## 5 Results and Discussion
### Short-Term Analysis
The analysis of GPS data has allowed us to follow the evolution of the phenomenon through the time changes of the tropospheric delay parameters and the phase residuals. Four-hour snapshots of LC residuals (MAFE station) for the days 16-17 November 2020 are shown (See Supplemental Materials Figure S2). It is clear that, in the last hours of 16 November and in the first hours of 17 November, the amplitude of the phase residuals was much higher than in the hours before and after the phenomenon, which is indicative of the increase of tropospheric water vapour strongly disturbing the propagation of GPS signal through the atmosphere. In fact, the root-mean-square (rms) of the phase residuals, which, on a dry day for MAFE, is nearly 5 mm, on 16 November was 9 mm and, on 17 November, 8 mm. The analysis of time correlation between phase residuals and satellite radar images confirms the coherence between the time changes of phase residuals (See Supplemental Materials Figure S2) and the evolution of the thunderstorm (Figure 7). Figure 9 depicts the 30-s PWV retrieved from CSRS-PPP service for some stations in Napoli and Vesuvius areas. Also, in that case, the soaring of the PWV curve a few hours before the raining events and the rapid decrease afterwards is quite evident. Thanks to the high temporal resolution of these PPP solutions, even minor raining events are well-traceable in the PWV curve. The rapid increase in PWV about 2 h before rain at the end of day 319 (14 November) was not repeated at the end of day 321 (16 November), however, the volume of rain that fell was much higher. This is probably due to the fact that the PWV content, before the rain at the end of day 319, is much lower than at the end of day 321. Rain seems to fall, at least for the events we studied, only if a particular PWV range is reached. In fact, the 2019 events (Figure 8) also show the same PWV trend. Before the 26 September event (DoY 269) there was a larger increase in PWV, although the amount of rain that fell was smaller. This hypothesis is in agreement with [PERSON] and [PERSON] [47], who showed that rain falls during high PWV values, but pointed out that the differences in PWV evolution are related to different weather systems. It is well known that the relationship between the temporal evolution of PWV and rainfall is complex. Several authors have explored the temporal variation of PWV before and after the onset of heavy precipitations. [PERSON] et al. [48] identify an increase in PWV, which peaks just before the onset of precipitation. This characteristic trend is the same as we have reconstructed in the analysed events (Figures 7 and 9). The state-of-the-art testifies that, after reaching peak values, the PWV can vary in different ways; it can remain constant, e.g., [49], or decrease abruptly, e.g., [50], as in the cases we analyzed. Figure 8: IR images from the SEVIRI instrument on-board Meteosat Second Generation (MSG) satellites “calibrated” by precipitation measurements from PMW satellite sensors in sun-synchronous orbits (EUMETSAT Data Service, 2021) [51]); the red box marks the target area (same as in Figure 1). The time evolution of PWV during the storms was mostly the same at all the other stations (Figure 10) in NeVoCGPS network, except for the topographic effect that offsets the PWV values according to an inverse correlation to the height above sea level. Various authors, e.g., [52; 53; 54], have studied the feasibility and prediction capabilities of GNSS-based PW-monitoring approaches to forecasting extreme precipitation. They applied techniques based on threshold values to trigger alarms, for example in the event of debris flows or flash floods. In the analyzed area, a dramatic example of a flash flood is the event that produced 147 casualties in Sarno (Vesuvius area), in May 1998. It was generated by a sudden extreme rainfall event and the resulting flash floods and mudflows, due to the mobilisation of the Vesuvian pyroclastic layers that blanket the surrounding hills [55].