## 2 Materials and Methods
### Ionospheric Models  
We used nine ionospheric models: Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC. These models require general information such as date-time and location and model-specific inputs such as broadcast coefficients or information about the solar and geomagnetic activity. Table 1 shows the models' input parameters and some peculiarities. All the models have different mathematical descriptions and coefficients. Figure 3 shows the spatial TEC distribution at 10:00 UT, 1 January 2020. The models differ in absolute values and time-space TEC peculiarities. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Input Parameters** & **References** \\ \hline Klobuchar & Broadcast coefficients & [15; 16] \\ NeQuickG & Broadcast coefficients, CCIR & [17] \\ BDGIM & Broadcast coefficients & [18; 19] \\ GLONASS 1 & _F10.7, Ap_ & [20] \\ IRI-2016 & IG12, URSI, topside—IRI-corr & [9] \\ IRI-2012 & IG12, URSI, topside—IRI-corr & [21] \\ IRI-Plas & IG12, URSI & [22] \\ NeQuick2 & _F10.7,_ CCIR & [10] \\ GEMTEC & _F10.7_ & [23] \\ \hline \hline \end{tabular} \({}^{1}\) We do not have broadcast coefficients, so we used indices _F10.7, Ap_, rather than broadcast parameters.  
\end{table} 
Table 1: Input parameters for the ionospheric models. Figure 3: TEC spatial distribution from different models (BDGIM, Klobuchar, NeQuickG, GLONASS, NeQuick2, GEMTEC, IRI-2016, and IRI-Plas) and GIM ISSG data. The model’s name is shown in the subtitle. The data is for 10:00 UT, 1 January 2020. GPS uses _the Klobuchar ionosphere model_ for single-frequency correction. The model was developed in the 1970-80s [16]; it has a simple mathematical formulation and, therefore, required low computational costs. Klobuchar model uses constant TEC (9.2 TECU) at nighttime and part of sine function during daytime. Parameters of sine function, which are eight coefficients, are calculated and broadcast through GPS satellite signals. The model provides ~50% ionospheric error correction. _NeQuick2_[10] is the latest version of ionospheric models based on the sum of Epstein layers [24]. It was developed by the Abdus Salam International Centre for Theoretical Physics (Trieste, Italy) in collaboration with the University of Graz (Austria). The model calculates median dynamics of the ionospheric density profile using 6 semi-Epstein layers with modeled thickness parameters and anchor points defined by foE, foF1, foF2, and M(3000)F2 values, modeled (ITU-R recommendations) or experimentally derived. NeQuick2 uses solar flux (\(F10.7\)) as input, providing an electron density profile at any location and time. The main advantage of the model is that it is quick-run and has easy calculations along any \"ground-to-satellite\" ray path. Using NeQuick formulation, the ESA developed _NeQuickG_[17] for single-frequency ionospheric correction. A Galileo satellite broadcasts three input coefficients (a0, a1, and a2) in the navigation message to compute effective solar flux (Az). NeQuickG uses the effective solar flux as an input to calculate slant TEC, while NeQuick2 uses \(F10.7\). NeQuickG also differs from NeQuick2 in the definition of the topside shape parameters. NeQuickG features high performance for single-frequency correction for both ground-based and space-borne users [25; 26]. BDS-3 uses a newly designed broadcast ionospheric model _BDGIM_--BeiDou Global Ionospheric delay correction Model--to mitigate the ionospheric delay errors in single-frequency positioning [18]. In contrast to the Klobuchar-like model adopted in the regional BDS-2 system, the BDGIM describes global VTEC distributions with a simplified spherical harmonic expansion referring to a sun-fixed geomagnetic reference frame. The BDGIM is a two-dimensional ionospheric correction model, which relies on an elevation-dependent mapping function to convert ionospheric delays from vertical to slant directions.