Tsunamis Generated by Underwater Volcanic Explosions

icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Open Access Nat. Hazards Earth Syst. Sci. Discuss., 1, 6399–6432, 2013 Natural Hazards www.nat-hazards-earth-syst-sci-discuss.net/1/6399/2013/ and Earth System doi:10.5194/nhessd-1-6399-2013 NHESSD © Author(s) 2013. CC Attribution 3.0 License. Sciences Discussions 1, 6399–6432, 2013

This discussion paper is/has been under review for the journal Natural Hazards and Earth Tsunamis generated System Sciences (NHESS). Please refer to the corresponding ﬁnal paper in NHESS if available. by underwater volcanic explosions

Numerical simulations of tsunami M. Ulvrová et al. generated by underwater volcanic explosions at Karymskoye lake Title Page (Kamchatka, Russia) and Kolumbo Abstract Introduction volcano (Aegean Sea, Greece) Conclusions References Tables Figures M. Ulvrová1,2,3, R. Paris1,2,3, K. Kelfoun1,2,3, and P. Nomikou4 J I 1Clermont Université, Université Blaise Pascal, Laboratoire Magmas et Volcans, BP 10448, 63000 Clermont-Ferrand, France J I 2Laboratoire Magmas et Volcans (LMV), UMR6524, CNRS, 63038 Clermont-Ferrand, France Back Close 3IRD, R 163, LMV, 63038 Clermont-Ferrand, France 4 Department of Geology and Geoenvironment, University of Athens, Athens, Greece Full Screen / Esc Received: 23 October 2013 – Accepted: 25 October 2013 – Published: 8 November 2013 Printer-friendly Version Correspondence to: M. Ulvrová ([email protected]) Published by Copernicus Publications on behalf of the European Geosciences Union. Interactive Discussion

6399 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract NHESSD Increasing human activities along the coasts of the world arise the necessity to assess tsunami hazard from diﬀerent sources (earthquakes, landslides, volcanic activity). In 1, 6399–6432, 2013 this paper, we simulate tsunamis generated by underwater volcanic explosions from 5 (1) a submerged vent in a shallow water lake (Karymskoye Lake, Kamchatka), and Tsunamis generated (2) from Kolumbo submarine volcano (7 km NE of Santorini, Aegean Sea, Greece). by underwater The 1996 tsunami in Karymskoye lake is a well-documented example and thus serves volcanic explosions as a case-study for validating the calculations. The numerical model reproduces realis- tically the tsunami runups measured onshore. Systematic numerical study of tsunamis M. Ulvrová et al. 10 generated by explosions of Kolumbo volcano is then conducted for a wide range of energies. Results show that in case of reawakening, Kolumbo volcano might represent a signiﬁcant tsunami hazard for the northern, eastern and southern coasts of Santorini, Title Page

even for small-power explosions. Abstract Introduction

Conclusions References 1 Introduction Tables Figures 15 While tsunamis generated by earthquakes and landslides are very well documented,

less attention is paid to not so frequent but potentially damaging sources of tsunamis J I such as underwater explosions of volcanic or anthropic origin (e.g. Freundt et al., 2007; Paris et al., 2013). Underwater volcanic explosions are at the origin of around 1 % of J I

all tsunamis listed for the last four centuries (Latter, 1981) and are particularly tsunami- Back Close 20 genic when occurring in shallow water geometries, i.e. where the depth of the crater is small compared to the crater size (or the energy of eruption). They typically generate Full Screen / Esc waves of short period limiting propagation and damage in space, but wave’s runup inland can be locally high, especially in narrow bays and lakes (Kranzer and Keller, 1959; Printer-friendly Version Basov et al., 1954; Le Méhauté, 1971; Mirchina and Pelinovsky, 1988; Egorov, 2007). Interactive Discussion 25 Existing tsunami warning systems are structured primarily to deal with earthquake- generated tsunamis and might be unsuited to deal with explosion-generated tsunamis. 6400 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Unpredictability coupled with high population densities at the coasts lying in potentially damaged areas make the risk clearly evident (e.g. Nicaragua lakes, Indonesia, and NHESSD Philippines etc.). However, Paris et al. (2013) point out that volcanic tsunamis, includ- 1, 6399–6432, 2013 ing underwater explosions, are rarely included in volcanic hazard studies, even though 5 they strongly expand the potential damage of many submerged volcanoes. Tsunamis produced by underwater volcanic explosions were observed several times Tsunamis generated during the 20th century. For instance, the Kick’em Jenny volcano in the Caribbean Sea by underwater caused 2 m tsunami waves at Grenada Island in 1939 (Smith and Shepherd, 1993). Lo- volcanic explosions cal tsunami waves generated by underwater explosions in the Krakatau caldera were M. Ulvrová et al. 10 described and photographed by Stehn et al. (1929). The Myojin-Sho (Japan) eruption in 1952 generated waves with amplitudes up to 1.4 m high at 130 km from the volcano (Niino, 1952; Dietz and Sheehy, 1954; Miyoshi and Akiba, 1954). Low ampli- Title Page tude tsunamis interpreted as the result of submarine explosions of Ritter Island volcano (Papua New Guinea) were reported in October 1972 and October 1974 in the Bismarck Abstract Introduction 15 Sea (Cooke, 1981). The 1974 tsunami runup was 0.5 m high in Sakar and Umboi islands, located 10 km from Ritter Island (Cooke, 1981; Soloviev and Kim, 1997). Numer- Conclusions References

ous small tsunamis were reported and sometimes photographed during explosions of Tables Figures Kavachi volcano in the Solomon Islands (Johnson and Tuni, 1987). Repeated explosions at Karymskoye Lake (Kamchatka, Russia) in 1996 produced waves with runups J I 20 up to 19 m on the shores of the lake, which has a diameter of 4 km and a mean depth of 50–60 m (Belousov et al., 2000). Older events worldwide are less documented and J I the precise nature of the tsunami sources is often uncertain. The 1716 tsunami in Taal Back Close Lake (Luzon, Philippines) is inferred to have been generated by underwater explosion because the eruptive centre was located oﬀshore (Masó, 1904), but a landslide origin Full Screen / Esc 25 cannot be excluded. It is worth to note that many underwater volcanic explosions are not tsunamigenic, depending on their depth, magnitude and on water-magma interac- Printer-friendly Version tions. In order to assess the potential hazard of tsunami with volcanic underwater explo- Interactive Discussion sion source we use numerical calculations performed by tsunami modelling package

6401 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion COMCOT (Liu et al., 1995a, 1998). Two different cases are simulated: (1) underwater explosions from a submerged vent at around 40 m depth in a shallow water (Karym- NHESSD skoye lake, Kamchatka, Russia) and (2) underwater explosion from Kolumbo subma- 1, 6399–6432, 2013 rine volcano in Aegean Sea (Greece). 5 The tsunami in Karymskoye Lake is taken as a case-study for calibrating the code, since runups onshore were measured all around the lake several months after the Tsunamis generated eruption at more than 20 locations (Belousov et al., 2000). Indeed, the subaqueous by underwater explosion dating back to 1996 provides a unique opportunity to compare tsunami runup volcanic explosions values obtained by numerical modeling with field runup measurements, cf. Fig. 1. Such M. Ulvrová et al. 10 an exercise has been done by Torsvik et al. (2010), who however neglected the nonlinear phenomena that in the case of hight velocity waves related to strong explosions play an important role. The scenario of the 1996 eruption, which lasted for 10 to 20 h, Title Page and the impact of the tsunami on the shores of the lake are described by Belousov et al. (2000). Abstract Introduction 15 The model is then applied to simulations of tsunamis generated by potential future explosions of Kolumbo submarine volcano (Fig. 2), which is located 7 km off the north- Conclusions References

east coast of Santorini island (Aegean Sea, Greece). Kolumbo has a diameter of 3 km, Tables Figures with a summit crater 1.7 km across and 500 m deep (Nomikou et al., 2012a). The last recorded volcanic activity at Kolumbo took place in 1650 AD and produced ash J I 20 plumes that perforated the water surface, ash falls and tsunami on the coasts of the neighboring islands, and around 70 fatalities by volcanic gases in Santorini (Fouqué, J I 1879; Dominey-Howes et al., 2000; Nomikou et al., 2012b). The choice of Kolumbo Back Close is motivated by evidences of seismicity beneath the volcano (Bohnhoﬀ et al., 2006; Dimitriadis et al., 2009), the existence of an active crustal magma chamber (Dimitri- Full Screen / Esc 25 adis et al., 2010), intense CO2 degassing from a hydrothermal ﬁeld (Sigurdsson et al., 2006; Nomikou et al., 2013a; Kilias et al., 2013), and accumulation of acidic water in Printer-friendly Version the crater (Carey et al., 2013). Interactive Discussion

6402 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2 Physical model of underwater explosion NHESSD Dynamics of an underwater volcanic eruption is a poorly known phenomenon. Com- plex interactions between dispersed pyroclasts of different sizes, gaseous bubbles and 1, 6399–6432, 2013 water make it hard to simulate this process dynamically. 5 A certain insight into the hydrodynamics of underwater explosions brings laboratory Tsunamis generated experiments by studying nuclear and chemical explosions (e.g Le Méhauté and Wang, by underwater 1996; Kedrinskii, 2005). It has been observed that just after detonation a cavity consist- volcanic explosions ing predominantly of water vapour is formed. Subsequent expansion, rise and collapse of the spherical vapour cavity are at the origin of water disturbances generating radially M. Ulvrová et al. 10 propagating water waves. Different flow characteristics produced after the discharge depend critically on the depth of the burst and its yield (i.e. the amount of energy released during the explo- Title Page

sion). Several types of surface eﬀects at underwater explosion comprise formation of Abstract Introduction a spectrum of jets with various features (Kedrinskii, 2005, p. 346). For a shallow det- 15 onation, a vertical jet is formed due to inertial motion of a liquid layer over the cavity Conclusions References followed by the second jet due to the cavity collapse upon decompression. Increasing Tables Figures the water depth of discharge is accompanied by the change of ﬂow topology and development of multiple jets. Very deep explosions and/or weak yields cause only small scale water disturbances. J I

20 While diﬀerent jet ﬂows are ejected, a development of water crater is initiated. The rim J I of the crater forms dissipative leading wave. Gravitational collapse of the crater makes the water rush inward and forms the secondary bore accompanied with a number of Back Close

smaller undulations. These surges expand radially while decreasing in amplitude (Le Full Screen / Esc Méhauté and Wang, 1996, p. 8). 25 Several dynamical aspects of underwater explosions have been addressed numeri- Printer-friendly Version cally. Barras et al. (2012) study the dynamics of the high pressure and high temperature gas bubble formed upon the detonation in an inﬁnite medium, i.e. they did not consider Interactive Discussion

6403 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion any interactions with water surface. They describe and model for the oscillation phenomena of the cavity during an underwater explosion. NHESSD Morrissey et al. (2010) numerically model a crater lake environment with subaqueous 1, 6399–6432, 2013 eruption in the middle represented by a sudden release of superheated vapour. They 5 reproduce the different flow dynamics observed in laboratory experiments depending on eruption pressure and additional mass of the steam. These simulations represent Tsunamis generated very well the event observed in 1996 in Karymskoye lake although they do not consider by underwater interactions of vapor with fragmented magma. volcanic explosions Yet, these calculations demand huge CPU times and massive parallelization since M. Ulvrová et al. 10 high resolution and continuous adaptive remeshing at each time step is needed. For large scale propagation of surges it is thus necessary to employ semi-analytical ap- proach. In this case, underwater eruption is approximated by imposing a specific initial Title Page water disturbance whose propagation is modelled numerically. Although this strategy might seem too simplistic, Le Méhauté and Wang (1996) show that it reproduces satis- Abstract Introduction 15 factorily characteristics of the wave field over a uniform depth bottom at a far distance using nonlinear and linear wave theory in comparison with artificially generated un- Conclusions References

derwater explosions. The “far distance” is generally the distance where leading wave Tables Figures characteristics are formed but the non-linear behaviour can be ignored, i.e. three to four characteristic radii far from the detonation centre. J I 20 Le Méhauté and Wang (1996) propose several uniformly valid mathematical models for the initial water displacement (η). Combining inverse transformation together with J I experimental wave records and theoretical solutions for simpliﬁed cases leads to the Back Close initial water disturbance that approximate the explosion source being a parabolic crater with a vertical steep water rim Full Screen / Esc

r 2 25 η = η 2 − 1 , ifr ≤ R (1) Printer-friendly Version 0 R η = 0, ifr > R, (2) Interactive Discussion

6404 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion that also physically corresponds to water surface displacement observed in near- surface explosion experiments (Van Dorn et al., 1968). r is the distance from the ex- NHESSD plosion center and η is the height of the water crater rim. R is the characteristic length 0 1, 6399–6432, 2013 scale of the explosion. Here, R represents the volcano mean crater radius where the 5 explosion takes place. Although R may change in time due to landslides, erosion or sediment transport, this has only a secondary influence. Tsunamis generated The same function for initial conditions has been also used to study tsunamis gener- by underwater ated by asteroid impacts (e.g. Ward and Asphaug, 2000). This choice is based on a real volcanic explosions physical resemblance with the cavity made by an impactor hitting water. In this case, M. Ulvrová et al. 10 the crater radius and its depth are linked to the physical properties of the impactor. Equation (1) contains the critical parameter η0 that controls the height of generated tsunami waves and its value should be linked to the explosion characteristics. There Title Page exist only purely empirical relations that estimate η0 as a function of explosion energy E [J] released. These were derived for shallow or intermediate depth explosions. The Abstract Introduction 15 generic scaling law is (Le Méhauté and Wang, 1996) Conclusions References 0.24 η0 = cE , (3) Tables Figures where c is a constant. According to the explosion yield, two cases are distinguished: 1/3 c = 0.014 for smaller explosions for which holds 0.076 < dc/W < 2.286 (dc is the J I depth of explosion, i.e. the depth of the volcano crater, in meters and W the explosion 1/3 J I 20 yield in pounds of TNT). Larger explosions, 0 < dc/W < 0.076, produce larger cavi- ties and c doubles, c = 0.029. Shallower explosion thus causes deeper water crater for Back Close the same yield. Explosion energy E [J] is generally proportional to the third power of the crater diam- Full Screen / Esc eter. Sato and Taniguchi (1997) give an empirical relationship Printer-friendly Version 7 3 25 E = 3.56 × 10 R , (4) Interactive Discussion where 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 6405 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion for fitting. The size of a volcanic crater represents the cumulated energy of multiple explosions (e.g Valentine et al., 2012) and might be modified by later erosion. Energy NHESSD obtained from the crater radius is thus a maximum estimation used for simulating past 1, 6399–6432, 2013 events such as the 1996 Karymskoye Lake volcanic explosions. Simulations of future 5 underwater explosions must be conducted for different energies which are determined from style of past eruptions. Energies considered typically range between 1012 and Tsunamis generated 1017 J, corresponding approximately to volcanic crater radius of 100 to 1500 m. by underwater volcanic explosions

3 Numerical model M. Ulvrová et al.

In order to perform numerical simulations of volcanic explosion resulting in tsunami 10 wave travelling across the water we adopt the Cornell multi-grid coupled tsunami model Title Page COMCOT (Liu et al., 1995a, 1998), that solves for the nonlinear shallow water equations (NSWE), cf. Appendix A. The COMCOT numerical model has been extensively Abstract Introduction

tested and validated against laboratory experiments (Liu et al., 1995b). Successful di- Conclusions References verse applications were computed including the 1992 tsunami in Babi Island, Indonesia 15 (Liu et al., 1995b), 1993 tsunami in Okushiri Island, Japan (Liu et al., 1995b), 1960 Chil- Tables Figures ian tsunami recorded at Hilo, Hawaii (Liu et al., 1995a) or 2004 Indian Ocean tsunami (Wang and Liu, 2006, 2007). J I Tsunami wave field generated by underwater explosions depends critically on the explosion power. However, other physical parameters can change the tsunami prop- J I 20 agation and in particular the influence of dissipative mechanisms might be important Back Close especially in shallow waters. Here, we neglect the interfacial shear stress and horizontal diffusion force, but examine the effect of bottom friction. The term describing the Full Screen / Esc bottom friction is introduced in governing equations using the Manning’s formula (cf. Appendix A) Printer-friendly Version

2 Interactive Discussion gnm 25 F|F|, (5) H7/3 6406 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion where g is the gravity, H the total water depth, F = Hv the volume flux with v the horizontal velocity vector at the seafloor, and nm the Manning coefficient. Manning coeffi- NHESSD cient should be spatially variable according to the surface roughness and in particular 1, 6399–6432, 2013 it should differ in between the sea bottom and populated coastal areas. However, it 5 is often considered constant in tsunami numerical simulations and its value around 0.025 m−1/3 s is used in calculations. This is a value that is adapted from water en- Tsunamis generated gineering studies and was empirically determined for natural channels (Linsley et al., by underwater 1992, p. 314). volcanic explosions

M. Ulvrová et al. 4 Grid preparation

10 4.1 Karymskoye lake Title Page

To perform simulations, topography and bathymetry data are needed. A 274 × 334 grid Abstract Introduction with a resolution of 21 m of the pre-eruption bathymetry and topography of Karymskoye Conclusions References lake and its surroundings was prepared by Torsvik et al. (2010). We further improve the quality of the grid on the shores by georeferencing and digitalizing 1 : 10 000 topograph- Tables Figures 15 ical maps of the lake dating 1974. The data are then interpolated on the 498×488 mesh

with resolution of 9 m in the both horizontal directions to obtain higher precision data. J I Time step ∆t = 0.01 s is chosen so as to satisfy the Courant–Friedrichs–Lewy (CFL) condition ensuring the stability of employed numerical scheme. The CFL condition is J I

given by the following formula Back Close

∆x Full Screen / Esc 20 ∆t ≤ , (6) p ghmax Printer-friendly Version where ∆x is the grid size and hmax is the greatest still water depth in the calculation domain. Interactive Discussion

6407 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 4.2 Kolumbo and Santorini NHESSD To perform simulations of tsunami generated by Kolumbo explosion registered at San- torini, we use topography and bathymetry data prepared in Nomikou et al. (2013b), cf. 1, 6399–6432, 2013 Fig. 2. The swath bathymetry was obtained from several oceanographic surveys. The 5 first data were collected in 2001, and further refined in 2006. The resulting computa- Tsunamis generated tional grid has a spatial resolution of 50 m. Time step size is chosen to be ∆t = 0.15 s by underwater that satisfies the CFL criterion, cf. Eq. (6). Artificial tide gauges were placed offshore volcanic explosions near areas of particular vulnerability in case of tsunami (harbors, touristic resorts, coastal towns). M. Ulvrová et al.

10 5 Results Title Page

5.1 Simulation of 1996 tsunami in Karymskoye lake Abstract Introduction

The measured runups record the largest tsunami that was probably generated by the Conclusions References

strongest explosion and can be matched by single event simulations (Belousov et al., Tables Figures 2000). 15 During the eruption, a new submerged crater with 200 m to 250 m in radius was J I formed. Using Eq. (4), energy release is estimated to lie around 5 × 1014 J. This is approximately 1800 times less than the surface energy released during the 2011 Tohoku J I earthquake (Ide et al., 2011) and 5 times more than the energy released during the Back Close nuclear tests conducted on Bikini Atoll in 1946 (Le Méhauté and Wang, 1996). The 20 initial water elevation η0 is thus (cf. Eq. 3) around 50 m. Equation (3) is approximative Full Screen / Esc due to its empirical character and limited source data and should be used only as a ﬁrst order formula. In order to assess the suitability of our model to reproduce the ﬁeld ob- Printer-friendly Version servations we thus conduct a set of calculations by systematically varying η0 around its estimated value in the range from 20 to 100 m, corresponding to explosion energies Interactive Discussion 13 16 25 10 –10 J.

6408 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion After the explosion, waves propagate radially away from the centre of detonation with a typical velocity of 25 ms−1 reaching the southern shore in about 2 min, cf. Fig. 3 (top). NHESSD Highest wave amplitudes are registered in the northern part of the lake that lies closest 1, 6399–6432, 2013 to the impact region. A typical simulation case with η0 = 55 m is depicted on Figure 3 5 (bottom) were ﬁeld measured runups are also reported. In order to quantify the match between simulated and measured values, we compute Tsunamis generated the root mean square error between observed runup values obsi and simulated runups by underwater numi volcanic explosions s PN 2 M. Ulvrová et al. (obsi − numi ) RMS error = i=1 . (7) N

10 From the data set we exclude three data points, TS17, TS18 and TS22 (cf. Fig. 1 Title Page for their position), as these measurements lie too close to the source where the flow experiences strong nonlinearities and more complex interactions of incoming waves Abstract Introduction with the coast are expected due to very shallow water along the wave path. Although Conclusions References there are other data points (north and north-east from the crater, cf. Fig. 1) that lies as Tables Figures 15 close as TS17 and TS18 (e.g. TS01 or TS02) less pronounced nonlinear phenomena are expected here because waves are crossing more profound water region in this direction. Thus, they are included in the comparison exercise. J I Figure 4 shows the results. We test two sets of experiments, one with no bottom −1/3 J I friction included and one with the Manning coefficient nm = 0.02 m s. The model Back Close 20 with zero roughness that best explains observations is one with η0 = 55 m that has the RMS error of 1.37 m, or about 27 % of the observed mean. This matches extremely Full Screen / Esc well the predicted heigh of initial water rim of 50 m using the empirical laws. A detailed comparison of observed and simulated runups for this simulation is shown on Fig. 5. Printer-friendly Version We observe a good prediction of the field data. Note, that no systematic underestima- 25 tion or overestimation of the measured data occur. This indicates that the presented Interactive Discussion model can be used to better constrain tsunamis generated by volcanic explosions and to understand their impact in the coastal areas. 6409 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Results are only slightly modified when including dissipative processes in calculations. Although in this case we observe a better global match, i.e. RMS error decreased, NHESSD this difference is small. In simulations we prefer to disregard the effect of friction, as this 1, 6399–6432, 2013 effect is negligible by itself and is probably up to an order of magnitude smaller than 5 other uncertainties in the system that we do not take into account such as interactions of surface and subsurface water with violent expulsion of magma. Tsunamis generated by underwater 5.2 Simulations of tsunami generated by future underwater explosions of volcanic explosions Kolumbo volcano M. Ulvrová et al. The submarine Kolumbo volcanic cone, that lies about 7 km north east from Santorini 10 island, has a diameter of around 3 km and its crater width ranges from 1500 m to 1700 m (Nomikou et al., 2012a). Title Page To investigate the consequences of an eventual future eruption of Kolumbo, we sys- Abstract Introduction tematically test different initial explosion powers. The circular source of 750 m radius whose middle point matches the physical center of the Kolumbo crater is imposed with Conclusions References 13 15 varying water rim height from 50 m to 350 m corresponding to energies from 3 × 10 J to 1017 J following the energy range expected for further event. Tables Figures The underwater explosion gives birth to waves radiating away from its centre. Col- lapse of the imposed initial water crater generates a positive leading wave propagating J I toward Santorini, cf. Fig. 6. J I 20 First waves reach the north east coast of Santorini in about three minutes after the explosion, cf. Fig. 7. Northern coast is touched by the first peak in about 4 min, the Back Close entire eastern coast in about 8 min and southern parts of the island (around Akrotiri) in Full Screen / Esc about 14 min (Fig. 7, Table 1). The corresponding waveforms registered near the six main coastal towns are shown Printer-friendly Version 25 on Fig. 8. The incoming first wave is always positive followed by a negative peak. Similar behaviour is also observed in mass flow generated tsunamis (e.g. Tinti et al., Interactive Discussion 1999; Lynett and Liu, 2002; Liu et al., 2005; Kelfoun et al., 2010; Giachetti et al., 2011)

6410 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion contrary to caldera collapse triggered tsunamis (e.g. Maeno et al., 2006; Maeno and Imamura, 2011; Novikova et al., 2011). NHESSD Periods are of the order of 30 s (Fig. 8). The larger the explosion power, the longer 1, 6399–6432, 2013 the wave length λ is registered. For the weakest explosion considered in our study, λ of 5 the leading wave is around 1000 m, that gives us around 20 grid points per wave length. This resolution satisfies the computational fluid dynamics requirements to obtain valid Tsunamis generated solutions. by underwater Arrival times are weakly sensitive to the explosion power and depends strongly on volcanic explosions the sea depth over which waves propagate, unlike the amplitudes of incoming waves. M. Ulvrová et al. 10 Those are given by the imposed water crater size or equivalently by the eruption energy. Figure 9 shows the maximum wave amplitudes for several η0. The highest waves are recorded in the centre of explosion and decrease with increasing distance away from Title Page the source. The amplitudes are slightly enhanced in the south west direction (direction toward Santorini) due to the presence of submarine ridge that decrease the sea floor Abstract Introduction 15 depth (cf. Fig. 2 for bathymetry). The highest tsunami incoming waves are registered on the northern and northeast- Conclusions References

ern coast of Santorini as these parts of the island are the most exposed to waves Tables Figures (Fig. 9). However, due to the rocky character of the northern coast, the inundation on this part is reduced. The highest tsunami impact is on the northeast and eastern coasts J I 20 along Santorini as most of these areas here consist of ﬁelds with a gentle slope so the incoming waves can enter easily inland. The amplitudes of tsunami on the southern J I coast in the vicinity of Akrotiri are substantially reduced and the danger here is due to Back Close interference of waves coming from west and east (Figs. 9 and 11). Here, the highest incoming wave is not the leading wave, but one of the trailing waves. The inner part Full Screen / Esc 25 of Santorini caldera is well protected. Arriving waves are greatly attenuated and steep high cliﬀs prevent large inundation (Fig. 9). Incoming waves have amplitudes inferior Printer-friendly Version to 1 m for explosion power smaller than about 1016 J. Larger explosion powers might impact harbors inside the caldera with 1–2 m high waves. Interactive Discussion

6411 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Figure 10 shows the maximum depth of the incoming water waves along the original coastline on the main Santorini island for several explosion powers. Maximum wave NHESSD amplitude A at four main coastal towns as a function of explosion energy is rep- max 1, 6399–6432, 2013 resented on Fig. 11. Highest amplitudes are recorded in Pori that lies closest to the 5 Kolumbo volcano. Increasing the explosion about approximately three orders of mag- 13 17 nitude (from 10 J to 10 J) more than triples Amax from 4 m to 13 m. Waves recorded Tsunamis generated in Monólithos, Kamari and Akrotiri, respectively, vary in amplitude from approximately by underwater 2.6 m to 9 m, 1.7 m to 6 m and 0.4 m to 1.9 m, respectively, over the explored energy volcanic explosions power range (Fig. 11, Table 1). The predicted values might suﬀer partly from inaccuracy M. Ulvrová et al. 10 inherited from imprecise near shore bathymetry data. However, this eﬀect is minimized by choosing the gauge points at certain distance from the coastal towns. At the same time all gauges lie closer than about 900 m from the coast. Title Page

Abstract Introduction 6 Conclusions Conclusions References We have considered underwater volcanic explosions as a tsunamigenic source and 15 model for tsunami propagation and inundation. Since such explosions contribute only Tables Figures by around 1 % to all tsunami cases registered on Earth (cf. Sect. 1) they are often neglected when estimating the potential tsunami hazard although they might be partic- J I ularly deadly at short distances from the volcano. To test the model, we first investigate the 1996 tsunami generated in Karymskoye J I 20 lake, Kamchatka. Shortly after the event, runups around the lake were measured, that Back Close provides a unique data set to calibrate the numerical model (Belousov et al., 2000). We show that our modelling is capable to reproduce all the measured runup values except Full Screen / Esc the ones that are too close to the explosion centre (closer than about 1.2 km). Present day unrest under the Kolumbo submarine volcano (Greece, Aegean Sea), Printer-friendly Version 25 that explosively erupted for the last time in 1650, indicates potential hazard of next Interactive Discussion eruption. Tsunami might be generated by underwater explosions, but other sources might be considered in further investigations (e.g. flank collapse, caldera subsidence, 6412 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion pyroclastic flows). In order to evaluate possible impacts of Kolumbo explosions on the coast of Santorini island, we simulate tsunami generated by a range of explosion pow- NHESSD ers. The predicted waves reaching Santorini are highest on the north east coast where 1, 6399–6432, 2013 registered amplitudes of incoming waves range from 4 m to 13 m, respectively, for small 13 17 5 and large explosions, respectively (varying energy from 3 × 10 J to 10 J). The east coast, where gentle slopes allow water to enter largely inland, is impacted by waves Tsunamis generated with amplitudes ranging from 2 m to 9 m for the same energy range. Southern parts by underwater of the island are well protected and incoming waves do not exceed mostly 4 m for the volcanic explosions strongest explosion. The smallest waves are registered inside the caldera with ampli- M. Ulvrová et al. 10 tudes lower than 2 m for all tested cases. Future eruptions of Kolumbo volcano would impact Santorini island in terms of gas emissions, tephra fallout, earthquake and tsunami, as occurred during the 1650 erup- Title Page tion (Fouqué, 1879). The numerical simulations proposed herein demonstrate that underwater explosions of different powers and related tsunamis represent a significant Abstract Introduction 15 hazard for Santorini. Existing volcanic hazard map of Santorini includes tsunami inundation in case of Kolumbo eruption (Fytikas et al., 1990; Vougioukalakis and Fytikas, Conclusions References

2005) and is based on eyewitness accounts of the 1650 tsunami. However, this doc- Tables Figures ument relies on the trustworthiness of these testimonies, and future eruptions might diﬀer from the 1650 one. J I

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6413 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Appendix A NHESSD Governing equations in COMCOT 1, 6399–6432, 2013 The standard non-linear shallow water equations are employed in COMCOT ∂η ∂P ∂Q Tsunamis generated + + = 0, (A1) by underwater ∂t ∂x ∂y volcanic explosions 2 ! ∂P ∂ P ∂ PQ ∂η τx 5 + + + gH + = 0, (A2) ∂t ∂x H ∂y H ∂x ρ M. Ulvrová et al. 2 ! ∂Q ∂ Q ∂ PQ ∂η τy + + + gH + = 0, (A3) ∂t ∂y H ∂x H ∂y ρ Title Page

where η is the water free surface elevation, and P and Q the volume ﬂuxes for which Abstract Introduction hold P = Hu and q = Hv. u and v are vertically averaged velocities in x and y directions, Conclusions References 10 respectively. H is the total water depth (H = h + η with h the still water depth), g the gravity acceleration and ρ the water density. The last terms in Eqs. (A2) and (A3) Tables Figures represent bottom friction in x and y directions, respectively. Bottom shear stresses τx and τy are then modeled using the Manning formula J I

2 J I τ gn p x = m P P2 + Q2, (A4) ρ H7/3 Back Close 2 τy gn m p 2 2 Full Screen / Esc 15 = Q P + Q , (A5) ρ H7/3 Printer-friendly Version where nm is the Manning’s roughness coefficient. For the simplicity, only equations in the Cartesian coordinate system are given here. Interactive Discussion However, COMCOT package also solves for the governing equations in the spherical 20 geometry with Coriolis force due to rotation of the Earth included. Cartesian coordinate 6414 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion system was used in all tsunami calculations in Karymskoye lake, whereas spherical coordinates were employed in the calculations of tsunamis generated by Kolumbo un- NHESSD derwater explosion. 1, 6399–6432, 2013 Acknowledgements. M. Ulvrová is grateful to Xiaoming Wang for his help with COMCOT. We 5 also thank participants of the field trip to Santorini island in May 2013. The support for this Tsunamis generated research has been provided by FP7-ENV-2013 program ASTARTE and the Laboratory of by underwater Excellence ClerVolc. This paper benefited from LATEX, GMT (Wessel and Smith, 1991) and Matplotlib (Hunter, 2007) magic. volcanic explosions

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10 The publication of this article is ﬁnanced by CNRS-INSU. Title Page

Abstract Introduction

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W. and Tuni, D.: Kavachi, an active forearc volcano in the western Solomon Islands: 1, 6399–6432, 2013 5 reported eruptions between 1950 and 1982, in: Marine Geology, Geophysics, and Geochem- istry of the Woodlark Basin: Solomon Islands, edited by: Taylor, B. J. and Exon, N. F., Earth Science Series 7, 89–112, Circum-Pacific Council for Energy and Mineral Resources, 1987. Tsunamis generated 6401 by underwater Kedrinskii, V. K.: Hydrodynamics of Explosion, Springer, Berlin, Heidelberg, 2005. 6403 volcanic explosions 10 Kelfoun, K., Giachetti, T., and Labazuy, P.: Landslide-generated tsunamis at Réunion Island, J. Geophys. Res.-Earth, 115, F04012, doi:10.1029/2009JF001381, 2010. 6410 M. Ulvrová et al. Kilias, S. P., Nomikou, P., Papanikolaou, D., Polymenakou, P. N., Godelitsas, A., Argyraki, A., Carey, S., Gamaletsos, P., Mertzimekis, T. J., Stathopoulou, E., Goettlicher, J., Steininger, R., Betzelou, K., Livanos, I., Christakis, C., Croff Bell, C., and Scoullos, M.: New insights Title Page 15 into hydrothermal vent processes in the unique shallow-submarine arc-volcano, Kolumbo (Santorini), Greece, Sci. Rep., 3, 2421, doi:10.1038/srep02421, 2013. 6402 Abstract Introduction Kranzer, H. C. and Keller, J. B.: Water waves produced by explosions, J. Appl. Phys., 30, 398– 407, 1959. 6400 Conclusions References Latter, J. H.: Tsunamis of volcanic origin: summary of causes, with particular reference to Tables Figures 20 Krakatoa, 1883, Bull. Volcanol., 44, 467–490, 1981. 6400 Le Méhauté, B. L.: Theory of explosion-generated water waves, in: Advances in Hydroscience, vol. 7, edited by: Chow, V. T., Academic Press, New York, London, 1–79, 1971. 6400 J I Le Méhauté, B. L., and Wang, S.: Water Waves Generated by Underwater Explosion, Adv. Ser. Ocean Eng., World Sci., New Jersey, 1996. 6403, 6404, 6405, 6408 J I 25 Linsley, R. K., Franzini, J. B., Freyberg, D. L., and Tchobanoglous, G.: Water-Resources Engi- Back Close neering, 4th Edn., Series in Water Resources and Environmental Engineering, McGraw-Hill Publishing Co., 1992. 6407 Full Screen / Esc Liu, P. L.-F., Woo, S.-B., and Cho, Y.-S.: Computer Programs for Tsunami Propagation and Inundation, Tech. rep., Cornell University, 1998. 6402, 6406 Printer-friendly Version 30 Liu, P. L.-F., Wu, T.-R., Raichlen, F., Synolakis, C. E., and Borrero, J. C.: Runup and rundown generated by three-dimensional sliding masses, J. Fluid Mech., 536, 107–144, 2005. 6410 Interactive Discussion Liu, P. L.-F., Cho, Y., Yoon, S., and Seo, S.: Numerical simulations of the 1960 Chilean tsunami propagation and inundation at Hilo, Hawaii, in: Tsunami: Progress in Prediction, Disaster 6417 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Prevention and Warning, edited by: Tsuchiya, Y. and Shuto, N., Advances in Natural and Technological Hazards Research, vol. 4, Springer, Netherlands, 99–115, 1995a. 6402, 6406 NHESSD Liu, P.L.-F., Cho, Y.-S., Briggs, M. J., Kanoglu, U., and Synolakis, C. E.: Runup of solitary waves on a circular island, J. Fluid Mech., 302, 259–285, 1995b. 6406 1, 6399–6432, 2013 5 Lynett, P. and Liu, P. L.-F.: A numerical study of submarine-landslide-generated waves and run-up, P. Roy. Soc. Lond. A, 458, 2885–2910, 2002. 6410 Maeno, F. and Imamura, F.: Tsunami generation by a rapid entrance of pyroclastic flow into the Tsunamis generated sea during the 1883 Krakatau eruption, Indonesia, J. Geophys. Res.-Sol. Ea., 116, B09205, by underwater doi:10.1029/2011JB008253, 2011. 6411 volcanic explosions 10 Maeno, F., Imamura, F., and Taniguchi, H.: Numerical simulation of tsunamis generated by caldera collapse during the 7.3 ka Kikai eruption, Kyushu, Japan, Earth Planets Space, 58, M. Ulvrová et al. 1013–1024, 2006. 6411 Masó, M. S.: Volcanoes and seismic centers of the Philippine Archipelago, vol. 3, Department of Commerce and Labor, Bureau of the Census, 1904. 6401 Title Page 15 Mirchina, N. R. and Pelinovsky, E. N.: Estimation of underwater eruption energy based on tsunami wave data, Nat. Hazards, 1, 277–283, 1988. 6400 Abstract Introduction Miyoshi, H. and Akiba, Y.: The tsunamis caused by the Myojin explosions, Journal of the Oceanographic Society of Japan, 10, 49–59, 1954. 6401 Conclusions References Morrissey, M., Gisler, G., Weaver, R., and Gittings, M.: Numerical model of crater lake eruptions, Tables Figures 20 Bull. Volcanol., 72, 1169–1178, 2010. 6404 Niino, H.: Explosion of Myojin Reef: Kagaku Asahi, December , Translation available at USGS Military Geology Branch, 3–23, 1952 (in Japanese). 6401 J I Nomikou, P., Carey, S., Papanikolaou, D., Croff Bell, K., Sakellariou, D., Alexandri, M., and Bejelou, K.: Submarine volcanoes of the Kolumbo volcanic zone NE of Santorini Caldera, J I 25 Greece, Global Planet. Change, 90, 135–151, 2012a. 6402, 6410 Back Close Nomikou, P., Carey, S., Bell, K., Papanikolaou, D., Bejelou, K., Cantner, K., Sakellariou, D., and Perros, I.: Tsunami hazard risk of a future volcanic eruption of Kolumbo submarine Full Screen / Esc volcano, NE of Santorini Caldera, Greece, Nat. Hazards, 1–16, doi:10.1007/s11069-012- 0405-0, 2012b. 6402 Printer-friendly Version 30 Nomikou, P., Papanikolaou, D., Alexandri, M., Sakellariou, D., and Rousakis, G.: Submarine volcanoes along the Aegean volcanic arc, Tectonophysics, 597, 123–146, 2013a. 6402 Interactive Discussion

6418 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Nomikou, P., Carey, S., Croff Bell, K., Papanikolaou, D., Bejelou, K., Alexandri, M., Cantner, K., and Martin, J. F.: Morphological slope analysis in the Kolumbo submarine volcanic zone NE NHESSD of Santorini Island, Z. Geomorphol., 57, 37–47, 2013b. 6408, 6423 Novikova, T., Papadopoulos, G. A., and McCoy, F. W.: Modelling of tsunami generated by the 1, 6399–6432, 2013 5 giant Late Bronze Age eruption of Thera, South Aegean Sea, Greece, Geophys. J. Int., 186, 665–680, 2011. 6411 Paris, R., Switzer, A. A., Belousova, M., Belousov, A., Ontowirjo, B., Whelley, P. L., and Tsunamis generated Ulvrova, M.: Volcanic tsunami: a review of source mechanisms, past events and haz- by underwater ards in Southeast Asia (Indonesia, Philippines, Papua New Guinea), Nat. Hazards, 1–24, volcanic explosions 10 doi:10.1007/s11069-013-0822-8, 2013. 6400, 6401 Sato, H. and Taniguchi, H.: Relationship between crater size and ejecta volume of recent mag- M. Ulvrová et al. matic and phreato-magmatic eruptions: implications for energy partitioning, Geophys. Res. Lett., 24, 205–208, 1997. 6405 Sigurdsson, H., Carey, S., Alexandri, M., Vougioukalakis, G., Croff, K., Roman, C., Sakellar- Title Page 15 iou, D., Anagnostou, C., Rousakis, G., Ioakim, C., Goguo, A., Ballas, D., Misaridis, T., and Nomikou, P.: Marine investigations of Greece’s Santorini volcanic field, Eos Trans. AGU, 87, Abstract Introduction 337–342, 2006. 6402 Smith, M. S. and Shepherd, J. B.: Preliminary investigations of the tsunami hazard of Kick’em Conclusions References Jenny submarine volcano, Nat. Hazards, 7, 257–277, 1993. 6401 Tables Figures 20 Soloviev, S. L. and Kim, K.: Catalog of tsunamis in the Pacific, 1969–1982, DIANE Publishing, 1997. 6401 Stehn, C., van Leeuwen, W., and Dammerman, K.: Krakatau – Part I. The Geology and Volcan- J I ism of the Krakatau Group, 1929. 6401 Tinti, S., Bortolucci, E., and Armigliato, A.: Numerical simulation of the landslide-induced J I 25 tsunami of 1988 on Vulcano Island, Italy, Bull. Volcanol., 61, 121–137, 1999. 6410 Back Close Torsvik, T., Paris, R., Didenkulova, I., Pelinovsky, E., Belousov, A., and Belousova, M.: Numer- ical simulation of a tsunami event during the 1996 volcanic eruption in Karymskoye lake, Full Screen / Esc Kamchatka, Russia, Nat. Hazards Earth Syst. Sci., 10, 2359–2369, doi:10.5194/nhess-10- 2359-2010, 2010. 6402, 6407 Printer-friendly Version 30 Valentine, G. A., White, J. D. L., Ross, P.-S., Amin, J., Taddeucci, J., Sonder, I., and John- son, P. J.: Experimental craters formed by single and multiple buried explosions and im- Interactive Discussion plications for volcanic craters with emphasis on maars, Geophys. Res. Lett., 39, L20301, doi:10.1029/2012GL053716, 2012. 6406 6419 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Van Dorn, W. G., Le Méhauté, B., and Hwang, L.: Handbook of explosion-generated water waves: state of the art, vol. 1, Tetra Tech report, vol. 1, Tetra Tech, Inc., 1968. 6405 NHESSD Vougioukalakis, G. and Fytikas, M.: Volcanic hazards in the Aegean area, relative risk eval- uation, monitoring and present state of the active volcanic centers, in: The South Aegean 1, 6399–6432, 2013 5 Active Volcanic Arc Present Knowledge and Future Perspectives Milos Conferences, edited by: Fytikas, M. and Vougioukalakis, G. E., Developments in Volcanology, vol. 7, 161–183, Elsevier, 2005. 6413 Tsunamis generated Wang, X. and Liu, P. L.-F.: An analysis of 2004 Sumatra earthquake fault plane mechanisms by underwater and Indian Ocean tsunami, J. Hydraul. Res., 44, 147–154, 2006. 6406 volcanic explosions 10 Wang, X. and Liu, P. L.-F.: Numerical simulations of the 2004 Indian Ocean tsunamis: coastal effects, J. Earthq. Tsunami, 1, 273–297, 2007. 6406 M. Ulvrová et al. Ward, S. N. and Asphaug, E.: Asteroid impact tsunami: a probabilistic hazard assessment, Icarus, 145, 64–78, 2000. 6405 Wessel, P. and Smith, W. H. F.: Free software helps map and display data, EOS Trans. AGU, Title Page 15 72, 441–446, 1991. 6415 Abstract Introduction

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M. Ulvrová et al. Table 1. Maximum wave amplitudes Amax and arrival times tA for different explosion powers, i.e. different sizes of initial water crater rim η0, at six different locations on Santorini. Values at gauges near the main towns (closer than about 900 m) on the coast of the island are reported, cf. Fig. 2. Number in parenthesis reports the water depth at a given gauge. Title Page

Paradisos Pori Monolithos Kamari Perissa Akrotiri Abstract Introduction (−4 m) (−6 m) (−14 m) (−4 m) (−14 m) (−3 m) Conclusions References Amax tA Amax tA Amax tA Amax tA Amax tA Amax tA [m] [s] [m] [s] [m] [s] [m] [s] [m] [s] [m] [s] Tables Figures

η0 = 50 m 1.9 195 4.0 167 2.6 261 1.7 374 1.6 516 0.4 864 η0 = 150 m 6.0 188 7.9 159 5.5 254 3.8 365 3.1 505 1.1 820 J I η0 = 250 m 8.7 183 10.6 154 7.6 249 5.1 360 4.0 498 1.6 813 η = 350 m 10.6 180 12.8 150 9.0 246 5.8 356 4.5 493 1.9 809 0 J I

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TS24 TS09 0 Conclusions References Elevation [m] TS13 TS10 Tables Figures 5980000 TS11 53˚58' −20 TS21 TS20 −40 J I

J I −60 0 km 1 km Back Close 53˚57' 528000 530000 532000 Full Screen / Esc Fig. 1. Pre-eruption bathymetry (negative) and topography (positive) of the Karymskoye lake, Kamchatka, and its surrounding. Contour lines with constant contour interval 50 m are also Printer-friendly Version depicted. Red points show locations where runup was measured. The yellow star represents Fig. 1. Pre-eruption bathymetrythe position of the (negative) centre of the and new topography formed crater. (positive) of the Karymskoye lake, Kamchatka,Interactive Discussion and its surrounding. Contour lines with constant contour interval 50 m are also depicted. Red points show locations 6422 where runup was measured. The yellow star represents the position of the centre of the new formed crater.

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Fig. 2. Bathymetry (negative) and topography (positive) of the Santorini island, Greece, and its surrounding used for numerical simulations. Contour lines are depicted with a contour line interval 100 m. Kolumbo volcano is represented by the yellow star. Main coastal towns are shown by pink triangles. (Modiﬁed after Nomikou et al. (2013b))

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Fig. 1. Pre-eruption bathymetry (negative) and topography (positive) of the Karymskoye lake, Kamchatka, and its surrounding. Contour lines with constant contour interval 50 m are also depicted. Red points show locations where runup was measured. The yellow star represents the position of the centre of the new formed crater. icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD 1, 6399–6432, 2013

B 500 Tsunamis generated Ridge by underwater 0 km 5 km 400 36˚30' volcanic explosions 300 Paradisos M. Ulvrová et al. A 200 Pori 36˚27' 100 Title Page 0 Monólithos 36˚24' −100 Abstract Introduction

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Fig. 2. Bathymetry (negative) and topography (positive) of the Santorini island, Greece, and Back Close its surrounding used for numerical simulations. Contour lines are depicted with a contour line Full Screen / Esc interval 100 m. Kolumbo volcano is represented by the yellow star. Main coastal towns are Fig. 2. Bathymetry (negative)shown by pink and triangles topography (Modiﬁed after (positive)Nomikou et of al., the2013b Santorini). island, Greece, and its surrounding Printer-friendly Version used for numerical simulations. Contour lines are depicted with a contour line interval 100 m. Kolumbo volcano Interactive Discussion is represented by the yellow star. Main coastal towns are shown by pink triangles. (Modiﬁed after Nomikou et al. (2013b)) 6423

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1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 Maximum water elevation [m] Printer-friendly Version Fig. 3. Results of explosion simulation in Karymskoye lake with initial water crater rim η = Fig. 3. Results of explosion simulation in Karymskoye lake with initial water crater rim η0 = 55m. (Top) First0 55 m. (Top) First wave travel times (in minutes). (Bottom) Maximum wave amplitude. Red points Interactive Discussion indicatewave travel positions times of (in ﬁeld minutes). measured (Bottom) runup Maximum withwave the runup amplitude. values. Red points indicate positions of ﬁeld measured runup with the runup values. 6424

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Fig. 5. Comparison of measured and simulated runups around the Karymskoye lake. Results are for simulation with η0 = 55m and no bottom friction. (Top) Runup as a function of distance from crater. (Bottom) Simulated runup as a function of the measured runup at 18 different locations. The dashed line corresponds to the simulated runups equal to the measured values.

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Fig. 5. Comparison of measured and simulated runups around the Karymskoye lake. Results Printer-friendly Version Fig. 5. Comparison of measured and simulated runups around the Karymskoye lake. Results are for simulation are for simulation with η0 = 55 m and no bottom friction. (Top) Runup as a function of distance from crater. (Bottom) Simulated runup as a function of the measured runup at 18 diﬀerent Interactive Discussion with η0 = 55m and no bottom friction. (Top) Runup as a function of distance from crater. (Bottom) Simulated locations. The dashed line corresponds to the simulated runups equal to the measured values. runup as a function of the measured runup at 18 different locations. The dashed line corresponds to the simulated runups equal to the measured values. 6426

200 18.0 s 0 200 Title Page 400 Abstract Introduction 200 27.0 s 0 Conclusions References Wave height profiles [m] 200 400 Tables Figures 200 36.0 s 0 200 J I 400 0 2 4 6 8 10 J I Distance [km] Back Close Fig. 6. A bathymetry and topography profile (shaded areas) along AB line in Fig. 2 north east Full Screen / Esc of Santorini. Red lines depict the wave height soon after the explosion and show the formation Fig. 6. A bathymetry andof the topography positive tsunami profile leading wave. (shaded The explosion areas) center along inside the AB Kolumbo line crater in Figure lies at 2 north east of Santorini. 9 km distance. Number in each figure shows time in seconds after the explosion. (Case with Printer-friendly Version η = 250 m.) Red lines depict the wave0 height soon after the explosion and show the formation of the positiveInteractive tsunami Discussion leading wave. The explosion center inside the Kolumbo crater6427 lies at 9 km distance. Number in each figure shows time in seconds after the explosion. (Case with η0 = 250m.)

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Fig. 7. First wave arrival times for Santorini island and its surroundings. Black lines are drown with an interval of 2 min. Results are for simulation with η0 = 50m and no bottom friction.

19 A B 200 0.0 s 0 200 400

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Wave height profiles [m] 200 400

200 36.0 s 0 200 400 0 2 4 6 8 10 Distance [km]

Fig. 6. A bathymetry and topography proﬁle (shaded areas) along AB line in Figure 2 north east of Santorini. Red lines depict the wave height soon after the explosion and show the formation of the positive tsunami leading wave. The explosion center inside the Kolumbo crater lies at 9 km distance. Number in each ﬁgure shows time in seconds after the explosion. (Case with η0 = 250m.) icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD 1, 6399–6432, 2013

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0 2 4 6 8 10 12 14 Back Close Arrival times [min] Full Screen / Esc Fig. 7. First wave arrival times for Santorini island and its surroundings. Black lines are drown with an interval of 2 min. Results are for simulation with η0 = 50 m and no bottom friction. Printer-friendly Version

Fig. 7. First wave arrival times for Santorini island and its surroundings. Black lines are drownInteractive with Discussion an interval of 2 min. Results are for simulation with η0 = 50m and no bottom friction. 6428

10 Paradisos η0 =50 m NHESSD 5 η0 =150 m

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5 0 1 2 3 4 5 15 Pori 10 Tsunamis generated 5 0 by underwater 5 volcanic explosions 10 0 1 2 3 4 5 10 Monolithos 5 M. Ulvrová et al. 0

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2 Back Close 0 1 2 3 4 5 Time [min] Full Screen / Esc Fig. 8. Water surface displacement registered near six coastal towns along Santorini (cf. Fig. 2 for map) and for three different explosion powers. Time signals are shifted so that zero time Printer-friendly Version corresponds to arrival time for a given simulation. Gauges are positioned 400 m, 900 m, 500 m, Fig. 8. Water surface500 m, displacement 800 m and 450 m registered off Paradisos, near Pori, six Monolithos, coastal Kamari,towns alongPerissa Santorini and Akrotiri. (cf. Note, Figure 2 forInteractive map) Discussion and for three differentthat explosion the vertical powers. scale is diff Timeerent for signals each location. are shifted so that zero time corresponds to arrival time for a given simulation. Gauges are positioned 400 m, 9006429 m, 500 m, 500 m, 800 m and 450 m off Paradisos, Pori, Monolithos, Kamari, Perissa and Akrotiri. Note, that the vertical scale is different for each location.

η =50 m η =150 m 36.50 0 36.50 0

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36.35 36.35 1e-01

36.30 36.30 25.25 25.30 25.35 25.40 25.45 25.50 25.55 25.25 25.30 25.35 25.40 25.45 25.50 25.55

Fig. 9. Results of numerical calculations of the Kolumbo explosion generating tsunami. Maximum wave amplitudes around Santorini for several η0. Note, that the color scale is logarithmic. Black thin line represents the original coastlines. Inundation of most east coast of Santorini is visible for all four scenarios.

20 10 Paradisos η0 =50 m 5 η0 =150 m

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2 0 1 2 3 4 5 Time [min] icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Fig. 8. Water surface displacement registered near six coastal towns along Santorini (cf. Figure 2 for map) and for three different explosion powers. Time signals are shifted so that zero time corresponds to arrival time for NHESSD a given simulation. Gauges are positioned 400 m, 900 m, 500 m, 500 m, 800 m and 450 m off Paradisos, Pori, 1, 6399–6432, 2013 Monolithos, Kamari, Perissa and Akrotiri. Note, that the vertical scale is different for each location.

Tsunamis generated η =50 m η =150 m 36.50 0 36.50 0 by underwater

100 36.45 36.45 volcanic explosions

36.40 36.40 M. Ulvrová et al.

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10 36.30 36.30 25.25 25.30 25.35 25.40 25.45 25.50 25.55 25.25 25.30 25.35 25.40 25.45 25.50 25.55 Title Page

Abstract Introduction η =250 m η =350 m 36.50 0 36.50 0 1 Conclusions References 36.45 36.45

36.40 36.40 Tables Figures Maximum water elevation [m]

36.35 36.35 1e-01 J I 36.30 36.30 25.25 25.30 25.35 25.40 25.45 25.50 25.55 25.25 25.30 25.35 25.40 25.45 25.50 25.55 J I Fig. 9. ResultsFig. 9. Results of numerical of numerical calculations calculations of of the the Kolumbo Kolumbo explosion explosion generating tsunami.generating Maximum tsunami. wave Maxi- Back Close mum waveamplitudes amplitudes around Santorini around for Santorini several η0. Note, for several that the colorη0. scale Note, is logarithmic. that the Blackcolor thin scale line represents is logarithmic. Black thin line represents the original coastlines. Inundation of most east coast of Santorini is the original coastlines. Inundation of most east coast of Santorini is visible for all four scenarios. Full Screen / Esc visible for all four scenarios.

Printer-friendly Version 20 Interactive Discussion

20 1, 6399–6432, 2013

η0 =50 m Monolithos Paradisos η =150 m Perissa Pori 0 Tsunamis generated Kamari η0 =250 m by underwater 15 η0 =350 m volcanic explosions

M. Ulvrová et al.

10 Title Page

Akrotiri Abstract Introduction

Conclusions References 5 Tables Figures

J I Wave amplitude on the coast [m] 0 J I 0 10 20 30 40 50 60 Distance [km] Back Close

Full Screen / Esc Fig. 10. Flow depth along the original coastline of the main Santorini island for several η0. Distance zero corresponds to the southernmost point of the island and increases counterclock- Fig. 10. Flow depth alongwise. the Distance original of the six maincoastline coastal towns of is the depicted main by vertical Santorini arrows and island dashed lines for severalPrinter-friendlyη0. Distance Version zero (cf. Fig. 2 for their locations). corresponds to the southernmost point of the island and increases counterclockwise. DistanceInteractive of Discussion the six main coastal towns is depicted by vertical arrows and dashed6431 lines (cf. Figure 2 for their locations).

Explosion energy [J] 3 1013 3 1015 2 1016 1017 · · · Pori Monolithos 12 Kamari Akrotiri 10

Maximum wave amplitude [m] 2

50 100 150 200 250 300 350 η0 [m]

Fig. 11. Maximum wave amplitude Amax as a function of explosion energy registered at four different locations on the east and south coasts of Santorini (cf. Figure 2 for their location).

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η0 =50 m Monolithos Paradisos η =150 m Perissa Pori 0 Kamari η0 =250 m

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Akrotiri

5 Wave amplitude on the coast [m] 0 0 10 20 30 40 50 60 Distance [km]

Fig. 10. Flow depth along the original coastline of the main Santorini island for several η0. Distance zero corresponds to the southernmost point of the island and increases counterclockwise. Distance of the six main coastal towns is depicted by vertical arrows and dashed lines (cf. Figure 2 for their locations). icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD

Explosion energy [J] 1, 6399–6432, 2013 3 1013 3 1015 2 1016 1017 · · · Tsunamis generated Pori by underwater Monolithos 12 volcanic explosions Kamari Akrotiri M. Ulvrová et al. 10

8 Title Page

Abstract Introduction 6 Conclusions References

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Fig. 11. Maximum wave amplitude Amax as a function of explosion energy registered at four Printer-friendly Version diﬀerent locations on the east and south coasts of Santorini (cf. Fig. 2 for their location). Interactive Discussion Fig. 11. Maximum wave amplitude Amax as a function of explosion energy registered at four different locations on the east and south coasts of Santorini (cf. Figure 26432 for their location).