## 3 Materials and Methods
### ZTD Model
#### 3.1.1 Combined Model  
The classic ZTD model requires in-site meteorological data, which is usually calculated by the meteorological model. The most popular classic ZTD model is the Saastanoienen model.  
In the Saastanoienen model, the troposphere is divided into two layers. The first layer is from the earth surface to 10 km height of the troposphere, where the temperature descent rate is 6.5 \({}^{\circ}\)C/km. The second layer is from the troposphere top at 10 km to the stratospheric top at 70 km, where the temperature is assumed to be constant. Via atmospheric refraction integral, the function is simplified as [8]  
\[\left\{\begin{array}{c}ZTD=0.002277\times\frac{[P+(0.05+\frac{1258}{72.215}) ]}{f(\varphi,H)}\\ f(\varphi,H)=1-2.66\times 10^{-3}cos(2\varphi)-2.8\times 10^{-7}H\end{array}\right. \tag{7}\]  
where \(P\), \(T\), and \(e\) are the pressure, temperature, and water vapor pressure at the station, \(f(\varphi,H)\) is the correction of gravitational acceleration caused by the rotation of the Earth, with \(\varphi\) and \(H\) denoting the latitude and the ortho height of the station, respectively.  
In-site meteorological elements used in Equation (7) can be estimated via a set of meteorological models, such as the norm, GPT/GPT2/GPT2w/GPT3 models.  
The standard meteorological element method (norm) is based on a set of standard meteorological parameters on sea level (usually specified as \(T_{0}=288.15\) K, \(P_{0}=1013.25\) mbar, \(e_{0}=11.691\) mbar), and adjusted to the station via a height correction.  
The Global Pressure and Temperature (GPT) model [30], which is based on spherical harmonics up to degree and order nine, provides pressure (\(P\)) and temperature (\(T\)) at any site on the Earth's surface. It is based on the atmospheric pressure and temperature products (resolution \(15^{\circ}\times 15^{\circ}\)) in the meteorological reanalysis data ECMWF Re-Analysis-40 (ERA-40) for 3 years from 1999 to 2002, and conforms to changes in air pressure and temperature on the global sea level.  
To precisely describe the spatial and temporal variability, GPT2 model [31] based on 10-year meteorological reanalysis data ERA-Interim were established. The model provides pressure (\(P\)), temperature (\(T\)), lapse rate (\(dT\)), water vapor pressure (\(e\)), and mapping function coefficients at any site, resting upon a global \(5^{\circ}\) grid of mean values, annual, and semi-annual variations in all parameters.  
Global Pressure and Temperature 2 wet (GPT2w) [32] is the successor of the former models GPT and GPT2, improving the capability to determine ZWDs empirically. It requires only information about time and location and provides mean values plus annual and semi-annual amplitudes of a set of quantities such as mapping function coefficients, pressure (\(P\)), temperature (\(T\)), water vapor pressure (\(e\)), mean temperature weighted with water vapor pressure (\(Tm\)), and water vapor decrease factor (\(\lambda\)), optionally on a \(5^{\circ}\times 5^{\circ}\) or a \(1^{\circ}\times 1^{\circ}\) grid. The coefficients were derived from monthly mean pressure-level data of ERA-Interim fields by the ECMWF. [PERSON] and [PERSON] [11] proposed a new GPT3 model, which provides the same meteorological elements as those in GPT2w. The several meteorological quantities from GPT2w are left unchanged for GPT3. In addition, the ray-traced delays are also utilized for determining an empirical gradient grid which outperforms currently existing models. Finally, primary information of the above five meteorological models are summarized in Table 1 for a detailed comparison.