# A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays
## 3 Experiment Description  
The tomographic experiment is implemented using data from 12 stations (HKLT, HKMW, HKNP, HKOH, HKPC, HKSC, HKSL, HKSL, HKSS, HKST, HKWS, T430 for tomographic modeling and HKKT for SWV comparison) of the Hong Kong Satellite Positioning Reference Station Network (SatRet) for a week (June 1-7, 2017). Figure 3 shows the GPS station distribution, the division of the grids, and radiosonde station 45004. GAMIT (v.10.61) is used to process the GPS data with a sampling interval of 30 s. The wet mapping function and the empirical formula of the weighted mean tropospheric temperature are used to project SWV on the basis of Equations (1) and (2). The tomographic period is 30 min and 48 tomographic experimental solutions can be processed every day. The scope of the tomographic region is (\(113.87^{\circ}\), \(114.35^{\circ}\)) for longitude, (\(22.19^{\circ},22.54^{\circ}\)) for latitude, and (0, 8 km) for altitude. The horizontal resolutions in the east-west and north-south directions are \(0.06^{\circ}\) and \(0.05^{\circ}\), respectively, and the vertical resolution is 800 m. It should be noted that water vapor density of the outer region (the north, east, south, and west) can be expressed by an unknown parameter (\(x_{n+1}\), \(x_{n+2}\), \(x_{n+3}\), and \(x_{n+4}\)), provided that the water vapor density in that region changes are relatively stable and as many as possible signal rays from the side face can be included in the region. To find the boundaries of the outer region that meet the above two requirements, the law of water vapor change, the size of the research area, and the distribution of the stations need to be carefully studied. The specific steps are as follows:  
1. To analyze the law of water vapor change. Figure 4 shows the relationship between water vapor density and altitude during the study period, with the red line being the fitted curve (upper for 45005, middle for 59,280, and lower for 59,316, respectively). The stations, 59,280 and 59,316, are located outside the tomographic area and their coordinates are (\(23.66^{\circ}\), \(113.05^{\circ}\)) and (\(23.35^{\circ}\), \(116.66^{\circ}\)), respectively. We can see that the water vapor concentrates in the lower troposphere, where it also changes more rapidly than above. In order to obtain the function between water vapor density (x) and altitude (h), the polynomial fitting method was used. Equation (10) was  
Figure 3: Geographic distribution of GPS and radiosonde station and the division of grids (the GPS stations in green are for tomographic modeling and the red one is for comparison). estimated by taking the altitude as the independent variable, while the water vapor density was regarded as the independent variable in Equation (11): \[x=26.34-9.22*10^{-3}h+1.19*10^{-6}h^{2}-5.51*10^{-11}h^{3}\] (10) \[h=7704.64-923.77x+47.90x^{2}-0.93x^{3}\] (11)
2. To find the suitable altitudinal boundary of the outer region. It can be computed by Equation (10) that the value of the water vapor density near the surface is 26.34 g/m\({}^{3}\). The range of the water vapor density in this research area is considered as around 0-26.34 g/m\({}^{3}\). For 10 layers in the altitude direction, if the change of the water vapor density with altitude in the outer region is within 0 to 2.634 g/m\({}^{3}\), it can be defined as a stable outer region. From Equation (11), the water vapor density of 2.634 g/m\({}^{3}\) corresponds to the height of 5586 m. Considering the convenience of rectification and the error caused by fitting, 5500 m can be selected as the alternative to the suitable altitudinal boundary of the outer region. 3. To decide the boundaries of the outer region in the east-west and north-south directions. The signal rays of all experimental periods acquired by satellite receivers in the research area are collected and their paths in the tomographic grid are calculated.