Volcano generated tsunami recorded in the near source

Domain: earth_science
Published: 2024-02-27
Editorial outcome: major_revision

Abstract
Volcano sector collapse and pyroclastic density currents are common phenomena on active volcanoes and potentially a fatal source of tsunami waves which constitute a serious hazard for local as well as distant coastal populations. Several examples in recent history, warn us on the urgent need to improve our mitigation counter-actions when tsunamis have volcanic origin. However, instrumental record of tsunami generated by mass movement along a volcano flank are still rare and not well understood yet. Small tsunamis (≤1 m) induced by pyroclastic density currents associated to violent explosions of Stromboli volcano were recorded in near-source conditions (<1.6 km). We show how tsunami waveform remains unaltered regardless of the two orders of variability in the landslide volume and dynamics. This unprecedented record is also providing the lesson to develop unconventional warning strategies necessary when the tsunamigenic source is expected to be very close (<10 minutes) to densely populated coasts and with a limited time to issue an alert based on simulation of wave propagation and inundation.

Introduction
Tsunamis are mostly (~80%) triggered by the sudden displacement of the fault plane during large earthquake1. After the devastating tsunamis generated by the Sumatra (Indonesia) and Tohoku (Japan) earthquakes in 2004 and 2011, respectively, a lot has been done globally to improve our ability in predicting tsunami and in reducing the risk2. However, since 2011, many tsunamis have devasted the coastline worldwide claiming for more than 5000 victims3. Only a small percentage (10%) of all tsunamis are generated by aerial and submarine landslides and by the instability of volcanic flanks or volcanic activity4. In the historical record landslide-generated tsunamis have triggered local wave heights and run up as large as 100 m and 500 m5, respectively, locally exceeding maximum wave and run up heights of tectonic tsunamis by more than an order of magnitude6.

On 22 December 2018, the partial collapse of ~280×106 m3 on the western flank of Anak Krakatau generated a 10–30 m tsunami wave on the closest (at ~3–5 km) islands of Sertung, Panjang and Rakata. Only 35–60 min after, waves of ~3 m high struck Sunda Strait in Indonesia in a 50 km range7. This event and a second tsunami in the same year in Palu Bay3,8 eluded the warning system killing more than 2000 people. In the emblematic case of Anak Krakatau the rapid detection of the collapse combined with an efficient alert system on the coast could have prevented fatalities. Recently, the January 2022 violent eruption of Hunga volcano in Tonga has triggered worldwide atmospheric driven tsunami9 which have globally surprised the modeling arriving almost 2 h before the expected “normal” earthquake-generated tsunami onset10. All these non-conventional tsunamis are calling for a better understanding of the tsunamigenic process and for a different approach in predicting and mitigating their effects.

The collapse of submerged flank of volcanic island are among the largest mass movements on Earth with potential volumes of order of km3 (109 m3), such as those in the Hawaian11, Canarian12,13, Cape Verdean14, Krakatau15 and Stromboli16 islands. These are considered one of the most dangerous geological phenomena able to trigger tsunamis propagating thousands of kilometres far from the source17–19. In addition, the collapse of part of the volcanic craters, or dome, and of the eruptive plume20 is at the origin of pyroclastic hot gas and particles mixture density current which can run at velocities of ~200 km/h along the volcano slopes. The impact of the pyroclastic flow with the sea can originate a tsunami with run-ups several meters high as observed during the Montserrat 1997 and 2003 eruptions21 and the Rabaul 1994 eruption22. This extends the volcanic risk from the local to regional scale involving a large number of population and infrastructure near the coast of the volcanic island14,15. Most of the causalities associated to volcanic eruption at regional scale are in fact caused also by tsunami1.

The dynamics of flank instability of volcanic islands are still poorly documented resulting in a great uncertainty on related tsunami generation. As many volcanic islands, Stromboli (southern Tyrrhenian sea, Italy) has in the north-western side a weak flank named Sciara del Fuoco (Fig. 1) which is the most impressive morphological feature of the volcano edifice with a mean slope, θ, of ∼35° extending also below the sea level for a total length of almost 3000 m. The Sciara del Fuoco represents the subaerial part of a partially filled sector-collapse scar (Fig. 1). In the last 13 ka it has been the source of potentially tsunamigenic large-scale (in the order of 109 m3) flank failures23,24 generating tsunamis probably with run-up of ~50 m18. Recent work on paleo-events16 has identified three well-preserved medieval (1300–1400 AD) tsunami deposits linked to the collapse of ~180×106 m3 of the Sciara del Fuoco, comparable to the 2018 Anak Krakatau flank collapse, and making victims in the Neapolitan Gulf16.

In the last century, volcanic activity at Stromboli has been responsible for at least six well-documented small-scale tsunamis25,26 with the largest one on 30 December 2002 due to the partial collapse of 10–30×106 m3 of the Sciara del Fuoco scar27. The tsunami badly damaged buildings at 10 m of elevation with inundation hundreds of meters in the nearby Stromboli coast, but also in the close (~20 km) islands (inlet in Fig. 1a). The tsunami was observed in several places along the coast of Italy, from the Campanian at north-east to the western part of Sicily southward18.

Numerical simulations evidence that tsunami generated in the Sciara del Fuoco, will reach the populated coast of Stromboli in less than 3–4 min18,27,28. After only 20–30 min the whole Aeolian Arc and the coast of Calabria and Sicily (at ~50 km) would be impacted (inlet in Fig. 1). Waves would travel across the southern Tyrrhenian sea entering in the Neapolitan Gulf after 1 h and 20 min28. The short propagation time and the densely inhabited nearby coasts calls at Stromboli, as well as in many other volcanic islands, for a rapid detection system, able to issue an alert without human validation.

Two violent explosive eruptions (paroxysms) at Stromboli volcano produced in 2019 a few km-high (6–8 km) eruption columns, large tephra fallout (~105 m3) and pyroclastic density currents (e.g. 29), which propagated along the Sciara del Fuoco flank (Fig. 2). The impact of the density currents on the water generated moderate (meter-high) tsunamis recorded at a distance of <1.6 km from the source by permanent tsunami gauges (elastic beacons) and by the geophysical network operating at Stromboli (see Methods and Supplementary Note 1).

In this work, the dynamics of the pyroclastic flows derived by image analysis and the record of the tsunamis in near-source condition are used to constrain numerical models and to improve our ability to detect tsunamis of volcanic origin. We show how waveform and period of the tsunamis do not change with the landslide volume nor seems to be affected by landslide cinematics. Velocity and geometry of the mass movement along the volcanic slope do not significantly alter tsunami waveform and, as first approximation, the volume of the sliding body can be derived by the height of the tsunami using granular flow empirical approach. In case of tsunami generated near the coast, when the time to alert population is short (<10 min), this approximation can be used to derive almost in real-time a rapid assessment of the associated hazard. Combined with the automatic early detection of the tsunami provides the base for an efficient tool to mitigate the tsunami risk associated to large explosions and/or flank instability of volcanic islands.

Results
In the summer 2019, on 3 July at 14:45:42 UTC and on 28 August at 10:17:15 UTC29 two violent explosive paroxysms struck Stromboli island. The partial collapse of the 6–8 km high eruptive column29 and, most probably, also of part of the crater rim, generated pyroclastic density current along the steep slope of Sciara del Fuoco impacting the sea surface and triggering tsunami waves (Fig. 3a).

On 3 July, georeferenced images of the visible camera located on the northern side of the Sciara del Fuoco at Punta Labronzo (LBZ in Fig. 1) show that during the initial phase of the paroxysm the fallout of large ejected blocks reached a distance of almost 500 m from the coast and ~1800 m from the vent, generating splash columns almost 50 m high (Fig. 2c and Supplementary Movie 1). The large quantity of ash and material ejected is masking the crater area and two density currents becomes visible only in the lower portion of the Sciara del Fuoco. The first density current propagates along the most southern part of the Sciara flank, covering the 730 m long visible portion of the slope in ~16 s with a front velocity u = 45.6 m/s and entering in the sea at 14:46:10 UTC (Fig. 2c and blue star in Fig. 3a), only 28 s after the onset of the paroxysm. At 14:46:20 UTC. the second pyroclastic flow is clearly visible in the video (Supplementary Movie 1) entering in the sea only 10 s after the first one.

On 28 August, two fronts of another pyroclastic flow are visible in the more central part of the Sciara slope (Supplementary Fig. 1a) impacting the water at 10:17:49 UTC (Fig. 2f), ~34 s after the paroxysm onset. The time interval between the onset of the paroxysm and the impact with the water (~34 s) is ~6 s longer than on 3 July (~28 s). Image analysis shows that also this pyroclastic flow was moving at the constant velocity of u = 45.7 m/s (Fig. 2g and Supplementary Fig. 1). The identical front velocity suggests that in both cases, density currents have almost reached a steady velocity already in the first 400 m of propagation, moving at a constant acceleration du/dt = g sinθ (where θ = 35° is the mean slope of Sciara del Fuoco) after only 8 s. Considering that both density currents have travelled the same distance of 1250 m along the Sciara’s slope with the same velocity, the time difference of 28 and 34 s, between the eruptive onset and the impact with the water, is indicating different initial conditions.

Considering a general multiphase mass flow landslide model30, the analytical solution for the observed motion of the pyroclastic flows moving with the terminal velocity u = 45.7 m/s along the Sciara del Fuoco can be calculated (see Methods) assuming a basal bed friction δ = 20°31 and a viscous drag coefficient β = 0.0019. The model indicates that terminal velocity is reached after only 15 s already in the first 400 m and it needs ~34 s to cover the 1250 m long Sciara del Fuoco slope. While this is fully compatible with the movement measured for the 28 August pyroclastic flow (Fig. 2g), the analytical solution indicates that the 28 s measured during the 3 July event can be explained only assuming a 35 m/s initial velocity (Fig. 2g). The violent blast, also visible on the images was then accelerating the pyroclastic flow to its terminal velocity in only 8 s.

The observed density currents are composed by an upper dilute suspension and a darker basal concentrated granular avalanche with a total thickness of ~30 m, and a front almost ~200 m wide (Fig. 2f and Supplementary Fig. 1). Entering in the water, both pyroclastic flows in July and August 2019 drastically decelerate (Fig. 2c, f). While the dense basal part keeps flowing underwater, the ash-rich lighter and finer component of the density current runs on the sea surface at a mean velocity of 28.3 m/s (Fig. 2g and Supplementary Fig. 1d-f), quickly (in ~10 s) moving outside the camera field of view and propagating at least for 1 km from the shoreline (Supplementary Fig. 1f). This suggests that only a small part of the visible total thickness moved underwater and is responsible for the tsunami.

For a sudden release of a finite volume of frictionless fluid down to an inclined plane, known as the dam-break problem, a gross estimate of the front velocity is also given by u = 1.4 sqrt(g H_c) cosθ32,33, where H_c is the height of the collapsed volume. In our case, the front velocity u = 45.7 m/s would corresponds to an effective collapse height H_c ~ 132 m. According to laboratory experiments of a fluidized granular flow33, we here consider that the minimum effective thickness (h_f = 6.5% H_c) of the pyroclastic front responsible for the tsunami should be larger than ~9 m and smaller than 30 m.

Tsunami source time constrain
After 43 s from the onset of the 3 July paroxysm, a tsunami wave with a peak-to-peak height A_PDC = 2.59 m (Fig. 3a) and a period of 40 s (Fig. 3b) was recorded (at 14:46:25 UTC) first at the PDC gauge and after 26 s (69 s from the paroxysm onset) at the PLB gauge with an amplitude A_PLB = 1.03 m (Fig. 3a) and a longer period of 55 s (black line in Fig. 3b). In line with video images (Fig. 2 and Supplementary Movie 1), differences in amplitude and time between the two elastic beacons indicate that the source of the tsunami was closer to the PDC than PLB gauge. The stretching of the period (Fig. 3b) from 40 s (at PDC) to 55 s (at PLB) is thus suggesting the dispersive nature of the tsunami in this near source conditions.

We used the arrival times at the two elastic beacons to search for the position of the tsunami source in an area 1600 m long by 500 m large extending offshore the Sciara del Fuoco (see Methods). The best solution gives a source located in the most southern-west part of the Sciara del Fuoco at a slant distance of ~610 and ~1590 m from the PDC and PLB gauges, respectively (Fig. 4), and a wave celerity c = 39 m/s. Source position does not coincide with the coastline but is ~150 m offshore (Fig. 4a) supporting the evidence that density current moved underwater and reached a depth of H_o ~ 105 m below the sea level.

After ~30 s from the onset, the record of the tsunami at PDC (Fig. 3a) is contaminated by a very large amplitude and high frequency sequence of transients probably due to the elastic perturbations generated by the splash on the sea surface of the large blocks (Fig. 2c) and by the material transported during the flow. Part of the density current severely impacted on the elastic beacon PDC, at 300 m from the coast (Supplementary Movie 1), which for this reason was not operating during the tsunami on 28 August 2019. Notably, data transmission continues also during the pyroclastic flow suggesting that hot and dense ash is not shielding radio transmissions as expected. The record at PDC stops almost 8 min after the onset of the tsunami for damages on the radio link located on land due to the large fall out of incandescent lapilli and scoriae (Fig. 3a).

The tsunami on 28 August, is recorded at 10:18:20 UTC (65 s after the onset of the paroxysm) only by the PLB gauge and shows a positive onset with peak-to-peak amplitude A_PLB = 0.6 m (Fig. 3c) smaller than what recorded on 3 July (A_PLB = 1.03 m) but with the same period of 55 s (0.0182 Hz - Fig. 3d). Images provide a clear view of the pyroclastic density current touching the sea surface at 10:17:49 UTC (Fig. 2f) and fix the distance of PLB gauge at ~1170 m from the impact (Fig. 4b). The time difference of 31 ± 1 s between the impact of the pyroclastic flow seen by video images and the tsunami onset gives an apparent celerity of c = 37.7 ± 1 m/s.

Tsunami waveform characteristics
Differently from submarine slides, tsunami waves produced by subaerial landslides are characterized by a first positive onset28,34. The waveform similarity between the two tsunamis (Fig. 3a, c) recorded at PLB gauge, or the positive onset and the almost identical impact velocity (u ~ 46 m/s) of the density current, points to the same dynamics process. Considering the mean tsunami wave celerity c = 39 m/s, the period of 55 s recorded at PLB gives a characteristic wavelength λ = 2145 m which is larger than the maximum distance (r = 1590 m) between the impact area and the PLB elastic beacon (Fig. 4a) indicating that the two tsunamis were recorded in the very near-field condition (r/λ ≤ 1).

Tsunami waveforms recorded at Stromboli are characterized by symmetrical wave profile with similar width and amplitude of the positive and negative pulse (Fig. 3a, c) consistent with the Froude number (F_r = u/sqrt(g H_o)) of 1.43. In line with the empirical relationship F_r < (4 * 7.5 S), the relative slide thickness S = h_f/H_o is limited to 0.34 and provides the maximum slide thickness h_f ≤ 36 m, fully consistent with the visible maximum thickness (30 m) of the pyroclastic flow. The dimensions of the flow (F_r = 1.43 and S ≤ 0.34) support the possibility to trigger tsunami with weakly nonlinear oscillatory wave35. Increasing the Froude number and/or for larger slide thickness, solitary wave could be generated36.

The period of the tsunami waves (Fig. 3b) of 40 s and 55 s recorded at PDC and PLB, respectively. Experimental results indicate that in the near-field, at a dimensionless distance 2r/λ < 0.75 from the splash zone33, amplitude, A, of the tsunami is contaminated by the rapid vertical granular jet of water enriched by the air entrainment in the splash zone and this reflects the maximum elevation of the granular jet. In addition, laboratory experiments indicate that the amplitude of the wave during the propagation, up to 2r/λ ~ 2, is independent on water depth H_o33.

In this scenario, our recording stations, PDC and PLB, on 3 July are located at dimensionless distance (2r/λ) of 0.8 and 1.5, respectively, suggesting that both stations are well outside the splash zone and their amplitudes are not affected by the vertical granular jet of the flow. Tsunami waveforms recorded at PDC and PLB can be thus considered as representative for the leading wave in both 3 July and 28 August events.

Many numerical models have been developed to simulate tsunami waves generated by subaerial landslide34 which have to account for a number of complex and quite often unknown parameters on the landslide dynamics, the interaction with the water and the bathymetric profile (e.g. angle of the slide, water depth, viscous drag coefficient, the speed and the duration of the sliding mass, thickness and width of the sliding front). Numerical models using both solid block and granular sliding body have been applied to simulate tsunami waves generated by the collapse of several millions of cubic meters of material along the Sciara del Fuoco slope18,27,28,38. Grounded on this extensive numerical modeling, we explore the possibility to use empirical equation to directly derive the volume of the pyroclastic flows from the height of the tsunami recorded during July and August, 2019 eruption.

Based on large scale two-dimensional laboratory experiments, several empirical relationships were derived to relate tsunami wave height to geometrical parameters of the sliding volumes33,36–43. Models to reproduce tsunamis generated by landslide and/or granular flow can be basically divided in two main groups: i) the release of solid block39–41 and ii) the flow of a granular body on inclined plane33,36–38,42,43. The use of these empirical relationships is still debated and only few three-dimensional experiments are considering the lateral variation of the tsunami height respect to the direction of the sliding flow propagation.

We compared the solid block41 and granular flow37 empirical 3D models (see Methods) with previous results of the 3D non-hydrostatic NHWAVE numerical simulations of tsunami waves generated by aerial landslides occurring in the Sciara del Fuoco28. We assumed a truncated hyperbolic secant function44 with a circular footprint to represent the volumes of the sliding block and the same initial parameters (Table 1) used in the numerical simulation for volumes ranging between 4.7 and 11.8×106 m3. The empirical granular equations (see Methods) give at PLB gauge tsunami height which within ±3% nicely fit the NHWAVE numerical simulations28 (Fig. 5b and Table 1). In line with previous conclusions34,45, we found that the analytical solid block model is overestimating by a 20–50% the tsunami height of the numerical simulation (Fig. 5b and Table 1). Given the dynamics of the modeled landslides remains constant among the different simulation28, the height of the modeled tsunami is mainly function of the landslide maximum thickness (h_f) and shows a linear correlation with landslide volume (Fig. 5b).

A granular model is then applied to the 2019 tsunamis considering the circular footprint volume shape with width 150 < b < 200 m. For the 3 July tsunami, the empirical model fits the wave height at both tsunami gauges (A_PDC = 2.59 and A_PLB = 1.03 m) for a slide thickness h_f = 20 ± 4 m and a volume of 2.14 ± 0.5×105 m3. In the case of the 28 August tsunami height A_PLB = 0.6 m recorded at PLB (Fig. 2b) is compatible with a volume of 1.05 ± 0.21×105 m3 and a slide thickness of h_f = 10 ± 1 m (Table 1).

These results are in good agreement with the linear relationship between tsunami amplitude and landslide volume found in the NHWAVE numerical simulations (Fig. 5b). Besides, the tsunamis simulated by NHWAVE numerical modeling (see Fig. 3f in ref. 28) have a waveform remarkably similar to the tsunamis recorded both on July and August 2019 (Fig. 5a). Surprisingly waveforms and period (T = 55 s) of the tsunamis remain the same regardless of the two orders of variability in the landslide volume (from ~107 to ~105 m3), the different location of the tsunami source and the landslide dynamics (Froude number). This similarity is evidencing the reliability of NHWAVE46 numerical model and that in near-field conditions, different source geometry (b and h_f), position of the impact (r and γ) and Froude number (u and H_o) of the landslide (see Table 1) do not affect tsunami waveform. This suggests that a linear relationship (V = 6.8x105 * A - 3.9x105) between tsunami height (A) and landslide volume (V) can be considered reasonably acceptable, with implications on our ability to promptly assess the hazard along nearby coast.

Tsunami and crater rim collapse
On 19 May 2021, the partial collapse of the crater rim induced by the increase of the internal conduit pressure associated to a small lava overflow triggered a dense flow of incandescent material which impacted the water at 12:51:15 UTC (http://lgs.geo.unifi.it/bulletins/?bulletin=171) generated a tsunami recorded at 12:51:49 UTC at the PLB gauge (Fig. 3e). At a distance of 1250 m (Fig. 4b), the tsunami was A_PLB = 0.54 m height, almost the same of the 28 August 2019 tsunami, and it moved with a similar celerity c = 36.7 m/s. The dense ash cloud rising up from lapilli and scoriae ejected by the explosions made not possible to track the front velocity of the pyroclastic density current using our visible camera, we then assumed the mean front velocity u = 50 m/s previously estimated by thermal camera47.

Using the same granular landslide empirical equations (see Methods) and considering a slide width b ranging between 150 and 200 m, the amplitude of the tsunami is consistent with a volume of 0.71 ± 0.15×105 m3 for a slide thickness h_f = 6.5 ± 1 m. This volume is well in harmony with the 0.8×105 m3 volume of material collapsed from the north flank of the NE crater estimated from images taken by helicopter immediately after the failure47.

Methods
The elastic beacons tsunami gauge system
Stromboli volcano is monitored by University of Florence (LGS), National Institute of Geophysics and Volcanology (INGV) and University of Palermo, with an integrated network of several geophysical and geochemical sensors (including broadband seismic stations, infrasound network, ground deformation, SO2 cameras, multigas sensors and thermal as well visible cameras) specifically designed to provide timely information on the possible magma intrusion which can lead to the tsunamigenic instability of the Sciara del Fuoco flank. For this reason, two tsunami gauges (Fig. 1) were deployed by the Laboratorio di Geofisica Sperimentale, LGS, (http://lgs.geo.unifi.it/) of the University of Florence in 2008 and 2017 offshore the Sciara del Fuoco, at 260 m and at 350 m distance from Punta dei Corvi (PDC) and Punta Labronzo (PLB) capes, respectively (Fig. 1). The extremely rough conditions of the sea in front of the Sciara del Fuoco (significative waves up to 8 m with periods of ~12 s), called for using elastic beacons (Fig. 1) instead of floating buoys as infrastructure for measuring the sea level at Stromboli. Tsunamis are measured at the sea bed (46 and 50 m depth at PDC and PLB, respectively) by hydrostatic pressure sensors sampled at 125 Hz (Supplementary Fig. 2). At this depth, wave dispersion reduces by ~87% the effect of the sea wave at periods <13 s and it preserves waves in the period range of 50–200 s (Supplementary Note 2, Supplementary Fig. 2b), typical of the tsunamis induced by landslide in general and volcanic activity in particular38,56. At depth larger than 1000 m, the attenuation is very large even at periods above 50 s (20% at 100 s, see Supplementary Fig. 2b). Sampling rate and sensors depth are the crucial factors to guarantee the best signal-to-noise ratio and for developing an efficient detection system for tsunami generated by volcanoes (Supplementary Note 2).

Pyroclastic flow velocity
The velocity u(x,t) of the pyroclastic flow along the Sciara del Fuoco slope has been calculated using the multiphase mass flow landslide model30:

∂u/∂t + u ∂u/∂x = α - β u^2

where β is the viscous drag coefficient and α is representing the net driving force in the system:

α = g_x - g_z α_s μ + h_g

which depends on the component g_x and g_z of the gravity acceleration along (x) and perpendicular (z) to the slope, respectively, the volume fraction of the solid particles α_s = 0.5633, the basal friction coefficient (μ = tan δ), where δ is the basal friction angle (20°), in the mixture material31, and h_g is approximating the surface gradient ∂h_f/∂x of the flow thickness h_f along the slope. The time-independent steady-state motion u(x) can be developed and takes the general solution30 of:

u(x) = (α/β * (1 - exp(-2β(x - x_o))))^1/2

where u_o is the initial velocity at the initial position x_o. For a sufficiently long distance and long time, the motion of the flow reaches a steady-state and Eq. (3) becomes u = sqrt(α/β) which represents the terminal velocity of the flow. Assuming a terminal velocity of 45.7 m/s we thus calculate the viscous drag coefficient β = 0.0019.

Tsunami source location
We applied finite difference time domain method based on a nonlinear shallow-water model of tsunami wave propagation57 to calculate the travel times t_PDC and t_PLB needed to cover, the distances r_PDC and r_PLB between the two (PLB and PDC) elastic beacons and the 19×6 nodes equispaced every 100 m along the shoreline and offshore the Sciara del Fuoco (Fig. 4a, Supplementary Movie 2). We used a gaussian source function 1500 m large with 1 m amplitude, to calculate the location of the tsunami source by comparing the observed delay time between the tsunami wave recorded at PLB and PDC (Δt_obs = 26 s) and the numerical delay time (Δt_num). The best agreement between the observed and the theoretical delay time indicates an unique solution for a source ~150 m offshore the Sciara del Fuoco and a celerity c = 39 m/s (Fig. 4).

Landslide volume
The 3D landslide geometry used for slide volume estimation was a truncated secant function44 having an elliptical foot-print on the slope, with length b and width w and vertical cross sections with maximum thickness T varying according to hyperbolic secant functions:

ζ = T * sech(k_b ξ) * sech(k_w η) * ε

with k_b = 2C/b; k_w = 2C/w; C = acosh(1/ε) and with the truncation parameter ε = 0.717. For the specified ε, the slide volume is estimated by the formula V = 0.3508 bwT58.

Solid block model
For a 3D block model experiment, the relative propagation time t_s of the landslide underwater, after the splash, is the key parameter41 to derive the tsunami source parameters40. This time can be empirically derived from the dimensionless surface of the landslide front impacting the water (S_l = bh_f/H_o^2), the Froude number F_r and the slope of the Sciara del Fuoco (θ = 35°):

t_s = 0.43 S_l^-0.27 F_r^-0.66 (sin θ)^-1.32

where b is the width and h_f is the thickness of the block41. From the maximum wave height (A), as function of the direction cosine (cos γ) of the tsunami wave propagation and the relative distance R = (r/H_o) from the source to the elastic beacons:

A(r, γ) = H_o * 0.07 t_s^-0.45 R^-0.44 (sin θ)^-0.88 exp(0.6 cos γ)

Using a propagation angle γ = 60° ± 4° and a distance r = 1150 from the impact area of the different landslide simulated scenario28, Eq. (6) predicts a maximum tsunami amplitude at the PLB gauge by 20–50% larger than expected (Fig. 5b and Table 1).

Granular flow model
We use the 3D parametric equations developed by Mohammed and Fritz37 to calculate the amplitude of the tsunami wave as function of the water depth H_o, radial propagation distance r and angular direction γ with respect to the landslide flow axis. Multi variable regression analysis leads to the empirical equations for the wave amplitude:

A = k_a R^n_a + k_b R^n_b H_o cos γ

where the parameters k_a and n_a are relative to the first crest

k_a = 0.31 F_r^2.1 S_l^0.6
n_a = -1.2 F_r^0.25 S_l^-0.02 B^-0.33

whereas k_b and n_b are relative to the first wave trough

k_b = 0.7 F_r^0.96 S_l^0.43 L^-0.5
n_b = -1.6 F_r^-0.41 L^-0.14 B^-0.02

defined as function of the Froude number (F_r), the relative distance R = (r/H_o), the relative slide thickness S = h_f/H_o, relative slide width B = b/H_o and relative slide length L = V/(h_f b H_o). As for the Block Model41, we used Eq. (7) to calculate the tsunami maximum height for the same landslide scenario calculated numerically by Fornaciai et al.28. We found that Granular Model of Eq. (7) is sensitive to the propagation direction (γ) but in a range between 56° and 64° better fits the results of the numerical simulation (Fig. 5b) predicting the maximum wave height within the ±3% of error (Table 1).

Tsunami early warning algorithm
The tsunami early-warning system developed for Stromboli is based on the short-term (STA) and long-term (LTA) average (Supplementary Note 3 and Supplementary Fig. 3). The STA and LTA values used by the Early Warning algorithm to detect tsunami waves has been specifically tuned for the sea wave conditions at Stromboli. Whereas STA is sensitive to rapid fluctuations in the sea amplitude, the LTA provides information on the signal background noise. We set the LTA window to 4500 s to include at least 300 times the longest sea wave period of 15 s (typical of Mediterranean sea), whereas the STA window was fixed to 40 s to get the highest ratio for tsunami with a period ranging between 50 and 200 s, as those expected for tsunami triggered by subaerial and underwater sliding mass like the one occurred at Stromboli in 200227,28,38 and at Anak Krakatau volcano56. To improve the signal-to-noise ratio, a signal decimation and a low-pass filter are applied before STA/LTA ratio is calculated (Supplementary Note 3). When the signal-to-noise ratio is high, the STA/LTA method is able to detect tsunami only few seconds after the onset, and several tens of seconds before the maximum amplitude is reached, providing the most as timely as possible alert (see Supplementary Note 3 for more details). The threshold ratio STA/LTA = 20 is 5 times larger than the ratio measured at Stromboli during the worst sea conditions (Supplementary Fig. 4) and gives the highest reliability to detect the tsunami before the first maximum amplitude is reached. The automatic alert is triggered when the STA/LTA ratio is larger than the detection threshold (>20) at both PDC and PLB stations for at least 120 s (Supplementary Fig. 3). This last logical filter increases the reliability of the system minimizing the possibility of false detections.

This tsunami detection algorithm is active since 9 September 2019, when the system was connected automatically to the syrens of the Italian Civil Defence alert system and it can work equally with two or only one tsunami gauge. No false alerts have been issued in this last four years. On 4 December 2022 for the first time an alert was automatically triggered by a tsunami 1.5 m (peak-to-peak) high induced by a pyroclastic flow originated by the partial collapse of the northern part of the crater sector (http://lgs.geo.unifi.it/bulletins/?bulletin=94592).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Dear colleagues,\nThe data you present here is unique and highly valuable. The scienfific community has very liftle data, especially in the near field, on the tsunamis generated by volcanic erupfions. It is a topical issue, following the events of Anak Krakatau in 2018 and Tonga in 2022. This work deserves to be widely disseminated and published in a presfigious journal such as Nature Communicafions.\nHowever, there is sfill a big effort to be made on the manuscript. The methodological protocole is well detailed and the data are well presented and processed in a relevant way.But the structure of the paper is a bit chaofic and needs to be completely reworked. Several secfions appearing in the results or discussion are in the area of methods or introducfion. The separafion between the results and their discussion is unclear (see my suggesfions in an annotated version of the manuscript).\nThis is one of the reasons that leads me to recommend a major revision.\nHere are also some other major points to improve:\n- The literature on tsunamis generated by subaerial landslides is not well \"digested\", which is understandable because the authors have rather an experfise in volcanology, but this is felt in certain phrases (eg lines 263-266). This literature is certainly abundant, but it lacks a paragraph menfioning the landslide parameters that influence tsunami generafion (eg from experimental and numerical studies).\n- The nofion of \"near-field\" must be defined. Many tsunami studies consider the near-field as an impacted area close to the source (typically several kilometers away), but here you are almost at the source. Your record is indeed unique, but two references should sfill be cited where measurements are available: Rabaul 1994 (fide-gage record of the tsunami generated by PDC: Nishimura et al 2005 In: K. Satake (ed.) Tsunamis: case studies and recent developments, Springer, 43-56) and Montserrat 2003 (dilatometer data: Maftioli et al 2007 GSA Bull 35). To come back to this idea of \"near-field\" I would suggest that either you keep wrifing \"very near-field\" everywhere in the manuscript, or you write \"at its source\" or \"near-source\".\n- The discussion on exisfing alert systems is somewhat peremptory and involves simplificafions. In any case, we cannot compare a system dedicated to ocean-wide tsunamis. For sources such as landslides and volcanic erupfions (except for atmospheric waves), local systems nested within regional systems must be used. This is, moreover, what is being done in Stromboli... but you are more aware of these steps than I am. This discussion should be redirected to the need to set up local warning systems and dedicated procedures on acfive volcanoes close to the coast, rather than to \"crificize\" the exisfing systems which remain essenfial for other types of sources.\n- It's a shame not to have NHWAVE simulafions with volumes comparable to the events of July and August 2019. This would bring real added value to your work. This is not a crificism, but a suggesfion to consider.\nSee also other comments on the annotated pdf aftached to this report.\nI am impafient to see this work published, even if there are sfill some efforts to provide. Good luck.\nRaphaël Paris", "reviewer_2": "The authors, Drs. Lacanna and Ripepe, present unprecedent records of tsunamis generated by volcano sector collapse and pyroclasfic density current from Stromboli volcano. The authors first show near-field records of tsunamis caused by pyroclasfic flows, for the first fime. They also aftempt to locate the tsunami source, and present a technique to tsunami alert system by detecfing volcanic tsunamis from Stromboli volcano.\nThe near-field tsunami records and their analyses shown in this manuscript are scienfifically important in the hot topic of volcanic tsunamis. Also, their analysis based on tsunami modeling with the pyroclasfic flow modeling, and their tsunami detecfion system will be helpful for coastal communifies around Stromboli volcano. I think that the research contents may be potenfial for publicafion from Nature Communicafion. However, I need to say that the manuscript, at this present form, is not well prepared and contains a lot of careless typos, duplicate words, grammafical errors, and wrong references to figures, most of which may be avoided by brief checks. Also, the structures need extensive revision; for example, research backgrounds which should be explained in Introducfion appear in the discussion part in a redundant way. These issues, mainly related to their presentafion, unfortunately make it difficult to understand the scienfific importance of their research. In the following, I list up major and minor comments one by one. These issues would be required to resolved before further considerafion.\n[Major comments]\n1. Paper structures\nFirst of all, the structure is not well organized. Here I list up parts that may need to be revised.\n- Lines 41–46: I do not think the Tonga erupfion case needs to be explained in an independent paragraph, because this study’s focus is rather on Anak Krakatau type. This part can be shortened and merged into the previous paragraph.\n- Lines 85–105: This part does not describe results of this study and should be moved to the introducfion secfion.\n- Three paragraphs in Discussion (Lines 257–261, 334–340, 392–398, and 420–428) do not fit here and most of the parts are just repeated explanafions that have already appeared in earlier parts. I recommend that the authors revised the parts carefully to avoid the redundant repeafing.\n2. Esfimafion of inifial tsunami locafion and tsunami propagafion speed\nIn “Tsunami data wavefield”, the authors assumed straight ray paths at constant speeds. But clearly the tsunami wave speeds depend on the bathymetry, and the ray paths are not straight. Are the assumpfions, straight ray paths and constant speeds, are truly valid? I think the ray path should travel slightly to a deeper part offshore and bent back to the shore due to the bathymetry slope. I recommend the authors perform basic tsunami simulafions (for example, I guess linear long-wave simulafion from a simple Gaussian-like source is enough) distributed in the same way, and compare the simulafion and observed arrival fimes.\n[Minor comments]\n- Lines 27–32:\nPlease provide references for the following parts for the two sentences, “More than 10% of all tsunamis are generated by landslides or volcano collapses with subaerial, parfially submerged or submarine origins” and “In recorded history landslide-generated tsunamis have triggered local wave heights and runup as large as 100 m and 500 m, respecfively…”\n- Line 52: extent => extends\n- Line 54: cost => coast\n- Line 70: The connecfion between this and the previous paragraphs are not clear. How about starfing this paragraph by “In addifion to the flank collapse, the impact of the pyroclasfic flow with the sea can originate tsunami with run-ups several meters high, as observed during the Montserrat 1997 and 2003 erupfions (23) and the Rabaul 1994 erupfion (24)”?\n- Lines 76 and many other parts: The date representafions are not unified; July 3rd, 3 July, or 3 July. Somefimes, 3th July.\n- Line 78: which propagafing => which propagates\n- Line 98: “in in” => in\n- Line 124: What does “involving most probably also part of the crater rim”?\n- Line 133: What do you mean by “in the second porfion of the Sciara del Fuoco”?\n- Line 136: yellow square => yellow star\n- Line 137: clear visible => clearly visible\n- Line159: during the 3 July => during the 3 July event\n- Line 160: the its => its\n- Line 164: concentrate granular avalanche => concentrated granular avalanche\n- Line 165: almost ~200m large => almost ~200m high\n- Secfions “Tsunami data wavefield” and “Tsunami waveforms”: Please reconsider the fitles of these secfions. The present fitles are similar, and readers may not understand the differences at first glances. Please describe what you’ve done in these secfions by concise but informafive fitles.\n- Line 182: After 43 seconds => After 43 s\n- Line 186: amplitudes and fime difference => differences in amplitude and fime\n- Lines 204 and 210: the second tsunami on August 28 => the tsunami on August 28 (this reads as two tsunami events occurred on August 28)\n- Lines 221–223: The waveform similarity between the two tsunamis (Fig. 3a,c) recorded at PLB gauge, or the posifive onset and the almost idenfical impact velocity (!~46 m/s) of the density current, points to the same dynamics process.\n- Line 305: remarkable similar => remarkably similar\n- Line 319: which impacfing => which impacts\n- Line 329: 0.67±0.15x105 => (0.67±0.15)x105\n- Line 334: the two-tsunami occurred => the two tsunamis that occurred\n- Line 334: are => gives or provide\n- Line 347: the a priori => the a-priori\n- Line 348: a quite difficult => quite difficult\n- Line 351: wait => waifing\n- Line 350: implies to => implies\n- Line 355: LTA/STA method has been already aftempted by a previous study for tsunami detecfion, for example, Wang et al. (2020).\n- Line 406: previous observed => previously observed\nAlso, please provide references to the previous studies.\n- Line 460: Fig. 4b => Fig. 4a\n- Lines 460: what does ”travel fimes should equals the PLB ≤ 41s and PDC ≤ 15 s fime interval” mean?\nFigure, tables, and the capfions\n- Line 694: extend => extends\n- Figure 2’s capfions: mulfiple “3th July”\n- Figure 3a: verfical axis “distancel” => distance\n- Line 754: 28 August 2019 (red line) => 28 August 2019 (black line)\n- Figure 5a: In legend, “Ago.” => “Aug.”\n- Line 733: remove “always”\n- Line 738: “different three different” => three different\n- Line 759: indicates that => indicates\n- Table 1: Please show the units for the physical values.\n[References]\nYuchen Wang, Kenji Satake, Takuto Maeda, Masanao Shinohara, Shin’ichi Sakai; A Method of Real-Time Tsunami Detecfion Using Ensemble Empirical Mode Decomposifion. Seismological Research Lefters 2020;; 91 (5): 2851–2861. doi: hftps://doi.org/10.1785/0220200115"}, "author_response": "Reviewer #1\nas suggested, we changed the title of the manuscript in “Volcano generated tsunami recorded in “the near-source”.\nStructure of the paper was reorganized. Some of the Results were moved into the Introduction and other parts in the Methods. The body of the text, the methods and the supplementary information have been largely modified.\nThe Early Warning algorithm which was before in the Discussion has been moved part in the Supplementary Material and in the Methods.\nPlease find our reply to the points raised by the Reviewer#1 also in the annotated PDF (Reply_to_Ref1_Comments_annotated_manuscipt.pdf).\npoint by point reply:\nQ. … the structure of the paper is a bit chaotic and needs to be completely reworked. Several sections appearing in the results or discussion are in the area of methods or introduction. The separation between the results and their discussion is unclear (see my suggestions in an annotated version of the manuscript).\nA. Following this suggestion, we have reorganized the structure of the manuscript, posing attention in separating the material between introduction and results. An other part of the text dealing with the instruments and the detection algorithm was moved in the Supplementary material.\nQ. - The literature on tsunamis generated by subaerial landslides is not well \"digested\", which is understandable because the authors have rather an expertise in volcanology, but this is felt in certain phrases (eg lines 263-266). This literature is certainly abundant, but it lacks a paragraph mentioning the landslide parameters that influence tsunami generation (eg from experimental and numerical studies).\nA. This comment is partially correct. We did not make explicit all the parameters needed to model tsunami generated by landslide. We agree that we have been generic on this aspect on the text, because we thought that the list of parameters is given in the Table I. However, we take this suggestion and we now make it clear also in the text.\nQ. - The notion of \"near-field\" must be defined. Many tsunami studies consider the near-field as an impacted area close to the source (typically several kilometers away), but here you are almost at the source. Your record is indeed unique, but two references should still be cited where measurements are available: Rabaul 1994 (tide-gage record of the tsunami generated by PDC: Nishimura et al 2005 In: K. Satake (ed.) Tsunamis: case studies and recent developments, Springer, 43-56) and Montserrat 2003 (dilatometer data: Mattioli et al 2007 GSA Bull 35). To come back to this idea of \"near-field\" I would suggest that either you keep writing \"very near-field\" everywhere in the manuscript, or you write \"at its source\" or \"near-source\".\nA, The two mentioned references about the tsunami of Rabaul 1994 and Montserrat 2003 are cited in the manuscript.\nA, We agree with the suggestion to change the definition of “very near-field” with “near-source”. This has been changed both in the title and in the text.\nA. It was not our intention to criticize the existing warning system, which is indeed very efficient, but only to point out the reason why we need a different approach with tsunami generated by volcanoes. This is a common and shared opinion among experts on tsunami (Bardet et al., 2003). However, we take greatly in consideration this suggestion and we have smoothed most of the sentences.\nQ. - It's a shame not to have NHWAVE simulations with volumes comparable to the events of July and August 2019. This would bring real added value to your work. This is not a criticism, but a suggestion to consider.\nA. We agree with the Reviewer but we prefer to leave the modeling using NHWAVE as the object of a following more dedicated paper.\nQ. See also other comments on the annotated pdf attached to this report.\nA. All the comments annotated in the attached pdf have been considered (see the annotated Reply_to_Ref1_Comments_annotated_manuscipt.pdf) and the text was accordingly modified.\nThe method to localize the source of the tsunami has been changed using, as suggested, finite difference elements. The result of this new location is now described in the Method. Besides we have added a new Supplementary Video 2, to show the propagation from the source with new methodology.\nAll the dates in the manuscript are now in the same uniform style (DD MM YYYY).\nPoint by point reply\n[Major comments]\nQ. First of all, the structure is not well organized. Here I list up parts that may need to be revised.\nA. This comment is in line with the suggestions of Revier#1. Many of the parts underlined by the Reviewer have been changed and/or moved in the Introduction and Supplementary Material\nQ. - Lines 41–46: I do not think the Tonga eruption case needs to be explained in an independent paragraph, because this study’s focus is rather on Anak Krakatau type. This part can be shortened and merged into the previous paragraph.\nA. As it was suggested we shortened and merged this paragraph into the previous one.\nQ.- Lines 85–105: This part does not describe results of this study and should be moved to the introduction section.\nA. Lines 85-105 was moved in the Introduction\nQ. - Three paragraphs in Discussion (Lines 257–261, 334–340, 392–398, and 420–428) do not fit here and most of the parts are just repeated explanations that have already appeared in earlier parts. I recommend that the authors revised the parts carefully to avoid the redundant repeating.\nA. This comment is right. We have deleted some of the paragraphs and moved others in the Introduction.\nQ2. Estimation of initial tsunami location and tsunami propagation speed In “Tsunami data wavefield”, the authors assumed straight ray paths at constant speeds. But clearly the tsunami wave speeds depend on the bathymetry, and the ray paths are not straight. Are the assumptions, straight ray paths and constant speeds, are truly valid? I think the ray path should travel slightly to a deeper part offshore and bent back to the shore due to the bathymetry slope. I recommend the authors perform basic tsunami simulations (for example, I guess linear long-wave simulation from a simple Gaussian-like source is enough) distributed in the same way, and compare the simulation and observed arrival times.\nA. We thank the Reviewer for having point-out this method to calculate the position of the tsunami source. As suggested, we have calculated the position of the source using Gaussian-like source with a finite time difference domain model with variable tsunami celerity based on the barìthimetry. The result gives the same location as for the straight ray path and a mean tsunami celerity of 39 m/s.\n[Minor comments]\nQ. - Lines 27–32:\nA. This sentence is from Titov, V. V. Hard lessons of the 2018 Indonesian Tsunamis, Pure Appl. Geophys., 178, 1121–1133., 2021).\nQ. and “In recorded history landslide-generated tsunamis have triggered local wave heights and runup as large as 100 m and 500 m, respectively…”\nA. This part of the sentence is now cited as Fritz, H. M., W. H. Hager, and H.-E. Minor, Lituya Bay case: rockslide impact and wave run-up, Sci. Tsunami Hazards, 19, 3–22, 2001.\nQ. - Line 52: extent => extends\nA. Done\nQ. - Line 54: cost => coast\nA. Done\nQ. - Line 70: The connection between this and the previous paragraphs are not clear. How about starting this paragraph by “In addition to the flank collapse, the impact of the pyroclastic flow with the sea can originate tsunami with run-ups several meters high, as observed during the Montserrat 1997 and 2003 eruptions (23) and the Rabaul 1994 eruption (24)”?\nA. We have now modified the text as suggested by Reviewer\nQ.- Lines 76 and many other parts: The date representations are not unified; July 3rd, 3 July, or 3 July. Sometimes, 3th July.\nA. All the dates have been corrected in the manuscript following the British nomenclature, that is 3 July 2019.\nQ. - Line 78: which propagating => which propagates\nA. Done\nQ. - Line 98: “in in” => in\nA. Done\nQ. - Line 124: What does “involving most probably also part of the crater rim”?\nA. We deleted “involving”, which was not very clear\nQ. - Line 133: What do you mean by “in the second portion of the Sciara del Fuoco”?\nA. This is good question. We mean in the “lower portion of …”. We changed the text\nQ. - Line 136: yellow square => yellow star\nA. Done\nQ. - Line 137: clear visible => clearly visible\nA. Done\nQ. - Line159: during the 3 July => during the 3 July event\nA. Done\nA. Done\nQ. - Line 164: concentrate granular avalanche => concentrated granular avalanche\nA. Done\nQ.- Line 165: almost ~200m large => almost ~200m high\nA.We changed in “~200 m wide”. This is the value of the b parameter.\nQ.- Sections “Tsunami data wavefield” and “Tsunami waveforms”: Please reconsider the titles of these sections. The present titles are similar, and readers may not understand the differences at first glances. Please describe what you’ve done in these sections by concise but informative titles.\nA. Following this suggestion we have now named the two paragraphs as “Tsunami source time constrain” and “Tsunami wavefield characteristics”\nQ.- Line 182: After 43 seconds => After 43 s\nA. Done\nQ. - Line 186: amplitudes and time difference => differences in amplitude and time\nA. Done\nQ. - Lines 204 and 210: the second tsunami on August 28 => the tsunami on August 28 (this reads as two tsunami events occurred on August 28)\nA. This is correct, we changed the text as suggested\nQ. - Lines 221–223: The waveform similarity between the two tsunamis (Fig. 3a,c) recorded at PLB gauge, or the positive onset and the almost identical impact velocity (𝑢!~46 m/s) of the density current, points to the same dynamics process.\nA. we changed the text as suggested\nQ. - Line 305: remarkable similar => remarkably similar\nA. Done\nQ. - Line 319: which impacting => which impacts\nA. Done\nQ. - Line 329: 0.67±0.15x105 => (0.67±0.15)x105\nA. we prefer to keep it without the brackets => 0.67±0.15x105\nQ. - Line 334: the two-tsunami occurred => the two tsunamis that occurred\nA. Done\nQ. - Line 334: are => gives or provide\nA. We changed “are” with “provide”\nQ. - Line 347: the a priori => the a-priori\nA. Done\nQ. - Line 348: a quite difficult => quite difficult\nA. Done\nA. Done\nQ. - Line 350: implies to => implies\nA. Done\nQ. - Line 355: LTA/STA method has been already attempted by a previous study for tsunami detection, for example, Wang et al. (2020).\nA. Our detection algorithm was operative already in 2019, before the paper of Wang, however we now cite Wang et al., 2020 as suggested,\nQ. - Line 406: previous observed => previously observed\nAlso, please provide references to the previous studies.\nA. We corrected the text and cite Murty, T.S. (2003). Tsunami Wave Height Dependence on Landslide Volume.\nQ. - Line 460: Fig. 4b => Fig. 4a\nA. Done\nQ. - Lines 460: what does ”travel times should equals the 𝑡PLB ≤ 41s and 𝑡PDC ≤ 15 s time interval” mean?\nA. We agree with this comment and we have deleted this part of the phrase, which was misleading\nFigure, tables, and the captions\nQ. - Line 694: extend => extends\nA. Done\nQ. - Figure 2’s captions: multiple “3th July”\nA. All the dates have been changed in 3 July\nQ. - Figure 3a: vertical axis “distancel” => distance\nA. The label of the vertical axis was corrected\nQ. - Line 754: 28 August 2019 (red line) => 28 August 2019 (black line)\nA. This mistake was corrected.\nQ. - Figure 5a: In legend, “Ago.” => “Aug.”\nA. corrected\nQ. - Line 733: remove “always”\nA. “always” was removed\nQ. - Line 738: “different three different” => three different\nA. corrected\nQ. - Line 759: indicates that => indicates\nA. corrected\nQ. - Table 1: Please show the units for the physical values.\nA. We have included the units for each parameter in the Table I\n7"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear authors,\nIn this revised version, you have addressed all my comments in an acceptable way, excepfing for my comment on the lack of numerical simulafion available with a similar volume as the 2019 events. I understand that you plan to work on a future paper including numerical simulafions, but your answer is not what is expected here. You should rather demonstrate that at this first stage you don't need numerical models (if I'm right). Anyway, the paper is now befter structured and easier to follow. I sfill have some minor remarks (mostly wording) that are recorded on an annotated pdf (see aftached).\nCongratulafions for this very nice and useful contribufion on these unique events.\nRaphaël Paris", "reviewer_2": "Journal: Nature Communicafions\nAuthors: M. Ripepe and G. Lacanna\nTitle: Volcano generated tsunami recorded in the near source\nManuscript #: NCOMMS-23-28596A\nThis includes my reviewing comments on the revised manuscript submifted by the authors, Drs. Ripepe and Lacanna, for publicafion from Nature Communicafions. First of all, I am happy to find the manuscript has been well revised and improved significantly by the authors’ effort, and appreciate them for considering carefully the comments raised by reviewers including myself. Now, I recommend the publicafion of this arficle after resolving remaining problems that are all minor (some of which I have overlooked in the first review). I hope these will be helpful.\nMinor comments\nL. 26–36:\nBefter that the two paragraphs are merged into a paragraph. The first paragraph should menfion the study topic, volcanic tsunamis.\nL. 33: Is “In the hystorical record history” correct? (also typo) Maybe “In the historical record”?\nL. 46: arriving almost 2 hours before the expected “normal” earthquake-generated tsunami onset\nThe delay fime should not be “almost 2 hours”, but different from stafion to stafion depending of the distance from the source. Please consider removing the specific delay fime.\nL.96: the permanent tsunami gauges\n“the” should be removed.\nL. 97: the geophysical network\nPlease specify what kind of geophysical observafion instruments are included in the network, and when the network was installed (maybe in Methods part around line 379).\nL. 107: tsunamis waves => tsunami waves\nFigure 2a: Could you add an approximated scale of this video image? for example, a note on the (approximated) elevafion of the mountain’s top captured in this video is helpful enough for readers to image how large the erupfions were.\nMany parts: The fime unit of second is “~6 s” in some parts but “10 seconds” in other parts. They need to be unified.\nL. 146: on July and August 2019 => in July and August 2019\nL. 191: The tsunami on 28 August, is recorded at 10:18:20.5 UTC (65.5 s after the onset of the paroxysm) only by the PLB gauge\nCould you explain here why the tsunami was not recorded by the PDC gauge?\nL. 201: Differently from the first large negafive wave produced by submarine slides,\nIs this correct? I think that submarine slides caused both negafive and posifive waves, and the first polarity should depend on the direcfion to the stafion from the source (for example, see the previous paper).\nWard, S. N. (2001). Landslide tsunami. Journal of Geophysical Research, 106(B6), 11201–11215. hftps://doi.org/10.1029/2000jb900450\nL. 235–250: Tsunamis generated by … and August, 2019 erupfion.\nI think that these three paragraphs can be merged into a paragraph, which will make easier for readers to follow the context.\nL. 254: are derived\n“were derived” or “have been derived” would be befter to menfion previous studies.\nL. 291: opening to implicafions on our ability => implying our ability (?)\nL. 347–374:\nThe three paragraphs sound like concluding remarks, which are independent from the subsecfion “tsunami detecfion algorithm”. How about start a new subsecfion at L347, for example, named as “Towards early-warning of volcanic tsunamis” (this is just a suggesfion, which you may ignore if you do not like this).\nL. 357: Regardless => Regardless of\nL. 391: Please check the reference number (38, 5653).\nL. 392: the aftenuafion becomes very large also above 50s\n=> the aftenuafion is very large even at periods above 50 s\nL. 416: Tsunami source locafion\nThank you for revision of this part, which solidifies your argument by the simulafion.\nWould you please also explain that the Gaussian source is assumed here, and specify the horizontal size and peak amplitude of the Gaussian? (Since the nonlinear equafions are used, the amplitude info. may affect the simulafion result.)"}, "author_response": "We thank both Referees for their careful check of the manuscript and their helpful comments which have greatly improve clarity of the manuscript.\nHereinafter our poi-by-point reply to their comments\nReferee#1\n- L.23: change “too close” in “very close”\nDone it\n- L. 24: “generate simulation of wave inundation”. 10 minutes is anyway not enough to start a simulation, so I would rather write that there is \"a limited time to issue a warning and a forecasting.\"\nSentence was changed following Referee’s suggestion in \"…with a limited time to issue an alert based on simulation of wave propagation and inundation\"\n- L. 33: “volcanic flank”.\nAs suggested we added also “volcanic acitivity”\n- L.48: change “tsunami-genic” in “tsunamogenic”\nDone it\n- L.55: change “is the origin” in “is at the origin”\nDone it\n- L. 62: and pyroclastic flows (Auker et al. 2013 Journal of Applied Volcanology).\nWe did not include pyroclastic flows as suggested, but we specify now that we refer to the causalities at regional scale.\n- L.85: You could also cite the seminal work of Tinti et al. 2003 (NHESS) and 2006 (Bull Volc).\nWe have included the reference to the Tinti et al., 2003 and 2006 work.\n- L.94: “huge” => “important”\n“huge” was changed in “large”\n- L.147. delete “most”.\nDone it.\n- L.151: change “This is suggesting” in “This suggests that”\nDone it.\n- L. 214: change “by the images” in “by visible camera”\nDone it.\n- L.218: change “can” in “could”\nDone it.\n-L. 223: “contaminated”. masked? (I don't like the use of the word contaminated here)\nWe think “contaminated” better describes the effect of the vertical spray jet of water on the tsunami amplitude.\n- L.224: change “is reflecting” in “this reflects”\nDone it.\n- L.235. change “current” in “currents”\nDone it.\n- L.238: change “large runup” in “large wave runup”\nDone it.\n- L.240-241: change “the tsunami wave fenrated by coastal landslide” in “tsunami waves generated by subaerial landslide”.\nSentence was changed following Referee’s suggestion.\n- L.254: change “are” in “were”\nDone it.\n- L.274: change “Granular” in “A granular”\nDone it\n- L.287-290: It's not clear what is the physical nature of the landslide, and the difference with source parameters. Please revise the sentence to make it clear.\nThe physical nature of the landslide and the difference with the NHWAVE modelling (lines 288-290) already described in Table I, have been made explicit.\n- L.292: change “risk” in “hazard”\nDone it.\n- L.317. “define at the first order\nWe did not understand the meaning of this comment.\n- L.317: change “with” in “for”\nDone it.\n- L.318: change “volcanic eruption” in “volcano flank collapses”\nWe change in “volcano flank instability”\n- L.320: change “The two-tsunamis occurred on the 2019 summer provide..” in “t The two-tsunamis that occurred at Stromboli in summer 2019 provide…”\nThis sentence was changed as suggested.\n- L.323: change “…was of only 2.59 m and fortunately had no significant…” in “…was of 2.59 m and fortunately the wave had no significant ….”\nWe changed the sentence as suggested.\n- L.324-325: “which during the summer are visited by more than 5000 people every day.”\nput this part of the sentence in brackets.\nwe prefer to leave it as it is. Personally I do not like brackets.\n- L. 347: change “The tsunamis generated by pyroclastic flows at Stromboli represent,…”\nin “he 2019 tsunamis at Stromboli represent...\"\nDone it.\n- L.348: change “…record of a tsunami at its early stage, when is forming.” In “… record of a voilcanic tsunami at its early stage, when it is still forming.”\nThis part of the sentence was changed as suggested.\n- L.351-352: You could briefly remind that the solid block model overestimates the wave amplitude, whereas the granular flow model gives a good approximation.\nFollowing this comment, we now also remind that “the granular material empirical solution better resolves the source parameters than the solid block model which overestimates the tsunami height”.\n- L.358: please clarify that the parameters you are referring to are “at the source”.\nWe changed this sentence in “no physical parameters of the source are available”\n- L.357: change “as first” in “as a first”\nDone it.\n- L.367: change “risk” in “hazard”\nDone it.\n- L.457: change “Granular flow” in n”Granular Flow Model”\nDone it\n- L.481: change the Tiltle “The Early Warning Algorithm” in “Tsunami Early Warning Algorithm”\nTitle was changed as suggested.\nour point-by-point reply have been directly made on the Reviewer PDF document:\nReply_Comments_Referee#1.pdf.\nReferee#2\n- L. 26–36: Better that the two paragraphs are merged into a paragraph. The first paragraph should mention the study topic, volcanic tsunamis.\nThe two paragraphs were merged.\n- L. 33: Is “In the hystorical record history” correct? (also typo) Maybe “In the historical record”?\n“history” was deleted and the typo was corrected.\n- L. 46: arriving almost 2 hours before the expected “normal” earthquake-generated tsunami onset. The delay time should not be “almost 2 hours”, but different from station to station depending of the distance from the source. Please consider removing the specific delay time.\nWe understand this comment, but the \"2 hours\" in advance described in our sentence is coming from the Kubota et al., Science paper. (ref. 10)\n- L.96: the permanent tsunami gauges “the” should be removed.\n“the” was removed\n- L. 97: the geophysical network Please specify what kind of geophysical observation instruments are included in the network, and when the network was installed (maybe in Methods part around line 379).\nAs suggested, we briefly specify at the beginning of the Methods in the “The elastic beacons tsunami gauge system” paragraph which instruments are used at Stromboli to monitor volcano activity\n- L. 107: tsunamis waves => tsunami waves\ncorrected\n- Figure 2a: Could you add an approximated scale of this video image? for example, a note on the (approximated) elevation of the mountain’s top captured in this video is helpful enough for readers to image how large the eruptions were.\nIn Figure 2a, we overlapped the georeferenced contour map of the topography on the image of the volcano slope. This should give a precise scale of the summit crater elevation.\n- Many parts: The time unit of second is “~6 s” in some parts but “10 seconds” in other parts. They need to be unified.\nTime unit “second” were unified and changed in “s”\n- L. 146: on July and August 2019 => in July and August 2019\n“on” was changed in “in”\n- L. 191: The tsunami on 28 August, is recorded at 10:18:20.5 UTC (65.5 s after the onset of the paroxysm) only by the PLB gauge. Could you explain here why the tsunami was not recorded by the PDC gauge?\nThe reason why the second tsunami on August 2019 was recorded only by PLB gauge is already given in the sentence (183-185) above: \".. density current severely impacted on the elastic beacon PDC, ..., which was not operating during the tsunami on 28 August 2019\".\n- L. 201: Differently from the first large negative wave produced by submarine slides. Is this correct? I think that submarine slides caused both negative and positive waves, and the first polarity should depend on the direction to the station from the source (for example, see the previous paper). Ward, S. N. (2001). Landslide tsunami. Journal of Geophysical Research, 106(B6), 11201–11215. https://doi.org/10.1029/2000jb900450.\nThis comment is correct. Landslide source is a dipole and when is located far underwater from the coast can generate also a positive wave. We then omit to specify the negative onset for the submarine landslide.\n- L. 235–250: Tsunamis generated by … and August, 2019 eruption. I think that these three paragraphs can be merged into a paragraph, which will make easier for readers to follow the context.\nAs suggested, the three paragraphs were merged together.\n- L. 254: are derived. “were derived” or “have been derived” would be better to mention previous studies.\n“are derived” is changed in “were derived” and previous studies have been cited.\n- L. 291: opening to implications on our ability => implying our ability (?)\nWe changed the sentence in \"with implication on ...\"\n- L. 347–374: The three paragraphs sound like concluding remarks, which are independent from the subsection “tsunami detection algorithm”. How about start a new subsection at L347, for example, named as “Towards early-warning of volcanic tsunamis” (this is just a suggestion, which you may ignore if you do not like this).\nThanks for this suggestion. We have included a new paragraph at the end of the “Results & Discussion” which is titled “Towards Early-Warning for Volcano-tsunami”\n- L. 357: Regardless => Regardless of\nChanged.\n- L. 391: Please check the reference number (38, 5653).\nThere was a typo, “5653” was correct in “56”\n- L. 392: the attenuation becomes very large also above 50 => the attenuation is very large even at periods above 50 s\nwe changed the sentence as suggested by the Referee.\n- L. 416: Tsunami source location. Thank you for revision of this part, which solidifies your argument by the simulation. Would you please also explain that the Gaussian source is assumed here, and specify the horizontal size and peak amplitude of the Gaussian? (Since the nonlinear equations are used, the amplitude info. may affect the simulation result.)\nWe now specify in the Methods that the finite difference time domain method based on a nonlinear shallow-water model is using a gaussian source 1500 m large and 1 m height to locate the position of the tsunami source."}]

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