## 2 GNSS RO Event Simulation and Assessment Approaches  
### GNSS RO Event Simulation  
As shown in Figure 1, during a GNSS RO event active period, the transmitting signal ray path from the transmitting satellite (TS, i.e., the GNSS satellite), first passes through the atmosphere and is captured by the receiving satellite (RS, i.e., the LEO satellite); then, with the relative motion of the TS and RS, the atmosphere is vertically scanned and remotely observed [60]. The Earth's atmosphere bending angle of the GNSS L-band occultation signal is generally less than 1\({}^{\circ}\), which has little effect on the RO tangent point position; thus, the signal path can be considered as a straight line in the RO event simulation and analyses [52]. An RO event occurs when the connecting line between the TS and RS and its tangent point with the atmospheric layers simultaneously satisfy a certain geometric relationship, and the mathematical criteria are as follows: \(\copyright\)the tangent point is between the TS and RS, \(\copyright\)the height of the tangent point is between the bottom and the top of the atmosphere (typically 0-120 km), and \(\copyright\)the azimuth angle of the TS relative to the RS's running direction is within a particular range (i.e., in the receiving antenna view field (\(\pm 40^{\circ}\)) in this study); specifically, the azimuth angle of the TS relative to the RS running direction ranges were set as 0\({}^{\circ}\)-40\({}^{\circ}\) and 320\({}^{\circ}\)-360\({}^{\circ}\) for rising GNSS RO events and 140\({}^{\circ}\)-220\({}^{\circ}\) for setting GNSS RO events [43]. Figure 1: Occultation geometry between one GNSS transmitting satellite (TS) and one LEO receiving satellite (RS). The unperturbed two-body orbits are always conic sections; therefore, the Earth orbits are commonly described as an ellipse by Keplerian elements, i.e., eccentricity (e), semimajor axis (a), inclination (i), longitude of the ascending node (\(\Omega\)), argument of periapsis (AP, \(\omega\)), and true anomaly (v). However, real Earth orbits have perturbations due to the gravitational pull of bodies other than the Earth, the nonsphericity of the Earth, atmospheric drag, relativistic effects, radiation pressure, electromagnetic forces, and so on. Therefore, in the simulation, RS and TS satellite positions and velocities were calculated from two-line element (TLE) sets through the simplified general perturbations-4/simplified deep space perturbations-4 (SGP4/SDP4) model propagator, which takes the general and deep space orbital perturbations into account [61]. Then, the TS and RS satellite positions and velocities at different epochs were used to calculate the RO geometric parameters, which involved the tangent point positions, in the following steps [60; 62]:  
Firstly, we calculated the latitude, longitude, and height of the occultation tangent point for each ray path using the TS and RS time and position data by the following formulas:  
\[r_{TR}=r_{TS}-r_{RS} \tag{1}\]  
\[\hat{n}_{TR}=(r_{TR})/\|r_{TR}\| \tag{2}\]  
\[R_{T}=\|r_{TS}\cdot\hat{n}_{TR}\| \tag{3}\]  
\[r_{TP}=r_{TS}-\hat{n}_{TR}\cdot R_{T}=(X_{TP},Y_{TP},Z_{TP}) \tag{4}\]  
\[\left\{ \begin{array}{l}\varphi_{TP}=\arctan\!\left(Z_{TP}(N+h_{TP})/\sqrt{X _{TP}^{2}+Y_{TP}^{2}}/\left(N\cdot\left(1-e_{E}{}^{2}\right)+h_{TP}\right) \right)\\ \lambda_{TP}=\arctan(X_{TP}/Y_{TP})\\ h_{TP}=Z_{TP}/\sin\varphi_{TP}-N\cdot\left(1-e_{E}{}^{2}\right)\\ N=a_{E}/\sqrt{1-e_{E}{}^{2}\sin^{2}\varphi_{TP}}\\ \varphi_{TP0}=\arctan\!\left(Z_{TP}/\sqrt{X_{TP}^{2}+Y_{TP}^{2}}\right)\\ |\varphi_{TPi+1}-\varphi_{TPi}|\leq 10^{-12}\end{array} \right.