# Review on the Role of GNSS Meteorology in Monitoring Water Vapor for Atmospheric Physics
## 2 GNSS Methodologies  
### Conversion of Tropospheric Delays to Water Vapor  
The conversion of ZWD to IWV is performed through the factor \(\Pi\). Typically, its value is estimated by the relation described by Equation (1),  
\[\Pi=\frac{10^{6}}{\rho R_{v}\big{[}k_{3}/T_{m}+k_{2}^{2}\big{]}}, \tag{1}\]  
where \(\rho\) is the density of liquid water, \(R_{v}\) the specific gas constant for water vapor, \(k_{3}\) and \(k_{2}^{\prime}\) are refractivity constants and \(T_{m}\) is the weighted mean temperature of the atmosphere, defined as Equation (2):  
\[T_{m}=\frac{\int(P_{v}/T)\mathrm{d}z}{\int(P_{v}/T^{2})\mathrm{d}z}. \tag{2}\]  
\(T_{m}\) is typically obtained by using a linear regression between surface temperature (\(T_{s}\)) and \(T_{m}\) (obtained from radiosondes). The relationship \(T_{m}-T_{s}\) given by [PERSON] et al. [7] was obtained using radiosondes in the United States. Logically, some efforts have been made to improve it for application to other locations. [PERSON] and [PERSON] [19] considered two models for \(\Pi\) in Europe: (1) series expansion of the deviation from mean surface temperature, and (2) a combination of the former with a seasonal variation based on decimal day of year and latitude. Both models presented RMSE values between 1.0% and 1.2%, fitting the coefficients to all Europe, by regions or by site. Slight increases in RMSE values were found as the fitting involved wider regions. In more equatorial regions, such as southern India, \(\Pi\) has been reported to be less dependent on \(T_{m}\) variations, allowing to set it to a fixed value without relevant precision loss [20]. Another work addressed the model to calculate \(T_{m}\) in tropical regions, finding that the Bevis formula is shown to be less adequate with high temperatures and low variability. In fact, the definition of \(T_{m}\) assumes that temperatures are not so high, and [PERSON] et al. [7] indicates a larger dispersion for high \(T_{s}\) values. Therefore, it is suggested that the redefinition of \(T_{m}\) should be addressed for tropical regions. NWP, as with the reanalysis from European Centre for Medium-Range Weather Forecasts (ECMWF), have been widely used to retrieve surface pressure and \(T_{m}\) since 2009 approximately. [PERSON] et al. [21] obtained a global 5-min data-set from the IGS GNSS network using this approach. The ECMWF reanalysis version used (ERA-Interim) had 6-h resolution, and the estimated uncertainty due to time interpolation was less than 0.2 mm. Later, [PERSON] et al. [22] compared the GNSS IWV product using the new ECMWF reanalysis (ERA5) for pressure and \(T_{m}\), on the one hand, and using the legacy version (ERA-Interim), on the other hand, against a reference GNSS IWV product using data from meteorological stations. The biases and RMSE of both products were of a few tenths of a millimeter. Against radiosondes, the RMSE was of about 2-4 mm. ERA5 interpolation data-set was found to be more stable than ERA-Interim one. [PERSON] et al. [23] showed that ERA5 GNSS IWV improved ERA-Interim GNSS IWV in China, thanks to ERA5's pressure enhancement, and with a similar performance on \(T_{m}\). The contribution of ERA5 to the IWV error was estimated to be less than 1 mm, and diurnal variations were better caught by ERA5 GNSS IW than by ERA-Interim GNSS IW. Moreover, there have been some approaches to use NWP data for retrieving mapping function parameters, pressure and temperature [24; 25]. These approaches can be useful when there are not any meteorological stations available nearby the GNSS station or when access to NWP data is difficult. Another possible approach is to use local models of temperature and pressure to convert ZTD to IWV, using local meteorological stations over a long time series. [PERSON] and [PERSON] [26] followed this methodology in Thailand, finding that RMSE was below 3 mm, therefore it was considered suitable for weather nowcasting. All of these different methodologies to convert ZTD to IWV have advantages and disadvantages.