# Effects of the 12 May 2021 Geomagnetic Storm on Georeferencing Precision
## 2 Materials and Methods
### Estimation of the Ionospheric Total Electron Content  
The slant TEC (STEC) and vertical TEC (VTEC) data were obtained from GNSS measurements based on dual-frequency signals \(f_{1}\) and \(f_{2}\). Then, STEC and VTEC were calculated using the program GPS-TEC from receiver independent exchange format (RINEX) files [62] ([[http://seemala.blogspot.com/](http://seemala.blogspot.com/)]([http://seemala.blogspot.com/](http://seemala.blogspot.com/)), accessed on 3 December 2021). In this work, VTEC values corresponding to satellite cut-off elevation angle 30\({}^{o}\) at 350 km altitude were selected to minimize possible errors. The temporal VTEC estimates were released every 30 s. The TEC values were corrected from the satellite and receiver bias using the data obtained  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Geomagnetic** & **Dst** & **Kp** & **AE** & **Stations** & & \\
**Storm** & **[nT]** & & **[nT]** & **N\({}^{\circ}\)** & & \\ \hline
7 January 2015 [56] & \(-\)99 & 6\({}^{+}\) & 2031 & 3 & GIPSY-OASIS & ROTI \\
17 March 2015 [57] & \(-\)223 & 8\({}^{-}\) & 2298 & \(\sim\)500 & GPS PPP Model & ROTI \\
17 March 2015 [58] & \(-\)223 & 8\({}^{-}\) & 2298 & 15 & gLAB software & DVTEC, TIDs \\
22, 23 June 2015 [59] & \(-\)204 & 8\({}^{+}\) & 2698 & 5172 & GAMP software & Spread-F, S4 \\
20 December 2015 [57] & \(-\)155 & 7\({}^{-}\) & 1946 & \(\sim\)500 & GPS PPP Model & ROTI \\
27 March 2017 [57] & \(-\)74 & 6\({}^{+}\) & 1505 & \(\sim\)500 & GPS PPP Model & ROTI \\
8 September 2017 [60] & \(-\)124 & 8\({}^{+}\) & 2677 & \(\sim\)700 & RTKLIB package & ROTI \\ \hline \hline \end{tabular}
\end{table}
Table 1: Example studies related to the impact of geomagnetic storms of Solar Cycle 24 (SC-24) on kinematic GPS positioning.  
from AIUB Data Center of Bern University in Switzerland ([[ftp://ftp.aiub.unibe.ch/CODE/](ftp://ftp.aiub.unibe.ch/CODE/)]([ftp://ftp.aiub.unibe.ch/CODE/](ftp://ftp.aiub.unibe.ch/CODE/)), accessed on 3 December 2021).  
The RINEX files were obtained from 868 GNSS stations (Figure 1), taked from: the International GNSS service (IGS) stations; the Chilean network of GNSS receivers operated by the National Seismological Center at University of Chile (CSN in Spanish); the Argentine Continuous Satellite Monitoring Network (RAMSAC in Spanish) [63]; the Brazilian Network for Continuous Monitoring of the Institute of Brazilian Geography and Statistics (IGBE in Portuguese); and the Crustal Dynamics Data Information System (CDDIS) of the National Aeronautics and Space Administration (NASA); University NAVSTAR Consortium (UNAVCO); the Geoscience Australia; and the African Geodetic Reference Frame (AFREF).  
In addition, the differential of VTEC (DVTE) in TECu and the percentage changes in VTEC (%DVTEC) were studied. These parameters are used in the analysis of ionospheric disturbances, defined as the relative variation of VTEC, epoch by epoch, with respect to the mean value (in time) of \(\overline{VTEC}\) as shown in Equations (1) and (2) [3].  
\[DVTEC_{t}=VTEC_{t}-\overline{VTEC_{t}} \tag{1}\]  
\[\%DVTEC_{t}=\frac{DVTEC_{t}}{\overline{VTEC_{t}}}\cdot 100 \tag{2}\]  
where \(t\) represents the epoch and \(\overline{VTEC}\) is calculated by averaging the values of VTEC for the reference DoVs 129, 130, and 131.  
Ionospheric TEC Maps  
We used the ordinary Kriging interpolation technique [64] to map the estimation of the VTEC at each ionospheric pierce point (IPP). We selected this interpolation technique to fill in the data gap of the global ionosphere TEC map and the inhomogeneous sparsity of GNSS receivers [65; 66; 67]. We performed the ordinary Kriging interpolation in Python with the package Kriging. The documentation for the package can be found in [[https://github.com/ERSSLE/ordinary_kriging](https://github.com/ERSSLE/ordinary_kriging)]([https://github.com/ERSSLE/ordinary_kriging](https://github.com/ERSSLE/ordinary_kriging)) (accessed on 3 December 2021).