Atmospheric Propagation Modelling for Terrestrial Radio Frequency Communication Links in a Tropical Wet and Dry Savanna Climate

: Atmospheric impairment-induced attenuation is the prominent source of signal degradation in radio wave communication channels. The computation-based modeling of radio wave attenuation over the atmosphere is the stepwise application of relevant radio propagation models, data, and procedures to effectively and prognostically estimate the losses of the propagated radio signals that have been induced by atmospheric constituents. This contribution aims to perform a detailed prognostic evaluation of radio wave propagation attenuation due to rain, free space, gases, and cloud over the atmosphere at the ultra-high frequency band. This aim has been achieved by employing relevant empirical atmospheric data and suitable propagation models for robust prognostic modeling using experimental measurements. Additionally, the extrapolative attenuation estimation results and the performance analysis were accomplished by engaging different stepwise propagation models and computation parameters often utilized in Earth–satellite and terrestrial communications. Results indicate that steady attenuation loss levels rise with increasing signal carrier frequency where free space is more dominant. The attenuation levels attained due to rain, cloud, atmospheric gases, and free space are also dependent on droplet depths, sizes, composition, and statistical distribution. While moderate and heavy rain depths achieved 3 dB and 4 dB attenuations, the attenuation due to light rainfall attained a 2.5 dB level. The results also revealed that attenuation intensity levels induced by atmospheric gases and cloud effects are less than that of rain. The prognostic-based empirical attenuation modeling results can provide ﬁrst-hand information to radio transmission engineers on link budgets concerning various atmospheric impairment effects during radio frequency network design, deployment, and management, essentially at the ultra-high frequency band.

To this end, the focus of this contribution is to carry out a detailed prognostic evaluation of the total radio wave propagation losses due to rain, free space, gases, and cloud over the atmosphere at the ultra-high frequency band, leveraging experimental measurements. In particular, the main contributions of this study are outlined as follows: I We propose a prognostic-based empirical attenuation model for terrestrial radio frequency communication links in tropical wet and dry savanna climates based on experimental data. I We present a classification of rain rate values based on rainfall depth levels obtained from experimental measurements. I We determine the propagation loss due to attenuation from atmospheric variables obtained from experimental measurements.
The remaining part of this paper is organized as follows. Section 2 presents the theoretical framework. Section 3 describes the materials and methods. Section 4 presents the results and discussion. Finally, Section 5 offers a concise conclusion to the study.

Theoretical Framework
The theoretical framework covers radio wave propagation through free space, rain, cloud, gases, and the total attenuation propagation loss.

Propagation through Free Space
In free-space propagation modeling, the signal transmission between a receiving and transmitting antenna is assumed to be located in an empty environmental setting devoid of obstructions [47][48][49][50][51]. Neither reflecting surfaces nor absorbing stumbling blocks or the like are considered. The power density w p at a given transmitting distance d with power p T in correspondence with the antenna gain G at is given by Equation (1) [52]: The received power P R that can be accessed at the receiving antenna with Gain G ar is given in Equation (2) as: and the effective aperture area A e f is given by Equation (3): With reference to Equation (3), the received power P R can be rewritten as Equation (4): where λ = transmission wavelength. Thus, the attenuation propagation γ att ( f ) (in dB) due to free space can be determined from Equation (4) as given in Equation (5): where f c and C s are the transmission frequency and light speed, respectively.

Propagation through the Rain
Rainfall through drops of liquid water is one key dynamic natural occurrence that undesirably attenuates the amplitudes of propagated microwave radio frequency signals in the atmosphere. The attenuation is initiated via scattering and absorption when the propagated electromagnetic waves encounter the showered liquid water droplets of different intensities, natures, and concentrations [53]. While the scattering disseminates the propagated microwave signals, the absorption result rises in molecular energy in correspondence with the atmospheric temperature, which causes a comparable loss of electromagnetic signal energies, particularly at higher frequencies.
The universal power-law model that describes attenuation due to rain is given by Equation (6) [54]: where L path (in km) and γ r express the propagation path length and rain rate in Equation (7), respectively. The real channel length (l) is related with the distance parameter d s in Equation (8) [55,56]: The power-law parameters β and α can be obtained by Equations (9) and (10), respectively: Implementation of rain and gaseous R re (mm/h) expresses the received depth of total water droplets due to rainfall (in mm) divided by the entire shower duration (in hours). It is given by Equation (11):

Propagation through Cloud
Apart from the rain, cloud is another key atmospheric parameter that attenuate the amplitudes of propagated microwave via reflection, absorption, scattering, refraction, and spreading phenomena. It is possible to reliably articulate or quantify attenuation due to a cloud utilizing its liquid contents. Mathematically, it can be conveyed by [57] in Equation (12): where LWC indicates the liquid water content and γ c is given by Equation (13), and its parameters are defined in Equations (14)-(18) as follows. where: where Λ = 330/T, ε 1 = 5.48 and ε 2 = 3.51.

Propagation through Gases
Key components of the atmospheric make-ups are the distribution of various gases at various altitudes, loftiness, and breadths, which also cause some levels of multipath attenuation. The electromagnetic wave attenuation due to atmospheric gases can be estimated for water vapour and dry air using the expressions in Equations (19) and (20) [58]: where r p = p/1013 and r t = 288(273 + T), T and f c being the temperature and frequency. The total attenuation due to water vapour and oxygen for up/downlink communication is given by Equation (21): where θ indicates the elevation angle in the range of: 10 ≤ θ ≤ 90.

Total Attenuation Propagation Loss
Total attenuation propagation loss statistics over Earth-satellite and terrestrial communication links are also fundamental in providing the necessary information for the effective design of such links. ITU-R P.618 [44] specifies that the relevant propagation parameters required to compute total attenuation loss also comprise individual attenuations. They are attenuations due to rain, atmospheric gases, cloud, free space, etc. Mathematically, the total attenuation propagation loss γ total (att) can be expressed by Equation (22): where γ att ( f ), γ att (r), γ att (c), γ att (g) are the respective individual attenuation losses due to free space, rain, gases, and cloud, all of which are defined in the expressions in Equations (5), (6), (12) and (21).

The Computational Complexity of the Proposed Framework
A computational modelling framework is not considered intrinsically difficult if its solution or implementation requires fewer essential resources (e.g., amount of time, storage) needed for implementation, regardless of the algorithm being used.
Generally, all propagated radio wave and microwave attenuation modelling is implemented using long-distance models [5,13]. Thus, the computational semi-empirically based models employed in this paper, as revealed in Equations (5)- (22), are mainly long-distance models, in the form of the expression in (23): where the a expresses the modelling coefficients and n indicates the parameters of input size. In terms of time computation complexity estimation, the expression in (23) follows the rule defined in (24): Here, the big-0 notation in Equation (24) is used to explain the upper bound running time or memory usage (space) of the implementation algorithm employed in this paper. The O log(n) means that the complexity running time of the implementation algorithm grows in proportion to the logarithm of the given input size n. This result is in line with the parameterized complexity estimation technique explored in [59], wherein complexity analysis depends on various parameters of the given output or input.

Materials and Methods
The computation-based modeling of radio wave attenuation over the atmosphere is the stepwise application of relevant radio propagation models, data, and procedures to effectively and prognostically estimate the losses of the propagated radio signals that have been induced by the atmospheric constituents.
A semi-empirically based method that combines empirical atmospheric data and appropriate signal attenuation propagation models has been engaged in this study. The MATLAB software interface platform has been explored to accomplish the computerized coding of scripts, computations, and extrapolative graphical display of the results obtained from experimental measurements. Moreover, the extrapolative attenuation estimation results and the performance analysis have been accomplished by engaging different computation and modeling parameters from those often utilized in Earth-satellite and terrestrial communications.

Description of Study Location
Lokoja, the river port and capital city of Kogi State in south-central (middle-belt) Nigeria, was used as a study location. The Kogi state capital is located on longitude and latitude 6 • 44 25 E and latitude 7 • 47 48 N of the Greenwich Meridian. Lokoja has a tropical wet and dry savanna climate. Additionally, Lokoja is bounded by the two main big rivers, Niger and Benue, as displayed in Figure 2. Historically, Lokoja was founded in 1860 by the Scottish explorer William Balfour Baikie after the British merchants established a trading post at the river Benue-Niger confluence. The city has 63.82 sq. km of total land coverage area [60] and has become the core hub of migration between southern and northern Nigeria. Most times, the city's foremost stresses and shocks are unrestrained rain, the constant rise in water levels, floods with gully erosions, and wind storms. In 2012 and 2018, several deaths were recorded, with about 2000 displaced persons due to excessive flooding from the Niger and Benue rivers. In addition, transportation along some major roads and highways was affected, thus resulting in interruption of the movement of people and distribution of goods and services in the surrounding cities, particularly Abuja and Benin. The region is also exceptionally hot during the dry season, with temperatures ranging between 37-41 °C. Mountains and hills surround the area. One well-known mountain in the heart of the built-up Lokoja city is Mount Pati, and it is about 750 m above sea level. This study location is appropriate for atmospheric raw data collection due to its geographical location with tropical wet and dry seasons in Nigeria.

Method of Data Collection
The raw rainfall, cloud and atmospheric gases dataset, and other parameters used to conduct the detailed prognostic evaluation of total radio wave propagation attenuation losses in this study, were collected entirely from the Nigerian Meteorological Agency (NIMET). It is the leading Nigerian government agency equipped with the appropriate facilities and charged with the responsibility to robustly monitor and collect data on all areas of meteorology for policy formulation, planning, guidance, and decision making. The agency also prepares, projects, and provides weather (and climate) information needed for aircraft safety and related operations.
Specifically, the 12-year atmospheric datasets from 2008 to 2020 contain monthly rainfall depth, rainy days, minimum temperature, average temperature, maximum temperature, average snowfall, average pressure, wind speed, and average temperature and humidity. Figures 3 and 4 show the mean yearly rainfall depths and the humidity percentage values for the study location. Most times, the city's foremost stresses and shocks are unrestrained rain, the constant rise in water levels, floods with gully erosions, and wind storms. In 2012 and 2018, several deaths were recorded, with about 2000 displaced persons due to excessive flooding from the Niger and Benue rivers. In addition, transportation along some major roads and highways was affected, thus resulting in interruption of the movement of people and distribution of goods and services in the surrounding cities, particularly Abuja and Benin. The region is also exceptionally hot during the dry season, with temperatures ranging between 37-41 • C. Mountains and hills surround the area. One well-known mountain in the heart of the built-up Lokoja city is Mount Pati, and it is about 750 m above sea level. This study location is appropriate for atmospheric raw data collection due to its geographical location with tropical wet and dry seasons in Nigeria.

Method of Data Collection
The raw rainfall, cloud and atmospheric gases dataset, and other parameters used to conduct the detailed prognostic evaluation of total radio wave propagation attenuation losses in this study, were collected entirely from the Nigerian Meteorological Agency (NIMET). It is the leading Nigerian government agency equipped with the appropriate facilities and charged with the responsibility to robustly monitor and collect data on all areas of meteorology for policy formulation, planning, guidance, and decision making. The agency also prepares, projects, and provides weather (and climate) information needed for aircraft safety and related operations.
Specifically, the 12-year atmospheric datasets from 2008 to 2020 contain monthly rainfall depth, rainy days, minimum temperature, average temperature, maximum temperature, average snowfall, average pressure, wind speed, and average temperature and humidity. Figures 3 and 4 show the mean yearly rainfall depths and the humidity percentage values for the study location.   The agency has workstations over the country. The average precipitation data in depth is collected yearly using an electronic data logger such as the tipping-bucket rain gauge and weather radar, which measure the rainfall millimetres and other atmospheric variables over twenty hours. Remarkably, the tipping-bucket is a specialized automatic mechanical device used by this agency to measure the amount of rainfall in increments of approximately 0.25 mm, on one tip and at a detached point with a collection pail and funnel, which is usually positioned at an uncluttered geographical point. With the aid of a connecting wireless transceiver, the rainfall depth can be recorded at each 'tip'. The tipping bucket rain gauge is designed to measure the depth of the rainfall in terms of precipitated water height accumulated by the gauge per given time. Once an equivalent of about 0.25 mm of rainfall has been collected employing the bucket at the pivot level, it is emptied (i.e., tipped off).

Results and Discussion
The computations and extrapolative graphical display of the results are implemented and highlighted briefly in this section. During rainfall incidents, the depth of rainfall, strength, and amount can continually change from very heavy to light or vice versa. The amount of rain that falls per unit of time can sometimes be light and for a long duration. Sometimes, it can be moderate, with a very long duration, and moderate or long in duration and heavy. It can also be short in duration and very heavy, or long in duration and heavy. When long-lasting and heavy rainfall, it can lead to rapid attenuations and total   The agency has workstations over the country. The average precipitation data in depth is collected yearly using an electronic data logger such as the tipping-bucket rain gauge and weather radar, which measure the rainfall millimetres and other atmospheric variables over twenty hours. Remarkably, the tipping-bucket is a specialized automatic mechanical device used by this agency to measure the amount of rainfall in increments of approximately 0.25 mm, on one tip and at a detached point with a collection pail and funnel, which is usually positioned at an uncluttered geographical point. With the aid of a connecting wireless transceiver, the rainfall depth can be recorded at each 'tip'. The tipping bucket rain gauge is designed to measure the depth of the rainfall in terms of precipitated water height accumulated by the gauge per given time. Once an equivalent of about 0.25 mm of rainfall has been collected employing the bucket at the pivot level, it is emptied (i.e., tipped off).

Results and Discussion
The computations and extrapolative graphical display of the results are implemented and highlighted briefly in this section. During rainfall incidents, the depth of rainfall, strength, and amount can continually change from very heavy to light or vice versa. The amount of rain that falls per unit of time can sometimes be light and for a long duration. Sometimes, it can be moderate, with a very long duration, and moderate or long in duration and heavy. It can also be short in duration and very heavy, or long in duration and heavy. When long-lasting and heavy rainfall, it can lead to rapid attenuations and total The agency has workstations over the country. The average precipitation data in depth is collected yearly using an electronic data logger such as the tipping-bucket rain gauge and weather radar, which measure the rainfall millimetres and other atmospheric variables over twenty hours. Remarkably, the tipping-bucket is a specialized automatic mechanical device used by this agency to measure the amount of rainfall in increments of approximately 0.25 mm, on one tip and at a detached point with a collection pail and funnel, which is usually positioned at an uncluttered geographical point. With the aid of a connecting wireless transceiver, the rainfall depth can be recorded at each 'tip'. The tipping bucket rain gauge is designed to measure the depth of the rainfall in terms of precipitated water height accumulated by the gauge per given time. Once an equivalent of about 0.25 mm of rainfall has been collected employing the bucket at the pivot level, it is emptied (i.e., tipped off).

Results and Discussion
The computations and extrapolative graphical display of the results are implemented and highlighted briefly in this section. During rainfall incidents, the depth of rainfall, strength, and amount can continually change from very heavy to light or vice versa. The amount of rain that falls per unit of time can sometimes be light and for a long duration. Sometimes, it can be moderate, with a very long duration, and moderate or long in duration and heavy. It can also be short in duration and very heavy, or long in duration and heavy. When long-lasting and heavy rainfall, it can lead to rapid attenuations and total degradation of radio and microwave signals, which is usually very unpleasant at the user equipment terminal. Rainfall rate value plots in Figure 5 reveal the quantity of rain that has fallen in depth levels per the duration of fall in mm/h in the study location from 2008 to 2020. The rain rate values were classified as light, moderate and very heavy based on the acquired depths of the rainfall data. As expected, the plots show a one-to-one relationship as greater rain depths result in greater rain rates. Greater rain depths mean greater rain rate intensities due to larger shower droplets. The moderate and heavy rain intensities are recorded for the wetter and wettest months, between April to June and July to September.
Information 2022, 13, x FOR PEER REVIEW 10 of 17 degradation of radio and microwave signals, which is usually very unpleasant at the user equipment terminal. Rainfall rate value plots in Figure 5 reveal the quantity of rain that has fallen in depth levels per the duration of fall in mm/h in the study location from 2008 to 2020. The rain rate values were classified as light, moderate and very heavy based on the acquired depths of the rainfall data. As expected, the plots show a one-to-one relationship as greater rain depths result in greater rain rates. Greater rain depths mean greater rain rate intensities due to larger shower droplets. The moderate and heavy rain intensities are recorded for the wetter and wettest months, between April to June and July to September. The displayed results of Figure 6 show that rain attenuation levels increase in correspondence with an increase in the frequency values. This result reveals that the most severe attenuation effects during rainfall are at a higher percentage at higher frequencies.
The attenuation levels are seen in each graph. Additionally, results reveal that rain depth due to different water droplets during fall is a significant factor. While moderate and heavy rain depths achieved a mean of 3 dB and 4 dB attenuations, respectively, the attenuation due to light rainfall attained a 2.5 dB level. The displayed results of Figure 6 show that rain attenuation levels increase in correspondence with an increase in the frequency values. This result reveals that the most severe attenuation effects during rainfall are at a higher percentage at higher frequencies. The attenuation levels are seen in each graph. Additionally, results reveal that rain depth due to different water droplets during fall is a significant factor. While moderate and heavy rain depths achieved a mean of 3 dB and 4 dB attenuations, respectively, the attenuation due to light rainfall attained a 2.5 dB level.
Information 2022, 13, x FOR PEER REVIEW 10 of 17 degradation of radio and microwave signals, which is usually very unpleasant at the user equipment terminal. Rainfall rate value plots in Figure 5 reveal the quantity of rain that has fallen in depth levels per the duration of fall in mm/h in the study location from 2008 to 2020. The rain rate values were classified as light, moderate and very heavy based on the acquired depths of the rainfall data. As expected, the plots show a one-to-one relationship as greater rain depths result in greater rain rates. Greater rain depths mean greater rain rate intensities due to larger shower droplets. The moderate and heavy rain intensities are recorded for the wetter and wettest months, between April to June and July to September. The displayed results of Figure 6 show that rain attenuation levels increase in correspondence with an increase in the frequency values. This result reveals that the most severe attenuation effects during rainfall are at a higher percentage at higher frequencies.
The attenuation levels are seen in each graph. Additionally, results reveal that rain depth due to different water droplets during fall is a significant factor. While moderate and heavy rain depths achieved a mean of 3 dB and 4 dB attenuations, respectively, the attenuation due to light rainfall attained a 2.5 dB level. The signal propagation degradation versus path elevation angle for light, moderate and heavy rain rates are shown in Figure 7. The graphical plot discloses higher attenuations at lower path elevation angles, but particularly for heavy rain rates compared to others. This trend implies that the attained attenuation intensities from the atmospheric impairment effects due to rain are directly proportional to the signal quality degradation, especially as the depth of rainwater droplets increases. Still, there is an exception to the angle of elevation, which is inversely proportional. The signal propagation degradation versus path elevation angle for light, moderate and heavy rain rates are shown in Figure 7. The graphical plot discloses higher attenuations at lower path elevation angles, but particularly for heavy rain rates compared to others. This trend implies that the attained attenuation intensities from the atmospheric impairment effects due to rain are directly proportional to the signal quality degradation, especially as the depth of rainwater droplets increases. Still, there is an exception to the angle of elevation, which is inversely proportional.    The specific attenuation values resulting from atmospheric gases and cloud impairment effects versus carrier transmission in the range of 1GHz to 4 GHz are shown in Figures 9 and 10. The plotted results were achieved by employing the following atmospheric parameters: T = 293 K, P = 101.300 kPa, water vapour density = 3, and p = 7.5/gm. An increasing attenuation loss trend can be seen in each figure at higher frequencies. This result implies fewer atmospheric impairments at lower frequencies. Generally, the lower the frequency of radio signal transmission, the higher the communication distance due to higher wavelength.
Total propagated electromagnetic signal attenuation losses over various atmosphere components, including cloud, gases, rain, and free space versus varied transmission distances, are shown in Figure 11. The graphs reveal that attenuation loss due to free space is more dominant from the total computed loss values. This result is followed by rain rate attenuation, then atmospheric gases and cloud values. These results also revealed that attenuation intensity levels induced by atmospheric gases, rain, and cloud effects are less than levels induced by free space. For example, while moderate and heavy rain depths achieved 3 dB and 4 dB attenuations, the attenuation due to light rainfall attained a 2.5 dB level. Even at a lower T-R distance, the acquired attenuation values are as high as 78.23 dB in free space. The specific attenuation values resulting from atmospheric gases and cloud impairment effects versus carrier transmission in the range of 1GHz to 4 GHz are shown in Figures 9 and 10. The plotted results were achieved by employing the following atmospheric parameters: T = 293 K, P = 101.300 kPa, water vapour density = 3, and p = 7.5/gm. An increasing attenuation loss trend can be seen in each figure at higher frequencies. This result implies fewer atmospheric impairments at lower frequencies. Generally, the lower the frequency of radio signal transmission, the higher the communication distance due to higher wavelength. The specific attenuation values resulting from atmospheric gases and cloud impairment effects versus carrier transmission in the range of 1GHz to 4 GHz are shown in Figures 9 and 10. The plotted results were achieved by employing the following atmospheric parameters: T = 293 K, P = 101.300 kPa, water vapour density = 3, and p = 7.5/gm. An increasing attenuation loss trend can be seen in each figure at higher frequencies. This result implies fewer atmospheric impairments at lower frequencies. Generally, the lower the frequency of radio signal transmission, the higher the communication distance due to higher wavelength.  Total propagated electromagnetic signal attenuation losses over various atmosphere components, including cloud, gases, rain, and free space versus varied transmission distances, are shown in Figure 11. The graphs reveal that attenuation loss due to free space is more dominant from the total computed loss values. This result is followed by rain rate attenuation, then atmospheric gases and cloud values. These results also revealed that attenuation intensity levels induced by atmospheric gases, rain, and cloud effects are less than levels induced by free space. For example, while moderate and heavy rain depths achieved 3 dB and 4 dB attenuations, the attenuation due to light rainfall attained a 2.5 dB level. Even at a lower T-R distance, the acquired attenuation values are as high as 78.23 dB in free space. Figure 11. Plot of propagation loss due to attenuation from atmospheric variables.
As stated earlier, the resultant effects of totally natural and artificial blockades are high attenuation, slow/fast deterioration and steady losses in the intensities of the transmitted waves in space. For a carrier frequency of 3.5 GHz, a transmission power of 43 dB, receiver/transmitter cable losses of 5 dB, and a transmitter and receiver gain of 15 dB, the  Total propagated electromagnetic signal attenuation losses over various atmosphere components, including cloud, gases, rain, and free space versus varied transmission distances, are shown in Figure 11. The graphs reveal that attenuation loss due to free space is more dominant from the total computed loss values. This result is followed by rain rate attenuation, then atmospheric gases and cloud values. These results also revealed that attenuation intensity levels induced by atmospheric gases, rain, and cloud effects are less than levels induced by free space. For example, while moderate and heavy rain depths achieved 3 dB and 4 dB attenuations, the attenuation due to light rainfall attained a 2.5 dB level. Even at a lower T-R distance, the acquired attenuation values are as high as 78.23 dB in free space. Figure 11. Plot of propagation loss due to attenuation from atmospheric variables.
As stated earlier, the resultant effects of totally natural and artificial blockades are high attenuation, slow/fast deterioration and steady losses in the intensities of the transmitted waves in space. For a carrier frequency of 3.5 GHz, a transmission power of 43 dB, receiver/transmitter cable losses of 5 dB, and a transmitter and receiver gain of 15 dB, the Figure 11. Plot of propagation loss due to attenuation from atmospheric variables.
As stated earlier, the resultant effects of totally natural and artificial blockades are high attenuation, slow/fast deterioration and steady losses in the intensities of the transmitted waves in space. For a carrier frequency of 3.5 GHz, a transmission power of 43 dB, receiver/transmitter cable losses of 5 dB, and a transmitter and receiver gain of 15 dB, the high attenuation and slow deteriorating power attained due to the natural and manufactured blockades, particularly atmospheric impairment-induced ones, versus distance plot is revealed in Figure 11. For example, slow fluctuations (attenuation) occur when atmospheric precipitation particles, particularly rainwater droplets, absorb, disperse, and scatter the amplitude and energy of transmitted electromagnetic signals in the Earth-satellite and terrestrial communication links. The received signal power quality at the user equipment reduces when the attenuation losses over the communication link also increase. The attenuated signal power plot versus T-R propagation distance is depicted in Figure 12.
is revealed in Figure 11. For example, slow fluctuations (attenuation) occur when atmospheric precipitation particles, particularly rainwater droplets, absorb, disperse, and scatter the amplitude and energy of transmitted electromagnetic signals in the Earth-satellite and terrestrial communication links. The received signal power quality at the user equipment reduces when the attenuation losses over the communication link also increase. The attenuated signal power plot versus T-R propagation distance is depicted in Figure 12.

Conclusions
Cellular mobile network operators often explore point-to-area radio wave connections in the telecom industry for their terrestrial network deployment. The focus of this research contribution was geared towards conducting a robust empirically based prognostic modeling of different attenuation impacts on key atmospheric impairment variables. These variables are mainly cloud, rain, gases, and free space at ultra-high frequencies over terrestrial cellular communication links. Firstly, the motivation was to employ relevant empirical atmospheric data and their appropriate propagation models for prognostic modeling. Secondly, the extrapolative attenuation estimation results and the performance analysis were accomplished by engaging different stepwise propagation models and computation parameters often utilized in Earth-satellite and terrestrial communications. Steady attenuation loss levels rise in correspondence with increasing signal carrier frequency, and free space is more dominant. The results noticeably showed that the attenuation levels attained due to rain, cloud, atmospheric gases, and free space depend on droplet depths, sizes, composition, and statistical distributions. The results also revealed that the attained attenuation intensities from the atmospheric impairment effects are directly proportional to the signal quality degradation at increasing propagation distances. This trend defines the trend of results except for an angle of elevation, which is inversely proportional. Generally, the results revealed that atmospheric impairment-induced attenuation is the prominent source of signal degradations on the microwave communication channels, particularly at higher frequencies of operations. Our future work would focus on optimizing the projected models for optimal performance.

Conclusions
Cellular mobile network operators often explore point-to-area radio wave connections in the telecom industry for their terrestrial network deployment. The focus of this research contribution was geared towards conducting a robust empirically based prognostic modeling of different attenuation impacts on key atmospheric impairment variables. These variables are mainly cloud, rain, gases, and free space at ultra-high frequencies over terrestrial cellular communication links. Firstly, the motivation was to employ relevant empirical atmospheric data and their appropriate propagation models for prognostic modeling. Secondly, the extrapolative attenuation estimation results and the performance analysis were accomplished by engaging different stepwise propagation models and computation parameters often utilized in Earth-satellite and terrestrial communications. Steady attenuation loss levels rise in correspondence with increasing signal carrier frequency, and free space is more dominant. The results noticeably showed that the attenuation levels attained due to rain, cloud, atmospheric gases, and free space depend on droplet depths, sizes, composition, and statistical distributions. The results also revealed that the attained attenuation intensities from the atmospheric impairment effects are directly proportional to the signal quality degradation at increasing propagation distances. This trend defines the trend of results except for an angle of elevation, which is inversely proportional. Generally, the results revealed that atmospheric impairment-induced attenuation is the prominent source of signal degradations on the microwave communication channels, particularly at higher frequencies of operations. Our future work would focus on optimizing the projected models for optimal performance.

Data Availability Statement:
The data that supports the findings of this paper is available from the corresponding author upon reasonable request.