## 3 Results and Analysis
### Ground-Truth Experiment Data for Validation
We have to note that the expected value is obtained from the PRN of which predicted Fresnel zones are in the green circle of the footprint (see Figure 12). Meanwhile, the TDR measurements were also implemented in this footprint. For the other satellites, the unexpected values could be ascribed to some interferences caused by the relative position of this satellite and the receiving antenna. The statistical characterization of the GNSS-R and TDR estimates is shown in Tables 4-7. In the TDR measurement of Grugliasco, an average value of 6 in the dry condition was calculated as shown. Then the soil moisture content of 11% was estimated by considering the average value of 6 for the permittivity and using the model reported in [61]. The value of 11% was low because the measurement was performed after a long period of drought. The soil moisture calculated was close to the minimum observable value in the experimental field, and was consistent with the results of [65]. After a rainy period of one week, the value of average permittivity was 9 that corresponded to a soil moisture of 16%. In the measurement of Agliano, the average relative permittivity evaluated with the TDR technique in dry condition was 15. After a rainy period of one week, the average measured permittivity value was also 22 that corresponded to a soil moisture of 28% and 36%, respectively. The standard deviation of permittivity obtained in Agliano was obviously greater than the case of Grugliasco. One reason could be that the roughness of the Agliano is larger than the Grugliasco (see Figure 9); another reason could be the complex environment of Agliano site (e.g., some sand, dust, and rock may fly into the site from the nearby high-way). The most traditional method of analyzing the quality of the soil moisture is the statistics methods (e.g., linear robust fit) [35; 38]. We also tested the correlation using the linear fitting function as follows:  
All the elevation angles of different PRNs were taken into account so a polynomial fitting with two input variables (three dimensional) are needed. The data of GNSS-R experiments (all elevation angle, SNR... ) and the TDR measurement (Figure 13) were collected together for analyzing the permittivity (Figure 14) and SMC (Figure 15) variation with respect to the variables \(\theta\) and the \(SNR\) as shown. In these four plots, each black point stands for one elevation angle, corresponding SNR and the permittivity obtained from the TDR measurement of Grugliasco and Agliano. In each plot, we aimed to obtain the slope that indicates the variation rate of permittivity and SMC to different variables (\(SNR\), \(\theta\)) when the soil changed from dry to wet. In each plot, the variation rate (slope) with respect to \(SNR\) was higher than \(\theta\). The largest sensitivity of SNR to SMC could be observed in the case of Grugliasco (Figure 15a), which showed the sensitivity to SM, 3.8 dB/% (slope = 0.26). This linear fitting indicates that the variable \(SNR\) was more sensitive to SMC retrieval than the variable \(\theta\) (elevation angle). The results showed good correlation with the conclusion when the XGBoost were performed on the simulated data set. Moreover, comparing the different soil types (loamy sand and silty clay loam), the linear equation to retrieve permittivity and SMC from elevation had good agreement of variation and also for the SNR for both sites. The variation rate (slope) with respect to \(SNR\) in high permittivity condition (Figure 15b) was higher than the value in low permittivity (Figure 15a). It demonstrates that the same changes of received SNR led  
Figure 14: The variation rate of GNSS-R permittivity for Grugliasco (**a**) and Agliano (**b**) measurement from dry to wet case. Figure 15: The variation rate of GNSS-R SMC for Grugliasco (**a**) and Agliano (**b**) measurement from dry to wet case. to much more permittivity variation in silty clay loam than in loamy sand soil. It also confirmed that the permittivity had a positive relationship with the soil moisture content [56].