## 5 Combined Approach for Paroxysmal Early Warning  
According to the previously described results, we developed a theoretical flow diagram of the possible integration of a fully automatic and operative EW system for the identification of Etna PEW (Figure 15). Typically, the EW1 and EW2 level notifications derived from TC and/or IS can be used to inform the WR that an eruption is ongoing. Figure 14: Time series of \(Q_{M}\) (kg/s), IP (-), and \(v_{ex}\) (m/s) shown as blue, red, and magenta lines, respectively, for the 23 February 2021 Etna lava fountain. The EW level time steps are plotted as vertical dashed lines with different colors, identifying the associated sensors. Figure 13: Time series of \(Q_{M}\) (kg/s), IP (-), and \(v_{ex}\) (m/s) shown as blue, red, and magenta lines, respectively, for the 16 February 2021 Etna lava fountain. Values are plotted together with the EW1 and EW2 (vertical dashed lines with different colors). In this scheme, both the IS and TC (yellow and blue boxes on the right side of Figure 15, respectively), separately or jointly, can be used as a trigger of an automatic procedure of analysis of the WR (detection and tracking of volcanic plume and ESPs retrieval). The first EW1 signal was used to activate the WR system in exploring mode and run the algorithm to monitor volcanic plumes (green box). In this phase, the WR keeps scanning the 3D surrounding area (azimuth, elevation, and distance). When the volcanic plume was observed (EW2), the WR system was switched into monitoring mode (red box), which detects and retrieves the ESPs (e.g., top plume height (\(H_{\text{TP}}\)), mass eruption rate (\(Q_{M}\)), and grain size distribution (GSD)). Regarding these results, we estimated the top plume height (\(H_{\text{TP}}\) (km)) above the crater and the GSD using a threshold algorithm and applying regressive relations, respectively, on the measured radar reflectivity factor, \(Z_{thr}\), of the probed volcanic plume [22; 25]. In a few cases, we noted that the TC allowed anticipating the first alert with respect to IS. Hence, the TC is an effective tool compared to IS for anticipating the paroxysmal, if the environmental conditions do not compromise the quality of the TC image. However, both the IS and TC are essential to switch the radar to the volcanic plume monitoring mode. To evaluate the performance of coupling the WR with TC and IS, we computed the alert times as the temporal difference between two equal levels, EWx (where x can be equal to 1 or 2), derived from the IS and TC. In order to test the sensitivity of the WR in detecting the paroxysmal phase, we also combined the EW levels with the WR-derived \(Q_{M}\) levels. We defined the PEW1 lead time, \(\Delta t_{PEW1}\), as:  
\[\Delta t_{PEW1}=t_{XX-EW1}-t_{YY-EW1/Q_{M}-low} \tag{1}\]  
where \(t_{XX-EW1}\) is the EW1 alert time from the first system (IS or TC) and \(t_{YY-EW1}\) is the EW1 alert time from the second system (WR or TC). Figure 15: Flow diagram of the combined WR, TC, and IS to perform the paroxysmal early warning (PEW). The first EW1 delivered by IS and TC was used, separately or jointly (blue box on the right side), for the WR set to exploring mode (green box) and to activate the area scan. If a volcanic plume was detected (EW2 level), the WR was switched into monitoring mode, activating the 3D plume tracking and detection mode, to quantitatively characterize the main features of the paroxysmal. Similarly, we defined the PEW2 lead time, considering in this case only the EW2 level, as derived from two systems:  
\[\Delta t_{PEW2}=t_{XX-EW2}-t_{YY-EW2/Q_{M}-high} \tag{2}\]  
It is worth noting that PEW2 data are not always available for the selected time windows, so in some cases, the lead time, \(\Delta t_{PEW2}\), cannot be properly computed. The times when TC and IS identified the EW levels and the WR detected the \(Q_{M}\) levels are summarized in Table 1. EW2 and Q\({}_{\text{M}}\) were not available (NA) for 10 April 2011, 3 and 5 December 2015, and 16 February 2021.