Study of Seasonal Surface Refractivity over North-Central Nigeria

Tropospheric radio wave signals experience loss due to multipath effect, scattering and other forms of attenuation through the atmospheric medium, primarily due to variations in weather conditions with time. The knowledge of surface refractivity profile is important for optimal planning of Very High Frequency/Ultra High Frequency (VHF/UHF) terrestrial radio links in a region. The study of surface refractivity (N s ) over the North-Central Nigeria was carried out using meteorological data from seven locations in North-Central zone of Nigeria. The seasonal variations of Ns were also derived using the monthly summaries of surface data obtained from Nigerian Meteorological Agency (NIMET) over seven stations of Abuja, Lafia, Lokoja, Makurdi, Jos, Minna and Ilorin between 2005 and 2010.The results indicated that the monthly averages of radio refractivity during the rainy season months (April to October) are greater than the N s values during the dry season months (November to March) for all the locations throughout the years of the study. The computed of mean monthly Ns over all the seven stations in the first 1 km above the ground level is 348 N-units, which gives mean refractivity gradient (dN/dh) of -49 N/k, these shows that the region is characterised by low scale super-refraction. The mean k-factor over the entire region in the first 1 km above the ground level is 1.4; the mean Field Strength Variability (FSV) in first 1 km of height in the region was calculated to be 14 dB. The mean Radio Horizon distance within 1 km height for a transmitter height of 100 m over the stations is 42 km. The results provide useful information needed by radio engineers to set up new terrestrial radio propagation links or to improve on the existing ones especially at VHF, UHF in the North-Central region of Nigeria, as recommended by International Telecommunication Union Recommendations (ITU-R P.453, 2013), which observed the need for local reference data on refractivity and refractivity gradients all over the world.


I. INTRODUCTION
adio communications use electromagnetic waves propagation through the earth's atmosphere to send information over long distances without the use of wires [1]. Tropospheric radio signal transmissions at frequencies above 30 MHz are prone to the effect of fluctuations of weather and climate, because of water vapour molecules with their permanent electric dipoles account for the atmosphere having a complex dielectric constant and a complex refractive index [2]. The molecules are largely subjected to varying temporally and spatially, and consequently refract as well as absorb the radio waves; and this leads to variability and attenuation of signals [3]. Radio propagation parameters are dependent on radio refractivity, which in itself is a function of the weather [4]. The effect of meteorological variables of pressure, temperature and relative humidity on radio wave propagation at UHF and microwave frequencies has been analysed from the study of radio refractive index derived from these three parameters [5]. When designing radio communication systems operating in these frequency bands, radio engineers normally use long-term data of atmospheric refractive index and its derivatives, based on statistical analysis in order to be able to predict the systems performance at such frequency bands [6]. An important derivative of the refractive index used in studying the effects of the troposphere on radio propagation is vertical refractivity gradient [7]. The variations in the vertical profile of the refractive index and its gradients are responsible for the change in the trajectory of radio rays in the troposphere [8]. The study of radio refractivity has aroused considerable interest primarily because of its influence on radio wave communication in the lower atmosphere. In particular, the manner in which the refractive index changes with height has much consequence for radio wave propagation at frequencies greater than 30 MHz, although these effects become significant at frequencies greater than about 100 MHz in the lower atmosphere [9]. Hence, the refractive index, 'n' of the troposphere is of major concern in the propagation of radio waves at these frequencies. The value of refractive index n at the earth's surface is slightly greater than unity and gradually decreases towards unity with increase in altitude [10]. At the earth's surface, radio refractive index is usually between 1.00025 and 1.00035 [11]. This study presents an easy method for calculating radio refractivity and enhances understanding of the concept of signal variations between the dry and rainy seasons in the North-central region of Nigeria.

A. Source of Data
The monthly summary of surface Temperature, Pressure and Humidity for the seven stations (Abuja, Lafia, Lokoja, Makurdi, Jos, Minna and Ilorin), were obtained from Nigeria Meteorological Agency (NIMET). NIMET has observatory stations (synoptic stations) across the country (at least one in each of the 36 states and the Federal Capital Territory, Abuja). These stations are called Data Points and recognised by the World Meteorological Organisation (WMO). The observatory stations or data points that are WMO certified in the North Central Region are: Abuja, Minna (Niger State), Ilorin (Kwara State), Lokoja (Kogi State), Lafia (Nasarawa State), Jos (Plateau State) and Makurdi (Benue State). These weather stations are manned by professional weather observers (WMO Certified). The observatories or data Points have all the weather measuring instruments ranging from rain gauge for measuring rain, thermometers for measuring temperature, barometers for measuring atmospheric pressure and hygrometers for measuring relative humidity. NIMET weather data were observed and recorded within some selected times intervals i.e. half hourly, hourly and daily throughout the year. The data from the stations was collected by NIMET throughout the country. The data used in this study were collected from the stations listed above, for a period of six (6) years from 2005 to 2010. Fig. 1 presents the map of the study area.

B. Computation of Radio Refractivity (N)
Radio refractivity (N) is evaluated using the relation defined by [12]: N = (n − 1) × 10 (1) Where 'n' is the refractive index of air For instance, when n = 1.000350, then we have N = 350. N is strictly the refractivity, but sometimes wrongly referred to as refractive index. For frequencies up to about 30 GHz, the radio refractivity of clear air is given by the formula proposed by [13], which is given in equation (2).
Where P is the atmospheric pressure in ( ), e is the water vapour pressure in mb and T is the absolute temperature in Kelvin. Equation (2) may be split into two and rewritten as:  The first and second parts of equation (3) are represent the dry ( ) and wet ( ) components of refractivity, respectively. The dry term contributes about 70 % to the total value of N and the wet term is responsible for a major part of the variation in N at a given location of the atmosphere. At very low temperatures, 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 to decrease but at the same time causes a rapid increase in the saturated value .
. At high temperatures, value of . may become larger than , so that N will vary with relative humidity. When both temperature and relative humidity are high, N becomes very sensitive to small changes in temperature and relative humidity. Consequently, the variability of water vapour content in the atmosphere (and hence the refractivity) in tropical areas is far greater than that of cold climate [12]. The atmospheric radio refractivity is an important factor in the propagation of radio waves at very high frequency (VHF) and higher frequency band, as the path and general characteristics of the signals are very much tied to the refractive conditions of the troposphere [14].
The refractivity, N (which is actually the refractive index in excess of unity in part per million) is as given in (1) to (3).
The vapour pressure, e is estimated by [12].
Where R.H is relative humidity (%) and is the saturated vapour pressure ( ).
is calculated as proposed by [12] : e .

C. Computation of reduced-to-sea-level refractivity (No) in North-Central part of Nigeria and its environs
The null refractivity (No) can be computed using the relation in (6) as proposed by [13]: Where is the average value of atmospheric refractivity extrapolated to sea level, N is the surface refractivity calculated using (3) above, h is the scale height in (km) and hs is the height of the earth's surface above the sea level (km) potential."

D. Computation of Gradient ℎ and k-factor
The Gradient dN dh and k-factor can be computed via (7), as reported by [15]: Where h is the height above the surface, and is taken to be 1 km for surface refractivity calculations. H is the scale height; H is 7 km, as obtained for tropical conditions [16]. However, N is the calculated surface refractivity from (3), but, dN dh is expressed as: Therefore, the equation for obtaining the gradient dN dh parameter is further expressed as: Meanwhile, the k-factor was given by [16]: Where k is the k-factor, a, is the earth radius, and the term dN dh is the gradient given in (9).

E. Field Strength Variation (FSV)
Using (11) as established by [17], the Field Strength Variation is defined as and are the maximum and minimum values of surface refractivity respectively.

F. Radio Horizon Distance ( ) Calculation
The radio horizon distance (d ) can be obtained via (12), as reported by [17]: is the effective earth's radius factor, is the equivalent earth's radius and h is the transmitter height.  Fig. 9 shows the graph of mean monthly Surface Refractivity (Ns) over the stations in the North-Central Nigeria. Fig. 10 shows the graph of Mean variation over the stations between Rainy and Dry season months. Fig. 11 shows the graph of yearly Refractivity variation for the years. Fig. 12 shows the graph of mean reduced-to-sea-level refractivity (No) for the entire North Central Zone. Fig. 13 shows the 2-D Contouring of mean yearly No with elevation for the seven stations. Fig. 14 shows the graph of mean monthly k-factor variations for the seven stations during this period. Fig. 15 shows the graph mean Field Strength Variability (FSV) for the seven stations. Furthermore, Fig. 16 shows the graph of mean yearly field strength variability over the stations. Fig. 17 shows the graph of variation of the Radio Horizon Distance across the seven stations.  2 shows that generally Ns increased steadily from January to May. This is followed by a gradual increase to the month of October, before a steep decrease to the month of December. The least value of 298 N-units is observed in January, while the highest value of 375 N-units occurred in the month of August, which is a typical rainy season month in the Middle Belt region of Nigeria. Thus, Ns is generally higher during the rainy season months of (April to October). This could be due to high air humidity observed in Makurdi during the period. Hence, in this period, Makurdi could have been under the influence of moisture-laden tropical maritime air, resulting from South to North migration of the inter-tropical discontinuity (ITD) with the Sun. In the month of December, Ns dropped because this is the period when the dry and dustladen northeasterly winds become dominant and the dry harmattan sets in, hence the low Ns values observed in January and February. On the other hand, between the months of April and October, the whole city would have been subjected to widespread rainfall, which leads to increase in moisture in the atmosphere, that results to in increase in humidity, hence Ns is increased. The month of January is the driest month, followed by February; while the months of March and April are transition months between dry and wet seasons, hence the observed Ns seasonal profile. This result is in agreement with the result obtained by [18] and [19]. Fig. 3 shows the variation of mean monthly surface refractivity for Abuja which is at an elevation of 0.339 km above mean sea level, during the period of study. The variations of surface refractivity over Abuja for a period of six years have been analysed and presented as follows. From Fig. 3, the months of January and February have low refractivity values ranging from 304 N-units to about 328 N-units. The months of November and December are also characterised by the similar Ns patterns. The factor responsible for this variability is the wet term factor given by (2). Generally, in the dry season, refractivity values range between 305 and 338 N-units. The data for these months reflect the strong influence of the dry continental air mass prevalent during the dry season due to the North-South migration of ITD; hence, pronounced variation is observed in these months. Low humidity and high temperature values combine to make the moisture content low, and as a result refractivity values are reduced.
Comparing the rainy season months from May to October in the same Fig. 3 Fig. 9 the results show that Ns values are generally higher during the rainy season months of April to October. This could be due to high air humidity observed in the zone during the period. Hence, in this period, the zone could have been under the influence of the moisture-laden tropical maritime air, resulting from the South to North migration of the intertropical discontinuity (ITD) with the sun. In the months of November to December, Ns values dropped, because this is the period when the dry and dust-laden north-easterly winds become dominant and the dry harmattan sets in, which accounts for the low Ns values observed in January and February. On the other hand, between the months of April and October, the whole zone would have been subjected to widespread rainfall, which leads to increased moisture in the atmosphere, that results in increased humidity, hence Ns values increased. The month of January is the driest month, followed by February; while the months of March and April are transition months between dry and wet seasons, hence the observed Ns seasonal profile. It can be said from the result in Fig. 9 that all the seven stations are under the same climatic conditions. The VHF/UHF signal propagation can be said to be better in the wet months in the zone because of high Ns values in those periods and less in the dry months due to decrease in Ns values in those months for all period of the study.   10 shows similarities between all wet season months and dry season months across all the seven stations, it is observed that all the stations have similar pattern, which could be due to the facts that all the seven stations have the same climatic conditions. The result agrees with all the standard works on refractivity because all the rainy season months have the highest Ns values and the dry season months have the least Ns values [20]. The increase in the Ns values in wet season and the decrease in the values of Ns in the dry months are due to the N-S migration of the ITD in the zone. Fig. 10 has shown that VHF/UHF signal propagation would be enhanced in wet season months in the zone, since the higher Ns the better the VHF/UHF propagation efficiency, and the wet months have the highest Ns values while least Ns occur in dry season months in all the seven States. Thus, the wet season months have better VHF/UHF signal propagation potential than the dry season months.   From the results obtained the curves are similar to those of surface refractivity except that reduced-to-sea level refractivity has higher values than the Surface Refractivity. The effect of station elevation is also seen between Lokoja and Jos values. Fig. 12 above it is observed that No values are higher at the rainy months than dry months.       [18]. The implication of this result to a radio engineer is that even when Jos has highest elevation over mean sea level, it has the least coverage value 4.17 km, which implies that the engineers have to increase the transmitter antenna's height in the area before achieving the same radio horizon as other states in the zone. From the result, it can be concluded that Lokoja has highest coverage of 4.21 km, which implies that better radio propagation at VHF/UHF bands are expected in the station. These results are in agreement with [21] and [22].

IV. CONCLUSION
Generally, from the results obtained, the Surface Refractivity values in the North-Central region are between 290 to 390 Nunits. Ns values obtained indicates seasonal variation with higher values in the rainy season and lower values in the dry season. The computed mean monthly Ns over all the seven stations in the first 1 km above the ground level is 348N-units, which gives refractivity gradient ℎ of −49 / , these shows that region is averagely characterised by low level Super-refraction. Jos has the highest of (401 − ), while Lokoja has the least value of (361 − ). These results conclude that refractivity varies according to height above the mean sea-level from one station to another. The computed mean monthly over all the stations is 368 − in the first 1 of height. The computed mean k-factor over the entire region in the first 1 is about 1.4. The observed seasonal variations of N cause corresponding field strength variations in the zone, especially at VHF band. From the FSV values obtained, Lokoja and Ilorin have the least values FSV of (10 and 11 dB) while Minna and Abuja have the highest values of (15 and 16 dB) respectively. The mean FSV over the region is 14 dB. The mean Radio Horizon for a transmitter height of 100 m over the stations is 42 . The result implies that the higher the refractivity values, the better would be the radio wave propagation. Thus, radio signals are better received in the wet season months than in dry season months. The results provide useful information needed by radio engineers to set up new terrestrial radio propagation links or to improve on the existing ones in the North-Central region of Nigeria. The results obtained from this study will be particularly useful in any planning of communication links in the North-Central region of Nigeria especially at VHF, UHF and microwave frequencies since several studies have shown that there is a very high correlation between signal strength and surface refractivity. The higher refractivity values observed in the rainy season will lead to less energy loss by the signals at the VHF range and above, thereby improving the signal strength received by the receiver. The signal level will be more stable in the wet season than in the dry season owing to higher vapour content in the atmosphere as shown by low field strength variability observed in the period.