# Realistic Prognostic Modeling of Specific Attenuation due to Rain at Microwave Frequency for Tropical Climate Region

Authors: Joseph Isabona; Agbotiname Lucky Imoize; Paresh Rawat; Sajjad Shaukat Jamal; Bhasker Pant; Stephen Ojo; Simon Karanja Hinga
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Absorption and scattering of propagated microwave radio signals by atmospheric variables, particularly rainfall, remained a major cause of propagation attenuation losses and service quality degradation over terrestrial communication links. The International Telecommunications Union Radio (ITU-R) reports and other related works in the literature provided information on attenuation due to rain and microwave propagation data. Such propagation attenuation information in the tropical region of Nigeria is destitute, especially at lower radio waves transmission frequencies. Therefore, this study addresses this problem by employing 12-year rainfall datasets to conduct realistic prognostic modeling of rain rate intensity levels. A classification of the rainfall data into three subgroups based on the depth of rainfall in the region is presented. Additionally, an in-depth estimation of specific rain attenuation intensities based on the 12-year rainfall data at 3.5 GHz is demonstrated. On average, the three rainfall classes produced rain rates of about 29.27 mm/hr, 73.71 mm/hr, and 105.39 mm/hr. The respective attenuation values are 0.89 dB, 1.71 dB, and 2.13 dB for the vertical polarisation and 1.09 dB, 1.20 dB, and 2.78 dB for the horizontal polarisation at 0.01% time percentage computation. Generally, results indicate that higher rain attenuation of 12% is observed for the horizontal polarisation compared to the vertical polarisation. These results can provide valuable first-hand information for microwave radio frequency planning in making appropriate decisions on attenuation levels due to different rainfall depths, especially for lower frequency arrays.


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## Body

## 1. Introduction

In designing and deploying meaningful Earth-space terrestrial radio and microwave network-based communication systems, several attenuation effects owing to different atmospheric conditions need to be examined [1, 2]. The effects due to scattering, absorption, and depolarization by hydrometeors (e.g., snow, ice, sleet, and water droplets in clouds, precipitation, etc.) and atmospheric gases are considered at different transmission frequencies around the 11 GHz band [3, 4]. Due to heavy rainfall depth and fade, attenuation can damage signal propagation and reception at the user terminal [5, 6]. It can also cause short-term and long-term impairments in radio signal communication links [7–9]. Adverse atmospheric weather conditions (bad weather) due to different raindrops can absorb microwave-range signals in both terrestrial point-to-point and Earth-space satellite communication systems [10–13]. Thus, resulting in substantial path loss and severe degradation in signal coverage and quality of service [14–21]. In order to address this problem, estimating rain rate attenuation will enable terrestrial radio and microwave network planners to determine the type of diversity techniques to explore to combat or compensate for it during and after antenna deployment [22–25].The knowledge of specific attenuation influenced by different rainfall drop sizes/depths and other weather-related issues is essential for efficient fade management processes. For instance, predictive quantification of rainfall attenuation impacts is critical to determining the requisite tracking speediness of fade moderation. The atmospheric earth surface comprises different layers with different characteristic features, properties, and structures. The troposphere, a vital component of the homosphere, is the most crucial sublayer for radio frequency engineers handling space terrestrial radio channels [26–28]. Studies on hydrometeors impacts, mainly due to rainfall intensity on propagated electromagnetic signal waves in recent decades, have been reported. Results indicate enormous path loss owing to high traffic and congestion issues in terrestrial cellular communication networks operating at lower higher frequency bands [22].Several reports on rain attenuation impacts on communication systems are detailed in [22, 29–36]. In particular, the work in [29] presented a predictive analysis of rainfall attenuation and their probable influence on propagated microwaves for Uttarakhand, a tropical region in India. Similar rain attenuation modeling, but based on practical measurements of different rainfall drop sizes, is reported in [30] for the same region. Predictive analysis of rain attenuation and rain rate for satellite-based communication using TURKSAT in the Ku Band Beacon has been investigated [31]. Rain attenuation studies at microwave propagation frequencies over Malaysia environment using ITU-R, Ajayi model, and Global Crane Model are presented in [32]. The authors [33, 34] provide detailed rainfall attenuation distribution statistics over the wireless link at a higher microwave frequency in Japan and Korean territories. Specific practical attenuation measurement and modeling-based investigation approaches to rainfall intensity effects conducted in different countries are presented [35–44].In recent literature, reconfigurable intelligent surface- (RIS-) based techniques for mitigating interference are gaining widespread popularity. RIS has been a candidate technology for the beyond 5G and 6G wireless networks. RISs can help improve the efficiency and performance of wireless communication networks [45, 46]. RISs are designed with passive materials to tackle interference in harsh and unfriendly environments [47]. In RIS deployment, wireless signals are transmitted from the transmitter to the receiver at a minimal loss [48, 49]. On the other hand, real-time control of the reflection amplitude and phase shift of RISs can present huge implementation issues [50]. In order to address this problem, machine learning, deep learning, and federated learning models are currently proposed [51–53]. Testing and training data acquisition will limit machine learning-based RIS techniques [54, 55].While a number of the reported attenuation studies are due to rain and microwave propagation data, such propagation attenuation levels information in the tropical region of Nigeria is still missing in the existing literature, especially at lower radio waves transmission frequencies. To this end, this study is designed to fill the gap in the open literature. In particular, the key contributions of the paper are as follows.(i)
We carried out realistic prognostic modeling of rain rate intensity levels based on 12-year experimental rainfall datasets(ii)
We classified the rainfall data into three clear groups based on the depth of rainfall in the region(iii)
We estimated specific rain attenuation intensities in-depth on the 12-year rainfall data at 3.5 GHz microwave radio frequency(iv)
Establish the connection between the raindrop size and rain rate valuesThe remaining part of this paper is prepared as follows. The theoretical framework is defined in Section2. The materials and methods comprising the study location, source of rainfall datasets collection method, and the stepwise procedure are briefed in Section 3. Section 4 presents the results and discussions, and a concise conclusion is drawn in Section 5.


## 2. Theoretical Framework

### 2.1. Specific Attenuation Model Based on Rec. ITU-R P.838-3 Power-Law

Specific attenuationSrdB/km due to rainfall depth over a terrestrial communication channel can be articulated using the power-law relationship, which combines the propagation path length Lpath (km) and rain rate Rrmm/hr given in equation (1), where γ is defined in equation (2) [22, 30]:
(1)Sr=γLpath,where
(2)γ=βRrα.The propagation path lengthLpath (km) can be obtained by multiplying the real channel length (l) with a distance parameter, d, and it is expressed in the following equation [28, 56]:
(3)d=10.477l0.633Rr0.073νfc0.123−10.5791−exp−0.024lα,where ν indicates the specific attenuation regression constant.The modeling parametersβ and α can be obtained from the scattering calculation method in combination with curve fitting given in the following equations [30]:
(4)logβ=∑j=14xjexp−logfc−yjzj2+mklogfc+zk,(5)logα=∑j=15xiexp−logfc−yizi2+mnlogfc+zn.The rain attenuationApdB exceeded at time percent, p in the range of 0.001–1% is expressed as given in the following equation:
(6)Ap=A0.01p0.01–t1–t2nA0.01–β1–psinθ,where θ is the elevation angle and the time t1 and t2 are defined in the following equations, respectively.
(7)t1=0.655+0.033lnp,(8)t2=0.045.The expression in equation (2) defines the popular power-law Rec. ITU-R P.838-3 for specific rain attenuation modeling.


### 2.2. Rain Drop Size Distribution Modeling and Connection with Rain Rate

Rainfall occurrence primarily expresses the wide-ranging formation of raindrop sizes [57–60]. Raindrop size distribution (DSD) describes the composition or formation variant of diverse raindrop sizes (number) based on their diameter (D). Information on predictive modeling of DSD is vital for the robust evaluation and classification of radio and microwaves propagation effects in space. It also provides valuable information on the general microphysics composition of the precipitation phenomenon [61, 62].There are many DSD models in the literature to analyse and evaluate rainfall events. In this paper, the two most popular ones with simplified computation convolution are considered, both of which are tagged model 1 and model 2 as described in equations (9), (10), (11), and (12).
(9)ND=NiDaexp−ΛsDb,(10)Ni=1.76×106Rr−1.2,(11)Λs=10Rr−0.31,where ND indicate the raindrop size number, with NiandΛs being the modeling intercept parameter and slope parameter. a and b are also ND modeling parameters where Rr and D indicate the raindrop diameter and rain rate. For a=0 and q=1, the expression in (1) turns
(12)ND=Niexp−ΛsD.While equation (4) explains the popular model developed by Marshall and Palmer [63] for raindrop size modeling, equation (1) describes the general form of the raindrop size model developed by proposed Ulbrich [64] to take into account a larger range of D values.


## 2.1. Specific Attenuation Model Based on Rec. ITU-R P.838-3 Power-Law

Specific attenuationSrdB/km due to rainfall depth over a terrestrial communication channel can be articulated using the power-law relationship, which combines the propagation path length Lpath (km) and rain rate Rrmm/hr given in equation (1), where γ is defined in equation (2) [22, 30]:
(1)Sr=γLpath,where
(2)γ=βRrα.The propagation path lengthLpath (km) can be obtained by multiplying the real channel length (l) with a distance parameter, d, and it is expressed in the following equation [28, 56]:
(3)d=10.477l0.633Rr0.073νfc0.123−10.5791−exp−0.024lα,where ν indicates the specific attenuation regression constant.The modeling parametersβ and α can be obtained from the scattering calculation method in combination with curve fitting given in the following equations [30]:
(4)logβ=∑j=14xjexp−logfc−yjzj2+mklogfc+zk,(5)logα=∑j=15xiexp−logfc−yizi2+mnlogfc+zn.The rain attenuationApdB exceeded at time percent, p in the range of 0.001–1% is expressed as given in the following equation:
(6)Ap=A0.01p0.01–t1–t2nA0.01–β1–psinθ,where θ is the elevation angle and the time t1 and t2 are defined in the following equations, respectively.
(7)t1=0.655+0.033lnp,(8)t2=0.045.The expression in equation (2) defines the popular power-law Rec. ITU-R P.838-3 for specific rain attenuation modeling.


## 2.2. Rain Drop Size Distribution Modeling and Connection with Rain Rate

Rainfall occurrence primarily expresses the wide-ranging formation of raindrop sizes [57–60]. Raindrop size distribution (DSD) describes the composition or formation variant of diverse raindrop sizes (number) based on their diameter (D). Information on predictive modeling of DSD is vital for the robust evaluation and classification of radio and microwaves propagation effects in space. It also provides valuable information on the general microphysics composition of the precipitation phenomenon [61, 62].There are many DSD models in the literature to analyse and evaluate rainfall events. In this paper, the two most popular ones with simplified computation convolution are considered, both of which are tagged model 1 and model 2 as described in equations (9), (10), (11), and (12).
(9)ND=NiDaexp−ΛsDb,(10)Ni=1.76×106Rr−1.2,(11)Λs=10Rr−0.31,where ND indicate the raindrop size number, with NiandΛs being the modeling intercept parameter and slope parameter. a and b are also ND modeling parameters where Rr and D indicate the raindrop diameter and rain rate. For a=0 and q=1, the expression in (1) turns
(12)ND=Niexp−ΛsD.While equation (4) explains the popular model developed by Marshall and Palmer [63] for raindrop size modeling, equation (1) describes the general form of the raindrop size model developed by proposed Ulbrich [64] to take into account a larger range of D values.


## 3. Materials and Methods

This section describes the study area, data collection method, and the methodology employed in this study.


### 3.1. Study Area

Kogi state, a midcentral (middle belt) zone of Nigeria, is a case study for the research work. Kogi, which connotes “River” in the Hausa language, houses a confluence town, where River Niger and Benue meet. The region holds a tropical climate with inconstant dry and rainy seasons in duration, timing, and severity. Despite the region’s relatively irregular dry and rainy seasons, the total annual rainfall depth varies between 805 mm and 1767 mm. It is a tropical region of Nigeria with low humidity of about 30% in the dry season and high humidity of approximately 70% during the wet season [65, 66]. The rainy wet season of the region usually brings cooler weather, mainly due to cloud cover increase that most time acts as a blockage to the intense tropical sunshine. However, during afternoons, this season can be as hot and humid due to the surrounding rocky soils and the riverine nature of the area. During dry seasons, the sun shines over the expanse with little or no blockades from the atmosphere, thus making the season in the region a period of hot and warm temperature conditions [67]. But in the mid-dry season, which is usually around December/January, the hot sun’s rays are partly blocked by the Harmattan haze and dust, which often results in lower temperatures. Its annual temperature is ranged between 27.7°C and 37.7°C in the wet and dry seasons. The average daily vapour pressure and wind speeds are 26 Hpa and 89.9 km/hr.


### 3.2. Data Collection

The 12-year rainfall datasets explored for this study were acquired with support from the Lokoja zone of the Nigerian Meteorological Agency (NIMET). It is the primary agency of the Nigerian government equipped with relevant meteorological facilities to collect the bulk of daily, monthly, and yearly data on weather and climate data. The agency has branches located in the 36 state capitals, Nigeria. The 12-year rainfall datasets ranged from 1st January 2008 to 31st December 2020. The datasets comprised the bulk of daily, monthly, and yearly rainfall amounts. Remarkably, such long-term datasets were engaged to thoroughly examine and make known the steadiness of the bearing effect of the rainfall amount and their attenuation level effects in the study location, especially about microwaves radio frequency cellular communication links.


### 3.3. Stepwise Procedure

This work employs a practical based stepwise method to actualize the research aim. The practical based stepwise methodology is highlighted:(i)
Obtain the rainfall data and its related modeling parameters(ii)
Convert the rainfall data to rain rate using the expression in the following equation(13)Rr=Lm60T,where T and Lm indicate the rainfall time interval in min and rainfall depth in mm. The Rr defines the rain rate.
(iii)
Explore the theoretical specific framework for the rain attenuation model, provided in detail in Section2(iv)
Engage the calculated rain rate values with the power-law ITU-R model [56] (see equation (2)) to determine the specific attenuation levels for the study location(v)
Compute the rain rate intensity attenuation levels for different time percentages in the range of 0.001–1% (see equation (6))(vi)
Examine the effect of different microwave radio propagation path lengths on the specific attenuation levels(vii)
Establish the connection between the rain rate values and the specific attenuation values(viii)
Examine the effect of different horizontal and vertical polarisation on specific attenuation levels(ix)
Establish the connection between the raindrop size and rain rate values


## 3.1. Study Area

Kogi state, a midcentral (middle belt) zone of Nigeria, is a case study for the research work. Kogi, which connotes “River” in the Hausa language, houses a confluence town, where River Niger and Benue meet. The region holds a tropical climate with inconstant dry and rainy seasons in duration, timing, and severity. Despite the region’s relatively irregular dry and rainy seasons, the total annual rainfall depth varies between 805 mm and 1767 mm. It is a tropical region of Nigeria with low humidity of about 30% in the dry season and high humidity of approximately 70% during the wet season [65, 66]. The rainy wet season of the region usually brings cooler weather, mainly due to cloud cover increase that most time acts as a blockage to the intense tropical sunshine. However, during afternoons, this season can be as hot and humid due to the surrounding rocky soils and the riverine nature of the area. During dry seasons, the sun shines over the expanse with little or no blockades from the atmosphere, thus making the season in the region a period of hot and warm temperature conditions [67]. But in the mid-dry season, which is usually around December/January, the hot sun’s rays are partly blocked by the Harmattan haze and dust, which often results in lower temperatures. Its annual temperature is ranged between 27.7°C and 37.7°C in the wet and dry seasons. The average daily vapour pressure and wind speeds are 26 Hpa and 89.9 km/hr.


## 3.2. Data Collection

The 12-year rainfall datasets explored for this study were acquired with support from the Lokoja zone of the Nigerian Meteorological Agency (NIMET). It is the primary agency of the Nigerian government equipped with relevant meteorological facilities to collect the bulk of daily, monthly, and yearly data on weather and climate data. The agency has branches located in the 36 state capitals, Nigeria. The 12-year rainfall datasets ranged from 1st January 2008 to 31st December 2020. The datasets comprised the bulk of daily, monthly, and yearly rainfall amounts. Remarkably, such long-term datasets were engaged to thoroughly examine and make known the steadiness of the bearing effect of the rainfall amount and their attenuation level effects in the study location, especially about microwaves radio frequency cellular communication links.


## 3.3. Stepwise Procedure

This work employs a practical based stepwise method to actualize the research aim. The practical based stepwise methodology is highlighted:(i)
Obtain the rainfall data and its related modeling parameters(ii)
Convert the rainfall data to rain rate using the expression in the following equation(13)Rr=Lm60T,where T and Lm indicate the rainfall time interval in min and rainfall depth in mm. The Rr defines the rain rate.
(iii)
Explore the theoretical specific framework for the rain attenuation model, provided in detail in Section2(iv)
Engage the calculated rain rate values with the power-law ITU-R model [56] (see equation (2)) to determine the specific attenuation levels for the study location(v)
Compute the rain rate intensity attenuation levels for different time percentages in the range of 0.001–1% (see equation (6))(vi)
Examine the effect of different microwave radio propagation path lengths on the specific attenuation levels(vii)
Establish the connection between the rain rate values and the specific attenuation values(viii)
Examine the effect of different horizontal and vertical polarisation on specific attenuation levels(ix)
Establish the connection between the raindrop size and rain rate values


## 4. Results and Discussions

The specific attenuation results are presented and discussed in this section. The results are obtained using a combination of the acquired 12-year rainfall dataset together with the ITU-R power law-based model and the rain rate conversion models, as expressed in equations (1), (2), (3), and (4). All the graphical results displayed (Figures 1–11) are plotted using MATLAB. First, the rainfall datasets were divided into three components based on their depth amount in mm. These include heavy, heavy, and extremely heavy, ranging from 10-59 mm, 60-89 mm, and 90-130 mm. The heavy rain depth falls from October to November, while very heavy and extremely heavy rains are obtained between April to June and July to September. Figure 1 and Table 1 display the cumulative distribution of the computed rain values due to the three classes of rain depths. The three rainfall classes produced average rain rates of about 29.27 mm/hr, 73.71 mm/hr, and 105.39 mm/hr during the investigation. Higher rain depths result in larger rain rate intensities from Table 1 and vice versa. For example, while heavy rain depth produced a 59.18 mm/hr maximum rain rate, 100.57 and 122.15 maximum rain rate values were attained due to very heavy rain and extremely heavy rain depths. Similarly, while heavy rain depth recorded a 12.28/hr minimum rain rate, 60.36 and 80.50 minimum rain rate values were achieved for the very heavy rain and extremely heavy rain depths.Figure 1
CDF statistical distribution of rain rates due to different rainfall depth.Figure 2
Raindrop size distribution evaluation with model 1.Figure 3
Raindrop size distribution evaluation with model 2.Figure 4
Connection between raindrop size and rain rate.Figure 5
Specific attenuation due to heavy rainfall at different path lengths.Figure 6
Specific attenuation due to very heavy rainfall at different path lengths.Figure 7
Specific attenuation due to extremely heavy rainfall at different path lengths.Figure 8
Specific attenuation versus path lengths of different rainfall depths.Figure 9
Specific attenuation versus frequency of different rainfall depths.Figure 10
Specific attenuation versus time percentage due to vertical polarisation.Figure 11
Specific attenuation versus time percentage due to horizontal polarisation.Table 1
Statistics of rain rates due to different rain depth.
Statistics
Rain rate due to heavy rainfall
Rain rate due to very heavy rainfall
Rain rate due to extremely heavy rainfall
Mean
29.27
73.71
100.39
Minimum
12.28
60.36
85.50
Maximum
59.18
100.57
122.15
Moment
12.28
60.36
85.50
Kurtosis
2.90
2.25
1.13
Skewness
0.71
0.56
-0.10Employing models 1 and 2, Figures2 and 3 display the resultant logarithm sales of DSDs versus linear values of D for the three different rain rate classes averaged over 12 months. The significant difference between models 1 and 2 is that the latter considers more modeling parameters and a more extensive range of D values than the former, as revealed in equations (12) and (9). The results in the two graphs indicate that more significant rain rates values are composed of a higher dimension of raindrop diameters than lower rain rates. Remarkably, both DSD results attained maximum divergence at higher raindrop diameters. Figures 2 and 3 suggest that ND depends on rain rates and D and other climatic parameters like rainfall type.Figure4 provides graphical information on the connection between raindrop size and rain rate at diameter D=1mm and D=2mm, respectively. A gradual increase in rain rate (intensity) at lower values is seen in the graph as the distribution rainfall sizes become higher and more expansive. However, the gradual increase becomes slower and tends to logarithm stability at larger peak rain rate values of 100-120 mm h −1. This trend may suggest that the ND may reach an equilibrium state at higher rain rates. Attaining an equilibrium state at higher rain rates agrees with the results of other authors in [68–71] that a peak ND value is attained in correspondence with specific rain rates, wherein the raindrop sizes either become stable or fall subsequently. It is also clear from Figure 4 that the ND results are mainly dependent on D sizes and the model engaged for its distributive analysis.Figures5–7 display the prognostic specific attenuation versus rain rate values at different path lengths for heavy, heavy, and extremely heavy rainfall depths. For higher rainfall rate values at higher path lengths, the aggregate atmospheric attenuation also rises steadily with heavy, very heavy, and extremely heavy rainfall depths. Higher rainfall depths lead to higher attenuation of propagated microwaves radio signals due to more signal scattering and absorption between the communication paths.Figure8 displays the computed rain-specific attenuation levels against different communication path lengths and rain depth for the study location. A quick observation from Figure 8 shows almost a direct relationship between specific attenuation levels and the communication path lengths. This trend indicates that increased communication paths between the transmitter and receiver would yield higher attenuation values due to path obstructions, especially where scattering and rain absorption are key components.Figure9 shows the computed rain-specific attenuation levels against frequency at different rain depth amounts for the study location. A key observation from Figure 9 shows a noticeable rise in attenuation values between 1 and 2 GHz and then drops a little as the frequency range increase. This trend reveals that signal transmission at higher frequencies would undoubtedly be more degraded by rain attenuation in the investigated area. Higher attenuation values were observed in Figure 9 for higher rainfall depths, which can be ascribed to more signal scattering and absorption as the raindrop increases.Now, consider Figures10 and 11 that display the rain attenuation amount computed at different percentages of time for horizontal and vertical polarisations under the three rain depth classes, respectively. The rain attenuation decreases gradually for higher time percentages, stretching up to 0.89 dB, 1.71 dB, and 2.13 dB for vertical polarisation and 1.09 dB, 1.20 dB, and 2.78 dB horizontal polarisation, respectively. These values show that higher rain attenuation is observed for horizontal polarisation compared to vertical polarisation. Specifically, horizontal polarisation has a higher 12% attenuation value than vertical polarisation.


## 5. Conclusions

Signal propagation at different radio waves and microwave carrier frequencies in terrestrial point-to-point and Earth-space satellite communication links is greatly influenced by precipitation, principally rain. Thus, attenuation effects based on different atmospheric conditions must be investigated and quantified for effective design and efficient deployment of communication links. The current contribution explores a 12-year rainfall dataset to conduct realistic prognostic modeling of rain rate amount and specific rain attenuation intensity levels at 3.5 GHz. The atmospheric attenuation-based predictive modeling has been achieved by combining the ITU-R model with the experimental 60-minute intervals of rainfall data measured from 2008 to 2020. The rainfall datasets were classified into three components based on their depth amount in mm. These are heavy rain, very heavy rain, and extremely heavy rain, all of which ranged from 10-59 mm, 60-89 mm, and 90-130 mm, respectively. On average, the three rainfall classes produced rain rates of about 29.27 mm/hr, 73.71 mm/hr, and 105.39 mm/hr, respectively. The corresponding attenuation values are 0.89 dB, 1.71 dB, and 2.13 dB for vertical polarisation and 1.09 dB, 1.20 dB, and 2.78 dB horizontal polarisation, and both occurred at 0.01% time percentage computation. Our future work would focus on optimizing the projected rain rate models for improved performance.



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