## 3 Results
### Point-by-Point Electron Density Comparison  
Next, the \(N_{e}\) values of the GNSS-RO profiles at each altitude were compared to ionosonde values between the \(fmin\) and \(hmE\) altitudes. The altitudes of the GNSS-RO and ionosonde profiles do not necessarily match, so the ionosonde \(N_{e}\) is interpolated to the altitudes used in the GNSS-RO profile using a cubic spline. Electron densities for each altitude of the GNSS-RO profile between the \(fmin\) and \(hmE\) of the ionosonde are shown for each site in the unshifted comparison in Figure 14, and the shifted comparison in Figure 15. Approximately 14 points per profile are used in the comparison within this altitude range for the 1 km vertical resolution of the GNSS-RO profiles. R2 and mean absolute error (MAE) values for the shifted and unshifted comparisons at each site are shown in Table 7.  
For the unshifted profiles shown in Figure 14, it is clear that for almost every altitude in all of the profiles, the ionosonde \(N_{e}\) is larger than the GNSS-RO \(N_{e}\). As displayed with the individual and average profile comparisons, the ionosonde profile tends to be at a slightly lower altitude than the GNSS-RO profile. Due to the nature of the E-region ionosphere where \(N_{e}\) is increasing rapidly with altitude, a separation of just a few kilometers can cause a significant difference in \(N_{e}\). Since the ionosonde profile is lower in altitude, at any given altitude it will have a higher \(N_{e}\) than the GNSS-RO profile. Hermanus had the highest R2 for the unshifted profiles, and the lowest was at Gakona and I-Cheon. Gakona had the largest difference between unshifted profiles, and I-Cheon had both the largest average \(fmin\) and the largest spread in \(N_{e}\) measurements. Fortaleza has the most profiles with data points above the 1:1 line, meaning the GNSS-RO \(N_{e}\) was larger for that point. In general, as \(N_{e}\) increases at higher altitudes, there is a larger variation between the GNSS-RO and ionosonde profiles. Figure 13: GNSS-RO—ionogram \(hmE\) histograms and CDFs. The red line is the CDF, the blue boxes are relative frequency, the solid black line is the mean, and the dashed black lines are \(\pm 1\) standard deviation. The profiles corresponding to large differences in \(foE\) are also displayed in Figure 14. For example, I-Cheon shows two profiles with RO estimates significantly larger than the ionosonde estimates, and a few profiles with ionosonde estimates much larger than the RO estimates. These profiles correspond to the \(foE\) differences outside of one standard deviation in Figure 11.  
In the comparison for the shifted profiles, shown in Figure 15, the R\({}^{2}\) is unchanged for Fortaleza and is stronger for Hermanus, I-Cheon, and Gakona. The method for shifting the profiles set the altitude at \(fmin\) equal for the GNSS-RO and ionosonde profiles, thus the first \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Site** & **Hermanus** & **I-Cheon** & **Gakona** & **Fortaleza** \\ \hline Unshifted R\({}^{2}\) & 0.66 & 0.44 & 0.39 & 0.54 \\ Shifted R\({}^{2}\) & 0.70 & 0.59 & 0.58 & 0.54 \\ Unshifted MAE (10\({}^{10}\) m\({}^{-3}\)) & 1.9 & 3.0 & 2.4 & 1.7 \\ Shifted MAE (10\({}^{10}\) m\({}^{-3}\)) & 1.3 & 1.5 & 1.4 & 1.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: R\({}^{2}\) and MAE values for the unshifted and shifted \(N_{e}\) for all altitudes between \(fmin\) and \(hmE\). Figure 14: Unshifted GNSS-RO and ionosonde \(N_{e}\) measurements for altitudes between \(fmin\) and \(hmE\) which show an under-prediction for the GNSS-RO values due to an altitude bias between the two sets of measurements. The black line is the 1:1 line, and the linear fit is in red. \(N_{e}\) value for each shifted profile falls on the 1:1 line. For all of the sites, the linear fit remains a shallower slope than the 1:1 line, meaning that as altitude increases, the ionosonde profile tends to have a larger \(N_{e}\) than the GNSS-RO profile.