## 5 Results and Discussion
### Quantitative Analysis of the ConvGRU Models Efficacy  
In this research, the ConvGRU methodology was employed, incorporating three distinct loss functions: ConvGRU-L\({}_{\text{C}}\), ConvGRU-L\({}_{\text{log-cosh}}\), and ConvGRU-L\({}_{\text{S}}\). The objective of this study was to facilitate real-time predictions of S4 values using these techniques. The processed S4 maps were divided into three distinct sets: training (70% of total data, covering the 1 st to 22 nd of January/March/July), validation (20% of total data, covering the 23 rd to 28 th of January/March/July), and testing (10% of total data, covering the 29 th to 31 st of January/March/July). In the experimental setup, the system utilized a NVIDIA GeForce RTX 3090 GPU, integrated with a CUDA 11.3 parallel processing architecture. The processing unit was complemented by an Intel Core i7-12700 KF CPU and a substantial 128 GB RAM capacity. For optimization in this research, the Adam algorithm, as outlined by [PERSON] and [PERSON] [64], was selected. The activation function employed was the Leaky ReLU, with a specified leakiness parameter of 0.1, following the methodology described by [PERSON] et al. [65]. Additionally, the learning rate and batch size for the experiments were configured at 0.00003 and 14, respectively, in accordance with the specifications in [35]. The training dataset was used to calibrate the model by updating its parameters via the gradient descent method. The validation set aimed to prevent overfitting to the training data, while the testing set was utilized to evaluate the trained model's efficacy in generalizing to new and previously unseen data, as outlined by [PERSON] et al. [66]. The initial phase of this part involved a comparative analysis of S4 modeling outputs generated by the ConvGRU method over a specific modeling interval against observed data collected during the same period. This research employed three statistical metrics to evaluate the modeling and predictive efficacy of the proposed machine learning approach: Mean Error (ME), Root Mean Square Error (RMSE), and Pearson Correlation Coefficient (CC). The equations for calculating these metrics are provided below:  
\[ME=\frac{1}{N}\sum_{i=1}^{N}\left(\hat{x}_{i}-x_{i}\right) \tag{25}\]  
Figure 5: Mean TEC values (red lines) and percentage of ionospheric scintillation occurrence (S4 > 0.2) (blue lines) derived from GNSS ground-based measurements across South America for January, March, and July in 2015 and 2020. \[RMSE=\sqrt{\frac{1}{N}{\sum_{i=1}^{N}{(\hat{x}_{i}-x_{i})^{2}}}} \tag{26}\]  
\[CC=\frac{cov(\hat{x}_{i},x_{i})}{\sigma_{\hat{x}_{i}}\sigma_{x_{i}}} \tag{27}\]  
The aforementioned equations incorporate the terms \(cov(\hat{x}_{i},x_{i})\), which represent the covariance between the variables \(\hat{x}_{i}\) and \(x_{i}\). Additionally, the parameters \(\sigma_{\hat{x}_{i}}\) and \(\sigma_{x_{i}}\) denote the standard deviations of \(\hat{x}_{i}\) and \(x_{i}\), respectively. Table 2 presents the parameter values for S4 during the modeling phases (training and validation) and the prediction (testing) interval. Additionally, this table includes the percentage occurrence of ionospheric flashes within the observation period. This metric is calculated based on the frequency of observations where S4 values exceed 0.2, signaling the presence of ionospheric flashes during that period. Analysis of the data from Table 2 reveals that the year 2015, a period of maximum solar activity, exhibited a higher percentage of ionospheric radiance compared to 2020, a year of minimal solar activity. In this research, the predictive accuracy of three advanced Convolutional Gated Recurrent Unit (ConvGRU) models--ConvGRU-L\({}_{\text{C}}\), ConvGRU-L\({}_{\text{log-cosh}}\), and ConvGRU-L\({}_{\text{5}}\)--was evaluated for modeling ionospheric scintillations in South America during January, March, and July of 2015 and 2020. The models were trained and validated using a substantial portion of the data, specifically encompassing the 1 st to the 28 th of each month.