# A Machine Learning-Based Method for Modeling TEC Regional Temporal-Spatial Map
## 3 Validation
The prediction error of the proposed model is the minimum at the low solar activity epoch, which is 7.94%, and the maximum at the middle solar activity epoch, which is 17.75%, both of which are lower than the IRI models. On the other hand, the IRI model with CCIR and URSI coefficients has the best predictions during the high solar activity year, and the prediction errors are 26.34% and 31.48%, respectively. 3. The IRI model is an empirical model applicable to the global scope, whereas the proposed model is a regional empirical model focusing on the parts of Europe region. The prediction accuracy of the regional model is better than that of the global model in specific regions. Namely, the regional model has better spatial adaptability and pertinence in ionospheric parameter prediction. The temporal resolution of the proposed model is 1h, and the spatial resolution can be accurate to \(1^{\circ}\times 1^{\circ}\) in geographic coordinates. Similarly, [PERSON] et al. used a \(2.5^{\circ}\times 5^{\circ}\) spatial grid and 1 h temporal resolution interpolated updated IG12 index to drive IRI-2016 to generate ionospheric TEC values consistent with IGS-TEC [17]. Figure 19 shows the spatial distribution of TECs predicted by the IRI model based on CCIR and URSI coefficients and the proposed model over parts of Europe at 06:00 UT in May 2009 (low solar activity year). It can be seen that TECs predicted by the three models show a similar spatial distribution. In particular, compared with the IRI model based on CCIR coefficients, the variation of the proposed model is closer to that of the IRI model based on URSI coefficients, which is consistent with the numerical validation results mentioned above. Furthermore, it can  
Figure 18: The comparison of the TEC prediction results between the model proposed in this paper and the IRI model: **(a)** RMSE of different stations; **(b)** RRMSE of different stations; **(c)** RMSE of different solar activity; **(d)** RRMSE of different solar activity; **(e)** total RMSE; **(f)** total RRMSE. be seen that the distribution of TEC contour lines at high latitudes is relatively scattered; that is, the TECs in this region are relatively gentle. While the TEC contour lines at low latitudes are more concentrated, indicating that the TEC variations in this region are more intense. In addition, the numerical range of TECs predicted by the three models is basically the same, and the changes in details are slightly different. Compared with the sampling values of the modeling stations, the predicted value of the model proposed in this paper is closer to the sampling value at a given station, which proves the validity and correctness. Figure 20 shows the spatial distribution of TECs predicted by the IRI model based on CCIR and URSI coefficients and the proposed model over parts of Europe at 06:00 UT in June 2014 (high solar activity year). In common with Figure 19, the TECs predicted by the three models show a similar spatial distribution; that is, the TECs located in the northwest region are smaller, while the TECs in the southeast region are larger. On the whole, the TECs predicted by the IRI model based on the URSI coefficients are the largest, followed by the IRI model based on the CCIR coefficients, and the predicted TECs of the model proposed in this paper are the smallest, which is consistent with the results mentioned in [42]; that is, when the IRI model predicts regional TEC, there will be an overall numerical deviation. Compared with the sampling values of the modeling stations, the predicted values of the proposed model are closer to the sampling values at a given station, and this model effectively improves the accuracy of the spatial TEC prediction model.