# Soil Moisture Retrieval from Multi-GNSS Reflectometry on FY-3E GNOS-II by Land Cover Classification
## 3 Methods  
### Calibration of Reflectivity from Multi-GNSS Observations  
The DDMs in raw counts collected by the receiver are firstly calibrated to the DDM power using the instrument gain, \(G\),  
\[P=C/G \tag{3}\]  
Figure 3: Distribution of in situ soil moisture stations. Figure 2: The overlap between GNOS-II tracks and SMAP tracks (**a**) The overlap between GNOS-II tracks and SMAP observations in one day (**b**) The overlap between GNOS-II tracks and SMAP observations in three days (the green tracks indicate the overlap of two measurements, whereas the red tracks represent the GNOS-R observations that are not coincident with the SMAP measurements). where \(C\) is the DDM in raw counts and \(P\) is the DDM power. The instrument gain is different for each GNSS system, measured by a pre-launch experiment [11]. The reflectivity under coherent reflection can be calculated as follows [15]:  
\[\Gamma(\theta)=\frac{\left(4\pi\right)^{2}(P_{r}-N)(R_{r}+R_{t})^{2}}{\lambda^{2 }P_{t}G_{r}} \tag{4}\]  
where \(\theta\) is the incidence angel; \(P_{r}\) is the peak power of the DDM; \(N\) is the noise floor; \(R_{t}\) and \(R_{r}\) are the distance from the transmitter and the receiver to the specular point, respectively, \(P_{t}G_{t}\) is the transmitter equivalent isotropic radiated power (EIRP) measured by a static station in Beijing, China; \(G_{r}\) is the reflected antenna gain; \(\lambda\) is the wavelength of GNSS signals, i.e., 0.1921 m for BDS and 0.1903 m for GPS and GAL. It is important to intercalibrate the reflectivity observations from the three systems before applying any retrieval method so that the observations are consistent and can be retrieved by a same model. Because of the complications that observations over land can be coherent and incoherent depending on the surface roughness, we first analyzed the reflectivity over sea ice since most observations over sea ice can be perfectly coherent. Four months of data from July 2022 to October 2022 (since the Galileo channel was enabled) were used for the analysis. Observations over sea ice with sea ice concentration (SIC) larger than 15% from either two systems were collocated when they locate in the same ease grid of 9 km on the same day. The SIC data are from the OSISAF sea ice concentration product [28]. According to our analysis, most signals are coherent when the SIC is larger than 15%. Figure 4 shows the comparison of reflectivity over sea ice from different systems. It is observed that the reflectivity from the three systems agree well with each other. This indicates that the calibration of the instrument gain in Equation (3), along with the transmitter EIRP and reflected antenna gain in Equation (4), has negligible bias. Then, in the same way, we collocated the observations over land from different systems when they locate in the same 9 km ease grid on the same day. The comparison of reflectivity over land from different systems is shown in Figure 5a. It is found that the reflectivity of BDS and GAL are close, whereas the reflectivity of GPS is a little higher than the others. This is because some observations over land are incoherent scattering and the reflected power under incoherent scattering is related to the scattering area [29]. As shown in Table 1, because GPS signals have a lower chipping rate, its chip length (\(\sim\)300 m) is twice of that of BDS and GAL (\(\sim\)150 m), resulting a larger scattering area. There is also a minor difference in the scattering area of BDS and GAL due to the difference in the signal modulation. A detailed comparison of scattering area of the three systems under incoherent scattering can be found in [30]. Figure 4: Density scatter plots for the comparison between reflectivity over sea ice from different GNSS systems (7 July–31 October 2022). Bias is also displayed on each sub-figure. In this work, GPS reflectivity and Galileo reflectivity are calibrated to be consistent with BDS reflectivity by using linear calibration coefficients in Table 2. P1 represents the slope, and P2 represents the intercede.