference in climatic conditions. Histograms showing the variation of refractivity with
the month of the year for each of the three stations are as shown in Appendix B.
From the seasonal variation observed in Ikeja region, the value of monthly
refractivity is at peak between the month of April and October which in Nigeria is the
rainy or wet season. After October, there is slight decrease of refractivity from the month
of November to march which is the harmattan or dry season.
The seasonal variation for Kano region which is a sub-sahelian region, the values
of monthly refractivity gradually rise between the month of May to October, which is a
slight difference from what was obtained at Minna which normally starts from April and
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4.5 REGIONAL VARIATION IN SURFACE REFRACTIVITY
By the fact that Ikeja is a coastal region, the water vapour content in the lower
atmosphere is higher. In Ikeja, the change in the refractivity value from one month to the
other is small compared to the kind of variation observed in kano and Minna.
For Minna which is a savannah region, the humidity of the atmosphere is not as
pronounced as that of Ikeja centre but the pressure is very high compared to the obtained
at Ikeja. For the yearly variation of refractivity in Minna, it has similar pattern of graph
for the period of eight years used as a case study (1998 to 2005). The measured value of
pressure for Ikeja is very small compared to Kano and Minna centres.Finally, for Kano region which has the relatively lowest value of refractivity, the
effect of high temperature in Kano is that it reduces the water content of the lower
atmosphere. The reason for higher pressure is due to the relative increase of pressure with
height which is 475.8m (higher compared to the regions).
Generally, sea level refractivity is much higher during the rainy season than in the
dry season. Seasonal variation of the refractivity depends on climatic condition. Western
Nigeria is more humid than northern Nigeria. As it is shown in equation (2.1) it is
obvious that the refractivity is greater in the rainy season than that in other seasons,
particularly in the coastal area.
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CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS
Seasonal and Regional variations of propagation conditions for Nigeria have been
studied using radiosonde data collected between 1998 to 2005 for three regions namely;
Kano, Minna, and Ikeja.Surface refractivity have been estimated and the effect of pressure
on refractivity determined.
Since pressure increases directly with height in the atmosphere, the pressure in
Ikeja is the lowest because the surface height is lowest. The surface height which is
128.55m is lower compared to that of Minna which is 259.59m and Kano which has thehighest surface level height of 475.8m. It was observed that, though Ikeja had a very low
pressure compared to Kano and Minna, the effect of change in atmospheric pressure is
minimal when compared to that of temperature and water vapour pressure.
With various season we have in Nigeria such as rainy and harmattan (wet and dry)
season, there is variation in seasonal refractivity in the three regions which is as a result
of difference in climatic conditions. Variation in season which occurs in the three region
used as case study results in differences in the value of atmospheric parameters which in
the end results in changes in the surface refractivity.
By the fact that the study was carried out for three regions which is Ikeja (coastal
region), Kano (sub-sahelian region), Minna (savanna region); the water content, pressure
and temperature of the various region differs with the atmospheric conditions. Ikeja
region has the highest water vapour content in the atmosphere, which implies greater
refractivity as observed from the result obtained from the study. Kano region has the
highest value of temperature, lowest water vapour content due to the dry atmosphere and
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this has the lowest value of refractivity compared to other station considered. Minna
which is in the savanna region has value of temperature, water vapour pressure and
atmospheric pressure that falls within the range for Ikeja and kano, it is however in a
closer range to that of Kano.
5.1 SUGGESTION FOR FUTURE WORK
(1) Other methods for the measurement of temperature, pressure and humidity profile
can be used other than radiosondes. For example the raman lidar measurement [9] can be
used, though the most commonly used method for the measurement of temperature andhumidity profiles is the use of radiosondes. The main benefit of lidar over radiosondes is
that measurements can be made continuously. Another substantial advantage is that the
direction of the measurements is well known, whereas the path of a radiosonde is affected
by the wind, which often varies with height. Disadvantages of lidar are that it is a more
complex technique than the use of radiosondes, both in its experimental equipment and
the measurement calibration process described above, and it cannot operate through
dense cloud.
(2) Future researchers should use more radiosonde stations in Nigeria for case study,
because refractivity is dependent on variations in weather parameters such as pressure,
temperature and water vapour pressure which changes with climatic conditions. By using
more radiosonde stations the significance of the study which is to determine information
required for design of communication links is achieved.
(3) A programming language that will aid in determining the surface refractivity from
the values of atmospheric measure should be used, which will aid in updating the surface
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refractivity as days, months and years pass-by without necessarily starting the computing
of the atmospheric values all over again.
In conclusion, the aim of the study which is to determine the effect of pressure on
the variation of refractivity in tropical region (Nigeria) is achieved and further studies can
be carried out in other tropical locations in Africa.
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REFERENCES
[1] Bayong Tjasyono HK and Djakawinata S (1999) The Influence of
Meteorological Factors on Tropospheric Refractive Index over Indonesia , from
http://www.google.com , page 1-12, Retrieved June 15, 2007.
[2] Skolnik, M. I. (1962), "Introduction to Radar System", McGraw - Hill, New
York.
[3] Pavel Valtr and Pavel Pechac (2005), Remote sensing of refractivity profile
using angle of arrival spectra, Technicka 2, 166 27 Praha 6, Czech Republic, pp
1-4.[4] Kolawole L.B. and Owonubi J.J (1982), "The surface radio refractivity over
Africa", Nigerian Journal of Science 16, pp 441-454.
[5] Bean B. and E. Dutton (1968): Radio meteorology , Dover Publications, 435 pp.
[6] Propagation of Radio Waves - Editors M.P.M Hall, L.W. Barclay, M.T. Hewitt,
Published by IEE 1996 ISBN 0 85296 819 1.
[7] G.O. Ajayi (1989), "Physics of the tropospheric radio propagation",International
Centre for Theoretical Physics, Trieste, Italy pp 1-28.
[8] CCIR, Conclusions of the Interim Meeting of Study Group 5 - Propagation in
non-ionized media, DOC 5/204-E (July, 1988).
[9] Final Report on Lidar Measurement of Tropospheric Radio Refractivity (June
2002), pp 1-2.
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APPENDIX A
1.0 Table for the calculated values of atmospheric parameters for Ikeja region.
TABLE 1.1 (Ikeja 1998)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 307 307 306 304 303 301 301 301 302 304 304
PRESSURE 5.1 5.9 4.1 4 6.2 7.9 8.1 7.7 7.4 6.3 4.4 4.8
HUMIDITY 49 54 54 62 70 73 76 72 78 76 66 61
CALCULATEDNo 273 319 323 365 391 392 391 370 404 404 362 339
CALCULATEDNs 268 313 317 358 384 385 384 364 397 397 356 333
TABLE 1.2 (Ikeja 1999)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECTEMPERATURE 304 305 305 304 303 302 300 301 301 301 304 304
PRESSURE 4.0 4.1 3.2 4 .6 5.5 6.1 8.2 8.0 6.4 6.4 5.0 4.5
HUMIDITY 66 57 64 69 70 77 83 74 78 77 72 63
CALCULATEDNo 363 322 362 379 383 401 418 381 400 399 395 345
CALCULATEDNs 357 316 355 372 376 395 411 374 393 392 389 339
TABLE 1.3 (Ikeja 2000)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 306 307 305 304 273 301 300 300 303 304 304
PRESSURE 3.8 5.1 3.5 4 .1 5.4 7.1 7.4 8.4 6.7 6.2 4.6 5.2
HUMIDITY 63 39 58 64 70 78 75 80 84 73 69 62
CALCULATEDNo 353 225 343 364 384 177 387 401 423 391 384 345
CALCULATEDNs 347 221 337 357 377 174 380 394 415 385 377 339
TABLE 1.4 (Ikeja 2001)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 306 307 305 303 301 301 300 301 303 304 304PRESSURE 5.5 4.9 5 5.4 6 7.9 8.6 10 8.1 7.5 6.7 5.9
HUMIDITY 65 59 59 69 73 81 79 80 78 73 72 69
CALCULATEDNo 360 342 349 392 399 413 402 397 400 394 396 383
CALCULATEDNs 354 336 343 386 392 406 395 390 393 387 389 376
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TABLE 1.5 (Ikeja 2002)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 306 306 305 304 302 300 300 301 302 304 305
PRESSURE 6.5 5.4 4.7 3 .9 5.9 7.9 8.9 8.7 7.9 6.6 6.3 6.4
HUMIDITY 51 60 62 69 71 78 84 78 77 77 72 57
CALCULATEDNo 286 347 361 389 395 407 426 395 398 405 398 323
CALCULATEDNs 281 341 355 382 388 400 419 388 391 398 391 318
TABLE 1.6 (Ikeja 2003)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 306 306 304 304 301 301 301 302 303 304 305
PRESSURE 6.2 4.9 4.7 5 .2 6.1 7.2 8.9 8.7 7.9 5.7 4.9 5.4
HUMIDITY 68 66 63 68 70 80 74 72 77 74 71 59CALCULATEDNo 374 380 364 381 390 414 383 375 403 402 397 337
CALCULATEDNs 367 373 358 374 383 407 376 369 396 395 390 331
TABLE 1.7 (Ikeja 2004)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 305 305 306 304 302 302 301 300 301 303 304 305
PRESSURE 4.6 5.4 4.7 5 .4 6.8 8.9 8.6 8.4 7.8 7.0 6.0 5.3
HUMIDITY 62 60 60 73 79 77 76 77 79 77 71 67
CALCULATEDNo 349 340 346 402 419 404 390 386 407 416 392 378
CALCULATEDNs 343 334 340 395 412 397 383 379 400 409 385 372
TABLE 1.8 (Ikeja 2005)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 303 306 305 303 301 300 301 301 303 304 305
PRESSURE 6.0 4.2 5.2 5 .1 6.5 7.6 9.2 8.9 8.2 7.2 5.5 4.6
HUMIDITY 49 66 65 69 77 82 81 73 80 76 72 68
CALCULATEDNo 275 359 374 393 414 425 409 373 1 405 401 382
CALCULATEDNs 270 353 368 387 407 417 402 366 405 398 394 375
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2.0 Table for the calculated values of atmospheric parameters for Minna region.
TABLE 2.1 (Minna 1998)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 305 310 309 308 305 303 301 300 301 304 308 307
PRESSURE 80.4 80.2 78.8 77.9 79.8 81.4 81.3 81.0 80.9 81.1 78.9 79.8
HUMIDITY 27 21 20 17 64 69 77 79 74 65 33 29
CALCULATEDNo 177 156 148 127 387 398 421 425 412 384 223 195
CALCULATEDNs 171 150 143 122 373 384 406 410 398 370 216 188
TABLE 2.2 (Minna 1999)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 306 307 308 308 305 303 301 300 301 303 307 307
PRESSURE 79.1 78.5 76.9 78.4 79.8 80.5 81.5 81.6 80.5 80.4 79.2 79.4
HUMIDITY 25 50 44 42 58 66 75 79 75 66 36 30
CALCULATEDNo 169 326 294 278 353 380 409 422 412 383 239 200
CALCULATEDNs 163 315 283 268 341 367 395 407 398 370 231 193
TABLE 2.3 (Minna 2000)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 306 305 308 308 306 302 301 300 301 303 307 306
PRESSURE 78.5 80.4 77.9 78.0 79.3 81.0 81.1 81.9 80.5 80.5 78.8 80.1
HUMIDITY 50 22 28 50 57 71 76 79 76 65 33 33
CALCULATEDNo 318 149 195 328 355 398 413 424 421 379 221 217
CALCULATEDNs 307 144 188 317 342 384 399 409 407 366 214 209
TABLE 2.4 (Minna 2001)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 306 307 309 307 305 302 300 300 301 305 308 308
PRESSURE 80.2 79.3 78.4 78.5 79.8 81.4 81.6 82.4 81.0 80.3 79.7 79.3
HUMIDITY 24 23 39 57 61 70 76 79 73 52 32 37CALCULATEDNo 162 159 269 362 370 395 412 423 400 319 218 248
CALCULATEDNs 156 154 260 350 358 381 397 408 386 308 210 239
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TABLE 2.5 (Minna 2002)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 304 308 309 306 306 303 301 301 301 303 273 306
PRESSURE 80.5 79 78 77 79 81 82 82 81 80.1 80 81
HUMIDITY 20 23 37 55 64 66 76 76 72 65 31 26
CALCULATEDNo 135 162 255 348 402 383 417 415 401 375 94.3 175
CALCULATEDNs 130 157 246 336 388 370 402 400 387 362 91 169
TABLE 2.6 (Minna 2003)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 306 309 310 307 306 302 301 300 301 304 307 306
PRESSURE 80.3 79.0 78.5 78.7 79.4 80.7 81.8 81.5 81.2 79.3 78.7 79.5
HUMIDITY 32 32 31 49 54 71 75 78 73 66 37 23
CALCULATEDNo 212 222 220 319 341 401 411 423 404 392 244 157
CALCULATEDNs 204 214 212 308 329 387 397 408 390 378 236 151
TABLE 2.7 (Minna 2004)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 306 308 309 307 304 302 301 300 302 304 306 307
PRESSURE 78.8 79.4 78.5 78.3 80.0 82.1 81.3 82.1 80.8 80.0 79.0 78.6
HUMIDITY 24 21 26 54 65 91 71 77 71 65 45 24
CALCULATEDNo 163 149 186 350 385 505 394 412 398 383 285 166
CALCULATEDNs 157 144 179 338 372 488 381 397 384 369 276 160
TABLE 2.8 (Minna 2005)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 305 309 310 308 305 302 300 300 302 303 307 307
PRESSURE 79.9 77.3 78.1 78.2 79.6 80.7 82.0 81.6 81.2 80.3 78.7 77.9
HUMIDITY 20 31 36 46 61 70 76 74 71 64 33 26
CALCULATEDNo 135 217 252 305 369 398 412 401 403 372 221 176
CALCULATEDNs 131 209 243 294 356 384 397 387 389 359 213 170
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3.0 Table for the calculated values of atmospheric parameters for Kano region.
TABLE 3.1 (Kano 1998)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 300 304 305 311 310 305 302 301 303 306 306 301
PRESSURE 60.3 60.3 59 56 56.7 59 58.4 58 58.1 58 58 59
HUMIDITY 25 17 31 15 39 55 68 72 67 42 24 19
CALCULATEDNo 147 116 199 119 275 345 396 408 393 273 160 119
CALCULATEDNs 137 109 186 111 257 323 370 381 367 255 150 111
TABLE 3.2 (Kano 1999)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 301 304 310 310 309 308 301 301 303 305 306 300
PRESSURE 59 57.6 55 56 56.8 57 58.5 59 58 58 58 58
HUMIDITY 18 17 13 17 31 40 70 71 65 41 17 60
CALCULATEDNo 114 116 101 130 221 269 397 397 384 261 119 333
CALCULATEDNs 106 108 95 121 206 251 370 371 358 244 112 311
TABLE 3.3 (Kano 2000)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 302 299 306 312 310 305 302 302 304 306 306 301
PRESSURE 57.9 60.7 57 54 55.4 57 57.3 58 57.2 58 57 60HUMIDITY 17 15 13 17 30 54 64 68 61.3 39 20 20
CALCULATEDNo 109 93.7 94 133 215 336 372 389 370 252 136 124
CALCULATEDNs 102 87.5 88 124 201 314 348 364 345 236 127 115
TABLE 3.4 (Kano 2001)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 300 301 308 308 308 304 302 301 303 306 305 302
PRESSURE 60.0 59.0 57.1 55.4 56.3 57.7 58.0 59.1 57.9 58.3 58.7 58.9
HUMIDITY 33 19 10 25 43 58 65 71 65 28 15 18CALCULATEDNo 189 118 80 174 288 352 379 402 383 186 105 116
CALCULATEDNs 177 110 74 162 269 329 354 376 358 174 98 108
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TABLE 3.5 (Kano 2002)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 299 302 308 311 311 307 304 302 303 304 305 302
PRESSURE 61.1 59.4 57.1 54.4 56.1 57.7 58.7 58.7 58.2 58.0 58.9 60.3
HUMIDITY 17 15 15 24 27 45 59 67 62 43 19 17
CALCULATEDNo 103 98.5 111 178 201 294 355 387 370 268 128 109
CALCULATEDNs 96.2 92 104 166 187 275 332 361 346 250 120 102
TABLE 3.6 (Kano 2003)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 301 304 306 311 310 304 302 302 303 307 306 300
PRESSURE 60.0 58.6 58.3 56.1 56.9 58.2 59.0 58.9 58.7 57.4 58.1 59.8
HUMIDITY 19 13 31 22 27 59 66 69 63 39 24 25CALCULATEDNo 119 92.3 207 165 195 356 382 397 375 260 161 149
CALCULATEDNs 111 86.3 193 154 183 332 357 371 351 242 150 139
TABLE 3.7 (Kano 2004)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 301 302 305 311 308 305 302 302 304 307 305 303
PRESSURE 58.9 59.9 58.2 56.0 56.9 58.6 58.6 58.9 58.0 57.8 58.1 58.4
HUMIDITY 14 13 11 24 44 54 65 67 61 27 23 26
CALCULATEDNo 91.4 87.7 82 178 298 334 376 385 371 186 154 162
CALCULATEDNs 85.4 81.9 77 167 278 312 351 360 347 174 144 151
TABLE 3.8 (Kano 2005)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
TEMPERATURE 299 307 309 311 308 305 302 301 304 305 305 303
PRESSURE 60.3 57.2 57.4 56.1 57.3 58.0 59.1 58.7 58.5 58.2 58.2 57.9
HUMIDITY 18 13 11 20 35 54 67 70 60 41 17 17
CALCULATEDNo 108 96.4 88 151 241 335 388 395 368 261 116 111
CALCULATEDNs 101 90.1 82 141 225 313 362 369 344 244 109 104
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APPENDIX B
1.0 Chart of surface refractivity against month of the year for Ikeja region.
FIGURE 1.1.1
FIGURE 1.1.2
FIGURE 1.1.3
IKEJA (2005)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
IKEJA (2003)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
s u r f a c e r e
f r a c
t i v
i t y
IKEJA (2004)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
IKEJA (2004)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
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FIGURE 1.1.4
FIGURE 1.1.5
FIGURE 1.1.6
IKEJA (2002)
050
100150200250300350400450
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
IKEJA (2001)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
IKEJA (2000)
050
100150
200250300350400450
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Month of the year
S u r f a c e r e
f r a c
t i v
i t y
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FIGURE 1.2.2
FIGURE 1.2.3
FIGURE 1.2.4
IKEJA (2004)
0.0
2.0
4.0
6.0
8.0
10.0
JA N FEB MA R APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
IKEJA (2002)
0.0
2.0
4.0
6.0
8.0
10.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
IKEJA (2003)
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
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FIGURE 1.2.5
FIGURE 1.2.6
FIGURE 1.2.7
IKEJA (2001)
0
2
4
6
8
10
12
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
p r e s s u r e
IKEJA (2000)
0.0
2.0
4.0
6.0
8.0
10.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
IKEJA (1999)
0.01.02.03.04.05.06.07.08.09.0
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
p r e s s u r e
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FIGURE 1.2.8
2.1 Chart of surface refractivity against month of the year for Minna region.
FIGURE 2.1.1
FIGURE 2.1.2
IKEJA (1998)
0
2
4
6
8
10
JAN FEB MAR APR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
p r e s s
u r e
MINNA (1998)
0
100
200
300
400
500
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
r e f r a c t i v
i t y
MINNA (1999)
74.0
76.0
78.0
80.0
82.0
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
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FIGURE 2.1.3
FIGURE 2.1.4
FIGURE 2.1.5
MINNA (2000)
75.076.077.078.079.080.0
81.082.083.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
MINNA (2001)
76.0
77.078.079.0
80.081.082.0
83.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
MINNA (2002)
74
76
78
80
82
84
JAN FEB MAR A PR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
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FIGURE 2.1.6
FIGURE 2.1.7
FIGURE 2.1.8
MINNA (2003)
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r
f a c e r e
f r a c
t i v
i t y
MINNA (2004)
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DECmonth of the year
s u r f a c e r e
f r a c
t i v
i t y
MINNA (2005)
74.075.076.077.078.0
79.080.081.082.083.0
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
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2.2 Chart of pressure against month of the year for Minna region.
FIGURE 2.2.1
FIGURE 2.2.2
FIGURE 2.2.3
MINNA (1998)
76.0
77.0
78.0
79.0
80.0
81.0
82.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
MINNA (1999)
74.075.076.077.078.079.080.081.082.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
MINNA (2000)
74.0
76.078.080.082.084.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
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FIGURE 2.2.4
FIGURE 2.2.5
FIGURE 2.2.6
MINNA (2001)
76.0
77.0
78.079.0
80.0
81.0
82.0
83.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
MINNA (2002)
757677787980818283
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
MINNA (2003)
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
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FIGURE 2.2.7
FIGURE 2.2.8
3.1 Chart of surface refractivity against month of the year for Kano region.
FIGURE 3.1.1
MINNA (2004)
76.0
77.078.079.080.081.082.083.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
MINNA (2005)
74.0
76.0
78.0
80.0
82.0
84.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (1998)
050
100150200250300350400450
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
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FIGURE 3.1.2
FIGURE 3.1.3
FIGURE 3.1.4
KANO (1999)
050
100150
200250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e
r e f r a c
t i v
i t y
KANO (2000)
050
100150200250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
KANO (2001)
050
100
150200250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r
f a c e r e
f r a c
t i v
i t y
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FIGURE 3.1.5
FIGURE 3.1.6
FIGURE 3.1.7
KANO (2002)
050
100150200250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r f a c e r e
f r a c
t i v
i t y
KANO (2003)
050
100150200250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (2004)
050
100
150200
250300350400
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
s u r
f a c e r e
f r a c
t i v
i t y
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FIGURE 3.2.3
FIGURE 3.2.4
FIGURE 3.2.5
KANO (2000)
5052
5456
5860
62
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (2001)
53.054.055.056.057.058.059.060.061.0
JA N FEB MA R A PR MAY JUN JUL A UG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (2002)
50.0
52.0
54.0
56.0
58.0
60.0
62.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
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FIGURE 3.2.6
FIGURE 3.2.7
FIGURE 3.2.8
KANO (2003)
54.055.056.057.058.0
59.0
60.061.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (2004)
54.055.056.057.058.059.060.061.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
KANO (2005)
54.0
55.056.0
57.0
58.0
59.0
60.0
61.0
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
month of the year
p r e s s u r e
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APPENDIX C Graph showing variation of surface refractivity with temperature, pressure and
humidity in Ikeja.
Figure 1.1
Figure 1.2
Figure 1.3
IKEJA (1998)
050
100150200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
Temperature
Pressure
Humidity
Surface refractivity
IKEJA (2000)
050
100150200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface r efractivity
IKEJA (1999)
050
100150200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
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Figure 1.4
Figure 1.5
Figure 1.6
IKEJA (2001)
050
100150200250
300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
Temperature
PressureHumidity
Surface Refractivity
IKEJA (2002)
0
50
100
150
200
250
300
350
400
450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface r efractivity
0
50
100150
200
250
300
350
400
450
0.0 5.0 10.0 15.0
temperature
pressure
humidity
surface refractivity
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Figure 1.7
Figure 1.8
2.0 Graph showing variation of surface refractivity with temperature, pressure
and humidity in Minna.
Figure 2.1
IKEJA (2004)
050
100150
200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
IKEJA (2005)
050
100150200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
MINNA (1998)
050
100150200250300350400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
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Figure 2.2
Figure 2.3
Figure 2.4
MINNA (1999)
0
50
100
150
200
250
300
350
400
450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
MINNA (2000)
050
100150200
250300350
400450
0.0 5.0 10.0 15.0
temperature
pressure
humidity
surface refractivity
MINNA (2001)
050
100150
200
250300350
400450
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface refractivity
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Figure 3.3
Figure 3.4
Figure 3.5
KANO (2000)
0
50100
150
200250
300
350
400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface r efractivity
KANO (2001)
0
50
100
150
200
250
300
350400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface r efractivity
KANO (2002)
050
100
150
200
250
300
350
400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humidity
surface r efractivity
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Figure 3.6
Figure 3.7
Figure 3.8
KANO (2003)
0
50
100
150
200
250
300
350
400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperaturepressure
humidity
surface r efractivity
KANO (2004)
0
50
100
150
200
250
300
350
400
0.0 5.0 10.0 15.0
temperature
pressure
humidity
surface refractivity
KANO (2005)
0
50
100
150
200
250
300
350
400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
temperature
pressure
humiditysurface r efractivity
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GLOSSARY
A. Ducting: is the two boundary surface between layers of air or a short leaky
waveguides which guided the electromagnetic wave between its walls.
B. Multi-path: is the collection of sizable irregularies or layers of random
elevations. It occurs mostly on clear nights with little or no wind.
C. Troposphere: is defined as the lower part of the atmosphere in which
temperature decreases with altitude. It extends from the earths surface up to a
distance of the order of 10km.D. Radiosonde: is the meteorological station where data for atmospheric parameters
are detected, measured and analysed.
E. Surface-Refraction: occurs when a ray of electromagnetic wave is bent away
from the normal when it enters a less dense medium and that the deviation from
the normal increases as the angle of incidence increases.
F. Sub-refraction: this occurs when ray of electromagnetic wave is bent towards the
normal.
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