## 4 PPP-B2b ZTD Estimation and Evaluation of the Results
### Comparison of the GNSS-Derived ZTD/PWV with TWT Derived from ERA5
\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{2-5}  & **Range** & **RMSE** & **Bias** & **RMSE** & **Bias** \\ \hline \multirow{4}{*}{IGS} & \(30\)–\(48^{\circ}\) N & \(18.3\) & \(-3.0\) & \(2.9\) & \(-0.5\) \\  & \(0\)–\(30^{\circ}\) N & \(22.4\) & \(0.8\) & \(3.6\) & \(0.1\) \\  & \(0\)–\(38^{\circ}\) S & \(16.4\) & \(-0.6\) & \(2.7\) & \(-0.1\) \\  & Mean & \(19.0\) & \(-0.9\) & \(3.1\) & \(-0.1\) \\ \hline \multirow{4}{*}{GBM} & \(30\)–\(48^{\circ}\) N & \(15.7\) & \(-3.5\) & \(2.5\) & \(-0.6\) \\  & \(0\)–\(30^{\circ}\) N & \(21.2\) & \(-0.9\) & \(3.4\) & \(-0.3\) \\  & \(0\)–\(38^{\circ}\) S & \(16.8\) & \(-1.0\) & \(2.7\) & \(-0.3\) \\  & Mean & \(18.4\) & \(-1.7\) & \(3.0\) & \(-0.4\) \\ \hline \multirow{4}{*}{CNES} & \(30\)–\(48^{\circ}\) N & \(17.8\) & \(-4.1\) & \(2.8\) & \(-0.7\) \\  & \(0\)–\(30^{\circ}\) N & \(22.3\) & \(-1.4\) & \(3.6\) & \(-0.4\) \\ \cline{1-1}  & \(0\)–\(38^{\circ}\) S & \(17.3\) & \(-0.7\) & \(2.8\) & \(-0.2\) \\ \cline{1-1}  & Mean & \(19.6\) & \(-2.0\) & \(3.2\) & \(-0.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison between ZTD/PWV derived from GNSS and ERA5 (unit: mm). Figure 9 illustrates the spatial variation in the RMSEs and biases in the GNSS-derived PWV using the ERA5-derived PWV as a reference. As shown in Table 8, the mean RMSE values for the IGS-, GBM-, and CNES-derived PWVs are 3.1 mm, 3.0 mm, and 3.2 mm, respectively. Similar to the spatial variation in the RMSEs of ZTD, the RMSEs of PWV also exhibit a latitude-dependent pattern, with higher values observed between 0\({}^{\circ}\) and 30\({}^{\circ}\) N than within the latitudinal bands from 30\({}^{\circ}\) N to 48\({}^{\circ}\) N and 0\({}^{\circ}\) to 38\({}^{\circ}\) S. The PPP-B2b solutions demonstrate the poorest agreement with the ERA5-derived PWV, with a mean RMSE of 4.4 mm. Generally, the PPP-B2b solution within the latitudinal band from 30\({}^{\circ}\) N to 48\({}^{\circ}\) N has a smaller RMSE (3.2 mm) than that of the stations within the latitudinal bands from 0\({}^{\circ}\) N to 30\({}^{\circ}\) N (5.0 mm) and from 0\({}^{\circ}\) to 38\({}^{\circ}\) S (4.8 mm). The biases of the GNSS-derived  
Figure 8: RMSE (**a**–**d**) and bias (**e**–**h**) of the ZTD derived with IGS, GBM, CNES, and PPP-B2b, using the ZTD calculated from ERA5 as a reference. PWVs compared to the ERA5-derived PWVs at these 32 stations are mostly within \(\pm 1\) mm for the IGS, GBM, and CNES solutions and \(\pm 2\) mm for the PPP-B2b solution. To further investigate the temporal characteristics of the differences between the GNSS-derived PWV and the ERA-derived PWV, the monthly RMSE of the GNSS-derived PWV was calculated. The results in Figure 10 show that the differences between the GNSS-derived PWV and the ERA-derived PWV strongly depend on the duration at which the PWV has a large seasonal variation. Taking station CHAN as an example (Figure 10c), the RMSE of the IGS-derived PWV increases from 2.44 mm to 5.58 mm when the PWV varies from approximately 1 mm (March 2022) to 60 mm (July 2022). For the COCO station (Figure 10k) located in the equatorial region where the PWV is approximately 40-60 mm throughout the year, the RMSE value remains at approximately 2 mm during the study period and shows no obvious seasonal variation. In addition to seasonal variations, previous studies have shown that there are strong diurnal variations in PWV time series. In this study, the hourly diurnal anomaly in PWV was calculated by subtracting the daily mean PWV from the corresponding observed hourly PWV. Figure 11 shows the mean diurnal PWV anomaly in March 2022 at six stations, which reveals that the amplitude of the diurnal PWV variation at these stations is approximately 1-2 mm. Figure 9: RMSE (**a–d**) and bias (**e-h**) of the PWV derived with IGS, GBM, CNES, and PPP-B2b using the PWV from ERA5 as a reference.