# Evaluation of CYGNSS Observations for Snow Properties, a Case Study in Tibetan Plateau, China
## 2 Method
### Data Description
#### 2.1.1 CYGNSS Data  
CYGNSS was successfully launched in December 2016. Eight small satellites carrying GNSS reflection signal receivers make up its constellation. Each CYGNSS satellite is equipped with four delay-Doppler map instruments (DDMI), and each DDMI includes two left-hand circularly polarized (LHCP) antenna and one right-hand circularly polarized (RHCP) antenna. The LHCP antenna receives GNSS signals from specular and scattering points on the Earth's surface. The RHCP antenna receives GNSS signals directly, to calculate its position and velocity. Each CYGNSS satellite can measure and observe reflections in four directions simultaneously, which means that the CYGNSS system can obtain data from 32 reflection points [29]. The delay-Doppler mapping (DDM) obtained by the receiver is a function of the surface medium, antenna gain, distance, statistical properties, and scattering geometry. The CYGNSS data used in this study were from level 1, version 2.1.  
At present, most studies consider that the receiver primarily collects the coherent scattered energy in the first Fresnel region. When only the coherent energy is considered, we can calculate the DDM based on the Friis transmission formula and the Fresnel reflection coefficient of an equivalent smooth surface [30].  
\[Pcoh=\frac{P_{T}G_{T}\lambda^{2}G_{R}}{(4\pi)^{2}(R_{R}+R_{T})^{2}}\Gamma(s, \theta i,\varepsilon) \tag{1}\]  
\(P_{T}\): The transmitted power of GNSS satellite;  
\(G_{T}\): The GNSS satellite antenna gain at specular point direction;  
\(G_{R}\): The receiver antenna gain;  
\(P_{T}G_{T}\): The GNSS equivalent isotopically radiated power (EIRP);  
\(\lambda\): The wavelength;  
\(R_{R}\) and \(R_{T}\): The distance between the receiver and the specular point and the distance between the transmitter and the specular point, respectively.  
According to Equation (1), the reflectivity can be expressed as:  
\[\Gamma(s,\theta i,\varepsilon)=\frac{(4\pi)^{2}Pcoh(R_{R}+R_{T})^{2}}{\lambda^ {2}G_{R}G_{T}P_{T}} \tag{2}\]  
Figure 1: The satellite image of the Tibetan Plateau, Landsat/Copernicus.  
where \(s\) is the surface rms height, which can characterize the surface roughness, \(\theta_{i}\) is the incidence angle and the dielectric constant of the geophysical parameters. Surface reflectivity (SR) is usually a small positive value, which is converted to decibel for visualization and data analysis according to Equation (3). Table 1 shows the main parameters for the L1 data used in this study.  
\[dB=10 log_{10}(\Gamma(s,\theta i,\varepsilon)) \tag{3}\]  
It is worth noting that the treatment of the coherent and incoherent scattering is an open issue when dealing with the CYGNSS data [31]. When using CYGNSS data for soil moisture retrieval, the coherent energy comes primarily from specular reflections of water inland within the GNSS-R footprint, which leads to the increase in DDM peak value. The peak energy of the coherent part is many times greater than that in the non-coherent portion. The satellite-based GNSS-R receiver mainly receives coherent scattered signals from the first Fresnel zone around the specular reflection point [32]. In fact, the signals received by GNSS-R receivers, in most cases, contain signals from both coherent and incoherent scattered fields, due to variations in surface roughness. Most of the currently available studies on satellite-based GNSS-R remote sensing of surface soil moisture simplify the scattering mechanism of the L-band on the actual surface, assuming that only coherent scattering occurs on the terrestrial surface, and incoherent scattering is ignored [31]. We removed data with SNRdB less than 2 dB and CYGNSS antenna gain of less than 0 dB. The elevation angle of the specular points is less than 65\({}^{\circ}\).