# Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation
## 3 GNSS-R Coverage Simulations  
### Effect of Orbit Inclination on Constellation Coverage  
One critical design feature of a constellation is the orbit inclination of its satellites. The inclination of a satellite's orbit determines the maximum possible latitude of its surface observations and hence affects the global distribution of its spatial coverage. The inclination will also affect the frequency with which samples are made at different latitudes, which in turn determines the ZTC. These two performance considerations should both be considered in the design optimization process.  
For this study, we consider design options in which one third of the total number of satellites is distributed between each of three orbit planes at distinct inclinations. We analyzed three cases, one where all three planes have an inclination of 30\({}^{\circ}\), another where the three planes have inclinations of 30\({}^{\circ}\), 60\({}^{\circ}\) and 90\({}^{\circ}\), and a third where all three planes have an inclination of 90\({}^{\circ}\).  
The ZSC results of these simulations are illustrated in Figures 2-4. Although these images depict a single orbit of these three constellations over a period of 1 h, 40 min, and 30 s, they can be extrapolated to form the full 24 h spatial coverage maps. The maximum inclination of the constellation can be seen to limit its latitudinal coverage. The coverage will not exceed the inclination by more than 10\({}^{\circ}\) north or south. For instance, the constellation with three planes at an inclination of 30\({}^{\circ}\) has non-zero ZSC at latitudes slightly lower than 40\({}^{\circ}\) north and south. However, after extrapolating the three orbit maps, this truncated coverage will contrast with the almost 100% ZSC performance demonstrated by the 30\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) and 90\({}^{\circ}\)-90\({}^{\circ}\) inclination constellations. In these situations where the maximum inclination of the constellation is set to 90\({}^{\circ}\), the constellations are capable of taking measurements over the entire Earth.  
Figure 3: Single-Orbit Spatial Coverage for 3-Plane 30\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) constellation at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. The inclination distribution provides greater coverage at the various orbit peaks, allowing for a greater GSC than the 30\({}^{\circ}\)-30\({}^{\circ}\)-30\({}^{\circ}\) constellation.  
Figure 2: Single-Orbit Spatial Coverage for 3-Plane 30\({}^{\circ}\)-30\({}^{\circ}\)-30\({}^{\circ}\) constellation at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. The lower maximum inclination limits spatial coverage to below 40\({}^{\circ}\) latitude.  
The ZTC results of these simulations are illustrated in Figure 5. When all constellation planes operate at the same inclination, the ZTC peaks around those latitudes. However, when the plane inclinations are more evenly spaced between latitude levels, as shown by the 30\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) constellations, we get more well-distributed sampling across the Earth at the cost of smaller coverage peaks.  
Figure 4: Single-Orbit Spatial Coverage for 3-Plane 90\({}^{\circ}\)-90\({}^{\circ}\)-90\({}^{\circ}\) constellation at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. The 90\({}^{\circ}\) maximum plane inclination allows the constellation to achieve near 100% GSC after 24 h.  
Figure 5: 24 h Temporal Coverage measurements at different latitudes for 3-Plane constellations at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. Raising the inclination of individual planes or the entire constellation can alter which latitudes are visited most often.