# LEO Constellation-Augmented Multi-GNSS for 3D Water Vapor Tomography
## 3 Experiments and Results
### Tomographic Accuracy Evaluation  
Three observation durations were chosen to analyze the precision and time resolution of the tomography, namely, 10, 20, and 30 min, respectively. The accuracy index was  
Figure 14: Distribution of empty and two-station voxels for five schemes in first 30 min of each hour of the day. (**a**) Number of voxels without rays that passed through. (**b**) Number of voxels observed by more than two stations. Figure 13: Number of voxels with different sampling rates. (**a**) Number of voxels without observed ray crossing. (**b**) Number of voxels with more than two stations to observe ray crossing. calculated according to Equation (11). Figure 15 shows that the accuracy of all five schemes improved with observation duration. The performance of the GRECL288 scheme is the best, while the G scheme is the worst. In addition, the accuracy of all the schemes improves with increasing the observation time, and the most obvious improvement is the L288 scheme. When the observation time was 10 min, the accuracy of the L288 scheme was worse than that of the GREC scheme, while the accuracy of L288 was better than that of GREC when the observation time was 30 min. Meanwhile, LEO was also better than GNSS for tomography accuracy improvement. A side-by-side comparison showed that GRECL288 took less time than GREC did to achieve the same level of accuracy. GRECL288 had an accuracy factor of 9.82% at 10 min of observation time, while GREC had an accuracy factor of 9.64% at 30 min of observation time. When the observation time is 10 min, the accuracy of GRECL288 is 1.27% and 5.24% higher than that of GREC and G, respectively. When the observation duration was 30 min, the accuracy of GRECL288 was improved by 0.75% compared to that of Greece, and 5.83% compared to that of G. However, a certain amount of observation time is beneficial for accumulating valid observation information. However, a shorter observation time is conducive to rapid tomographic modeling. The water vapor density profiles that were extracted from ERA5, the sounding station, and the five schemes within 30 min, are presented in Figure 16, respectively. Data from the sounding station were used as the initial background field for the tomography, and ERA5 data were used for the tomography without errors and could be considered to be true values. The closer the calculated value profile line was to the value of ERA5, the better the calculation was. There were some errors between the initial and true values. All five schemes showed a tendency to approach the true value, and showed good agreement with the true value at the middle and high levels, but a large gap with the true value at the bottom level. More information on the accuracy at different altitude levels can be derived from Figures 17 and 18. Figure 17 shows the distribution of the difference between the five schemes, and the ERA5 data at different altitudes. The maximal difference values in all five schemes occurred at an altitude of 0.4 km, followed by 1.2 km. This indicates that, despite the increase in the number of observations, the worst accuracy at the bottom still existed. Comparing the five schemes, the G scheme showed the sharpest fluctuations in horizontal distribution, while the GRECL288 and L288 schemes showed significantly flatter fluctuations. This indicates that the addition of LEO satellites made the tomography results more stable, especially those of the L288 scheme, which showed better stability, even without GNSS data. Figure 15: Comparison of accuracy of different observation durations. Figure 16: Comparison of water vapor density profiles from tomographic results. (**a–e**) Water vapor density profiles of G, Greece, GRECL60, GRECL288, and L288, respectively, compared with those of ERA5 and radiosonde. The vertical profile of the radiosonde is related to the position of the radiosonde. Radiosonde and ERA5 data were presented within the same planar voxel.