# A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography
## 3 Experiment and Analysis
### Analysis of the Proposed Method  
For each tomographic solution, the period covered was 0.5 h, and the sampling rate was 30 s. A total of 3 \(\times\) 60 \(\times\) 12 virtual SWVs could be constructed within the 12 GNSS stations. To analyze the influence of the proposed method in Scheme #2 on the number of voxels, where signal rays passed through, relevant experiments were conducted. The corresponding results for Scheme #1 and Scheme #2 are shown in Figure 3. It can be seen that Scheme #2 allowed for more voxels that were passed through by rays. Specifically, the average number of crossed voxels was raised from 382 to 438, and the percentage of total voxels was increased from 68% to 78% in this period. Figure 4 shows the results per 30 min at DOY of 182, 2017. Obviously, the number of voxels that were passed through by signal rays was improved by exploiting the virtual SWV of Scheme #2. The largest increase occurred in the 28 th solution, reaching 94 voxels (Solution #a, highlight by green circle), whereas the 37 th solution had the least increase, reaching only 32 voxels (Solution #b, highlight by green squares). The average increase was 56 voxels at DOY of 182, 2017.  
To further illustrate the effects of the proposed method, Figure 5 shows the grayscale graph of the number of signal rays passing through each voxel. In this graph, the deepening of the grayscale represents an increase in the number of rays passing through the voxel (white represents no ray through). Thus, it can also be used to display the specific location of the increased voxel crossed by virtual SWV of Scheme #2. (a) and (b) stand for Solutions #a and #b, respectively. The upper one adopted Scheme #1 and the lower one utilized the Scheme #2 in each graph. It can be seen that the addition of virtual SWV can effectively supplement the situation of no signal rays passing through the voxels around the GNSS stations. In the high level tomographic layer, more voxels in the tomographic boundary region were penetrated by signal rays because of the virtual SWV of Scheme #2, which was a good complement to Scheme #1. However, the change of gray in the images reveals that the number of rays passing through voxels was significantly increased with the addition of virtual SWV. Table 3 lists the detailed values corresponding to Figure 5, and these values were counted from the perspective of the layer.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Strategy** \\ \hline Choice of Observable & LC\_AUTCLN \\ Choice of Experiment & BASELINE \\ Sampling rate & 30 s \\ Elevation Cutoff & 10\({}^{\circ}\) \\ Zenith Model & PWL (piecewise linear) \\ Tropospheric correction model & Saastamoinen \\ Mapping Function & GMF \\ IGS stations & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: GAMIT processing strategy for tropospheric estimation.  
Figure 4: Number of voxels crossed by signal rays in two schemes for each tomographic solution at DOY 182, 2017.  
Figure 5: _Cont_.  
Figure 3: Average number (histogram) and percentage (line) of voxels crossed by signal rays for Scheme #1 and Scheme #2 of DOY 182 to 188, 2017.