# Analysis of Key Issues on GNSS-R Soil Moisture Retrieval Based on Different Antenna Patterns
## 3 Results and Discussion of Key Issues in Application Scenarios  
### Ground-Based Observation in Single-Antenna Pattern  
The PBO Program of the United States investigates the changes in the three-dimensional stress field of the tectonically active crust of the West Pacific and North American plates, and it currently has 1100 continuously operating GPS stations. Based on the SNR data recorded by these GPS stations, the University of Colorado launched a soil moisture product ([[http://xenon.colorado.edu/portal/](http://xenon.colorado.edu/portal/)]([http://xenon.colorado.edu/portal/](http://xenon.colorado.edu/portal/))). Figure 8: Dependence of the penetration distance of the GPS L1 band signal on soil moisture for different soil types. Figure 7: Dependence of the penetration distance on soil moisture for different frequency bands. In this study, Station P041 in Colorado (39.9495\({}^{\circ}\) N, 105.1943\({}^{\circ}\) W) is used as an example to address the three key issues mentioned above. The antenna height at Station P041 is 2 m, and the PRN 1 satellite data from 1 January 2012, which were acquired with an elevation angle range of 5-25\({}^{\circ}\) and a sampling interval of 1 min, were chosen. Given the known antenna height, the specular reflection point can be determined based on the elevation and azimuth angles. Then, the first Fresnel zone is determined based on Formula (3), as shown in Figure 9. In this figure, the origin of the coordinates is the location of the GPS observation station, and the sub-map is the sky map of the PRN 1 satellite on 1 January 2012. On this date, a total of two satellites rose and set, and the elevation angles of the four sections were in line with the range of 5-25\({}^{\circ}\). The resultant four specular reflection point trajectories were distributed in four quadrants. In the ground-based single-antenna observation pattern, the surface soil moisture information is directly extracted from the interference waveforms of direct and reflected signals [19], and the interference requires changes to the satellite's elevation angle. Thus, the soil moisture estimated from an interference pattern represents the soil moisture information in the surface range passed through by the first Fresnel zone during the time period. The area covered by each ellipse cluster in Figure 8 is the spatial resolution of the corresponding soil moisture estimate, and the average area of the ellipse clusters in four quadrants is 205 m\({}^{2}\). According to Formula (5), the area of the first Fresnel zone is determined by the wavelength of the microwave, the antenna height, and the grazing angle, while the area of the ellipse cluster also depends on the azimuth angle and the range of the satellite's elevation angle. Based on the soil moisture estimates from the SNR data using the elevation angle range of 5-25\({}^{\circ}\)[19] and setting the elevation angle of the GNSS signals to 15\({}^{\circ}\), the daily soil moisture data of the entire year of 2012 at Station P041 is derived from the PBO product. The corresponding detection depth can be calculated using Formulas (10) and (11), as shown in Figure 10. This figure shows that when the soil moisture is in the range of 0.2-0.4 cm\({}^{3}\)/cm\({}^{3}\), the detection depth is approximately 5 cm. Figure 9: The specular reflection point and the first Fresnel zone of the PRN 1 satellite signal at Station P041 on 1 January 2012, where the sub-map is the sky map of the PRN 1 satellite. When the soil is very dry, the detection depth can be deeper than 20 cm. [PERSON] et al. used the wire net that covers the first Fresnel zone to determine the detection depth of the GNSS signal in the soil and found that when the soil moisture was 0.1 cm\({}^{3}\)/cm\({}^{3}\), the detection depth of the L2-band signal was 5 \(\pm\) 1 cm, in contrast to 7.6-9.2 cm under the same conditions using the model described in Section 2.3. This model assumes that the soil moisture is uniform, but in reality, the soil moisture changes with soil depth, which should be the main cause of error.