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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) xxx-xxx

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Journal of Atmospheric and Solar-Terrestrial Physics

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journal homepage: www.elsevier.com

Radio refractivity gradients in the lowest in the rainy-harmattan transition phase

of the atmosphere over Lagos, Nigeria

O.F. Dairo∗⁠ , L.B. Kolawole Department of Physical Sciences, Redeemer's University, P.M.B. 230 Ede, Osun State 232102, Nigeria

ABSTRACT

Keywords: Radio refractivity Meteorology Ducting Late-monsoon Post-monsoon

Radio engineers and researchers in conjunction with the International Telecommunication Union (ITU) have established the pivotal role of radio refractivity to the propagation of electromagnetic energy in the troposphere. In particular, the refractivity gradient statistics for the lowest in the troposphere are used to determine the probability of occurrence of anomalous propagation conditions known as ducting. The major challenge to characterising the propagation condition over any environment is accessing the data of the lowest boundary layer of the atmosphere, which is highly dynamic and turbulent in evolution. High resolution radiosonde data from the Nigerian Meteorological Agency (NiMet) were used for a synoptic study of the rain-harmattan transition phase. The rain-harmattan transition phase marks the onset of the dry season due to the movement of the intertropical convergence zone interplay between (north-easterly and south-westerly) trade winds and monsoonal circulation. The lowest data were analysed to determine the frequency of ducting per month. Progressive increase in the occurrence of ducting was observed during the rain-harmattan transition phase, which coincides with the West African Monsoon retreat. The results show significant divergence from previous studies, which reported that the tropospheric condition over Lagos (Geo. N, E), Nigeria, is predominantly super-refractive.

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ARTICLE INFO

1. Introduction

As the urbanisation of coastal cities dramatically increases around the world, so the need for radar and microwave communication services continues to surge. It is important to improve on the previous radio meteorological studies over these regions in order to mitigate the adverse effects of weather on radio propagation (Falodun and Ajewole, 2006; Falodun and Kolawole, 2004; Falodun and Okeke, 2013; Hughes, 1993; Kolawole, 1993, 1981; Owolabi and Williams, 1970; Willoughby et al., 2002). The weather phenomenon occurs in the troposphere, which is the lowest atmosphere with almost all the atmospheric water vapour content. Meteorological conditions are in one way or the other an interplay between temperature and water vapour. Latitudinal variation of water vapour is observed over the Earth, with the poles having the lowest concentration and highest over the tropics. Water vapour in the form of hydrometeors, such as fog, clouds or rain, significantly affects microwave frequency above , making radio propagation

challenging in the tropics, particularly, in the coastline (Zheng and Han-Xian, 2013). The prevalence of sea and land breezes which play a major role in the development and intensification of weather events in the coastal cities accounts for the high concentration of water vapour (Gadgil, 2003; Leroyer et al., 2014; Sikka and Gadgil, 2003, 1980). Lagos (Geo. N, E), Nigeria, being a coastal city in the tropics, is one of the most populous coastal cities in the world and not alien to these weather anomalies. This study builds on previous studies (Adediji et al., 2013; Adediji and Ajewole, 2010; Ali et al., 2011; Ayatunji et al., 2011; Falodun and Lawal, 2015; Igwe and Adimula, 2009; Kaissassou et al., 2015; Kolawole, 1983; Okoro and Agbo, 2012) using three months of radiosonde data to gain further insight into the coastal-urban atmospheric boundary layer (ABL) evolution of radio refractivity in the lowest . The data spatio-temporal resolution is . As a preliminary guide to the prevailing propagation conditions over this coastal city, the onset of the dry season, between September and November, serves as the rain-harmattan transition phase and is chosen for consideration. The seasonal rain-harmattan transition

Abbreviations: ITU, ; International Telecommunication Union, ; LMM, ; Late monsoon month, ; NiMet, ; Nigerian Meteorological Agency, ; PMM, ; Post monsoon months, ; WAM, ; West African monsoon, ∗ Corresponding author. Email address: [email protected] (O.F. Dairo) https://doi.org/10.1016/j.jastp.2017.12.001 Received 28 July 2017; Received in revised form 21 November 2017; Accepted 1 December 2017 Available online xxx 1364-6826/ © 2017.

O.F. Dairo, L.B. Kolawole


phase, is dry and characterised by dust-laden north-easterly wind, which pushes southwards towards the coastal cities of West Africa due to the West African Monsoon (WAM) (Cornforth, 2013; Janicot et al., 2011, 2009; Redelsperger et al., 2006; Thorncroft and Lamb, 2005) as part of the global circulation system (Ramage, 1971; Webster, 1987) in response to the Madden-Julian Oscillation (MJO) (Hsu and Lee, 2005; Lavender and Matthews, 2009). The transition occurs in rain-harmattan phase (Aro and Willoughby, 1992), also known as monsoon-post-monsoon transition phase (Kulshrestha and Chatterjee, 1966, 1967). Willoughby et al. (2013) reported low variability of radio refractivity at Ota (Geo. N, E), Nigeria, during the monsoon. A major challenge, not to be neglected, is the inability of the previous instruments deployed to represent small-scale features in the lowest troposphere, which were captured by Falodun and Kolawole (2005) at Akure (Geo. N, E), Nigeria and Řezáčová et al. (2003) from 304 m a.s.l. to ∼404 m a.s.l. at Prague-Libnus Station, Czech. Hence, the major interest of this study in the lowest troposphere is because most radio antennas are located within this region of the ABL, particulary, the lowest . Insight into the local refractive condition is crucial for space-time estimation and prediction of radar and microwave ranges. The ABL extends from the surface to an altitude of depending on the thermal convective conditions in the afternoon and classified thus: the skin layer - a few centimetre deep, the surface layer - typically 10 m–100 m and the outer layer - from the top of the surface layer to the height of the ABL (Sikka and Narasimha, 1995).

lated to refractivity, N, as (5), (5)

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For example, a typical value of n = 1.000378 was observed at the Earth's surface in January 2014 for Lagos ( N, °E), Nigeria (Falodun and Lawal, 2015). Consequently, radio engineers have found it convenient to work with the term radio refractivity (6) to ease knotty mathematical manipulations. (6)

The radio refractivity, N, is a function of the local meteorological parameters and formalised as (7) (ITU-R P.453-12, 2016) (7)

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where, is the total atmospheric pressure the absolute air temperature and the water vapour pressure. Radio refractivity formula (7) is reduced to a two-term expression with trade-off within 0.02% of the values obtained in (7) for the temperature range from − 50°C to + 40°C as (8)

N (8) is commonly rewritten as (9) using the Clapeyron formalism:

2. Propagation theory

The fluctuating radio refractive index, n, of the troposphere refracts and scatters electromagnetic waves propagating in the troposphere. Hence the variation of the electric field intensity of a plane wave propagating in the troposphere results in the changes of the intensity, direction and coherence (Doss-Hammela et al., 2015). The electric field in a region of refractive index, n, is given as a function of space and time in equations (1)–(3) (Barclay, 2003; Syms and Cozens, 1992)

(9)

Vis-à-vis N (eqn. (8)) expression, the dry term and wet term are due to the polarisability of both non-polar (chiefly, nitrogen and oxygen) and polar (mainly, water vapour) molecules, respectively. 4. Anomalous propagation: ducting and multipath

(1)

is

(2) (3)

The refractivity gradient dN/dh obtained from the derivative of (9) (10)

where (10) is rewritten to show the sensitivity of N to meteorological parameters

where, ω = 2πf, k0 is a space vector normal to the wave front with a magnitude equal to the free-space wave number, r the space vector and t time. As a matter of fact, the refractive index of the troposphere cannot be regarded as constant at microwave frequencies because the relative permittivity is a function of frequency. Therefore, the spatio-temporal variations of the electric field of the plane wave is accounted for in (4):

(11)

From equation (11), the two processes that can cause high refractivity lapse rate are:

(4)

The observation of the variability of n(r) is fundamental to the understanding of propagation of electromagnetic waves through the troposphere. In fact, according to (2), the propagation constant of the medium is related to propagation constant of free-space by the refractive index. The variation in n(r) is a function of the local atmospheric environment and constituents.

1. A rapid decrease in water vapour pressure with height, de/dh, and 2. An increase in temperature with height, dT/dh > 0. Evidently, these mechanisms occur simultaneously. The hydrostatic pressure gradient, dP/dh, never deviates much from its standard value because winds rapidly restore pressure equilibrium. The first term occurs at the rate of in the lowest atmosphere, while the second and third terms usually occur closer to the earth surface where high pressure exists and are subject to strong variations of local weather conditions. The second term takes a negative sign with temperature inversion, dT/dh > 0, making the value of dN/dh more nega

3. Formalism of radio refractivity

The observed variability of n(r) diverges from unity (which is that of free-space) in parts per million. Hence, the refractive index, n, is re

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tive. Similarly, a rapid decrease in relative humidity with height makes the third term more negative, thereby resulting in more negative dN/dh , known as high refractivity lapse rate. In radio engineering, the effect of the vertical lapse rate of refractivity, dN/dh, on wave propagation is largely grouped into four categories, namely sub-refraction, standard refraction, super-refraction and ducting (Fig. 1). A radiowave propagation duct is formed if refractivity gradient, dN/dh, exceeds , as a result of the cumulative effect of the two processes responsible for high refractivity lapse rate. The occurrence of large-scale refractivity effects inducing ducting results in bending of radio waves downward with a curvature greater than that of the Earth. In other words, the wave is bent backward from the incident boundary towards the emergent boundary. This may lead to trapping of radiowaves between a boundary or layer in the troposphere and the Earth's surface, which is known as surface duct. In addition, the radiowave may be trapped between two boundaries in the troposphere, which is known as elevated duct (Barclay, 2003; Baumgartner et al., 1983). Radiowave becomes trapped within a super-refractive layer when it has two tangents in the layer. In this waveguide-like propagation, very high signal strengths can be received at very long range (far beyond line-of-sight) and the signal strength may exceed its free-space value (Akiyama, 1977; Bean et al., 1966). This propagation mechanism is sometimes referred to as anomalous propagation (AP) known as ducting. The layer where it occurs is known as a ducting layer. AP of signals may lead to interference between widely separated microwave links operating on the same frequency subject to the prevailing meteorological conditions at both locations (Mufti and Siddle, 2012). Typically, ducting occurs in the lowest with majority of occurernce below . The term ‘multipath’ is often used to describe the situation where radio waves propagate from transmitter to receiver by more than one path, especially on a line-of-sight link (Samir, 1993). The secondary path may occur by ground reflection or by refraction. The distinction between ducting and multipath caused by interference between two or more refractive paths through the atmosphere is more of a descriptive convenience than a fundamental difference in mechanism (Dennis and John, 1992). At longer (trans horizon) ranges, the number of multiple paths becomes very large, and it is more appropriate to use models based on ducting theory.

tion condition of geometrical-optics, the maximum angle of incidence (degrees) is related to the change in refractivity ΔN (N − units) across the layer by (12)

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As ΔN in (12) rarely exceeds , θimax is limited to 0.5? − 1?. The geometrical consideration of the Earth's curvature shows that the angle of incidence of a wave propagated horizontally intercepting an elevated layer is nonzero. The implication is that terrestrial radio links will not be significantly affected by the occurrence of ducting layers at altitudes higher than about . However, satellite and radar communications are not spared at higher altitudes (Battaglia et al., 2015, 2006). The field strength of the ducted energy is a function of the frequency and path geometry. Likewise, the strength of the duct for a simple case of surface or elevated duct is expressed in terms of the maximum wavelength (or minimum frequency) trapped by the duct is expressed by (Brooks et al., 1999) (13)

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where λmax is the maximum trapped wavelength (m), St the duct thickness, Ss the duct strength and CS = 3.77×10 − 3 for surface duct ( CE = 5.66×10 − 3 for elevated duct) (Turton et al., 1988). Typically, the cutoff wavelength (13) for a duct is not abruptly defined due to the graded nature of the index of refraction of the atmosphere. Hence, wavelengths longer than λmax will be ducted to some extent. In other words, a duct is not a perfect waveguide for wavelengths shorter than λmax, which implies that duct will always be leaky and some energy will be lost. The strongest coupling of energy into or out of a duct occurs when both the transmitter and receiver lie within the duct (Barclay, 2003; Dougherty and Hart, 1976). Ducts are expressed in terms of the modified radio refractivity, M, as (ITU-R P.453-12, 2016) (14)

where is the height. The predominant feature of a duct is a ducting layer which is characterised by a negative M gradient of equation (14). Its top and bottom are at the elevations where the relative minimum and maximum of M are respectively attained (Saxton, 1951). The useful property of M profiles is the readily recognisable dM/dh value less than zero for ducting conditions, which appears left of the dM/dh = 0 line. Ducts are characterised by their strength, or and their thickness, or , for both surface and elevated ducts, respectively. The strength is the M lapse, ΔM and the thickness is the difference in height between the top and bottom, Δh , across the ducting layer (Fig. 2). Elevated ducts are further characterised by two additional parameters: namely, the base height of the duct, and the height within the duct of maximum M, . The existence of ducts is important because they can give rise to anomalous radiowave propagation, particularly on terrestrial or very low-angle earth-space link. Ducts provide a mechanism for radiowave signals of sufficiently high frequencies to propagate far beyond their normal line-of-sight range, giving rise to potential interference with other services (Tatsuo, 1993). At microwave frequencies, where the typical dimensions of a duct are large compared with the wavelength, geometrical optics in the form of ray can be used to provide insights into the interrelation among such parameters as the amplitude, angles of arrival and time delays of multiple atmospheric rays under specified conditions. It should be noted that “trapping” of radio rays within the duct occurs only for relatively shallow angles of elevation. For the simplified case of a ‘normal’ refractivity profile above a surface duct having a fixed refractivity, the critical elevation angle, αc, for rays to be

5. Propagation in ducting layers

A ducting layer is known to trap radio waves if certain geometrical constraints apply. For coupling of electromagnetic energy into a duct, the angle of incidence of the radio wave at the layer boundary must be very small. According to Barclay (2003), using the total-internal-reflec

Fig. 1. Refraction classifications (Turton et al. 1988).

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stratosphere ( ). In most cases, NiMet filters out the fine structure of the atmosphere, thereby limiting the scope of the high resolution radiosonde data available for this work. Hence only three months of fine structure radiosonde data were obtained from NiMet for this study. However, for the purpose of radioclimatological studies such daily fine structures are required. According to the African Monsoon Multidisciplinary Analysis (AMMA), the only available fine structures were thus classified as a special observing period (SOP), which focused on the details of ducting from the late monsoon month (LMM) to post monsoon months (PMM) (Redelsperger et al., 2006). The SOP data were analysed for the occurrence of ducting and the results have been plotted for both the N and M-gradient profiles. MATLAB (2014b and 2015a) software was used to process the data and to plot the graphs. For the purpose of estimating the radio refractivity gradient, ΔN, of the lowest and of the troposphere, which are considered necessary for ducting observation (ITU-R P.834-8, 2016), each ascent data was grouped such that between the surface and was classified as the lowest , while between the surface and was classified as the lowest . Therefore, refractivity gradient of the lowest , ΔN65 = N∼65 − Ns, while that of the lowest , ΔN100 = N∼100 − Ns. 7. Results and analysis

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Fig. 2. Definition of parameters describing a) surface, b) elevated surface and c) elevated ducts (ITU-R P.453-12, 2016).

A progressive increase in occurrence of ducting was observed from late monsoon month (September) to the post-monsoon months (October–November), i.e., LMM-PMM transition phase. According to Falodun and Kolawole (2005); Falodun and Lawal (2015); Kulshrestha and Srivastava (1990), the coastal areas are more prone to super-refraction and that lowest values of refractivity gradient are observed during monsoon months, where the frequency of occurrence of ducting may be considered lowest. As a result, both the N and M-gradient profiles (Figs. 3–8) of the LMM-PMM transition phase show an increasing frequency of high refractivity gradients. In Fig. 3, the N profile of 14 September 2013 shows strong vertical decrease of radio refractivity with height, which corresponds to steep negative M gradient of the same in Fig. 4. Similarly, the N profiles of 2 and 29 September 2013 were observed with marked vertical decrease of radio refractivity with height corresponding to marginal negative M gradients in Fig. 4. Hence the N profiles of 2, 14 and 29 September 2013 showed the occurrence of surface ducts seen in Fig. 4 and all appeared to the left of the black vertical line. The black vertical line has a

trapped is given by the expression (ITU-R P.834-8, 2016) as (15)

(15)

where Δh is the thickness of the duct (height of duct top above antenna). It should be noted that the existence of a duct, even if suitably situated, does not necessarily imply that energy will be efficiently coupled into the duct in such a way that long-range propagation will occur. In addition to satisfying the critical elevation angle condition (15), the frequency of the wave must be less than a critical value determined by the physical depth of the duct and by the refractivity profile. Below this minimum trapping frequency, every increasing amount of energy will ‘leak’ through the duct boundaries.The dearth of both spatio-temporal properties of ducting and resolution of radiosonde data in the lowest troposphere gave birth to a proposed analytical approach (16) to model refractivity profiles (Grábner and Kvičera, 2011; Ikegami et al., 1966; Webster, 1990): (16)

where the refractivity , the gradient , the duct depth , the duct height and the duct width are model parameters. 6. Methodology

The source of refractivity data is the radiosonde. A radiosonde is a freely ascending, gas-filled balloon carrying aloft an instrument package. The instruments measure the meteorological data such as pressure, temperature and relative humidity, from which other derived parameters (radio refractivity, refractive index and altitude) are obtained along the ascent. The sampled data from the throw-away sensors is transmitted from the portable instrument to a receiver on the ground. The radiosonde is launched daily by NiMet upper air station in Lagos at 12:00 h LT. The radiosonde is capable of profiling the fine structure, which is in vertical resolution of the atmosphere up to the

Fig. 3. Typical September N profiles for ducting layers.

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Fig. 4. Typical September M gradient profiles for ducting layers.

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Fig. 7. Typical November N profiles for ducting layers.

Fig. 8. November M gradient profiles for ducting layers.

modified refractivity gradient value of zero, i.e., dM/dh = 0. For M gradient less than zero, such that dM/dh < 0, atmospheric ducts occur. In other words, any M gradient to the left of the black vertical line is a duct bending electromagnetic energy towards the surface at low latitudes (Liao et al., 2016). On the other hand, the slant black line has positive M gradient, i.e., dM/dh = 78. Hence for any M gradients having its value within the boundary 0 < dM/dh < 78, i.e., the region between the black vertical line and the slant black line is classified as super-refractive. In other words, the atmospheric condition of the layer is super-refractive and refracts signals beyond the radio horizon. However, the lapse rate of the N profile of 10 September 2013 in Fig. 3 is not readily noticed at the surface to exhibit the formation of a duct, which is readily seen in its M gradient profile in Fig. 4. The M-gradient profile of 10 September 2013 is an elevated duct. In turn, the high refractivity gradient has favoured an increase in the occurrence of ducting. The high-refractivity gradients during the SOP in Lagos are due to the interaction between high moisture content sea breeze and the onset of high insolation regime in the surface layer. The increasing frequency of occurrence of ducting is due to the onset of phase reversal of the inter-tropical discontinuity (ITD) from northward shift during the monsoon to southward during the post-monsoon regime. The southward movement of the ITD is the phase re

Fig. 5. Typical October N profiles for ducting layers.

Fig. 6. Typical October M gradient profiles for ducting layers.

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versal of the monsoon, which brings in the dry harmattan spell known as dry season in Nigeria. The dry, warm air overlays the high moisture sea breeze during the phase reversal of the monsoon season. Consequently, the high water vapour gradient and the temperature inversion occurring simultaneously (equation (11)) in the surface layer result in ducting. Super-refraction dominates the LMM-PMM phase in the outer layer of the ABL (Figs 9–11). Figs 9–11 are extensions of the M gradients (Figs. 4, 6 and 8) and revealed that above an altitude of up to the atmosphere over Lagos is predominantly super-refractive. In other words, above the atmospheric condition is between the two black lines, i.e., the region with a modified refractivity gradient between dM/dh > 0 and dM/dh < 78 is defined as super refraction. The statistics of the refractive conditions observed in the lowest during the LMM-PMM transition phase are thus tabulated (Table 1). According to Table 1, September, the LMM, recorded the least occurrence of ducting in the lowest with super-refraction being the dominant refractive condition. During the northward latitudinal drift of the West African monsoon (WAM), which is a highly variable climate system, the rain belt abruptly shifts northward to the Sahel as the low-level moist southwesterly flow is diverted inland between the Atlantic cold tongue and the Saharan heat low (Cornforth, 2013; Peyrillé et al.,

Fig. 11. Typical November M gradient profiles in first kilometre.

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Table 1 Typical Refractive Conditions in the lowest (

).

Refractive Condition

SEPT (%)

OCT (%)

NOV (%)

Ducting Super-refraction Standard refraction sub-refraction

17 50 0 33

42 27 8 23

43 14 11 32

2007; Thorncroft et al., 2011). In the other words, the ITD shifts northwards and the dry, northeasterly trade winds (locally known as harmattan) are pushed back towards the northern latitudes (Cornforth, 2013). The northward shift of the monsoon ushers in warm and dry air over Lagos resulting in the low frequencies of ducting observed in September LMM. At this time, the monsoon is over the northern part of Nigeria ushering in the northern rainy season and resulting in low humidity gradient over Lagos. Consequently, the LMM phase marks the onset of the WAM retreat, with increasing moisture content at the surface layer and a layer of very low temperature gradient or temperature inversion just above the skin or surface layer. The retreat hits the Lagos coast during the PMM, bringing in the second rainy season observed in the West African coastal cities (Cornforth, 2013). This southward drift increases vapour gradient at the skin and surface layers with an overlay of positive or very low temperature gradient. The dynamics of this retreat with a quasi-static underlay increases the occurrence of ducting in the lowest troposphere during the PMM. The chances of occurrence of ducting decrease with altitude (Figs. 4, 6 and 8 and 9-11) from 17%, 42% and 43% in the lowest to 4%, 27% and 19% in the lowest during the LMM-PMM transition phase namely, September, October and November, respectively. Considering the statistics of the total typical refractive conditions during the LMM-PMM transition phase highlighted in Table 2, from the skin layer to the surface layer ( ), the highest occurrence of ducting

Fig. 9. Typical September M gradient profiles in first kilometre.

Table 2 Typical refractive conditions during LMM-PMM phase.

Fig. 10. Typical October M gradient profiles in first kilometre.

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Refractive Condition

SEPT (%)

OCT (%)

NOV (%)

Ducting Super-refraction Standard refraction sub-refraction

18 50 0 32

48 22 22 8

43 14 11 32



African coastal cities are thought to be necessary to better understand the development of radio propagation anomalies and its interplay with the West African monsoon driving the deep convection into the tropopause. Both satellite and terrestrial radio communications in this region suffer significant variability and attenuation resulting from refraction, scattering and defocussing of electric fields, particularly, while watching interesting events on the television or internet.

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was observed in October. Similarly, the highest variability of refractivity gradient was observed in October, ranging from 57.77M-units/km to 57.86M-units/km in the lowest to , respectively. In September, the range of variability is from 37.73M-units/km to 47.6M-units/ km, and in November from 40.41M-units/km to 44.59M-units/km in the lowest to , respectively. On the average, the dominant refractive condition observed during the LMM-PMM transition phase in the lowest 100 m is ducting, with 36% average chances of occurrence on the overall (Table 2). Super-refraction trails ducting with 29% average of occurrence. On the contrary, Igwe et al. (2011) observed predominant 50% sub-refractive conditions in the first over Minna (Geo. N, E), North Central, Nigeria, with 40% and 10% super-refractive and normal refractive conditions, respectively, which is typical of Sahelian climatic zone. These results are inconsistent with the ITU values and statistics (Falodun and Okeke, 2013). The convergence of the refractive conditions to super-refraction in the upper ABL highlights a correlation between an increasing reflectivity and rainfall rates close to the ABL using the precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM), which provides a unique three-dimensional rainfall structure measurements between latitudes S and N (Hamada and Takayabu, 2014). In fact, Sohn et al. (2013) examined the PR echo profiles over Korean Peninsula and demonstrated that heavy rainfall in this region is associated more with low-level clouds rather than deep convective clouds (Song et al., 2017). Houze (2010) and Romatschke et al. (2010) corroborated the propagation effects of hydrometeors by using the reflectivity of 3-D PR to define extreme convective system. These capture some of the attendant effects of weather on radio communications in the tropics, where Nigeria is located (Hirose et al., 2009).

Acknowledgments

The authors would like to thank the Nigerian Meteorological Agency (NiMet), Mr. Abayomi Vincent Ezimene, Head, Oshodi, Lagos Data Centre of NiMet and Dr. Anthony C. Anuforom, the former Director-General/CEO of NiMet for the data, his support and approval to access the Upper Air data, respectively. Appendix A. Supplementary data

Supplementary data related to this article can be found at https:// doi.org/10.1016/j.jastp.2017.12.001. Funding

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References

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8. Conclusion

The statistics of the radio refractivity gradients in the lowest of the atmosphere over Lagos, Nigeria have shown the significance of the need to study the anomalous propagation conditions over West African coastal cities. This is because the rainfall cycle across West Africa, which results from the northward drift of the low-level monsoon flux from March to August and its southward retreat during September to November, would significantly affect radio communication. Particularly, the LMM-PMM transition phase, which is the SOP of this work, shows the dominance of ducting in the lowest against the backdrop of earlier reports. Also, it confirms the oscillation of the Inter Tropical Front (ITF, popularly known as Inter Tropical Discontinuity, ITD), which is formed when the humid air masses of the WAM meet the drier and warmer air northeasterly from the Sahara desert. The monsoon pushes the ITD northward latitudinally which later retreats during the post monsoon. The southward oscillation of the ITD is responsible for the second rainfall cycle, which results in the high variability of the refractivity gradient within the surface layer of the ABL during the LMM-PMM. The lowest of the troposphere over Lagos is characterised by ducts of two types, namely surface duct and elevated surface duct during the LMM-PMM transition phase. In general, the chances of occurrence of ducting over the coastal city is high during the SOP while super-refraction dominates the outer ABL. Highest variability of the refractivity gradient is observed in the PMM, particularly in October. However, the statistics of the LMM-PMM transition phase may not totally explain the spatio-temporal evolution of ducting and seasonal variability of duct formation in the lowest troposphere. For instance, the ABL over Lagos, being a coastal city located in the low-latitudes, is strongly affected by dynamic forcing of the land-sea breeze evolution pre-WAM, during WAM and post-WAM. Therefore, more frequent and high resolution radiosonde or other observations of ABL along the West

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