# Towards a Real-Time Description of the Ionosphere:
## 5 Validation Results for _fo_F2 Based on Ground-Based Ionosonde Observations  
### Statistics on the Full Dataset  
The full _fo_F2 ionosonde dataset includes 10,133,987 observations obtained cumulating measurements recorded from 2000 to 2019 at the 40 ionospheric stations under consideration. This dataset has been used to calculate the two-dimensional density plots of IRI-_fo_F2 vs. ionosonde-_fo_F2 and IRTAM-_fo_F2 vs. ionosonde-_fo_F2, along with the histograms of corresponding residuals, as shown in Figure 3. The comparison between IRI and IRTAM results highlights that overall IRTAM turns out to be more accurate and precise than IRI. In fact, the statistical distribution of IRTAM residuals around the zero value is less widespread than the IRI one, and _Res. Mean_IRTAM = 0.005 MHz is smaller than _Res. Mean_IRI = 0.051 MHz. Furthermore, the comparisons \(RMSE_{\text{IRTAM}}\) = 0.674 MHz vs. \(RMSE_{\text{IRI}}\) = 1.002 MHz and \(NRMSE_{\text{IRTAM}}\) = 12.270% vs. \(NRMSE_{\text{IRI}}\) = 18.258% show also that the IRI _fo_F2 modeling precision is significantly improved by IRTAM. This point is also reinforced by the IRTAM density plot which appears less scattered than the IRI one (\(R_{\text{IRTAM}}\) = 0.959 vs. \(R_{\text{IRI}}\) = 0.908). Similar conclusions can be made also when IRI and IRTAM performances are evaluated on both the cumulative _fo_F2 time series binned according to Section 4.2, and to the three different level of solar activity defined in Section 3.1, as highlighted by Table 2, and the _fo_F2 time series available for each considered ionospheric station, as highlighted by Table 3. In fact, Table 2 shows values of _Res. Mean_, _RMSE_ and _NRMSE_ that are always lower for IRTAM, which means that IRTAM models _fo_F2 better than IRI during daytime, nighttime, solar terminator hours, in all seasons, and during different solar and magnetic activity conditions. The improvement made by IRTAM is quite consistent and, more importantly, does not show any particular diurnal, seasonal, or solar activity dependence (as also evidenced by [29]), i.e., IRTAM outperforms IRI in all the conditions. The assimilation of real-time data is particularly efficient during magnetically disturbed conditions where the ionosphere exhibits very steep spatial gradients of the electron density distribution and very fast time variations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ionosonde Stations Dataset**} & \multirow{2}{*}{**Model**} & **Res. Mean** & **RMSE** & **NRMSE** & **R** & **Counts** \\  & & **[MHz]** & **[MHz]** & **[\%]** & **R** & **Counts** \\ \hline Daytime & IRI & \(-0.048\) & 1.026 & 14.861 & 0.887 & \\  & IRTAM & \(-0.015\) & 0.676 & 9.789 & 0.952 & 4,091,455 \\ \hline Nighttime & IRI & 0.125 & 1.003 & 23.790 & 0.842 & \\  & IRTAM & 0.013 & 0.674 & 15.983 & 0.930 & 4,198,762 \\ \hline Solar terminator & IRI & 0.106 & 0.946 & 18.011 & 0.885 & \\  & IRTAM & 0.032 & 0.668 & 12.721 & 0.944 & 1,843,770 \\ \hline March Equinox & IRI & 0.179 & 1.040 & 18.129 & 0.914 & \\  & IRTAM & 0.015 & 0.685 & 11.934 & 0.963 & 2,710,599 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Res. Mean, RMSE, NRMSE, and \(R\) values calculated for the IRI and IRTAM models on the basis of the _f_oF2 ground-based ionosonde observations, for the bins defined in Section 4.2, according to the three levels of solar activity defined in Section 3.1, and for the full dataset (bottom row). The number of counts on which the statistics were calculated is reported in the rightmost column._  
Figure 3: Density plots between measured (\(x\)-axis) and modeled (\(y\)-axis) _f_oF2 values, for (**a**) IRI and (**c**) IRTAM. Measured values are those from the entire ionosonde dataset. The black solid lines represent the best linear fit. Corresponding slope and intercept values, along with the correlation coefficient, are reported in the upper left box of each plot. Statistical distributions of the resultant residuals for (**b**) IRI and (**d**) IRTAM. Corresponding _Res.