Temporal Variations of Refractivity and Field Strength at some Locations in Nigeria Modupe E. Sanyaolu1 , Johnson O. Afape1 , Olufemi O. Sanyaolu2 , and Alexandar A. Willoughby1 © The Author(s) 2025 I. Adimula et al. (eds.), Proceedings of the 8th URSI-NG Annual Conference (URSI-NG 2024), Advances in Physics Research 12, https://doi.org/10.2991/978-94-6463-644-4_11 1Department of Physical Sciences, Redeemer’s University, Ede, Osun State, Nigeria 2Department of Mechanical Engineering, Redeemer’s University, Ede, Osun State, Nigeria sanyaolum@run.edu.ng Abstract. Radio field strength is often degraded due to surface refractivity on communication links. Results from the computation of surface refractivity presented in this study are based on the collection of data of relative humidity, temperature, and pressure across three locations in Nigeria, namely, Ikeja (6,6018°N, 3.3515°E), Calabar (4.9757°N, 8.3417°E), and Kano (12.002°N, 8.5920°E). ERA5 (Euro- pean Centre for Medium-Range Weather Forecasts) provided the two years (2019 and 2020) archived data used. In addition to having higher values in coastal locations than in inland regions, surface refrac- tivity (Ns) values were also found to be low in the dry season and high in the rainy season. Ikeja, Calabar, and Kano had average Ns values of 413.308715, 410.81065, and 335.1383 N-units, respectively. Addi- tionally, the average Field Strength Variations at each location is 13.258175 dB, 3.116676 dB, and 21.733525 dB, for Ikeja, Calabar, and Kano respectively. The FSV values fluctuated alongside the sur- face refractivity. The study shows a good correlation between the radio field strength and refractivity. This is result has provided important information for proper planning in the selected regions. Keywords: Distortion, Surface Refractivity, Radio Field Strength, Propagation Path. 1 Introduction Propagation in free space refers to the transmission of electromagnetic waves through a vacuum or space with no significant obstacles or obstructions. In other words, it is the propagation of radio waves through the atmosphere without being affected by the ground, buildings, or other objects [1]. Modern radio communications, from cell phone use, ground digital transmissions, to the propagation of satellite TV for computer radio signals through the troposphere, have had a significant impact on the im- portance of electromagnetic waves propagation [2]. The wide bandwidth of the microwave frequency bands makes them useful for mobile communication systems. Its application of conversation technology includes Smartphones, laptops, and computer systems in each day lifestyles to ease the manner of doing groups and social sports along with cell banking, and companies, get the right of entry to information and utilization of social media [3]. Environmental effects on communication systems include distortion of the radio signal due to atmospheric chaos, and changes of mediums during radio wave propagation which is attributed to variations in atmos- pheric density along the transmission links, scattering, and absorption [4]. Radio refractivity is the difference between a radio wave's speed in a specific medium and its speed while traveling through empty space. Changes in the air's radio refractive index affect how radio waves propagate [5]. By comparing them to the refraction predicted from a standard environment, refractive conditions are defined. Variations in water vapour density and temperature are the causes of deviations from standard con- ditions. Horizontal propagation channels on the surface can be significantly impacted by a large gradient of these factors close to the ocean's surface [6]. It is clear that anomalous radio wave propagation can occur due to various meteorological factors, and that understanding these factors is important for designing and oper- ating reliable radio communication systems According [7], poorer propagation conditions cause communication links to fade more and the transmit- ter/receiver power levels to drop. As a result, well- planned and engineered radio connection systems are necessary for achieving peak performance. mailto:sanyaolum@run.edu.ng http://orcid.org/0000-0002-6340-9028 http://orcid.org/0000-0002-3173-9700 http://orcid.org/0000-0003-3379-3333 http://orcid.org/0000-0003-3270-7724 https://doi.org/10.2991/978-94-6463-644-4_11 http://crossmark.crossref.org/dialog/?doi=10.2991/978-94-6463-644-4_11&domain=pdf Anomaly radio wave propagation exists when atmospheric propagation circum- stances differ from those expected. It is clear that anomalous radio wave propagation can occur due to various meteorological factors, and that understanding these factors is important for designing and operating reliable radio communication systems [8]. 1.1 Background A transmitter emitting isotropically in all directions having power (Pt) in free space will produce at a dis- tance ‘d’ (km ) a power flux density, S, the flux density is thereby ex- pressed as: 𝑆 = 𝑝𝑡 4𝜋𝑑2 1 on log ratios, 𝑆 = P𝑡 − 20 log 𝑑 − 41 2 The equivalent field strength, E, is expressed as: 𝐸 = √𝑆. 120𝜋 3 = √30𝑃𝑡 𝑑 4 or 𝐸 = (𝑚𝑉𝑚) = 173 𝑝𝑡(𝑘𝑤) 𝑑(𝑘𝑚) 5 or 𝐸 = 𝑃𝑡 − 20 𝑙𝑜𝑔𝑑 + 10.48 ln 𝑑𝐵(1𝜇𝑉𝑚) 6 Whenever the power is radiated isotropically, this relationship holds true. Also, when the impedance of a receiving antenna is matched to the transmitting power (Pt) in a load, (Pt) is then expressed as: 𝑃𝑡 = S(𝑎𝑒) 7 where 𝑎𝑒 is the antenna’s effective aperture. The presence of a nearby poorly conduction of the ground will degrade an antenna's effective- ness. It may be useful to distinguish between signals that come straight from the antenna and signals that results from reflections from the ground when the antenna is above the ground by some waelengths. It is no longer reasonable to think so when the antenna is near or on the ground [9]. Surface wave propagation depends mostly on the electrical factors of the ground surface. These electrical parameters are mainly conductivity, σ, and relative permittivity ɛ, of the ground. The permeability can be taken as that of free space be- cause the Earth can be considered to be non-magnetic at these frequencies. Relative permittivity plays a less Significances role than conductivity as the earth is more of a conductor at these frequencies [10]. Hence, ground conductivity constitutes the major electrical parameter to be taken into consideration at these frequencies. However, these two ground constants jointly influence wave propagation and are related to the complex permittivity relative to vacuum 𝜀. Usually, transmitters operating in the upper end of the broadcast band operate on low powers just for local broadcasts covering about 50 km (max) and transmitters operating at higher powers generally operate at the lower end of the broadcast band [11]. 2 Methods Data used in this study were gathered over two years (2019-2020) from atmospheric reanalysis of the fifth generation (ERA-5) of the European Centre for Medium-Range Weather Forecasts, 2017 (ECMWF). The archival data from provides variables such as pressure, temperature, and relative humidity. ERA5 has gridded data type with regular latitude-longitude grid at 0.25° × 0.25° (atmosphere). At 31 km spatial resolution and 137 levels vertically from the surface to 0.01 hPa (about 80 km), it offered worldwide hourly temporal resolution of atmospheric, ocean-wave, and land-surface data. Temporal Variations of Refractivity and Field Strength 115 2.1 Computation of Surface Refractivity and the Radio Field Strength Radio refractivity is obtained using [12]. 𝑁 = (𝑛 − 1)(106) = 77.6 𝑇 (𝑃 + 4810 𝑋 𝑒 𝑇 ) 8 T (K) indicates the absolute temperature of the air, P (hPa) is the pressure of the atmosphere, while e (hPa) is the pressure of water vapor, the value of surface refractivity at sea level, 𝑁𝑜 𝑁𝑜 = 𝑁𝑠 𝑒𝑥p(𝑍𝑠/𝐻) 9 where H is the scale height and Zs is the surface's height above sea level. The significance of 𝑁𝑜 comes from the fact that the examination of surface refractivity using the reduced-to-sea level eliminates the majority of the variability in N. It was determined that H=7.0 and Z=0.375km for this region [11]. Equation (9) can therefore be written directly as; 𝑁𝑜 = 𝑁𝑠 𝑒𝑥p(0.0536) 10 𝑁𝑠 decreases with height exponentially in the troposphere, N (h) is expressed as 𝑁(ℎ) = 𝑁𝑠 𝑒𝑥p(−𝑏ℎ) 11 𝑁𝑠 is the refractive index at the surface, whereas b is a location-dependent variable. The component b may also change depending on the time of year and be expressed as 𝑏 = 𝑙𝑛 𝑁𝑠 𝑁𝑠+∆𝑁 12 ∆𝑁 = −1.46 𝑒𝑥𝑝 (0.00918𝑁𝑠) Surface refractivity and radio field strength demonstrate considerable connections, mostly at high band fre- quencies. At frequencies above 30 MHz, 0.2 dB variation in field strength is utilized for every change per unit of Ns. The maximum (𝑁𝑠𝑀𝑎𝑥) and the minimum (𝑁𝑠𝑀𝑖𝑛) values of Ns were used to determine the monthly ranged as: 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑟𝑎𝑛𝑔𝑒 = (𝑁𝑠𝑀𝑎𝑥 − 𝑁𝑠𝑀𝑖𝑛 ) 13 The field strength variation is calculated form the monthly ranges as: 𝐹𝑆𝑉 = (𝑁𝑠 𝑀𝑎𝑥 − 𝑁𝑠𝑀𝑖𝑛 ) X 0.2 dB 14 3 Results and Discussion Figure 1 illustrate the daily variations in surface refractivity over the stations. It shows the sur- face-level average hourly time mean for 24 hours local time for the wet season months of 2019. From early morning till about 7 am, the surface refractivity peaks at 387 N-units and also peaks about the same value of 387 N- units between 7 pm and 11 pm at night before starting to drop at 7:00 am., as shown in Fig. 1. In Ikeja, a maximum value of approximately 388 N-units at noon local time was seen. Calabar recorded high values of surface refractivity between 397 and 398 N-units between 12 am and 7am in the morning and between 7: pm and 11:00 pm at night, it subsequently begins to decline at 7:00 pm. Again, it slightly rises to around 397 N- units in the noon before falling once more to a minimum value of 385 N-units at 1:00 pm. Additionally, surface refractivity in Kano shows a value of 273 N- units in the morning (0:00- 7:00 hr) and 270 N- units in the night (19:00-23:00 hr), then starting to decline at 20:00 hr reaching the lowest value of about 253 N- units at about 10:30 pm. 116 M. E. Sanyaolu et al. Fig. 1. A typical day surface refractivity (6th July 2019) As seen in Figure 2, the surface refractivity in Ikeja peaks at about 23 hr, reaching a peak value of 393 N- units, with values ranging from 392 to 391 N-units at 12:00 am and 7:00 am respectively, the 7:00pm to 11:00 pm. Between 0:00 - 7:00 hr in the morning and 19:00 - 23:00 hr at night, the surface refractivity in Calabar varies from the peak of around 393N units to 391 N- units. It then starts to decline at 6:45, a slight increase of 392 N- units was experienced before dropping again to 392 N- units at 3:30 pm. Fig. 2. A typical day surface refractivity (6th July 2021) As shown in Figure 3, the surface refractivity in Ikeja varies from a peak of 381 N units to a low of 328 N units depending on the time of day. It reaches its lowest value at about 11 h local time. During the early morning hours (0:00 -7:00 hr ) and late at night (19:00 -23:00 hr), the surface refractivity in Calabar reaches a the peak of 386 N-units to 388 N-units. It then starts to decline at noon to 362 N-units, and then increases to a maximum of 386 N-units. Additionally, surface refractivity in Kano recorded between 273 and 270 N-units for both morning (0:00–7:00 hr) and evening (19:00–22:30 hr) respectively, lowest value of 253 N- units was recorded at 23:00 hr 100 200 300 400 500 1 .0 0 2 .0 0 3 .0 0 4 .0 0 5 .0 0 6 .0 0 7 .0 0 8 .0 0 9 .0 0 1 0 .0 0 1 1 .0 0 1 2 .0 0 1 3 .0 0 1 4 .0 0 1 5 .0 0 1 6 .0 0 1 7 .0 0 1 8 .0 0 1 9 .0 0 2 0 .0 0 2 1 .0 0 2 2 .0 0 2 3 .0 0 2 4 .0 0 R ef ra ct iv it y N -u n it s Time (hr) Ikeja Calabar Kano 370 375 380 385 390 395 1 .0 0 2 .0 0 3 .0 0 4 .0 0 5 .0 0 6 .0 0 7 .0 0 8 .0 0 9 .0 0 1 0 .0 0 1 1 .0 0 1 2 .0 0 1 3 .0 0 1 4 .0 0 1 5 .0 0 1 6 .0 0 1 7 .0 0 1 8 .0 0 1 9 .0 0 2 0 .0 0 2 1 .0 0 2 2 .0 0 2 3 .0 0 2 4 .0 0 R e fr ac ti vi ty N -u n it s Time (hr) Ikeja Calabar kano Temporal Variations of Refractivity and Field Strength 117 Fig. 3. A typical day surface refractivity (6th January 2020) Figure 4 and 5 showed the pattern of the seasonal variation in refractivity for the research locations across the period (2019–2020) taken into consideration for this study. It was found that the outcome was consistent with the writings of [13-14]. All of the stations analyzed have seasonal variations in surface refractivity, ranging from about 221 N- units at Kano to about 407 N-units at Calabar station. Additionally, it can be shown that Calabar will have the highest refractivity in 2020, at 407 N- units in April. This is caused by the station's exposure to the Atlantic Ocean, together with high humidity and water vapor levels [13]. Kano has the lowest refractivity in December with 221 N units. In April 2021, Calabar's maximum refractivity will be 407 N-units. Ikeja, Calabar, and Kano have had mean surface refractivity values for the past two years of 413.308715 N-units, 410.81065 N- units, and 335.1383 N-units. Kano has an extremely low value of refractivity. The height, which is 1217 meters above sea level, could be the cause of this. Pressure variation appears modest at this altitude Seasonal variations can also be seen in the refractive index, as illustrated in Figures. 1 and 2. Additionally, it is demonstrated that the surface refractivity is higher toward the coast than inland. This is a result of how the Atlantic Ocean affects the coastal region. Fig. 4. Surface refractivity for the year 2019, showing seasonal variation 0 50 100 150 200 250 300 350 400 1 .0 0 2 .0 0 3 .0 0 4 .0 0 5 .0 0 6 .0 0 7 .0 0 8 .0 0 9 .0 0 1 0 .0 0 1 1 .0 0 1 2 .0 0 1 3 .0 0 1 4 .0 0 1 5 .0 0 1 6 .0 0 1 7 .0 0 1 8 .0 0 1 9 .0 0 2 0 .0 0 2 1 .0 0 2 2 .0 0 2 3 .0 0 2 4 .0 0 R e fr ac ti vi ty ( N -u n it s) Time (hr) Ikeja Calabar Kano 0 50 100 150 200 250 300 350 400 450 JAN FEB MAR APRIL MAY JUN JUL AUG SEP OCT NOV DEC R e fr ac ti vi ty N -U n it s Months Ikeja Calabar Kano 118 M. E. Sanyaolu et al. Fig. 5. Surface refractivity for the year 2020, showing seasonal variation From Figure 6 and 7, the field strength variations for the selected stations were computed. 56.25 dB in April and 46.66 dB in March was recorded in Kano which denotes a high reading. This could be explained by how the local meteorology in the area reacts to the earth's solar insolation, a main force in the observed weather. The radio field strength exhibits irregular changes in Figure. 8, peaking in January and declining in Decem- ber. Ikeja displays 34.85 dB in February, while Kano registers a high of 46.66 dB in March. In Ikeja, Calabar, and Kano, the annual mean radio field strength is 13.258, 3.116, and 21.73 dB, respectively. Fig. 6. Seasonal variations in radio field strength for the year 2020 (FSV 2020) 100 200 300 400 500 JAN FEB MAR APRIL MAY JUN JUL AUG SEP OCT NOV DECR e fr ac ti vi ty N -U n it s Months Ikeja Calabar Kano 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10 11 12 R ad io f ie ld s tr e n gt h ( d B ) Months Calabar Ikeja Kano Temporal Variations of Refractivity and Field Strength 119 Fig 7. Seasonal variations in radio field strength for the year 2020 (FSV 2020) Tables 1 and 2, respectively exhibit the average values of Ns and radio field strength for the selected loca- tions from 2019to 2020. The table shows that the average Ns values over the stations Ikeja, Calabar, and Kano in the year 2019 are 413.9656, 411.2872, and 33.1666 Ns-units respectively, and in the year 2020, they are 412.2087, 410.3341, and 337.11 Ns-units respectively. Additionally, it was found that Ns average values in 2020 were greater than in 2019. This could be explained by higher tropospheric humidity in 2020 than in 2019, Ns readings were greater in 2020 than they were in 2019. According to the field strength variability, Calabar has the lowest average value (3.116676 dB) and Kano has the highest average value (21.733525 dB). Other factors, like dust scattering would mostly affect Kano being in the Sahara region in Nigeria. This has an impact on field strength variations between Kano and Ikeja). Table 1. Variation of surface refractivity for each year STATIONS Ns(N-units) 2019 Ns(N-units) 2020 Mean Ns (N-units) Ikeja 413.96 412.20 413.30 Calabar 411.28 410.33 410.81 Kano 333.16 337.11 335.13 Table 2. Calculated field strength variability for each year STATIONS FSV (dB) 2019 FSV (dB) 2020 Mean FSV (dB) Ikeja 13.29984 13.21651 13.258175 Calabar 3.616775 2.616577 3.116676 Kano 22.1593 21.30775 21.733525 4 Conclusion A two-year archive of atmospheric variable data (Jan. 2019–Dec. 2020) of three locations (Ikeja, Calabar, and Kano) in Nigeria were used in this study to investigate the diurnal and temporal variation of surface refractivity on radio field strength. The surface refractivity value increases over Nigeria, rising from approx- imately 335.1 N-units in Kano to approximately 267.64 N-units in Ikeja. Seasonal surface refractivity over Nigeria varies from year to year, reaching peak values in the wet season and reduced values in the dry season months. 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