# A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays
## 5 Conclusions  
The observation equations of GPS water vapor tomography are constructed by signal rays, and an increase in the quantity of signal rays added to the tomographic model contributes to an improved tomographic result. This paper proposed a new method that utilizes the signal rays coming from the top boundary and the side face of the tomographic area. Four outer regions were added to the tomographic equation as unknown parameters, and their boundaries were reasonably determined in the experiment. The traditional method using 8 \(\times\) 7 \(\times\) 10 voxels with the selected research area (Scheme #1) and another method using 10 \(\times\) 9 \(\times\) 10 voxels with an extended research area (Scheme #3) were utilized as comparisons. The tropospheric parameters were estimated using GAMIT software based on the Hong Kong Satellite Positioning Reference Station Network. The tomographic experiment was subsequently conducted using the three schemes. Numerical results from DOY 152 -158, 2017 show that the proposed method increases the number of voxels crossed by signal rays (15.14% on average) and improves the utilization of the observed data (19.68% on average) in comparison with the traditional method (Scheme #1). For Scheme #3, the cost of increasing the number of signal rays and the quantity of voxels crossed by rays was to add voxels in total from 560 to 900, which makes the proportion of crossed voxels drop. Radiosonde data were used as a reference to validate the tomographic result. In a comparison of the PWV time series, the RMS, MAE, and bias values of the proposed method were 4.00, 3.39, and 2.76 mm, respectively, which were smaller than those of the two traditional methods. A comparison of the water vapor density profiles at different altitudes showed that the profile of the proposed method matches the radiosonde data well. This finding was supported by the statistical results for RMS/MAE/bias/SD, which changed from 1.97/1.51/\(-\)0.33/1.87 gm\({}^{-3}\) of Scheme #1 and 2.23/1.68/-0.41/2.11 gm\({}^{-3}\) of Scheme #3 to 1.39/1.07/\(-\)0.21/1.30 gm\({}^{-3}\) of Scheme #2. In addition, an SWV comparison using data from station HKKT was conducted using different schemes; the RMS and MAE values of the SWV changed from 11.74/9.15 mm of Scheme #1 to 10.46/8.17 mm of Scheme #2 and 12.51/9.87 mm of Scheme #3. In all comparisons mentioned above, the proposed method achieved the best performance, and Scheme #3 with the extended research area performed worst. This suggests that increasing the percentage of voxels crossed by rays is key to improving tomographic accuracy, rather than simply increasing the number of signal rays. Figure 13: RMS (upper) and MAE (lower) of SWV using Schemes #1 and #2 for every tomographic solution of DOY 152, 2017. The experiments were only carried out in Hong Kong at a specific time period, in which the boundaries of the outer regions were suitable. When changes occur in the tomographic region, GPS receivers' location, or resolution of voxels, the boundaries of outer regions should be appropriately adjusted. So, 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.Z., L.Z. and S.S.; Formal analysis, F.Y., J.G. and J.S. ; Methodology, F.Y. ; Resources, J.S., Y.Z., L.Z. and Shengdeng Song; Validation, F.Y. ; Writing - original draft, F.Y. ; Writing - review & editing, J.G., J.S., Y.Z. and L.Z. This research was funded by [National Natural Science Foundation of China] grant number [41474004], and [Power Construction Corporation of China Project] grant number [DJ-ZDXM-2017-09]. The authors would like to thank the Lands Department of HKSAR for providing the GPS 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. * [PERSON] et al.