# Characterizing Ionospheric Effects on GNSS Reflectometry at Grazing Angles from Space
## 4 Results
### Relative Ionospheric Group Delay Analysis  
The relative ionospheric group delay \(\left(\Delta_{p_{iono}}\right)\) denotes the additional delay caused by the ionosphere along the aggregated path of the incident and reflected signals, in comparison to the direct signal. The mitigation of ionospheric delay holds significant importance in reflectometry LEO single-frequency missions, particularly within altimetry applications. The analysis of the relative ionospheric delay follows a similar approach to the sTEC analysis, encompassing the established regions, elevation angle ranges, local time variations, and the change in solar flux index. Figure 9 illustrates the potential ionospheric delays that arise from utilizing the sTEC derived from the NEDM2020 and NeQuick 2 models in conjunction with the GPS L1 frequency and F10.7 = 75. Consistent with the sTEC analysis outcomes, it is observed that \(\Delta_{p_{iono}}\) exhibits greater magnitudes within the tropics region, with the highest values occurring at very low elevation angles for both models. The occurrence of negative values in the relative ionospheric delay is attributed to the dominance of the direct signal contribution in the computation of \(\Delta_{p_{iono}}\). \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l l l l l} \hline \hline  & & & & & & & & & & & & & & & & & & & & & & & & \\ \hline \multicolumn{12}{c}{**sTEC NEDM (TECU)**} \\ \multicolumn{12}{c}{**sTEC**} \\ \multicolumn{12}{c}{**Ele. : 5\({}^{\circ}\)–10\({}^{\circ}\)**} & \multicolumn{1}{c}{**Ele. : 10\({}^{\circ}\)–20\({}^{\circ}\)**} & \multicolumn{1}{c}{**Ele. : 20\({}^{\circ}\)–30\({}^{\circ}\)**} & \multicolumn{1}{c}{**Ele. : 5\({}^{\circ}\)–10\({}^{\circ}\)**} & \multicolumn{1}{c}{**Ele. : 10\({}^{\circ}\)–20\({}^{\circ}\)**} & \multicolumn{1}{c}{**Ele. : 20\({}^{\circ}\)–30\({}^{\circ}\)**} \\ \hline \multicolumn{12}{c}{**sTEC**} \\While the outcomes from both models exhibit very similar behavior in terms of relative ionospheric delay, including their dependence on region, elevation angle, and local time, there are noticeable relative differences across the established groups. Taking as a reference the NEDM2020 model, the mean relative difference is computed as follows:  
\[\% RD=\frac{mean\Big{(}\Big{|}\Delta_{Piano}^{NeQuick~{}2}-\Delta_{Piano}^{ NEDM2020}\Big{|}\Big{)}}{mean\Big{(}\Big{|}\Delta_{Piano}^{ NEDM2020}\Big{|}\Big{)}}*100 \tag{7}\]  
Table 4 presents the mean relative differences between low- and high-solar-activity conditions. During LSA, the most significant relative differences occur at very low elevation angles in both the north and south regions during nighttime, showing a notable 64% variation between the two models. This difference decreases as the elevation angle increases. Conversely, during daytime, the differences in the polar regions remain relatively consistent across all scenarios, while variations are more pronounced in the tropics region. During HSA, during nighttime in the north region, the differences can reach up to 98% at very low elevation angles, while in the south region, the differences remain relatively similar when comparing low and high solar activity. In the tropics, an increase in the F10.7 index leads to a higher relative difference between the models during nighttime. However, during daytime, this difference decreases compared to the low-solar-activity condition (F10.7 = 75).