# A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China
## 2 Data and Processing Strategy
### Reanalysis Data and ZTD Estimation Method  
ERA-Interim is the reanalysis product from the European Centre for Medium-Range Weather Forecasts (ECMWF). It provides 6-hourly data with the horizontal resolution of 0.75\({}^{\circ}\)\(\times\) 0.75\({}^{\circ}\), and 37 vertical pressure levels from 1000 hPa up to 0.1 hPa. Fields including geopotential, temperature and specific humidity on each level were used.  
Similar to the method used in [19; 25], the final ZTD at a given location is the sum of two sections, namely the ZTD section from the location to the top level (estimated by integration method) (\(ZTD_{level}\)) and the hydrostatic section above the top level (there is almost no water vapor above this level) of reanalysis data (estimated by Saastamoinen model) (\(ZHD_{top}\)). The value of \(ZHD_{top}\) depends on the pressure on the top level of reanalysis product. For reanalysis products like NCEP/NCAR, the top level is 1 hPa, which corresponds to about 2 mm of \(ZHD_{top}\) according to Saastamoinen model, while for ERA-Interim used in this work, the top level pressure is only 0.1 hPa, corresponding to about 0.2 mm of \(ZHD_{top}\), which is far below the GPS ZTD estimation errors. Although ignoring \(ZHD_{top}\) will not introduce significant biases to ERA-Interim-based ZTD when comparing with GPS, in order to estimate ZTD as accurate as possible, we still write the final ZTD as:  
\[ZTD=ZHD_{top}+ZTD_{level} \tag{1}\]  
\[ZHD_{top}=0.0022768\cdot\frac{P_{top}}{1-0.00266\cdot\cos(2\varphi)-0.00028 \cdot h_{top}} \tag{2}\]  
\[ZTD_{level}=10^{-6}\int_{h_{given}}^{h_{top}}Ndh=10^{-6}{\sum_{i}N_{i}\Delta s _{i}} \tag{3}\]  
where \(P_{top}\) is the atmospheric pressure at the top level in hPa, \(\varphi\) is the latitude, \(h_{top}\) is the altitude of the top level in meters, \(h_{given}\) is the given location altitude, and \(N\) is the refraction which can be calculated by:  
\[N=\frac{k_{1}(P-e)}{T}+(\frac{k_{2}e}{T}+\frac{k_{3}e}{T^{2}}) \tag{4}\]  
\[e=qP/0.622 \tag{5}\]  
where \(k_{1}\) = 77.604 K/hPa, \(k_{2}\) = 64.79 K/hPa, \(k_{3}\) = 377,600.0 K\({}^{2}\)/hPa [26]. The \(P\) and \(e\) denote the atmospheric pressure and water vapor partial pressure in hPa, respectively. \(T\) denotes the air temperature in K, and \(q\) is the specific humidity in kg/kg.  
For GPS antenna level above the lowermost level of the reanalysis product, the temperature at the antenna level was estimated by linear interpolation, while for GPS antenna level below the lowermost level, the temperature at the antenna level was estimated by linear extrapolation, assuming a constant temperature lapse rate of \(-6.5\) K/km\({}^{-1}\), and constant relative humidity of the value at the lowermost level. The hydrostatic and ideal gas equations were used to adjust pressure from reanalysis to the GPS antenna level as described in [27].  
In order to evaluate the accuracy of ZTD derived from ERA-Interim, IGS final ZTD products at six IGS stations located in China were taken as references for comparisons for one year (2014). The mean bias as shown in Table 1 is 0.36 cm and the RMS is 1.40 cm, which is basically consistent with the results in [28].