## 4 Experiments and Results
### Comparison with the Existing Correction Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scheme** & **Data** & **RMSE** & **STD** & **Bias** \\ \hline Scheme East & \begin{tabular}{c} _Integral_ only \\ _Integral_+_inside_ \\ _Integral_ only \\ _Integral_+_inside_ \\ _Integral_ only \\ _Integral_+_inside_ \\ \end{tabular} & 13.08 & 12.83 & \(-\)0.33 \\ Scheme West & \begin{tabular}{c} _Integral_+_inside_ \\ _Integral_ only \\ _Integral_+_inside_ \\ \end{tabular} & 9.97 & 9.49 & \(-\)0.17 \\ Scheme South & \begin{tabular}{c} _Integral_ only \\ _Integral_+_inside_ \\ _Integral_+_inside_ \\ \end{tabular} & 12.05 & 11.55 & \(-\)0.29 \\ Scheme West & \begin{tabular}{c} _Integral_+_inside_ \\ _Integral_ only \\ _Integral_+_inside_ \\ \end{tabular} & 9.50 & 9.36 & \(-\)0.25 \\ Scheme West & \begin{tabular}{c} _Integral_+_inside_ \\ _Integral_+_inside_ \\ \end{tabular} & 13.69 & 13.26 & \(-\)0.25 \\ Scheme West & \begin{tabular}{c} _Integral_+_inside_ \\ _Integral_ only \\ _Integral_+_inside_ \\ \end{tabular} & 11.09 & 10.64 & \(-\)0.24 \\ Scheme North & \
\begin{tabular}{c} _Integral_ only \\ _Integral_+_inside_ \\ \end{tabular} & 10.46 & 10.39 & \(-\)0.27 \\ Scheme West &
\begin{tabular}{c} _Integral_+_inside_ \\ _Integral_+_inside_ \\ \end{tabular} & 9.19 & 9.04 & \(-\)0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical results of the comparison of SWV between reconstructions and measurements for the four schemes (unit: mm). Figure 13, where a similar exponential relationship can be observed. It is noticeable that owing to the neglection of GNSS signals with an elevation angle of less than 15\({}^{\circ}\), all of the heights of the intersection points are higher than approximately 1 km. Accordingly, the coefficients \(a\) and \(b\) were estimated by the least-squares method, and the results are given in Table 5([PERSON] et al., 2017). With the scale factor in the Yao model and the HFM proposed in this paper, the SWV of the side signals could be estimated based on the height of the intersection points. Consequently, Figure 14 presents a comparison of the SWV value of effective side rays between the Yao model and HFM at two tomography epochs during each of the test days. It is clear that the HFM can estimate slightly higher SWV values than the Yao model for most signals, and the latter provides a rather small SWV estimation, with a value of approximately 20 mm, for several observation rays. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & \(a\) & \(b\) & **RMSE** & **R-Square** \\ \hline Yao model & 2.233 & \(-\)1.119 & 0.9882 & 0.0145 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The fitting coefficient and accuracy of the Yao model. Figure 14: Comparison of the SWV value of effective side rays obtained from the Yao model and the HFM for two tomography epochs. (**a**) 00:00-00:30 UTC; (**b**) 12:00–12:30 UTC. Figure 13: The scale factor changes with the height of the intersection point between the effective side signals and the side face of the tomographic area during the period of DOY 213-243, 2017. To assess the water vapor reconstruction capabilities of different methods, the tomographic results derived from the three schemes, described in Figure 15, were employed to illustrate the water vapor vertical profile at 00:00 UTC and 12:00 UTC on DOY 220 (sunny day) and DOY 234 (rainy day). It can be observed that the water vapor profiles derived from the three considered schemes agree with the reference profile obtained by the radiosonde data. Furthermore, a higher coincidence of the vertical profile can be seen on majority layers when combining the inside signals.