## 2 Data and Methodologies
### ZTD and PWV Estimation with PPP
The signal-in-space ranging error (SISRE) is a key performance indicator for comparisons of different navigation systems [79]. The instantaneous SISRE, considering that the clock and orbit can be calculated using Equation (11), and the orbit-only SISRE can be calculated using Equation (12):  
\[SISRE_{clk+orb}=\sqrt{(w_{R}\cdot\Delta r_{R}-\Delta\mathcal{C})^{2}+w_{A,C}^{ 2}\cdot\left(\Delta{r_{A}}^{2}+\Delta{r_{C}}^{2}\right)} \tag{11}\]  
\[SISRE_{orb}=\sqrt{\left(w_{R}\cdot\Delta r_{R}\right)^{2}+w_{A,C}^{2}\cdot \left(\Delta{r_{A}}^{2}+\Delta{r_{C}}^{2}\right)} \tag{12}\]  
where \(w_{R}\) and \(w_{A,C}^{2}\) are GNSS-dependent SISRE weight factors for the statistical contribution of radial (R), along-track (A), and cross-track (C) errors to the line-of-sight ranging error; \(\Delta r_{R}\), \(\Delta r_{A}\), and \(\Delta r_{c}\) are the residuals of the satellite orbit in the R, A, and C directions, respectively; and \(\Delta\mathcal{C}\) is the clock error. The weight factors \(w_{R}\) and \(w_{A,C}^{2}\) used for different satellite constellations were suggested by [PERSON], [PERSON], and [PERSON] [79]. With the instantaneous SISREs at different epochs for a specific satellite during the period from DOY 069 to 311 in 2022, the RMSE values of \(SISRE_{clk+orb}\) and \(SISRE_{orb}\) for each satellite type were calculated and are presented in Table 4. The RMSE of \(SISRE_{clk+orb}\) varies from 0.60 m to 3.05 m, with a mean value of 1.12 m for GPS, and from 0.36 m to 1.25 m, with a mean value of 0.72 m for BDS-3. It should be noted that GPS satellites with large \(SISRE_{clk+orb}\) values mostly belong to the block IIR series. To further investigate the contributions of the orbit and clock errors to \(SISRE_{clk+orb}\), the orbit-only SISRE, that is, \(SISRE_{orb}\), was calculated. The mean RMSE values of \(SISRE_{orb}\) are 0.11 m and 0.13 m for GPS and BDS-3, respectively. These values were much smaller than those of \(SISRE_{clk+orb}\), indicating that clock systematic errors have a much larger contribution to \(SISRE_{clk+orb}\) than satellite orbit errors. Therefore, \(SISRE_{clk+orb}\) is confirmed to be dominated mainly by clock errors. For tropospheric parameter estimation, we were more concerned about the accuracy of the ZTD estimation than about the convergence time. Therefore, the STD of \(SISRE_{clk+orb}\) was investigated in this study. As shown in Table 4, the STD of \(SISRE_{clk+orb}\) for BDS-3 (0.03 m) was smaller than that for GPS (0.06 m), which may have benefited from \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\mathbf{DCB_{DLR}\text{-DCB}_{PPP-B2b}}\)} & \multicolumn{2}{c}{\(\mathbf{DCB_{CAS}\text{-DCB}_{PPP-B2b}}\)} & \multicolumn{2}{c}{\(\mathbf{DCB_{DLR}\text{-DCB}_{CAS}}\)} \\ \hline Frequency & B1I & B1C(P) & B2a(P) & B1I & B1C(P) & B2a(P) & B1I & B1C(P) & B2a(P) \\ STD & 0.36 & 0.37 & 0.22 & 0.35 & 0.37 & 0.27 & 0.15 & 0.14 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: STD values of the differences between different DCB products (unit: ns). the use of intersatellite laser measurements for the generation of the BDS-3 satellites in the PPP-B2b product. Figure 3a,b present the variations in the daily \(SISRE_{clk+orb}\) [STD] for GPS and BDS-3, respectively, which show obvious fluctuations during the period of DOY 193-216. For GPS, 54.5% and 90.7% of the days have \(SISRE_{clk+orb}\) [STD] values smaller than 0.05 m and 0.1 m, respectively. BDS-3 has a much better performance than GPS, with approximately 93.8% of the days having \(SISRE_{clk+orb}\) [STD] values less than 0.05 m.