# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 5 Conclusions  
In this paper, LEO constellation-augmented multi-GNSS for 3D water vapor tomography was investigated by simulated LEO constellation data. Three aspects of the study were proposed, namely, observed ray distribution, tomographic water vapor accuracy, and horizontal resolution. Then, 60 and 128 LEO constellations were simulated for tomographic water vapor experiments. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Empty Voxels (\%)**} & \multicolumn{3}{c}{**2-Station Voxels (\%)**} & \multicolumn{3}{c}{\(\eta\) (\%)**} \\ \cline{2-10}  & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** & **Max** & **Min** & **Mean** \\ \hline GRECL288-GREC & 5.22 & 2.08 & 3.25 & 11.03 & 7.74 & 8.61 & 2.06 & 1.42 & 1.80 \\ GRECL288-G & 22.53 & 9.53 & 13.83 & 49.36 & 31.25 & 39.23 & 6.32 & 5.09 & 5.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of distribution and accuracy of GRECL288 with GREC and G at different horizontal resolutions. From the tomographic observation value distribution experiment, the scheme with LEO satellites showed a more uniform distribution of observation rays. The GRECL288 scheme could shorten the observation time by 66.7% when it reaches the 30-min ray distribution effect of the GREC scheme. In the 10-min and 30-min experiments, the number of non-repetitive effective observation rays of GRECL288 was 2.38 times and 2.77 times that of GREC, respectively. From the experiment with different sampling rates, it could be concluded that a large amount of data both increases the difficulty of designing the matrix calculations and makes tomographic results unstable. However, for the fast angular rate of LEO, a low sampling rate would miss some valid observations. Hence, appropriate sampling rates of multi-GNSS and LEO were analyzed, and set to be 300 and 15 s, respectively. In addition, L60 was less effective than L288 for the smaller number of satellites, so a higher number of LEO satellites could bring better advantages. From the results of 1 day, compared to GREC and G, the average empty voxels of GRECL288 were improved by 2.12% and 10.68%, respectively; the average two-station voxels of GRECL288 were improved by 7.67% and 33.29%, respectively. From the experiment of accuracy comparison, GRECL288 had the highest accuracy, with an improvement of 0.75% and 5.83% compared with that of GREC and G, respectively. Otherwise, the integrated strategy with adding LEO constellation requires less observation time to achieve the same level of accuracy. In this respect, introducing the LEO constellation enhances the time resolution of tomography. The horizontal resolution experiment shows that when the horizontal resolution increases, adding LEO constellation can effectively suppress the increase in the number of empty voxels, the decrease in the number of two-station voxels, and the decrease in accuracy. At a horizontal resolution of 13 \(\times\) 14, compared to GREC and G, the empty-voxel ratio of GRECL288 increased by 5.22% and 22.53%, respectively; the two-station voxel ratio of GRECL288 increased by 11.03% and 49.36%, respectively; and the accuracy factor \(\eta\) increased by 2.06% and 6.32%, respectively. LEO constellations can bring obvious benefits to water vapor tomography. This result provided a new solution for the improvement of spatial and temporal resolution, and accuracy, in water vapor tomography. However, the above improvements are still affected by the distribution of ground stations. As the density of ground stations increases, integrated with LEO constellation data, the water vapor stratification yields even more promising results. This paper was conceptualized by [PERSON] and [PERSON]; LEO constellations were designed by [PERSON]; software was written by [PERSON]; validation was done by [PERSON]; data were collated by [PERSON]; original draft was written by [PERSON] All authors have read and agreed to the published version of the manuscript.