# GNSS Real-Time ZTD/PWV Retrieval Based on PPP with Broadcast Ephemerides
## 2 Data and Methods
### GNSS ZTD/PWV Retrieval Based on BE-PPP  
1. ZTD estimation: Based on the carrier and pseudorange raw observation equations, the ionosphere-free combined BE-PPP raw equation can be obtained in the following form [29]: \[\left\{ \begin{array}{l}p_{IF}=\rho+c\cdot dt+\phi\cdot T+ISB+sise+\varepsilon\\ \varphi_{IF}=\rho+c\cdot dt+\phi\cdot T+ISB+N+sise+\xi\end{array} \right.\] (1) where \(p_{IF}\) and \(\varphi_{IF}\) are the ionosphere-free pseudorange and carrier phase combinations; \(\rho\) is the geometric range including corrections, such as the relativistic effect in Table 1; \(c\) is the speed of light; \(dt\) is the receiver clock; \(\phi\) is the tropospheric mapping function; \(T\) is the tropospheric delay; \(ISB\) is the inter-system bias; \(N\) is the ionosphere-free ambiguity; \(sise\) is the SISE of the broadcast ephemerides; and \(\varepsilon\) and \(\xi\) are the pseudorange and carrier-phase noise, respectively. The formula for the ZTD is as follows:  
\[\text{ZTD}=mf_{w}\cdot\text{ZWD}+mf_{h}\cdot\text{ZHD} \tag{2}\]  
Figure 2: The flowchart of ZTD/PWV data retrieval based on BE-PPP. where ZWD and ZHD are the zenith wet delay (ZWD) estimated with Kalman and the zenith hydrostatic delay (ZHD), and \(mf_{w}\) and \(mf_{h}\) are their mapping functions. ZHD is calculated using the Saastamoinen model:  
\[\text{ZHD}=0.0022768\frac{P_{s}}{1-0.00266\cos(2\varphi)-0.28\cdot 10^{-6}\cdot h _{0}} \tag{3}\]  
where \(P_{s}\) is the atmospheric pressure at the measurement station obtained using the standard meteorological element method or the empirical global pressure and temperature (GPT) model; \(\varphi\) is the latitude of the measurement station; and \(h_{0}\) is the elevation of the measurement station. \(P_{s}\) is not the actual measured atmospheric pressure, so the obtained ZHD value is not accurate. Although using an inaccurate prior ZHD value cannot directly lead to obtaining an accurate ZWD value, it can obtain a relatively accurate ZTD value. 1. PWV retrieval: After obtaining an accurate ZTD value, the wet delay is calculated as below: \[\text{ZWD}=\text{ZTD}-\text{ZHD}\] (4) where the ZHD is calculated using Equation (3), and the pressure is taken from ERA5. Then, the ZWD is converted into the PWV (unit: m) [36]: \[\text{PWV}=\kappa\times\text{ZWD}\] (5) where \(\kappa\) is the conversion factor, which can be expressed as \[\kappa=\frac{10^{6}}{\rho_{lw}R_{w}\left(k^{\prime}{}_{2}+\frac{k_{2}}{T_{m}}\right)}\] (6) where \(\rho_{lw}\) is the density of liquid water and takes the value 1000 kg/m\({}^{3}\); \(R_{w}\) is the specific gas constant for water vapor, which takes the value of 461.495 J/(kg\cdot\text{K})\); \(k^{\prime}{}_{2}\) and \(k_{3}\) are the atmospheric refractivity constants, taking the values of 0.1625 K/hPa and \(0.03776\times 10^{5}\) K\({}^{2}\)/hPa, respectively; and \(T_{m}\) is the atmospheric weighted mean temperature (K). In this study, we used the Bevis formula improved by [PERSON] et al. [37] based on 10 years of data from 135 global radiosonde stations: \[T_{m}=0.8116\cdot T_{s}+43.69\] (7) where \(T_{s}\) is the observed surface temperature, which can be derived based on ERA5. 2. PWV retrieval based on ERA5: ERA5 is the fifth-generation atmospheric reanalysis dataset of the global climate from January 1940 to the present, produced by the ECMWF. The retrieval in this case utilized the relative humidity, air pressure, and temperature from the ERA5 hourly data on a pressure-level dataset to calculate the PWV. The formula is as follows: \[\text{PWV}=\frac{1}{g}\int\limits_{P_{bottom}}^{P_{top}}qdP\] (8) where \(q\) is the specific humidity (%RH); \(g\) is the gravity acceleration of Earth (m/s\({}^{2}\)); \(P\) is the pressure (hPa) between the bottom and top of a certain atmosphere layer; \(P_{bottom}\) is the atmospheric pressure (hPa) at the elevation of the measurement station; and \(P_{top}\) is the pressure (hPa) at the top of the atmosphere. 3.