## 3 Materials and Methods
### ZTD Model
#### 3.1.2 Empirical Model  
[PERSON] et al. [33] proposed the UNB3 model for the Wide Area Augmentation System (WAAS) users. The UNB3 model depends on a look-up table to calculate the five meteorological parameters; namely, pressure (\(P\)), temperature (\(T\)), water vapor pressure (\(e\)), temperature lapse rate (\(\beta\)), and water vapor pressure height factor (\(\lambda\)) on the station. These meteorological parameters are estimated by inputting the receiver's height, latitude, and day of year (DOY), and are interpolated from the yearly averages and seasonal variations of the parameters that are primarily derived from North American meteorological data. These meteorological parameters are then used to compute the hydrostatic and non-hydrostatic zenith delays using a model which is similar as the Saastamoninen models.  
UNB3m [9] is a modified version of the UNB3, with changes on parameter values in the look-up table and the associated UNB3 algorithms. The part of the table that was related to water vapor pressure was replaced with values that computed from the relative humidity. Hydrostatic delay will not be affected by this modification in the model, since it does not depend on the water vapor pressure. By ray-tracing analyses of 703,711 profiles from 223 stations in North America and surrounding territory from 1990 to 1996, it is evaluated that the prediction errors of UNB3m is similar to that of UNB3, and the absolute mean error has been reduced by almost 75%.  
The European Geo-stationary Navigation Overlay System (EGNOS) guidelines recommend that a user applies a correction for tropospheric delay that is compliant with the  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Meteorological** & **Data Sources** & **Representation** & **Temporal Variability** & **Output Parameters** \\
**Models** & **Data Sources** & **Representation** & **Temporal Variability** & **Output Parameters** \\ \hline \multicolumn{5}{c}{a set of standard} \\ norm & meteorological parameters on & / & / & \(P\), \(T\), \(e\) \\  & sea level & & \\  & meteorological reanalysis data & Spherical harmonics up & & \\ GPT & ERA-40 for 3 years from 1999 & to degree and order 9 at & mean and annual terms & \(P\), \(T\), (\(ah\), \(aw\)) \\  & to 2002 & mean sea level & & \\ GPT2 & 10-year meteorological & \(5^{\circ}\times 5^{\circ}\) global grid & mean, annual and & \\  & reanalysis data ERA-Interim & & semi-annual terms & \\  & monthly mean pressure-level & \(5^{\circ}\times 5^{\circ}\) and \(1^{\circ}\times 1^{\circ}\) & mean, annual and & \\ GPT2w & data of ERA-Interim fields by & \(5^{\circ}\times 5^{\circ}\) and \(1^{\circ}\times 1^{\circ}\) & & \\  & the ECMWF & & global grid & semi-annual terms & \\  & 10 years of ECMWF & \(5^{\circ}\times 5^{\circ}\) and \(1^{\circ}\times 1^{\circ}\) & mean, annual and & \\  & ERA-Interim re-analysis data & & global grid & semi-annual terms & \\ \hline \end{tabular}
\end{table}
Table 1: Primary information of five meteorological models. (\(P\)—pressure, \(T\)—temperature, \(e\) -water vapor pressure, \(dT\)—lapse rate, \(Tm\)—mean temperature weighted with water vapor pressure, \(\lambda\)—water vapor decrease factor, \(ah\), \(aw\)—mapping function coefficients, \(G_{ah}\), \(G_{ah}\), \(G_{new}\), \(G_{ew}\)—gradient, GPT—Global Pressure and Temperature, ECMWF—European Center for Medium-Range Weather Forecasts).  
International Civil Aviation Organization (ICAO) Standards and Recommended Practices (SARPs) for Satellite-Based Augmentation Systems (SBAS). The recommended SBAS model, termed simply the EGNOS model, utilizes the same look-up table as UNB3 to provide empirical meteorological parameters, and then calculates the ZTD by simplified equations where the Earth Gravity parameter is assumed to be constant [10].  
Finally, Table 2 summarizes the major information of the above three empirical models, where similarities and differences among them are listed.