## 4 Result
### The Impacts of the Residual Zenith Tropospheric Delay on the SPP Solution  
In this subsection, impacts of the dZTD on the SPP solution are analyzed. Table 5 shows the means and RMSs of the SPP biases on North (N), East (E), and Up (U) direction produced by the dZTD of the nine models. One can see that the biases mainly occur on the U direction, nearly to decimeter level. In contrast, biases on the horizontal (N and E) direction are significantly smaller, just at the centimeter level. Among all these models, the SPP biases by using the saas+norm model are the largest, with means being 0.16 cm, 0.04 cm, \(-\)35.6 cm, and RMSs being 4.08 cm, 3.31 cm, 44.55 cm on the N, E, U directions respectively. The SPP biases of using the EGNOS/UNB3/UNB3m models are slightly larger and less stable than those of saas+GPT2/GPT2w/GPT3 models. It is noted that SPP biases on the vertical direction are negative when using saas+ models, and those values are positive when using EGNOS/UNB3/UNB3m models. At last, the SPP biases by using the VMF3 model are the smallest, with means being \(-\)0.01 cm, 0 cm, 0.79 cm, and RMSs being 0.59 cm, 0.43 cm, 5.93 cm on N, E, U directions respectively. In general, the dZTD impacts on SPP solutions are negligible on horizontal directions and significant on vertical direction. Therefore, only the SPP solution impacts on the vertical direction are further analyzed below. To evaluate the SPP solutions influenced by the uncorrected ZTD when using different models in different seasons, the RMSs of the SPP biases on the vertical direction produced by dZTD of the nine models are shown in Figure 6 by season. Compared with Figure 4, one can see that similar tendencies on the SPP solutions are observed. The RMSs in summer are generally the largest, and RMSs in spring and winter are equivalent and slightly smaller than those in autumn. One exception is the saas+GPT, where RMSs in spring and winter are much larger than those in summer and autumn. For VMF3, the seasonal discrepancies are less significant, even though the RMSs in summer are still slightly larger. In generally, it can be concluded that SPP solution stability would be relatively lower in summer regardless of the ZTD model. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{\begin{tabular}{c} **Mean** \\ **N (cm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **U (cm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **N (cm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **RMS** \\ **E (cm)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **U (cm)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **U (cm)** \\ \end{tabular} } \\ \hline saas+norm & 0.16 & 0.04 & \(-\)35.60 & 4.08 & 3.31 & 44.55 \\ saas+GPT & \(-\)0.08 & 0.01 & \(-\)8.51 & 3.55 & 2.80 & 38.22 \\ saas+GPT2 & 0.03 & 0.01 & \(-\)1.20 & 1.97 & 1.49 & 20.37 \\ saas+GPT2w & 0.03 & 0.01 & \(-\)3.13 & 1.86 & 1.40 & 19.14 \\ saas+GPT3 & 0.03 & 0.01 & \(-\)3.13 & 1.86 & 1.40 & 19.14 \\ EGNOS & \(-\)0.02 & 0.00 & 7.83 & 2.54 & 1.88 & 26.11 \\ UNB3 & \(-\)0.03 & 0.00 & 8.03 & 2.56 & 1.89 & 26.28 \\ UNB3m & 0.04 & 0.01 & 1.81 & 2.42 & 1.78 & 24.75 \\ VMF3 & \(-\)0.01 & 0.00 & 0.79 & 0.59 & 0.43 & 5.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Means and RMSs of the Single Point Positioning (SPP) solutions generated by the dZTD obtained by the 9 methods (saas+norm/GPT/GPT2/GPT2w/GPT3, EGNOS, UNB3, UNB3m, VMF3) on North (N), East (E), and Up (U) direction (unit: cm). To compare the model discrepancies in different geographical locations, the dZTD RMSs (upper panels) and RMSs of the SPP biases on the vertical direction (lower panels) generated by dZTD from saas+GPT (left panels) and UNB3 (right panels) models at globally distributed IGS stations are shown in Figure 7. Triangulation linear interpolation is used for the demonstration. One can see that the saas+GPT model performs worst around the equator, and best around middle latitude areas.