# GNSS Real-Time ZTD/PWV Retrieval Based on PPP with Broadcast Ephemerides
## 3 Results and Discussion
### Evaluation of Real-Time ZTD  
Two real-time ZTD products, denoted as BE-ZTD and RT-ZTD, were obtained using the BE-PPP and RT-PPP models, respectively, and the final tropospheric product (IGS-ZTD) from the IGS Analysis Center was used for validation to assess the accuracy of the ZTD. The time series of the BE-ZTD, RT-ZTD, and IGS-ZTD at the DYNG stations on December 21, 2022 (DOY 356), is shown in Figure 3. It can be seen that the BE-ZTD agrees better with the IGS-ZTD than the RT-ZTD does in the DYNG station. Statistically, the mean bias and STD of the RT-ZTD's deviation are \(-5.7\) mm and \(6.3\) mm, respectively, and the mean bias and STD of the BE-ZTD's deviation are \(-2.6\) mm and \(7.1\) mm, respectively. Undoubtedly, the mean bias of the BE-ZTD is less than that of the RT-ZTD, but the difference in the STD between the two models is small, specifically \(0.8\) mm. In addition, we analyzed the bias distribution of the RT-ZTD and BE-ZTD at eight stations in the same period. As can be easily seen in Figure 4, the largest departures of both BE-ZTD and RT-ZTD are no more than \(3\) cm. The mean STDs of the BE-ZTD and RT-ZTD at the eight stations are \(8.6\) mm and \(7.0\) mm, respectively, showing agreement at the millimeter level, which indicates that the BE-PPP and RT-PPP solutions show comparable accuracy in the real-time estimation of the ZTD. The mean values of the ZTD biases from the eight stations are \(-0.1\) mm for the BE-ZTD and \(-0.25\) mm for the RT-ZTD. No obvious systematic biases can be seen between RT-ZTD and BE-ZTD.  
To further validate the above conclusions, we analyzed the results of 80 IGS stations. For real-time ZTD products applied to NWP forecasting, the accuracy requirements of a 0.6 cm target and 3 cm threshold value need to be met [38]. Figure 5 depicts the mean bias and STD of the BE-ZTD and RT-ZTD from 80 IGS stations on 21 December 2022 (DOY 356). The bias of the RT-ZTD is \(-\)1.0-1.2 cm, and the bias of the BE-ZTD is \(-\)5.3-5.4 cm, as shown in subgraph (a). The STD of the ZTD differences is 0.4-1.4 cm for the RT-ZTD and 0.4-2.9 cm for the BE-ZTD, as shown in subgraph (b). It can be seen that the stability of the RT-ZTD is significantly better than that of the BE-ZTD. The performance is consistent among the stations for the RT-ZTD, whereas the BE-ZTD varies greatly among the different stations, with the more stable ones being consistent with the RT-ZTD, but the STDs of the stations all meet the threshold requirement  
To comprehensively compare the differences between the real-time ZTD estimated using RT-PPP and BE-PPP, the mean bias and STD of the 30-day RT-ZTD and BE-ZTD were determined and are plotted in Figure 6. Following the principle of \(1.5\times IQR\) (interquartile range), after excluding the outliers, the data availability was 95.8% for both BE-ZTD and RT-ZTD. Figure 5 shows that the mean bias of the RT-ZTD is \(-0.79\)-\(0.72\) cm, while that of BE-PPP is \(-6.83\) cm to \(4.49\) cm. The STD of the RT-ZTD is \(0.13\)-\(1.12\) cm, and that of BE-PPP is \(0.28\)-\(2.46\) cm. The average bias value is \(-0.04\) cm for the RT-ZTD, and the average STD value is \(0.6\) cm, while the average bias value is \(-1.11\) cm for the BE-ZTD, and the average STD value is \(1.07\) cm. In summary, the ZTD products with real-time estimation of RT-PPP are characterized by their high accuracy and stability; however, the difference in the average STD between the BE-ZTD and RT-ZTD is only \(4.7\) mm, which indicates that it is feasible to use real-time BE-ZTD estimation to compute NWPs when the network link is outage. This is also consistent with the study of [PERSON] et al., which reported a standard deviation of 15.7 mm for the inverted ZTD with real-time PPP based on the Galileo broadcast ephemeris [39].