# A Machine Learning-Based Method for Modeling TEC Regional Temporal-Spatial Map
## 3 Validation
That is, there is an apparent variation trend of the day, month, season, and year as well as periodic variation with the solar activity. Furthermore, the maximum TEC value in high solar activity years is obviously higher than that in low solar activity years, which further confirms the close relationship between the variation of TEC and solar activity. 2. The prediction curve of the proposed model is closer to the TEC observation curve than that of the IRI model. Especially in Roquetes and Dourbes, the prediction effect of the proposed model is significantly better than that of the IRI model. 3. In Nicosia, the prediction error of both the IRI model and the proposed model is the maximum. The RRMSE of the IRI model using CCIR coefficients and URSI coefficients and the proposed model are 98.65%, 78.18%, and 21.71%, respectively, in predicting the monthly mean values of TEC of Nicosia station. The main reason is that the station is located at the junction of Asia and Europe, and the dynamic characteristics of the ionosphere are complex. In addition, the valid observation data provided by the observation station are insufficient, or the observation data provided by the limited ionospheric observation station are not accurate due to the limitation of observation technology, which significantly impacts the modeling accuracy. 4. When the IRI model was used to predict TEC of Sopron and Chilton stations, it could be found from the results that both CCIR coefficients and URSI coefficients showed double peaks that did not conform to the law of diurnal variation of TEC. This is one reason that the prediction error of the IRI model is higher than that of the proposed model. To make the data more intuitive, Figure 18 shows the predicted RMSEs and RRMSEs of three models in six stations during three solar activity epochs, respectively. By comprehensively analyzing Figure 18 and Table 3, we can draw the following three conclusions:  
1. Compared with the IRI model with CCIR and URSI coefficients, the predicted accuracy of the proposed model is improved by 38.63% and 35.79%, respectively, which is a significant improvement in parts of Europe. Similarly, other study [42] have also provided several sets of comparison graphs showing that the IRI model does have a significant deviation in TEC prediction, which further demonstrates the effectiveness \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical Analysis**} & \multicolumn{3}{c}{**RMSE (TECU)**} & \multicolumn{3}{c}{**RRMSE (\%)**} & \multicolumn{2}{c}{**Difference between**} & \multirow{2}{*}{
\begin{tabular}{c} **Difference between** \\ **CCIR and Prop. (\%)** \\ \end{tabular} } \\ \cline{2-3} \cline{5-10}  & **Item** & **CCIR** & **URSI** & **Prop.** & **CCIR** & **URSI** & **Prop.** & **CCIR** & **URSI** & **Prop.** \\ \hline \multirow{5}{*}{Station} & San Vito & 3.10 & 2.17 & 2.00 & 18.56 & 14.03 & 9.11 & 9.45 & 4.92 \\ \cline{2-3} \cline{5-10}  & Roquetes & 3.80 & 4.63 & 2.17 & 32.30 & 42.25 & 11.74 & 20.56 & 30.51 \\ \cline{2-3} \cline{5-10}  & Dourbes & 3.68 & 3.54 & 1.08 & 43.45 & 44.27 & 12.58 & 30.87 & 31.69 \\ \cline{2-3} \cline{5-10}  & Nicosia & 4.92 & 3.86 & 2.46 & 98.65 & 78.18 & 21.71 & 76.94 & 56.46 \\ \cline{2-3} \cline{5-10}  & Sopron & 2.01 & 2.09 & 0.51 & 42.30 & 48.57 & 7.04 & 35.26 & 41.53 \\ \cline{2-3} \cline{5-10}  & Chilton & 1.56 & 1.83 & 0.53 & 32.34 & 41.60 & 8.74 & 23.60 & 32.86 \\ \cline{2-3} \cline{5-10}  & High & 3.47 & 3.61 & 2.08 & 26.34 & 31.48 & 10.50 & 15.84 & 20.98 \\ \cline{2-3} \cline{5-10}  & Middle & 4.34 & 3.70 & 1.90 & 76.23 & 63.53 & 17.75 & 58.48 & 45.78 \\ \cline{2-3} \cline{5-10}  & Low & 1.80 & 1.97 & 0.52 & 37.65 & 45.22 & 7.94 & 29.71 & 37.28 \\ \hline \multicolumn{2}{c}{Average} & 3.37 & 3.20 & 1.65 & 51.39 & 48.55 & 12.76 & 38.63 & 35.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSE and RRMSE of different models in TEC prediction. of the PCA decomposition method in ionospheric parameters modeling and the necessity of the proposed model. 2.