# A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China
## 2 Data and Processing Strategy
### GPS Data and the Processing Strategy  
The observation equations of the ionospheric-free code and phase combinations in GPS data processing can be expressed as:  
\[\left\{ \begin{array}{l}P_{r}^{s}(t)=|\overset{\rightarrow}{X}(t)-\overset{ \rightarrow}{X}(t)|+\Delta t_{r}(t)-\Delta t^{s}(t)+\Delta trop_{r}^{s}(t)+ \varepsilon_{r}^{s}(t)\\ L_{r}^{s}(t)=|\overset{\rightarrow}{X}_{r}(f)-\overset{\rightarrow}{X}(f)|+ \Delta t_{r}(t)-\Delta t^{s}(t)+\Delta trop_{r}^{s}(t)+\lambda\cdot N_{r}^{s}+ \varepsilon_{r}^{s}(t)\end{array} \right. \tag{6}\]  
where \(P_{r}^{s}(t)\) and \(L_{r}^{s}(t)\) denote the code and carrier phase observations between satellite \(s\) and receiver \(r\) at time \(t\). \(\overset{\rightarrow}{X}_{r}\) represents the receiver position vector with Phase Center Correction (PCO), Phase Center Variation (PCV) and tide loading effects considered, while \(\overset{\rightarrow}{X}^{s}\) represents satellite position vector with PCO and PCV corrected. \(\Delta t_{r}\) and \(\Delta t^{s}\) denote receiver and satellite clock errors, respectively. \(\varepsilon\) and \(e\) are the residual noises and un-modeled errors. \(\Delta trop\) is the total tropospheric delay along the signal path which can be written as:  
\[\Delta trop=mf_{h}\cdot ZHD+mf_{nh}\cdot ZWD+mf_{\text{G}}\cdot(G_{ns}\cdot \cos(a)+G_{ew}\cdot\sin(a)) \tag{7}\]  
where \(mf_{h}\) and \(mf_{nh}\) denote the hydrostatic and non-hydrostatic mapping functions and \(mf_{\text{G}}\) represents the gradient mapping function. \(G_{ns}\) and \(G_{ew}\) represent the two horizontal gradients in north-south and east-west component, respectively, and \(a\) is the azimuth of the line of sight. The Crustal Movement Observation Network of China (CMONOC) is the national scientific infrastructure aiming to monitor the current intra-plate deformation in China, using space geodetic techniques such VLBI, SLR and GPS [29]. Currently, it comprises about 260 continuous GPS stations with the average station separation of about 200 kilometers. GPS data from CMONOC covering the period of four months (Jan., Apr., Jul. and Oct.) in four seasons in 2015 with time interval of 30 s were processed using Position And Navigation Data Analyst (PANDA) [30; 31; 32; 33] in simulated real-time PPP mode. Simulated real-time mode means that the data are processed only in forward direction but read from Receiver Independent Exchange Format (RINEX) files instead of the real-time stream, and all time delays existing in real-time situations are neglected. The archived real time GPS orbit and clock products from IGS ([[ftp://cddis.gsfc.nasa.gov/gnss/products/rtpp/](ftp://cddis.gsfc.nasa.gov/gnss/products/rtpp/)]([ftp://cddis.gsfc.nasa.gov/gnss/products/rtpp/](ftp://cddis.gsfc.nasa.gov/gnss/products/rtpp/))) (i.e., IGS01) were used [34]. ZHD and ZWD were first calculated by _a priori_ [PERSON] model and the corrections to ZWD, which can also assimilate ZHD residual errors, were estimated as random walk parameters. The final ZTD were acquired by summing over ZWD corrections and _a priori_ ZHD and ZWD. The global pressure and temperature 2 wet (GPT2w) model [13] was used in the processing. Tropospheric gradients in the north-south and east-west directions were estimated at 12 h intervals. The details of the processing strategy are summarized in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Station Name** & **Bias** & **RMS** \\ \hline BJFS & 0.29 & 1.25 \\ CHAN & \(-\)0.19 & 1.09 \\ LHAZ & 0.76 & 1.43 \\ SHAO & \(-\)0.53 & 0.94 \\ URUM & 1.94 & 2.30 \\ WUHN & \(-\)0.14 & 1.38 \\ \hline Mean & 0.36 & 1.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The bias and RMS of differences between IGS final ZTD products and ZTD derived from reanalysis for year 2014 (unit: cm).