Introduction

In this work, we present and share the data and results of the May 2022 Stromboli campaign which consist of 1.6-cm resolution orthomosaic, a 10-cm resolution DSM, vectorial data of the detected clasts, and the percentage map of ground covered by the clasts.

The island of Stromboli is the 924-m-high emerged portion of a ~ 3000-m-high active stratovolcano located in the Tyrrhenian Sea, off the southern coast of Italy (Fig. 1). It is in a persistent state of activity, consisting of ordinary low intensity explosions that occur every 10–20 min. During these explosions, jets of gas, ash, and bombs are launched at heights up to 300–400 m and they can reach 200–250 m from the vents (Chouet et al. 1974; Patrick et al. 2007; Ripepe et al. 2008). Stromboli daily activity is occasionally interrupted by sudden, more violent explosions that range from “major explosions” to “paroxysms” (Barberi et al. 1993; Rosi et al. 2013; Bevilacqua et al. 2020). During major explosions, the bombs can reach distances of about 1 km from the craters (Bertagnini et al. 1999; Coltelli et al. 2000; Andronico and Pistolesi 2010; Giudicepietro et al. 2019), while during paroxysms, the ejected ballistics can reach even greater distances and impact on populated areas, i.e., 1.5 to 2.5 km, down to the coast (Rosi et al. 2006; Calvari et al. 2006; Pistolesi et al. 2008; Andronico et al. 2013).

Fig. 1
figure 1

Geographical setting of Stromboli Island by using the 2012 LiDAR DEM (Di Traglia et al. 2020; Nannipieri et al. 2023). The orange area of frame a and the white line of frame b represent the area covered by the UAS May 2022 survey of this work. The black and white line represents the hiking trail from Ginostra. Supporting Material S1 shows a 3D view of the survey area

Full size image

In May 2022, we conducted an Unmanned Aerial System (UAS) photogrammetric campaign over a portion of the W flank of Stromboli Island, aimed at mapping the areal percentage of ground covered by the volcanic clasts during the paroxysm of July 3, 2019 (Fig. 1). Despite almost 3 years having passed since the paroxysm, the large size of the ballistic projectiles that traveled for more than 850 m from the craters, and the relatively slow post-fire regrowth of the Mediterranean brush on the rocky ground, enabled the preservation of the clasts and their identification by image processing.

This study builds on the information collected by the previous field observations on the distribution of the ballistic projectiles (Giordano and De Astis 2021; Andronico et al. 2021; Pichavant et al. 2022). However, our UAS campaign provides a systematic mapping of thousands identifiable clasts, dispersed on a rough terrain up to hundreds of meters from the hiking trails. In fact, we could describe the progressive transition from scattered clasts to an almost continuous ground cover. Our approach enabled statistical analysis and uncertainty quantification that were impossible otherwise. In addition, this study integrates a previous UAS campaign made on a different area on the East flank of the volcanic edifice, not overlapping with our domain of acquisition and characterized by a less distant dispersion (Bisson et al. 2023).

Geological setting

During the summer of 2019, two paroxysms occurred at Stromboli. The first on July 3rd and the second on August 28th, 54 days apart. Both paroxysms erupted abundant bombs, lapilli, ash, and they also generated pyroclastic density currents in the Sciara del Fuoco, a large collapse scar on the NW flank of the volcano (Fig. 1). In particular, during the July 3rd paroxysm, some of the ejected ballistics on the W side of the Island impacted at elevations below 250 m and the bomb fallout ignited a wildfire that burned for days and caused the death of one tourist (Turchi et al. 2020).

The analysis of images and videos recorded during the onset of the paroxysm of July 3, 2019, showed that the initial explosive ejecta were dominantly directed towards W, with visible “fingers” associated with large ballistics (Giordano and De Astis 2021). The eruptive column rose in 10 s over the first km above the vent and, after the convective uprise, produced an umbrella cloud attaining 8.4-km elevation and spreading towards SW.

The eruption produced a large fall of ballistic blocks and an almost continuous spatter deposits on the volcano summit extending down to 500 m. a.s.l on the western flank, i.e., up to about 750–800 m from the craters (Andronico et al. 2021; Pichavant et al. 2022). The isopleths of ballistics were asymmetrical with a westerly dispersal axis, in agreement with the images and videos of the initial explosion (Giordano and De Astis 2021). Scattered ballistic bombs were collected down to 100–250-m elevation on the western lower flanks, which were also affected by the plume fallout (Pichavant et al. 2022). At 100 m a.s.l., Andronico et al. (2021) estimated an average of 1–4 pumiceous bombs of 20–40 cm size per decameter square.

Material and methods

UAS campaign

In May 2022, we carried out an Unmanned Aerial System (UAS) campaign on the W flank of Stromboli volcano over an area heavily affected by the July 3, 2019, ballistic fall. We conducted a survey of 5 flights using a DJI Phantom 4 V2 Pro, and we acquired 949 photographs at 50–55-m mean flight elevation above ground level, from a field camp located at about 150 m a.s.l. Supporting Material S1 summarizes the flight trajectories and the camera locations.

Figure 1 shows the total extension of the imaged area, which consisted of 0.18 km2 of the W sector of the Island, from less than 150 m to over 450 m elevation a.s.l. The surveyed area was rectangular-shaped, WSW × NNE oriented, and bounded towards N by the southern edge of Sciara the Fuoco. It had a WSW length of 630 m and a NNE width of about 300 m. This area is only a portion of the entire ballistic field, in the direction of the maximum observed ballistic range and focusing on the transition from scattered clasts to an almost continuous ground cover (Giordano and De Astis 2021).

The photographs acquired during the UAS surveys were used for generating the DSMs and orthomosaic of the area through Structure from Motion (SfM) and Multi-view Stereo Matching (MSM) methods (Favalli et al. 2012, 2018; James et al. 2020). We processed the photos using the Agisoft Metashape Professional version 1.6.2. software, which implements SfM and MSM algorithms. In Supporting Material S1, we summarize the differences between the UAS-derived DSM and the 2012 1-m resolution digital elevation model (DEM) obtained from an airborne LiDAR technique. The root mean square error is equal to 0.48 m and symmetrically distributed around zero.

Field observations

We supported the UAS survey by simultaneous field observations, during which we collected the position of a set of several clasts with a low-accuracy GPS (ca. 2–3-m error), summarized in Fig. 2. In particular, we acquired ca. 150 GPS points along and near the hiking trail of Ginostra, up to 440–450 m a.s.l., while collecting a dataset of photos and measurements of all the observed clasts. Because of the very rough terrain conditions, all the clasts mapped in the field were along the trail or up to 30 m from it, in a few places.

Fig. 2
figure 2

a Overview of the ground survey along the Ginostra trail (yellow dashed line). The red dots are GPS acquisitions. We selected fourteen example sites (A-N) where we measured the diameter of the larger clasts. The UAS-based orthomosaic, the 2012 LiDAR DEM and its elevation isolines are included in the background for reference. In b, c, we show the diameter of the measured clasts at sites (A-N), as a function of b the distance from the craters and c the elevation a.s.l. The measurement error is about 5–10 cm for the clasts below 1-m diameter, and about 20–25 cm for those above

Full size image

We selected fourteen example sites where we measured the diameter of the larger clasts. The measured diameters spanned from 0.10 to 0.15 m to over 2 m, and they generally increased by reducing the distance from the craters, although with large fluctuations (see Fig. 2b, c). For example, a large dark-coloured spatter bomb with a diameter above 2 m was located in site G (see Fig. 3), at 370 m a.s.l. and quite far from other similarly large clasts. We also observed smaller clasts, but they may have been fragments of largest projectiles, or could have been easily transported in the plume for a few seconds while falling, therefore having an uncertain characterization as ballistics (e.g., Osman et al. 2019).

Fig. 3
figure 3

Photos of the example clasts in sites A–J of Fig. 2, i.e., collected along the Ginostra trail from 250 m to 405 m a.s.l. The foot included for reference is about 25 cm long. In each photo, we show the outline of the clast (in red), the measure of diameter, the elevation a.s.l. and the distance from the craters

Full size image

Figures 3 and 4 show a selection of photos at the fourteen sites, focusing on variably vesicular juvenile clasts. Specifically, Fig. 3 summarizes the clasts up to 400–405 m a.s.l., transitioning from scattered items to the first discontinuous patches, while Fig. 4 focuses on the sites from 410 to 440 m a.s.l., where the discontinuous patches became common and some of the adjacent patches were connected without interruption.

Fig. 4
figure 4

Photos of the example clasts in sites K-M of Fig. 2, i.e., collected along the Ginostra trail from 410 m to 440 m a.s.l.. The foot included for reference is about 25 cm long. In each photo, we show the outline of the clast (in red), the measure of diameter, the elevation a.s.l., and the distance from the craters

Full size image

The clasts ranged from highly vesicular mostly light-coloured pumice (in site D), to moderately vesicular and variably mingled items (e.g., in site N), to more dense darker scoriae (e.g., in site G). They had irregular shapes and they were often broken in pieces or stretched significantly, or deformed in a cow-pie shape. We also identified older clasts generated by the historical paroxysms, e.g., in 1930, especially at low elevation where the recent clasts were less common. However, the clasts of July 3, 2019, were easily distinguishable from the historical products, which were significantly more weathered and partially buried in the ground. The robustness of our mapping against this uncertainty source, and others, is further detailed in the Discussion section.

Clasts identification and mapping

By using GIS platforms (Qgis 3.22 and ArcMap 10.4.1), we visually analyzed the orthomosaic to identify and map all the visible clasts in the surveyed area. In particular, we partitioned the orthomosaic in five subsets of similar extent and then visually scanned them. We individually worked on each part of the domain and then repeated the process after switching the parts between us. Every subset was independently scanned by at least two people. Also, we carefully examined the original dataset of UAS-acquired photos, eventually searching for additional views of the identified items, i.e., not only azimuthal. This “brute-force” approach was possible because the surveyed area was relatively small, and it might become a much heavier work for a significantly greater extent.

More specifically, we produced a dataset of 2813 polygons (outlines of mapped ballistics), which were consistent with the ground observations of the products of July 3, 2019. A number of items had an uncertain characterization, for example because they could be older clasts, or they were too covered by the Mediterranean brush. Therefore we classified as uncertain 329 polygons, i.e., 12% of the total. In the statistical analysis described in the “Results” section, we evaluated how the results on the areal percentage of ground cover could change by including these uncertain items or not.

Figure 5 shows an overview of the upper portion of the surveyed area, and then zooms in six different locations: Fig. 5a and f are examples of scattered clasts of various sizes found at low elevation; Fig. 5b is the intermediate zone where we found the first over 2-m sized clast; Fig. 5c, d, and e are the uppermost zones where patches of clasts were evident, and several adjacent patches were connected. We visited locations in Fig. 5a, b, and c during our ground survey, while those in Fig. 5d, e, and f were hundreds of meters from the hiking trail and they would have been very difficult to map without using the UAS.

Fig. 5
figure 5

Examples of the clast identification in the high-resolution orthomosaic. Plots a–f zoom in different locations of the surveyed area (g), as summarized on top. Red polygons mark the clasts of July 3, 2019, while orange polygons mark the uncertain clasts, possibly older. Supporting Material S4 shows the images without polygons. Plots a–e are reported at the same scale, while f is shown at a slightly lower scale. The 2012 LiDAR DEM is shown in background of g

Full size image

Results

Spatial distribution of clast centroids and of clast diameter

In Fig. 6, we display the spatial distribution of the clast centroids, as well as the spatial distribution of the clasts equivalent diameter, i.e., the diameter of a circle with the same area of the clast. The uncertain clasts are highlighted in blue. In particular, Fig. 6a, c, and e focus on the radial distributions, and Fig. 6b, d, and f on the angular distributions of the mapped clasts, with respect to the source, i.e., distance and directionality. For calculating distances and defining polar coordinates, we assumed a source located at the South crater (Andronico et al. 2021; Bisson et al. 2023), i.e., UTM coordinates 518277 E, 4293871 N. This analysis only considers a rectangular subdomain in polar coordinates (i.e., a circular sector intersected to a circular crown) between 260° and 271° North, and over 875 m from the source. In fact, the edges of the ballistic field were caught inside the mapped domain only towards West. The subdomain contains 1840 clasts, 65% of the total. In Supporting Material S2, we show that this subdomain provides results similar to those obtained by considering the 2813 clasts over whole domain.

Fig. 6
figure 6

a, b Spatial distribution of the clast centroids in polar coordinates. Dashed lines mark the subdomain considered in c–f: over 875 m from the source and between 260° and 271° North. c, d Radial and angular distribution of the clast equivalent diameters, i.e., the diameters of a circle with the same area of the clast. The 5th, 50th, and 95th percentile values are reported, based on the statistics on moving windows of 50 m and 1°, respectively. e, f Radial and angular density of clasts. In a–d, the red dots are the identified clasts, the blue dots highlight the uncertain clasts. Supporting Material S2 shows the same plots over the entire mapped domain

Full size image

Figure 6a and b show the spatial map in polar coordinates, used as a reference for the radial and angular distributions of the clasts. Figure 6c and d describe the spatial distribution of the diameters, which is also consistent with the 19 field measurements reported in Fig. 2b, but enables the statistical analysis of ca. 100 times more samples. We note that the UAS dataset contains a significant number of smaller clasts that had not been considered in the field measurement examples, mostly focused on the largest clasts. The 5th, 50th, and 95th percentile values of diameters are 0.12, 0.40, and 0.94 m, respectively. The mean diameter is 0.45 m.

Figure 6c and d show also the 5th, 50th, and 95th percentile values of the diameters, based on a moving window of ± 25 m and of ± 0.5°, respectively. Any statistics of less than 20 samples is discarded from the plot. In Fig. 6c, the 95th percentile values show a flat trend at ca. 0.9 m, from 875 m to 975 m radial distance, followed by a local maximum, i.e., 1.1 m, at about 1025 m from the source and then a decrease. Median values show similar trends, but at about three times smaller scale, e.g., the first flat interval is between 0.3- and 0.4-m diameter. The 5th percentile values are relatively flat and close to the minimum size of mapped clasts, i.e., between 0.05 and 0.1 m. In Fig. 6d, the 95th percentile values show a decreasing trend from left to right, i.e., by approaching Sciara del Fuoco, from oscillating values between 0.9 and 1.1 m to about 0.7 m. The median also shows a similar trend, but at half scale; it starts between 0.4 and 0.6 m and decreases to about 0.3 m. The 5th percentile values are relatively flat overall, but show a minor decreasing trend too, clockwise.

Figure 6e,f display the total count of the clasts as a function of the radial distance and of the azimuth angle with respect to the source, based on the same moving windows of Fig. 6c and d. In Fig. 6e, the maximum count is about 23 clasts/m at 900 m radial distance from the source, and then linearly decreases of ten times at 1025-m distance, to less than 2.5 clasts/m. The count then remains relatively flat and oscillates between 0 and 2 clasts/m. In Fig. 6f, there are two local maxima in 265° and 269° directions, of about 230 and 260 clasts/degree, respectively. Between them, there is a minimum count of about 55 clasts/degree.

Areal percentage of ground covered by clasts

We analyzed the mapped polygons by rasterizing their distribution at 0.1-m cell size and assuming each cell equal to 1 if contained clasts, or 0 otherwise. We treated the uncertain items by weighting their cells 0.5. We processed the resulting 3443 × 3637 rectangular array by ad hoc R scripts for kernel density estimation. In particular, we first rescaled the data to 1-m cell size by evaluating the percentage of clasts cover in each 1-m cell. Then, we run a two-dimensional Gaussian kernel over the resulting 384 × 384 square array (Connor et al. 2012; Bevilacqua et al. 2015; Mazzarini et al. 2016).

A Gaussian kernel function is completely described by its mean (or drift), μ, that we assumed null, and by its covariance (or bandwidth) matrix M (Bevilacqua et al. 2017, 2021; Tadini et al. 2017). In our case, the kernel is isotropic and therefore M = σ2Id, where σ is the standard deviation of the Gaussian along any direction, and Id is the identity matrix in 2D.

Figure 7a shows the results of applying a kernel with fixed σ = 10 m smoothing coefficient. The map ranges up to 7–9% of areal percentage at about 450 m a.s.l., i.e., ca. 875-m radial distance from the source. The density values over 0.1% are concentrated above 350 m a.s.l., i.e., ca. 1025-m radial distance, except for a few isolated zones between 0.1 and 0.5% areal percentage over 270 m a.s.l., i.e., 1200-m radial distance. This value of σ was selected arbitrarily and filters out the short-scale effects of impact clusters. However, we tested various other values and also a variable kernel that produced similar results.

Fig. 7
figure 7

Spatial density of the clasts obtained by Gaussian kernel estimators. In a, we assume σ = 10 m, while in b a variable σ. Different colours correspond to the areal percentage of ground cover by the clasts. We marked with a black and yellow line where the boundary of the mapped domain cuts the class distribution, and may generate boundary effects. The larger dots are the GPS-mapped ballistics and the smaller dots are the UAS-mapped clasts. The UAS-based orthomosaic and the 2012 LiDAR DEM and its isolines are shown in background

Full size image

Figure 7b describes the results obtained by applying such a variable kernel. In particular, we used an empirical bootstrap strategy that plugged-in a variable σ-1 equal to the square root of the average density in a neighborhood (x ± 10 m, y ± 10 m) of the current location (x,y). This approach is equivalent to reducing the kernel bandwidth where the identified clasts were clustered and increasing the bandwidth where they were relatively scattered. The results shown in Fig. 7b are similar to Fig. 7a for the intermediate density values, i.e., between 0.5 and 3%, but the smoothing is reduced on the higher density values. Therefore, the maximum areal percentage reaches 12%.

Uncertainty quantification on the clast distribution

Figure 8a and b show the areal percentage map of ground cover obtained by applying a kernel with fixed smoothing coefficients σ = 2.5 m and 5 m, respectively. The two maps differ from those in Fig. 7 because they more closely describe the inhomogeneous distribution of the clasts, instead of smoothing it. The density values reach 10% and 16%, respectively, bracketing the 12% value obtained under the assumption of a variable kernel function. In particular, the spatial location of the highest observed density values is again at 450 m a.s.l., i.e. at the boundary of our mapped domain, ca. 850 m from the source.

Fig. 8
figure 8

Alternative estimations of the clast spatial density obtained by fine-grain Gaussian kernels. In a, we assume σ = 2.5 m, while in b σ = 5 m. Different colours correspond to the areal percentage of ground cover by the clasts. We marked with a black and yellow line where the boundary of the mapped domain cuts the clast distribution and may generate boundary effects. The larger dots are the GPS-mapped ballistics and the smaller dots are the UAS mapped clasts. The UAS-based orthomosaic and the 2012 LiDAR DEM and its isolines are shown in background

Full size image

Figure 9 shows an uncertainty analysis by plotting the statistics of areal percentage as a function of the distance d from the source. In particular, we calculated mean and percentiles of the density values along the arcs, i.e., azimuth from the source. Like in Fig. 6, in this summary, we consider the subdomain between 260° and 271°, and further than 875 m, which is rectangular in polar coordinates. Supporting Material S2 shows the results obtained over the entire mapped domain.

Fig. 9
figure 9

Statistical analysis of the clast spatial density, as a function of the distance from the source. Plot a shows the mean, the median, the 5th and 95th percentile, and the maximum value of the areal percentage of ground cover by the clasts, by assuming a variable σ (Fig. 6b). Plot b, c compare the mean and the maximum clast density by assuming a variable σ, and σ = 2.5 m, 5 m, 10 m (Figs. 6 and 7). We consider the subdomain over 875 m from the source and between 260° and 271° North; Supporting Material S2 shows the same plots over the entire mapped domain

Full size image

In Fig. 9a, we show the mean, the median, the 5th and 95th percentile, and the maximum value from the map in Fig. 7b. This describes the distribution along the arcs, under the assumption of a variable kernel. The median is lower than the mean, indicating a skewed distribution with a tail of low density values, for every distance evaluated.

In Fig. 9b, we compare the mean values from the maps Figs. 7 and 8. In this way, we show that the mean results obtained by using fixed kernels are consistent and reaching 3.5–4.0%. We note that the smaller σ = 2.5 m produces a few high-frequency oscillations that are smoothed in the other cases.

In Fig. 9c, we display the maximum values from the maps in Figs. 7 and 8. Between 875 and 940 m, the variable kernel density results are intermediate to those related to σ = 2.5 m and σ = 5 m. Between 940 m and 1000 m, they are intermediate to those related to σ = 5 m and σ = 10 m. If d > 1000 m, the maximum density values are lower than those related to σ = 10 m. High-frequency oscillations that affect the results with σ = 2.5 m are particularly evident, and they have periods of 12–20 m.

In Fig. 10, we compare the mean and the maximum effects of including all the uncertain items or excluding all them, instead of weight them 0.5. These effects are negligible if d > 950 m, but can produce an uncertainty of about ± 10% on the average density values, and up to ± 15% on the maximum density values. We note that our identification limits may have meant underrecording of the smaller and light-coloured clasts, i.e., 10–15 cm of diameter.

Fig. 10
figure 10

Statistical analysis of the clast spatial density, as a function of the distance from the source. Plot a compares the mean clast density by including and excluding all the uncertain clasts (Fig. 5), and plot b compares the maximum clast density. We consider the subdomain over 875 m from the source and between 260° and 271° North; Supporting Material S2 shows the same plots over the entire mapped domain

Full size image

Finally, Fig. 11 shows the effect of applying an areal buffer around the mapped clasts. In fact, hazard effects of the projectile and any fragments released at the impact are not limited to the area of the clast. The buffer has a strong effect on the estimates of areal cover, and a 10-cm buffer almost doubles both the mean and the maximum density values. Larger buffers of 30 cm and 50 cm produce mean values four and six times greater than the density not assuming any buffer.

Fig. 11
figure 11

Statistical analysis of the clast spatial density, as a function of the distance from the source. Plot a compares the mean clast density by applying an areal buffer around the mapped clasts, and plot b compares the maximum clast density. We consider the subdomain over 875 m from the source and between 260° and 271° North; Supporting Material S2 shows the same plots over the entire mapped domain

Full size image

Discussion

The results describing areal percentage of ground cover by volcanic clasts are affected by several sources of uncertainty. Firstly, the attribution of all the mapped clasts to the paroxysm of July 3rd is based on field evidences that are only related to the region investigated during the GPS campaign. Based on the literature sources, the surveyed area was not significantly affected by the paroxysms of May 5, 2003, March 15, 2007, and August 28, 2019. However, in 1916, 1930, and 1959, at least, other paroxysms affected portions of the surveyed area (Ponte 1921; Rittmann 1931; Cavallaro 1962). Nevertheless, 60 or 90 years old clasts are distinguishable from three years old clasts, especially if the new clasts are deposited on top of the old deposit. The possible clast number overestimation due to other explosions acts against to the likely underestimation due to weathering and breakdown of the clasts, as well as the vegetation regrowth.

Although our pixel resolution is centimetric, the identification of the boundary of the clasts required several pixels. Therefore, in the orthomosaic, we were able to map only the clasts with a diameter above 0.05–0.1 m. During the GPS survey below 250 m a.s.l., we identified a few relatively small scattered pumice clasts, i.e., about 0.1-m diameter, which were impossible to map in the orthomosaic (see Fig. 2a and Fig. 3a). In fact, colour and texture of the smaller clasts, i.e., below 10–15 cm, affected their identification, with darker scoriaceous and more fluidal clasts being easier to identify than light-coloured pumice fragments. Therefore, our UAS-based density estimates go to zero at about 270 m a.s.l. We note that Andronico et al. (2021) estimated 1–4 bombs of 0.2–0.4-m diameter per decameter square at about 100 m a.s.l., i.e., ca. 1600 m from the source. By considering that a clast of 0.2 m covers an area of about 0.03 m2 and a clast of 0.4 m an area of 0.13 m2, these values correspond to a mean ground cover percentage between 0.03 and 0.5%. However, these values may represent peak values in a relatively limited area and not the average density at that distance.

As expected, the areal density of clasts decreases with increasing distance from the vent; however, the geometry of the affected zones is often dependent on the specific case (Kilgour et al. 2010; Gurioli et al. 2013; Fitzgerald et al. 2014). Physically realistic 3D models should include the drag of the surrounding gas on the particles, their in-flight deformation, rotation, temperature, and collisions, which can all have significant effects on their trajectory (de’Michieli Vitturi et al. 2010; Suzuki et al. 2013; Taddeucci et al. 2017). These models need detailed assumptions regarding the ejection velocity, the mass and shape of the particles, their size distribution, and the physical properties of the explosion, which are beyond the scope of this study. Supporting Material S3 describes the ideal clasts distribution as a function of the distance from the source, based on isotropic initial velocities and parabolic trajectories. Such a simplistic model is not able to replicate our observations, but can provide insights on some possible reasons for the observed local maxima and oscillations in the clast distribution, besides the nontrivial effects of anisotropies in the source conditions. In fact, spatial density changes across the area though could be related to multiple eruption jets that might help to explain the two density peaks in different azimuths. Topographic shielding and vent geometry could have produced similar effects as well.

Bisson et al. (2023) provided the clast mapping of July 3, 2019, over a 0.41 km2 area on the E flank of Stromboli, and a spatial resolution of 8 cm, i.e., more than four times lower than the 1.6-cm resolution in our survey. The study has a minimum detectable area of 0.03 m2 for the clasts, which is about 0.2 m of equivalent diameter, and they counted a total number of ca. 150,000 clasts, i.e., 65 times more than in our survey. The authors reported a boundary line beyond which they did not detect any spatter clast and enveloped an affected area between a minimum of 250-m radial distance and a maximum of 950 m from the source. This maximum distance is only reached by two lobes directed towards E and SE, respectively, and is 300 m lower than our most distant detected clasts, i.e., 1250 m from the source towards W.

The clast size distribution in Bisson et al. (2023) ranges from 0.2 to 2.4 m equivalent diameter, which is consistent with our observed range of 0.05 to 2 m. They found ca. 50% of all the mapped spatters are below 0.3 m equivalent diameter; in our survey, the median is 0.38 m. In terms of areal percentage of ground cover, Bisson et al. (2023) estimated negligible percentages at more than 700-m radial distance in every direction, i.e., much closer to the source than our entire area of study. At ca. 500 m from the source they recorded similar percentages to the 12% maximum recorded in our survey at 875-m radial distance, i.e., 375 m more distant. Maximum percentage values are recorded less than 400 m from the source, up to ca. 35% coverage. In summary, despite the differences in the resolution of the survey and in the size of the mapped domain, the lower-than-ours spatial density found by Bisson et al. (2023) at the same distance from the source is probably related to the westward directionality of the explosion observed by Giordano and De Astis (2021).

Finally, we note that before our ballistic mapping data can feed into risk calculations, the uncertainty on the clast outline should be considered. By summing along the boundaries of all the clasts, even a 10-cm radial buffer can produce a large increase in the areal percentage of ground cover. Hazardous hot fragments can affect the impact surroundings and, therefore, the areal percentages that we described are not equivalent to the probability of being hit by a projectile if affected by the phenomenon. In fact, shards and fiery drops released by the impact may result in a greater probability of being hit than the estimated ground cover. The values shown in Fig. 11, obtained by applying a variable buffer around the mapped clasts, are possible examples of such increased probabilities.

Conclusions

The presented results represent useful information for hazard assessment and for physical modeling of the phenomenon. In summary:

  • We produced a dataset of 2813 clast polygons outlining the products of July 3, 2019, over a 0.18 km2 wide area on the W flank of Stromboli. We classified as uncertain 329 polygons, i.e., 12% of the total. Few and relatively small, i.e., ca. 10–15 cm, light-coloured pumiceous clasts observed along the trail and below 250 m a.s.l. could not be identified in the aerial photos, thus characterizing our observation limits.

  • We described the spatial distribution of the clast diameters inside a rectangular-shaped subdomain in polar coordinates, containing 65% of the clasts. The size range is consistent with the estimates over the entire mapped domain. The 5th, 50th, and 95th percentile values of diameters are 0.12, 0.40, and 0.94 m, respectively. The mean diameter is 0.45 m.

  • The 95th percentile values of clast diameter are between 0.9 and 1.1 m from 875- to 1025-m radial distance, followed by a decrease. Median values show similar trends, but at about three times smaller scale. The clast diameters also show a slightly decreasing trend from left to right, i.e., by approaching Sciara del Fuoco.

  • The count of clasts/m linearly decreases of about ten times between 900 m and 1025 m from the source, i.e., from ca. 23 to 2.5 clasts/m over a circular sector of 11°. There are two local maxima of clast count in 265° and 269° directions; these variations are not apparently correlated to significant changes in clast size.

  • The map of ground cover based on σ =10 m smoothing coefficient ranges up to 7–9% of areal percentage ca. 875 m from the source. The density values over 0.1% are concentrated closer than 1025 m, except for a few isolated zones between 0.1 and 0.5% coverage ca. 1200 m from the source. The mean results between 260° and 271° are up to 4.0% at 875 m distance from the source.

  • An empirical bootstrap strategy of the smoothing coefficient produces maximum areal percentage of 12%. Smaller smoothing coefficients σ = 2.5 m and 5 m produce maximum density values of 8% and 14%, respectively. High-frequency oscillations affect the results with σ = 2.5 m with periods of 12–20 m.

  • Including all the uncertain clasts or excluding all them produce an uncertainty of about ± 10% on the average density values, and up to ± 15% on the maximum density values. Applying a 10-cm buffer around the mapped clasts almost doubles both the mean and the maximum density values. Larger buffers of 30 cm and 50 cm produce mean and maximum values that are four and six times greater than without assuming any buffer.