# A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory
## 3 Results  
To show the effect of the HAS method comprehensively, Figure 4 illustrates the change in the predicted RRMSE of the HAS method with the number of iterations at seven modeling stations during various randomly chosen times. As shown in Figure 4, the predicted RRMSE of the HAS model progressively diminished and exhibited a convergence trend as the iterations increased. The convergence rates differed across the stations, and the  
Figure 3: Gaussian equations for the left side of the coefficient matrix: (a) L (Green color) and (b) J (Orange color). Both L and J were fixed only at specific points, with the remaining values set to zero.  
final prediction errors were also significantly different, with some stations achieving better results with more than 30 iterations and others requiring more than 40 iterations to achieve better results.  
The choice of the number of iterations is crucial in the HAS regional foF2 spatial reconstruction method. To ensure the accuracy of the model and avoid overfitting, we adopted the following strategies:  
1. Based on experience and experimental results, we set the maximum number of iterations to 40. This setting was based on the observed model convergence and performance in multiple experiments.
2. During the iteration process, we continuously observed the model's performance, tracking the trend of the RRMSE at the validation station in particular. The judgment criteria for overfitting were mainly based on the results of cross-validation. When the RRMSE of the validation station showed a significant upward trend in several consecutive iterations, we considered that the model may have started to overfit and stopped the iteration immediately.  
1. The Darwin station has the best prediction effect, converging at iteration 31 with an RRMSE of 1.44%. The Learmonth station had a worse prediction effect, with an RRMSE of 9.26% at iteration 40, mainly because Learmonth had a higher amount of missing data during the modeling time, which had a certain negative impact on the effect of the iteration.
2. The Brisbane station had a better convergence effect, and a stable prediction error was obtained at 35 iterations. The Perth station reached convergence at iteration 38, with an RRMSE of 6.20%. The Canberra, Hobart, and Learmonth stations reached a better prediction effect after 40 iterations, but their errors still showed a decreasing trend.
3. The Townsville station achieved better prediction at the 26 th iteration, but after continuing the iteration, the prediction error showed a slight increase in the trend of overfitting. Therefore, applying the HAS method requires proper selection of the number of iterations to obtain a smaller error rate.
4. Taken together, the average RRMSE of 40 iterations for the seven stations above at different times was 4.83%, which demonstrates the accuracy and efficacy of the HAS method. Additionally, we employed the same approach to ascertain the necessary number of HAS iterations required to achieve the foF2 prediction using the HAS method, and the prediction results all converged to a satisfactory accuracy.