# Tsunamis generated by subaqueous volcanic explosions in Taal Caldera Lake, Philippines

Raphael Paris, Martina Ulvrova

► To cite this version:

Raphael Paris, Martina Ulvrova. Tsunamis generated by subaqueous volcanic explosions in Taal Caldera Lake, Philippines. Bulletin of Volcanology, 2019, 81 (3), 10.1007/s00445-019-1272-2. insu-03708960

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# Tsunamis generated by subaqueous volcanic explosions in Taal

## Caldera Lake, Philippines

Raphaël Paris<sup>a,*</sup>, Martina Ulvrova<sup>b</sup>

<sup>a</sup> Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, F-63000 Clermont-Ferrand, France.

<sup>b</sup> Institute of Geophysics, Department of Earth Sciences, ETH Zürich, Zürich, Switzerland

* Corresponding author at: Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, F-63000 Clermont-Ferrand, France. Tel.: +33 473346717. E-mail: [Raphael.Paris@uca.fr](mailto:Raphael.Paris@uca.fr)

**Abstract** Volcanic subaqueous explosions can generate hazardous tsunamis, especially in lakes. In this paper, we simulate different scenarios of subaqueous explosions and related tsunamis in Taal Caldera Lake (Luzon, Philippines). Taal volcano is one of the most active volcanoes in Southeast Asia, and eruptive processes are mostly explosive. We test different energies of explosions at eight different explosion sites in the lake. The initial water surface displacement ($\eta_0$) generated by the explosion is estimated as a function of explosion energy at a given depth. We estimate the tsunami travel times, maximum wave heights and wave periods at the shoreline. This type of hazard is typically neglected and our work has important implications for hazard assessment around Taal Lake. Due to fast propagation of tsunamis in the lake (waves typically crossing the lake in less than 10 minutes), there is only a short time available for issuing a warning. For $\eta_0 \le 50$ m, wave heights at the shoreline are less than 2 m with a non-dispersive numerical model, and less than 0.5 m with a dispersive model, whatever the explosion depth and location. Powerful explosions with $\eta_0 >> 100$ m generate wave heights greater than 2 m all around the lake and local peaks higher than 10 m.
**Introduction**

Subaqueous volcanic eruptions represent only 8% of all recorded eruptions but they are particularly deadly (~20% of all fatalities associated with historical volcanism: Mastin and Witter, 2000). Hazards related to eruptions through surface water include phreatomagmatic explosions, base surges, tephra fall (from ash to blocks), lahars (e.g. lake outburst, dam failure), and tsunamis or seiches. In enclosed basins or lakes such as Taal Lake in the Philippines (cf. Fig. 1), tsunamis are referred to as the initial waves, and the seiche as the later-stage harmonic resonance within the lake (Ichinose et al. 2000; Freundt et al. 2007). We thus prefer using the term tsunami rather than seiche. During a subaqueous eruption, tsunamis can be generated by different processes such as a pyroclastic flow (e.g. pyroclastic density current resulting from the collapse of a Plinian column), slope instability (landslides on the crater walls), and the explosion itself (Paris, 2015). The mechanisms of interaction between a pyroclastic flow and water as well as the conditions required to generate a tsunami remain partly elusive due to a lack of observations and experimental data (Paris, 2015).

On the contrary, the theory of waves generated by subaqueous explosions is well documented (Le Méhauté, 1971; Mirchina & Pelinovsky, 1988; Duffy, 1992; Le Méhauté & Wang, 1996; Egorov, 2007). This particular type of tsunami consists of two main waves followed by smaller undulations propagating radially from the source, as demonstrated by experiments and numerical simulations (e.g. Le Méhauté & Wang, 1996; Kedrinskii, 2005; Torsvik et al., 2010; Ulvrova et al., 2014 & 2016). The water is initially pushed upward (Fig. 2), forming a crater with a cylindrical bore that expands radially to form the leading wave, followed by a
wave trough. Initial surface displacement (i.e. maximum height of the bore) can be estimated
directly as a function of explosion energy at a given water depth (Le Méhauté, 1971), or
indirectly using the size of the submerged volcanic crater formed by the successive explosions
(Sato & Taniguchi, 1997; Goto et al., 2001). The water crater collapses as in a dam break
model, generating a steep cone of water in the centre that turns to a second cylindrical bore
(Le Méhauté & Wang, 1996). Subaqueous explosions typically generate short-period waves
compared to earthquakes, and most of the time the impact in the far-field is limited (Latter,
1981; Begét, 2000; Paris, 2015). The Myojin-Sho (Japan) submarine eruption in 1952
generated waves with amplitudes of less than 1.5 m at 130 km from the volcano, while near
the source a survey vessel was capsized (Nakano et al., 1954). In shallow-water lakes, runup
inland can be locally high, as illustrated by the 1996 tsunami in Karymskoye Lake (Belousov
et al., 2000). The nature of subaqueous volcanic explosions is controlled by a range of
physical parameters such as the water depth, geometry of the crater, and complex magma-
water interactions (Kokelaar, 1986; Wohletz, 1986; Morrissey et al., 2010). While many
Surtseyan-type phreatomagmatic explosions are not tsunamigenic, violent explosions of the
Taalian eruptive style (Kokelaar, 1986) have the potential to generate hazardous tsunami
waves, especially on lakes (Falvard et al., 2018). Experimental studies (Craig, 1974)
demonstrated that maximum wave heights occur for a two-third submerged explosion, i.e. an
explosion at two thirds of the total water depth towards the lake bed. The amplitudes of the
incoming waves at this critical depth are twice as high as those for explosions at a lower
critical depth (fully submerged). In the case of a subaqueous volcanic explosion, the explosion
depth *d* compared to the total water depth *D* in the vicinity of the eruptive vent is thus a
critical parameter (Fig. 2).

In this paper, we simulate tsunamis generated by subaqueous explosions in the Taal Caldera
Lake (Luzon Island, Philippines, cf. Fig. 1). Historical eruptions at Taal volcano have
79 regularly produced tsunamis (Paris et al., 2014; Delos Reyes et al., 2018), including
80 sublacustrine eruptions such as the 1716 eruption. It is thus of primary importance to
81 consider tsunami hazards in Taal lake. Here, we provide the first detailed case-study of
82 tsunami hazards related to subaqueous explosions in the lake.

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84 **Historical eruptions and tsunamis at Taal volcano**

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86 Taal volcano is located in the southern part of Luzon Island, Philippines (Fig. 1). It is one of
87 the most active volcanoes in Southeast Asia (Delos Reyes et al., 2018). About two million
88 people live less than 35 km from the volcano, including thousands of people living along the
89 shores of Taal Caldera Lake and Taal Island (Delos Reyes et al., 2018). The lake is an
90 important source of fresh water and food (fish-farming), as well as being a recreational area
91 (Ramos 2002).

92 Historical volcanism (33 identified eruptions) has been concentrated on Taal volcanic island
93 (Delos Reyes et al., 2018), which is a post-caldera composite edifice within the 25 × 30 km-
94 wide Taal Caldera Lake. The spatial distribution of the eruptive vents is controlled by NE-SW
95 and NW-SE tectonic structures intersecting at Taal volcanic island (Listanco, 1997). Eruptive
96 styles range from hydrothermal to Plinian, with most of the eruptions being dominated by
97 phreatomagmatic explosions (including phreatoplinian ones). Pyroclastic flows, base surges
98 and ash falls are the primary hazards at Taal volcano. Lakeshore communities were affected
99 by base surges and ash falls during the major historical eruptions (e.g. 1754 eruption). At least
100 five historical eruptions generated tsunamis in the lake (1716, 1749, 1754, 1911, and 1965)
101 (Delos Reyes et al., 2018). The 1716, 1749, 1754 and 1911 eruptions were described by Maso
102 and Saderra (1904, 1911), and the 1965 eruption was studied by Moore et al. (1966). The
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1731 sublacustrine eruption might have been tsunamigenic, but there is no clear mention of waves in the lake during this eruption (Maso and Saderra, 1904).

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The 1716 eruption was also sublacustrine. Descriptions collected by Maso and Saderra (1904) situate the eruption in the southern basin of the caldera lake, near the southeastern point of Taal Island. A “great commotion in the earth” stirred up the water in the lake, “forming immense waves which lashed the shores” (Maso and Saderra, 1904). Waves inundated the southwestern shore of the lake up to 17 m inland.

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As for the 1716 eruption, the origin of the waves observed during the 1749 eruption remains unclear. This violent phreatomagmatic eruption (VEI 4) lasted three months and severely impacted the northern and northeastern shores of the lake (Delos Reyes et al., 2018). One earthquake led to land subsidence in the northeastern part of the caldera (near Tanauan). Explosions were located in the main crater of Taal Island (Fig. 1), with a possible extension to coastal or sublacustrine vents near the northeastern point of the island.

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The 1749 eruption was closely followed by a Plinian eruption in 1754 (Delos Reyes et al., 2018). Twelve people were killed by roof collapse (due to intense ash falls) and waves on the western shore of the lake. Tsunamis were observed during the third and fourth phases of the eruption. However, few descriptions of the waves are available (Maso and Saderra, 1904, 1911; Delos Reyes et al., 2018).

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The 1911 phreatomagmatic to phreatoplinian eruption is better documented. Villages on the western shore of the lake were hit by waves three meters high and 20-50 people were drowned (Maso and Saderra, 1911). Since the eruption was not sublacustrine, subaqueous explosions cannot be the cause of the tsunami. Nor did the earthquakes of the initial phase generate tsunamis. Thus, as for the 1754 Plinian eruption, a pyroclastic flow mechanism is more likely (Delos Reyes et al., 2018). However, atmospheric shock waves generated by the strongest explosions (Pratt, 1911) are another possible source mechanism of the tsunamis.

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Moore et al. (1966) also related the tsunamis observed during the 1965 eruption to shock waves, although the transfer of energy from air to water (or phase-coupling) operates mostly on large areas of deep water (Yokoyama, 1987), i.e. larger and deeper than Taal Caldera Lake.

The initial Strombolian phase of the 1965 eruption was followed by a phreatomagmatic phase that opened a new crater on the southwestern flank of Taal Island (Moore et al., 1966, Delos Reyes et al., 2018). Many of the 190-355 fatalities occurred when tsunami waves capsized boats containing residents fleeing from Taal Island to the western shore of the lake (near Agoncillo). The waves inundated areas up to 4.7 m above the level of the lake (Moore et al., 1966).

## Methods

We have selected eight different sites for simulated explosions in Taal Caldera Lake (Fig. 1): three sites in deep water (>100 m water depth), and five sites corresponding to submerged eruptive vents in shallower water (<70 m water depth). Note that one of the sites is located near the possible location of the 1716 sublacustrine eruption (Fig. 1). Following the method proposed by Torsvik et al. (2010) and Ulvrova et al. (2014, 2016), the initial surface displacement generated by the explosion is estimated as a function of explosion energy at a given depth d, using the empirical formula of Le Méhauté and Wang (1996):

$$ \eta_0 = c E^{0.24} \quad (\text{Eq. 1}) $$

where $\eta_0$ is the vertical initial surface displacement in meters, E the energy of explosion in joules, and c a constant. According to the explosion yield and water depth, two cases are distinguished (Le Méhauté and Wang, 1996): (1) $c = 0.0143$ if $6.15 \times 10^{-4} < d/E^{1/3} < 1.85 \times 10^{-2}$ (where d is the depth of explosion in meters); or (2) $c = 0.0291$ if $d/E^{1/3} < 6.15 \times 10^{-4}$. We
assume that the explosion occurs at the rim of the submerged crater, which corresponds to an optimal explosion depth in terms of tsunami generation (Fig. 2). Explosions deeper inside the crater would be less tsunamigenic, but the extent of the influence of this parameter remains to be tested.

Explosion energy *E* is estimated following the empirical relationship given by Sato and Taniguchi (1997):

$$E = 3.56 \times 10^7 R^3 \quad (\text{Eq. 2})$$

where *R* is the radius of the volcanic crater in meters (Fig. 2). Data from experimental and volcanic explosions varying over 14 orders of magnitude up to E~10¹⁷ J (corresponding to a crater radius up to R~1.5 km) were used for fitting (see Fig. 2 in Sato & Taniguchi, 1997; and Fig. 5 in Goto et al., 2001). We assume that the size of the crater reflects the most powerful explosion at shallow depth (Goto et al., 2001; Taddeucci et al., 2010), regardless of the cumulated energy of all explosions that participated in the formation of the crater. In fact, the morphology of the crater often results from multiple vertically and horizontally-migrating explosions (Sonder et al., 2015; Valentine et al., 2015). Thus, assuming that the diameter of the crater corresponds to the size of the largest explosion at an optimal depth could lead to an overestimation of the explosion energy (Valentine et al., 2014; Sonder et al., 2015). The diameters of the craters on Taal Island range from 90 to 1700 m and the submerged volcanic cones observed on the bathymetry apparently fall in the same range. Crater diameters selected for the simulations range from 200 to 1500 m (Table 1), corresponding to explosion energies $3.5 \times 10^{13} \le E \le 1.5 \times 10^{16}$ J, and initial surface displacements $30 \le \eta_0 \le 200$ m that were tested for each explosion site. Explosions corresponding to crater diameters lower than 90 m ($E < 3.5 \times 10^{12}$ J) do not produce waves on the shores of the lake.

All numerical simulations were performed using COMCOT (Cornell multi-grid coupled tsunami model: Liu et al., 1998) solving for the non-linear shallow water equations, and
FUNWAVE-TVD solving for the fully non-linear Boussinesq-type wave equations (Kirby et al., 1998; Tehranirad et al., 2013). The shallow water equations are valid for horizontal wavelengths greater than ~5 times the water depth. Boussinesq models are able to reproduce the effects of non-linearity (e.g. amplitude dispersion) and frequency dispersion in the case of intermediate-to-deep water waves (up to wavelengths equivalent to water depth). Simulations were all stopped at the shoreline and the inundation phase is thus not simulated, because both models have intrinsic limitations in modelling the nearshore hydrodynamics.

The simulations were performed using a 546×496 grid with an initial resolution of 100 m. The grid was obtained by combining the bathymetry displayed in Ramos (2002) and SRTM topography (Shuttle Radar Topography Mission, Farr et al., 2007). In order to have a homogenous circular water crater at the apron of the explosion and to avoid artificial directivity of propagation, grid resolution was refined to 25 m in some cases. Wave heights and arrival times at the coast are calculated at 12 virtual tide gauge stations distributed all around the lake (Fig. 1).

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## 193 Results

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Tsunami propagation in the lake

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Simulated waves travel through the lake at velocities between 20 and 40 m/s, which correspond to the typical velocity of shallow water waves in 50-170 m water depth.

Consequently, waves propagate faster in the southern basin, which is deeper (a third of its area being deeper than 160 m) than the northern basin (water depth < 105 m). In our simulations, there is no significant difference between the shallow water (non-dispersive) and the Boussinesq (dispersive) models in terms of wave velocity (Fig. 3). For identical explosion
parameters (location, energy, water depth), both models give similar wave arrival times at a particular coastal site (e.g. Ambulong and Balete on Fig. 3). The velocity of propagation of a tsunami in the lake is mostly controlled by the water depth, and secondarily by the explosion energy (i.e. initial surface displacement). As an example, an explosion at a water depth of 50 m with an initial surface displacement $\eta_0$ = 50 m generates a leading wave that arrives at Agoncillo (Fig. 4) one minute later compared to a case with $\eta_0$ = 200 m.

Due to the short distance between the tsunami sources (i.e. explosion sites) and the shore of the lake, all simulated tsunamis propagate in less than 10 minutes across the whole lake (Fig. 5). In the southern basin, wave arrival times range between 1 and 5 minutes when the explosion is located in the same basin. The southern coast of Taal Island is inundated 1-2 minutes after the explosion. The southwestern (Agoncillo, San Nicolas) and eastern shorelines (Balete) of the lake are reached in 2-5 minutes, depending on the energy and location of an explosion in the southern basin. Propagation of waves from one basin to another is slowed by shoals, especially in the narrow strait west of Taal Island (Fig. 1). Waves generated by explosions in the southern basin reach the main localities of the northern basin (Laurel, Talisay) in 5-9 minutes. As explained above, waves propagate slightly slower in the shallower northern basin. However, typical wave arrival times are similar (2-5 minutes) because the northern basin is also slightly smaller than the southern one. Explosions in the northern basin invade the southern basin after 4 minutes of propagation and hit the eastern and southwestern shorelines in 5-7 and 8-10 minutes, respectively (Fig. 5).

Note that oscillations of the lake surface may last for several hours after the explosion due to resonance effect (i.e. seiche). For instance, waves with an amplitude of up to 20 cm persist in both basins for more than 3 hours after an explosion at 50 m water depth in the southern basin ($\eta_0$ = 115 m).

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228 Wave heights at the shoreline

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230 Maximum wave height ($H_{max}$) calculated at the shoreline of the lake increases with increasing initial surface displacement $\eta_0$ at the source (Fig. 6). For similar explosion parameters (energy and depth), the wave heights at the shorelines are not significantly different from one basin to another. However, shoals between the two basins reduce by a factor of two to ten the amplitude of the waves in the opposite basin to that of the explosion (Figs. 7 and 8). Wave heights at the shoreline rapidly decrease with distance from the explosion site (Fig. 9).

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252 For $\eta_0 \le 50$ m, wave heights calculated at the different virtual tide-gauges are less than 2 m with the non-dispersive model, and less than 0.5 m with the dispersive model. The overestimation of wave heights calculated by the non-dispersive model is particularly marked (typically a factor of two) for explosions with $\eta_0 \le 80$ m in the deep southern basin (Fig. 9), because the non-dispersive model is not able to faithfully reproduce the propagation of waves that are relatively short compared to water depth.

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252 Wave heights up to 4 m (non-dispersive) and 2 m (dispersive) at ~5 km from the explosion site are obtained with $\eta_0 = 80$ m (or $110 \le \eta_0 \le 130$ m for very shallow explosions). An explosion at 50 m depth with $\eta_0 = 110$ m in the northern basin generates waves up to 2-3 m on Napayong Island (Fig. 1), whereas a similar explosion at 160 m depth in the southern basin produces wave heights up to 7-8 m on the same island. For $\eta_0 > 110$ m there are fewer differences between the non-dispersive and dispersive models in terms of wave heights at the shoreline. For $110 \le \eta_0 \le 130$ m, wave heights up to 5 m are recorded at ~5 km from the explosion site, and even 10 m on the eastern coast of Taal Island. The most powerful explosions ($\eta_0 = 200$ m) generate waves up to 15-20 m high on the coasts of Taal Island and 12 m on the other coasts of the lake. Figure 10 shows a sensitivity test for $\eta_0$ versus wave height for explosions situated near the 1716 eruption site (cf. submerged cone southeast of
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Taal Island on Fig. 1). The wave heights calculated both in the northern and southern basins increase exponentially with increasing $\eta_0$ (i.e. with increasing explosion energy $E$ for a given depth $d$).

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Wave spectrum

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Using a dispersive Boussinesq-type model allows both the non-linearity and frequency dispersion effects to be reproduced. Spectral analysis of the virtual tide gauge records produced by this model shows that three kinds of wave periods can be distinguished. Short-period waves (70-130 s) are superimposed on longer-lived intermediate-period waves (200-260 s), and longer periods (550-750 s) are detected in the case of deep explosions (>100 m water depth). Figures 11 and 12 display examples of a wavelet power spectrum and periodogram at two different virtual tide gauge stations (Fig. 11: northern basin; Fig. 12: southern basin) for an explosion at 105 m water depth in the northern basin ($\eta_0$ = 120 m). As wave period, amplitude and velocity are linked, different wave scenarios can be distinguished, depending on the geometry of the source (i.e. the explosion) and bathymetry. The leading wave is usually highest at a relatively short distance from the explosion (<5 km: Figs. 4 and 11) and represents the short-period component of the wave spectrum. Wavelet analysis shows that these short periods tend to disappear within 10-12 minutes after the explosion (Fig. 11). As the distance from the explosion increases, the wave spectrum displays more complex trends (Fig. 12). The intermediate-to-long periods predate the short periods, and the maximum wave height is often reached several minutes after the arrival of the leading wave at the shoreline.

Implication for tsunami hazard evaluation
278

279 The results of the numerical simulations presented above have important implications for
280 tsunami hazard evaluation in Taal Caldera Lake. First, there is only a short time available for
281 issuing a warning. All the subaqueous explosions generate tsunamis that propagate throughout
282 the lake in less than 10 minutes, while the nearest shorelines (e.g. coasts of Taal Island) are
283 impacted in less than 2 minutes. Thus, tsunami propagation is too fast to initiate evacuation at
284 the time of explosion. An exclusion zone should be set up prior to, or at the onset of, a
285 sublacustrine eruption. The efficiency of a tsunami warning system in Taal Lake partly relies
286 on monitoring techniques that would detect evidence of volcanic reawakening in the lake (e.g.
287 increased degassing leading to bubbles or jacuzzi, smoke at the surface of the lake, or changes
288 in water colour) as early as possible.

289 Secondly, a single tsunami event in the lake can have a very long duration. The effect of wave
290 resonance in the two basins can last several hours, thus prolonging the mechanical impact of
291 waves on anchored boats, harbours and fish-farming infrastructure. Repeated tsunamis during
292 a sublacustrine eruption would also cause severe coastal erosion. Sediments mobilised by the
293 waves at the lake bottom and those entrained offshore by the tsunami backwash would
294 threaten fish-farming activities.

295 Modelling tsunami waves breaking, interaction with coastal structures, and inundation inland
296 is beyond the scope of this paper, because it would require high-resolution elevation models
297 (typically 1 m grid resolution) and 3D models based on the Navier-Stokes equations.
298 However, as a first approach we have estimated wave heights at the shoreline for different
299 scenarios of subaqueous explosions. It is difficult to assign a probability to each of the
300 scenarios simulated. Observations of tsunami waves during historical eruptions do not provide
301 many constraints on wave heights and inundation distances. We know that waves inundated
302 the southwestern shore of the lake up to 17 m inland during the 1716 sublacustrine eruption
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(Maso and Saderra, 1904). Also that wave runup reached 4.7 m above the level of the lake during the 1965 eruption, even though the cause of the tsunami itself is debated (Moore et al., 1966).

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The size of the craters observed on Taal Island gives a rough estimate of the range of energies delivered by the most powerful explosions (Eq. 2; Sato and Taniguchi, 1997). Craters have diameters between 90 and 1700 m (central crater), but the majority of them are between 200 and 500 m, corresponding to explosion energies $3.5×10^{13} \le E \le 5.6×10^{14}$ J and initial surface displacement $\eta_0 \le 100$ m (Eq. 1; Le Méhauté and Wang, 1996). These source parameters can be considered as the most probable scenario of tsunamis generated by an explosion in Taal Caldera Lake. It is also consistent with the range of energies produced by phreatomagmatic explosions ($3×10^9$ to $3×10^{14}$ J after Valentine et al., 2014).

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Note that constant $c$ in Eq. 1 is an important parameter as it depends on explosion depth $d$ vs. energy $E$. As an example, for explosions with a diameter of 500 m, the critical water depth is 50 m: below a depth of 50 m, explosions generate an initial surface displacement $\eta_0 = 100$ m, whereas above 50 m water depth $\eta_0 = 50$ m. For $\eta_0 \le 50$ m, wave heights at the shoreline are less than 2 m with the non-dispersive model, and less than 0.5 m with the dispersive model, whatever the explosion depth and location. Increasing the value of $\eta_0$ at 80 m or $110 \le \eta_0 \le 130$ m for very shallow explosions (depending on the constant $c$) yields wave heights up to 4 m (with the non-dispersive model) and 2 m (dispersive model) at a distance of ~5 km from the explosion site. Worst-case scenarios of explosions with $\eta_0 >> 100$ m generate wave heights higher than 2 m all around the lake and locally higher than 10 m. However, the occurrence of such large explosions outside the main crater is not supported by available historical or geological observations, so it is uncertain whether such events are plausible.

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Concluding remarks
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Taal is one of the most active volcanoes in the Philippines and Southeast Asia, and its proximity to human activities makes it challenging in terms of risk mitigation. Most of the historical eruptions occurred in the central crater (e.g. 1749, 1754 and 1911 eruptions), but sublacustrine activity is evidenced by the 1716 eruption and numerous emerged volcanic cones around Taal Island. We simulated different scenarios of subaqueous explosions and related tsunamis. This study has implications for tsunami hazard and risk evaluation in Taal Caldera Lake. The dataset includes maps of tsunami propagation, time, and water surface elevation, together with wave heights at the shoreline for 12 different coastal sites (virtual tide gauge stations). These sites were chosen to represent crucial areas at risk from a tsunami.

Among all the activities distributed around the lake, schools, churches, coastal resorts (e.g. northern coast), markets, fire stations, city halls (e.g. San Nicolas), the Taal Volcano Observatory (east of Talisay), and fish-farming activities are the main vulnerable elements.

In this study, we only consider explosions occurring at an optimal depth for generating tsunamis, i.e. explosions at the rim of the crater. However, tsunami generation is also influenced by the evolution of the crater geometry during the eruption (crater excavation, growth of the ejecta ring) and location of the explosion inside the crater, but these relationships have not been tested experimentally or numerically. Horizontal and vertical migrations of the successive explosions and their consequences in terms of tsunami generation are quite unpredictable. More investigations are needed to understand why a minority of subaqueous volcanic eruptions are tsunamigenic or evolve into conditions that can generate tsunamis (e.g. decrease in the explosion depth).

**Acknowledgements** This research was financed by the French Government Laboratory of Excellence initiative n° ANR-10-LABX-0006, the Region Auvergne and the European Regional Development Fund, and by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska Curie grant
agreement n°753755. We acknowledge three anonymous reviewers for their relevant comments. This is
Laboratory of Excellence ClerVolc contribution n° 328.

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459 **Figure captions**

460

**Fig. 1** Volcanic hazards zonation in Taal Caldera Lake (based on hazard maps provided by the Philippine Institute of Volcanology and Seismology - PHIVOLCS), and tsunamis observed during historical eruptions. Subaqueous volcanic explosions and related tsunamis are numerically simulated at several explosion sites and the wave heights are calculated at 12 virtual tide gauge stations around the lakeshore.

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467 **Fig. 2** Physical parameters controlling the initial displacement of the water surface and subsequent tsunami in the case of a subaqueous volcanic explosion. E: explosion energy; d: explosion depth; D: total water depth around the volcanic cone; R: crater radius; η₀: initial water surface displacement.

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472 **Fig. 3** Simulations of tide gauge records of tsunamis generated by two different subaqueous explosions (scenarios 3 and 14 in Table 1), using a non-dispersive (COMCOT) and a dispersive model of tsunami propagation (FUNWAVE-TVD).

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476 **Fig. 4** Simulations of tide gauge records of tsunamis generated by an explosion at a water depth of 50 m for three different values of initial surface displacement (η₀) corresponding to three different explosion energies (scenarios 19, 20 and 21 in Table 1).

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480 **Fig. 5** Tsunami wave arrival times following subaqueous explosions in the northern (A) and southern (B) basins of Taal Caldera Lake. White stars indicate the explosion sites.

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**Fig. 6** Initial surface displacement (η₀) vs. maximum tsunami wave heights (Hmax) calculated at four different virtual tide gauges (see Fig. 1 for location) for different scenarios of explosions in the northern (A) and southern (B) basins of the Taal Caldera Lake.

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**Fig. 7** Maximum tsunami wave heights (Hmax) calculated at 12 virtual tide gauge stations around Taal Caldera Lake for a subaqueous volcanic explosion in the southern basin (scenarios 2 and 3 in Table 1). Histograms represent the results obtained with two values of initial surface displacement (η₀) both for the non-dispersive and dispersive model of tsunami propagation.

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**Fig. 8** Maximum tsunami wave heights (Hmax) calculated at 12 virtual tide gauge stations around Taal Caldera Lake for a subaqueous volcanic explosion in the northern basin (scenarios 14 and 15 in Table 1). Histograms represent the results obtained with two values of initial surface displacement (η₀) both for the non-dispersive and dispersive model of tsunami propagation.

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**Fig. 9** Maximum tsunami wave height (Hmax) vs. distance from the explosion. Two scenarios of explosions are considered: a first explosion with η₀ = 80 m in the southern basin and a second explosion with η₀ = 140 m in the northern basin.

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**Fig. 10** Initial surface displacement (η₀) vs. maximum tsunami wave height (Hmax) at six different tide gauges for an explosion close to the 1716 eruptive vent (sublacustrine eruption in the southern basin). Six different values of η₀ are tested.

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**Fig. 11** Spectral analysis of wave height vs. time at a virtual tide gauge station located in the northern basin (Laurel) for an explosion at 105 m water depth in the northern basin ($\eta_0$ = 120 m) (scenario 11 in Table 1). A: wave height vs. time profile calculated at the Laurel virtual tide gauge; B: wavelet power spectrum (continuous wavelet transform); C: frequency spectrum (Lomb periodogram).

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**Fig. 12** Spectral analysis of wave height vs. time at a virtual tide gauge station located in the southern basin (Balete) for an explosion at 105 m water depth in the northern basin ($\eta_0$ = 120 m) (scenario 11 in Table 1). A: wave height vs. time profile calculated at the Laurel virtual tide gauge; B: wavelet power spectrum (continuous wavelet transform); C: frequency spectrum (Lomb periodogram).