A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory
Abstract
:1. Introduction
2. Data and Methods
2.1. Data Collections
- The raw GIRO dataset includes 24 h of data collected daily. Initially, we computed the monthly average of the data at the seven stations and stored them sequentially. Missing data between 2013 and 2018 at the seven stations were supplemented with foF2 data predicted by the International Reference Ionosphere (IRI) model to facilitate spatial reconstruction.
- Given that the resolution of the data used for HAS modeling was 5° × 5°, we approximated the latitude and longitude of each station to the closest whole number and stored the monthly average foF2 values at fixed times in corresponding grid points to facilitate interpolation.
2.2. Modeling Data
2.3. Modeling Methods
- Generate a grid covering the modeling range, complete the data on the grid using the foF2 predicted by the IRI model, and then fill in the corresponding grid with the actual foF2 observations at the training station to generate the foF2’s initial value surface.
- Normalize the foF2’s initial value surface and compute the surface’s first class of fundamental quantities B, C, and D, second class of fundamental quantities E and F, and the Gaussian system of equations with the coefficients , , , and .
- For n ≥ 0, solve the iterative equations Lfn+1 = Mn and Jfn+1 = Nn for the latitudinal and longitudinal directions, respectively.
- For n ≥ 0, perform appropriate iterations to solve the iterative equation AFn+1 = R and obtain the numerical solution of the surface under the given boundary conditions. Then, apply inverse normalization to derive the predicted foF2 value at the validation station.
3. Results
- 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.
- 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.
- 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.
- 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.
- The Townsville station achieved better prediction at the 26th 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.
- 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.
4. Discussion
4.1. Comparison between the IRI Model and HAS Method
4.2. Comparison between the Kriging Method and HAS Method
- 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%. Therefore, the prediction effects of both methods varied with the solar activity level, and the prediction RRMSEs became smaller when the solar activity improved in the middle solar activity period relative to the low solar activity period, while the prediction RRMSE became larger in the high solar activity period relative to the middle solar activity period. This shows the important influence of solar activity on the foF2 from this side.
- The RRMSEs of the predictions using the two methods during the four seasons are given in Figure 8b. In spring, the HAS method predicted better results than the Kriging method, with a difference of 10.83% in the RRMSEs. In summer, the Kriging and HAS methods achieved the worst predictions. In autumn, the Kriging method reached the best prediction, but the prediction was still poor compared with that of the HAS method. In winter, the HAS method predicted the best results, with an RRMSE of 8.09%. Overall, the HAS method predicted better results than the Kriging method under all four seasons.
- The RRMSEs of both methods during the day and at night are shown in Figure 8c. The prediction RRMSE of the Kriging method decreased by 7.66% during the daytime compared with nighttime, and the prediction RRMSE of the HAS method increased by 1.94% during the nighttime compared with daytime. Overall, the HAS method’s predictions were better than the Kriging method both during the day and at night, and both method’s predictions were better during the day.
- Overall, the HAS method outperformed the Kriging method in different seasons, solar activity levels, and at daytime and nighttime. This confirms the effectiveness and precision of the HAS method introduced in this paper and provides a new approach and methodology for the prediction of ionospheric parameters.
- The reconstruction outcomes of the HAS and Kriging methods at 12:00 p.m. local time for the high solar activity year in November 2014 are illustrated in Figure 9a,b, respectively. The figures show that the value domains reconstructed by the HAS method ranged from 7.5 to 12, and the value domains reconstructed by the Kriging method ranged from 7.5 to 11.5, indicating that the values reconstructed by the HAS method would be larger than those reconstructed by the Kriging method in some regions. In addition, the results of the reconstruction by the HAS method can be observed as multiple obvious contour circles, which represent the large value variations of the local regions, with obvious high-value areas. In contrast, the contour lines in the reconstructed results of the Kriging method are relatively smooth, and there is no obvious local variation in the HAS method.
- Figure 9e,f shows the distribution of the RRMSEs of the HAS and Kriging methods in predicting the seven stations at 12:00 p.m. local time for the high solar activity year in November 2014, respectively, and the RRMSE plots of the HAS method show that the RRMSEs were larger at some points in the plots but smaller at most stations. Compared with the prediction of the RRMSEs for the Kriging method, the HAS method predicted the RRMSEs of all seven stations better than the Kriging method.
- The reconstruction outcomes of the HAS and Kriging methods at 12:00 a.m. local time for the low solar activity year in July 2018 are illustrated in Figure 9c,d, respectively. The figure shows that the local area reconstructed by the HAS method had a large change in value. For example, an obvious high-value area can be seen in the upper right of the figure. The transition between the high-value and low-value areas in the reconstructed results of the Kriging method is relatively smooth, and the characteristics of the spatial distribution are not as obvious as those of the HAS method, which lacks some details.
- Figure 9g,h shows the RRMSE distributions of the seven stations predicted by the HAS and Kriging methods, respectively, at 12:00 a.m. local time for the low solar activity year in July 2018. The RRMSE plots of the HAS method show that it was larger at the Perth station. All the other stations had smaller values than the predicted RRMSEs of the Kriging method, and as a whole, the HAS method was better. Overall, the HAS method is suitable for applications which are sensitive to local variations. However, it is important to note that some regions may have large RRMSEs.
- Overall, the HAS method showed high accuracy and reliability in the spatial reconstruction of the foF2 at different times and locations. Compared with the Kriging interpolation method, the HAS method can more accurately capture the spatial variation characteristics of the ionospheric parameters with smaller prediction RRMSEs.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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No. | Solar Activity Epoch | Year | Season | Month | Local Time | RRMSE (%) | Increase (%) | |||
---|---|---|---|---|---|---|---|---|---|---|
Time | Day | Night | Kriging | HAS | ||||||
(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 | |
Mean | 19.33 | 10.20 | 9.13 |
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Wang, J.; Han, H.; Shi, Y. A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory. Remote Sens. 2024, 16, 3247. https://doi.org/10.3390/rs16173247
Wang J, Han H, Shi Y. A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory. Remote Sensing. 2024; 16(17):3247. https://doi.org/10.3390/rs16173247
Chicago/Turabian StyleWang, Jian, Han Han, and Yafei Shi. 2024. "A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory" Remote Sensing 16, no. 17: 3247. https://doi.org/10.3390/rs16173247