# A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays
## 4 Results and Discussion
### SWV Comparison  
To further evaluate the performance of the proposed method, the SWV of station HKKT is computed using the three schemes and their differences against the G  
\begin{table}
\begin{tabular}{l l c c c} \hline  & & **Scheme \#1** & **Scheme \#2** & **Scheme \#3** \\ \hline \multirow{3}{*}{RMS} & Mean & 1.97 & 1.39 & 2.23 \\  & Max & 2.98 & 1.90 & 3.37 \\  & Min & 1.32 & 0.78 & 1.67 \\ \hline \multirow{3}{*}{MAE} & Mean & 1.51 & 1.07 & 1.68 \\  & Max & 2.42 & 1.62 & 2.80 \\  & Min & 1.06 & 0.66 & 1.33 \\ \hline \multirow{3}{*}{Bias} & Mean & \(-\)0.33 & \(-\)0.21 & \(-\)0.41 \\  & Max & 0.59 & 0.53 & 0.72 \\  & Min & \(-\)1.15 & \(-\)0.87 & \(-\)1.28 \\ \hline \multirow{3}{*}{SD} & Mean & 1.87 & 1.30 & 2.11 \\  & Max & 2.89 & 1.82 & 3.30 \\ \cline{1-1}  & Min & 1.17 & 0.76 & 1.56 \\ \hline \end{tabular}
\end{table}
Table 2: Statistical results of water vapor profile comparisons between radiosonde and different schemes for the period of DOY 152 to 158, 2017 (unit: g/m\({}^{3}\)).  
Figure 11: RMS and relative error change with the altitude of Schemes #1 and #2 compared with radiosonde for 7 days.  
identified. It should be noted that only the SWV penetrated from the top boundary in Scheme #1 were used in this comparison. To better show the results, SWV residuals are grouped into individual elevation bins of \(5^{\circ}\), such that all residuals with an elevation angle between \(15^{\circ}\) and \(20^{\circ}\) are evaluated as a single unit. The RMS of each elevation bin are calculated and are shown in Figure 12, in which the upper and lower one represent the rainy and rainless scenario, respectively. It is clearly visible that the RMS of SWV residuals reduced as the elevation angle decreased. Colors in the figure indicate that better RMS results can be achieved by Scheme #2 in different weather conditions. Scheme #3 also is worse than Scheme #1 in this comparison. In summary, the residuals of SWV are reduced by the proposed method compared with the other two schemes.  
To further show the superiority of the proposed method in the SWV comparison, the RMS and MAE of every tomographic solution in DOY 152, 2017 are compared in Figure 13. The red marks acquired by Scheme #2 are smaller than the blue markers obtained by Scheme #1, and also smaller than the green markers obtained by Scheme #3 in the solutions of every period of time, which illustrates the superiority of the proposed method over the traditional methods. Moreover, Table 3 shows the average RMS and MAE calculated from the three schemes for 7 days. A similar situation as that in Figure 13 shows that the RMS and MAE of SWV reduced by the proposed method in the experimental period from 11.74/9.15 mm (Scheme #1) and 12.51/9.87 mm (Scheme #3) to 10.46/8.17 mm, respectively. In summary, it is clear evidence that the proposed method improves the accuracy of the tomographic result.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**DOY**} & \multicolumn{3}{c}{**RMS**} & \multicolumn{3}{c}{**MAE**} \\ \cline{2-7}  & **Scheme \#1** & **Scheme \#2** & **Scheme \#3** & **Scheme \#1** & **Scheme \#2** & **Scheme \#3** \\ \hline
152 & 9.81 & 8.61 & 10.73 & 7.41 & 6.96 & 7.99 \\
153 & 11.58 & 9.49 & 12.40 & 9.00 & 7.59 & 9.93 \\
154 & 11.48 & 10.48 & 12.64 & 8.99 & 7.33 & 10.38 \\
155 & 13.26 & 12.57 & 14.21 & 10.93 & 10.01 & 11.08 \\
156 & 11.76 & 10.98 & 12.08 & 8.99 & 8.00 & 9.64 \\
157 & 11.21 & 9.95 & 11.67 & 8.72 & 8.01 & 9.28 \\
158 & 13.07 & 11.13 & 13.81 & 9.98 & 9.34 & 10.80 \\ \hline Average & 11.74 & 10.46 & 12.51 & 9.15 & 8.17 & 9.87 \\ \hline \hline \end{tabular}
\end{table}
Table 3: RMS and MAE of SWV using Schemes #1 and #2 for 7 days (unit: mm).  
Figure 12: Comparison of SWV residuals for each elevation bins, upper for the rainy scenario and lower for the rainless scenario.