# Algorithm Research Using GNSS-TEC Data to Calibrate TEC Calculated by the IRI-2016 Model over China

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## Abstract

**:**

_{12}used as a driving parameter in the standard IRI model; thus, the errors between IRI-TEC and GNSS-TEC were minimized, and IRI-TEC was calibrated by modifying IRI with the updated IG

_{12}index (IG-up). This paper investigates various interpolation strategies for IG-up values calculated from GNSS reference stations and the calibrated TEC accuracy achieved using the modified IRI-2016 model with the interpolated IG-up values as driving parameters. Experimental results from 2015 and 2019 show that interpolating IG-up with a 2.5° × 5° spatial grid and a 1-h time resolution drives IRI-2016 to generate ionospheric TEC values consistent with GNSS-TEC. For 2015 and 2019, the mean absolute error (MAE) of the modified IRI-TEC is improved by 78.57% and 77.42%, respectively, and the root mean square error (RMSE) is improved by 78.79% and 77.14%, respectively. The corresponding correlations of the linear regression between GNSS-TEC and the modified IRI-TEC are 0.986 and 0.966, more than 0.2 higher than with the standard IRI-TEC.

## 1. Introduction

_{12}, is used as the main driving control parameter of the model to calculate the peak electron density, NmF2; and the 12-month global average number of sunspots, RZ

_{12}, is used as the main driving control parameter of the model to calculate the peak electron density height, hmF2 [13].

_{12}index and the RZ

_{12}index to improve the model’s accuracy [35,36,37,38,39,40,41]. For instance, Nicholas Ssessanga et al. ingested GNSS-TEC data into the IRI-2012 model, and by adjusting the IG

_{12}and RZ

_{12}indices simultaneously, obtained a modified IRI-2012 model that was more accurate than the original model in estimating TEC [39]. Lei Liu et al. incorporated global ionosphere map (GIM) TEC data from Europe into IRI-2016 and retrieved the effective ionospheric index per hour at different latitudes to improve the accuracy of the IRI model [41]. Notably, in this method, the updated IG

_{12}/RZ

_{12}index is a parameter that includes the error of the CCIR/URSI coefficient rather than a means of characterizing the original sunspot and ionospheric variation activities.

_{12}index is a driving parameter of IRI model which was introduced by Liu et al. It is obtained by adjusting the CCIR model of foF2 to the noontime measurements of several reference ionosonde stations [42]. At present, the index is produced based on four stations (two from the Northern Hemisphere and two from the Southern Hemisphere), which limits the reliability of this index to represent the global ionospheric conditions. This paper mainly focuses on the second approach to improve the IRI-2016 model based on GNSS-TEC data, namely updating the IG

_{12}index with GNSS-TEC data to improve the accuracy of the TEC values calculated by the IRI-2016 model. Importantly, the updated values of the IG

_{12}index based on GNSS-TEC are different in different regions and at different times. Therefore, the interpolation of the updated IG

_{12}for engineering users without GNSS-TEC to obtain the calibrated TEC from the modified IRI-2016 model, such as users of navigation and positioning or users of radar communication, is important for reducing the impact of the ionosphere on such systems. Consequently, this paper proposes various methods of interpolating the updated values of the IG

_{12}index in time and space and will demonstrate and evaluate the impact of these different interpolation methods on the accuracy of the TEC values over China calculated using the IRI-2016 model.

_{12}index, we do not update the RZ

_{12}index.

## 2. Data and Methodology

#### 2.1. Data

_{12}index of the IRI-2016 model, and the TEC data obtained from the remaining 12 stations were used to evaluate the accuracy of the TEC results calculated using the improved IRI-2016 model. The locations of the GNSS receiver stations are shown in Figure 1. Considering the close relationship between the ionosphere and solar activity [47,48], we chose data spanning one day a week in 2015 and 2019 to include the variations occurring during high solar activity and low solar activity; moreover, considering the impact of geomagnetic activity on the ionospheric TEC, only dates when the disturbance storm time (Dst) index was greater than −30 nt, namely, quiet days, were selected in this study.

#### 2.2. Methodology

_{12}index to optimize the model performance. Afterward, the updated IG

_{12}index (IG-up) is interpolated using various temporal and spatial interpolation methods to obtain spatiotemporally continuous and high-precision IRI-TEC values to meet the needs of users in China. First, to obtain the IG-up values, the difference (DTEC) between GNSS-TEC as estimated from the observation data of GNSS stations at 46 different locations and IRI-2016-TEC is used to iteratively adjust the IG

_{12}index, such that DTEC is below a set threshold (|DTEC| < 0.5 TECu). To some extent, the IG-up values reflect the error of the CCIR coefficient in describing foF2 at different times and spatial locations; consequently, IG-up varies greatly with time and space. Taking the first four days of 2015 as an example, Figure 2 shows the changes in time and space between the original IG

_{12}index of the IRI-2016 model and IG-up at stations HRBN (45.70°N, 126.62°E) and GDZJ (21.15°N, 110.30°E). On this basis, this section will discuss various interpolation methods for IG-up values at different temporal and spatial scales and evaluate the accuracy of the TEC results estimated by the IRI-2016 model when driven by the interpolated IG-up values.

_{12}values of the two stations are directly obtained from the internal ig_rz.dat in the IRI model, and the updated IG

_{12}values are calculated iteratively by ingesting GNSS-TEC data into the IRI-2016 model. The difference between IRI-TEC and GNSS-TEC determines the changing trend of the updated IG

_{12}. The updated IG

_{12}index (IG-up value) varies greatly with time, as shown in Figure 2. Using different time intervals when designing an IG-up interpolation scheme will affect the accuracy of TEC estimation using the improved IRI-2016 model. Thus, this paper designs and compares three different temporal interpolation schemes for IG-up:

_{12}index is iteratively updated at time intervals of 1 h, that is, at 0:00, 1:00, 2:00, …, 24:00, to obtain the IG-up value for each hour.

_{12}index is iteratively updated at time intervals of 2 h, that is, at 0:00, 2:00, 4:00, …, 24:00, to obtain the IG-up value every two hours.

_{12}index is iteratively updated at time intervals of 4 h, that is, at 0:00, 4:00, 8:00, …, 24:00, to obtain the IG-up value every four hours.

_{i}and T

_{i+}

_{1}are two consecutive epochs and IG

_{i}and IG

_{i+}

_{1}are the IG-up values corresponding to these two epochs, respectively.

_{i}is the IG-up value at the i-th GNSS observation station surrounding the grid node, and ${d}_{i}$ is the spherical distance from this observation station to the grid node. k is the power of the inverse distance; generally, $0\le k\le 3$. The larger the value of k is, the more prominent the role of adjacent points [49,50]; in this study, k = 2. After obtaining the grid map of the IG-up values, the user can refer to the interpolation method for TEC products in the International GNSS Service (IGS) IONEX format [51] and use Expression (3) to interpolate IG-up:

#### 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:$$\mathrm{MAE}=\frac{1}{n}\sum _{k=1}^{n}|TECG(k)-TECiri(k)|,$$$$\mathrm{RMSE}=\sqrt{\frac{{\sum}_{k=1}^{n}|TECG(k)-TECiri(k){|}^{2}}{n}},$$$$\mathrm{PI}=\frac{{X}_{UPDATE}-{X}_{ORIGIN}}{{X}_{ORIGIN}}\cdot 100[\%],$$

## 3. Results and Analysis

#### 3.1. Comparison of IG-Up Interpolation Schemes with Different Time Intervals

_{12}index and the results are substituted back into the IRI-2016 model, it can be seen that there is no obvious difference in the TEC values between the improved IRI-TEC and GNSS-TEC. In addition, compared with scheme 3 (4-h intervals), the TEC values under scheme 1 (1-h intervals) and scheme 2 (2-h intervals) exhibit a more accurate TEC “noontime bite-out” phenomenon that is more consistent with the GNSS-TEC behavior. From the data for 8–12 UT at station GXHC in Figure 3 and for 12–16 UT at station NMTK in Figure 4, it can be seen that when the TEC value becomes complex, the TEC results of schemes 2 and 3 exhibit obvious fluctuations compared with GNSS-TEC, while the TEC results of scheme 1 are consistent with GNSS-TEC.

_{12}values and GNSS-TEC and between the modified IRI-TEC results calculated using the IRI-2016 model driven by the three different IG-up temporal interpolation schemes and GNSS-TEC in 2015 and 2019. The sampling interval used is 1 min.

#### 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

_{12}index (IG-up) values on the TEC precision of the IRI-2016 model was discussed. Considering that the IG-up values vary greatly in time and space, 1-h, 2-h, and 4-h temporal interpolation schemes, a grid-based spatial interpolation scheme with spatial resolutions of 2.5° in latitude and 5° in longitude, and a spatial interpolation scheme based on the division into latitude zones over China were proposed, and their respective impacts on the accuracy of the TEC estimates calculated using the improved IRI-2016 model were demonstrated. Using high-precision TEC data obtained from 12 other GNSS reference stations in 2015 and 2019, the optimally integrated interpolation scheme for IG-up, with a 1-h temporal resolution and a 2.5° × 5° spatial resolution, was then evaluated in terms of its effectiveness in driving the IRI-2016 model to compute the TEC. The conclusions derived from the results are as follows:

- 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

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**Figure 1.**Distribution of the 58 GNSS stations used in this work (the red triangles represent the stations used to improve the IRI-2016 model, and the green five-pointed stars represent the stations used to evaluate the improvement effect on the IRI-2016 model).

**Figure 2.**Updated IG

_{12}index (IG-up) at stations HRBN and GDZJ (HRBN-Updated and GDZJ-Updated) and the original IG

_{12}index (IG-Orig).

**Figure 3.**Comparison between TEC estimates corrected using different temporal interpolation schemes and GNSS-TEC at six receiver stations on the first day of 2015.

**Figure 4.**Comparison between TEC estimates corrected using different temporal interpolation schemes and GNSS-TEC at six receiver stations on the first day of 2019.

**Figure 5.**2-D distributions of GNSS-TEC, the TEC estimates calculated using the original IRI-2016 model, and the TEC estimates obtained using schemes A and B in the parts of China region at the four time points of 0, 6, 12, and 18 UT on April 9 (DOY099) 2015.

**Figure 6.**2-D distributions of GNSS-TEC, the TEC estimates calculated using the original IRI-2016 model, and the TEC estimates obtained using schemes A and B in the parts of China region at the four time points of 0, 6, 12, and 18 UT on April 9 (DOY099) in 2019.

**Figure 7.**Boxplots of the differences (DTEC) between GNSS-TEC and the TEC estimates calculated using the original IRI-2016 model, scheme A and scheme B at 12 verification stations in 2015 (green, blue, and red boxes correspond to IRI-2016, scheme B and scheme A, respectively).

**Figure 8.**Boxplots of the differences (DTEC) between GNSS-TEC and the TEC estimates calculated using the original IRI-2016 model, scheme A and scheme B at 12 verification stations in 2019 (green, blue, and red boxes correspond to IRI-2016, scheme B and scheme A, respectively).

**Figure 9.**Linear regression diagrams between GNSS-TEC data from 2015 and the corresponding results of IRI-2016 and upda-IRI-2016 for 12 stations divided by latitude.

**Figure 10.**Linear regression diagrams between GNSS-TEC data from 2019 and the corresponding results of IRI-2016 and upda-IRI-2016 for 12 stations divided by latitude.

(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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Zhang, 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