# A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory
## 4 Discussion
### Comparison between the Kriging Method and HAS Method  
In addition to our comparison with the IRI prediction model initially used in the modeling process, we also considered a comparison with the now most-used Kriging interpolation method. Kriging interpolation is widely utilized for reconstructing regional ionospheric parameters like the foF2 and is known for proving high-quality reconstructions [31]. The Kriging method was chosen for comparison with the HAS method. The step of using the enhanced Kriging method for foF2 interpolation is outlined below. Firstly, we used the variational function established by the Euclidean distance between the observation station points and found the spatial relativity. Secondly, we used the optimal linear unbiased estimation as the foundation and the minimum estimation variance as the standard to solve for the weight coefficients of each training station relative to the validation station. We ensured that the sum of these weight coefficients was equal to one. According to the weight coefficients, the actual observations of the training stations were used to achieve the foF2 reconstruction results of the validation stations. Next, six out of  
Figure 7: Comparison of the results of the two predictions of the IRI model and the HAS method. the seven modeling stations were sequentially designated as training stations, while the remaining one served as the validation station. The foF2 predictions for the validation station were then computed using both the Kriging method and the HAS method. The RRMSEs of the seven stations were calculated as the final prediction RRMSE of the six validation datasets mentioned above, and the results shown in Table 1 were obtained. As shown in Figure 8, it can be seen that the predictions of the HAS method were significantly better than those of the Kriging interpolation method. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Solar Activity**} & \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Season**} & \multirow{2}{*}{**Month**} & \multicolumn{2}{c}{**Local Time**} & \multicolumn{2}{c}{**RRMSE (\%)**} & \multirow{2}{*}{**Increase**} \\ \cline{5-10}  & & & & & **Time** & & & **Day** & & **Night** & **Kriging** & **HAS** & **(\%)** \\ \hline (1) & High & 2014 & Spring & November & 10:00 & Yes & & 20.10 & 9.27 & 10.83 \\ (2) & Middle & 2016 & Summer & January & 12:00 & Yes & & 15.28 & 8.13 & 7.15 \\ (3) & Low & 2018 & Autumn & March & 15:00 & Yes & & 11.11 & 10.28 & 0.83 \\ (4) & High & 2014 & Summer & December & 03:00 & & Yes & 34.37 & 18.07 & 16.30 \\ (5) & Middle & 2017 & Autumn & April & 22:00 & & Yes & 15.01 & 7.34 & 7.67 \\ (6) & Low & 2018 & Winter & July & 21:00 & & Yes & 20.09 & 8.09 & 12.00 \\ \hline \multicolumn{10}{c}{Mean} & \multicolumn{10}{c}{19.33} & 10.20 & 9.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Validation dataset prediction results based on solar activity epochs, seasons, and local time. Figure 8: Comparison of the results of the two predictions of the Kriging and HAS methods. (**a**) Solar activity epochs. (**b**) Season. (**c**) Local time. The RRMSEs at different solar activity levels are given in Figure 8a. The Kriging and HAS methods obtained the optimal forecasting outcomes with prediction RRMSEs of 15.15% and 7.74%, respectively, during the middle solar activity period. During the high solar activity period, the prediction RRMSEs of both the Kriging and HAS methods decreased relative to the medium solar activity period, with the prediction results of the Kriging method decreasing by 15.80% and those of the HAS method decreasing by 8.13%. At low solar activity periods, the difference between the prediction RRMSEs of the Kriging method and the HAS method is 6.41%.