## 3 Ionospheric Model Quality
### Ionospheric Models in TEC Domain
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ionosphere** & \multirow{2}{*}{\(\sigma_{\text{3D}}\), **m**1  } & **25\%** & **50\%** & **75\%** & **90\%** & **95\%** \\
**Correction** & & **\textless{}TECU** & **\textless{}TECU** & **\textless{}TECU** & **\textless{}TECU** & **\textless{}TECU** & **\textless{}TECU** \\ \hline BDGIM & 1.995 & 0.9 & 2.3 & 4.7 & 8.1 & 10.8 \\ NeQuick2 & 2.032 & 1.0 & 2.6 & 5.3 & 10.0 & 14.5 \\ GEMTEC & 2.042 & 0.6 & 1.8 & 4.1 & 8.1 & 11.9 \\ IRI-2016 & 2.042 & 1.0 & 2.6 & 5.3 & 10.4 & 15.4 \\ NeQuickG & 2.044 & 0.8 & 2.2 & 4.3 & 7.4 & 10.4 \\ Klobuchar & 2.082 & 1.9 & 4.2 & 7.5 & 15.2 & 23.1 \\ IRI-2012 & 2.083 & 1.0 & 2.5 & 5.1 & 9.8 & 14.4 \\ IRI-Plas & 2.168 & 1.0 & 2.7 & 5.9 & 11.3 & 15.7 \\ GLONASS & 2.185 & 1.9 & 4.4 & 8.7 & 15.0 & 20.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: TEC error limits for different data sets with the smallest error. 25%, we could rank the models as GEMTEC, NeQuickG, BDGIM, NeQuick2, IRI-2012, IRI-2016, IRI-Plas, Klobuchar, and GLONASS. Figures 12 and 13 show the dependence of absolute TEC error on solar (Figure 12) and geomagnetic (Figure 13) activity. The operational models' TEC errors depend on _F10.7_ almost linearly, while empirical models feature stronger variations. IRI-Plas shows higher errors at low _F10.7_. Obtained TEC error dynamics can be used to improve ionospheric models. We should note that under typical conditions (_F10.7_ within 60-160 s.f.u. or _Kp_ within 0-7) BDGIM performs better than the NeQuickG model. This disagrees with the previous ranking from the cumulative distribution of the error. To understand the discrepancies in our estimation for different models, Figures 14-16 have been produced. They show mean absolute and mean absolute percentage models' errors vs. local time (Figure 14), geographic latitude (Figure 15), and total electron content (Figure 16). From Figure 14, it is evident that models' errors depend on local time. The IRI-Plas model, taking into account the plasmasphere, shows the highest errors during daytime with a maximum of 12 LT. Previously, we mentioned that the model overestimated IGSG TEC. However, MAPE is maximum at sunrise when TEC is small. The Klobuchar model's absolute TEC error is maximum at 15 LT, while MAPE is maximum at night when the Klobuchar model provides constant TEC. GLONASS error also peaks during the daytime. The mean percentage error of NeQuickG and BDGIM is lower if compared with GLONASS and Klobuchar. BDGIM features the weakest LT dependence. NeQuickG, NeQuick2, and IRI-2012/IRI-2016 models peak in absolute error at ~14 LT, while the highest relative error is found at night. The latitudinal dependence of TEC errors (Figure 15) reveals that almost all the models' maximum error occurred at low latitudes, except for BDGIM. It is interesting to note that the Klobuchar model features a local maximum at 60\({}^{\circ}\)N, while GLONASS shows a local minimum. Probably, it is due to data coverage involved in the model design. It was unexpected that BDGIM shows the highest mean absolute error at high latitudes, where its precision almost reaches the Klobuchar model level (in the Southern hemisphere). GEMTEC features the lowest errors among the models; the errors peak at equatorial latitudes. Figure 16 demonstrates how the models' errors vary with TEC magnitude. All the models increase in error when TEC increases but with different trends. We noted a sharp increase in the Klobuchar model error at high TEC values. The model is also insufficient to reproduce small TEC values, which is why it features high MAPE at high latitudes (Figure 15). We see a sharp increase in BDGIM error at high TEC (which can be an additional point to improve the model). The main difference between IRI-2012 and IRI-2016 appears at high TEC values. We should note, that if at low TEC IRI-Plas, errors exceed (up to two times) those of IRI-2012/IRI-2016/NeQuick2 models, then at high TEC values, IRI-Plas performance is better.