The phenomenon known as “rain attenuation” describes how rain weakens radio signals as they travel through the sky. Raindrops’ absorption and scattering of the radio signal are the major phenomena influencing signal impairment. In most cases, too, signal attenuation is influenced by its frequency, the size of the drops of rain, and the volume of precipitation. In addition, heavy rainfall causes more attenuation than lighter rainfall because higher-frequency signals are more vulnerable to attenuation than lower-frequency signals [1]. Regarding satellite communication systems, rain attenuation is a critical issue since it can seriously impair signals sent from the satellite to the ground. As a result, signal propagation may be lost, data speeds may be decreased, and bigger or more potent satellite antennas may be required. Terrestrial-Satellite communication systems frequently employ strategies like frequency diversity, which involves transmitting the same signal on various frequencies, or adaptive power regulation, which modifies the signal’s power depending on the degree of attenuation, to lessen the impacts of rain attenuation. In millimeter-wave telecommunication systems, rain in propagation channels reduces the performance of signals, particularly radio signals over 10 GHz, via both terrestrial and satellite paths [2]. Various approaches have been proposed to mitigate the adverse effects of rain attenuation on communication networks. These include adaptive transmission power control, frequency diversity, and dynamic link adaptation techniques. However, the effectiveness of such mitigation strategies depends largely on the availability of accurate attenuation prediction models. Predictive models, therefore, play a vital role in network planning by enabling engineers to anticipate signal degradation and design communication systems that maintain acceptable quality of service under varying atmospheric conditions [3].

Time-series analysis has proven to be an effective tool for modelling meteorological phenomena and predicting future atmospheric behavior using historical datasets. The Autoregressive Integrated Moving Average (ARIMA) model and its seasonal extension, the SARIMA model, are widely used statistical models for time-series forecasting. SARIMA models are particularly beneficial when analyzing datasets with seasonal or periodic fluctuations, such as rainfall patterns and attenuation time series. Because rainfall often follows seasonal climatic cycles, SARIMA provides a suitable framework for modelling temporal variations in rain-induced signal attenuation [4].

In recent years, advances in artificial intelligence have introduced machine learning techniques as alternative approaches for forecasting complex environmental phenomena. LSTM systems, in particular, have proven to be highly effective at modeling non-linear temporal correlations within sequential datasets. LSTM systems are a class of recurrent neural networks designed to capture long-term dependencies in time-series data through memory cells and gating mechanisms. These characteristics allow LSTM models to learn complex patterns that may not be easily captured by traditional statistical models [5].

Although both statistical and machine learning approaches have been widely applied to forecasting environmental and atmospheric variables, their relative performance varies with the characteristics of the dataset and the geographic region under consideration. For instance, several studies have applied artificial neural networks and time-series models to predict rainfall patterns and attenuation effects in different climatic environments. Nevertheless, the effectiveness of these approaches in subtropical regions such as South Africa remains an important area of investigation, particularly for high-frequency communication systems where rainfall can significantly affect signal propagation [6].

The literature [7] uses rain rate and % of exceedance as input data to train machine learning artificial neural networks (ANNs) to anticipate rain-induced attenuation on higher bands on terrestrial and satellite connections in South Africa. It is also essential for estimating cost and predicting short and long-term performance of connection paths, which is crucial in the construction of dependable networks. [6] presented the use of ANNs as a method for assessing rain-induced attenuation via terrestrial-satellite connections at a higher frequency in South Africa. [4] compared the ARIMA and SARIMA models in a subtropical site to ascertain the attenuation of the signal by rain and make real-time forecasts of the attenuation of the rain signal to be applied to microwave, terrestrial, and satellite communication systems. The conclusions of the study showed that SARIMA was superior to ARIMA in predicting the attenuation due to rainfall in South Africa since it produced better results in its error measures.

Many methods have been applied to predict such events, such as numerical and machine-learning methods using historical time series and radar system information [8]. Today, the most widely used technique for forecasting rain attenuation is obtained and evaluated using radar image data from many sources, with a large body of quantitative research frequently used in forecasting attenuation [9]. The Box and Jenkins model [10]. One methodology that stands out for its effectiveness is ARIMA, which is generally acknowledged as one of the best approaches for evaluating time series data [10]. The ARIMA method can handle monthly rain attenuation time series data, but it does not support time series that involve seasonality. SARIMA has been extensively applied over the years in predicting the trend of rainfall [11], streams and lakes modelling [12], manufacturing and finances modelling [13], and water loss modelling [14], and water loss modelling [14]. Its fascination has attracted researchers’ interest in its strategy, owing to its distinctive features. It simplifies the forecasting process in that it enables researchers to use only one variable, a time series of data, in easy scenarios, but also in many more complex scenarios. A time series forecasting SARIMA model that will be used to forecast rains will need to be developed and assessed to effectively recognize signal attenuation caused by rains, limit the impact of attenuation, and allow network organizations to take the necessary actions ahead, and this will contribute towards enhancing the reliability of the broadband networks. [15] reported that different forecasting models must be used, examined, and compared in various geographic locations to enhance performance for locations under consideration. In making important decisions and executing strategic planning, attenuation forecasting is required to manage signal and aquatic difficulties successfully, for instance, landslides, loss of signal, quality of service (QoS), and extreme temperatures, amongst other concerns. There should also be the ability to objectively predict and estimate attenuation [16]. A time-series model used for future forecasting is the SARIMA model. Because it is based on a historical precipitation datum across time, the time series’s stochastic, seasonal, and periodic variables can be investigated [12]. [17] utilized the rainfall dataset in Dhaka city from 2000 to 2014 for their study on LSTM, Neural Network, and they achieved 76% accuracy in the LSTM model performance.

This model employs the LSTM methodology for data training; however, testing data indicates that the LSTM neural network yields significant outcomes with high accuracy compared to other weather prediction methods. The data collected from November 2007 to October 2017, at the National Climate Data Center (NCDC), provided a historical weather dataset, and the dataset includes a variety of meteorological characteristics, including pressure, temperature, humidity, and dew point [18]. LSTM networks were used [19] to efficiently capture non-linear traffic dynamics [19] by comparing his study to the existing literature, it was an intriguing possibility to show that the LSTM networks were made up of three layers, with the hidden layer made up of memory blocks, and, with the right training technique, the LSTM networks could determine the ideal time delays.

Research also indicates that the LSTM recurrent neural network on cloud data center workload forecasting models has produced empirical findings that suggest that the approach reduces the average squared errors by up to 3.17 × 10³, resulting in good prediction accuracy [20].

Since both approaches may resolve issues for both linear and non-linear data sets, we employ both models in this work. The objectives of the study are to make comparisons between SARIMA and LSTM models and to use the best model to find out the rain-induced attenuation and to make monthly rain attenuation time series predictions, based on information of the applications to wireless terrestrial and satellite transmission systems. Moreover, the hybrid model combination will be compared with either of the approaches in the current study. The most suitable model among all the stations that are considered in this study is the SARIMA model (0, 1, 0) (0, 1, 1) ₍₁₂₎.

Moreover, the results of this research can aid the Ku and Ka spectrum networks users in determining an effective way to measure and alleviate rain attenuation for better radiocommunication systems, the Internet of Things, natural disasters, and transport network control.

The first step in time series modeling is to visualize the dataset to check for a stationary mean and variation. If the dataset is not stationary with respect to the mean or variance, then differencing is employed; otherwise, a transformation is needed. Figures 4(a)-(f) present the trends of time series of rain-induced attenuation at Bloemfontein, Durban, East London, Nelspruit, Polokwane, and Pretoria, respectively. The results show that the time series has a seasonal cycle and is not stationary since the data are time series attenuation data. The ACF and PACF of the actual data, which can be seen in Figures 5-10, show that the attenuation data is not steady. To fit a SARIMA model, stationary data are needed for both the variance and mean. The seasonality tendency was evident in the attenuation time series data from 2023 to 2024 due to its nature. Moreover, the SARIMA model was used in this paper to predict attenuation for subsequent years. The comparative performance of SARIMA and LSTM models across the six locations reveals distinct patterns influenced by regional climatic characteristics. SARIMA demonstrates superior performance in inland regions such as Bloemfontein, Nelspruit, Polokwane, and Pretoria. These locations exhibit relatively stable and seasonal rainfall patterns, which are effectively captured by the linear and seasonal structure of the SARIMA model.

In contrast, the LSTM model outperforms SARIMA in coastal regions, particularly Durban and East London. These regions are characterized by higher rainfall variability and complex atmospheric interactions influenced by oceanic conditions. The ability of LSTM to model non-linear dependencies enables it to better capture these dynamics.

Furthermore, model performance varies across different months. Both models show improved accuracy during low-attenuation periods, while performance decreases during high-attenuation months such as March to April and October to November. This indicates the challenge of predicting extreme attenuation events. An important observation is the underestimation of peak attenuation values, where measured attenuation (~8 dB) exceeds predicted values (2 - 5 dB). This discrepancy is primarily attributed to normalization and smoothing effects during pre-processing, which tend to suppress extreme values. This limitation suggests the need for improved scaling techniques or hybrid modelling approaches for better peak prediction.

(a) (b)

(c) (d)

(e) (f)

Figure 4.Trends of time series of rain-induced attenuation at (a) Bloemfontein, (b) Durban, (c) East London, (d) Nelspruit, (e) Polokwane, and (f) Pretoria.

Figures 4(a)-(f) show a change in the monthly rain attenuation time series and a reduction in attenuation strength. Nelspruit experiences the most attenuation for roughly 60 seconds, or 8.2 dB, whereas Durban and Pretoria experience the lowest attenuation (Figure 4(b) and Figure 4(f)). The average attenuation between 2003 and 2024 was 8.5 dB, with a 0.1 standard deviation. The attenuation data are steady in terms of their mean and variance, as can be seen by looking at Figure 4(a)-(f). The ADF model is utilized for stationary data analysis.

ACF and PACFIdentification:

The ACF is used to measure the correlation between a time series and the lagged values. Important time-dependent trends are identified, and they help in establishing the impact of past values on future values [51]. The PACF computes the correlation between the time series and its lagged values after taking the effect of intermediate delays into consideration. It is employed in SARIMA models to ascertain the autoregressive (AR) component’s order to determine if SARIMA models have an MA component [52]. It helps determine the optimal number of lag observations (p) in SARIMA models. ACF and PACF must be employed to choose the optimum time-series models for predicting rain attenuation. They help determine if a deep learning technique (LSTM) or a standard statistical approach (SARIMA) is more suitable for certain locations based on their climatic factors. When the data is stable, it is ready for identification to produce the SARIMA model forecast (p, d, q) (P, D, Q) ₍₁₂₎. The attenuation statistics, ACF and PACF, are shown to help identify them. Figures 5-10 display rain attenuation data for ACF and PACF figures in Durban, Pretoria, Polokwane, Bloemfontein, East London, and Nelspruit, accordingly.

Prediction of SARIMA and LSTM Models:

We examine SARIMA and LSTM models within several frameworks. The evaluation of their performance metrics can be seen in Table 1.

Table 1.Evaluation of RMSE, MAPE, and MAE based on the SARIMA and LSTM models.

Figure 5.Bloemfontein’s ACF and PACF trends.

Figure 6.Durban’s ACF and PACF trends.

Figure 7. East London’s ACF and PACF trends.

Figure 8.Nelspruit’s ACF and PACF trends.

Figure 9. Polokwane’s ACF and PACF trends.

Figure 10.Pretoria’s ACF and PACF trends.

Time series analysis’s main objective is to predict future values [53]. Once we select the best model, we prepare it for prediction. The goal of the forecasting method is to boost confidence in the future prediction of the data; meanwhile, the decrease in reception for each research location was found to follow the same trend, suggesting that attenuation will happen at different places throughout South Africa within the same time of signal transmission. The time series plot and correlogram of the series were analyzed to determine the presence of non-stationarity, seasonality, and trend [54]. It is evident from the figures that the time series plot exhibits wave-like patterns, and Figure 4(a)-(f) shows that there are seasonal elements in the signal time series, which proves the sinusoidal wave-like shape on ACF plots in Figures 5-10.

Additionally, it can be inferred from Figures 5-10 that there were no apparent fluctuations in the series’ mean or variance across the time span covered for this investigation. The PACF plots in Figures 5-10 show significant rises during the first two seasonal lags (Lags 2 - 10, where lags are expressed in months). Figures 5-10 also display large increases in the non-seasonal lags from ACF plots, with one notable spike occurring at the first seasonal lag (Lag 7). The seasonally differenced series’ correlogram indicates that SARIMA (0, 1, 0) (0, 1, 1) ₍₁₂₎ would be a suitable model for time series attenuation. The model with the lowest values of the specified criteria is the best one.

Figures 11 through 16 clearly demonstrate the SARIMA, LSTM attenuation forecasting, residual, seasonality, and trend snap around zero to 0.10, as well as the consistent variance across time. The ACF and PACF plots in Figures 5-10also show that every spike, except Bloemfontein and East London, is within boundaries, indicating that none of them are significant and, thus, not autocorrelated. The efficacy of the fitted LSTM and SARIMA models in predicting rain-induced attenuation of the stations in question is then shown using actual and forecast performance measure graphs in Figures 11-16 and Table 1. To evaluate the forecast performance of the two approaches, we first look at their performance metrics. Table 1 illustrates that the values forecasted by the fitted SARIMA model are more accurate than those of the LSTM model at more time points. Figures 11-16, March to April and October to November appear to experience higher attenuation, and these months likely coincide with rainy seasons or periods of high atmospheric conditions in the location under consideration. As a result, when designing or operating communication systems in Bloemfontein, Durban, East London, Nelspruit, Polokwane, and Pretoria, there must be a plan for higher attenuation in specific months, such as March to April and October to November.

From the sequential data of March-April 2023 to October-November 2024, the trend of the plots presented in Figure 11 and Figure 16 shows the period during which we have signal loss during the months of the year. We can clearly see that there is fluctuation in the signal because of rain-induced attenuation during the months of March-April to October-November. The measured data were found to

Figure 11.Bloemfontein SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

Figure 12.Durban SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

Figure 13.East London SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

Figure 14.Nelspruit SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

Figure 15. Polokwane SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

Figure 16.Pretoria SARIMA, LSTM attenuation forecast, and the SARIMA seasonal series.

be around 8 dB, while the predicted attenuation ranges from about 2 to 5 dB. The observed underestimation of peak attenuation values (measured ~8 dB versus predicted 2 - 5 dB) can be attributed to the normalization and smoothing effects introduced during data pre-processing, particularly Min-Max scaling. While normalization improves model convergence, it may suppress extreme values if not properly inverse-transformed. This limitation highlights the need for improved scaling techniques or the incorporation of extreme value modelling to better capture peak attenuation events, which are critical for communication system design. Table 2 clearly shows the best model per station.

Table 2. Model comparison table.

The SARIMA and LSTM models for forecasting monthly rain-induced attenuation in South Africa’s subtropical areas were compared in this study. The results demonstrate that SARIMA provides better performance in inland regions characterized by stable and seasonal rainfall patterns, while LSTM is more effective in coastal regions with higher variability and non-linear dynamics. The findings highlight the significance of choosing predictive models because of regional climatic characteristics rather than adopting a single universal approach. Additionally, the observed underestimation of peak attenuation values indicates the need for improved modelling techniques capable of capturing extreme events. Generally, this research will lead to more credible attenuation prediction techniques, which are required in the design and optimization of high-frequency terrestrial and satellite communication systems.

The study has effectively evaluated the forecast performance of LSTM and SARIMA when it comes to estimating the rain attenuation of the studied stations in South Africa, using correlation analysis and performance measures to show the significant difference. Even while SARIMA has the lowest forecast error, the correlation index suggests that there is no discernible difference between the two approaches’ prediction values, and the performance metrics support these. As a result, they can be employed successfully to offset the predicted signal loss in the South African province. After the signatures of a set of various models were tested, the findings show that SARIMA tends to work better than LSTM in inland areas like Bloemfontein, Nelspruit, Polokwane, and Pretoria. However, LSTM demonstrates superior performance in coastal regions such as Durban and East London, where rainfall patterns exhibit higher variability and non-linear characteristics. This suggests that statistical models perform better in stable climatic regions, while deep learning models are more suitable for complex and highly dynamic environments. For subtropical terrestrial-to-satellite communication systems, the model could be used to determine the optimal planning time to reduce the impact of signal attenuation. These predictions can aid in developing climate-resilient communication infrastructure by identifying potential periods of significant signal degradation in communication systems. A limitation of the research lies in the infrastructure for collecting the data. In the future, hybrid models will be developed to examine, compare, and investigate the phenomena of signal loss in South Africa.

The authors would like to extend their sincere gratitude to Tshwane University of Technology in Pretoria, South Africa, as well as to the SAWS for supplying the data used in this study.