## 3 Ionospheric Model Quality
### Ionospheric Models in TEC Domain  
Table 2 summarizes also errors in the TEC domain for all the models for the period when we have all the models together (2015-2020 is the declining phase and solar minima). IRI-Plas and Klobuchar overestimate TEC, while other models underestimate TEC. Errors in the positioning domain differ from those in the TEC domain. With reference to mean absolute TEC error, GLONASS and Klobuchar show the highest errors in the TEC domain, while empirical IRI-2012, IRI-2016, and NeQuick2 models show similar results. GEMTEC and BDGIM models show the best results. Figure 8: Geomagnetic activity influence on positioning error. \(Kp\) dependence of 3D error of single-frequency positioning without applying (**a,b**, grey) and applying ionospheric corrections from different models: GLONASS (**a**, red), Klobuchar (**a**, blue), NeQuickG (**a**, magenta), BDGIM (**a**, black), GIM IGSG (**a,b**, forest green), GEMTEC (**b**, orange), NeQuick2 (**b**, purple), IRI-2012 (**b**, sea green), IRI-2016 (**b**, light green), and IRI-Plas (**b**, green). Figure 7: Solar activity influences positioning errors. \(F10.7\) dependence of 3D error of single-frequency positioning without applying (**a,b**, grey) and applying ionospheric corrections from different models: GLONASS (**a**, red), Klobuchar (**a**, blue), NeQuickG (**a**, magenta), BDGIM (**a**, black), GIM IGSG (**a,b**, forest green), GEMTEC (**b**, orange), NeQuick2 (**b**, purple), IRI-2012 (**b**, sea green), IRI-2016 (**b**, light green), and IRI-Plas (**b**, green). GEMTEC model features the smallest TEC bias. This is because GEMTEC is based on CODG GIM, but input data for the model covered only 2000-2009, while, here, we used another solar cycle for testing (2015-2020). Additionally, BDGIM relies on GIM, so it displays a small TEC bias and mean absolute error. Figure 9 shows the dynamics of TEC error for different models. The errors vary as a function of solar activity. The highest absolute errors occur at solar maxima, while the highest relative errors (especially for the Klobuchar model) occur at solar minima. TEC biases (Figure 9a,b) vary mostly within \(\pm\)5 TECU. All the models except GEMTEC and BGDIM show a drop in TEC bias during solar maximum. IRI-Plas overestimate TEC except during solar maxima. BDGIM slightly underestimates TEC during all periods, but the TEC bias is stable. The Klobuchar model displays a high error and significant change in mean TEC bias. The mean relative TEC error reaches 100% for Klobuchar and is at \(-\)\(-\)20% for GLONASS, NeQuick2, IRI-2012, and IRI-2016. Huge variations in Klobuchar's mean relative TEC error are due to its constant values at night. To better visualize this feature, we considered local time dependence for different models. Except for BDGIM, absolute TEC errors (Figure 9e,f) of the operational model exceed those of the empirical ones. GLONASS model exhibits the highest mean absolute error, while BDGIM--is the lowest. NeQuickG features lower MAPE than BGIM but higher MAE. The mean absolute TEC error in 2014 (when we have data for all the models but a poorer statistic for NeQuickG) reached 7.7-12.7 TECU. There are large differences in the statistical parameters that we used for precision/accuracy estimation. Even in the TEC domain, a model could be better in one parameter but worse in the other. The MAPE of BDGIM exceeds that of NeQuickG; it is the opposite of the mean absolute error. That is due to where the highest errors occur. The mean absolute percentage error (Figure 9g,h) for NeQuick2 is stable during two solar cycles. Such stability is typical for GLONASS, IRI-2012, IRI-2016, GEMTEC, and probably for NeQuickG (but we do not have enough data to check the latter). Figure 9: Dynamics of the yearly mean TEC error: GLONASS (red), Klobuchar (blue), NeQuickG (magenta), BDGIM (black), GEMTEC (orange), NeQuick2 (purple), IRI-2012 (sea green), IRI-2016 (light green), and IRI-Plas (green).