## 2 Materials and Methods
### Ionospheric Models
The nine broadcast parameters drive BDGIM; they are transmitted in a BDS-3 navigation message with an update rate of 2 h. The BDGIM model reduced 25%-98% of the ionospheric error (against GIM ISSG) under different solar activity [19]. The Russian Federal Space Agency suggested a _GLONASS model_ for single-frequency ionospheric correction [20]. New GLONASS-K satellites transmit CDMA signals broadcasting three parameters for the adaptive semi-empirical ionosphere model of electron density. We used the TEC formula suggested for ground-based users. The input parameters are _c_A_, _c_F10.7_, _c_Ap_, i.e., the numerical factor for the F2-peak electron density \(NmF2\), the corrected value of solar activity index, and daily geomagnetic activity index. We do not have a database of these parameters, so we used \(F10.7\) ([[ftp://ftp.seismo.nrcan.gc.ca/spaceweather/solar_flux/daily_flux_values/fluxtable.txt](ftp://ftp.seismo.nrcan.gc.ca/spaceweather/solar_flux/daily_flux_values/fluxtable.txt)]([ftp://ftp.seismo.nrcan.gc.ca/spaceweather/solar_flux/daily_flux_values/fluxtable.txt](ftp://ftp.seismo.nrcan.gc.ca/spaceweather/solar_flux/daily_flux_values/fluxtable.txt)) (accessed on 1 January 2022)) and \(Ap\) ([[ftp://ftp.gfz-potsdam.de/pub/home/obs/kp-ap/wdc/](ftp://ftp.gfz-potsdam.de/pub/home/obs/kp-ap/wdc/)]([ftp://ftp.gfz-potsdam.de/pub/home/obs/kp-ap/wdc/](ftp://ftp.gfz-potsdam.de/pub/home/obs/kp-ap/wdc/)) (accessed on 1 January 2022)) indexes and _c_A_ = 0.95 (an example from [20]). The international reference ionosphere (IRI) is an international project coordinated and sponsored by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI). The IRI models are semi-empirical models of electron density, ion composition, electron and ion temperatures, and other ionospheric parameters. The model ingested data from both ground-based (ionosondes and incoherent scatter radars) and satellite-borne (topside sounders, in situ satellites, and rockets observations). The model input is solar (\(F10.7\), \(IG\)) and geomagnetic (\(Ap\)) indices, but it can also obtain ionospheric F2 layer critical frequency and maximum ionization height. _IRI-2012_[21] and _IRI-2016_[9] are the two most proven available versions of IRI. In 2022, _IRI-2020_[27] source code appeared at [[https://irimodel.org/](https://irimodel.org/)]([https://irimodel.org/](https://irimodel.org/)) (accessed on 1 February 2023). _IRI-Plas_ is an IRI model extended with the plasmasphere model [22]. The model calculates electron density until medium Earth GNSS orbits (20,000 km). As input, the model can get the same parameters as IRI and additionally TEC. The _GEMTEC_ model is an empirical global TEC model based on GIM CODG data through a full solar cycle (2000-2009 in the first version [23] and 2000-2012 in the revised one [28]). The model is built on empirical orthogonal functions (on local time, month latitude, solar activity, and the expansion coefficients on longitude) and involves only one parameter--solar activity index _F10.7_. Klobuchar, NeQuickG, and BDGIM are operational models for GPS, Galileo, and BeiDou systems. Using the broadcast coefficients for the relevant GNSS model, a user can calculate ionosphere correction for positioning. GLONASS model is also an operational model for GLONASS, but for the studied period, the coefficients were not broadcast and are not available now, so it can be considered as a long-term model. _IRI-2016_, _IRI-2012_, IRI-Plas, NeQuick2, and GEMTEC are empirical climatological models.