Vertical Refractivity Gradient Research Articles

Exploring vertical gradients of radio refractivity and their significance for radio wave propagation in Abuja, Jos and Makurdi of North-Central Nigeria

Vertical radio refractivity gradients are essential for monitoring propagation conditions when designing and planning terrestrial radio links for communications in the lower atmosphere. Average data gathered from meteorological factors such as temperature, pressure, and relative humidity was used from 1980 to 2020 n this study. This study focuses on the vertical gradient of radio refractivity within the lower atmospheric layer, investigating its influence on factors like signal propagation, route clearance, and line-of-sight communication. The analysis encompasses three cities - Abuja, Makurdi, and Jos. In Figure 2 monthly average changes in the refractivity gradient are presented for Abuja. In addition, the seasonal radio refractivity gradient shows mean values of -110.000N/km for Abuja which shows that the refractivity condition is Super-Refraction, -77.553N/km for Jos which shows that the refractivity condition is Normal-Refraction and -97.209N/km for Makurdi which shows that the refractivity condition is Normal-Refraction respectively. Higher gradient values, G1, G2, and G3 were observed during the dry season (December-February) which could be attributed to dry air and steeper refractivity gradients. In contrast, lower gradient values were observed during the wet season (June-October) due to increased atmospheric moisture. Similarly, measured vertical radio refractivity gradient data, G1 N/km, G2 N/km, and G3 N/km for Jos displayed consistent fluctuations throughout the year. Similarly, measured vertical radio refractivity gradient data, G1 N/km, G2 N/km, and G3 N/km for Jos displayed consistent fluctuations throughout the year. Notably, wetter months exhibit higher refractivity gradient values, while drier months show lower values. G2 consistently records the highest gradient values, and despite varying magnitudes, the trends remain consistent. Finally, measured vertical radio refractivity gradient data, G1 N/km, G2 N/km, and G3 N/km for Makurdi indicate distinct fluctuations with the most negative values observed in November and December. The Dry Season witnesses relatively lower gradient values, while the Transition and Wet Seasons experience rising values, influenced by atmospheric shifts. The Higher negative values during the wet season suggest pronounced variations in the refractive index, affecting radio wave propagation. These findings emphasize the significance of refractivity gradient variations and their implications for radio wave behaviour particularly during different seasons.

Tropical Cyclone Planetary Boundary Layer Heights Derived from GPS Radio Occultation over the Western Pacific Ocean

According to GPS radio occultation data from previous studies, the height of the planetary boundary layer (PBLH) is defined as the altitude at which the vertical gradient of refractivity N is at its local minimum, called the gradient approach. As with its density, the atmosphere’s refractivity falls broadly exponentially with height. The spherically symmetric refractivity Nss(r) was established to account for the standard deviation of atmospheric refractivity with altitude. Ni is the residual from the fundamental vertical variations of refractivity, defined as Ni(r) = N(r) − Nss(r). In this study, the vertical gradient of N is replaced by the vertical gradient of Ni to optimize the gradient approach, called the local gradient approach. Using the US radiosonde and Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) radio occultations (ROs) data from 2007–2011, these two PBLH-determining approaches are evaluated. The PBLHs estimated by the gradient approach and the local gradient approach have RMSE values of 0.73 km and 0.65 km, respectively. The PBLH obtained by the local gradient approach is closer to the radiosonde-derived value. In this paper, the COSMIC-2 ROs data and the western Pacific typhoon best track data are collocated in time and space during 2020–2021, and the axisymmetric composite structural characteristics of the tropical cyclone (TC) PBLs are analyzed. The lowest vertical gradients of N and Ni of TCs correspond closely with the average PBLHs. We find that the mean PBLHs of tropical depressions (TD), tropical storms (TS), and typhoons (TY) all have their local maxima at a radial distance of 125 km with heights of 1.03 km, 1.12 km, and 1.36 km, respectively. After 375 km, 575 km, and 935 km of TD, TS, and TY radial distances, the mean PBLHs become stable and cease to vary. The mean PBLH undulations increase significantly with the increase in tropical cyclone intensity. Niwet is the residual from the fundamental vertical variations of wet refractivity, defined as Niwet(r) = Nwet(r) − Nsswet(r). Local minima of Niwet and Ni vertical gradients of TD, TS, and TY have comparable distributions and are concentrated between 0.5 km and 1 km.

Evaluation of GNSS Radio Occultation Profiles in the Vicinity of Atmospheric Rivers

Increasing the density of Global Navigation Satellite System radio occultation (RO) with commercial Smallsats and the next generation COSMIC-2 constellation is expected to improve analyses of the state of atmosphere, which is essential for numerical weather prediction. High vertical resolution RO profiles could be useful to observe atmospheric rivers (ARs) over the ocean, which transport water vapor in shallow, elongated corridors that frequently impact the west coasts of continents. The multi-year AR Reconnaissance campaign has extensively sampled ARs over the northeastern Pacific with dropsondes, providing an invaluable dataset to evaluate the reliability of RO retrievals. These dropsondes, and a reanalysis product that assimilates them, are compared to three RO datasets: (1) established operational missions, (2) COSMIC-2, and (3) the commercial Spire constellation. Each RO dataset has biases relative to reanalyses of less than 0.5% N in the upper troposphere and negative biases in the lower troposphere. Direct colocations with dropsondes indicate that vertical refractivity gradients present within ARs may be contributing to negative biases at higher altitudes inside than outside ARs, where the greatest variability and vertical gradients are at the well-defined boundary layer top. Observations from Spire are overly smooth, affecting the ability to resolve the low-level structure of an AR. Surprisingly, the depth of penetration into the lower troposphere is greater inside an AR than outside for all datasets. The results indicate that the observation errors used for assimilation of RO within ARs should consider the height dependent biases that are associated with the structure of the atmosphere.

COSMIC-2 RO Profile Ending at PBL Top with Strong Vertical Gradient of Refractivity

The Formosa Satellite-7/Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (Satellite-7/COSMIC-2), which was successfully launched on 25 June 2019, provides dense radio occultation (RO) observations over the tropics and subtropics. This study examines the RO-observed lowest altitude and its possible relationship to refractivity gradients and planetary boundary layer (PBL) heights. COSMIC-2 RO data over the Southeast Pacific region (SEP) and the South-Central Pacific (SCP) from August 2020 are employed to determine their RO-observed lowest altitudes, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis data are used to obtain the gradients of refractivity. Results show that there are no ray perigees below the PBL top when the vertical gradient of N−N(r) is strong (<−65 N-unit km−1), where N(r) represents the vertical profile of the spherically symmetric refractivity. Significantly strong local vertical gradients due to atmospheric ducting occur more frequently over the SEP than the SCP areas. For some cases, a strong local horizontal gradient of refractivity in the tangent direction of a ray near its perigee point can also limit the RO profile from going further below even when the vertical gradient of N−N(r) is relatively weak. Fortunately, only about 0.6% COSMIC-2 RO profiles are unaffected by the above factors but cannot observe below 2-km altitude.

Determination of radio wave propagation conditions in the atmosphere of Hanoi using the meteorological data

This article uses the data of radio occultation and the radiosonde data to determine radio refractive index and wave propagation conditions in the atmosphere of the Hanoi area. The content of this article uses the data of radio occultation in 2014-2016 and the radiosonde data in 2016-2018, showing that the radio refractive index tends to decrease with altitude, the maximum average value of radio refractivity is 370 N-units, the largest radio refractivity difference between years is not more than 11 N-units, at high altitudes the radio refractivity value is close to the value at standard model of the ITU-R while at a small altitude the difference between the model value and the observed value is up to 60 N-units, the vertical gradient of refractivity and the effective earth radius coefficient is independent with altitude. Based on radio refractivity, it is possible to determine tropospheric delay, which is input data for problems such as satellite positioning, altimetry satellite and under-the-horizon radar.

Raytracing Simulated GPS Radio Wave Propagation Paths Experiencing Large Disturbances When Going through the Top of the Sub-Cloud Layer

Global positioning satellite system (GPS) radio waves that reach the tropical lower troposphere are strongly affected by small-scale water vapor fluctuations. We examine along-the-ray simulations of the impact parameter at every ray integration step using the high-resolution European Centre for Medium-Range Weather Forecasts ERA5 reanalysis as the input model states. We find that disturbances to the impact parameter arise when ray paths go through the top of the sub-cloud layer, where there is a pronounced reduction with increasing height in the humidity, and wet refractivity has a strong local vertical gradient, creating multipath. Additionally, the horizontal gradients of refractivity cause the impact parameter to vary along the ray. The disturbances to the impact parameter are confined to an area about 250 km horizontally and 4 km vertically from the perigee point. Beyond 250 km from the perigee, the impact parameter remains constant. The vertical gradient of refractivity is largest at the top of the sub-cloud layer, usually between 1.5 and 3.0 km, and becomes negligibly small above 4 km.

An analysis of anomalous propagation parameters and its effect on the intensity of clutter in weather radars

Weather radar is used by forecasters for identifying storms and estimating its corresponding precipitation. Anomalous propagation of the radar beam may lead to misinterpretation of the weather events and associated errors in precipitation estimates. As the weather radar transmits electromagnetic waves, it is affected by the refractive index of the atmosphere which depends on the temperature, pressure and water vapor content. It is important to understand the refractive index of the atmosphere and how it affects the beam propagation of the radar to interpret the echoes better. Meteorological conditions causing anomalous propagation is well described in literature by Battan (1973), Doviak and Zrnik (2006) and Rinehart (2001). The vertical refractivity gradient (VRG) affects the propagation of radio waves in the atmosphere (Gossard, 1977). These anomalous propagation cause clutter to be displayed in the radar images. The intensity of the clutter was differentiated into various groups by the amount of clutter present in the radar image. Refractivity parameters at various heights and the height of the temperature inversion layer were calculated using radiosonde observational data at the Visakhapatnam (VSK) station. The observed values from the radiosonde data were compared with the intensity groups and it was found that three parameters were influential in determining the intensity of the clutter which is the presence of the temperature inversion layer above the radar, the VRG of the temperature inversion layer above the radar and the VRG from the radar to a height of 1 km from sea level.

Geostatistical Distribution of Vertical Refractivity Gradient Over Nigeria

AbstractAnomalous propagation conditions may cause multipath fading and strong signal enhancement on terrestrial line of sight links or interference on transhorizon paths. In detecting this conditions, spatial distribution of vertical refractivity gradient and ducting index were estimated across Nigeria using atmospheric data obtained from Era5 archive of European Centre for Medium‐Range Weather Forecasts (ECMWF). Refractivity and refractivity gradient were calculated from the obtained temperature, relative humidity, and pressure data using International Telecommunication Union (ITU) recommendation expression. Vertical refractivity gradient (VRG) and ducting index (Di) were deducted from refractivity gradient and modified the refractivity gradient. Correlation between vertical refractivity gradient, Di, and latitude were also computed. The result shows that the VRG values range between −5 and −65 N units/km in the Coastal and Guinea Savannah regions, and between −30 and −95 N units/km in the Midland and Sahelian regions. The Di values range between 10 and 60 in the Coastal and Guinea Savannah regions, between −10 and 110 in Midland and Sahelian region. Likewise, superrefraction and ducting are more prominent in the northern part, while superrefraction with minor subrefraction were noticed in the south. The Di performed better than VRG in detecting propagation conditions. Correlation between VRG and latitude ranges between −0.75 and −0.92. Correlation between Di and latitude is between 0.84 and 0.95. The values of VRG decrease northward, while those of the Di increase northward. Both VRG and Di revealed high variability in the dry months than in the wet months.

2-D Propagation Modeling in Inhomogeneous Refractive Atmosphere Based on Gaussian Beams Part II: Application to Radio Occultation

The Gaussian beam for atmospheric refraction (GBAR) method is used to model the effects of the refractive atmosphere between a global navigation satellite system (GNSS) satellite and a low earth orbit (LEO) satellite in a radio occultation (RO) configuration. The wave transmitted by the GNSS satellite is expanded into Gaussian beams using a multibeam expansion procedure (MEP). The wave is modeled in the troposphere by Gaussian beams, and additional MEPs are processed if needed. The refractive atmosphere is modeled by a grid of rectangular cells within each of which is defined a constant and vertical refractivity gradient. The propagation factor at the LEO satellite is used to retrieve the refractivity profile at the perigees. The inverse method is recalled, and the global spherical symmetry assumption is emphasized. The inversion of the simulated propagation factor amplitude data is tested in two simulations. The first one considers a spherically symmetrical refractive atmosphere characterized by a standard exponential refractivity distribution. The second one uses data from weather research and forecast (WRF) simulations in the Caribbean region. The error brought by the spherical symmetry assumption is investigated. The GBAR method provides a new tool for the remote sensing of planetary atmospheres.

Long‐Term Evolution of The Surface Refractivity for Arctic Regions

AbstractIn this paper, local meteorological data for a period of 35 years (from 1979 to 2013) from Kuujuaq station have been used to calculate the surface refractivity, N (a link for the data is available in the acknowledgements), and to estimate the vertical refractivity gradient, dN1, in the lowest atmospheric layer above the ground. Monthly and yearly variations of the mean of N and dN1 are provided. The values obtained are compared with the corresponding values from the ITU maps. The long‐term trend of the surface refractivity is also investigated. The data demonstrate that the indices N and dN1 are subject to an evolution that may have significance in the context of climate change. Monthly means of N show an increasing departure from ITU‐R values since 1990. Yearly mean values of the dN1 show a progressive decrease over the period of study. Seasonal means of dN1 show a decrease over time, especially for summer. Such a trend may increase the occurrence of superrefraction. However, currently available ITU‐R recommendations for microwave link design assume a stationary climate, so there is a need for a new modeling approach.

Climatological Beam Propagation Conditions for China’s Weather Radar Network

AbstractThe vertical refractivity gradient (VRG) is critical to weather radar beam propagation. The most common method of calculating beam paths uses the 4/3 Earth radius model, which corresponds to standard refraction conditions. In the present work, to better document propagation conditions for radar electromagnetic waves, which is essential for hydrology and numerical weather forecast models to more fully benefit from observations taken from the new-generation weather radar network in China, VRG spatial and temporal variations in the first kilometers above the surface are explored using 6-yr sounding observations. Under the effects of both regional climatic and topographic conditions, VRG values for most of the radars are generally smaller than those of the standard conditions for much of the year. There are similar or slightly larger values at only a few radar sites. Smaller VRG values are more frequent and widespread, especially during rainy seasons when weather radar observations are important. In such conditions, beam heights estimated using standard atmospheric refraction are overestimated relative to actual heights for most of the radars. Underestimates are much less common and of much shorter duration. However, height deviations are acceptable for being well within the uncertainty of radar echo height owing to the ~1° beamwidth. In coastal areas and the middle and lower reaches of the Yangtze River, radar observations should be applied with much more caution because of the greater risk of beam blockage and clutter contamination.

On horizontal distribution of vertical gradient of atmospheric refractivity

AbstractThe horizontal distribution of the vertical gradient of atmospheric refractivity is important for the assessment of the propagation of electromagnetic waves on nearly horizontal paths. A 5‐year set of meteorological data, obtained from the ERA‐Interim numerical weather product, has been used to analyze this distribution statistically. Vertical gradient maps of the Central European region have been processed to derive empirical probability distributions of the difference between local point gradient values at two locations. The difference of the effective (path‐averaged) gradient along the path and the local gradient is shown to be statistically distributed so that the quantiles increase linearly with distance in the interval from 100 to 1000 km. Finally, a spatial correlation function is obtained and described by an exponential model with correlation distances determined in the range of 400–700 km.

Open-loop GPS signal tracking at low elevation angles from a ground-based observation site

Abstract. A 1-year data set of ground-based GPS signal observations aiming at geometric elevation angles below +2° is analysed. Within the "GLESER" measurement campaign about 2600 validated setting events were recorded by the "OpenGPS" open-loop tracking receiver at an observation site located at 52.3808° N, 13.0642° E between January and December 2014. The measurements confirm the feasibility of open-loop signal tracking down to geometric elevation angles of −1 to −1.5° extending the corresponding closed-loop tracking range by up to 1°. The study is based on the premise that observations of low-elevation events by a ground-based receiver may serve as test cases for space-based radio occultation measurements, even if the latter proceed at a significantly faster temporal scale. The results support the conclusion that the open-loop Doppler model has negligible influence on the derived carrier frequency profile for strong signal-to-noise density ratios above about 30 dB Hz. At lower signal levels, however, the OpenGPS receiver's dual-channel design, which tracks the same signal using two Doppler models differing by 10 Hz, uncovers a notable bias. The repeat patterns of the GPS orbit traces in terms of azimuth angle reveal characteristic signatures in both signal amplitude and Doppler frequency with respect to the topography close to the observation site. Mean vertical refractivity gradients, extracted from ECMWF meteorological fields, correlate weakly to moderately with observed signal amplitude fluctuations at geometric elevation angles between +1 and +2°. Results from multiple phase screen simulations support the interpretation that these fluctuations are at least partly produced by atmospheric multipath; at negative elevation angles diffraction at the ground surface seems to contribute.

The Seasonal and Diurnal Cycles of Refractivity and Anomalous Propagation in the Sahelian Area from Microwave Radiometric Profiling

AbstractThe Sahelian zone of West Africa is a semiarid area where strong amplitude of the seasonal and diurnal cycles of water vapor and temperature is observed. One year of continuous observation of vertical profiles of water vapor and temperature gathered from Niamey, Niger, with a profiling microwave radiometer is used to analyze the climatology of refractivity and microwave propagation regimes in the low troposphere. Seasonal and diurnal cycles of refractivity and ground-based radar anomalous propagation are emphasized. It is shown that the combined effect of water vapor and temperature vertical gradients is responsible for strong seasonal and diurnal cycles of the ducting propagation regime. Statistics of propagation regimes are given. The probability density functions of the refractivity gradient are found lognormally distributed. Three months of C-band radar data simultaneous with the profiling microwave radiometer observations have also been collected. Relations between the vertical refractivity gradient and the ground-based radar anomalous propagation echoes (APE) are illustrated and discussed. APE spatial distributions are found strongly related to the main features of the orography and topography inside the radar-observed area. Contingency tests show that the probability for APE to be linked to ducting is higher than 95%. In addition, this paper suggests that observing the refractivity vertical profiles from a microwave radiometer profiler located close to a meteorological radar provides information on whether anomalous propagation has to be considered as a potential cause of spurious signal in the measured reflectivity field.

Improving Radar Refractivity Retrieval by Considering the Change in the Refractivity Profile and the Varying Altitudes of Ground Targets

AbstractAccurate radar refractivity retrievals are critical for quantitative applications, such as assimilating refractivity into numerical models or studying boundary layer and convection processes. However, the technique as originally developed makes some simplistic assumptions about the heights of ground targets () and the vertical gradient of refractivity (). In reality, the field of target phases used for refractivity retrieval is noisy because of varying terrain and introduces estimation biases. To obtain a refractivity map at a constant height above terrain, a 2D horizontal refractivity field at the radar height must be computed and corrected for altitude using an average . This is achieved by theoretically clarifying the interpretation of the measured phase considering the varying and the temporal change of . Evolving causes systematic refractivity biases, as it affects the beam trajectory, the associated target range, and the refractivity field sampled between selected targets of different heights. To determine and changes, a twofold approach is proposed: first, can be reasonably inferred based on terrain height; then, a new method of estimation is devised by using the property of the returned powers of a pointlike target at successive antenna elevations. The obtained shows skill based on in situ tower observation. As a result, the data quality of the retrieved refractivity may be improved with the newly added information of and .

A long term (1999–2008) study of radar anomalous propagation conditions in the Western Mediterranean

In this paper a study of the radio propagation environment of electromagnetic waves prevailing in the lower troposphere of the Western Mediterranean basin is presented. Deviations from atmospheric average or standard radio propagation conditions (anomalous propagation or AP) can affect significantly the quality of weather radar observations and other telecommunication systems. This is particularly important when ducting or superrefraction is present and spurious echoes resulting from the interaction of the beam with the ground or sea surface may appear. These AP conditions occur mainly when temperature inversions or strong moisture gradients are present. The period covered in this study ranges from 1999 to 2008 and conditions were derived from the Weather Research and Forecasting (WRF) modeling system, using the Japanese 25-year Reanalysis (JRA25) dataset as initial and boundary data. From the WRF model, we use the temperature, moisture, and pressure fields with a grid length of 30-km horizontal resolution and 250m vertical resolution to compute several indices such as the Vertical Refractivity Gradient, Vertical Modified Refractivity Gradient and a Ducting Index. Results obtained show that on the Western Mediterranean coast the most favorable conditions for superrefraction are found in summer, while the most affected areas are the Gulf of Valencia, the Strait of Gibraltar and the Northern Gulf of Lion. Additionally, a comparison with radiosonde data recorded in Barcelona (NE Spain) is also performed indicating an overall agreement between model and observational data despite a tendency to decrease subrefractive events by the WRF model.

New Methodology for Predicting Vertical Atmospheric Profile and Propagation Parameters in Subtropical Arabian Gulf Region

A new simplified approach is proposed to evaluate the vertical refractivity profile within the lowest 1 km of atmosphere from the analysis of surface refractivity $\bm{N}_{\bm{s}}$ in areas where upper-air data are not available. Upper-air measurements from the nearest available radiosonde location with similar surface profile to these sites are utilized. The profiles of $\bm{N}_{\bm{s}}$ and refractivity extrapolated to sea level $N_o$ obtained from surface meteorological data using both fixed stations and radiosonde are investigated and compared. Vertical refractivity gradient $\boldsymbol{\Delta} {\bm{N}}$ is evaluated at three atmospheric layer heights within the first kilometer above the ground in addition to propagation parameters relevant to each atmospheric layer. At six sites, different approaches are compared for the analysis of three important parameters; namely effective earth radius factor $k$ anomalous propagation probability parameter ${\boldsymbol{\upbeta}_0}$ and point refractivity gradient at 65 m not exceeded for 1% of time $dN_1$ . The ${\bm{k}}$ -factor parameter is investigated using a new weighted average approach of $\boldsymbol{\Delta} {\bm{N}}$ at 65-m, 100-m, and 1-km layers above the ground. The results are compared with the latest ITU maps and tables for the same area.

Climatology of radar anomalous propagation over West Africa

A comprehensive examination of 5 years of European Centre for Medium-Range Weather Forecasts (ECMWF) data from T511 L60 version of the ECMWF model to determine ducting conditions over West Africa and the computation of statistical distributions of the vertical gradient of refractivity determined from 2 years of radiosonde data over Dakar (14.41°N, 17.26°W), Douala (4°N, 9.7°E) and Niamey (13.35°N, 2.03°E) were carried out. It is found that diurnal and seasonal variations of the refractivity of the atmosphere are influenced by air temperature and water vapor pressure fluctuation. Refractivity gradients lower than −157km−1 often results in spurious returned echoes and misinterpretation of radar images such as erroneous precipitation detection. The results obtained show that the local climate has an appreciable influence on the vertical profile of refractivity, especially the seasonal north–south movement of the Inter Tropical Discontinuity which is associated with the alternance of wet and dry seasons over the region. It is found that most of ducts occur in the night, morning (0000, 0600 UTC) and late afternoon (1800 UTC). The occurrence probability of abnormal propagation events, such as ducts, can provide some valuable information about the propagation of electromagnetic waves over West Africa.

New Approaches and Algorithms for the Analysis of Vertical Refractivity Profile Below 1 km in a Subtropical Region

In this communication, 17 years of high resolution surface and radiosonde meteorological data from 1997-2013 for the subtropical Gulf region are analysed. Relationships between the upper air refractivity, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> , and vertical refractivity gradient, ΔN, in the low troposphere and the commonly available data of surface refractivity, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> are investigated. A new approach is discussed to estimate N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> and ΔN from the analysis of the dry and wet components of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , which gives better results for certain cases. Results are compared with those obtained from existing linear and exponential models in the literature. The investigation focusses on three layer heights at 65 m, 100 m and 1 km above ground level. Correlation between the components of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> with both N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> and ΔN are studied for each atmospheric layer. Where high correlations were found, empirical models are derived from best-fitting curves.

Microwave Anomalous Propagation Conditions in the First 100-m Altitude in a Tropical Location

In-situ measurement of radio climatological parameters of pressure, temperature and relative humidity to investigate anomalous propagation conditions in the first 100-m altitude in a tropical location are presented in this study. The analysis has been based on the dependence of average value of radio refractivity, N, on different times of the day along the year. The results of the analysis was used to determine the vertical radio refractivity gradient and k-factor over this region, which is useful for the determination of optimum performance of digital terrestrial point to point links.The results showed that N-values for the wet months were higher than in the dry months, and it also decreases with increasing altitude. It was also found that maximum values of N averaged over the month occurred at 6:00 h local time, and the minimum N values occurred at 18:00 h. The maximum variation between maximum and minimum N-value over 50 m altitude was 34.07 N-units in the month of September, while maximum variation between maximum and minimum N-value over 100 m height was 54.00 N-units during the month of December. Results of the minimum values of k-factor averaged over the month occurred at 18:00 h local time, and the maximum values averaged over the month occurred at 6:00 h during the year 2012 is analyzed.It was also observed that k-factor is low in the dry months (Jan-Mar and Nov-Dec) while the values rise during the wet months. Overall, results show that propagation in this region is mostly super-refractive.