Exposure-based risk assessment and emergency management associated with the fallout of large clasts at Mount Etna

Fallout of ballistic blocks and bombs ejected from eruptive vents represents a well-known hazard in areas proximal to volcanoes (mostly < 5 km from the vent). However, fallout of large clasts sedimenting from plume margins that extend to medial areas and have the potential to produce severe injuries to people and cause damage to infrastructure, is often overlooked. Recent eruptive events at Mount Etna (Italy) provide a clear example where large-clast fallout from plume margins (>5 cm) has posed a real threat both to the many visitors reaching the summit area and to local infrastructure, and, therefore, has been selected as a case study. To quantify this hazard, a new particle sedimentation model was calibrated with field data and then used for probabilistic hazard assessments. For a fully probabilistic scenario the hazard zone covered 72 km2 and included some 125 km of paths and roads, as well as 15 buildings. Evacuation on foot to a safe area was estimated at almost 4 h, but this could be reduced to less than 3 h if two shelters were provided. Our results show the importance of integrating probabilistic hazard analysis of large-clast fallout within effective strategies of risk management and reduction, especially in the case of volcanoes where visitors can reach the summit areas.


Introduction
Tephra sedimentation associated with explosive volcanic eruptions includes particles ranging from ash (<2mm) to lapilli (2-64mm) and blocks (>64mm). Ash mostly falls out from the umbrella cloud and from the top of buoyant plumes and, unless aggregated, can reach distances of hundreds of kilometres from the vent; lapilli mostly fall out from the plume margins within 25 tens of kilometres from the vent, while blocks ejected directly from the vent can fall ballistically within a few kilometres, or be entrained within the plume and sediment from its margins together with the coarsest lapilli (e.g. Bursik et al. 1992). The hazard associated with the sedimentation of ash and fine to medium lapilli (i.e. particles <16mm) and with ballistic blocks has already been analysed and discussed in many studies (e.g. Biass et al. 2016a;Fitzgerald et al., 2014;Biass et al. 2014;Costa et al. 2009). However, the hazard associated with the sedimentation of coarse lapilli and blocks from the convective region of 30 eruptive plumes (i.e. particles >16 mm; hereon defined as "large clasts") has never been characterized. The risk associated with the sedimentation of large clasts from plume margins is more localised than for ash and fine to medium lapilli, where the area affected can extend over hundreds of kilometres and the impact can be felt across several economic sectors including agriculture and transport (Jenkins et al. 2015). However, physical impact associated with ash and lapilli is rarely dangerous for people, with the exception of eye irritation and long-term respiratory health issues (e.g. Horwell and Baxter, 2006). The impact area associated with the sedimentation of large clasts from plume margins is, however, potentially much larger than the area at risk of ballistic impact, which extends no more than 5 km from the vent (e.g., Bertin, 2017;Biass et al., 2016a;5 Fitzgerald et al., 2014). In fact, for small explosive eruptions (e.g. large lava fountains and small Vulcanian events), ballistic blocks are confined in very proximal areas (1-2 km from vent) (Calvari and Pinkerton, 2002) but large clasts can fall out some 10 km from the eruptive vent (Andronico et al., 2015(Andronico et al., , 2008, and this poses a particular risk at Mount Etna where many people visit the summit area throughout the year. This also implies a risk of damage to infrastructure, including buildings and roads (e.g. Andronico et al. 2015, Wardman et al. 2012. Impact from large clasts (up to 10s cm) is particularly evident for small 10 explosions that do not generate thick and widely dispersed tephra deposits, but it has also been reported for higher intensity eruptions (e.g. Vesuvius 79AD, 472AD, 1631and 1906eruptions: Cioni et al. 1992, Barsotti et al. 2015, Rosi et al. 1993, Sulpizio et al. 2005andSoufriere St Vincent 1902 eruption: Zuccaro et al. 2015). It is therefore important to assess the hazard models and probabilistic strategies.
As an example, we present the assessment of the hazard associated with the sedimentation of 5 cm clasts from lava-fountain 15 fed plumes at Mount Etna using the sedimentation model of Rossi et al. (2019). Explosive activity occurs frequently at the summit craters of Mount Etna, often consisting of Strombolian eruptions and lava fountains (e.g., Andronico et al., 2015;Corsaro et al., 2017;De Beni et al., 2015;Vulpiani et al., 2016). Tephra fallout is a well-documented hazard from these explosive eruptions (e.g., Donnadieu et al., 2016;Scollo et al., 2013), and proximal to the vent there is a high risk of injury to people and damage to infrastructure both from large clasts sedimented from the eruptive plume and from ballistic projectiles 20 (Andronico et al., 2015;Calvari and Pinkerton, 2002). Results provide an opportunity to also assess the associated risk to infrastructure and consider emergency management (i.e. analysis of time required for people to reach a safe area based on a dedicated USGS modelling tool (Jones et al., 2014)). Validation of the model with Etna observations, model parameters and both eruptive and atmospheric parameters are described in Appendices A, B and C, respectively; in addition, data on historical activity at Mount Etna (Table S1), wind analysis (Figs S1-6), model sensitivity analysis , and additional hazard 25 and evacuation-time analyses (Figs S11-14) are presented in the supplementary material..

Lava-fountain fed plumes at Mount Etna
Explosive eruptions at Mount Etna often take the form of lava fountains, when jets of lava reach heights ranging from a few tens to several hundreds of metres, and many generate ash plumes that can rise up to 15 km above sea level (a.s.l.) (Andronico et al., 2015 and references therein). More than 200 such events have occurred in the past 20 years (Andronico et al., 2015). 30 High intensity lava fountains are often short-lived but they can be extremely hazardous when large clasts are sedimented out proximal to the vent (Andronico et al., 2015). Some details of lava fountains since 1998 have been published and listed in Table S1. In order to explore the variability of lava fountain events during which large clasts sedimented out from plume margins, two reference events have been considered, for which data on clast type and dispersal is available.
A sequence of eight eruptive events occurred between October and December 2013 at the New Southeast Crater (NSEC). The paroxysm of 23 November 2013 was unusually explosive although the total erupted DRE volume was similar to previous events (~1.6 x 10 6 m 3 ; Bonaccorso et al., 2014). A lava fountain from 09:30 to 10:10 UTC reached a height of around 1 km 5 above the vent (Andronico et al., 2015) and volcanic blocks damaged cars at Rifugio Citelli, around 5 km from the crater (shown in Fig. 1). Large clasts were sedimented from the rising plume, with the average diameter of scoria collected near the refuge being over 10 cm (Andronico et al., 2015).
Deposits from a lower intensity eruptive event on 12 January 2011 were also extensively surveyed (Andronico et al., 2014). A lava fountain from 21:50 to 23:30 UTC reached around 800 m height, with an ash plume estimated at 9 km a.s.l. and lapilli up 10 to 5 cm in diameter collected 5 km from the vent (Andronico et al., 2014;Calvari et al., 2011;Donnadieu et al., 2016). Large clast deposition from the eruptive plume is also described for many smaller lava fountains, which produced less extensive ash plumes with fallout of large clasts confined to a small area proximal (<5 km) to the vent (for example, Andronico et al., 2009).

Proximal exposure at Mount Etna
Large clast sedimentation is likely to be a hazard within 10 km of the summit craters, an area within the Ente Parco dell'Etna 15 Regional Nature Park which has no permanent population. However the Park is very popular with visitors and an estimated 1.3 million people visited the craters in 2010 (Parco dell'Etna, 2013) with visitor number increasing by 50 % since the park was made a UNESCO world heritage site in 2013 (Perricone, 2017). Infrastructure at risk of impact includes some 1390 km of footpaths, unpaved tracks and paved roads, as well as over 4600 buildings, including commercial and residential properties but no critical facilities such as hospitals or schools ( Fig. 1 and Table 1 using data from OpenStreetMap and Ente Parco  20 dell'Etna). In addition, there is a cable car and two ski areas (Etna Nord and Etna Sud) with ski lifts and around 21 km of ski trails (OpenStreetMap Foundation, 2017a, 2017b. For the purposes of this work, we have considered the most-used buildings and infrastructure around the summit area of Etna ( Fig. 1). On the southern slope they are: the top station of the Funivia dell'Etna cable car (waiting area for hundreds to thousands of tourists who daily visit the volcano summit or use the ski slopes in winter), and Baita delle Guide (a transportable  25 shelter located at around 2900 m in the waiting area for tourists using four-wheel drive buses). On the northern slope there are: the INGV Pizzi Deneri Observatory (2847 m; a building used by volcanologists for field schools, research and monitoring activities), Rifugio Citelli (at the end of a no-through secondary road, used by hundreds of people especially at weekends and during the ski season). Furthermore, our study also covers the infrastructure in two main tourist areas, i.e. Etna Sud (at 1920 m) and Etna Nord (at 1810 m), commonly known as Rifugio Sapienza (an area visited by up to thousands of visitors during 30 the day) and Piano Provenzana (a very popular ski station), respectively. Finally, several secondary mountain huts are also located along tracks at mid-slopes, especially on the western and northern slopes of the volcano (Fig. 1).
We make use of the particle sedimentation model of Rossi et al. (2019) in order to simulate the transport of clasts within a volcanic plume and their sedimentation. This model modifies the well-known methodology introduced by Carey and Sparks (1986) in order to take into account the effects of wind on the eruptive column. Particles are first released into the atmosphere from the clast support envelope, a region of the plume where the velocity of the gas mixture equals the terminal velocity of the 5 clast. Clast' trajectories are then computed solving the second law of motion in a windy atmosphere. The model applies best to centimetre-scale particles that show a reduced, but not negligible, coupling with the gas mixture of the plume. Plume dynamics are described based on the model of Degruyter and Bonadonna (2012).
The main inputs to the model are: • Particle parameters: size, density, the Stokes drag coefficient kS (for particles falling in random orientation) and the 10 Newtonian drag coefficient kN (for particles falling in a gas). kS and kN are as described by Bagheri and Bonadonna (2016b).
• Three-dimensional wind profiles (in this model wind profiles are space-dependent with distance from vent).
• The number of particles to be sedimented.
• The mass eruption rate (MER) of the event. 15 • A digital elevation model (DEM) of the area.
The model takes a three-dimensional wind profile and creates the wind field across the modelled area, it then uses the input MER to model the maximum height of the plume above the eruptive vent. The clast diameter and the number of particles to be sedimented are fixed for each simulation and particles are released from the vent. When their (downward) terminal velocity exceeds the plume upward velocity they start to fall and the model calculates the trajectory of each particle until it reaches the 20 ground, with the terrain being defined by the DEM. The modelled ground surface is gridded, and the size of the grid cells is equal to the cell size in the DEM (90 metres in our case). For each simulation the point of impact of each sedimented particle is recorded on that grid. The model also calculates the kinetic energy of each particle immediately before impact with the ground.

Deterministic versus probabilistic approach 25
The plume model described above can be used deterministically (with one three-dimensional wind profile and fixed eruptive parameters) to compare clast sedimentation with field observations for a specific eruptive event. The model can also be used probabilistically in order to compile maps that contour the probability of a clast of a given diameter reaching a certain location.
In the probabilistic approach the model is run several times, with one or more of the initial parameters selected randomly from a statistical distribution. At the end of each simulation, a contour is created from the most external points of ground impact 30 and all grid cells inside that contour are assumed to be impact locations for that simulation. When all the simulations are complete, the number of times each grid cell has been impacted is counted and divided by the total number of simulations, to give the probability of impact for each cell in the grid, which can then be mapped.

Wind data 5
Four-time daily wind profiles from the National Oceanographic and Atmospheric Administration (NOAA, 2017) were analysed for the period 1997-2015 using the Matlab package TephraProb (Biass et al., 2016c). Wind conditions were found to be very similar for one year (2013), 10 years (2006-2015) and the full dataset (19 years, from 1997-2015) (see Figs S1 to S6, for full wind analysis). Results are also in agreement with those of Scollo et al. (2013). Little seasonal difference was found for the expected plume heights up to 15 km a.s.l., with prevailing winds towards the NE to SSE sector. The 2006-2015 dataset 10 was selected for the probability assessment and given the limited extent of large-clast fallout (< 10 km from the vent), wind profiles are not considered space-dependent in this assessment (i.e. only one wind profile centred on the vent is considered).

Field observations
The 23 November 2013 event was selected to validate and calibrate the plume model for the description of lava-fountain fed plumes. In fact, this event represents a lava fountain with one of the largest mass eruption rates at Mount Etna (Andronico et 15 al., 2015;Bonaccorso et al., 2014). For samples collected following the event (Russo, 2016), both the median and the average of the 5 largest clasts (measured using the method of Bagheri and Bonadonna (2016a)) were calculated and the drag coefficients, kS and kN, derived for use in the hazard analysis, as described in Appendix A. We found that the median is more stable than the average of the 5 largest clasts at the scale of the outcrop (Tables A1 and A2), as also concluded by Bonadonna et al. (2013); however, isopleth maps compiled based on the median values (and corresponding downwind and crosswind 20 ranges) are not more stable than the isopleth maps compiled based on the average of the 5 largest clasts (Fig. A1). In addition, modelled contours more closely match values calculated using the average of the 5 largest clasts (Fig. A2).

Model validation and calibration
The model was validated and calibrated to the 23 November 2013 lava fountain by varying the modelled MER to produce the observed plume height of 11 km a.s.l. (Corradini et al., 2016), using wind conditions for the time of the eruption. Table B1  25 summarises the model input parameters that were fixed for this study and Table B2 lists the input parameters used for the model calibration. During an eruption MER will vary, but because reported plume heights are usually the maximum height achieved by the plume and MER is estimated based on plume height (Degruyter and Bonadonna, 2012), the modelled MER represents the maximum MER for the eruptions. Given that a range of MER values could equally produce the observed plume height, the best-fit MER (5.4 x 10 6 kg s -1 ) was found by comparing modelled clast size contours and the field data. Fig. A2  30 shows the modelled contours for this MER, which most closely match the field observations calculated using the average of the 5 largest clasts method (see Appendix A for use of the 5 largest clasts in model validation).

Number of particles
The optimum number of particles to be released from an eruptive plume was tested using simulations of 100, 500, 1000 and 5 5000 particles, keeping both the wind and the particle diameter (5 cm) fixed, in order to maximize model performance in terms of machine time. For this analysis we used the three-dimensional wind profile for 12 December 2015 14:00 to 16:00 UTC, when wind speeds were high, which results in particle sedimentation over a wide area, making the effect of changing particle numbers easier to identify. Using 100 particles produced an angular contour, indicating particle density within the contour is low and hence the contour is likely to change with each simulation. In contrast, contours for 500 or more particles were smooth 10 and almost completely overlapped (Fig. S7a). As a result, 500 particles were selected as suitable for the hazard analysis as described below.

Particle density
The sensitivity of the model output to particle density was tested using simulations with particle densities selected from end member values measured at Mount Etna. In particular, we considered the events of 12 January 2011 (1000 kg m -3 ), 23 15 November 2013 (865 kg m -3 ) and 3 December 2015 (760 kg m -3 ) (Andronico et al., 2015(Andronico et al., , 2014Russo, 2016). The wind was fixed to 12 December 2015 14:00 to 16:00 UTC as for the particle number test. The contour for the lowest density clasts is 26 % larger than for the highest density clasts (Fig. S7b), mostly due to the clasts reaching a greater distance from the crater. Therefore, particle density is an important variable for the hazard analysis: the lower the density, the larger the impacted area.

Number of simulations 20
The stability of the results in terms of the impacted area is dependent on the number of runs used and to test this, different numbers of runs were compiled for a 5 cm clast. More simulations give a more stable result, but as each additional simulation takes time, a balance must be found between confidence in the output and a realistic timescale for the simulations. For very low impact probabilities (< 1 %), the hazard area is very sensitive to the number of simulations (as shown in Figs S8 and S9) because for each additional run, new locations will receive one impact. Areas with probability < 1 % were excluded from 25 further analysis because of the high level of uncertainty, and for each simulation the probability contours were treated as stable if the associated area changed by < 3 % between different numbers of simulations. Different numbers of simulations are used for the different probabilistic scenarios considered (e.g. Appendix B).

Choice of eruption crater
As mentioned earlier, lava fountains have been produced at different vents on Mount Etna and it is not easy to predict where the next lava fountain will occur. In order to identify the sensitivity of model outputs to the choice of eruptive vent, the 23 November 2013 event was separately modelled as an eruption from each of the five summit vents. Although the hazard zones largely overlap, lava fountains from the Northeast Crater (NEC), Voragine or Bocca Nuova are likely to extend the hazardous 5 area further north compared to events from Southeast Crater (SEC) and NSEC (Fig. S10). NSEC was chosen as the primary vent for our hazard assessment, as this vent has produced most of the lava fountains over the past 5 years (Table S1). However, given the prevailing westerly winds, a probability map from NSEC may underestimate the northern extent of clast fallout from NEC, Voragine and Bocca Nuova. To investigate how the location of the eruptive vent affects the infrastructure at risk of impact, the exposure analysis was conducted for high MER events from both NSEC and Voragine (Supplementary material). 10

Hazard assessment
To allow a range of eruptive and atmospheric conditions to be investigated, a probabilistic hazard assessment was completed for three scenarios from NSEC: • One Eruption Scenario for a high mass eruption rate event (OEShigh MER) based on 23 November 2013 lava fountain (MER = 5.4 x 10 6 kg s -1 ). 15 • One Eruption Scenario for a low mass eruption rate event (OESlow MER) based on 12 January 2011 lava fountain (MER = 2.5 x 10 5 kg s -1 ).

•
Eruption Range Scenario (ERS), using a Monte Carlo approach where values of particle density and MER were randomly sampled from within a statistical distribution based on previous activity at Mount Etna (MER = 2.5 x 10 5 -5.4 x 10 6 kg s -1 ). 20 For OES, eruptive parameters are fixed but the wind is selected randomly from the available dataset, while for ERS the eruptive parameters are also randomly selected from an associated probability density function. The OEShigh MER event was selected as being the largest MER so far experienced from a lava fountain at Mount Etna and the OESlow MER event was the smallest MER likely to cause significant hazard beyond the immediate proximal area. For the ERS, a uniform distribution was chosen for particle density, but to account for small eruptions occurring more frequently than large ones, a logarithmic 25 distribution of MER was used (Biass et al., 2016b;Bonadonna, 2006). In Appendix C we report the frequency distributions for the sampled particle density and MER, the distribution of sampled wind profiles and the resulting distribution of plume height (calculated from the combination of MER and wind speed) (Fig. C1). These confirm that the sampled values are within the expected frequency distributions and the winds are representative of the 2006-2015 dataset. The low frequency for the smallest MER (≤ 3 x 10 5 kg s -1 ) suggests that some plumes with this MER are not buoyant and so are discarded by the model. 30 The modelled plume heights (Fig. C1c) range from 6.0 to 14.9 km a.s.l.
For each scenario a clast diameter of 5 cm was selected as being likely to cause significant injury (P. Baxter personal communication, 2017). Hereon particles >5 cm are defined as hazardous clasts. The damage caused by a particle on impact depends on its kinetic energy and the modelled particles showed a bimodal distribution of kinetic energies, with peaks at 15 J and 21 J and a maximum value of 46 J (shown in Fig. 2). Biomechanical experiments have shown that a dynamic load (such as a falling clast) can cause skull fracture at energies of around 28 J (Yoganandan et al., 1995) and 2 % of modelled clasts had 5 energies above this value. 98 % of clasts had impact energies >10 J and hence may cause building damage, as impact energies of 2 J can damage glass windows, and energies >10 J can penetrate roof tiles (Jenkins et al., 2014). Table B3 summarises the variable input parameters for each scenario, with the fixed parameters being listed in Table B1. For each simulation a wind profile was randomly selected from the 14608 (4 times daily for 10 years) available in the [2006][2007][2008][2009][2010][2011][2012][2013][2014][2015] year NOAA dataset (NOAA, 2017) (Appendix C). The hazard zone, defined as the model grid cells with probability of impact 10 ≥1 %, was classified into 5 categories and for each scenario a map was produced showing the area where the probability of impact was >40 %, 30-40 %, 20-30 %, 10-20 % and 1-10 % (Fig. 3). Areas with probability of impact < 1 % were excluded because, at very low probabilities, the hazard area is very sensitive to the number of simulations (as shown in Figures S8 and   S9). In each scenario the highest probabilities occur east of the vents, with probabilities no higher than 20 % west of the vent, confirming the influence of the prevailing westerly winds. Table 2 shows the area included within each probability category 15 for each scenario. For probabilities ≥1 %, the hazard zone covers a total area of ~129 km 2 , extending up to 8 km from the vent, for the OEShigh MER, and ~72 km 2 , extending up to 6.5 km from the vent, for the ERS. The hazard zone for the OESlow MER covers ~5 km 2 and is limited to the area immediately proximal to the craters, confirming that for lava fountain events with MER lower than that for the 12 January 2011 event (2.5 x 10 5 kg s -1 ), any hazardous clast fallout is unlikely to pose a risk to people or infrastructure. 20

Exposure analysis
The amount of infrastructure at risk was calculated for each scenario. Table 3 summarises the infrastructure exposed within each hazard zone for each scenario and Fig. 3 shows the infrastructure within the hazard zone for the OEShigh MER, the OESlow MER and the ERS (for the NSEC scenario). In order to investigate how this exposure varies for lava fountains from different eruption vents, the probability map for the OEShigh MER at NSEC was translated to be centred on Voragine, 25 which is at the same height as NSEC and so we expect particle sedimentation to follow similar trends (Table 3 and Supplementary material: Fig. S11).
For the OEShigh MER from NSEC, no buildings are in areas with >30 % probability of impact and the only building in the 20-30 % area is a hut (Baita delle Guide). The seven buildings in the area with 10-20 % probability include Rifugio Citelli, the INGV Pizzi Deneri Observatory and the top station of the Funivia dell'Etna cable car. The Baita del Guide hut and the 30 observatory are both in a higher hazard category for this scenario from Voragine, although overall fewer roads and buildings are within the total hazard zone (roads: 252.5 km compared to 274.2 km; buildings: 104 compared to 118, for fountains vented from Voragine compared to NSEC). All the ski lifts are in the hazard zone, with two fully within the 10-20 % probability area for the NSEC eruption and only one for the Voragine eruption. In both cases one lift crosses the 10-20 % and 1-10 % areas, as does the Funivia dell'Etna cable car, and the remaining ski lifts are fully in the 1-10 % area.
For the OESlow MER scenario, very little infrastructure is at risk, with only 0.2 km roads in the 10-20 % probability area and a further 5.7 km plus the Baita delle Guide hut in the 1-10 % probability area. For the ERS, no infrastructure is within the 5 area having a probability of impact >30 %. 1.5 km of roads are in the 20-30 % probability area, with a further 11 km plus the Baita delle Guide hut in the 10-20 % probability area. A total of 112 km of roads, 14 buildings, 14 km of ski trails, 6 ski lifts and the Funivia dell'Etna cable car are in the 1-10 % probability area.

Pedestrian evacuation analysis
The USGS Pedestrian Evacuation Analyst (PEA) tool (Jones et al., 2014) was used to estimate how long it would take for 10 people at the summit to descend to a safe area for each of the hazard scenarios. The main inputs are: • Digital elevation model of the area (90 m resolution SRTM data).
• Hazard area, defined here as the hazard zone described in Section 4.
• Safe zone, defined as the area outside the hazard area.
• Landcover within the hazard area. Each landcover type is assigned a speed conservation value (SCV) which 15 compares the ease of walking on the various surfaces. Values vary from 0 (building) to 1 (road). All roads, paths and tracks were assigned a value of 1 and ski trails were not included as they are likely to be too steep to walk down. Moreover, we assumed that most visitors to the summit area will be within a maximum distance (buffer) from a path or track. The 'buffer' was set to 300 m, but to investigate sensitivity to the maximum distance, the OES high MER scenario was also run with a buffer of 500 m. As there is no detailed information on the terrain around 20 each path and track, but it is likely to be slower to walk on than a road, an SCV of 0.65 was assigned.
• Walking speed, taken as 3.3 km h -1 , which is defined as a slow walking speed within the PEA tool. Figure 4 shows evacuation times to reach the safe zone for each scenario, assuming people are a maximum of 300 m from any path. For the OEShigh MER, people near to the craters who are furthest from the path will take more than five hours (313 minutes) to reach the safe zone. The maximum evacuation time for the OESlow MER is 30 minutes and for the ERS, it is 25 236 minutes (about 4 hours). Sensitivity to the buffer size is low when increased to 500 m for the OEShigh MER, as the maximum time to reach the safe zone increased by only 1 minute (Fig. S12).
This analysis shows that for large events, people near the summit would, in many cases, be several hours from safety. In addition, given that even relatively minor impact to the head can cause concussion, escape can be difficult (Baxter and Gresham, 1997). Hence possible locations for one and two shelters were selected and the analysis was rerun to investigate how 30 that would reduce the time taken to reach a safe location (considering the shelters as additional safe zones). For one shelter, the location was chosen to be within the hazard zone for the OESlow MER, so that it could be used for the whole range of expected events. For two shelters, one was chosen as the top station of the Funivia dell'Etna cable car and the second shelter was located towards the north. Figure 5 shows that, for the ERS, provision of one shelter reduced the maximum evacuation time to 176 minutes, with only a minor further reduction (18 minutes) for two shelters. For the OEShigh MER, the maximum evacuation time was reduced to just under 4 hours (233 minutes) when one shelter is provided and to 199 minutes with two 5 shelters (Fig. S13). Increasing the buffer zone around footpaths to 500 m, evacuation times increased to 238 and 207 minutes respectively (Fig. S12). For the OESlow MER, adding a shelter did not reduce the maximum evacuation time below 30 minutes (Fig. S14).

Risk assessment 10
Large-clast fallout from plumes generated by the frequent lava fountains at Mount Etna poses a substantial risk to people and infrastructure (e.g., Andronico et al., 2015;De Beni et al., 2015). It is therefore important to identify the area likely to be impacted and to understand how long it would take people to evacuate to a safe area. For large eruptions, an area of up to 130 km 2 is in the hazard zone; roads have a probability of impact of up to 40 % and the Funivia dell'Etna cable car is also at risk.
The area affected depends on the eruptive vent, with lava fountains at Voragine, Bocca Nuova and NEC resulting in a hazard 15 zone shifted further north and impacting fewer roads and buildings, compared to events from SEC and NSEC. It is important to bear in mind that even though the majority of lava fountains over the past 5 years have occurred from NSEC, more than 80% of the eruptions occurring at Voragine in the past 20 years have been characterized by large plumes (>10 km a.s.l) (Andronico et al., 2015;Bonaccorso and Calvari, 2017;Calvari and Pinkerton, 2002;Vulpiani et al., 2016) (see also Table   S1). The probabilistic analysis took account of the range of MER observed in the recent lava fountains at Mount Etna (detailed 20 in Table S1), but it cannot be excluded that a future event could have a higher MER. However, our analysis has identified the smallest MER that could produce hazardous impact from 5 cm clasts (i.e., 2.5 x 10 5 kg s -1 ), as the hazardous clast fallout from lava fountains smaller than the One Eruption Scenariolow MER will only affect the area very proximal (≤2 km) to the eruptive vent.
As well as the hazard from large clast fallout, it is also important to consider impact from ballistic projectiles and hazard from 25 tephra fallout which may all occur simultaneously during an eruption. Probabilistic modelling based on the large explosive eruption at Mount Etna on 5 January 1990 showed that tephra accumulations over 200 kg m -2 occurred up to 10 km from the eruptive vent . The area around the Funivia dell'Etna cable car had a 10-20 % probability of tephra deposit density ≥100 kg m -2 and this is the same area that had a 1-10 % probability of fallout of 5 cm clasts in the current study.
Ballistic projectiles ejected from the vent could also pose a hazard on the paths very close to the summit, as happened on the 30 Tongariro Alpine Crossing hiking trail in New Zealand in August 2012 (Fitzgerald et al., 2014). Modelling at La Fossa, Vulcano in Italy also indicated a range of around 3 km for projectiles with sufficient impact energy to cause injury (Biass et al., 2016a). Large ballistic projectiles have also been observed proximal (<1 km) to the vent at Mount Etna (e.g. Calvari & Pinkerton, 2002).
In order to quantify the exposure of people to hazardous clast fallout, further work is required to characterize visitor numbers and behaviour. For example, tourists are likely to stay near the paths and tracks, while hikers may walk further from the paths.
In addition, many scientists visit the summit area, although they are likely to be in contact with colleagues who could warn 5 them of ongoing volcanic activity.

Emergency management
The PEA tool was run using several assumptions, which require more detailed analysis to confirm the results. The most sensitive assumptions are: • Paths and tracks are the fastest routes down from the summit. In most cases this will be true, and people unfamiliar 10 with the area are likely to retrace their steps to descend. However, there may be routes that are faster than using the paths, particularly where slopes are gentle and/or are covered in loose tephra. If these were to be considered as evacuation routes they would, of course, need to be clearly identified to ensure people descending did not get lost.
In addition, this study did not consider pedestrian evacuation during the months when the area is covered in snow.
During the winter more people may be 'off piste' in areas with no paths, resulting in different evacuation routes 15 compared to the paths used during the summer.
• The same buffer zone was applied around all paths, tracks and roads and the assumption of a constant buffer zone width can be considered as a worst case. Moreover, the landcover and associated walking speed was assumed to be constant in this zone. In reality, once away from paths the land cover will be variable, and walking speeds could vary considerably between ash, lava and densely vegetated areas. 20 • The analysis considered people walking slowly, but as speeds could vary, the results have therefore identified maximum times to walk to a safe zone. Moreover, visibility may be limited by ash fallout or sudden changes in weather conditions (e.g. dense fog formation, very frequent at Etna high elevations). Therefore, values need to be assessed empirically.
• Evacuation from the summit was assumed to be only on foot. However, vehicles may also be available, particularly 25 in the southern sector.
The analysis of evacuation times indicates that, for a large eruption, walking out to a safe area could take several hours, and given that the paroxysmal phase of an eruption often only lasts around an hour (Table S1), provision of short-term emergency shelters near the summit could limit potential casualties. The results for the ERS show that shelters could reduce evacuation times by more than an hour, and further investigation is needed to identify optimal locations. The shelters would have to 30 withstand impact energies of around 46 J, identified as the highest kinetic energy of clasts on impact. Data on likely numbers of visitors at the summit at any time, for example from numbers of people using the cable car, would also be required, in order to identify the size of shelters needed. Exercises to evaluate the evacuation routes and times would also be needed. It is important to bear in mind that access to the summit is restricted during orange/red alerts issued by Civil Protection authorities, and hence the expected number of tourists on the summit may be significantly reduced. However, some eruptions (e.g. 23 November 2013) do not give enough warning for the orange/red alert to be issued in time.

Conclusions
The hazard associated with the fallout of large clasts from the convective portion of a volcanic plume has been often overlooked 5 even though field evidences clearly show that it is a common feature of small to high intensity eruptions. As an example, in this study the hazard associated with sedimentation of hazardous (>5 cm) clasts from lava-fountain fed plumes at Mount Etna was assessed using a new dedicated plume sedimentation model. The model was calibrated using field and wind data for the largest eruption to date for a lava fountain at Mount Etna, and a probabilistic hazard assessment was then carried out using three scenarios. Hazard scenarios were based on events with high and low MER plus one scenario which sampled both a range 10 of eruptive parameters (e.g., MER, particle density) and wind conditions. The area at risk of impact from sedimentation of hazardous clasts (>5 cm in diameter) was mapped for each scenario, the exposed infrastructure was quantified and pedestrian evacuation times from the summit were investigated. From the hazard analysis of NSEC we can conclude that: 1) For the One Eruption Scenariohigh MER, the hazard zone (area with probability of impact ≥1 %) covered an area of 129 km 2 and extended up to 8 km from the vent. Exposed infrastructure for an eruption from NSEC included some 274 15 km of paths and 118 buildings, while for an eruption from Voragine 235 km of paths and 104 buildings were exposed.
2) For the One Eruption Scenariolow MER, the hazard zone covered 5 km 2 and extended up to 1.4 km from the vent.
Exposed infrastructure included 6 km of paths and only one building (a mountain hut).
3) For the Eruption Range Scenario, the hazard zone covered 72 km 2 and extended up to 6.5 km from the vent. Exposed infrastructure included some 125 km of paths and 15 buildings, including mountain huts, an observatory and a refuge. 20 4) The maximum evacuation time for people walking down from the summit was just under 5 hours for the One Eruption Scenariohigh MER, almost 4 hours for the Eruption Range Scenario and 30 minutes for the One Eruption Scenariolow MER. 5) For large eruptions, provision of one or two shelters could reduce maximum evacuation times by up to 2 hours. Impact of an eruption from Voragine, Bocca Nuova or NEC is of similar magnitude but with the affected area slightly 25 shifted to the north (Table 3 and Fig. S11). Future work is needed to confirm how land cover (and hence likely walking speed) varies across the area and to understand how evacuation routes change in winter, when paths may be covered in snow.
The proposed approach could also help in locating the shelters; their structure and capacity should be decided by the Civil Protection authorities, based on information provided by the private companies that manage tourist excursions to the summit, i.e. ski lifts, four-wheel drive vehicles, and hiking. A communication strategy would also be important to ensure that shelters 30 do not encourage reckless behaviour, with people feeling safer about going into the hazard zone when the paroxysmal phase of an eruption has started. The model has already been implemented within the operational platform of INGV-OE for rapid daily hazard assessment for Civil Protection use. The proposed methodology can be easily applied to other volcanoes and results obtained for Mount Etna show how the assessment of the hazard associated with hazardous clasts (>5 cm) from eruptive plumes should be accurately characterized, in particular for all those volcanoes that are a popular destination for tourists and where visitors can reach the summit areas.

Data availability 5
Most data is made available in main tables and supplementary material. Additional data is available upon request, based on a collaborative agreement.

Appendices Appendix A Field survey analysis: median versus the average of the 5 largest clasts
A detailed field survey was carried out by Russo (2016)  where flatness, f = S/I and elongation, e = I/L (Bagheri et al., 2015). The Stokes drag coefficient, kS, (for particles falling in random orientation) and the Newtonian drag coefficient, kN, (for particles falling in a gas) were then calculated for use in the 20 hazard analysis (Bagheri and Bonadonna, 2016b): At individual field locations, median values were found to be more stable than values using the average of the largest 5 clasts, confirming the results of Bonadonna et al. (2013) (Table A1); however, over the whole sampling area both methods produced 25 widely varying values of crosswind and downwind ranges ( Fig. A1 and Table A2) indicating that the use of the median values does not improve the stability of isopleth maps at the scale of the deposit. In addition, Fig. A2 shows that modelled contours contain the median values but more closely match the values calculated using the average of the 5 largest clasts. Based on this analysis, we conclude that the use of the average of the 5 largest clasts for the comparison of field data with clast sedimentation modelling (e.g. Burden et al., 2011;Carey and Sparks, 1986;Rossi et al., 2019) is the most appropriate and induces a variability 30 stable at the level of the outcrop).

Median
Average of the

Competing interests
The authors declare that they have no conflict of interest.

Acknowledgements
The authors are grateful to Mauro Rosi and Peter Baxter for discussion on the potential impact of large clasts from volcanic 10 plumes. Wim Degruyter is thanked for discussion on plume modelling, while Sebastien Biass is thanked for assistance for the wind analysis.  Table 2 Area within each probability category in the hazard zone (in km 2 ) for One Eruption Scenariohigh mass eruption rate, One Eruption Scenariolow mass eruption rate and Eruption Range Scenario. Hazard zone is the area with probability of impact from 5 cm clast ≥ 1 %.   Table 3 Infrastructure within the hazard zone for One Eruption Scenariohigh mass eruption rate (from New South East Crater (NSEC) and Voragine), One Eruption Scenariolow mass eruption rate (from NSEC) and Eruption Range Scenario (from NSEC). Hazard zone is the area with probability of impact from 5 cm clast ≥ 1 %.