Evaluation of Refractivity Gradient and k-factor within the Lower
Troposphere of Maiduguri and Enugu under Two Climatic Zones in
Nigeria
FASHADE O. O.1,2, AKINWUMI S. A.1*, OMOTOSHO T. V.1, ARIJAJE T. E.1,
AYO-AKANBI O. A.1, OGUNDOLIE O. I.2, OMETAN O. O.3, ADEWUSI O. M.3
1Department of Physics,
Covenant University, Ota,
Km 10, Idiroko Road, Canaan Land, P.M.B 1023, Ota, Ogun State.
NIGERIA
2Department of Space Engineering,
African Regional Centre for Space Science and
Technology Education in English Ile-Ife, Osun State,
NIGERIA
3Department of Physics,
Lagos State University, Ojo,
NIGERIA
*Corresponding Author
Abstract: - Estimation of radio refractivity is important in the planning and design of terrestrial radio
communication links for the availability and accessibility of strong networks and signals. This paper
investigates the refractivity gradient, effective earth radius factor (k), and the geo-climatic factor K in the first
1km of the troposphere of two selected stations (Maiduguri and Enugu) under different climatic zones in
Nigeria. The indirect method of measuring radio refractivity was employed in this study to take measurements
over the two selected stations. Vertical profile values of pressure (hPa), Temperature (°C), and Relative
humidity (%) within the first 1 km were extracted from MERRA MAIMCPASM V5.20 database profile
obtained from a satellite sounding instrument by NASA in the United States. MatLab programming language
was used to evaluate the refractivity gradient, k-factor, and geo-climatic factor using the equations
recommended by ITU. The results showed that Enugu was predominantly sub-refractive due to the tropical
savannah climate while Maiduguri encountered both sub-refractive and normal refractive conditions due to the
hot semi-arid climate, and unstable and extreme weather conditions in the region.
Key-Words: - Refractivity, Meteorology, MERRA, MatLab, Troposphere, Geo-climatic and k-factor.
Received: August 19, 2022. Revised: February 14, 2023. Accepted: March 14, 2023. Published: April 5, 2023.
1 Introduction
The propagation of radio waves through the earth's
atmosphere encounters some path bending due to
diverse spatial distribution of the refractive index of
air, thereby causing severe effects such as multipath
fading, interference, and attenuation due to
diffraction. These effects significantly damage radio
communication, navigation, environmental
monitoring, and disaster forecasting systems, [1]. In
practice, the change of refractive index n is very
low, and can be difficult to have an accurate
measure of its variation, [2]. Nevertheless, this
variation impedes the transmission of radio wave.
For this reason, the refractive index n is increased
and denoted with N, [3], [4]. The anomalous
propagation that occurs during radio waves
propagation is called bending. Bending waves are
surface waves that appear in thin media, the width
of the media is small compared to the wavelength.
The refractive index N helps to characterize the
curving of the electromagnetic waves, but not the
bending phenomena.
The gradient of the radio refractive index, dN/dH is
the index used to characterize the bending of
electromagnetic waves, [5]. As electromagnetic
waves continually bend as they pass through the
atmosphere, the gradient of the radio refractivity
index can be categorised as normal, sub-refraction,
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
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Volume 2, 2023
super-refraction, and trapping/ducting. Figure 1.
Illustrates the propagation paths for different
refractivity conditions.
Fig. 1: Propagation paths for different refractivity
conditions, [6]
1.1 Effective Earth Radius Factor
and Geo-climatic Factor
The effective earth radius factor is derived using
the gradient of the refractive index N as radio waves
rise through the altitude of the troposphere. It is also
used to characterize refractive conditions as normal
refraction or standard atmosphere, sub-refraction,
super-refraction, and trapping/ducting. The
variability of the k-factor is dependent on the value
endorsed by the ITU standard which is 1.33. This
value will either underrate or overrate the k-factor
value of the study locations, [7]. According to the
ITU-R-P-530 recommendation, the geo-climatic
factor is used to determine the worst month outage
probability. The estimation of this factor is based on
the point refractivity gradient, which is a
function of temperature, pressure, humidity, and
vapour pressure which enhances the seasonal
variation of radio refractive gradient, [8], [9], [10].
Many research studies had been carried out in this
field in West Africa, amongst these studies are
found in the journals, [11], [12], [13], [14], [15],
[16].
1.2 Study Area
Nigeria is a country in West Africa located between
the Equator and the Tropic of Cancer. Nigeria lies
amid latitude 4N and 14N and longitude 2E and
15E respectively with a total area of 923,768
square kilometres. The climatic condition differs in
most parts of the country, in the north the climatic
condition is arid and to the south, there is an
equatorial type of climate or tropical in nature. The
weather condition can be generally categorized into
two; In the North, from April to October is the wet
season, and from November to March is the dry
season, while in the South, from March to October
is the wet season and from November to February
dry season. The two selected areas (Enugu and
Maiduguri) for this study are located under two
different climatic zones in the country. Table 1
presents the geographical information of the two
selected stations in Nigeria.
Table 1. The Geographical Information of the Two
Selected Stations in Nigeria
2 Research Methodology
The in-situ method of measuring refractivity was
employed in this study to take measurements over
two selected stations in Nigeria namely: Enugu and
Maiduguri. Vertical profile values of pressure (hPa),
Temperature (), Geopotential height (m), and
Relative humidity () were extracted from the
measurements obtained from the Satellite Sounding
instrument by NASA in the USA via MERRA
MAIMCPASM V5.20 database profile.
A programming language was written using MatLab
to determine the radio refractivity (N) and
refractivity gradient
applying equations (1) and
(2) recommended by [3].
(1)
(2)
The effective earth radius factor (k) for each
selected state was computed on a Microsoft Excel
spreadsheet using the formula in equation (3):
(3)
The geo-climatic factor (K) was determined using
the point refractivity gradient in the lowest
100 m of the atmosphere not exceeded for 1% of the
average year. The was deduced from the
probability distribution frequency curve of an
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
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Volume 2, 2023
average refractive gradient of each of the two
stations over the period of years (2010 - 2014) under
consideration. The point refractivity gradient dN1
values were computed on a Microsoft Excel
spreadsheet to estimate the geo-climatic factor (K)
using equation (4):
(4)
3 Results and Discussion
This section presents the results and discussion of
the estimation and analysis of meteorological
parameters (pressure, temperature, relative
humidity) at an altitude of 1 km of the troposphere
in two selected stations from different climatic
zones in Nigeria.
3.1 Monthly Variations of Radio Refractivity
Gradient
The refractivity gradient is strongly dependent on
the radio refractivity and geopotential height. It
was derived from equation (2). The results obtained
of the mean values of monthly variations of radio
refractivity gradient of the first 1 km for Enugu and
Maiduguri are presented in Table 2 and Table 3. The
result shows that Enugu had positive values both in
the wet season and dry season months and it falls
within the range of 1 N-unit/km and above. The
bending or refractive gradient that occurs within this
range is classified as sub-refractive. On the other
hand, Maiduguri had a high positive value of 54 N-
units/km observed in July (wet season) and negative
values of -3 N-units/km and -4 N-units/km observed
from November to February (dry season). The range
of these negative values is classified as normal
refractive which is within -24 N-units/km to 0 N-
unit/km. This implies that Maiduguri is
predominantly sub-refractive in the wet season and
normal refractive in the dry season. Figure 2 and
Figure 3 show the graphical bar chart of the values
of the refractivity gradient obtained in Table 2 and
Table 3.
Table 2. The mean values of monthly variations of
radio refractivity gradient of the first 1 km for
Enugu
Fig. 2: The mean values of monthly seasonal
variations of radio refractivity gradient of the first
1km for Enugu
3.2 The Result of the Effective Earth Radius
The result of the k-factor was reliant on the type of
season. The mean values of the k-factor during dry
and wet seasons for the two selected stations in
Nigeria from (January 2010 –December 2014) are
presented in Table 4. The value of 1.33
recommended by the ITU will either underrate or
overrate the variability of k-factor values obtained
in the two stations under consideration. The results
showed that Enugu had low values of k-factor
compared to the Northern station, Maiduguri which
had higher values of k-factor due to the extreme
climatic conditions that occur in this region. Figure
4 shows the graphical bar chart representation of the
results obtained in Table 4.
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
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Volume 2, 2023
Table 3. Mean values of monthly seasonal variations
of radio refractivity gradient of the first 1 km for
Maiduguri.
Fig. 3: Mean values of monthly seasonal variations
of radio refractivity gradient of the first 1km for
Maiduguri
Table 4. Mean effective earth radius factor of
monthly variations of radio refractivity gradient of
the first 1km for Enugu and Maiduguri from (2010-
2014).
Fig. 4: Mean effective earth radius factor of monthly
variations of radio refractivity gradient of the first
1km for Enugu and Maiduguri from (2010-2014).
3.3 The Result of the Geo-climatic Factor ()
The geo-climatic factor (K) determines the worst
month outage probability. The higher the values of
the geo-climatic factor, the more the radio wave
signals in these regions fade away. Table 5 presents
the mean point refractivity gradient and geo-
climatic factor (K) for the period of five years (2010
- 2014) in these two selected stations. It was
observed that in Enugu and Maiduguri, the worst
months outage are found in March and June which
had geo-climatic factors K of (4.370E-05 and
3.506E-05) respectively. The geo-climatic factor
signifies the path fade depth and this also implies
that radio wave propagating signal could encounter
ducting condition in these months. The mean
monthly variations of geo-climatic factor (K) of the
first 1km for Enugu and Maiduguri from (2010-
2014) are presented in Figure 5.
-10
0
10
20
30
40
50
60
2010 2011 2012 2013 2014
Mean refractivity gradient (N-
units/km)
Year
MAIDUGURI
JAN FEB MAR APR MAY JUN
JUL AUG SEP OCT NOV DEC
0,00000
0,50000
1,00000
JAN MAR MAY JUL SEP NOV
Mean effective earth
radius factor (k)
Months
ENUGU MAIDUGURI
Month
Average
refractivity
gradient
(2010 -
2014) Enugu
Effective
earth
radius
factor (k)
Enugu
Average
refractivity
gradient
(2010 -
2014)
Maiduguri
Effective
earth
radius
factor (k)
Maiduguri
JAN
53
0.74762
2
0.98742
FEB
49
0.76214
7
0.95732
MAR
49
0.76214
13
0.92353
APR
47
0.76961
19
0.89205
MAY
43
0.78500
31
0.83511
JUN
37
0.80928
34
0.82199
JUL
32
0.83069
37
0.80928
AUG
33
0.82632
40
0.79695
SEP
37
0.80928
38
0.80513
OCT
34
0.82199
36
0.81347
NOV
42
0.78894
8
0.95152
DEC
42
0.78894
13
0.92353
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
4
Volume 2, 2023
Table 5. Mean values of monthly variations of point
refractivity gradient and geo-climatic factor (K) of
the first 1km for Enugu and Maiduguri from (2010-
2014).
Fig. 5: Mean monthly variations of geo-climatic
factor (K) of the first 1km for Enugu and Maiduguri
from (2010-2014).
4 Conclusion
In this study, the evaluation of radio propagation
parameters in the first 1 km of the troposphere has
been examined in two selected stations (Enugu and
Maiduguri) under two climatic regions in Nigeria
from (January 2010 – December 2014). The method
recommended by the International
Telecommunication Union (ITU) was adopted in
this study. Radio refractivity gradient, effective
earth radius (k-factor), point refractivity gradient
and Geoclimatic factor (K) was estimated and
analysed from the measurements of air temperature,
relative humidity, and atmospheric pressure
obtained from MERRA MAIMCPASM V5.20
database software using a satellite sounding
instrument by NASA, USA. In conclusion, Enugu
had positive values of refractivity gradient in both
wet and dry season throughout the period of
consideration which implies that this region was
predominantly sub-refractive, while, Maiduguri had
both positive and negative values in wet and dry
seasons respectively which indicates that this region
was predominantly sub-refractive in the wet season
and normal refractive in the dry season. The values
obtained from the refractive gradient were used to
characterize the bend in the radio wave signals in
the region if it’s either normal refractive, sub-
refractive, super-refractive, or ducting.
The application of the effective earth radius (k-
factor) in the radio link design will help to calculate
the antenna height required to estimate the
diffraction fading or multipath fading, while the
geo-climatic factor (K) will be applicable in the
calculation of fade depth A (dB). Therefore, it is
important to estimate the correct value of the radio
refractivity gradient, k-factor, and geo-climatic
factor in other to ascertain an adequate fade margin
for a reliable radio link performance.
Acknowledgements:
The authors are grateful to the University’s
Research Centre (CUCRID) of Covenant
University, Ota, Nigeria for sponsoring the
publication of this article.
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4,370E-05
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24
5.375E-
05
55
4.370E-05
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
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Volume 2, 2023
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
-Fashade O. O, carried out the data acquisition,
analysis and evaluation.
-Omotosho T. V supervision of research activity and
mentorship.
-Ometan O.O, Ayo-Akanbi O. A and Adewusi O. M
implemented the Algorithm used in the MatLab
programming language.
-Arijaje T. E and Ogundolie O. I was responsible for
the Statistics.
-Akinwumi S. A responsible for preparation of the
work for publication from the original research
group.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
The authors are grateful to the University’s
Research Centre (CUCRID) of Covenant
University, Ota, Nigeria for sponsoring the
publication of this article.
Conflict of Interest
The authors have no conflict of interest to declare
that is relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.1
Fashade O. O., Akinwumi S. A.,
Omotosho T. V., Arijaje T. E.,
Ayo-Akanbi O. A., Ogundolie O. I.,
Ometan O. O., Adewusi O. M.
E-ISSN: 2945-0489
6
Volume 2, 2023
