# Improvement of Global Ionospheric TEC Derivation with Multi-Source Data in Modip Latitude
## 4 GIM Derivation from Multi-Source Data in Modip Latitude
### GIM Results  
The GIMs obtained by GACI are shown in Figure 7, where the red line represents the true magnetic equator. It can be seen from the GIMs that the phenomenon of EIA is clear near the magnetic equator, and there is no obvious unreasonable value due to the use of multi-source data.  
We used the data generated from the IRI model to study the impacts of the coordinate system in the global ionospheric TEC derivation in Section 3, and the conclusion remains unchanged when using the observation data, where the RMSE of the fitting residuals in different coordinate systems can be found at Figure 8. The mean improvement by using the modip latitude is about 7.02% in the 12 days of geomagnetic quiet conditions in 2014, and the performances of using geomagnetic and modip reference frames in the 3 days of June are quite close, but there are obvious improvements in the 3 days of March, September and December.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **DOY 081** & **DOY 173** & **DOY 265** & **DOY 356** & **Improvement** \\ \hline IRI(G)-GM & 5.1793 & 3.2043 & 4.2219 & 4.1886 & - \\ IRI(GAC)-GM & 4.9823 & 3.1556 & 3.9890 & 4.0723 & 3.54\% \\ IRI(G)-Modip & 4.4595 & 2.9835 & 3.8641 & 3.8950 & 9.48\% \\ IRI(GAC)-Modip & 4.2884 & 2.9768 & 3.8121 & 3.8889 & 10.88\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: RMSE in simulation by International Reference Ionosphere (IRI) model in 4 days of 2014.  
In Section 3, Figure 2 shows that the main differences between the reference data with the derived values in the modip latitude mainly exist in two regions: the SAMA region and EA, which is related to the position of the EIA. The SAMA region is a place where the lowest value of the total magnetic field intensity is situated, and has a relation with equatorial electrodynamic processes [31]. To investigate the fitting situation in these areas, data from the IRI model in the area of 20\({}^{\circ}\) S-20\({}^{\circ}\) N in modip latitude and 180\({}^{\circ}\) W-180\({}^{\circ}\) E in longitude were selected, and the residuals were studied. On DOY 265, 2014, the residuals have a mean value of 6.39 TECU, which ranges from 35.85 to \(-\)19.59 TECU and has an obvious diurnal variation. The mean value of the residuals starts to increase at around 9:00 UT and reaches the maximum at 17:00 UT, which has a relation with the positions of the EA and SAMA regions. According to Figure 7, the EIA started to reach the SAMA region at around 8:00 UT, and the residual values began to increase at the same time, reaching the maximum at around 17:00-19:00 UT, which happens to be the time when the longitude of the EIA coincides with the SAMA region.  
We also investigated the data for 3 days in September 2020 (DOY 264, 266, 268), which was a year of low solar activity, and the GIMs obtained by GACI on DOY 266, 2020 are shown in Figure 9. COSMIC-2 and JASON-3 were used in this calculation on the date  
Figure 8: RMSE of fitting residual with observation data in different coordinate systems in 2014.  
Figure 7: Global ionospheric maps (GIMs) calculated with GACI (DOY 265, 2014).  
we chose. Currently, COSMIC-2 is able to provide about 4000 radio occultations per day, which is helpful for global ionospheric mapping due to the increased number. Comparing Figures 7 and 9, the TEC fluctuations decrease obviously in the year of low solar activity, the maximum value dropping from about 100 TECU to 40 TECU. In 2014, the RMSE in a global scale decreases from [2.31; 3.33] TECU in geomagnetic latitude to [1.96; 2.91] TECU in modify latitude, while in 2020, the RMSE decreases from [1.35, 1.87] TECU in geomagnetic latitude to [1.29, 1.81] TECU in modify latitude, where the mean improvements are about 8.54% and 3.25% in the 3 days of September in 2014 and 2020, respectively. The performance using the modip latitude is less obvious in the year of low solar activity.