# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 3 Experiments and Results
### Horizontal Tomography Resolution  
[PERSON] and [PERSON] (2010), and [PERSON] and [PERSON] (2011), analyzed the influence on the size of the voxel for tomography. [PERSON] et al. (2015) also indicated that one of the main limitations to solve the horizontal domain of the storm system is horizontal resolution, which is constrained by the GPS network resolution. To investigate the effect of LEO constellation on the horizontal resolution, eight different horizontal resolution strategies were proposed. As the initial grid resolution, \(7\times 8\) was selected. Then, the latitudinal direction was fixed, and the number of longitude grids was changed, followed by fixing the longitudinal direction and changing the number of latitudinal grids. The detailed settings are shown in Table 4. The percentage of overall empty and two-station voxels, and precision factor \(\eta\), were also used for analysis. Figure 19 shows the calculation for the five schemes of the percentage of empty to total voxels, the percentage of two-station to total voxels, and accuracy factor values. Figure 19a shows the empty-voxel values of all five constellation combination schemes increasing with the increase in horizontal resolution. However, GRECL288 had the smallest empty voxels, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scheme** & **Lat**\(\times\)** **Lon** & **Lat**(\({}^{\circ}\)) & **Lon**(\({}^{\circ}\)) & **Total Voxels** \\ \hline
1 & \(7\times 8\) & 0.055 & 0.060 & 672 \\
2 & \(7\times 10\) & 0.055 & 0.048 & 840 \\
3 & \(7\times 12\) & 0.055 & 0.040 & 1008 \\
4 & \(7\times 14\) & 0.055 & 0.0343 & 1176 \\
5 & \(9\times 8\) & 0.04278 & 0.06 & 864 \\
6 & \(11\times 8\) & 0.0350 & 0.06 & 1056 \\
7 & \(13\times 8\) & 0.0296 & 0.06 & 1248 \\
8 & \(13\times 14\) & 0.0296 & 0.0343 & 2184 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters for horizontal resolution in eight schemes. Figure 18: (**a**) RMS distribution with altitude for the difference in water vapor density between five schemes and ERA5; (**b**) MAE distribution with altitude for the difference in water vapor density between five schemes and ERA5. followed by L288, while the largest were in G. The comparison shows that the slope of the data change of the G scheme is also the largest. This shows that when the observation data is insufficient, the proportion of empty voxels to total voxels will be accelerated when the horizontal grid division becomes dense. Meanwhile, this trend was much flatter with a larger number of satellites. Figure 19b shows two-station voxels for different constellations at different horizontal resolutions. The results still showed that GRECL288 performed the best. Comparing the data of empty voxels and two-station voxels, the gap between the empty-voxel data is relatively close. The two-station voxels data gap is relatively sparse. This shows that LEO has a greater impact on two-station voxels indicators, and the growth of two-station voxels indicates the growth of non-parallel observations. Figure 19c shows the accuracy-factor values for different constellations at different resolutions. Compared with the empty and two-station voxels, the accuracy factor also responded to similar findings as described above. Moreover, GRECL288 had the smallest percentage of empty voxels and the largest percentage of two-station voxels at different horizontal resolutions. The addition of multiple systems and LEO constellations facilitated the improvement of the horizontal resolution of the layer analysis, without the need for additional ground stations. Compared with the G scheme, the multisystem had a higher stability in ray distribution with increased horizontal resolution, and a smoother transition between empty voxels and two-station voxels. L288 performed better than GREC and worse than GRECL288. Even without GNSS, L288 presented the best performance. Figure 19: Comparison of distribution and accuracy of tomographic analysis at different levels of resolution.