## 4 Experiments and Results
### Experimental Schemes  
The GNSS data with the sampling rate of 30 s from 17 stations (red dot in Figure 7) provided by the Hong Kong Satellite Positioning Reference Station Network (SatRef) were processed using GAMIT/GLOBK (v:10.7). In the processing, the four International GNSS Service (IGS) stations (BJFS station, HKWS station, LHAZ station, and SHAO station) were introduced. The ZTD and the gradient delay were estimated with the time resolution of 5 min, which was sufficient to reveal the variation characteristics of water vapor. The Saastamoinen model was set as the expression for the ZHD [45], and Vienna Mapping Function 1 (VMF1) was used for calculating the SWDs [46]. In addition, the post-fit residuals calculated by GAMIT/GLOBK exceeding 2.5 times the standard deviation were removed [47]. The 30-year radiosonde observation data was obtained from the King's Park Meteorological Station (HKKP, the blue dot in Figure 7a). The research area of the tomography model spanned from 113.82\({}^{\circ}\)E to 114.36\({}^{\circ}\)E and 22.16\({}^{\circ}\)N to 22.56\({}^{\circ}\)N. Moreover, the horizontal resolution was 0.09\({}^{\circ}\) in longitude and 0.08\({}^{\circ}\) in latitude, as shown in Figure 7a. In the current tomography studies based on the Hong Kong SatRef, about a month of GNSS data and the radiosonde observations derived from the HKKP station were processed for modeling the tomography area [14,20,36,41]. Therefore, the experimentation time in this work was set as August 2017, i.e., day of year (DOY) 213-243, when Hong Kong was in the summer and there were more rainstorms. The tomography region was segmented into 15 nonuniform layers from 0 to 11 km (August top boundary determined in Figure 2) [14]. In the most common voxel-based tomography model, to assess the accuracy of tomographic results, water vapor profiles of the voxel columns (small blue rectangles in Figure 7b) where the radiosonde is located are compared with radiosonde-derived vertical profiles. However, the empty voxels are mainly distributed on the side of the three-dimensional tomographic model. Consequently, as shown in Figure 8, four special test schemes based on four different tomography areas (red boxes of Figure 8a-d) were implemented. The RS-voxels (the blue voxels, shown in Figure 7b, where the radiosonde is located) were placed on four boundaries of the tomographic region in the four schemes, for instance, RS-voxels on the east side (Figure 8a), RS-voxels on the west side (Figure 8b), RS-voxels on the south side (Figure 8c), and RS-voxels on the north side (Figure 8d). Table 2 shows the accurate range of the tomographic area and the number of voxels in these four schemes. Figure 8: The tomographic region (red rectangles) for four schemes. (**a**) Scheme East; (**b**) Scheme West; (**c**) Scheme South; and (**d**) Scheme North. The blue square refers to the RS-voxels. Figure 7: (**a**) Plane map of the Hong Kong area obtained by Mercator projection with 17 Global Navigation Satellite System (GNSS) reference stations (red dots) and radiosonde King’s Park Meteorological Station (HKKP) (blue dot) in Hong Kong; (**b**) 3-D distribution of GPS signals for the proposed tomography model. Red lines represent signals passing from the top boundary of the tomographic area, whereas green lines denote rays penetrating from the side face of the tomography region. The blue vertical columns represent the radiosonde (RS)-voxels where the radiosonde is located. In addition, to verify the accuracy and reliability of the HFM, two sub-groups of solutions were generated for the four schemes; one only used the rays travelling from the top boundary, while the others combined both rays passing from the top and side boundaries. It should be noted that if the effective observations from the HKSC station are included, the data is not consistent with the signal distribution of the general tomographic model.