Algorithm Research Using GNSS-TEC Data to Calibrate TEC Calculated by the IRI-2016 Model over China
Abstract
:1. Introduction
2. Data and Methodology
2.1. Data
2.2. Methodology
2.3. Evaluation Methodology
- Evaluation scheme for the temporal interpolation of IG-up: High-precision TEC data extracted from six GNSS stations at different latitudes are used to drive the IRI-2016 model to calculate the IG-up values at different integer hours, and the IG(t) corresponding to a 1-min sampling interval is calculated via interpolation under scheme 1, scheme 2 and scheme 3 using Expression (1). Then, the interpolated results are substituted back into the IRI-2016 model to drive the output TEC. On this basis, we calculate the mean absolute error (MAE), root mean square error (RMSE), and precision improvement (PI) of the TEC estimates obtained with different time-interval schemes using Expression (4), Expression (5), and Expression (6), respectively, to evaluate the interpolation effects of the different time-interval schemes for IG-up.
- Evaluation scheme for the spatial interpolation of IG-up: High-precision TEC data extracted from 46 GNSS stations at different latitudes are used to drive the IRI-2016 model to calculate the IG-up values at different integer hours, and Expression (2) is used to calculate an IG-up map with a spatial resolution of 2.5° in latitude and 5° in longitude within the latitudinal range of 20°N–55°N and the longitudinal range of 70°E–135°E. On this basis, the IG-up values at integer hours corresponding to 12 other GNSS stations at different latitudes are then calculated via interpolation using Expression (3). At the same time, the average value of IG-up in each latitudinal zone is calculated, and the results are then substituted back into the IRI-2016 model to drive the output TEC. The two-dimensional (2-D) distribution of the calculated TEC output is compared with that of GNSS-TEC in China, the difference (DTEC) between the calculated TEC output and GNSS-TEC is calculated, and the DTEC distributions are compared using boxplots to evaluate the effects of different spatial interpolation schemes for IG-up.
- Evaluation scheme for the integrated interpolation of IG-up in time and space: Using high-precision TEC data extracted from 12 GNSS stations at different latitudes as a reference, the IG-up values obtained using the integrated interpolation scheme are substituted back into the IRI-2016 model to drive the output TEC. Then, the accuracy indices MAE, RMSE, and PI are calculated using Expression (4), Expression (5) and Expression (6), respectively, and the linear regression correlations of the TEC values are analyzed:
3. Results and Analysis
3.1. Comparison of IG-Up Interpolation Schemes with Different Time Intervals
3.2. Comparison of Spatial Interpolation Schemes for IG-Up
3.3. Evaluation of an Integrated Scheme for Interpolating IG-Up in Time and Space
4. Conclusions
- Taking GNSS-TEC as a reference, we compared the ionospheric TEC estimates calculated using the IRI-2016 model driven by IG-up values obtained with different temporal interpolation schemes: ① The MAEs of the TEC estimates under the 1-h interpolation scheme for 2015 and 2019 are 0.5 TECu and 0.4 TECu, respectively; the MAE PIs relative to IRI-2016-TEC are 90.00% and 86.21%, respectively; the RMSEs are 0.6 TECu and 0.5 TECu, respectively; and the RMSE PIs relative to IRI-2016-TEC are 90.91% and 86.84%, respectively. ② The MAEs of the TEC estimates under the 2-h interpolation scheme for 2015 and 2019 are 0.6 TECu and 0.5 TECu, respectively; the MAE PIs relative to IRI-2016-TEC are 88.00% and 82.76%, respectively; the RMSEs are 0.9 TECu and 0.6 TECu, respectively; and the RMSE PIs relative to IRI-2016-TEC are 86.36% and 84.21%, respectively. ③ The MAEs of the TEC estimates under the 4-h interpolation scheme for 2015 and 2019 are 1.4 TECu and 0.8 TECu, respectively; the MAE PIs relative to IRI-2016-TEC are 72.0% and 72.41%, respectively; the RMSEs are 2.0 TECu and 1.1 TECu, respectively; and the RMSE PIs relative to IRI-2016-TEC are 69.70% and 71.05%, respectively. From these results, it can be seen that the 1-h interpolation scheme is the best.
- Taking GNSS-TEC as a reference, we compared the ionospheric TEC estimates calculated using the IRI-2016 model driven by IG-up values obtained with different spatial interpolation schemes. According to the boxplots of the statistical results, the median differences (DTEC) between the TEC estimates calculated using the IRI-2016 model driven by IG-up values obtained via the grid interpolation scheme with a 2.5° × 5° spatial resolution and the GNSS-TEC data are closer to zero and more stable than those corresponding to the latitudinal-zone-averaging scheme. In addition, the upper and lower quartiles of the DTEC results of the grid interpolation scheme are more concentrated than those of the latitudinal-zone-averaging scheme, indicating that the former is the optimal space interpolation scheme for the IG-up values.
- Taking GNSS-TEC as a reference, we evaluated the ionospheric TEC estimates calculated using the IRI-2016 model driven by IG-up values obtained with the optimally combined interpolation scheme: The MAE and RMSE for 2015 are 1.2 TECu and 1.4 TECu, respectively; compared with those of the original IRI-2016 model (5.6 TECu and 6.6 TECu), the PIs are 78.57% and 78.79%, respectively. The MAE and RMSE for 2019 are 0.7 TECu and 0.8 TECu, respectively; compared with those of IRI-2016 (3.1 TECu and 3.5 TECu), the PIs are 77.42% and 77.14%, respectively. The correlations of linear regression with the GNSS-TEC data reach 0.986 and 0.966 for 2015 and 2019, respectively, being more than 0.2 higher than the corresponding correlations of IRI-2016-TEC with GNSS-TEC (0.770 and 0.738). In addition, overall, the TEC estimates calculated using the IRI-2016 model driven by IG-up values obtained with the comprehensive interpolation scheme show obvious improvements in years of both high and low solar activity, although the improvement effect in a year of high solar activity is better than that in a year of low solar activity.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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(a) | |||||||
---|---|---|---|---|---|---|---|
MAE (TECu) | MAE PI | ||||||
Station | IRI-2016 | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 1 | Scheme 2 | Scheme 3 |
GXHC | 11.5 | 0.5 | 1 | 2.8 | 95.65% | 91.30% | 75.65% |
XZNM | 4.2 | 0.5 | 0.7 | 1.3 | 88.10% | 83.33% | 69.05% |
NMAG | 3.5 | 0.4 | 0.5 | 1.0 | 88.57% | 85.71% | 71.43% |
SNXY | 3.4 | 0.4 | 0.6 | 1.1 | 88.24% | 82.35% | 67.65% |
NMTK | 3.5 | 0.4 | 0.5 | 1.0 | 88.57% | 85.71% | 71.43% |
HLHG | 3.6 | 0.5 | 0.5 | 1.0 | 86.11% | 86.11% | 72.22% |
Average | 5.0 | 0.5 | 0.6 | 1.4 | 90.00% | 88.00% | 72.00% |
(b) | |||||||
RMSE (TECu) | RMSE PI | ||||||
Station | IRI-2016 | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 1 | Scheme 2 | Scheme 3 |
GXHC | 16.3 | 0.6 | 1.5 | 4.2 | 96.32% | 90.80% | 74.23% |
XZNM | 5.7 | 1.0 | 1.2 | 1.9 | 82.46% | 78.95% | 66.67% |
NMAG | 4.3 | 0.5 | 0.6 | 1.3 | 88.37% | 86.05% | 69.77% |
SNXY | 4.5 | 0.5 | 0.8 | 1.5 | 88.89% | 82.22% | 66.67% |
NMTK | 4.3 | 0.5 | 0.7 | 1.3 | 88.37% | 83.72% | 69.77% |
HLHG | 4.6 | 0.7 | 0.8 | 1.7 | 84.78% | 82.61% | 63.04% |
Average | 6.6 | 0.6 | 0.9 | 2.0 | 90.91% | 86.36% | 69.70% |
(a) | |||||||
---|---|---|---|---|---|---|---|
MAE (TECu) | MAE PI | ||||||
Station | IRI-2016 | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 1 | Scheme 2 | Scheme 3 |
GXHC | 5.1 | 0.4 | 0.6 | 1.2 | 92.16% | 88.24% | 76.47% |
XZNM | 3.1 | 0.4 | 0.5 | 0.9 | 87.10% | 83.87% | 70.97% |
NMAG | 2.0 | 0.4 | 0.4 | 0.7 | 80.00% | 80.00% | 65.00% |
SNXY | 2.5 | 0.4 | 0.5 | 0.7 | 84.00% | 80.00% | 72.00% |
NMTK | 2.2 | 0.4 | 0.5 | 0.7 | 81.82% | 77.27% | 68.18% |
HLHG | 2.2 | 0.4 | 0.5 | 0.8 | 81.82% | 77.27% | 63.64% |
Average | 2.9 | 0.4 | 0.5 | 0.8 | 86.21% | 82.76% | 72.41% |
(b) | |||||||
RMSE (TECu) | RMSE PI | ||||||
Station | IRI-2016 | Scheme 1 | Scheme 2 | Scheme 3 | Scheme 1 | Scheme 2 | Scheme 3 |
GXHC | 7.3 | 0.5 | 0.7 | 1.8 | 93.15% | 90.41% | 75.34% |
XZNM | 4.2 | 0.5 | 0.6 | 1.3 | 88.10% | 85.71% | 69.05% |
NMAG | 2.5 | 0.4 | 0.5 | 0.9 | 84.00% | 80.00% | 64.00% |
SNXY | 3.1 | 0.5 | 0.6 | 0.9 | 83.87% | 80.65% | 70.97% |
NMTK | 2.7 | 0.5 | 0.5 | 0.9 | 81.48% | 81.48% | 66.67% |
HLHG | 2.7 | 0.5 | 0.5 | 1.0 | 81.48% | 81.48% | 62.96% |
Average | 3.8 | 0.5 | 0.6 | 1.1 | 86.84% | 84.21% | 71.05% |
MAE (TECu) | MAE PI | RMSE (TECu) | RMSE PI | |||
---|---|---|---|---|---|---|
Station | IRI-2016 | upda-IRI-2016 | IRI-2016 | upda-IRI-2016 | ||
GXNN | 11.2 | 2.6 | 76.79% | 13.6 | 3.2 | 76.47% |
YNJD | 11 | 2.3 | 79.09% | 13.5 | 2.8 | 79.26% |
SCNN | 10 | 2.6 | 74.00% | 12 | 3 | 75.00% |
HNLY | 5.9 | 1.9 | 67.80% | 7.5 | 2.4 | 68.00% |
SNAK | 3.6 | 1.1 | 69.44% | 4.3 | 1.2 | 72.09% |
XZSH | 3.7 | 0.5 | 86.49% | 4.5 | 0.6 | 86.67% |
NXZW | 3.6 | 0.6 | 83.33% | 4.1 | 0.7 | 82.93% |
XJQM | 3.6 | 0.5 | 86.11% | 4.2 | 0.6 | 85.71% |
BJFS | 3.6 | 0.5 | 86.11% | 4 | 0.6 | 85.00% |
XJXY | 3.6 | 0.6 | 83.33% | 4 | 0.7 | 82.50% |
NMAL | 3.6 | 0.7 | 80.56% | 4.1 | 0.8 | 80.49% |
XJBE | 3.4 | 0.4 | 88.24% | 3.9 | 0.5 | 87.18% |
Average | 5.6 | 1.2 | 78.57% | 6.6 | 1.4 | 78.79% |
MAE (TECu) | MAE PI | RMSE (TECu) | RMSE PI | |||
---|---|---|---|---|---|---|
Station | IRI-2016 | upda-IRI-2016 | IRI-2016 | upda-IRI-2016 | ||
GXNN | 4.8 | 1.2 | 75.00% | 5.8 | 1.5 | 74.14% |
YNJD | 4.6 | 0.7 | 84.78% | 5.5 | 0.9 | 83.64% |
SCNN | 4.0 | 0.7 | 82.50% | 4.7 | 0.8 | 82.98% |
HNLY | 3.5 | 1.2 | 65.71% | 4.2 | 1.5 | 64.29% |
SNAK | 2.6 | 0.5 | 80.77% | 2.9 | 0.6 | 79.31% |
XZSH | 2.7 | 0.8 | 70.37% | 3.0 | 0.9 | 70.00% |
NXZW | 2.7 | 0.6 | 77.78% | 3.0 | 0.7 | 76.67% |
XJQM | 2.4 | 0.4 | 83.33% | 2.7 | 0.5 | 81.48% |
BJFS | 2.3 | 0.5 | 78.26% | 2.6 | 0.5 | 80.77% |
XJXY | 2.5 | 0.6 | 76.00% | 2.8 | 0.7 | 75.00% |
NMAL | 2.4 | 0.7 | 70.83% | 2.7 | 0.8 | 70.37% |
XJBE | 2.4 | 0.5 | 79.17% | 2.6 | 0.6 | 76.92% |
Average | 3.1 | 0.7 | 77.42% | 3.5 | 0.8 | 77.14% |
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Zhang, W.; Huo, X.; Yuan, Y.; Li, Z.; Wang, N. Algorithm Research Using GNSS-TEC Data to Calibrate TEC Calculated by the IRI-2016 Model over China. Remote Sens. 2021, 13, 4002. https://doi.org/10.3390/rs13194002
Zhang W, Huo X, Yuan Y, Li Z, Wang N. Algorithm Research Using GNSS-TEC Data to Calibrate TEC Calculated by the IRI-2016 Model over China. Remote Sensing. 2021; 13(19):4002. https://doi.org/10.3390/rs13194002
Chicago/Turabian StyleZhang, Wen, Xingliang Huo, Yunbin Yuan, Zishen Li, and Ningbo Wang. 2021. "Algorithm Research Using GNSS-TEC Data to Calibrate TEC Calculated by the IRI-2016 Model over China" Remote Sensing 13, no. 19: 4002. https://doi.org/10.3390/rs13194002