# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
## 3 Data Collection
### Radiosonde Data  
Radiosonde observations are obtained from the IGRA and GSL observations ([[https://ruc.noaa.gov/raobs/](https://ruc.noaa.gov/raobs/)]([https://ruc.noaa.gov/raobs/](https://ruc.noaa.gov/raobs/)), accessed on 15 December 2022), which provide the vertical profiles of pressure, temperature, dew point, and wind parameters, among other meteorological variables [38]. Radiosonde can monitor and help understand the composition of lower atmosphere and track changes in water vapor fields for many decades. This observation technique is one of the most reliable techniques, which can study meteorological information of atmospheric vertical profiles [39]. However, it costs more than GNSS and other current techniques. Radiosonde data launched from dedicated stations using radiosonde balloons have low temporal resolutions, typically twice a day (0:00, 12:00 Coordinated Universal Time), and poor horizontal resolution, such as several hundreds of kilometers [40]. The radiosonde stations not far from the GNSS stations are marked by the red circle in Figure 1. The horizontal distance between the selected radiosonde stations and the GNSS stations is less than 25 km, and the altitude distance between them is less than 100 m to ensure that the deviation of ZTD between two different data sources is not large. Although there are many radiosonde stations, only a few that meet the criteria are selected. This paper unifies the ZTD at radiosonde station altitude to GNSS station using the GZTD2 model [41]. Table 2 displays the information of the nine radiosonde stations used, including the differences in height and distances between GNSS and radiosonde locations.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Strategies** \\ \hline Estimator & Sequential least squares estimator \\ Observations & Raw carrier phase and pseudo-range observations; \\ GPS + BDS + Galileo + GLONASS, about 126 satellites \\ Signal selection & GPS: L1/L2; GLONASS: L1/L2; Galileo: E1/E5a; BDS: B1/B2 \\ Sampling rate & 30s \\ Elevation cut-off & 7\({}^{\circ}\) \\ Weight for observations & Elevation-dependent weighting strategy \\ Receiver clock & Estimated, white noise \\ Satellite clock & Fixed \\ Satellite orbit & Fixed \\ ISB and IFB & Estimated as constant, GPS as reference \\ Phase wind-up effect & Corrected \\ Mapping function & GMF \\ Zenith Tropospheric delay & Initial modal + random walk model \\ Station displacement & Solid Earth tide, pole tide, ocean tide loading \\ Satellite antenna phase center & Corrected \\ Receiver antenna phase center & Corrected \\ Station coordinate & Fixed to coordinates of weekly solution \\ \hline \hline \end{tabular}
\end{table}
Table 1: Multi-GNSS Data Processing Strategy for estimating ZTD.  
The ZTD is obtained from radiosonde data by the integration method on different pressure layers. Due to the lesser ZWD above the top layer of the troposphere, the ZTD is equivalent to ZHD obtained by the [PERSON] model [34]. The integration method is given as follows,  
\[ZTD=ZTD_{level}+ZHD_{top} \tag{10}\]  
\[ZTD_{level}=1\times 10^{-6}\int_{h_{Level}}^{h_{T}}Ndh \tag{11}\]  
\[N=k_{1}\times\frac{P-e}{T}+k_{2}\times\frac{e}{T}+k_{3}\times\frac{e}{T^{2}} \tag{12}\]  
\[e=\frac{q\times P}{0.622} \tag{13}\]  
\[ZHD_{top}=\frac{2.2767\times 10^{-3}\times P_{T}}{1-2.667\times 10^{-3}\times \cos(2\varphi)-2.8\times 10^{-7}\times h_{T}} \tag{14}\]  
where \(ZTD_{level}\) represents ZTD below the top pressure level; \(P_{T}\) and \(h_{T}\) is the top pressure and height; \(N\) is the refractivity; \(P\) is the pressure; \(e\) is the vapor pressure; \(q\) is the specific humidity; \(T\) is the temperature; \(k_{1}\) = 77.604 K/hPa, \(k_{2}\) = 64.79 K/hPa, \(k_{3}\)=377,600.0 K/Pa; \(\varphi\) is the latitude.