# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
## 4 Results and Analysis
### Validation by Radiosonde and ERA5  
Radiosondes are used to validate the ZTD results obtained from the multi-GNSS solutions. The ZTD is set to estimate once every 1 h while radiosonde-retrieved ZTD is 12 h. Consequently, we consider the ZTD from the same epochs when comparing. Figure 10 illustrates a comparison of the ZTD results at stations POAL and HOB2 from the four-system solution solutions and nearby radiosonde solutions during DOY 80\(-\)180, 2019. The four-system combined ZTD is in considerable agreement with the ZTD from the radiosondes, with a disparity of a few millimeters, which implies the ZTD value can effectively be estimated by multiple systems at the bottom of the atmosphere. At nine GNSS stations, where radiosonde at a distance of 25 km or less can be found, RMSs of ZTD differences for single- and multi-system solutions in relation to the radiosonde solutions are shown in Figure 11. For some stations, such as POAL and CUTO, the RMS was reduced much from single-system to two-system solutions, but the improvement in accuracy is not very significant from two-system to four-system solutions, with an increase of 0.3-1.8 mm. Probable reasons are the good geographical location of some stations themselves, and in all ZTD values over a year, the abnormal ZTD values of different seasons will be diluted by other time periods. Therefore, increased multi-system observation can effectively solve this problem. We can see that there are very few inconsistencies between the four-system solution and radiosondes. The RMS value decreases noticeably as the number of multi-system observation data increases. The average RMS of the ZTD differences for the GPS-only solution is 8.7 mm; for the two-system solutions, 8.3 mm; for the three-system solution, 7.8 mm; and for the four-system solution, 7.6 mm. Compared to the BDS-only solution, an improvement of 13-20% in accuracy can be achieved with the two-system, three-system,  
Figure 9: RMS and mean absolute bias for the ZTD differences of single- and multi-system solutions with respect to IGS final products (**top panel**: RMS; **bottom panel**: absolute bias). and four-system solutions. The average RMSs of ZTD differences from multi-GNSS solutions are summarized in Table 3. This demonstrates the potential benefits of multi-system estimated ZTD in climatic research. In this analysis, the ZTDs generated by the ERA5 data are also used to validate those obtained from multi-GNSS processing. The time series of ZTD from multi-system solutions and ERA5 date at stations RGDG and STJ3 during DOY 120-160, 2019 are shown in Figure 12. Even if in some time periods, such as DOY 154-157 at station STJ3 and DOY 144-145 at station DGRG, where frequent changes in tropospheric water vapor cause significant fluctuations in ZTD time series, both multi-GNSS and ECMWF can correctly track these changes. RMSs of the ZTD differences with respect to the ERA5 data for single-system (G), two-system (GR), three-system (GER), and four-system (G  
Figure 11: RMSs of ZTD differences for single- and multi-system solutions with respect to the radiosonde solutions. Figure 10: ZTD derived from the four-system solution and radiosonde solution during DOY 80\(-\)180, 2019 (**top panel**: FOAL; **bottom panel**: HOB2). calculated because the ZTDs of these solutions are more accurate and reliable in single-system, two-system, and three-system solutions; this is detailed in Section 4.3. Figure 13 shows that RMSs of ZTD differences are clearly decreasing from single-system to multi-system solutions and the average RMS values of stations are 10.6, 9.2, 8.7, and 7.8 mm, respectively. In general, high-latitude stations show better agreement in ZTD estimates than low-latitude ones in terms of geographical patterns. The average RMS value of stations for four-system above 30 latitudes is 6.8 mm while the average RMS in low-latitude (0-30 \({}^{\circ}\)) is 9.0 mm.