## 4 Result
### The Residual Zenith tropospheric Delay (dZTD)  
Firstly, the mean and RMS values of the dZTD by the nine models were calculated via data from all stations and in all days, as shown in Figure 2. It shows that among these models, the dZTD mean and RMS values by saas+norm/GPT were significantly larger than those by other models. The reason for this is that the meteorological parameters used in the saas+norm/GPT are quite rough and have low accuracy. Comparably, saas+GPT2/GPT2w/GPT3 show much better performances. The dZTD means and RMSs by these three models are all less than 1 cm and 5 cm, respectively. The performances of EGNOS/UNB3/UNB3m were also comparative, and were all slightly worse than the saas+GPT2/GPT2w/GPT3. The biases by EGNOS/UNB3 were less than 2 cm, while that of UNB3m was significantly reduced to 0.35 cm. This is because the UNB3m model uses relative humidity instead of water vapor pressure in the look-up table, which improves the calculation accuracy of the ZWD. However, dZTD RMSs of the three models were similar, all around 6 cm. Also, it is interesting to note that biases by combined models (saas+) were positive, and biases by empirical models (EGNOS/UNB3/UNB3m) were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Spring**} & \multicolumn{2}{c}{**Summer**} & \multicolumn{2}{c}{**Autumnn**} & \multicolumn{2}{c}{**Winter**} \\ \hline DOY & num & DOY & num & DOY & num & DOY & num \\
80 & 386 & 172 & 404 & 266 & 374 & 356 & 376 \\
81 & 374 & 173 & 400 & 267 & 372 & 357 & 377 \\
82 & 390 & 174 & 401 & 268 & 372 & 358 & 380 \\
83 & 392 & 175 & 403 & 269 & 373 & 359 & 379 \\
84 & 382 & 176 & 394 & 270 & 377 & 360 & 377 \\
85 & 381 & 177 & 394 & 271 & 381 & 361 & 382 \\
86 & 386 & 178 & 399 & 272 & 384 & 362 & 380 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The corresponding day of year (DOY) and the number of global International GNSS Service (IGS) GPS stations (num). Figure 1: Distribution of global International GNSS Service (IGS) GPS sites. negative. As a more accurate product, the bias of VMF3-ZTD is ignorable, and the RMS is just 1.31 cm. Therefore, it can be concluded that IGS-ZTD and VMF3-ZTD products are on similar accuracy level. From Figure 3 we can see that dZTD means by most models show obvious discrepancies in different seasons. For the saas+norm model, the dZTD mean value in summer is the largest (around 9 cm), and those in spring and winter were much smaller (around 5 cm). Figure 4: RMS between the IGS ZTD and the 9 models (saas+norm/GPT/GPT2/GPT2w/GPT3, EGNOS, UNB3, UNB3m, VMF3) in different seasons. Figure 3: Mean between the IGS ZTD and the 9 models (saas+norm/GPT/GPT2/GPT2w/GPT3, EGNOS, UNB3, UNB3m, VMF3) in different seasons. Figure 2: Mean and RMS between the IGS ZTD and the 9 models (saas+norm/GPT/GPT2/GPT2w/GPT3, EGNOS, UNB3, UNB3m, VMF3). To evaluate the model accuracies in different seasons, dZTD means and RMSs by different models are calculated and summarized by using each 7 day period’s data, as shown in Figures 3 and 4. The seasonal discrepancy of the saas+GPT model was most significant, with biases mainly existing in summer and autumn, and nearly ignorable in spring and winter. Biases of saas+GPT2/GPT2w/GPT3 models were remarkably reduced, and were also slightly larger in summer. Comparably, biases of saas+GPT2 were always smaller than the other two in different seasons. In terms of the three empirical models, the biases of EGNOS and UNB3m were similar, and both larger than those of UNB3m models. It is noted that the biases of EGNOS and UNB3 models in summer were much smaller than those in other three seasons, and biases of UNB3m were most significant in winter and almost ignorable in other three seasons. At last, the biases of VMF3-ZTD were comparable in the four seasons, and always close to 0. Figure 4 show the dZTD RMSs of different models by season. Generally, RMSs in summer are always the largest, and RMSs in the other three seasons are comparable for all these nine models.