# A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography
## 5 Conclusions  
In this paper, an improved GNSS water vapor tomographic method was proposed to improve the distribution of observations. It was validated by tomographic experiments using GNSS data from 12 stations of Hong Kong SatRet for 7 days from DOY 182 to 188, 2017. The influence of the virtual observations on the number of voxels, where signal rays were passing through, aws analyzed. Results showed that the proposed method allowed for more voxels crossed by rays, and the average increase in quantity and proportion was 56 voxels and 10%, respectively. Most of the increased voxels were located in the region of tomographic upper boundary and near the stations.  
The comparison between SWV derived from tomographic results and that of GAMIT calculated was conducted using the conventional and proposed method. The MAE, STD, and RMS values decreased from 10.532/11.353/14.087 mm to 8.735/9.696/11.643 mm, respectively. In a comparison of the PWV time series, the MAE, STD, and RMS of the proposed method were smaller than those of the conventional method, whose values were 2.632/2.839/2.937 and 3.839/4.290/4.143 mm, respectively. The water vapor density of the proposed method agreed with that of radiosonde, particularly at the bottom altitudes of the tomographic area, compared with the conventional method. In addition, the results of regression analysis further demonstrated the superiority of the proposed method in obtaining the water vapor density. From the perspective of the ill-conditioned equation, the improvement in observations could not decrease the condition number.  
With the effective addition of other observations, including InSAR, water vapor radiometer, and COSMIC radio occultation data, the distribution of observations was further improved. However,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(A_{\text{save}}\) & \(A_{\text{save}}+A_{h}\) & \(A_{\text{save}}+A_{h}+A_{\text{v}}\) & \(A_{\text{save}}+A_{h}+A_{\text{v}}+A_{\text{save}^{\prime}}\) \\ \hline
**Condition Number** & INF & \(2.113\times 10^{5}\) & \(2.127\times 10^{3}\) & \(7.055\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Condition number of each coefficient matrix in the tomography solution at 12:00 UTC a.m. DOY 182, 2017.  
whether the condition number of the tomographic matrix was reduced should still be analyzed. Furthermore, the experiments were only carried out in Hong Kong at a specific time period. The feasibility and superiority remain to be further verified for various periods, regions, and weather conditions.  
Conceptualization, F.Y. and J.G.; Data curation, Y.X.; Formal analysis, J.G.; Methodology, F.Y.; Resources, J.S., L.Z., and M.C.; Validation, F.Y.; Writing-original draft, F.Y.; Writing-review & editing, J.G., J.S., L.Z., Y.X., and M.C.  
This research was funded by National Natural Science Foundation of China grant number [41474004].  
The authors would like to thank the Lands Department of HKSAR for providing the GNSS data from the HONG KONG Satellite Positioning Reference Station Network (SatRef). Acknowledgements are also given to the editor in charge and anonymous reviewers for their valuable comments and suggestions to improve this manuscript.  
The authors declare no conflict of interest.