# Characterizing Ionospheric Effects on GNSS Reflectometry at Grazing Angles from Space
## 2 GNSS-R Data and Reflection Events
### Specular Point Positions and Ray Points  
The specular point positions and the ray tracing of the direct, incident, and reflected signals are calculated based on the methodology presented in [11; 20]. A geometrical model is employed to characterize specular reflections and determine the specular point position, considering the Earth's surface curvature. For this model, the transmitter \((T_{x})\) and receiver \((R_{x})\) positions are needed in an Earth-centered Earth-fixed (ECEF) frame. The \(R_{x}\) position is extracted from the Spire data files. To obtain this position, the Lemur-2 satellites are equipped with a zenith dual-frequency (L1 and L2) antenna, which facilitates precise orbit  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Region** & **Number of Events** & **Total Minutes** \\ \hline North & 474 & 1704 \\ Tropics & 168 & 760 \\ South & 546 & 2335 \\ \hline Total & 1188 & 4798 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Total number of events per region and durations.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Spire SVN** & **GPS PRN** \\ \hline
79, 84, 99, 100, 101, 102, 103, 104, 106, & 1, 3, 5, 6, 7, 8, 9, 10, 12, 15, 17, 24, 25, 26, \\
113, 115, 116, 117, 119, 120, 121, 122, 124, & 27, 29, 30, 31, 32 \\
125, 128, 129 & \\ \hline Total & 21 & 19 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Space Vehicle Numbers of Lemur-2 CubeSats and GPS Satellite PRNs on 01/03/2021.  
Figure 2: Specular point tracks provided by the Spire Lemur-2 CubeSats on 1 March 2021, color-coded according to coordinated universal time (UTC) in hours.  
determination (POD). The \(T_{x}\) position is derived from the broadcasted GPS ephemeris. The Earth's curvature is modeled with an osculating spherical surface with respect to the WGS-84 ellipsoid at a reference specular point. An iterative solution is employed to find the best-fitting sphere that satisfies the condition of equal incident and reflected angles (specular reflection) [20]. The specular point positions are calculated at 10 s intervals on the receiver trajectory. A ray-tracing module is set to compute ray points every 10 km along the three ray paths: \(T_{x}\) to \(SP\) (incident), \(SP\) to \(R_{x}\) (reflected), and \(T_{x}\) to \(R_{x}\) (direct). The positions of the ray points (latitude, longitude, and ellipsoidal height) are subsequently utilized to obtain the electron density from the ionospheric electron density models. Figure 3 illustrates an example of the electron density retrieval from the NEDM2020 model depicting the change along the specular point tracks every 10 s (blue stars), and the ray points change every 10 km (red dots) along the incident (in), reflected (re), and direct (dr) ray paths.  
Following the ray tracing, a total of 28,790 reflection events are obtained. The total number of reflection events by region is depicted in Figure 4a. Additionally, Figure 4b illustrates the distribution of reflection events concerning the elevation angle by region. Notably, the south pole region exhibits a higher number of events; however, all regions show similar behavior, with a higher concentration of events in the elevation range between 5\({}^{\circ}\) and 20\({}^{\circ}\).  
Figure 4: (a) Total number of reflection events on 1 March 2021 by region. (b) The number of reflection events across grazing angles, ranging from 5\({}^{\circ}\) to 30\({}^{\circ}\).  
Figure 3: Representation of the specular point change along track (blue stars) for the SVN 79 and PRN 30 every 10 s (–45 km) and the ray points every 10 km along the direct, incident, and reflected ray paths (red dots).