## 4 PPP-B2b ZTD Estimation and Evaluation of the Results
### Comparison of the GNSS-Derived ZTD/PWV with That Derived from Radiosonde Data  
To further investigate the accuracy of the GNSS-derived ZTD/PWV, the ZTD/PWV data were compared with those derived from co-located radiosonde observations. As shown in Table 9, the RMSEs of the GNSS-derived ZIDs are 13.1 mm, 11.7 mm, 13.4 mm, and 22.4 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively, which are much smaller than the RMSEs calculated using ERA5 as a reference for these 11 stations.  
Figure 11: Diurnal anomaly variations in the PWV time series obtained from GNSS and ERA5 in March 2022.  
Figure 10: PWV variations and the monthly RMSEs of differences between GNSS-derived PWV and ERA5-derived PWV.  
The mean biases are 0.2 mm, \(-\)3.2 mm, \(-\)3.8 mm, and 2.9 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively. As depicted in Figure 12, the RMSEs for the IGS, GBM, and CNES solutions are generally less than 15 mm at most stations. However, for the PPP-B2b solution, the RMSE of the ZTD exhibits significant variation with latitude. Only three stations, namely, ULAB (47.9\({}^{\circ}\) N, 107.1\({}^{\circ}\) E), URUM (43.8\({}^{\circ}\) N, 87.6\({}^{\circ}\) E), and CHAN (43.8\({}^{\circ}\) N, 125.4\({}^{\circ}\) E), had RMSEs smaller than 20 mm. The largest value was observed at station SEYG (4.7\({}^{\circ}\) S, 55.5\({}^{\circ}\) E), with a value of 31.6 mm.  
Regarding the RMSE of the PWV shown in Table 9, the GBM solutions have the best agreement with the radiosonde-derived PWV, with an RMSE of 2.1 mm, followed by the IGS and CNES solutions, with RMSEs of 2.3 mm and 2.4 mm, respectively. The worst agreement was found between the PPP-B2b solution and the radiosonde results, with an RMSE of 3.7 mm. As shown in Figure 13, for the IGS, GBM, and CNES solutions, the RMSE is smaller than 3 mm at most stations, while the RMSE for the PPP-B2b solution shows an obvious latitude-dependent pattern and is smaller than 3 mm only at stations ULAB, URUM, and CHAN. Like the ZTD comparison results, the GNSS-derived PWVs agree better with the radiosonde-derived PWV than with the ERA5-derived PWV. The biases of the GNSS-derived PWV are mostly within \(\pm\)2 mm for the four solutions.  
Figure 12: RMSE (**a**–**d**) and bias (**e**–**h**) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b using the ZTD from radiosonde as a reference.  
Figure 13: This RMSE (**a–d**) and bias (**e–h**) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from radiosonde as a reference.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Solutions**} & **Latitude** & \multicolumn{2}{c}{**ZTD**} & \multicolumn{2}{c}{**PWV**} \\ \cline{3-6}  & **Range** & **RMS** & **Bias** & **RMS** & **Bias** \\ \hline \multirow{4}{*}{IGS} & 30–48\({}^{\circ}\) N & 12.7 & 2.3 & 2.1 & \(-\)0.1 \\  & 0–30\({}^{\circ}\) N & 15.3 & \(-\)1.4 & 2.5 & \(-\)0.5 \\  & 0–38\({}^{\circ}\) S & 11.6 & \(-\)0.9 & 2.2 & \(-\)0.8 \\  & Mean & 13.1 & 0.2 & 2.3 & \(-\)0.4 \\ \hline \multirow{4}{*}{GBM} & 30–48\({}^{\circ}\) N & 10.2 & \(-\)1.7 & 1.9 & \(-\)0.8 \\  & 0–30\({}^{\circ}\) N & 12.2 & \(-\)3.4 & 2.2 & \(-\)1.0 \\  & 0–38\({}^{\circ}\) S & 13.1 & \(-\)5.2 & 2.4 & \(-\)1.4 \\  & Mean & 11.7 & \(-\)3.2 & 2.1 & \(-\)1.0 \\ \hline \multirow{4}{*}{CNES} & 30–48\({}^{\circ}\) N & 13.5 & \(-\)1.9 & 2.4 & \(-\)0.9 \\  & 0–30\({}^{\circ}\) N & 12.9 & \(-\)3.9 & 2.4 & \(-\)1.1 \\  & 0–38\({}^{\circ}\) S & 13.9 & \(-\)6.4 & 2.6 & \(-\)1.7 \\  & Mean & 13.4 & \(-\)3.8 & 2.4 & \(-\)1.2 \\Figure 14 shows the variations in the radiosonde-derived PWV (red dots) and the monthly RMSEs of the GNSS-derived PWV. The results also show that the RMSE of the GNSS-derived PWV usually increases with the PWV values when the PWV has a large seasonal variation, which is very evident at stations CHAN, BJFS, and LHAZ.