*4.2. Relative Ionospheric Group Delay Analysis*

The relative ionospheric group delay Δ*piono* 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 Δ*piono* 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 Δ*piono* .

**Figure 9.** Relative ionospheric delay in the distinct regions and grazing angle elevation ranges along with local time variations.

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:

$$\%RD = \frac{mean\left(\left|\Delta\_{p\_{i000}}^{NeQuick\ 2} - \Delta\_{p\_{i000}}^{NEDM2020}\right|\right)}{mean\left(\left|\Delta\_{p\_{i000}}^{NEDM2020}\right|\right)} \* 100\tag{7}$$

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).

**Table 4.** Mean relative difference in the relative ionospheric delay between NEDM2020 and NeQuick 2 during high and low solar activity.


The sTEC outcomes obtained from the NEDM2020 model, utilized as the reference model in this study, form the basis for the following analysis. Figure 10 illustrates the ionospheric delay distribution during low solar activity, categorized by elevation angles, regions, and local time distinguishing between daytime and nighttime. At low and mid-low elevation angles, the contribution of each ray to the delay remains relatively similar in magnitude, resulting in positive values for the relative ionospheric delay. Overall, during daytime events, the Δ*piono* is on average 120% greater compared to nighttime events.

**Figure 10.** Distribution of relative ionospheric delay depending on elevation, daytime (DT), and nighttime (NT) using NEDM2020 sTEC retrievals with F10.7 = 75.

During HSA periods (F10.7 = 180), the relative ionospheric delay range can increase by up to 200% with respect to low-solar-activity periods, as seen in Figure 11. In lowand mid-low-elevation scenarios, the distribution of Δ*piono* behaves similarly to LSA but with higher magnitude values. Notably, in the tropics region at very low elevations, the distribution is more widespread, with relative delays primarily consisting of negative values. This highlights the higher influence of the direct ray on Δ*piono* compared to lowsolar-activity periods.

**Figure 11.** Distribution of relative ionospheric delay depending on elevation, daytime (DT), and nighttime (NT) using NEDM2020 sTEC retrievals with F10.7 = 180.

Group Delay Altimetry and Ionospheric Delay Uncertainty Analysis

As a single-frequency GNSS-R mission, PRETTY relies on ionospheric correction models to ensure precise sea surface height measurements, introducing a level of model uncertainty in the correction process. Figure 12 presents the altimetric uncertainty at grazing elevation angles. Figures 10 and 11 depict the distribution of the relative ionospheric delay, showing a noticeable diurnal cycle effect where daytime observations exhibit higher relative ionospheric delays compared to nighttime observations. This diurnal variation is also reflected in the sea surface height uncertainties. Furthermore, it is evident that ionospheric uncertainties have a significantly greater impact on sea height retrievals in the Tropics region, where the general level of ionization is higher. In this geographical area, we observe a higher altimetric uncertainty dispersion, particularly in the mid-low elevation angle regime (during daytime, 0.22 m mean and 4.08 m std), where the combined delay of the incident and reflected rays surpasses that of the direct ray. Consequently, this leads to higher relative delays and, by extension, a more pronounced impact on GNSS-R altimetric retrievals within this specific elevation range and region.

**Figure 12.** Altimetric uncertainty due to uncertainty in ionospheric delay model depending on elevation, daytime (DT), and nighttime (NT) using NEDM2020 during LSA.
