Spatial and Seasonal Estimation of Tropospheric Radio Refractivity in Nigeria

The spatial and seasonal variation of tropospheric radio refractivity of Nigeria has been studied using meteorological variables (temperature, relative humidity and pressure) retrieved from the archive of the United States’ National Aeronautics for Space Administration (NASA). This work established a seasonal variation. The results also revealed an increase in radio refractivity from minimum of about 270N-units at Abadam to maximum of about 415N-units at Warri. The variation of radio refractivity is synchronous with rainfall in most of the stations especially those in the Guinea Savannah, Tropical Rainforest and Coastal areas where the e ﬀ ects of august break manifest vividly on the curves. Intense refractivity was measured mostly in the tropical rainforest and coastal areas. This could be attributed to the intensity of rain and the length of the wet season in those locations. The Sahel, Sudan and Guinea savannah which experience less rain with short period of wet season recorded reduced refractivity. Just like rainfall, the movement of Inter Tropical Discontinuity (ITD) is also found to be linked to the variation of the radio refractivity. The northward movement of the ITD brings with it elevated refractivity while the southward movement leads to reduced refractivity. This is because the ITD is an element of two high pressure cells which inﬂuences its motion. Majorly, the seasonal variation is found to be the product of climate except in some high ground areas where the topography was found to be majorly responsible.


Introduction
Propagation of signal and data transmission through a certain channel determines the quality of wireless communication system that is why users around the world enjoy the mobility of wireless communication [1]. The transmission channel of radio wave signal is the atmosphere which is largely non-homogenous. This property of the atmosphere give rise to the distortion of the signal as it travel in the medium. This distortion can be in form of reflection, refraction and scattering.
Refraction is the most important effects of the earth's atmosphere on the propagation of radio wave, particularly at frequencies of 30 MHz and above [2]. Because of changes in refractivity, radio waves may bend as they travel through different atmospheric layers. Meteorological parameters, primarily temperature and humidity, which are highly variable depending on geographical location and time of year, determine this variation. The troposphere's radio refractive index is crucial in predicting the scale of performance of terrestrial radio communications. Variations in the tropospheric radio refractive index have a considerable impact on frequencies above 100 MHz in the troposphere. Even at lower frequencies above 30 MHz, this impact can be seen [3].
The temporal and spatial variation of radio refractivity has been observed, this can be season to season, day to night, hour to hour, as well as location to location [4]. The outcomes of random spatial fluctuations in radio refractive index in the troposphere include absorption and scattering of radio signals, amplitude and phase scintillations, and other complex phenomena that can cause transmission losses and interference between channels. Because of the presence of high-intensity tropical rainfall, the influence of interference owing to tropospheric fluctuation of refractivity is significantly more widespread in the tropics than in the temperate environments [5].
The influence of earth's and atmosphere's properties on radio wave propagation in the atmosphere is highly significant [6]. The "curvature of the earth and the condition of the atmosphere" are responsible for the multi-directional refraction of electromagnetic waves. The refractive index of the medium of oscillation of the radio wave determines the clearing of the microwave route.

Data and Methods
Meteorological data comprising of relative humidity (%), temperature ( o C), pressure (hPa) and rainfall (mm) was retrieved from the NASA at 2-meter height for the period of five years (2016-2020). These data is however obtained daily.
The analysis of the surface radio refractivity depends on air temperature, relative humidity and pressure. The propagation of electromagnetic in the air depends largely on the moisture in the atmosphere. The computation of radio refractivity N (N-units) is done as proposed by [7]: where P is atmospheric pressure (hpa), T is absolute temperature (K), and e is the atmospheric water vapour pressure (hpa). The water vapour pressure is calculated as follows [8]: Where H is the relative humidity and e s is the saturated vapor pressure which can be obtained from equation (3).
where H is the relative humidity and t is temperature in Celsius (º C).

Study Area
The study is undertaken from the 61 stations within Nigeria. These stations were sampled from the five geoclimatic in the country using the definition of [9]. These stations are:

Seasonal Variation of Radio Refractivity across Nigeria
This study has observed a seasonal variation of radio refractivity for the area under study as shown from Fig. 2 to Fig. 7. This work reveals a seasonal variation. This is in agreement with the work of [10], [11], [12], [3], and [13]. The results also revealed an increase in radio refractivity from minimum of about 270N-units at Abadam to maximum of about 415N-units at Warri. This is in agreement with [10].
Due to the large number of stations involve in the study we narrowed the discussion of the result to geo-climatic zones of the country. Using the definition of [9] and considering the meteorological factors we have five geo-climatic zones in the country (Sahel, Sudan Savannah, Guinea Savannah, Tropical Rainforest and Coastal).  Fig.3 (a), you will observe that there is sudden increase between March and May, after which a steady increase is observed until a peak in September followed by a steady decease to December. This followed the pattern of the rain in the zone as shown in Fig. 3(b). The maximum refractivity was measured at Birnin-Kebbi while the minimum was measured at Katsina. The result obtained from the analysis revealed that all the maximum values of refractivity during the study period in Sahel were measured in Birnin-Kebbi, while the minimum values were measured in Katsina and Abadam. This clearly validate the fact that the stations covered in this study, Katsina and Abadam are the stations with shortest rainy season. For about half of the year the stations in Sahel are above the Inter Tropical Discontinuity (ITD). This further explains why lower values of refractivity are prevalent in the zone. The rainfall curve in Fig. 3(b) shows a single peak in the month of August while the peak in the seasonal variation of refractivity is in September. This is because refractivity doesn't directly depends on the amount of rainfall but the relative humidity which always high during the rainy season. The average refractivity recorded for this zone is about 331.99N-unit.  season in the zone as depicted in Fig. 5(b). The slight dip observed in August may be attributed to the reflection of the little dry season experience in the coast and the tropical rainforest. The seasonal variation of refractivity over Tropical Rainforest of Nigeria is shown in Fig. 6(a) revealing a sudden increase from January at about 371N-units to a peak of about 403N-units in April from where a steady decrease to August at about 394N-units is observed. A steady increase from a dip in August to October at about 397N-units is recorded until a sharp drop in December at about 381N-units. The mild dip is due to the August break experience in some part of the zone. The higher values of refractivity recorded in the zone during the study period are widely spread across the zone just like the Guinea Savannah. However, the lower values were recorded in the western and eastern 55 flanks high grounds of the zone (Ado-Ekiti and Obudu). Even though these two stations recorded substantial amount of rain during the period but recorded lower refractivity due to their elevated height which affects the station pressure.

Conclusion
The spatial and seasonal variation of tropospheric radio refractivity of Nigeria has been studied from a satellite meteorological parameters (temperature, relative humidity and pressure) sourced from NASA. Just like [10], [11], [12], [3], [13], [15] and [16], this work established a seasonal variation. These researches looked into more than 5 stations each covering most part of Nigeria randomly. The study also revealed an increase in radio refractivity from about 270N-units at Abadam to about 415N-units at Warri. This is in agreement with [10], [3], [13] and [11]. The variation of radio refractivity is synchronous with rainfall in most of the stations especially those in the Guinea Savannah, Tropical Rainforest and Coastal areas where the effects of august break manifest vividly on the curves. Intense refractivity was measured mostly in the tropical rainforest and coastal areas. This could be attributed to the intensity of rain and the length of the wet season in those locations. The Sahel, Sudan savannah which experience less rain with short period of wet season recorded reduced refractivity. The massive injection of the dust plum from the Sahara desert into the atmosphere in the month of February give rise to reduce humidity which consequently affects the refractivity of both Sahel and Sudan zones in the month. When dust is raised, both the dew point temperature and relative humidity drop because the dust dampen the available moisture, given rise to a dry air. The dip observed is largely attributed to the fall in relative humidity in the month. However, agreeing with [14], it is worthy of note that this study found out that large percentage of the values of refractivity can be determined by temperature in the wet season compared to dry season which is largely driven by relative humidity. Just like rainfall, the oscillation of Inter Tropical Discontinuity (ITD) is also found to be linked to the radio refractivity variation. The northward movement of the ITD brings with it elevated refractivity while the southward movement leads to reduced refractivity. This is because the ITD is an element of two high pressure cells which influences its motion.