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Linkage of meteorological parameters and anomalous radio propagation profile over Nigeria
Journal of Atmospheric and Solar–Terrestrial Physics 191 (2019) 105047
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Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
Linkage of meteorological parameters and anomalous radio propagation profile over Nigeria I. Emmanuel Physics Department, Federal University of Technology, PMB 704, Akure, Nigeria
A R T I C L E I N F O
A B S T R A C T
Keywords: Meteorological Linked Ducting Refractive
The vertical distribution of refractivity gradient is important in determining anomalous propagation condition. Thirty five years of meteorological parameters, obtained from Era-Interim archive of European Centre for Medium-Range Weather Forecasts has been used to analyze and investigated surface meteorological data linked with refractivity gradient aloft altitude across Nigeria. Spatial distribution of surface temperature, relative hu midity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km over Nigeria were plotted. Vertical dis tribution of temperature, relative humidity, refractivity and refractivity gradient were obtained for some locations across Nigeria. Similarly, spatial distribution of coefficient of determination between surface temper ature, relative humidity and refractivity gradient at four different height were estimated. Linear regression were developed to investigate the relationship between surface data and refractivity gradient at different altitude. The result revealed existence of sub refractive, super refractive, and ducting across the country at 0.1 km and 0.5 km however occurrence of ducting and sub refractive disappeared at 1.0 km and 1.5 km. Likewise, the existence of temperature inversion was noticed between surface and 100 m across all the locations except in Lagos. Values of refractivity across the observed locations converged around 0.5 km. Through result of correlation coefficient and statistical parameters, significant linked have been established between surface data and refractivity gradient at different height.
1. Introduction Tropospheric refraction significantly affect terrestrial propagation of electromagnetic radio waves at ultra-high frequency (UHF) and micro wave frequency (Adeyemi and Emmanuel, 2011; Hitney et al., 1985). Impair in the communication links (mobile radio communications, telecommunication and other wirelesss) are associated to small change in propagation medium of radio waves (Manjula et al., 2016). This effect is anchored on the refractive index which varies with atmospheric altitude due to non-uniform condition of the atmospheric parameters (Emmanuel et al., 2017; Sirkova and Mikhalev, 2004; Ulaby et al., 1981; Steiner and Smith, 2002). In troposphere radio waves emanated from terrestrial-based may be trapped or deflected toward or away from the surface known as anomalous propagation, due to the existence of different meteorological effects such as temperature inversion, high evaporation (Manjula et al., 2016; Kaissassou et al., 2015). Radio trap ping conditions produce signals multipath fading which vary with time, geographical location and radio frequency (Saleem, 2016; Emmanuel et al., 2018). Radio ducting is a function of vertical component of
atmospheric refractivity, within the troposphere, the variation of this component is linear in the lowest 1 km and exponential with geometric height above 1 km (Mufti and Siddle, 2012; Louf et al., 2015). The profile of the atmospheric refractivity gradient within 1 km altitude above the ground surface is highly vital in investigating anomalous propagation (Willoughby et al., 2002; Dairo and Kolawole, 2017; AbouAlmal et al.,2015; Adediji, 2017). Performance of communication garget, surveillance, wireless and radar system can be improved via the detail study and information provide from refractivity variability to the design engineers. This information is also useful in remote sensing. Foggy conditions (a situation where transmitted signal result to communication breakdown between receiver and transmitter) is one of the effect of refractivity variation on UHF (Alam et al., 2016). To minimize the effects of anomalous condition on microwave propagation, it is needful to investigate and document the meteorological link of at mospheric refractivity distribution at troposphere (Louf et al., 2015). Previous studies across Nigeria revealed seasonal, monthly, diurnal refractivity (Oyedum et al., 2011; Adediji et al., 2014); refractivity gradient condition (Adeyemi and Emmanuel, 2011) and the profile of
E-mail address: [email protected]. https://doi.org/10.1016/j.jastp.2019.05.011 Received 19 February 2019; Received in revised form 22 April 2019; Accepted 24 May 2019 Available online 1 June 2019 1364-6826/© 2019 Elsevier Ltd. All rights reserved.
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
refractivity below 500 m above the ground surface [14]. This paper showed detailed link between the surface temperature, surface relative humidity and refractivity gradient across Nigeria. Nigeria lies between latitude (4oN) and (14oN) and longitude (3oE) and (15oE) and has a total area of 923 770 km2. The total surface area of water bodies in Nigeria is estimated to be about 149,919 km2 which constitutes about 15.9% of the total area of Nigeria. The climate is tropical, characterized by high temperatures and humidity as well categorized into wet and dry seasons, nevertheless seasonal variation exist between South and North region. Total rainfall decreases from the coast northwards. The southern part (below Latitude 8� N) has an annual rainfall ranging between 1,500 and 4,000 mm and the extreme North between 500 and 1000 mm. Nigeria weather is govern by the tropical maritime (mT), the tropical maritime (cT) and equatorial easterlies which influence the migration of inter tropical discontinuity (ITD) (Emmanuel et al., 2017; Ojo, 1977).
refractivity gradient were observed across nine locations across Nigeria as shown Table 2. A linear link were also developed and validated for these locations (see Table 3). 3. Results 3.1. Spatial distribution of surface meteorological parameters and altitudinal anomalous propagation Using grads software spatial distribution of long term values of sur face relative humidity (H), surface temperature (T), refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km denoted by G 0.1km, G 0.5km, G 1.0km and G 1.5km respectively were plotted as shown in Fig. 1. Values of H decreases with increase in latitude across Nigeria. In coastal region, highest values of H ranges between 96% and 99% were obtained, whereas the lowest values ranges between 72% and 75% were observed in saharia region of Nigeria. This variation can be attributed to quantity of water vapour retain in the air in these regions. In another view, highest value of temperature was observed in Sokoto and part of coastal region, whereas lowest values of temperature is noticed around Jos plateau and Adamawa hill. This is in consonant with earlier finding in Adedayo (2016). The values of temperature oscillating between 292 K and 300 K across Nigeria. From G0.1 km distribution, ducting phenom enon are noticed in the part of sahara and part of the coastal area. This can be associated to nocturnal surface cooling and temperature inver sion (Von Engeln and Teixera, 2004). Sub refraction is observed in some of the inland region. Similarly, occurrence of ducting, super refractive and sub refractive were also observed across Nigeria at G0.5km. However, occurrence of super refractive is about 90% and 100% at G1.0km and G1.5km respectively across Nigeria. Occurrence of radio trapping disap pear at 1.0 km upward.
2. Data source and analysis Meteorological parameters (temperature, relative humidity) used in this work was obtained from the Era interim archive of European Centre for Medium-Range Weather Forecasts (ECMWF). The data which covered the period of thirty five years (1979–2014) was obtained for surface and four atmospheric pressure levels (1000 hPa, 950 hPa, 900 hPa and 850 hPa) and extracted for Nigeria. 2.1. Data analysis Surface refractivity and altitude refractivity were calculated from the obtained meteorological parameters using the expression in equation (1) ITU-R, 2016a,b: N ¼ 77:6
� e p þ 3:73 � 105 2 T T
(1)
3.2. Altitudinal variation of temperature, relative humidity, refractivity and refractivity gradient
where N is refractivity (N-units) correspond to either surface or any height above the ground, P represent pressure in hPa, T is temperature in kelvin and e is water vapour pressure in hPa. e is a function of relative humidity, H in % and temperature, t in degree Celsius as shown in equation (2) e¼
aH bt exp 100 tþc
Altitudinal distribution of temperature, relative humidity, refrac tivity and refractivity gradient across eight locations in Nigeria are presented in Fig. 2. This vertical variation of T, H and N follow similar trend across the observed locations. Kastina and Kano were leading in vertical temperature variation with Lagos, Ibadan and Akure lagging. The rate of change of temperature between surface and 100 m altitude are 8.3 � C/m, 1.8 � C/m, 25.7 � C/m, 26.5 � C/m, 32.9 � C/m, 10.4 � C/m, 3.3 � C/m, 9.9 � C/m and 18.7 � C/m in Lokoja, Lagos, Kastina, Kano, Jos, Ilorin, Ibadan, Akure and Abuja respectively (Fig. 2a). The rate of change in the northern region of the country is far higher than the southern region. In Jos, which is in high altitude (mountainous places) area experience low temperatures at the surface, this also contribute to the variation. However, temperature start to decrease at altitude 100 m upward. For relative humidity, negative rate of change is observed across all the locations and altitude (Fig. 2b). Aside from little variation of refractivity between surface and 100 m above the ground, refractivity profile decreases linearly with height (Fig. 2c). The rate of change across all the locations ranges between
(2)
where a, b and c are constants define in Table 1 (ITU-R, 2015). Refractivity gradient, G (N-units/km) is calculated using the expression in equation (3) (ITU-R, 2016a,b): G¼
Ns hs
N1 h1
(3)
Ns and N1 represent refractivity, N, at surface and at any particular height above the ground respectively and the corresponding height (km) is hs and h1 respectively. The analysis were carried out using relevant package such as excel, SPSS and matlab. Spatial distribution of some meteorological parameters and anomalous propagation at four different altitudes were examined. Long term spatial distribution of correlation coefficient between some meteorological parameters and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km were also analysed. Altitudinal variation of temperature, pressure, refractivity and
Table 2 Selected locations across Nigeria.
Table 1 Refractive conditions. Parameters
Water
Ice
A B C
6.1121 18.678 257.14 valid between
6.1115 23.036 279.82 valid between
40� to þ50�
80� to þ0�
2
Location
Latitude (degree North)
Longitude (degree East)
Lagos Ibadan Ilorin Akure Abuja Jos Lokoja Kano Kastina
6.52 7.38 8.48 7.26 9.08 9.90 7.80 12.00 12.51
3.38 3.94 4.54 5.21 7.40 8.86 6.73 8.59 7.61
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
(Fig. 2d). However, the values of G across the locations almost converge at 500 m and partially increase upward.
Table 3 Statistical parameters for surface relative humidity, temperature and profile refractivity gradient. Location
Altitude (km)
CD (%)
SE
P-value
Durbin-Watson
Lagos
0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5
51.0 38.5 38.1 35.3 47.7 57.0 47.6 37.0 76.3 68.7 56.9 45.5 41.4 67.0 52.3 38.8 92.5 91.0 82.5 72.6 89.6 88.7 80.4 67.9 93.0 91.1 82.5 72.6 90.0 88.0 75.4 66.0 89.9 84.8 72.4 63.7
43.1 19.8 11.4 8.2 64.4 17.8 10.8 7.8 72.6 20.9 12.1 8.2 71.0 16.7 10.3 7.3 77.3 13.6 9.8 6.8 64.2 13.8 9.2 6.5 77.3 13.6 9.8 6.8 66.1 11.5 8.1 5.4 88.5 17.3 11.4 7.4
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1.3 0.6 0.6 1.2 0.9 0.7 0.7 0.7 1.1 0.7 0.6 0.7 0.8 0.7 0.6 0.7 1.2 1.2 0.7 0.7 1.2 0.9 0.7 0.8 1.2 0.7 0.7 0.9 1.0 0.9 0.7 0.7 1.1 0.8 0.7 0.7
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
3.3. Correlation between surface relative humidity and refractivity gradient profile Fig. 3 represent the correlation coefficient of long term data (1979–2014) between surface relative humidity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km respectively. Positive correlation exist between H and G across the four points. At 0.1 km, the correlation between H and G 0.1 km varies between 0.1 and 0.98. Similarly, correlation coefficient varies between 0.008 and 1.05 at 0.5 km altitude. This show the degree of relationship between H and G. Monthly correlation between surface relative humidity, H, and G were also observed for six locations across Nigeria as represented in Fig. 4. 3.4. Correlation between surface relative temperature and refractivity gradient profile The spatial distribution of correlation coefficient between surface temperature and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km as presented in Fig. 5. Except in part of Atlantic Ocean where strong negative correlation exist, weak negative correlation exist be tween T and G0.1 km across Nigeria. However weak positive correlation are noticed in some northern part of the country. The correlation coef ficient here varies between 0.76 and 0.18. Similarly, correlation co efficient between T and G 0.5 km varies between 0.7 and 0.3. The result of other levels are also similar. Fig. 6 connote monthly correlation between surface temperature and refractivity gradient in six selected locations across the country. The correlation coefficient follow similar trend of Lagos and Ibadan. Strong negative correlation exist between T and G0.1km in October–May in the two locations. Negative deep was observed in July September. This period correspond to the peak of rainy season at three locations. Result of Abuja, Ilorin and Jos are similar with the value of correlation coefficient between T and G0.1 km oscillating between poor positive correlation and strong negative correlation. Strong negative correlation across most of the months at Kastina. Strong positive correlation exist between T and G0.5km, G1.0 km and G1.5km in
0.1 N-units/m and 12.1 N-units/m across the locations and altitude. Refractivity gradient, G, increases with height between 100 m and 500 m in Kastina, Kano, Lagos and Lokoja. Whereas, G decreases with height within this altitude in Abuja, Ibadan, Ilorin, Jos and Akure
Fig. 1. Spatial distribution of long term (1979–2014) (a) relative humidity, (b) temperature, (c) refractivity gradient at 0.1 km, (d) refractivity gradient at 0.5 km. (e) refractivity gradient at 1.0 km and (f) refractivity gradient at 1.5 km. 3
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 2. Vertical distribution of (a) temperature, (b) relative humidity, (c) refractivity and (d) refractivity gradient in Nigeria.
Fig. 3. Spatial distribution of correlation coefficient between relative humidity and refractivity gradient.
October–May at Lagos and Ibadan. This period correspond to the dry season and onset of rainy season. In Abuja, Ilorin and Kastina, strong/ moderate correlation exist between T and G at 0.5 km, 1.0 km and 1.5 km in most of the locations. Jos experienced exceptional variation in correlation coefficient oscillating between 0.008 and 0.98 across the months.
surface relative humidity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km. G ¼ γ þ αT þ βH
(4)
where γ, α and β are constants which are location and altitudinal dependent. From the relation, coefficient of determination (CD), standard error (SE), p value and Durbin-Watson were deducted for different location across Nigeria as shown Table 2. The Durbin Watson statistic which ranges between 0 and 4 is a number that tests for autocorrelation in the residuals from a statistical regression analysis. Positive autocorrelation exist when the values ranges between 0 and less than 2, while negative
3.5. Linear link between surface meteorological parameters and profile refractivity gradients Linear regression of the expression in equation (4) is constructed to investigate the statistical relationship between surface temperature, 4
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 4. Monthly distribution of correlation coefficient between relative humidity and refractivity gradient.
Fig. 5. Spatial distribution of correlation coefficient between temperature and refractivity gradient.
autocorrelation exist when the values is greater than 2 and less than or equal to 4. A value of 2 means that there is no autocorrelation in the sample. The p value across the stations and altitude is zero, this showed that the predictors (surface temperature and surface relative humidity) variables are significant in determining refractivity gradient. The values of Durbin-Watson across the locations and altitude are less than 2 which indicate positive autocorrelation between the surface data and profile refractivity gradient. The coefficient of determination, CD, which mea sures the extent that the dependent variable, G, can be predicted by the
independent variables (H, T) show a good result across the stations. Good CD established over all the staitons in Nigeria which is above 37%. Table 4 show the coefficient values of the constants in equation (4). Refractivity gradient values obtained from model linear regression were compared with the values obtained using ITU expression in equation (4). The values were subjected to mean bias error (MBE) and root mean square error (RMSE) test as shown in Table 5. Mean bias error show the average deviation of the predicted values from the actual measured values (Igbal and Muhammed, 1993). Positive values of MBE indicates 5
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 6. Monthly distribution of correlation coefficient between temperature and refractivity gradient. Table 4 Coefficients values of the constants in the linear regression. Coefficients
Altitude (km)
Lagos
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
γ
0.10 0.50 1.00 1.50 0.10 0.50 1.00 1.50 0.10 0.50 1.00 1.50
246.50 152.00 685.30 748.20 10.59 4.50 4.19 3.55 33.40 11.29 5.01 2.40
4314.00 735.30 365.40 521.10 20.99 0.31 2.65 2.60 19.19 7.73 3.62 1.84
2403.00 936.00 397.60 619.10 15.67 1.13 2.35 2.69 23.09 5.55 2.42 1.14
61.85 1455.00 179.70 482.40 6.77 2.13 1.97 2.39 20.29 7.82 3.52 1.64
3796.00 216.90 550.40 675.10 19.91 1.52 2.89 2.88 21.23 6.17 2.52 1.13
3751.00 153.80 276.70 356.30 20.05 2.26 1.86 1.77 22.86 4.76 2.26 1.09
170.90 489.90 5.36 229.60 9.00 3.17 0.84 1.34 27.09 4.33 2.13 1.09
2477.00 667.30 545.20 459.50 16.22 3.69 2.58 2.03 24.47 3.86 1.65 0.77
2989.00 812.80 612.00 487.30 17.84 4.15 2.80 2.11 24.00 3.69 1.59 0.72
α
β
Table 5 Statistical test on predicted and observed refractivity gradient. Parameter
Altitude (km)
Lagos
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
ITU
0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5
129.59 85.80 74.26 76.59 137.28 86.03 73.48 75.98 0.90 0.04 0.01 0.00 22.02 0.20 0.12 0.09
29.44 69.07 67.11 72.26 45.10 67.68 66.11 71.62 0.24 0.04 0.01 0.00 16.91 0.22 0.13 0.09
8.69 67.51 67.39 71.82 18.10 62.76 64.98 70.17 1.79 0.04 0.00 0.01 33.00 0.28 0.17 0.11
59.51 54.45 61.07 68.30 50.91 53.23 58.20 65.18 0.83 0.06 0.02 0.03 32.83 0.26 0.15 0.10
61.23 77.31 68.70 72.51 91.16 75.62 68.24 73.01 1.00 0.06 0.02 0.02 52.25 0.25 0.14 0.10
0.88 65.44 63.52 67.75 19.66 63.36 60.76 65.45 0.37 0.07 0.01 0.02 3.45 0.31 0.15 0.10
54.28 36.04 57.96 64.00 47.69 38.19 54.67 61.52 0.12 0.58 0.02 0.02 2.22 12.87 0.17 0.11
299.65 108.27 85.70 78.97 263.02 108.60 80.78 77.02 0.32 0.05 0.04 0.02 3.36 0.17 0.12 0.08
326.68 117.94 88.46 80.67 289.79 108.90 84.75 78.43 0.35 0.06 0.03 0.02 3.03 0.15 0.11 0.08
Predicted
MBE
RMSE
6
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
overestimation, while negative values connote underestimation of the predicted values. The expression for MBE is shown in equation (5) MBE ¼
n 1X Xo n i¼1
Xp
�
Adediji, A.T., 2017. Reduced-to-sea-level value of microwave radio refractivity over three stations in Nigeria. Niger. J. Pure Appl. Phys. (NJPAP) 7 (1), 19–25. Adeyemi, B., Emmanuel, I., 2011. Monitoring tropospheric radio refractivity over Nigeria using CM— SAF data derived from NOAA — 15, 16 and 18 satellites. Indian J. Radio Space Phys. 40, 301–310. Alam, I., Mufti, N., Shah, S.A.A., Yaqoob, M., 2016. The effect of refractivity on propagation at UHF and VHF frequencies. Int. J. Antennas Propag. (4138329), 8. Dairo, O.F., Kolawole, L.B., 2017. Radio refractivity gradient in the lowest 100 m of the atmosphere over Lagos, Nigeria in the rainy-harmattan transition phase. Adv. Space Res. 167, 169–176. Emmanuel, I., Adeyemi, B., Ogolo, E.O., Adediji, A.T., 2017. Characteristics of the anomalous refractive conditions in Nigeria. J. Atmos. Sol. Terr. Phys. 164, 215–221. Emmanuel, I., Adeyemi, B., Adedayo, K.D., 2018. Estimation of refractivity gradient and geoclimatic factor for radio link design in Nigeria. Phys. Sci. Int. J. 19 (2), 1–9. Hitney, H.V., Richter, J.H., Pappert, R.A., Anderson, K.D., Baumgartner, G.B., 1985. Tropospheric radio wave propagation. Proc. IEEE 73 (2), 265–283. Igbal, M., Muhammed, A., 1993. An Introduction to Solar Radiation. Academic Press, Melbourne, Australia. ITU-R, 2015. Propagation Data and Prediction Methods Required for the Design of Terrestrial Line-of-sight Systems. International Telecommunications Union, Geneva. Recommendation of ITU-R P.530-16. ITU-R, P.453-12, 2016. The Radio Refractive Index; its Formula and Refractivity Data. Tech. rep. ITU, Geneva, Switzerland. ITU-R, P., 2016. Effects of Tropospheric Refraction on Radiowave Propagation, pp. 834–838. Kaissassou, S., Lenouo, A., Tchawoua, C., Lopez, P., Gaye, A.T., 2015. Climatology of radar anomalous propagation over West Africa. J. Atmos. Sol. Terr. Phys. 123, 1–12. Louf, V., Pujol, O., Sauvageot, H., Ri� edi, J., 2015. Seasonal and diurnal water vapour distribution in the Sahelian area from microwave radiometric profiling observations. Q. J. R. Meteorol. Soc. 2015 (141), 2643–2653. Liu, Q., Bakker-Arkema, F.W., 1997. Stochastic modelling of grain drying: Part 2. Model development. J. Agric. Eng. Res. 66, 275–280. Manjula, G., Roja Raman, M., Venkat Ratnam, M., Chandrasekhar, A.V., Vijaya Bhaskara Rao, S., 2016. Diurnal variation of ducts observed over a tropical station, Gadanki, using high resolution GPS radiosonde observations. Radio Sci. 51, 247–258. https:// doi.org/10.1002/2015RS005814. Mufti, N., Siddle, D.R., 2012. Determination of the effective earth radius factor and its impact on propagation of signals on over-sea paths in the English channel. In: Antennas & Propagation Conference. Loughborough, UK. Ojo, O., 1977. The Climate of West Africa. Heineman, London. Oyedum, O.D., Ezenworah, J.A., Igwe, K.C., Eichie, J.O., Moses, A.S., 2011. Diurnal and annual cycles of surface refractivity and related parametersin Minna, Central Nigeria. Nigerian J. Space Res. 10, 141–156. Saleem, M.U., 2016. Statistical investigation and mapping of monthly modified refractivity gradient over Pakistan at the 700 hectopascal level. Open J. Antenn. Propag. 4, 46–63. https://doi.org/10.4236/ojapr.2016.42005. Sirkova, I., Mikhalev, M., 2004. Parabolic-equation-based study of ducting effects on microwave propagation. Microw. Opt. Technol. 42, 390–394. Steiner, M., Smith, J.A., 2002. Use of three dimensional reflectivity structures for Automated detections and removal of non-precipitating echo in radar data. J. Atmos. Ocean. Technol. 19, 673–686. Ulaby, F.T., Moore, R.K., Fung, A.K., 1981. Microwave remote sensing fundamentals and radiometry. In: Microwave Remote Sensing: Active and Passive, vol. 1. AddisonWesley. von Engeln, A., Teixeira, J., 2004. A ducting climatology derived from ECMWF global analysis fields. J. Geophys. Res. 109 (D18), D18104. https://doi.org/10.1029/ 2003JD004380. Willoughby, A.A., Aro, T.O., Owolabi, I.E., 2002. Seasonal variations of radio refractivity gradients in Nigeria. J. Atmos. Sol. Terr. Phys. 64, 417–425.
(5)
where Xo and Xp are observed and predicted values respectively. Root mean square error (RMSE) is a measure o the variation of the predicted values from actual measured values. RMSE is always positive and approximately zero or low value of RMSE is an ideal (Liu and Bakker-Arkema, 1997). The expression for RMSE is shown in equation (6): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n �2 1X RMSE ¼ Xo Xp (6) n i¼1 4. Summary and conclusion Using thirty five years meteorological data obtained from Era Interim, statistical significant linked between surface data and refrac tivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km have been estab lished. Occurrence of ducting were only noticed at 0.1 km and 0.5 km, but disappeared at 1.0 km and 1.5 km. High and positive correlation exist between relative humidity and refractivity gradient aloft the alti tude, whereas negative correlation coefficient exist between surface temperature and refractivity gradient. From the analysis of variance techniques, a linear relation has been established between surface temperature, surface relative humidity and refractivity aloft. Statistical test on the predicted values from the developed model compared with ITU values revealed that the model performed well across the observed locations. Acknowledgments I acknowledge ECMWF for providing acess to the ECMWF data archive. References AbouAlmal, A., Abd-Alhameed, R.A., Jones, S.M.R., Al-Ahmad, H., 2015. New methodology for predicting vertical atmospheric profile and propagation parameters in sub-tropical Arabian Gulf region. IEEE Trans. Antennas Propag. 63 (9), 4057–4068. Adedayo, K.D., 2016. Statistical analysis of the effects of relative humidity and temperature on radio refractivity over Nigeria using satellite data. Afr. J. Environ. Sci. Technol. 10 (7), 221–229. Adediji, A.T., Ismail, M., Mandeep, J.S., 2014. Variation of radio field strength and radio horizon distance over three stations in Nigeria. J. Atmos. Sol. Terr. Phys. 109, 1–6.
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Linkage of meteorological parameters and anomalous radio propagation profile over Nigeria I. Emmanuel Physics Department, Federal University of Technology, PMB 704, Akure, Nigeria
A R T I C L E I N F O
A B S T R A C T
Keywords: Meteorological Linked Ducting Refractive
The vertical distribution of refractivity gradient is important in determining anomalous propagation condition. Thirty five years of meteorological parameters, obtained from Era-Interim archive of European Centre for Medium-Range Weather Forecasts has been used to analyze and investigated surface meteorological data linked with refractivity gradient aloft altitude across Nigeria. Spatial distribution of surface temperature, relative hu midity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km over Nigeria were plotted. Vertical dis tribution of temperature, relative humidity, refractivity and refractivity gradient were obtained for some locations across Nigeria. Similarly, spatial distribution of coefficient of determination between surface temper ature, relative humidity and refractivity gradient at four different height were estimated. Linear regression were developed to investigate the relationship between surface data and refractivity gradient at different altitude. The result revealed existence of sub refractive, super refractive, and ducting across the country at 0.1 km and 0.5 km however occurrence of ducting and sub refractive disappeared at 1.0 km and 1.5 km. Likewise, the existence of temperature inversion was noticed between surface and 100 m across all the locations except in Lagos. Values of refractivity across the observed locations converged around 0.5 km. Through result of correlation coefficient and statistical parameters, significant linked have been established between surface data and refractivity gradient at different height.
1. Introduction Tropospheric refraction significantly affect terrestrial propagation of electromagnetic radio waves at ultra-high frequency (UHF) and micro wave frequency (Adeyemi and Emmanuel, 2011; Hitney et al., 1985). Impair in the communication links (mobile radio communications, telecommunication and other wirelesss) are associated to small change in propagation medium of radio waves (Manjula et al., 2016). This effect is anchored on the refractive index which varies with atmospheric altitude due to non-uniform condition of the atmospheric parameters (Emmanuel et al., 2017; Sirkova and Mikhalev, 2004; Ulaby et al., 1981; Steiner and Smith, 2002). In troposphere radio waves emanated from terrestrial-based may be trapped or deflected toward or away from the surface known as anomalous propagation, due to the existence of different meteorological effects such as temperature inversion, high evaporation (Manjula et al., 2016; Kaissassou et al., 2015). Radio trap ping conditions produce signals multipath fading which vary with time, geographical location and radio frequency (Saleem, 2016; Emmanuel et al., 2018). Radio ducting is a function of vertical component of
atmospheric refractivity, within the troposphere, the variation of this component is linear in the lowest 1 km and exponential with geometric height above 1 km (Mufti and Siddle, 2012; Louf et al., 2015). The profile of the atmospheric refractivity gradient within 1 km altitude above the ground surface is highly vital in investigating anomalous propagation (Willoughby et al., 2002; Dairo and Kolawole, 2017; AbouAlmal et al.,2015; Adediji, 2017). Performance of communication garget, surveillance, wireless and radar system can be improved via the detail study and information provide from refractivity variability to the design engineers. This information is also useful in remote sensing. Foggy conditions (a situation where transmitted signal result to communication breakdown between receiver and transmitter) is one of the effect of refractivity variation on UHF (Alam et al., 2016). To minimize the effects of anomalous condition on microwave propagation, it is needful to investigate and document the meteorological link of at mospheric refractivity distribution at troposphere (Louf et al., 2015). Previous studies across Nigeria revealed seasonal, monthly, diurnal refractivity (Oyedum et al., 2011; Adediji et al., 2014); refractivity gradient condition (Adeyemi and Emmanuel, 2011) and the profile of
E-mail address: [email protected]. https://doi.org/10.1016/j.jastp.2019.05.011 Received 19 February 2019; Received in revised form 22 April 2019; Accepted 24 May 2019 Available online 1 June 2019 1364-6826/© 2019 Elsevier Ltd. All rights reserved.
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
refractivity below 500 m above the ground surface [14]. This paper showed detailed link between the surface temperature, surface relative humidity and refractivity gradient across Nigeria. Nigeria lies between latitude (4oN) and (14oN) and longitude (3oE) and (15oE) and has a total area of 923 770 km2. The total surface area of water bodies in Nigeria is estimated to be about 149,919 km2 which constitutes about 15.9% of the total area of Nigeria. The climate is tropical, characterized by high temperatures and humidity as well categorized into wet and dry seasons, nevertheless seasonal variation exist between South and North region. Total rainfall decreases from the coast northwards. The southern part (below Latitude 8� N) has an annual rainfall ranging between 1,500 and 4,000 mm and the extreme North between 500 and 1000 mm. Nigeria weather is govern by the tropical maritime (mT), the tropical maritime (cT) and equatorial easterlies which influence the migration of inter tropical discontinuity (ITD) (Emmanuel et al., 2017; Ojo, 1977).
refractivity gradient were observed across nine locations across Nigeria as shown Table 2. A linear link were also developed and validated for these locations (see Table 3). 3. Results 3.1. Spatial distribution of surface meteorological parameters and altitudinal anomalous propagation Using grads software spatial distribution of long term values of sur face relative humidity (H), surface temperature (T), refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km denoted by G 0.1km, G 0.5km, G 1.0km and G 1.5km respectively were plotted as shown in Fig. 1. Values of H decreases with increase in latitude across Nigeria. In coastal region, highest values of H ranges between 96% and 99% were obtained, whereas the lowest values ranges between 72% and 75% were observed in saharia region of Nigeria. This variation can be attributed to quantity of water vapour retain in the air in these regions. In another view, highest value of temperature was observed in Sokoto and part of coastal region, whereas lowest values of temperature is noticed around Jos plateau and Adamawa hill. This is in consonant with earlier finding in Adedayo (2016). The values of temperature oscillating between 292 K and 300 K across Nigeria. From G0.1 km distribution, ducting phenom enon are noticed in the part of sahara and part of the coastal area. This can be associated to nocturnal surface cooling and temperature inver sion (Von Engeln and Teixera, 2004). Sub refraction is observed in some of the inland region. Similarly, occurrence of ducting, super refractive and sub refractive were also observed across Nigeria at G0.5km. However, occurrence of super refractive is about 90% and 100% at G1.0km and G1.5km respectively across Nigeria. Occurrence of radio trapping disap pear at 1.0 km upward.
2. Data source and analysis Meteorological parameters (temperature, relative humidity) used in this work was obtained from the Era interim archive of European Centre for Medium-Range Weather Forecasts (ECMWF). The data which covered the period of thirty five years (1979–2014) was obtained for surface and four atmospheric pressure levels (1000 hPa, 950 hPa, 900 hPa and 850 hPa) and extracted for Nigeria. 2.1. Data analysis Surface refractivity and altitude refractivity were calculated from the obtained meteorological parameters using the expression in equation (1) ITU-R, 2016a,b: N ¼ 77:6
� e p þ 3:73 � 105 2 T T
(1)
3.2. Altitudinal variation of temperature, relative humidity, refractivity and refractivity gradient
where N is refractivity (N-units) correspond to either surface or any height above the ground, P represent pressure in hPa, T is temperature in kelvin and e is water vapour pressure in hPa. e is a function of relative humidity, H in % and temperature, t in degree Celsius as shown in equation (2) e¼
aH bt exp 100 tþc
Altitudinal distribution of temperature, relative humidity, refrac tivity and refractivity gradient across eight locations in Nigeria are presented in Fig. 2. This vertical variation of T, H and N follow similar trend across the observed locations. Kastina and Kano were leading in vertical temperature variation with Lagos, Ibadan and Akure lagging. The rate of change of temperature between surface and 100 m altitude are 8.3 � C/m, 1.8 � C/m, 25.7 � C/m, 26.5 � C/m, 32.9 � C/m, 10.4 � C/m, 3.3 � C/m, 9.9 � C/m and 18.7 � C/m in Lokoja, Lagos, Kastina, Kano, Jos, Ilorin, Ibadan, Akure and Abuja respectively (Fig. 2a). The rate of change in the northern region of the country is far higher than the southern region. In Jos, which is in high altitude (mountainous places) area experience low temperatures at the surface, this also contribute to the variation. However, temperature start to decrease at altitude 100 m upward. For relative humidity, negative rate of change is observed across all the locations and altitude (Fig. 2b). Aside from little variation of refractivity between surface and 100 m above the ground, refractivity profile decreases linearly with height (Fig. 2c). The rate of change across all the locations ranges between
(2)
where a, b and c are constants define in Table 1 (ITU-R, 2015). Refractivity gradient, G (N-units/km) is calculated using the expression in equation (3) (ITU-R, 2016a,b): G¼
Ns hs
N1 h1
(3)
Ns and N1 represent refractivity, N, at surface and at any particular height above the ground respectively and the corresponding height (km) is hs and h1 respectively. The analysis were carried out using relevant package such as excel, SPSS and matlab. Spatial distribution of some meteorological parameters and anomalous propagation at four different altitudes were examined. Long term spatial distribution of correlation coefficient between some meteorological parameters and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km were also analysed. Altitudinal variation of temperature, pressure, refractivity and
Table 2 Selected locations across Nigeria.
Table 1 Refractive conditions. Parameters
Water
Ice
A B C
6.1121 18.678 257.14 valid between
6.1115 23.036 279.82 valid between
40� to þ50�
80� to þ0�
2
Location
Latitude (degree North)
Longitude (degree East)
Lagos Ibadan Ilorin Akure Abuja Jos Lokoja Kano Kastina
6.52 7.38 8.48 7.26 9.08 9.90 7.80 12.00 12.51
3.38 3.94 4.54 5.21 7.40 8.86 6.73 8.59 7.61
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
(Fig. 2d). However, the values of G across the locations almost converge at 500 m and partially increase upward.
Table 3 Statistical parameters for surface relative humidity, temperature and profile refractivity gradient. Location
Altitude (km)
CD (%)
SE
P-value
Durbin-Watson
Lagos
0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5
51.0 38.5 38.1 35.3 47.7 57.0 47.6 37.0 76.3 68.7 56.9 45.5 41.4 67.0 52.3 38.8 92.5 91.0 82.5 72.6 89.6 88.7 80.4 67.9 93.0 91.1 82.5 72.6 90.0 88.0 75.4 66.0 89.9 84.8 72.4 63.7
43.1 19.8 11.4 8.2 64.4 17.8 10.8 7.8 72.6 20.9 12.1 8.2 71.0 16.7 10.3 7.3 77.3 13.6 9.8 6.8 64.2 13.8 9.2 6.5 77.3 13.6 9.8 6.8 66.1 11.5 8.1 5.4 88.5 17.3 11.4 7.4
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1.3 0.6 0.6 1.2 0.9 0.7 0.7 0.7 1.1 0.7 0.6 0.7 0.8 0.7 0.6 0.7 1.2 1.2 0.7 0.7 1.2 0.9 0.7 0.8 1.2 0.7 0.7 0.9 1.0 0.9 0.7 0.7 1.1 0.8 0.7 0.7
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
3.3. Correlation between surface relative humidity and refractivity gradient profile Fig. 3 represent the correlation coefficient of long term data (1979–2014) between surface relative humidity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km respectively. Positive correlation exist between H and G across the four points. At 0.1 km, the correlation between H and G 0.1 km varies between 0.1 and 0.98. Similarly, correlation coefficient varies between 0.008 and 1.05 at 0.5 km altitude. This show the degree of relationship between H and G. Monthly correlation between surface relative humidity, H, and G were also observed for six locations across Nigeria as represented in Fig. 4. 3.4. Correlation between surface relative temperature and refractivity gradient profile The spatial distribution of correlation coefficient between surface temperature and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km as presented in Fig. 5. Except in part of Atlantic Ocean where strong negative correlation exist, weak negative correlation exist be tween T and G0.1 km across Nigeria. However weak positive correlation are noticed in some northern part of the country. The correlation coef ficient here varies between 0.76 and 0.18. Similarly, correlation co efficient between T and G 0.5 km varies between 0.7 and 0.3. The result of other levels are also similar. Fig. 6 connote monthly correlation between surface temperature and refractivity gradient in six selected locations across the country. The correlation coefficient follow similar trend of Lagos and Ibadan. Strong negative correlation exist between T and G0.1km in October–May in the two locations. Negative deep was observed in July September. This period correspond to the peak of rainy season at three locations. Result of Abuja, Ilorin and Jos are similar with the value of correlation coefficient between T and G0.1 km oscillating between poor positive correlation and strong negative correlation. Strong negative correlation across most of the months at Kastina. Strong positive correlation exist between T and G0.5km, G1.0 km and G1.5km in
0.1 N-units/m and 12.1 N-units/m across the locations and altitude. Refractivity gradient, G, increases with height between 100 m and 500 m in Kastina, Kano, Lagos and Lokoja. Whereas, G decreases with height within this altitude in Abuja, Ibadan, Ilorin, Jos and Akure
Fig. 1. Spatial distribution of long term (1979–2014) (a) relative humidity, (b) temperature, (c) refractivity gradient at 0.1 km, (d) refractivity gradient at 0.5 km. (e) refractivity gradient at 1.0 km and (f) refractivity gradient at 1.5 km. 3
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 2. Vertical distribution of (a) temperature, (b) relative humidity, (c) refractivity and (d) refractivity gradient in Nigeria.
Fig. 3. Spatial distribution of correlation coefficient between relative humidity and refractivity gradient.
October–May at Lagos and Ibadan. This period correspond to the dry season and onset of rainy season. In Abuja, Ilorin and Kastina, strong/ moderate correlation exist between T and G at 0.5 km, 1.0 km and 1.5 km in most of the locations. Jos experienced exceptional variation in correlation coefficient oscillating between 0.008 and 0.98 across the months.
surface relative humidity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km. G ¼ γ þ αT þ βH
(4)
where γ, α and β are constants which are location and altitudinal dependent. From the relation, coefficient of determination (CD), standard error (SE), p value and Durbin-Watson were deducted for different location across Nigeria as shown Table 2. The Durbin Watson statistic which ranges between 0 and 4 is a number that tests for autocorrelation in the residuals from a statistical regression analysis. Positive autocorrelation exist when the values ranges between 0 and less than 2, while negative
3.5. Linear link between surface meteorological parameters and profile refractivity gradients Linear regression of the expression in equation (4) is constructed to investigate the statistical relationship between surface temperature, 4
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Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 4. Monthly distribution of correlation coefficient between relative humidity and refractivity gradient.
Fig. 5. Spatial distribution of correlation coefficient between temperature and refractivity gradient.
autocorrelation exist when the values is greater than 2 and less than or equal to 4. A value of 2 means that there is no autocorrelation in the sample. The p value across the stations and altitude is zero, this showed that the predictors (surface temperature and surface relative humidity) variables are significant in determining refractivity gradient. The values of Durbin-Watson across the locations and altitude are less than 2 which indicate positive autocorrelation between the surface data and profile refractivity gradient. The coefficient of determination, CD, which mea sures the extent that the dependent variable, G, can be predicted by the
independent variables (H, T) show a good result across the stations. Good CD established over all the staitons in Nigeria which is above 37%. Table 4 show the coefficient values of the constants in equation (4). Refractivity gradient values obtained from model linear regression were compared with the values obtained using ITU expression in equation (4). The values were subjected to mean bias error (MBE) and root mean square error (RMSE) test as shown in Table 5. Mean bias error show the average deviation of the predicted values from the actual measured values (Igbal and Muhammed, 1993). Positive values of MBE indicates 5
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
Fig. 6. Monthly distribution of correlation coefficient between temperature and refractivity gradient. Table 4 Coefficients values of the constants in the linear regression. Coefficients
Altitude (km)
Lagos
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
γ
0.10 0.50 1.00 1.50 0.10 0.50 1.00 1.50 0.10 0.50 1.00 1.50
246.50 152.00 685.30 748.20 10.59 4.50 4.19 3.55 33.40 11.29 5.01 2.40
4314.00 735.30 365.40 521.10 20.99 0.31 2.65 2.60 19.19 7.73 3.62 1.84
2403.00 936.00 397.60 619.10 15.67 1.13 2.35 2.69 23.09 5.55 2.42 1.14
61.85 1455.00 179.70 482.40 6.77 2.13 1.97 2.39 20.29 7.82 3.52 1.64
3796.00 216.90 550.40 675.10 19.91 1.52 2.89 2.88 21.23 6.17 2.52 1.13
3751.00 153.80 276.70 356.30 20.05 2.26 1.86 1.77 22.86 4.76 2.26 1.09
170.90 489.90 5.36 229.60 9.00 3.17 0.84 1.34 27.09 4.33 2.13 1.09
2477.00 667.30 545.20 459.50 16.22 3.69 2.58 2.03 24.47 3.86 1.65 0.77
2989.00 812.80 612.00 487.30 17.84 4.15 2.80 2.11 24.00 3.69 1.59 0.72
α
β
Table 5 Statistical test on predicted and observed refractivity gradient. Parameter
Altitude (km)
Lagos
Ibadan
Ilorin
Akure
Lokoja
Abuja
Jos
Kano
Kastina
ITU
0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5 0.1 0.5 1.0 1.5
129.59 85.80 74.26 76.59 137.28 86.03 73.48 75.98 0.90 0.04 0.01 0.00 22.02 0.20 0.12 0.09
29.44 69.07 67.11 72.26 45.10 67.68 66.11 71.62 0.24 0.04 0.01 0.00 16.91 0.22 0.13 0.09
8.69 67.51 67.39 71.82 18.10 62.76 64.98 70.17 1.79 0.04 0.00 0.01 33.00 0.28 0.17 0.11
59.51 54.45 61.07 68.30 50.91 53.23 58.20 65.18 0.83 0.06 0.02 0.03 32.83 0.26 0.15 0.10
61.23 77.31 68.70 72.51 91.16 75.62 68.24 73.01 1.00 0.06 0.02 0.02 52.25 0.25 0.14 0.10
0.88 65.44 63.52 67.75 19.66 63.36 60.76 65.45 0.37 0.07 0.01 0.02 3.45 0.31 0.15 0.10
54.28 36.04 57.96 64.00 47.69 38.19 54.67 61.52 0.12 0.58 0.02 0.02 2.22 12.87 0.17 0.11
299.65 108.27 85.70 78.97 263.02 108.60 80.78 77.02 0.32 0.05 0.04 0.02 3.36 0.17 0.12 0.08
326.68 117.94 88.46 80.67 289.79 108.90 84.75 78.43 0.35 0.06 0.03 0.02 3.03 0.15 0.11 0.08
Predicted
MBE
RMSE
6
I. Emmanuel
Journal of Atmospheric and Solar-Terrestrial Physics 191 (2019) 105047
overestimation, while negative values connote underestimation of the predicted values. The expression for MBE is shown in equation (5) MBE ¼
n 1X Xo n i¼1
Xp
�
Adediji, A.T., 2017. Reduced-to-sea-level value of microwave radio refractivity over three stations in Nigeria. Niger. J. Pure Appl. Phys. (NJPAP) 7 (1), 19–25. Adeyemi, B., Emmanuel, I., 2011. Monitoring tropospheric radio refractivity over Nigeria using CM— SAF data derived from NOAA — 15, 16 and 18 satellites. Indian J. Radio Space Phys. 40, 301–310. Alam, I., Mufti, N., Shah, S.A.A., Yaqoob, M., 2016. The effect of refractivity on propagation at UHF and VHF frequencies. Int. J. Antennas Propag. (4138329), 8. Dairo, O.F., Kolawole, L.B., 2017. Radio refractivity gradient in the lowest 100 m of the atmosphere over Lagos, Nigeria in the rainy-harmattan transition phase. Adv. Space Res. 167, 169–176. Emmanuel, I., Adeyemi, B., Ogolo, E.O., Adediji, A.T., 2017. Characteristics of the anomalous refractive conditions in Nigeria. J. Atmos. Sol. Terr. Phys. 164, 215–221. Emmanuel, I., Adeyemi, B., Adedayo, K.D., 2018. Estimation of refractivity gradient and geoclimatic factor for radio link design in Nigeria. Phys. Sci. Int. J. 19 (2), 1–9. Hitney, H.V., Richter, J.H., Pappert, R.A., Anderson, K.D., Baumgartner, G.B., 1985. Tropospheric radio wave propagation. Proc. IEEE 73 (2), 265–283. Igbal, M., Muhammed, A., 1993. An Introduction to Solar Radiation. Academic Press, Melbourne, Australia. ITU-R, 2015. Propagation Data and Prediction Methods Required for the Design of Terrestrial Line-of-sight Systems. International Telecommunications Union, Geneva. Recommendation of ITU-R P.530-16. ITU-R, P.453-12, 2016. The Radio Refractive Index; its Formula and Refractivity Data. Tech. rep. ITU, Geneva, Switzerland. ITU-R, P., 2016. Effects of Tropospheric Refraction on Radiowave Propagation, pp. 834–838. Kaissassou, S., Lenouo, A., Tchawoua, C., Lopez, P., Gaye, A.T., 2015. Climatology of radar anomalous propagation over West Africa. J. Atmos. Sol. Terr. Phys. 123, 1–12. Louf, V., Pujol, O., Sauvageot, H., Ri� edi, J., 2015. Seasonal and diurnal water vapour distribution in the Sahelian area from microwave radiometric profiling observations. Q. J. R. Meteorol. Soc. 2015 (141), 2643–2653. Liu, Q., Bakker-Arkema, F.W., 1997. Stochastic modelling of grain drying: Part 2. Model development. J. Agric. Eng. Res. 66, 275–280. Manjula, G., Roja Raman, M., Venkat Ratnam, M., Chandrasekhar, A.V., Vijaya Bhaskara Rao, S., 2016. Diurnal variation of ducts observed over a tropical station, Gadanki, using high resolution GPS radiosonde observations. Radio Sci. 51, 247–258. https:// doi.org/10.1002/2015RS005814. Mufti, N., Siddle, D.R., 2012. Determination of the effective earth radius factor and its impact on propagation of signals on over-sea paths in the English channel. In: Antennas & Propagation Conference. Loughborough, UK. Ojo, O., 1977. The Climate of West Africa. Heineman, London. Oyedum, O.D., Ezenworah, J.A., Igwe, K.C., Eichie, J.O., Moses, A.S., 2011. Diurnal and annual cycles of surface refractivity and related parametersin Minna, Central Nigeria. Nigerian J. Space Res. 10, 141–156. Saleem, M.U., 2016. Statistical investigation and mapping of monthly modified refractivity gradient over Pakistan at the 700 hectopascal level. Open J. Antenn. Propag. 4, 46–63. https://doi.org/10.4236/ojapr.2016.42005. Sirkova, I., Mikhalev, M., 2004. Parabolic-equation-based study of ducting effects on microwave propagation. Microw. Opt. Technol. 42, 390–394. Steiner, M., Smith, J.A., 2002. Use of three dimensional reflectivity structures for Automated detections and removal of non-precipitating echo in radar data. J. Atmos. Ocean. Technol. 19, 673–686. Ulaby, F.T., Moore, R.K., Fung, A.K., 1981. Microwave remote sensing fundamentals and radiometry. In: Microwave Remote Sensing: Active and Passive, vol. 1. AddisonWesley. von Engeln, A., Teixeira, J., 2004. A ducting climatology derived from ECMWF global analysis fields. J. Geophys. Res. 109 (D18), D18104. https://doi.org/10.1029/ 2003JD004380. Willoughby, A.A., Aro, T.O., Owolabi, I.E., 2002. Seasonal variations of radio refractivity gradients in Nigeria. J. Atmos. Sol. Terr. Phys. 64, 417–425.
(5)
where Xo and Xp are observed and predicted values respectively. Root mean square error (RMSE) is a measure o the variation of the predicted values from actual measured values. RMSE is always positive and approximately zero or low value of RMSE is an ideal (Liu and Bakker-Arkema, 1997). The expression for RMSE is shown in equation (6): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n �2 1X RMSE ¼ Xo Xp (6) n i¼1 4. Summary and conclusion Using thirty five years meteorological data obtained from Era Interim, statistical significant linked between surface data and refrac tivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km have been estab lished. Occurrence of ducting were only noticed at 0.1 km and 0.5 km, but disappeared at 1.0 km and 1.5 km. High and positive correlation exist between relative humidity and refractivity gradient aloft the alti tude, whereas negative correlation coefficient exist between surface temperature and refractivity gradient. From the analysis of variance techniques, a linear relation has been established between surface temperature, surface relative humidity and refractivity aloft. Statistical test on the predicted values from the developed model compared with ITU values revealed that the model performed well across the observed locations. Acknowledgments I acknowledge ECMWF for providing acess to the ECMWF data archive. References AbouAlmal, A., Abd-Alhameed, R.A., Jones, S.M.R., Al-Ahmad, H., 2015. New methodology for predicting vertical atmospheric profile and propagation parameters in sub-tropical Arabian Gulf region. IEEE Trans. Antennas Propag. 63 (9), 4057–4068. Adedayo, K.D., 2016. Statistical analysis of the effects of relative humidity and temperature on radio refractivity over Nigeria using satellite data. Afr. J. Environ. Sci. Technol. 10 (7), 221–229. Adediji, A.T., Ismail, M., Mandeep, J.S., 2014. Variation of radio field strength and radio horizon distance over three stations in Nigeria. J. Atmos. Sol. Terr. Phys. 109, 1–6.
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