## 2 Data and Background  
We use the GNSS data from the IGS network [39] as the TuRBTEC input data. We use the data from three stations: IRKJ, NTUS, and THU2. Table 1 shows the stations' coordinates: geographic latitude (Lat), geographic longitude (Lon), geomagnetic latitude (MLat), geomagnetic longitude (MLon). The coefficient \(\alpha\) is a parameter for the modified single-layer model mapping function (see below). To compare with the obtained results, we used data from the IONOLAB software ([[http://www.ionolab.org/](http://www.ionolab.org/)]([http://www.ionolab.org/](http://www.ionolab.org/))) [40] and software by Seemala [41], as well as data from ionospheric maps: Madrigal TEC [42] and CODE GIM [34]. It is free-to-use software and data. Figure 1 shows TEC from different techniques for the IRKJ region (52\({}^{\circ}\) N, 104\({}^{\circ}\) E). The upper panels display the IONOLAB-TEC (left, red line for vertical TEC) and SEEMALA-TEC (right, blue line for vertical TEC). The left bottom panel shows Madrigal TEC (orange line for vertical TEC). The right bottom panel shows TEC from all the above methods and TEC from CODE GIM.  
The IONOLAB software is based on a single-station solution [40]. The software uses only GPS data. The input is a pseudorange slant TEC corrected by CODE DCB. Slant TEC is projected to the local zenith to obtain the vertical TEC. Actually it is a zero order expansion. The least-squares method is used to obtain TEC estimates. Our experience showed the problem when negative or zero values appear: negative TEC values result in rejecting data for the whole day.  
[PERSON] developed a software for TEC calculations (referred to as SEEMALA-TEC) [41] based on a similar approach as that in the IONOLAB. However, it uses phase TEC leveled by pseudorange TEC. The vertical TEC is estimated as a mean from all satellites' vertical TECs. The software can estimate its own DCB, but our experience showed that it is better to use CODE DCB.  
Madrigal TEC is also based on projection of slant TEC to vertical TEC, but for different cells (1\({}^{\circ}\times 1^{\circ}\)) on the map [42]. They use a novel 3-steps technique to estimate DCB. Averaging data in  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Lat**, \({}^{\circ}\) & **Lon**, \({}^{\circ}\) & **MLat**, \({}^{\circ}\) & **MLon**, \({}^{\circ}\) & \(\alpha\) \\ \hline IRKJ & 52.2 & 104.3 & 47.7 & 178.3 & 0.97 \\ NTUS & 1.3 & 103.7 & \(-\)7.2 & 176.3 & 0.87 \\ THU2 & 76.5 & 291.2 & 83.8 & 27.1 & 0.94 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Position of GNSS stations.  
cells improves the data. However, in the regions, where there are few stations, it is difficult to have continuous and reliable data. Thus, we use a \(5^{\circ}\times 5^{\circ}\) region around a GNSS station and choose the median value as a Madrigal vertical TEC. Spline is used to smooth median TEC series.  
Global ionosphere maps are used for a long time to monitor and model the ionosphere [27]. We used CODE GIMs [30] that are based on spherical harmonics and modified single layer mapping function. We also used JPL GIMs based on multi-layer model. The GIM time resolution was 2 h for the analyzed data. We performed an algorithm operation simulation based on the international reference ionosphere model IRI-2012 [43] and the IRI-plas model [44] as a test.