## 2 Materials and Methods  
The tropospheric wet delay is caused by the amount of water vapor in the troposphere. The zenith wet delay is at a level of several mm at the poles and at a value range of about 40 cm or more in the equatorial region. It is an important source of error in order to achieve a millimeter accuracy in GNSS positioning applications. Water vapor in the atmosphere has a structure that changes very rapidly in spatial and temporal terms. Therefore, it is quite difficult to establish a correlation between the temperature and amounts of water vapor on the Earth's surface and the water vapor along the troposphere layer. Although many empirical and analytical models have been developed in order to estimate the wet delay, they have not been able to achieve a sufficient accuracy. For this reason, wet delay is considered as unknown in the evaluation of GNSS measurements and estimated by the least squares method. Furthermore, an accurate estimation of the amount of water vapor in the troposphere as a function of wet delay is important to making accurate meteorological estimates. ZWD values obtained from the troposphere models can be used as a preliminary value in GNSS evaluations. The Saastamoinen wet delay model is based on the fact that the temperature shows a linear decrease, depending on the height. Accordingly, the calculation of the zenith wet delay based on ideal gas laws using a basic equation is given by the following equation:  
\[\text{ZWD}=0.0022768(1255+0.05T)\frac{e}{T}. \tag{1}\]  
If no surface meteorological observations are available, the water vapor pressure \(e\) can be determined as a function of relative humidity \(f\) and based on standard atmospheric rules with the following model:  
\[e=\frac{f}{100}\text{exp}(-37.2465+0.213166T-0.000256908T^{2}). \tag{2}\]  
In this study, observations from 40 stations of the EPOSA GNSS Network (Echtzeit Positionierung Austria) were processed using Bernese 5.0 software [32], in order to estimate zenith total delays. Zenith total delay values were estimated by the Precise Point Positioning (PPP) method at 1 h intervals. Then, the ZWD values were calculated by Equation (3). \[\text{ZTD}=\text{ZHD}+\text{ZWD} \tag{3}\]  
In total, 90% of the total tropospheric delay is due to the dry (hydrostatic) component. The troposphere delay caused by the hydrostatic component is 2.3 m on average. The calculation of the hydrostatic delay can be calculated precisely by using pressure measurements at the station location based on troposphere delay models. Afterwards, the calculated value is assumed to be the default value for ZWD estimation by GNSS measurements, and the ZWD is estimated by the least square adjustment method. In this estimation, the accuracy of the ZHD value calculated as the preliminary value is important for the accuracy of the estimation of the ZWD. The accuracy of the ZHD value is directly related to the accuracy of pressure measurements. A 1 hPa error in pressure measurementsresults in a 2.3 mm error in the zenith hydrostatic delay [4; 7]. The hydrostatic troposphere delay is calculated along the signal path and expressed as below:  
\[SHD=10^{-6}\int\limits_{5}\left(k_{1}\frac{R}{m_{d}}\rho\right)ds. \tag{4}\]  
By using the mapping functions, zenith hydrostatic delay in meters can be calculated as below:  
\[ZHD=0.0022768\frac{P_{0}}{f(\theta,h_{0})}, \tag{5}\]  
where \(\theta\) and \(h_{0}\) are the latitude and orthometric (or ellipsoidal) height of the station, and \(P_{0}\) is the pressure at the height of the receiving GNSS antenna. In addition, the International GNSS Service (IGS) precise orbit products were used to process GNSS data. The satellite elevation angle was set to \(5^{0}\) and the Global Mapping Function (GMF) was used to calculate the ZTD values. By using this empirical model, hydrostatic zenith delay can be calculated with a 1 mm accuracy [1].