# A Machine Learning-Based Method for Modeling TEC Regional Temporal-Spatial Map
## 2 Modeling
### Modeling Determination  
#### 2.3.1 Modeling of Temporal Characteristics  
It is well known that photoionization is the main mechanism of ionospheric plasma generation, and solar radiation's energy mainly determines photoionization's intensity. The main parameters used to describe solar activity are the flux of the solar radio waves at 10.7 cm (\(F10.7\)) and sunspot number (\(R\)), which show similar periodic variation due to the influence of the corona and atmosphere. The 12-month mean \(F10.7\) (\(F10.7_{12}\)) is used to characterize the energy of extreme ultraviolet radiation (EUV) in the empirical model of solar radiation intensity [59]. The 12-month mean \(R\) (\(R12\)) reflects the average intensity of solar activity. Specifically, in a month, \(F10.7_{12}\) has 24 data points, corresponding to the 24 h of a day; that is, each hour corresponds to a value of \(F10.7_{12}\). The \(R_{12}\) and TEC are consistent with \(F10.7_{12}\). Studies have shown that \(F10.7_{12}\) and \(R12\) can better reflect photoionization intensity than daily \(F10.7\) and \(R\)[60]. In addition, [PERSON] [61] also used \(F10.7_{12}\) and \(R_{12}\) to establish a TEC prediction model suitable for low latitude areas of the equator, which was proved to have a great prediction effect, further illustrating the correctness and applicability of using \(F10.7_{12}\) and \(R_{12}\) to establish a long-term TEC prediction model. Figure 5 compares \(F10.7_{12}\), \(R_{12}\), and TEC in the same period using the data of the Fairford station at UT 0:00 from 2004 to 2020. It is evident that TEC keeps the same variation cycle with \(F10.7_{12}\) and \(R_{12}\); that is, rising or falling at the same time points. However, the variation of TEC in detail is slightly different from that of \(F10.7_{12}\) and \(R_{12}\). The value of TEC increased significantly in high solar activity years, showing prominent annual variation characteristics, which are also drawn in [62; 63]. Furthermore, we calculated the correlation  
Figure 4: Modeling and validation stations data and corresponding solar activity parameters: (**a**) the valid data period of the modeling and validation stations; (**b**) \(F10.7_{12}\) and \(R_{12}\) variation curve. coefficients between TEC and different solar activity parameters in 12 months and 24-h, which are given in Figure 6. The circle size corresponds to the correlation coefficients value. It can be seen that the corresponding correlation coefficients of the three solar activity parameters and TEC are all concentrated above 0.8, indicating that the three solar activity parameters have an obvious correlation with TEC. However, there are still some differences in the correlation coefficients of different parameters at the same time points. For example, at 19h in February, the correlation coefficient between \(F10.7_{12}\) and TEC is significantly greater than that of \(R_{12}\). Considering the coupling effect of two solar activity parameters on TEC in different aspects, \(F10.7_{12}\) and \(R_{12}\) are introduced into the temporal model together as independent variables. This paper focuses on the prediction and analysis of TEC, so we assume that the prediction of solar activity parameters is known [64; 65]. The time resolution of the temporal model is 1h. Given specific geographic coordinates and universal time, we can  
Figure 5: Comparison of monthly mean values of \(F10.7_{12}\), \(R_{12}\), and TEC in the same period using the data of the Fairford station at UT 0:00 from 2004 to 2020: (**a**) \(F10.7_{12}\); (**b**) \(R_{12}\); (**c**) TEC. Figure 6: The correlation coefficients between TEC and different solar activity parameters in 12 months and 24-h: (**a**) \(F10.7_{12}\); (**b**) \(R_{12}\); (**c**) mean values of \(F10.7_{12}\) and \(R_{12}\). establish a temporal map from solar activity parameters and periodic oscillations to TEC, as shown in (4):  
\[