# A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography
## 3 Experiment and Analysis
### Comparison with Radiosonde Data  
The PWV calculated from radiosonde was suitable as a standard for evaluating the accuracy of the tomographic results. Thus, the PWV over the radiosonde station was also computed by the water vapor density of voxels from different tomographic schemes. In this experiment, eight tomographic solutions were selected daily to calculate PWV. Figure 7 presents the PWV time series of Scheme #1 and Scheme #2 and their comparison with radiosonde data. It can be seen that the trend of the PWV time series was basically consistent. Compared with radiosonde data, the two schemes match, and Scheme #2 was more consistent than Scheme #1. The statistical results of PWV differences between radiosonde data and tomography are listed in Table 5. Scheme #2 had an advantage compared with Scheme #1 in terms of MAE, STD, and RMS. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**DOY**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**STD**} & \multicolumn{2}{c}{**RMS**} \\ \cline{2-7}  & **Scheme \#1** & **Scheme \#2** & **Scheme \#1** & **Scheme \#2** & **Scheme \#1** & **Scheme \#2** \\ \hline
182 & 11.53 & 9.66 & 11.70 & 9.79 & 15.75 & 12.87 \\
183 & 12.75 & 9.70 & 8.47 & 6.69 & 14.49 & 11.17 \\
184 & 12.37 & 11.33 & 15.33 & 14.87 & 16.94 & 15.85 \\
185 & 10.33 & 9.57 & 12.24 & 11.06 & 14.05 & 12.81 \\
186 & 10.47 & 9.19 & 14.68 & 12.80 & 15.98 & 13.32 \\
187 & 9.73 & 6.75 & 9.92 & 6.82 & 12.94 & 9.15 \\
188 & 6.55 & 4.95 & 7.13 & 5.84 & 8.46 & 6.35 \\ \hline Average & 10.53 & 8.74 & 11.35 & 9.70 & 14.09 & 11.64 \\ \hline \end{tabular}
\end{table} 
Table 4: Accuracies in terms of MAE, STD, and RMS using two schemes for 7 days (Unit: mm). Figure 6: Accuracies in terms of MAE (**top**), STD (**middle**), and RMS (**bottom**) using two schemes in every tomographic solution of DOY 182, 2017. Although the PWV time series derived from Scheme #2 was in better agreement with the radiosonde data, while low MAE, STD and RSM were shown, we may not conclude that the vertical water vapor distribution of Scheme #2 was better than that of Scheme #1 because the PWV value was unchanged if two vertical layers were exchanged arbitrarily. Thus, the water vapor density profile should be compared between the two schemes and radiosonde data during the tomographic period. The data of UTC 00:00 and 12:00 of DOY 182 to 188, 2017 were selected to further test the accuracy of the tomographic results from different schemes. Figure 8 represents the WVD profiles for different altitudes at individual dates. It can be seen that the WVD obtained by Schemes #1 and #2 were in conformity with that derived from radiosonde. Evidently, the red line was more consistent with the green line than the blue one, thereby suggesting that the WVD of the proposed method better matches the radiosonde. This consistency was particularly evident at the bottom altitudes and implies that the proposed method achieves better water vapor density than the conventional method. Figure 8 shows the differences between the results of Schemes #1 and #2 and the radiosonde data in the low-altitude atmosphere from the red and blue dashed lines. It could be more clearly found that the differences between the result of Scheme #2 and radiosonde data were smaller than that of Scheme #1. Table 6 lists the statistical results of the water vapor density profile comparison between radiosonde and different schemes at UTC 12:00 from DOY 182 to 188, 2017, showing consistency with Figure 8. Thus, tomographic results of Scheme #2 were better than those of Scheme #1. Figure 8: (**a-g**) represent water vapor density profile comparisons between radiosonde and different schemes at UTC 00:00 from DOY 182 to 188, 2017. Figure 7: Comparison of PWV time series derived from various tomographic schemes and radiosonde data for the period of DOY 182 to 188, 2017. To explore the overall accuracy of WVD obtained by different schemes, all values from radiosonde data in the experimental period were selected for linear regression analysis.