## 4 Methods and Data Analysis
### GPS-Derived tropospheric Parameters  
The GPS positioning technique, which has become GNSS (global navigation satellite system), in recent years, due to the advent of other orbiting positioning systems, is based on measuring signal travel time from the satellites to the receiving antenna, which could be located on or near the Earth's surface or on other satellites, to estimate the geometric  
Figure 1: NeVoCGPS network. Selection of GPS sites used for the study of the thunderstorms (red and yellow squares) and the long-term PWV time series (blue and yellow squares). The map was produced by the INGV-OV Laboratory of Geomatics and Thermography. © LGT INGV OV. distance between them. GNSS signals, propagating through space to the receivers, undergo delay due to the total electron content (TEC) in the ionosphere and the amount of moisture and total density of the troposphere. Multi-frequency receivers allow accounting for ionospheric delay. GPS meteorology is concerned with inverting the remaining time delay due to a neutral troposphere, in order to retrieve useful atmospheric information. The two main branches of GPS meteorology are: (a) radio occultation (RO), a satellite-to-satellite, limb sounding technique based on measuring how the ray paths of GPS radio signals are bent by atmospheric refractive index gradients; and (b) ground-based GPS measurements. The additional transit time required to cross the troposphere is equivalent to an excess path length \(\Delta L\), which is related to the refractive index of the atmosphere (\(n\)). \[\Delta L=cdt=\int\limits_{L}(n-1)dL \tag{1}\]  
where the integral is taken over the actual path \(L\) distance between the transmitter and receiver antennae. This has a magnitude of around 2.5 m, for a GPS transmitter at zenith, and, to a first approximation, it increases as \(1/sin\alpha\), where \(\alpha\) is the elevation angle of the satellite above the horizon. In meteo GPS, the refractivity index [\(N=(n-1)\cdot\)10\({}^{6}\)] is routinely used instead of the refractive one. To better understand why refractivity is a measure of the physical state of the troposphere it is advisable to explicitly state the definition of N according to [PERSON] [22]:  
\[N=K_{1}\frac{P_{d}}{T}Z_{d}^{-1}+K_{2}\frac{P_{w}}{T}Z_{w}^{-1}+K_{3}\frac{P_ {w}}{T^{2}}Z_{w}^{-1} \tag{2}\]  
where, \(K_{1}\) = 77.6 K hPa\({}^{-1}\), \(K_{2}\) = 64.8 K hPa\({}^{-1}\), \(K_{3}\) = 3.776 \(\times\) 10\({}^{5}\) K\({}^{2}\) hPa\({}^{-1}\) are empirical constants [22]; \(P_{d}\) is the partial pressure of dry air and \(P_{w}\) is the water vapor partial pressure; \(Z_{d}\), \(Z_{w}\) are the Bulk modulus of dry air and water vapor, respectively, and \(T\) is the atmospheric temperature (in Kelvin). Bearing in mind that the refractive index in the atmosphere is a function of water vapour content, pressure and temperature, the tropospheric delay induced in any electromagnetic signal can be exploited for meteorological and climatological purposes. The zenith tropospheric delay (ZTD) is typically split into two parts, the hydrostatic (ZHD) and wet delay (ZWD), and routinely treated as a combination of a zenith component, along the vertical to the antenna, and a corresponding mapping function that gives the slant delay at a whatever elevation angle of the satellites. The raytracing through a numerical weather model, such as the European Centre for Medium-Range Weather Forecasts (ECMWF), allows the retrieval of the coefficients of the mapping functions. The ZHD (in mm) can be determined precisely by measuring the surface pressure (\(P_{s}\), in hPa) at the station position [23] or assumed from models:  
\[\text{ZHD}=\frac{(2.2768\pm 0.0005)P_{s}}{1-2.66\times 10^{-3}\times\cos(2 \phi)-2.8\times 10^{-7}h} \tag{3}\]  
where, \(h\) is the station ellipsoidal height (in meters). The formal error (\(\pm 0.0005\) mm/hPa) in the Equation (1) is suggested by [24], under the assumption that all uncertainties of the \(P_{s}\) and \(h\) parameters are uncorrelated.