# Node-Based Optimization of GNSS Tomography with a Minimum Bounding Box Algorithm
## 4 Test Results and Analysis  
Data from the Hong Kong Satellite Positioning Reference Station Network (SatRef) were processed by the new node-based tomographic approach and the common node-based tomographic approach, for verification. These results were also compared against water vapor data, from King's Park Meteorological Station (HKKP) to assess their quality. The horizontal and vertical distributions of these stations are presented in Figure 7. The initial data contain information on 17 reference stations from the SatRef, which are evenly distributed in Hong Kong (see Figure 7). In this study, a window, on the top of the tomographic region, is used as a sampling method for data acquisition. The window size is shown in Figure 7, which is an attempt to utilize the GNSS signals with large satellite elevation angles in the denser regions. Due to these GNSS data, the most important datasets generally have relatively small errors (i.e., relatively large satellite elevation angles). The new approach can build a high-quality tomographic model. The tomographic data use the Day-of-Year (DOY) numbering system. This is a common format used in research data. The DOY is the sequential day number starting with day 1 on 1 January. The data throughout May 2015 (i.e., DOY 121-151) with a fixed sampling interval (the 30s). For simplicity, the results from the common node-based tomographic approach and the new node-based tomographic approach are called CNT and NNT, respectively. The water vapor data from HKKP are called WVD for short. Some statistics, e.g., the root-mean-square error (RMSE) and bias, are applied to quantify the results of CNT and NNT. The values of the tomographic results at all WVD sampling points were calculated first using the interpolation method, then the statistics between the interpolated values and WVD observations at all the sampling points of the WVD profile from the ground surface to 11000m at each epoch was calculated. Figure 7: The distribution of the SatRef. (**a**) The horizontal position of SatRef (red triangles) and HKKP (yellow square); (**b**) The vertical position of SatRef (black dots) and vertical layers for the tomographic model; (**c**) The enlarged view of the vertical position of SatRef (black dots). For the new and the common node-based tomographic modeling, the SWV observations were collected with a sampling rate of 5 min. The tomographic results at Coordinated Universal Time (UTC) 12 throughout the whole month are compared with the water vapor data acquired by a sounding balloon at HKKP. Since the reference data from HKKP only provides one moisture profile at each epoch, the interpolated tomographic results at the position of the HKKP are used for validation of the new node-based tomographic model. Figure 8 shows the RMSE estimates for the CNT and NNT results at UTC 12 every day in May. This is calculated by subtracting the WVD from the tomographic results (CNT or NNT) at all sampling points of the sounding balloon below 10,800 m. The figure reveals that the NNT, for most of the time, outperformed the CNT technique except for DOY's 127, 131 and 141, which are marked by yellow circles in Figure 8. Overall, the mean percentage improvement of RMSE between the CNT to NNT is 38 percent. Although CNT fared better than NNT in three days of this month, the mean percentage decline of RMSE from NNT to CNT is only 9 percent. Focusing more clearly on these DOYs (see Figure 9), there is no apparent difference between the NNT and CNT derived water vapor profiles for these three days. DOY 139 (bottom right panel), shows the most significant differences in RMSEs values between NNT and CNT, which reveals that the results from CNT are poorer on this day. This may also suggest that in some instances, the GNSS tomographic solutions from CNT are largely beyond the predicted results and that the tomographic model of the CNT may be unstable. Table 3 contains the RMSE, bias and the Pearson correlation coefficient (PCC) values for the CNT and NNT results at UTC 12 for the whole month of May.