## 5 Combined Approach for Paroxysmal Early Warning
In the cases where the IS-EW did not provide an alert, such as the lava fountain on 3 December 2015, the TC-EW levels could be a valid complementary warning. On the other hand, in cases where the WR-Q\({}_{\text{M}}\) levels and TC-EW were missing, due to the particularly low explosive activity (\(Q_{M}\) lower than \(10^{6}\) kg/s), with lower particle sizes and possible partial or total occlusion of the field of view due to meteorological clouds, respectively, the IS-EW could be a complementary warning without any lead time. The PEW allowed combining the IS with the WR or the TC, as IR-PEW and IT-PEW, respectively, and the TC with the WR, resulting in TR-PEW, as listed in the upper section of Table 2. The TR and IR can be successfully used, jointly or separately, as precursors of the paroxysmal phase, whose tephra plume can be detected by the WR-EW alert in any weather conditions. Moreover, the IS-EW and TC-EW can be effectively used as a trigger for the WR monitoring, with specific and rapid sector scans. The red values listed in Table 2 are related to the lead times of the PEW of both levels, which were anticipated by the WR (IR-PEW and TR-PEW) and the TC (IT-PEW). Only in three cases did the WR preempt the PEW with respect to the first sensors (IS or TC): on 3 December 2015 (IR-PEW1), in the morning on 4 December 2015 (IR-PEW2), and on 16 February 2021 (TR-PEW1). In eight cases, we observed that TC preempted the PEW with respect to the IS: on 10 April 2011, (IT-PEW1), on 12 April 2012 (IT-PEW1 and IT-PEW2), on 23 November 2013 (IT-PEW1), on 3 December 2015 (IT-PEW1), on 5 December 2015 (IT-PEW2), and on 23 February 2021 (IT-PEW1 and IT-PEW2). Consequently, the TC can be considered as a valid pre-alert system, followed by IS, with similar performance for the selected paroxysms, as long as the former operates in good visibility conditions; conversely, the IS was confirmed as an important pre-alert system. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Data** & **WR-QML** & **WR-QMH** & **TC-EW1** & **TC-EW2** & **IS-EW1** & **IS-EW2** \\ \hline
**2011-04-10** & 11:25 & NA & 09:04 & 10:18 & 09:38 & 10:00 \\ \hline
**2012-04-12** & 14:19 & 14:36 & 11:30 & 12:28 & 11:59 & 13:33 \\ \hline
**2013-11-23** & 09:30 & 09:46 & 08:02 & 08:54 & 08:29 & 08:33 \\ \hline
**2015-12-03** & 02:01 & 02:23 & 01:44 & 01:53 & 02:38 & NA \\ \hline
**2015-12-04** & 08:50 & 09:06 & 08:45 & NA & 07:02 & 09:13 \\ \hline
**2015-12-04** & 20:18 & 20:37 & 20:06 & 20:32 & 07:02 & 20:30 \\ \hline
**2015-12-05** & 14:51 & NA & 14:30 & 14:40 & 07:02 & 14:46 \\ \hline
**2021-02-16** & 16:30 & NA & 16:38 & NA & 16:15 & 16:19 \\ \hline
**2021-02-23** & 23:30 & 23:44 & 18:39 & 22:47 & 21:44 & 23:11 \\ \hline \end{tabular}
\end{table} 
Table 1: EW times of levels 1 and 2, as detected by the TC and IS and the WR-Q\({}_{\text{M}}\) levels (low and high) for the considered Etna explosive eruptions. NA stands for Not Available value. The statistical values of each PEW were computed as the percentage of positive (PosAlert), negative (NegAlert), and not detected (NotAlert) alerts among all studied cases (lower section of Table 2). Regarding the IR, we found a rate of 88.90% of PosAlert, with only 11.10% of NegAlert and no NotAlert (NA) for the PEW1, and 44.45% of PosAlert with only 11.10% of NegAlert for the PEW2. There was a rate of 44.45% of NotAlert for the PEW2 due to the lack of the WR-Q\({}_{\text{M}}\)H and IS-EW2. With the IT coupling, we obtained only 44.45% of PosAlert, with 55.55% of NegAlert and no NotAlert detected for PEW1. Instead, for PEW2, each case was identified with an equal rate of 33.33%. The TR coupling showed a rate of 88.90% of PosAlert, 11.10% of NegAlert, and no NotAlert for PEW1, whereas there was a rate of 55.55% of PosAlert without any NegAlert and 44.45% of NotAlert for PEW2. For IR-PEW1 and TR-PEW1, we obtained a rate of success of 88.90%. This indicates that both systems were reliable in detecting Strombolian activity, while the rate of 55.55% for TR-PEW2 was sufficiently reliable in detecting paroxysmal activity.