# A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays
## 4 Results and Discussion
### Water Vapor Profile Comparison  
In general, if two vertical layers are exchanged arbitrarily, then the PWV remains the same, but the vertical distribution of the water vapor changes. Therefore, the PWV comparison mentioned above may not denote a correct tomographic result obtained, although the PWV derived from the different schemes are in good agreement with that from the radiosonde. To validate the accuracy of the vertical water vapor density, the water vapor profiles between the radiosonde and the two schemes are compared, as shown in Figure 10. Two dates are selected because they correspond to the maximum and minimum RMS during the week-long experimental period.  
Figure 10 shows that the tomographic water vapor profiles of the three schemes agree well with those from the radiosonde data. The water vapor density profile of Scheme #2 better matches that from radiosonde than the other two schemes, especially in the low layers. Scheme #3 has the worst performance. Compared with radiosonde, the numerical results of the tomography from Scheme #2 for the two selected epochs (RMS are 1.90 and 0.78 g/m\({}^{3}\)) are superior to those of Scheme #1 (RMS are 2.98 and 1.32 g/m\({}^{3}\)) and Scheme #3 (RMS are 3.37 and 1.67 g/m\({}^{3}\)).  
Table 2 lists the statistical results of the three schemes in all water vapor profile comparisons, including RMS, MAE, bias, and SD. The numerical results reveal that the average RMS/MAE/bias/SD values are 1.97/1.51/\(-\)0.33/1.87, 1.39/1.07/\(-\)0.21/1.30, and 2.23/1.68/-0.41/2.11 gm\(-\)3 for Schemes #1, #2, and #3, respectively. The maximum and minimum values of each statistic are shown in the table. These findings show that the proposed method is more consistent with the radiosonde data than the other two traditional methods. It should be noted that Scheme #3 does worse than Scheme #1, which indicates the total number of voxels and the selection of the entire tomographic area size are important to the tomographic result.  
Figure 10: Water vapor profiles derived from radiosonde and Schemes #1 and #2; left and right are the dates with maximum and minimum RMS, respectively.  
To make a further comparison of the relationship between the altitude and the errors in different schemes, the tomographic results (DOY 152-158, 2017) are analyzed. The average RMS error and relative error at different layers for the three schemes are calculated in this period to show the pattern of the vertical water vapor distribution and altitude. Figure 11 gives the RMS and relative error changes with height throughout the experimental period. It can be seen that the RMS, generally, decreases with altitude, whereas the relative error shows an opposite trend. A large relative error appears in the upper layers because the water vapor density is very low in those layers and a small discrepancy between the tomographic result and radiosonde data will result in a large value. In addition, the RMS and relative error of the proposed method (Scheme #2) are generally less than those of the traditional methods (Scheme #1 and #3) for the different layers, which validates the improved nature of the proposed method over the traditional methods.