# A Machine Learning-Based Method for Modeling TEC Regional Temporal-Spatial Map
## 3 Validation  
As described in Section 2, the Nicosia, Chilton, and Sopron stations, which have less than 11 years of continuous data and are not involved in modeling, are used as validation stations. Meanwhile, to satisfy the comprehensiveness of validation, the Roquetes, San Vito, and Dourbes stations are selected from the modeling stations for validation. From the perspective of space, the geographical location distribution of validation stations is shown in Figure 15.  
Considering the distribution of the modeling region, we took 10\({}^{\circ}\) east longitude as the dividing line, adhering to the principle of taking 3 stations for each side. From the perspective of time, the stations used for validation cover the four seasons of spring, summer, autumn, and winter in low and high solar activity years. The selection of validation stations fully ensures the non-overlapping of spatial and temporal distribution and the comprehensiveness of validation. The details are listed in Table 2.  
For a given geographic latitude and longitude coordinates, year, month, universal time, \(F10.7_{12}\), and \(R_{12}\), the TECs for any time and location can be predicted using the process shown in Figure 16. The specific process is as follows:  
1. Using the temporal regression map (10) to calculate the time component \(\widehat{\text{T}}\)EC. 2. Using the temporal regression value \(\widehat{\text{T}}\)EC and the given geographical latitude and longitude coordinates, the final predicted \(\widetilde{\text{T}}\)EC value can be obtained by the modified Kriging interpolation method (5) for spatial reconstruction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Station**} & **Latitude** & **Longitude** & **Solar Activity** & **Seson** & **Month** & **Including in** \\  & & **(\({}^{\circ}\)N)** & **(\({}^{\circ}\)E)** & **Epoch** & **Year** & **Season** & **Month** & **Modeling** \\ \hline
1 & San Vito & 40.60 & 17.80 & High & 2015 & Spring & May & Yes \\ \hline
2 & Roquetes & 41.00 & 0.00 & High & 2014 & Summer & September & Yes \\ \hline
3 & Dourbes & 50.10 & 4.60 & Middle & 2004 & Autumn & October & Yes \\ \hline
4 & Nicosia & 35.10 & 33.20 & Middle & 2016 & Winter & February & No \\ \hline
5 & Sopron & 47.63 & 16.72 & Low & 2020 & Summer & August & No \\ \hline
6 & Chilton & 51.60 & \(-\)1.30 & Low & 2009 & Spring & June & No \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Validation stations data information. Figure 15: The geographical distribution of the validation stations. The predicted TECs of the 6 validation stations calculated by the proposed model (marked as Prop., black) are compared with the observed TECs (marked as Obs., blue) and the predicted TECs calculated by the IRI model with the CCIR coefficients (marked as CCIR, green) and the URSI coefficients (marked as URSI, red), respectively. Figure 17 shows the scatter plots of monthly mean values of TEC for a given year and month calculated using three models during three periods of solar activity. To better evaluate the performance of the models, the statistical RMSEs and RRMSEs of predicted TECs for different models are listed in Table 3. At the end of Table 3, we give  
Figure 16: Prediction flowchart. Figure 17: Day and night prediction results of TEC in different seasons: (**a**) San Vito station in May 2015; (**b**) Roquetes station in September 2014; (**c**) Dourbes station in October 2004; (**d**) Nicosia station in February 2016; (**e**) Sopron station in August 2020; (**f**) Chilton station in June 2009.  
the average prediction error when using different models to predict any station; that is, the error of different models when predicting six validation stations is calculated again to obtain the average value. Combined with Figure 17 and Table 3, we can draw the following four conclusions:  
1. The TEC curve predicted by the IRI model and the model proposed in this paper has a highly fitting variation trend with the observed TEC curve.