# Characterizing Ionospheric Effects on GNSS Reflectometry at Grazing Angles from Space
###### Abstract
Simulations conducted within this study under diverse conditions, involving variations in temporal resolution, solar activity levels, and the number of reflection events, have demonstrated enhanced accuracy in vTEC estimations when coherent GNSS-R observations are incorporated. In the domain of GNSS-R, it has been empirically established that coherent observations are more frequently observed in the presence of smooth reflecting surfaces, such as sea ice, regions with low sea states, or inland waters, and at low grazing angles [10; 11; 12]. Nonetheless, within this range of elevation angles, it is important to note that the trajectories of the LEO GNSS-R rays entail a longer path through the ionosphere. This extended path results in a more pronounced ionospheric impact on the signals themselves. The representation (not to scale) of the LEO GNSS-R configuration along the grazing angle rays' paths and its interaction with the ionosphere are illustrated in Figure 1.  
Figure 1: (**a**) LEO GNSS-R representation at 30\({}^{\circ}\) elevation angle at specular point. (**b**) LEO GNSS-R representation at 5\({}^{\circ}\) elevation angle. \(sTEC_{x}\) denotes the slant total electron content. Subscripts dr, in, and re correspond to the direct ray (transmitter \(T_{x}\) to receiver \(R_{x}\)), incident ray (transmitter to specular point \(SP\)), and reflected ray (specular point to receiver), respectively. \(Hm_{x}\) represents the peak electron density height for the incident and reflected ray paths. As described in [13], dual-frequency receivers possess the capability to mitigate these first-order ionospheric effects through the utilization of a linear combination (ionosphere-free) of either code or carrier measurements. Conversely, single-frequency receivers must rely on applying a model to correct for ionospheric refraction, which can introduce delays of several tens of meters. For the Galileo GNSS constellation, the European GNSS Open Service has adopted the Neustrelitz Total Electron Content Model NTCM [14] (NTCM-G) or NeQuick 2 [15] (NeQuick-G) models to provide real-time ionospheric corrections for single-frequency receivers [16]. This study is in preparation for the European Space Agency's GNSS-R CubeSat mission \"PRETTY\" (passive reflectometry and dosimetry) [17]. The mission's primary goal is to retrieve sea surface height using grazing angle observations. Since PRETTY operates at a single frequency (L5), it requires model-based ionospheric corrections. This study provides a comprehensive characterization of ionospheric effects, at the grazing angle range (5\({}^{\circ}\)-30\({}^{\circ}\)), considering satellite geometry, latitude-dependent regions, temporal variations, and solar activity. It analyzes variability in the ionospheric group delay, Doppler shift, and peak electron density height. Additionally, the uncertainty in model-based ionospheric corrections for GNSS-R group delay altimetry is assessed. The analysis is based on utilizing the sTEC obtained from three-dimensional, time-dependent models. To assess model uncertainty, the sTEC values computed using the Neustrelitz Electron Density Model (NEDM2020) [18] are used as a reference and compared with the sTEC retrievals from NeQuick 2. Simulations are conducted to replicate conditions similar to those of the PRETTY mission, utilizing orbit data from the GNSS-R Spire Global Lemur-2 constellation. To provide a comprehensive analysis, the results are categorized into three elevation angle ranges: very-low (5\({}^{\circ}\)-10\({}^{\circ}\)), low (10\({}^{\circ}\)-20\({}^{\circ}\)), and mid-low (20\({}^{\circ}\)-30\({}^{\circ}\)). These categories are further grouped by latitude into three distinct regions: north, tropics, and south. Additionally, this study considers variations in local time and solar activity. Low solar activity (LSA) is represented by F10.7 = 75 in March 2021 and high solar activity (HSA) by F10.7 = 180 in March 2023.