## 3 Results and Discussion
### The Spatial and Temporal Distributions of the Reflections Obtained by the Optimal Constellations  
The latitudinal and the longitudinal distributions of the average numbers of the GNSS reflections in the \(1^{\circ}\times 1^{\circ}\) cells obtained by the optimal constellations are shown in Figure 3. From Figure 3a, it can be seen that the latitude distribution pattern of the average numbers of GNSS reflections obtained by the four different optimal 2D-LFCs were similar (i.e., the numbers of the reflections are higher in high latitudes than in middle and low latitudes), and the peaks were related to the inclinations of the GNSS-R LEO satellites. In comparison, the average numbers of GNSS reflections were generally uniformly distributed at different longitudes for all four optimal constellations, as shown in Figure 3b. More specifically, the average numbers of points fluctuated around the values of 40, 120, 300, and 600 for the optimal 8-, 24-, 60-, and 120-satellite 2D-LFCs, respectively. What needs to be mentioned is that [PERSON] et al. (2015) simulated the distribution of the GNSS-R reflection points observed by a LEO constellation with main orbit parameters similar to CYGNSS and found that there is a peak of average numbers of reflection points at 120\({}^{\circ}\) E, which was attributed to the denser reflections to BDS GEO and IGSO satellites in the  
Figure 3: Average numbers of the GNSS-R specular reflection points in the \(1^{\circ}\times 1^{\circ}\) grid cells at **(a)** different latitudes and **(b)** different longitudes obtained by the optimal 8-, 24-, 60-, and 120-satellite 2D-LFCs, respectively, during one day. Figure 2: Coverage and revisited coverage as a function of time during one day obtained by the optimal 8-, 24-, 60-, and 120-satellite 2D-LFCs, respectively. Black solid lines, blue dotted lines, and dashed lines represent the coverage, the revisited coverage, and 90% coverage (revisited coverage), respectively. Asia-Pacific region, while in our work, this peak did not exist. This could be due to the fact that both the LEO constellation configurations and the settings for the selection of observable reflections were different between [PERSON] et al. 's and our studies. It is clear that missions that allow different simultaneous measurements and different antenna gain patterns will have different coverage statistics [16]. We followed [16] by using RCG values as the criteria to pick out the observable reflections and followed [2] by allowing 10 simultaneous measurements, which was different to that of [PERSON] et al. 's simulation strategy. In [PERSON] et al. [15], the available specular reflection points were selected based on the elevations and azimuths of the vectors between the reflections and the LEO satellites in the body-fixed coordinate system, and the azimuth and elevation ranges were obtained using the beam widths and face directions of the antennae. The spatial distributions of the mean revisit time for the \(1^{\circ}\times 1^{\circ}\) cells of the optimal 8-, 24-, 60-, and 120-satellite 2D-LFCs are shown in Figure 4. It can be seen that the distribution patterns of the revisit time were similar to that of a 24-satellite polar orbiting constellation with each satellite tracking up to 10 GPS and Galileo measurements, as shown by [2]. For each optimal constellation, the mean revisit time in the high and middle latitudes was generally shorter than that in the low latitudes. Furthermore, due to the spatial distribution of the specular reflections caused by the LEO GNSS-R observatory's orbit inclination 15, in each of the subfigures, a short revisit time was obtained at the high latitudes near to the orbit inclination angles of the GNSS-R LEO satellites, which is also consistent with [2]. The comparisons of the four subfigures revealed that the mean revisit time generally decreased with the increase in the number of the satellites.