## 3 Ionospheric Model Quality  
### Ionospheric Models in Positioning Domain  
The dynamics of 3D-error changes in the solar cycle. The year 2000 features the greatest error, as seen from Figure 4, where the errors peak. Until May 2000, selective availability was on, so we excluded the year 2000 from our analysis. Positioning error depends on the solar cycle phase, and, in general, they decrease as solar activity decreases. Applying GIM data, the errors differ in 2008 and 2018. To avoid bias caused by different statistics, we used data during 2014-2020 only when all the models were executable below. From Figure 4, we see that all models perform in a similar way, and, in particular, IRI and NeQuick are very close to each other, while the Klobuchar and GLONASS models provide slightly worse corrections. All the models improve the position estimates with respect to the case when no ionospheric correction is applied but cannot achieve the performance of the GIM-corrected solutions. Each station features its own error, so mean values are smoothed. Figure 5 shows yearly mean 3D positioning error dynamics without ionospheric correction (a) and with the Klobuchar-based correction (b) at each station at high (blue dots), mid- (black dots), and low (red dots) latitudes. Low-latitude stations (CATA, CUSV, RIOP, and MBAR in red dots) depend stronger (compared with mid- and high latitude stations) on the solar cycle. We see that correction is most effective for low-latitude stations, where high TEC values in the equatorial anomaly crest produce high errors in non-corrected single-frequency GNSS positioning. Table 2 reports the mean 3D error and the previously mentioned statistical parameters (Section 2.5.2) for different models. The models were sorted by \(\sigma\)3D from smallest to highest. The differences in mean \(\sigma\)3D for models are small. However, due to the huge data set (-75 million independent measurements), the differences are statistically significant at the level (at least) \(\alpha\) < 0.001 except GEMTEC vs. IRI-2016 difference. Figure 4: Dynamics of the yearly mean three-dimensional single-frequency positioning error with different ionospheric corrections: GLONASS (red), Klobuchar (blue), NeQuickG (magenta), BDGIM (black), GIM IGSG (forest green), GEMTEC (orange), NeQuick2 (purple), IRI-2012 (sea green), IRI-2016 (light green), and IRI-Plas (green). (**a**,**c**) show the data for operational models; (**b**,**d**) show the data for empirical models; all the panels show errors of GIM-based positioning and positioning without ionospheric correction. Figure 5: Dynamics of the yearly mean single-frequency positioning error at different stations at high latitudes (blue dots), mid-latitudes (black dots), and low latitudes (red dots). (**a**) shows the dynamics without ionospheric correction, and (**b**) shows the dynamics with Klobuchar ionospheric correction. Figure 6 shows the Cumulative Distribution Function of the observed 3D errors--i.e., the fraction of cases (with respect to the total) having an error less than or equal to a given value. The closer the distribution line is to the \(y\)-axis, the better the model performance is. The difference in operational models can be clearly seen: BDGIM features the best performance, while GLONASS features the worst one. Empirical models feature close distributions, NeQuick2 being slightly better and IRI-Plas a little worse. Figures 7 and 8 show how _F10.7_ and _Kp_ influence the 3D positioning errors for different models. Linear dependence for _F10.7_ dependence is quite clear. The slope shows the difference in correction effectiveness. We should note the relatively low efficiency of GEMTEC. Among operational models, GLONASS features the worst results (probably due to the incorrectly used \"correction factor\").