# A New GNSS-Derived Water Vapor Tomography Method Based on Optimized Voxel for Large GNSS Network
## 3 Experiment and Validation
### Validation of the Optimized Tomographic Method  
We use two strategies for tomographic experiments, the conventional method (Method 1; Section 2.3), which introduces three constraints for the tomographic solution, and the improved method (Method 2) proposed is this paper (Section 2.4), which does not impose empirical constraints but only considers ray-passed voxels for the tomographic solution. Using the two methods, the experiments are carried out in the tomographic zone shown in Section 3.2 during the two periods mentioned in Section 3.1 based on the gridding scheme descried in the last section. The RS provides the most accurate WV products, usually assumed as truth to validate the quality of tomographic results. Another resource of WV data, the European Center for Medium-Range Weather Forecast (ECMWF) products, is often used as a reference in the verification of the performance of the tomographic method. However, our previous study [25] has demonstrated that the 3D WV products derived from ECMWF cannot match the products acquired by the RS. Thus, the WV products derived from ECMWF are not used as a reference in this study. In this experiment, the mean absolute error (MAE), root mean square error (RMSE), and bias are used as statistical quantities to evaluate the quality of the tomographic results. As RS balloons are launched twice (at UTC 00:00 and 12:00) per day, we can obtain two-epoch accurate WV profiles daily for tomographic method comparison. Meanwhile, the WV profiles for the location of the RS are calculated using the GNSS WV tomographic technique based on the two aforementioned methods at the corresponding epoch of RS balloons launched, respectively. Figure 8 shows the RMSE statistics of the WV profile differences between the above methods and RS data over the test period. The RMSEs of Method 2 are smaller than those of Method 1 at all test epochs. The RMSEs of Method 1 and Method 2 at DOY 244-246, 2019 (rainy weather), are better than those at DOY 182-184, 2019 (rainless weather). Besides, the statistics in Table 3 show that Method 2 has higher accuracy in both rainy and rainless weather compared with Method 2, indicating again that Method 2 exhibits better performance and applicability with respect to Method 1. Figure 7: Horizontal grid strategy. The Nanjing area is divided by a \(12\times 14\) grid in the horizontal domain (14 in the latitudinal direction, 12 in the longitudinal direction). The horizontal resolution is \(0.1^{\circ}\) in both the latitude and longitude directions. We selected the two epochs with the minimum and maximum RMSEs for both Method 1 and Method 2 and compare the WV profiles of the two tomographic methods and RS method at these epochs in Figure 9. As shown in Figure 9a, the WV profiles obtained using Method 1 and Method 2 are in good agreement with that obtained using the RS data at UTC 00:00 DOY 245, 2019. Nevertheless, Figure 9b shows that the WV profiles generated using the two tomographic methods do not match well with the WV profile obtained using the RS at UTC 00:00 DOY 183, 2019. Thus, the two tomographic strategies exhibit higher performances in the rainy period than in the rainless period (recall Figure 8 and Table 3). Figure 9 shows that the vertical distributions of WV appear more even during the rainy day than during the rainless day. As shown in Figure 9b, the tropospheric WV exhibits a large change at heights below 4 km and a small change at heights above 4 km. This indicates that the moisture content near the ground is abundant but irregular on clear days. According to the study by [PERSON] et al. [24], the WV with an even distribution is beneficial for good tomographic results obtained by the GNSS WV tomographic technique. Thus, the GNSS tomographic algorithm has a higher performance in the rainy period than in the clear period.