*4.3. Doppler Shift Analysis*

The analysis extends to the Doppler shift observed at the GPS L1 frequency across varying ranges of elevation angles, while considering effects during both day and night periods. Figure 13 illustrates the distribution of the Doppler shift during low solar activity. The electron density variations in grazing angle reflectometry can induce a maximum Doppler shift of ±2 Hz in the GPS L1 signal during daytime. The attenuation in the Doppler shift demonstrates a strong correlation with diurnal cycles, resulting in a reduction during nighttime periods. This phenomenon can be attributed to the decrease in the rate of electron density changes, which in turn leads to a corresponding decrease in the magnitude of the Doppler shift.

The Doppler shift histograms reveal a symmetrical distribution centered around approximately 0 Hz with a distinct separation in very-low-elevation cases. The distribution is also influenced by the transmitter motion relative to the specular point elevation angle. In Figure 14, it becomes evident that at very low elevation angles, a rising transmitter (ascendant elevation) induces a positive Doppler shift, while a setting transmitter (descendant elevation) results in a negative Doppler shift. However, at higher elevation angles (20◦ to 30◦), the relationship may vary or even reverse.

**Figure 13.** Distribution of Doppler shift depending on elevation, daytime (DT), and nighttime (NT) using NEDM2020 sTEC retrievals with F10.7 = 75.

**Figure 14.** Distribution of Doppler shift depending on elevation and rising or setting event using NEDM2020 sTEC retrievals with F10.7 = 75.

The distribution of the Doppler shift for F10.7 = 180 exhibits an increase in dispersion, approximately doubling in all scenarios. In the elevation range of 5◦–10◦ within the tropics region, the range of *fd* is more extensive during daytime, reaching maximum values of up to ±4 Hz. The rising and setting event analyses present similar behavior, with negative magnitudes primarily observed during rising events and positive magnitudes during setting events.

#### *4.4. Peak Electron Density Height Analysis*

The NEDM2020 model is employed to determine the height at which the maximum electron density peak *Hm* is observed along the paths of both the incident and reflected rays. This altitude is significant as it represents the point of maximum ionization within the ionosphere that the signals traverse.

From a geometrical standpoint within the grazing GNSS-R configuration, variations in elevation angles directly correspond to changes in the segment of the signal ray that travels along the ionosphere. Furthermore, throughout the diurnal cycle, electron densities within the E and F layers exhibit greater magnitudes during daylight hours compared to nighttime, with the F layer generally obtaining higher electron concentrations. These fluctuations are examined to comprehend the intricate ionospheric interactions that the signals undergo

during their propagation. This phenomenon results in variations in the height of the maximum electron density peak, as depicted in Figure 15 for both day and nighttime.

**Figure 15.** Peak electron density height variations depending on elevation ranges, regions, and day and nighttime using NEDM2020 sTEC retrievals with F10.7 = 75.

The overall average of the *Hm* during the LSA period is 270 km. Nevertheless, noticeable variations are evident with respect to daytime and nighttime. In general, during nighttime, the *Hm* is on average 10% higher than during daytime. The tropics region stands out as one of the most dynamically changing areas within the ionosphere. In this zone, the distribution of *Hm* during daytime exhibits a spread ranging from 236 to 326 km, lacking a distinct peak value. However, during nighttime, *Hm* reaches its maximum value at approximately 305 km. This highlights the substantial variations in electron density within this region, particularly during daytime. During HSA, the *Hm* exhibits a consistent increase of 21% across all scenarios.
