## 3 Simulation and Analysis
### Spatial Distributions of the Reflections  
To analyze the spatial distribution characteristics of the reflections, the global Earth surface is gridded using \(1^{\circ}\times 1^{\circ}\) bins and the numbers of reflected points are counted for each bin. Figures 7 and 8 show the average numbers of specular reflection points in the GPS-R and four-system GNSS-R cases, respectively, in \(1^{\circ}\times 1^{\circ}\) grids at different longitudes during 13 days, a complete cycle, at the GPS L1 and L2 frequencies.  
From Figures 7 and 8, we see that the numbers of reflected points in each bin for the four-system GNSS are more than three times those in the GPS-R case at the same frequency and longitude. The reason for this difference is that the number of GPS satellites used in the GPS-R case is 31, while the number of satellites in the four-system GNSS case is 119, including the eight Chinese BDS GEO/IGSO satellites, which is also approximately four times the number of GPS satellites. The numbers of reflection points at the L2 frequency are nearly twice the numbers at the L1 frequency. The main reason for this difference is that the GNSS-R antenna beamwidth at the L1 frequency is \(34^{\circ}\times 35^{\circ}\), while that at the L2 frequency is \(49^{\circ}\times 41^{\circ}\).  
Figure 8: Average numbers of four-system GNSS-R specular reflection points in \(1^{\circ}\times 1^{\circ}\) grids at different longitudes during a complete 13-day cycle at the GPS L1 (**a**) and L2 (**b**) frequencies.  
Figure 7: Average numbers of GPS-R specular reflection points in \(1^{\circ}\times 1^{\circ}\) grids at different longitudes during a complete 13-day cycle at the GPS L1 (**a**) and L2 (**b**) frequencies.  
Additionally, five BDS GEO satellites are operating in orbit at an altitude of 35,786 km and these satellites are positioned at 58.75\({}^{\circ}\)E, 80\({}^{\circ}\)E, 110.5\({}^{\circ}\)E, 140\({}^{\circ}\)E and 160\({}^{\circ}\)E. The sub-satellite tracks for three of the IGSO satellites coincide, while the longitude of the intersection point is 118\({}^{\circ}\)E. As a result, the number of reflected points increased between latitudes of approximately 35\({}^{\circ}\)E and 5\({}^{\circ}\)W, as shown in Figure 8. However, in Figure 7, the average numbers of points fluctuate around values of 380 and 710 for the GPS-R L1 and L2 cases, respectively, while there is a peak at 120\({}^{\circ}\)E in Figure 8. Therefore, the BDS GEO and IGSO satellites will cause the reflections to be denser in the Asia-Pacific region than in other areas of the world.  
Figures 9 and 10 show the average numbers of specular reflection points in the 1\({}^{\circ}\times 1^{\circ}\) grids at different longitudes during a complete 13-day cycle at the GPS L1 and L2 frequencies for the GPS-R and four-system GNSS-R cases, respectively. The reflection points cover the regions between approximately 38\({}^{\circ}\)N and 38\({}^{\circ}\)S, which will be helpful in investigation of the generation processes of typhoons and hurricanes by enabling frequent high-density measurements.  
It can be seen that there are two peaks at \(\pm\)32\({}^{\circ}\) and \(\pm\)37\({}^{\circ}\) and one trough at \(\pm\)35\({}^{\circ}\) in Figures 9 and 10, which can be explained as follows. First, the peaks are related to the inclinations of the GNSS-R LEO satellites, which means that the numbers of reflection points at the peaks are several times those of the other regions. Second, the two nadir antennae are designed to face in opposite directions with some obliquity, which means that the nadir measurements are lower than the off-nadir measurements.