**5. Conclusions**

In this paper, the performances of the four navigation satellite systems and their combinations in the water vapor tomography were analyzed and assessed using the GNSS data of SatRef in Hong Kong. In the tomographic modeling, the signal rays that can be used, the voxels crossed by signal rays, and the number and distribution of the effective voxels were computed and counted for these different combinations. For the tomographic results, the GAMIT-estimated SWV of HKQT and the water vapor density derived from radiosonde were selected as references to assess these 15 tomographic solutions.

In the experimental period, the average number of available signal rays was 507, 704, 329, and 351 for GPS, BDS, GLONASS, and Galileo, respectively. Combining satellite systems in water vapor tomography can increase the number of available signal rays, especially as the value of four-system combination reaches close to 2000. The average number of voxels crossed by signal rays are 425, 424, 392, and 377 for GPS, BDS, GLONASS, and Galileo, respectively, showing that the number of penetrated voxels is not entirely determined by the number of available signal rays. The combinations improved the number of voxels crossed by signal rays; for example, the number and coverage rate of penetrated voxels achieved by GCRE are 468 and 83.6%, respectively. When the voxels with sufficient signal rays are concerned, these 15 tomographic solutions differ very little in both number and coverage rate. The distribution diagram of effective voxels based on black and white rectangle also indicated the small differences in the 15 solutions. The numerical statistics showed that the RMSE in SWV comparison are 1.66, 1.59, 1.75, 1.74, 1.68, 1.64, 1.67, 1.62, 1.63, 1.60, 1.59, 1.64, 1.65, 1.65, and 1.63 mm for G, C, R, E, GC, GR, GE, CR, CE, RE, GCR, GCE, GRE, CRE, and GCRE, respectively. In the comparison with radiosonde data, the average RMSE are 1.42, 1.41, 1.45, 1.46, 1.33, 1.34, 1.41, 1.34, 1.36, 1.40, 1.30, 1.34, 1.36, 1.37, and 1.32 gm−<sup>3</sup> for these 15 tomographic results. The above comparisons indicated that the differences in the tomographic results of a single satellite system are small, and the combinations of satellite systems have limited improvement in the water vapor tomography results.

In the follow-up research, the impact of different satellite systems and their combination on water vapor tomography need to be explored in more representative regions. In addition, the number, distribution, and density of GNSS stations in the research region is another important factor determining the structure of the tomographic model. Thus, it is necessary to pay more attention to the influence of the GNSS sites on water vapor tomographic results in the case of a determined satellite system.

**Author Contributions:** Conceptualization, F.Y.; data curation, J.W., H.W., X.G. and L.W.; funding acquisition, F.Y.; investigation, J.W.; methodology, F.Y.; resources, J.W., H.W., X.G. and L.W.; software, B.H.; validation, F.Y.; writing—original draft, F.Y.; writing—review and editing, F.Y., J.W., H.W., X.G., L.W. and B.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Beijing Natural Science Foundation (No. 8224093), China Postdoctoral Science Foundation (No. 2021M703510), Fundamental Research Funds for the Central Universities (No. 2021XJDC01), Key Laboratory of South China Sea Meteorological Disaster Prevention and Mitigation of Hainan Province (No. SCSF202109), Open Fund of State Key Laboratory of Geodesy and Earth's Dynamics Innovation Academy for Precision Measurement Science and Technology (No. SKLGED2022-3-1), and Beijing Key Laboratory of Urban Spatial Information Engineering (No. 2022017). We thank all anonymous reviewers for their valuable, constructive, and prompt comments.

**Data Availability Statement:** The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

**Acknowledgments:** We thank the Hong Kong Geodetic Survey Services for providing the GNSS data of the Hong Kong Satellite Positioning Reference Station Network (SatRef). We also thank all the anonymous reviewers for their valuable, constructive, and prompt comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

