# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 3 Experiments and Results
### Tomographic Observation Distribution
The figure also reflects a denser distribution of rays along the north-south direction than that in the east-west direction, because LEO satellites were designed to be polar satellites. We have counted all the observed rays, and defined an effective observation ray. If the observation rays are observed by the same receiver, the numbers of passing voxels are exactly the same, and the distances of the rays passing through each voxel are also similar; we consider these observation rays as repeated observation rays. The repeated observation rays are deleted and only one of them is kept, then the remaining observation rays are defined as effective observation rays. Figure 12 shows the heat map of the number of times that the top voxels of five different satellite combinations were passed by the number of effective rays under six observation times. The sampling rate of G, R, E, C is set to 30 s, and the sampling rate of the LEO satellites is set to 15 s. All the sub-pictures in the first row in Figure 12 are the first epoch data. The observation time of each row of the sub-picture is the same, and each column is the same scheme. The figure reflects that increasing the observation time is beneficial to increase the number of effective observation rays. As the  
Figure 10: The visible satellite distribution map of GPS and LEO constellations within 30 min. The observation time is 12:00 UTC. The abscissa is the observation time, and the ordinate is the number of visible satellites. (**a**) The red in the figure is the GPS satellite, (**b**) and the blue is the LEO satellite. observation time increases, the number of times that the top voxel of GRECL288 is passed by effective rays varies greatly, followed by L288. In the whole scheme, the best result appears in (d7). In addition, the effect of the GRECL288 observation for 10 min (d3) is comparable to the effect of GNSS for 30 min (b7). This shows that when GRECL288 achieves the 30-min ray distribution effect of GNSS, the observation time can be shortened by 66.7%. Shortening the observation time is conducive to the rapid modeling of tomography. Figure 11: Distribution of observation rays in space. **(a)** Distribution of GPS observation rays in 30 min. **(b)** Distribution of LEO observation rays in 30 min. Figure 12: Heat map of the number of times that the voxel at the top of the tomogram has been passed by effective rays. The ordinate is the observation time **(a1–a7)** is G, **(b1–b7)** is GREC, **(c1–c7)** is GRECL60, **(d1–d7)** is GRECL288, **(e1–e7)** is L288. Table 3 shows the number of effective rays (effective rays), and the total number of times that the top voxel observations were passed by effective rays (voxel passed). It can be seen from the table that when the observation time is 10 min, the number of effective rays of GRECL288 is 2.38 times that of GREC, and the number of voxel passed is 3.69 times that of GREC. When the observation time is 30 min, the number of effective rays of GRECL288 is 2.77 times that of GREC, and the number of voxel passed is 2.83 times that of GREC. The above experiment shows that appropriate sampling intervals should be used for different constellations. For constellations with slow angular velocity, the sampling interval should be appropriately increased. If the sampling interval is too small, there will be more repeated observations. For fast-moving constellations, the sampling interval should be reduced. Sampling intervals that are too large will cause the effective observation value to be missed. To test the appropriate sampling rate, two indicators were employed. The first indicator was the number of voxels without observation rays crossing (empty voxels). The other indicator was the number of voxels that were observed by more than two ground stations (two-station voxels). There were relatively few cases where the rays that were observed by different ground stations were parallel, and they mostly crossed in space. The two-station voxel index indicates that voxels are traversed by nonparallel rays.