# Preliminary Validation of Surface Reflections from Fengyun-3C Radio Occultation Data
## 3 Methods and Results
### Reflected Bending Angle Model of FY-3C  
In the COSMIC RO mission, the L2 signal was mainly used to improve the quality of the ionosphere at a higher altitude, and the atmospheric products in a lower troposphere were obtained with the L1 signal [41]. It is known that the FY-3C receiver has tracking problems in a GPS L2 signal, and most problems occur in rising occultations [42]. Only about 70% of the rising occultations can go below 20 km [42]. Due to lack of observation data, it may prevent the generation of bending angles of L2 at a lower height, especially near the surface of Earth. Therefore, a new L2 extrapolation method was applied to effectively improve the combination of bending angles with L1 and L2 [42]. However, by means of an open-loop tracking technique implemented in FY-3C, the L1 signal penetration depth can reach below 5 km, and even below 2 km, with proportions of about 95.7% and 79.5%, respectively [33]. Meanwhile, due to the super refraction and ducting effect, especially above the ocean's surface, the refractive index and impact parameter are multivalued functions [43; 44]. In order to separate the reflected signals from the raw data and avoid the  
Figure 6: FY-3C event on 28 September 2015: received SNR of L1 channel (**upper** panel), radio hologram spectrum from FY-3C Level_1 data (**middle** panel), geographical location of FY-3C event (**bottom** panel). tracking problems of the L2 signal of FY-3C, we just focus here on the L1 signal. We picked three FY-3C events with clear reflections in Section 3.2 (Figures 4-6), and computed the bending angles from raw data of L1 signal by GO method [2]. Based on the assumption of spherical symmetry, we obtained the single-path bending angles with the refractive index and the impact parameter from the surface to 40 km altitude. Under Bouguer's rule and spherical symmetry assumptions, the propagation of occultation ray can be described with Geometrical Optics. The bending angle can be obtained by a forward Abel transform [2; 45]:  
\[\alpha(a)=-2a\int_{a}^{\infty}\frac{1}{\sqrt{r^{2}n(r)^{2}-a^{2}}}\frac{d\ln n }{dr}dr \tag{6}\]  
where the integral starts from the tangent point above the surface. As the occultation ray reaches Earth's surface, the ray may reflect there. At the reflected point, where \(r=R_{E}\) and \(a_{E}=R_{E}n(r_{E})\), the additional bending angle due to reflection is [11]:  
\[\alpha_{E}=2\mathrm{arccos}\bigg{(}\frac{a}{a_{E}}\bigg{)} \tag{7}\]  
Based on Equations (6) and (7), we will attain the reflected portion from total bending angles [11]:  
\[\alpha_{R}(a)=-2a\int_{a_{E}}^{\infty}\frac{1}{\sqrt{r^{2}n(r)^{2}-a^{2}}} \frac{d\ln n}{dr}dr-2\mathrm{arccos}\bigg{(}\frac{a}{a_{E}}\bigg{)} \tag{8}\]  
where the integral starts at the impact parameter of Earth's surface level and the \(a\) is slightly less than \(a_{E}\); thus, the signal could reach the surface and be reflected. Figures 7-9 show the reconstructed bending angles of three FY-3C events. In detail, the left panels show the bending angles from RO profiles of FY-3C Level_2 (red lines), the bending angles (dashed green lines) reconstructed by single-valued forward Abel integral of Equation (6) and the bending angles from raw data of L1 signal by GO method (blue lines). The right panels show the reflected bending angle models which were calculated by Equation (8). The bending angles (red lines) of FY-3C Level_2 above the cutting height are shown in Figures 7-9. The bending angle profiles of FY-3C Level_2 are determined by a geometric optics algorithm (GO) above an altitude of 25 km, where a single path ray propagates through the atmosphere. Below 25 km, bending angle profiles from Level_2 are determined by a wave optics (WO) algorithm due to the multipath [32]. Before the signal is completely obscured by the earth, the signal may reach the appropriate surface and can be reflected there. In the data processing center, bending profiles were truncated at a certain altitude and did not reach the surface in most cases.