Numerical Simulations of Tsunami Generated by Underwater Volcanic Explosions at Karymskoye Lake (Kamchatka, Russia) and Kolumbo Volcano (Aegean Sea, Greece) M

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ; ; ). 2007 1959 2007 , , Open Access , Egorov ; Discussions Sciences Freundt et al. 1988 , 4 Kranzer and Keller Natural Hazards Hazards Natural and Earth System System and Earth ) and are particularly tsunami- 1981 , , and P. Nomikou Latter 3 , 2 , 1 6400 6399 Mirchina and Pelinovsky ; 1971 , , K. Kelfoun 3 , 2 , erent sources (earthquakes, landslides, volcanic activity). In 1 ff Le Méhauté ; ). Underwater volcanic explosions are at the origin of around 1 % of , R. Paris 3 , 1954 2 2013 , , 1 , This discussion paper is/has beenSystem under Sciences review (NHESS). for Please the refer journal to Natural the Hazards corresponding and final Earth paper in NHESS if available. Clermont Université, Université Blaise Pascal, Laboratoire Magmas et Volcans, BPLaboratoire 10448, Magmas et Volcans (LMV), UMR6524,IRD, R CNRS, 163, 63038 LMV, Clermont-Ferrand, 63038 France Clermont-Ferrand,Department France of Geology and Geoenvironment, University of Athens, Athens, Greece such as underwater explosions of volcanic or anthropic origin (e.g. 1 Introduction While tsunamis generated byless earthquakes attention and is landslides paid are to very not well so documented, frequent but potentially damaging sources of tsunamis (2) from Kolumbo submarineThe 1996 volcano tsunami (7 in km Karymskoyeas NE lake a is of case-study a for Santorini, well-documented validating example thetically Aegean and calculations. the The Sea, thus tsunami numerical serves runups Greece). model measured reproducesgenerated onshore. realis- Systematic by numerical explosions study of ofenergies. tsunamis Results Kolumbo show volcano that is ina case then significant of tsunami conducted reawakening, hazard Kolumbo for for volcano theeven might a northern, for represent wide eastern small-power explosions. and range southern coasts of of Santorini, Increasing human activities along thetsunami coasts of hazard the from world arise di this the paper, necessity to we assess simulate(1) tsunamis a generated submerged by vent underwater in volcanic a explosions from shallow water lake (Karymskoye Lake, Kamchatka), and Abstract Nat. Hazards Earth Syst. Sci.www.nat-hazards-earth-syst-sci-discuss.net/1/6399/2013/ Discuss., 1, 6399–6432, 2013 doi:10.5194/nhessd-1-6399-2013 © Author(s) 2013. CC Attribution 3.0 License. Existing tsunami warninggenerated systems tsunamis are and might structured be primarily unsuited to to deal with deal explosion-generated with tsunamis. earthquake- Basov et al. all tsunamis listed for the lastgenic four when centuries occurring ( in shallowsmall water compared geometries, to i.e. where the thewaves crater depth of size of short (or the period the crater limitingland energy is can propagation of be and eruption). locally damage high, They in especially typically in space, narrow generate but bays wave’s and runup lakes in- ( Paris et al. Numerical simulations of tsunami generated by underwater volcanic explosions at Karymskoye lake (Kamchatka, Russia) and Kolumbo volcano (Aegean Sea, Greece) M. Ulvrová 1 63000 Clermont-Ferrand, France 2 3 4 Received: 23 October 2013 – Accepted: 25Correspondence October to: 2013 M. – Ulvrová Published: ([email protected]) 8 November 2013 Published by Copernicus Publications on behalf of the European Geosciences Union. 5 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ; , ). Lo- 2006 ). The . Such Dimitri- , 1 Fouqué Belousov ). Numer- the north- 1993 , ff et al. 2012a ). Low ampli- , 1997 ff , Sigurdsson et al. 1954 ). Repeated explo- , Bohnho ), but a landslide origin 1987 , ). The choice of Kolumbo ). Indeed, the subaqueous 1904 , Nomikou et al. Smith and Shepherd 2000 2012b Soloviev and Kim ). The Myojin-Sho (Japan) erup- , , ; Masó ), who however neglected the non- ), which is located 7 km o 2 ), and accumulation of acidic water in Miyoshi and Akiba 1929 1981 ( ; 2010 , ( ) point out that volcanic tsunamis, includ- shore ( erent cases are simulated: (1) underwater 2013 ff ff Johnson and Tuni 1954 , 6402 6401 , 2013 Cooke ( Nomikou et al. Belousov et al. ; ). Two di ). Older events worldwide are less documented and Stehn et al. Torsvik et al. degassing from a hydrothermal field ( 2000 Kilias et al. 2 , 1998 2000 ; ). , , Paris et al. 2013 ), the existence of an active crustal magma chamber ( 2013a , Dietz and Sheehy 1995a , ; , ). The 1974 tsunami runup was 0.5 m high in Sakar and Umboi is- 2009 , ), intense CO 1952 , 1981 Belousov et al. , Liu et al. ). 2010 Carey et al. , Niino Dominey-Howes et al. Nomikou et al. 2000 Cooke ( ; ; The model is then applied to simulations of tsunamis generated by potential future The tsunami in Karymskoye Lake is taken as a case-study for calibrating the code, Tsunamis produced by underwater volcanic explosions were observed several times In order to assess the potential hazard of tsunami with volcanic underwater explo- COMCOT ( damaged areas make thePhilippines etc.). risk However, clearly evident (e.g. Nicaragua lakes, Indonesia, and Unpredictability coupled with high population densities at the coasts lying in potentially the crater ( is motivated by evidencesDimitriadis of et seismicity al. beneathadis the et al. volcano ( 2006 and the impact ofet al. the tsunami on the shores ofexplosions the of lake Kolumbo submarine are volcano describedeast (Fig. coast by of Santorini islandwith (Aegean Sea, a Greece). Kolumbo summit haslast a crater diameter recorded 1.7 of km volcanic 3 km, activity acrossplumes at that and Kolumbo perforated 500 took m theneighboring place water deep islands, in surface, ( and ash 1650 around falls1879 AD 70 and and fatalities tsunami produced by on volcanic ash the gases coasts in of Santorini the ( explosion dating back to 1996 providesvalues a obtained unique by opportunity numerical to modeling compare withan tsunami field runup exercise runup has measurements, cf. been Fig. linear done phenomena by that in theplay case an of important hight role. velocity The waves scenario related of to the strong 1996 explosions eruption, which lasted for 10 to 20 h, explosions from a submergedskoye vent lake, at Kamchatka, around Russia) 40 andrine m volcano (2) depth in underwater in Aegean explosion Sea a from (Greece). shallow Kolumbo water subma- (Karym- since runups onshoreeruption were at measured more all than around 20 the locations lake ( several months after the caused 2 m tsunami waves at Grenada Island in 1939 ( ing underwater explosions, are rarelythey included strongly in expand volcanic the hazard potential studies, damage even though of many submerged volcanoes. during the 20th century. For instance, the Kick’em Jenny volcano in the Caribbean Sea cal tsunami waves generated bydescribed underwater and explosions photographed in the by Krakatau caldera were tion in 1952volcano generated ( waves with amplitudes up to 1.4 m high at 130 km from the tude tsunamis interpreted as the result(Papua of New submarine Guinea) were explosions of reported Ritter inSea Island October volcano ( 1972 and October 1974 in the Bismarck ous small tsunamis were reportedKavachi volcano and sometimes in photographed thesions during Solomon at explosions Islands of Karymskoye ( Lake (Kamchatka,up Russia) to in 19 m 1996 on producedof the waves 50–60 shores with m of runups ( the lake, which has a diameter of 4 km and a mean depth the precise nature of theLake tsunami (Luzon, sources Philippines) is is often inferred uncertain.because to The the have 1716 eruptive been tsunami centre generated in was by Taal located underwater o explosion lands, located 10 km from Ritter Island ( tions. sion source we use numerical calculations performed by tsunami modelling package cannot be excluded. Itnot is tsunamigenic, worth depending to on note their that depth, many magnitude underwater and volcanic on explosions water-magma are interac- 5 5 25 15 20 10 10 20 15 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , Le (1) Le Méhauté and Wang , p. 346). For a shallow det- ) show that it reproduces satis- 2005 erent sizes, gaseous bubbles and ff , 1996 ( Kedrinskii 6404 6403 ). Combining inverse transformation together with η ects at underwater explosion comprise formation of ff ) propose several uniformly valid mathematical models , (2) R 1996 R Le Méhauté and Wang , p. 8). ( ≤ > ) study the dynamics of the high pressure and high temperature ) numerically model a crater lake environment with subaqueous r r ). It has been observed that just after detonation a cavity consist- 1996 , if , 2012 2010 ( ( erent flow dynamics observed in laboratory experiments depending 1 2005 ff , − 2 erent jet flows are ejected, a development of water crater is initiated. The rim r R ff 2 Kedrinskii erent flow characteristics produced after the discharge depend critically on the Barras et al. 0 ; ff η 0, if Le Méhauté and Wang Yet, these calculations demand huge CPU times and massive parallelization since Morrissey et al. While di Several dynamical aspects of underwater explosions have been addressed numeri- Di A certain insight into the hydrodynamics of underwater explosions brings laboratory = = nomena of the cavity during an underwater explosion. any interactions with water surface. They describe and model for the oscillation phe- experiments by studying nuclear and chemical explosions (e.g Dynamics of an underwaterplex volcanic interactions between eruption dispersed is pyroclasts ofwater a di make poorly it known hard to phenomenon. simulate Com- this process dynamically. 2 Physical model of underwater explosion experimental wave records andinitial theoretical water solutions disturbance that for approximate simplified thewith explosion cases a source vertical leads being steep to a water parabolic the rim crater η η factorily characteristics of the waveusing field nonlinear over a and uniform linearderwater depth explosions. wave bottom The at theory “far a incharacteristics distance” far comparison distance is are with generally formed the artificially butfour distance characteristic the generated where radii non-linear un- far leading from behaviour wave the can detonation be centre. ignored,for i.e. the three initial to water displacement ( water disturbance whose propagationmight is seem modelled too simplistic, numerically. Although this strategy interactions of vapor with fragmented magma. high resolution and continuouslarge adaptive scale remeshing propagation at of eachproach. surges In time this it step case, is is underwater eruption needed. thus is For necessary approximated by to imposing employ a semi-analytical specific initial ap- eruption in the middlereproduce represented the by di a suddenon release eruption of pressure superheated and vapour.very They additional well mass the event of observed in the 1996 steam. in These Karymskoye lake simulations although represent they do not consider cally. gas bubble formed upon the detonation in an infinite medium, i.e. they did not consider of the crater forms dissipativethe leading water wave. Gravitational rush collapse inward ofsmaller and the undulations. crater forms These makes the surges secondaryMéhauté expand and bore radially Wang accompanied while with decreasing a in number amplitude of ( onation, a vertical jetfollowed is by formed the second due jet tothe due inertial water to depth motion the of of cavityvelopment discharge collapse a of is upon liquid multiple accompanied decompression. layer jets. by Increasing over Veryscale the deep the water change disturbances. explosions cavity of and/or flow weak topology yields and cause de- only small sion). Several types ofa surface spectrum e of jets with various features ( ing predominantly of water vapour isof the formed. spherical Subsequent vapour expansion, cavity rise arepropagating and at collapse water the waves. origin of water disturbances generating radially depth of the burst and its yield (i.e. the amount of energy released during the explo- 1996 5 5 15 20 25 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and is the 12 c d ), 1960 Chil- the explosion 2.286 ( ). Successful di- W < 1995b 1.5 km) were used , 3 ∼ / 1 1995b R , W / is the characteristic length c 0.076, produce larger cavi- d Liu et al. is the distance from the ex- R < < r 3 ). This choice is based on a real / ). ) or 2004 Indian Ocean tsunami 1 Liu et al. as a function of explosion energy ) W 0 / 2000 η that controls the height of generated 1968 erent energies which are determined c , ff 0 , 1995a d 1996 η , , < 6405 6406 ect of bottom friction. The term describing the Liu et al. ff ) and might be modified by later erosion. Energy may change in time due to landslides, erosion or ), that solves for the nonlinear shallow water equa- R Van Dorn et al. represents the volcano mean crater radius where the 2012 , ) give an empirical relationship . The COMCOT numerical model has been extensively R Ward and Asphaug 1998 A , ). 1997 ( 0.029. Shallower explosion thus causes deeper water crater for Le Méhauté and Wang [J] is generally proportional to the third power of the crater diam- 2007 is the height of the water crater rim. J (corresponding to a crater radius up to 1995a = , , 0 E 17 c η , (4) 10 ), 1993 tsunami in Okushiri Island, Japan ( 3 2006 Valentine et al. ∼ , R ) contains the critical parameter 7 E 1 ) Liu et al. , (3) 10 doubles, 1995b A , (5) × , is a constant. According to the explosion yield, two cases are distinguished: | c 0.24 F c | usion force, but examine the e F Sato and Taniguchi ff cE J, corresponding approximately to volcanic crater radius of 100 to 1500 m. 3.56 3 0.014 for smaller explosions for which holds 0.076 2 m / = 17 [J] released. These were derived for shallow or intermediate depth explosions. The Explosion energy Tsunami wave field generated by underwater explosions depends critically on the Equation ( The same function for initial conditions has been also used to study tsunamis gener- = 7 = 0 Wang and Liu Liu et al. gn H explosions (e.g for fitting. The size of a volcanic crater represents the cumulated energy of multiple surface explosion experiments ( that also physically corresponds to water surface displacement observed in near- E where data from experimental andnitude volcanic up explosions to varying over 14 orders of mag- yield in pounds of TNT).ties Larger and explosions, 0 the same yield. eter. η where c depth of explosion, i.e. the depth of the volcano crater, in meters and COMCOT ( Appendix 3 Numerical model In order to performwave travelling across numerical the simulations water we of adopt the volcanic Cornell multi-grid explosion coupled resulting tsunami model in tsunami explosion power. However, otheragation physical parameters and in can particular changeespecially the the in influence shallow tsunami waters. of prop- Here, dissipativetal we mechanisms neglect di the might interfacial be shearbottom important stress friction and horizon- is introduced in governing equations using the Manning’s formula (cf. tsunami waves and itsexist value only should purely be empirical linked relationsE that to estimate the explosiongeneric characteristics. scaling There law is ( obtained from the crater radiusevents is such thus as a the maximum 1996underwater estimation explosions Karymskoye used must Lake for be simulating volcanic conducted past explosions.from for Simulations di style of of future past10 eruptions. Energies considered typically range between 10 ( physical resemblance with thethe cavity crater made radius by and an its impactor depth are hitting linked water. to In the this physical case, properties of the impactor. tions (NSWE), cf. Appendix tested and validated against laboratory experiments ( verse applications were computed including the( 1992 tsunami in Babi Island,ian Indonesia tsunami recorded at Hilo, Hawaii ( ated by asteroid impacts (e.g. plosion center and scale of the explosion.explosion Here, takes place. Although sediment transport, this has only a secondary influence. 5 5 25 15 20 25 10 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , - ffi ), cf. shore 0.15 s ). The ff around the hor- = 334 grid 0 t 488 mesh v × η 2013b ∆ 1996 ( × , J. This is ap- Linsley et al. 14 Belousov et al. 10 ) is approximative 3 × cient. Manning coe ffi ). We further improve the Nomikou et al. 2010 ( the volume flux with v H Le Méhauté and Wang = F the Manning coe m Torsvik et al. n ) around 50 m. Equation ( ). Artificial tide gauges were placed o 6408 6407 3 6 is the greatest still water depth in the calculation max h ) and 5 times more than the energy released during the the total water depth, is thus (cf. Eq. 2011 0 H , η ), energy release is estimated to lie around 5 4 0.01 s is chosen so as to satisfy the Courant–Friedrichs–Lewy (CFL) = , (6) Ide et al. t er in between the sea bottom and populated coastal areas. However, it s is used in calculations. This is a value that is adapted from water en- ff 3 ∆ is the grid size and J. max / x 1 is the gravity, x 16 − ∆ gh ∆ g . The swath bathymetry was obtained from several oceanographic surveys. The p ). , p. 314). 2 –10 ≤ 13 During the eruption, a new submerged crater with 200 m to 250 m in radius was t To perform simulations of tsunamitorini, generated we by Kolumbo use explosion topography registered and at bathymetry San- data prepared in 4.2 Kolumbo and Santorini gineering studies and was empirically determined for natural channels ( izontal velocity vector at thecient seafloor, should and be spatially variableit according should to di the surfaceis roughness often and in considered particular 0.025 constant m in tsunami numerical simulations and its value around where servations we thus conductits a estimated set value in of the calculations10 range by from 20 systematically to varying 100 m, corresponding to explosion energies initial water elevation due to its empirical character andorder limited formula. source In data order and should to be assess used the only suitability as of a first our model to reproduce the field ob- nuclear tests conducted on Bikini Atoll in 1946 ( earthquake ( 2000 formed. Using Eq. ( proximately 1800 times less than the surface energy released during the 2011 Tohoku 5.1 Simulation of 1996 tsunami inThe Karymskoye measured lake runups recordstrongest the explosion largest and tsunami can that be was matched probably by generated single by event the simulations ( near areas ofcoastal particular towns). vulnerability in case of tsunami (harbors,5 touristic resorts, Results Fig. first data were collectedtional in grid 2001, has and a further spatialthat refined resolution satisfies in of the 50 2006. CFL m. The criterion, Time resulting step cf. computa- size Eq. is ( chosen to be where domain. 1992 To perform simulations, topography and bathymetrywith data a are resolution of needed. 21 A mlake 274 of and the its pre-eruption surroundings bathymetry was and prepared topography by of Karymskoye 4 Grid preparation 4.1 Karymskoye lake given by the following formula ∆ quality of the grid on theical shores maps by of georeferencing and the digitalizing lake 1 datingwith : 1974. 10 The resolution 000 data of topograph- are 9 then m interpolatedTime in on step the the 498 both horizontalcondition directions ensuring to the obtain stability higher of precision employed data. numerical scheme. The CFL condition is 5 5 25 20 15 10 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , . ) J 3 1 5 13 (top). 2011 10 , 3 × Tinti et al. ) that lies as 1 s. The model 3 / 1 55 m that has the − = ect of friction, as this 0 ff Giachetti et al. and simulated runups η i ; 0.02 m = 2010 55 m is depicted on Figure m , n = 0 η cient ffi Kelfoun et al. ; 6410 6409 2005 , . (7) 2 ) i ). ). reaching the southern shore in about 2 min, cf. Fig. Liu et al. num 1 ; 1 . − − 6 i 2012a N , 2002 , (obs . Northern coast is touched by the first peak in about 4 min, the , Table 1 erent initial explosion powers. The circular source of 750 m radius 7 7 = ff N i P s shows the results. We test two sets of experiments, one with no bottom = 4 . The incoming first wave is always positive followed by a negative peak. Nomikou et al. 8 J following the energy range expected for further event. erence is small. In simulations we prefer to disregard the e Lynett and Liu ff Kolumbo volcano ; 17 i ect is negligible by itself and is probably up to an order of magnitude smaller than The corresponding waveforms registered near the six main coastal towns are shown First waves reach the north east coast of Santorini in about three minutes after the Results are only slightly modified when including dissipative processes in calcula- To investigate the consequences of an eventual future eruption of Kolumbo, we sys- The underwater explosion gives birth to waves radiating away from its centre. Col- After the explosion, waves propagate radially away from the centre of detonation with In order to quantify the match between simulated and measured values, we compute From the data set we exclude three data points, TS17, TS18 and TS22 (cf. Fig. Figure ff 5.2 Simulations of tsunami generated byThe submarine future Kolumbo volcanic underwater cone,island, that explosions has lies about a of 71700 km diameter m north ( of east around from Santorini 3 km and its crater width ranges from 1500 m to tions. Although in this case wethis observe a di better global match, i.e.e RMS error decreased, other uncertainties in the systemof that surface we and do subsurface not water take with into violent account expulsion of such magma. as interactions a typical velocity of 25 ms on Fig. Similar behaviour is also1999 observed in mass flow generated tsunamis (e.g. entire eastern coast in aboutabout 8 min 14 min and (Fig. southern parts of the island (around Akrotiri) in explosion, cf. Fig. tematically test di whose middle point matches thevarying physical water center rim of height the from Kolumboto crater 50 10 m is to imposed 350 with m corresponding to energies from 3 lapse of the imposed initialtoward water Santorini, crater cf. generates Fig. a positive leading wave propagating Highest wave amplitudes are registered into the the northern impact part region. of A the lake typical that simulation lies case closest with We observe a good predictiontion of or the overestimation field of data.model Note, the can that measured be no used data systematic toto occur. underestima- better understand This constrain their indicates tsunamis impact generated that in by the the volcanic coastal presented explosions areas. and num RMS error friction included and onewith zero with roughness the that best ManningRMS explains coe observations error is of one 1.37 with well m, the or predicted about heigh of 27comparison % initial of water of rim observed the of and observed 50 simulated m mean. using runups the This for empirical this matches laws. simulation extremely A is detailed shown on Fig. (bottom) were field measured runups are also reported. the root mean square error between observed runup values obs for their position), asexperiences these strong measurements nonlinearities lie too andwith close the more to coast complex the are interactionsthere expected source of are due where other incoming to the data very waves flow pointsclose shallow (north as water and TS17 along north-east and the from TS18are wave the (e.g. path. crater, expected TS01 cf. Although here Fig. or TS02) becausedirection. less Thus, waves they pronounced are are nonlinear included phenomena crossing in more the comparison profound exercise. water region in this 5 5 25 10 15 20 20 25 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | of λ ). We 2000 , Maeno and ; ect is minimized ) they are often ff 1 2006 , ). Here, the highest 11 . The highest waves are er partly from inaccuracy 0 ff Belousov et al. η and 9 Maeno et al. J. Larger explosion powers might from 4 m to 13 m. Waves recorded 16 max A ). Incoming waves have amplitudes inferior 9 ). The larger the explosion power, the longer 6411 6412 8 ). 2011 , ). The predicted values might su 1 J) more than triples 17 , Table . Highest amplitudes are recorded in Pori that lies closest to the is registered. For the weakest explosion considered in our study, 11 11 J to 10 Novikova et al. for bathymetry). at four main coastal towns as a function of explosion energy is rep- λ ; 13 2 shows the maximum depth of the incoming water waves along the original max A 2011 10 shows the maximum wave amplitudes for several , s prevent large inundation (Fig. ff 9 ). However, due to the rocky character of the northern coast, the inundation on 9 The highest tsunami incoming waves are registered on the northern and northeast- Figure To test the model, we first investigate the 1996 tsunami generated in Karymskoye Present day unrest under the Kolumbo submarine volcano (Greece, Aegean Sea), Arrival times are weakly sensitive to the explosion power and depends strongly on Periods are of the order of 30 s (Fig. contrary to caldera collapse triggered tsunamis (e.g. to 1 m for explosionimpact power harbors inside smaller the than caldera about with 10 1–2 m high waves. 2.6 m to 9 m,power 1.7 range m (Fig. to 6 m and 0.4 m to 1.9 m, respectively, over the explored energy coastline on the mainamplitude Santorini island forresented several on explosion Fig. powers. Maximum wave in Monólithos, Kamari and Akrotiri, respectively, vary in amplitude from approximately 6 Conclusions We have considered underwatermodel volcanic for tsunami explosions propagation asby and a inundation. around tsunamigenic Since 1 % such source explosions to and contribute all only tsunami cases registered on Earth (cf. Sect. that explosively erupted foreruption. the Tsunami last might time bemight in be generated considered 1650, by in indicates underwater further potential explosions, investigations (e.g. but hazard flank other of collapse, sources next caldera subsidence, ern coast of(Fig. Santorini as these parts of the island are the most exposed tocoast waves in the vicinity ofinterference Akrotiri of are waves substantially coming reducedincoming from and wave west the is and danger not east hereof (Figs. the is Santorini due leading caldera to wave, is but wellhigh protected. one cli Arriving of waves the are trailing greatly attenuated waves. and The steep inner part Kolumbo volcano. Increasing the explosionnitude about (from 10 approximately three orders of mag- inherited from imprecise near shoreby bathymetry choosing data. the However, this gauge e pointstime at all gauges certain lie distance closer from than the about coastal 900 m towns. from At the the coast. same lake, Kamchatka. Shortly after theprovides event, a runups unique data around set the toshow lake calibrate that were the our measured, numerical modelling that model is ( the capable ones to that reproduce are all too the close measured to runup the values except explosion centre (closer than about 1.2 km). the source. The amplitudes aretoward slightly Santorini) enhanced due in the to southdepth the west (cf. presence direction Fig. of (direction submarine ridge that decrease the sea floor this part is reduced. The highestalong tsunami Santorini impact as is most on of theincoming northeast these waves and areas eastern here can coasts consist enter of easily fields with inland. a The gentle amplitudes slope so of the tsunami on the southern neglected when estimating the potentialularly tsunami deadly hazard although at they short might distances be from partic- the volcano. the sea depth over whichThose are waves given propagate, by the unlike imposed the waterFigure crater amplitudes size of or equivalently incoming by waves. therecorded eruption in energy. the centre of explosion and decrease with increasing distance away from the wave length the leading wave is around 1000 m,This that resolution gives satisfies us around the 20 computationalsolutions. grid fluid points per dynamics wave requirements length. to obtain valid Imamura 5 5 15 25 10 25 15 20 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ) x τ the A3 g directions, ) and ( J). The east y A2 17 and x J to 10 13 10 the volume fluxes for which the still water depth), × Vougioukalakis and Fytikas ; h Q 1990 and with , η P + 0, (A3) 0, (A2) h = = cient. = y x ffi ρ τ ρ τ H 6414 6413 + + y Fytikas et al. x directions, respectively. Bottom shear stresses ∂η ∂ ∂η ∂ y are vertically averaged velocities in gH gH v + + and the water density. The last terms in Eqs. ( x erent powers and related tsunamis represent a significant and H ff ρ H PQ u PQ . , (A5) , (A4) x 2 y 2 Hv ∂ ∂ ∂ ∂ Q Q ). The numerical simulations proposed herein demonstrate that un- = 0, (A1) + + + + q = 2 is the total water depth ( 2 ! ! P P 2 1879 y 2 Q H H , and H p ∂ Q p P ∂ Q P is the Manning’s roughness coe

3 3 Hu is the water free surface elevation, and 2 2 m m / / m y x x P 7 7 are then modeled using the Manning formula ∂ = ∂ η n ∂ ∂ ∂ ∂ gn gn H H y Fouqué ) and is based on eyewitness accounts of the 1650 tsunami. However, this doc- P τ + + + = = er from the 1650 one. For the simplicity, only equations in the Cartesian coordinate system are given here. Future eruptions of Kolumbo volcano would impact Santorini island in terms of gas t t t ff Q P x y ∂ ∂ ρ ρ ∂ τ τ ∂ ∂η ∂ Governing equations in COMCOT The standard non-linear shallow water equations are employed in COMCOT Appendix A with amplitudes ranging fromof 2 the m island to are 9strongest well m protected explosion. for The and the incoming smallest same wavestudes waves do are lower energy than not registered range. 2 exceed inside m Southern mostly the for parts 4 all caldera m tested with for cases. ampli- the emissions, tephra fallout, earthquake andtion tsunami, ( as occurred during the 1650 erup- coast of Santorini island, weers. simulate The tsunami predicted generated waves by reaching a Santoriniregistered range amplitudes are of of highest incoming explosion on waves pow- the rangeand north from large 4 east m explosions, coast to respectively where 13 (varying m,coast, respectively, energy for where small from gentle 3 slopes allow water to enter largely inland, is impacted by waves pyroclastic flows). In order to evaluate possible impacts of Kolumbo explosions on the where However, COMCOT package also solvesgeometry for with the Coriolis force governing due equations to in rotation of the the spherical Earth included. Cartesian coordinate where hold respectively. gravity acceleration and represent bottom friction in and ument relies on thedi trustworthiness of these testimonies, and future eruptions might 2005 derwater explosions of di hazard for Santorini. Existing volcanicdation hazard in map case of of Santorini Kolumbo includes eruption tsunami inun- ( 5 5 15 20 10 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 6403 6415 , M., ) and ff 1991 , 6412 , 6402 6400 6408 , 6413 Wessel and Smith 6413 , 6402 6402 , 2007. 6402 6401 , 6402 X, GMT ( 6401 E T A 6410 6416 6415 degassing from hydrothermal vents at Kolumbo submarine 10.5194/nhess-7-65-2007 2 6402 ) magic. M. Ulvrová is grateful to Xiaoming Wang for his help with COMCOT. We financed by CNRS-INSU. The publication of this article is . This paper benefited from L 2007 6401 , ClerVolc Hunter 6400 , M., Rische, M., Meier, T., Becker, D., Stavrakakis, G., and Harjes, H.-P.: Microseismic ff , M., Rische, M., and Meier, T.: Seismicity and active tectonics at Coloumbo Reef (Aegean ff Earth Syst. Sci., 7, 65–69, doi: triggered by the Guimar debrisbased data, avalanche, Tenerife Mar. (Canary Geol., Islands): 284, comparison 189–202, with 2011. field- of the 1650 Mt.Hazards, Columbo 21, 83–96, (Thera 2000. Island) eruption and tsunami, Aegean Sea, Greece, Nat. World III, editedDruitt, by: T. Hardy, H., D. vol.9 A., 2, September 1989, Proceedings Keller, 183–198, J., of The Thera the Galanopoulos, Foundation, third 1990. V. international P., Flemming, congress, N. 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A t

Elevation [m] Elevation 3 m) [m] Elevation − max A 0 0 80 60 40 20 500 400 300 200 100 100 −100 −200 −300 −400 −500 −20 −40 −60 A t 14 m) ( − erent explosion powers, max ﬀ

54˚00' 53˚59' 53˚58' 53˚57' for di A t A t 4 m) ( 1 km −

B 159˚30' Kamari max erent locations on Santorini. Values at TS08 TS07 Monólithos ﬀ A Perissa TS06 TS09 TS05 A t 0 km

Ridge 159˚29' TS10 TS04 Pori , at six di 16 14 m) ( TS11 A 0 6422 6421 − η and arrival times TS21 Akrotíri max TS03 A Paradisos TS02

max 159˚28' TS01 A A t 6 m) ( TS22 TS20 −

max 159˚27' A TS13 5 km A t TS24 TS18

4 m) ( 159˚26' TS17 − TS14 TS16 ( TS15 25˚15' 25˚18' 25˚21' 25˚24' 25˚27' 25˚30' 25˚33' 0 km max 528000 530000 532000 [m] [s] [m] [s] [m] [s] [m] [s] [m] [s] [m] [s] Paradisos Pori Monolithos Kamari Perissa Akrotiri A Maximum wave amplitudes 36˚30' 36˚27' 36˚24' 36˚21' 36˚18' 5984000 5982000 5980000 . Number in parenthesis reports the water depth at a given gauge. Pre-eruption bathymetry (negative) and topography (positive) of the Karymskoye lake, 2 50 m150 m 1.9250 m 6.0350 m 195 8.7 188 10.6 4.0 183 7.9 180 167 10.6 159 12.8 154 2.6 150 5.5 7.6 261 9.0 254 249 1.7 246 3.8 5.1 374 5.8 365 360 1.6 356 3.1 4.0 516 4.5 505 498 0.4 493 1.1 1.6 864 1.9 820 813 809 erent sizes of initial water crater rim ﬀ = = = = 0 0 0 0 η η η η i.e. di Kamchatka, and itsdepicted. surrounding. Red Contour points lines showthe with locations position constant where of runup the contour centre was interval of measured. the 50 The m new yellow formed are crater. star also represents Fig. 1. gauges near the main townscf. (closer Fig. than about 900 m) on the coast of the island are reported, Table 1.

Bathymetry (negative) and topography (positive) of the Santorini island, Greece, and its surrounding Pre-eruption bathymetry (negative) and topography (positive) of the Karymskoye lake, Kamchatka, and

et al. (2013b))

is represented by the yellow star. Main coastal towns are shown by pink triangles. (Modiﬁed after Nomikou used for numerical simulations. Contour lines are depicted with a contour line interval 100 m. Kolumbo volcano

Fig. 2. where runup was measured. The yellow star represents the position of the centre of the new formed crater.

Elevation [m] Elevation Elevation [m] Elevation . (Top) First 0 0 80 60 40 20 500 400 300 200 100 100 −100 −200 −300 −400 −500 −20 −40 −60 = 55m 0

54˚00' 53˚59' 53˚58' 53˚57' ). 4.3 1.9 3.3 2.4 2.0

12.0

1 km 1.6 4.3 532000 532000

B 159˚30' Kamari 2013b TS08 TS07 Monólithos 10.5

5.8 ,

Perissa 3.8 1.2 1.6 TS06 TS09 4.8 9.0 TS05 5.8 531000 531000 4.7 0 km 7.6 1.2 7.5

0.4 6.2

Ridge 159˚29' TS10 TS04 Pori 17

0.4 6.0 16 TS11 A 6424 6423 0.8 530000 530000 4.3 TS21 Akrotíri TS03 4.5 Arrival times [min] Paradisos 4.3 Nomikou et al. 0.4 TS02 3.0

Maximum water elevation [m] 159˚28' TS01 4.8 529000 529000 0.8 1.5 0.0 9. 6.2 +5.979e6 +5.979e6 6.2 TS22 TS20 1000 1000 5000 3000 5000 3000 2000 2000

4000 4000 159˚27' TS13 5 km TS24

TS18 159˚26' TS17 TS14 TS16 TS15 25˚15' 25˚18' 25˚21' 25˚24' 25˚27' 25˚30' 25˚33' 0 km 528000 530000 532000 Results of explosion simulation in Karymskoye lake with initial water crater rim 36˚30' 36˚27' 36˚24' 36˚21' 36˚18' 5984000 5982000 5980000 Results of explosion simulation in Karymskoye lake with initial water crater rim Bathymetry (negative) and topography (positive) of the Santorini island, Greece, and Fig. 3. wave travel times (in minutes).measured (Bottom) runup with Maximum the wave runup amplitude. values. Red points indicate positions of field Fig. 2. its surrounding used forinterval numerical simulations. 100 m. Contour Kolumbo linesshown are volcano by pink depicted is triangles with represented (Modified a after by contour line the yellow star. Main coastal towns are Fig. 3. 55 m. (Top) First wave travel timesindicate (in positions minutes). of (Bottom) field Maximum measured wave amplitude. runup Red with points the runup values.

et al. (2013b))

Fig. 2. where runup was measured. The yellow star represents the position of the centre of the new formed crater. its surrounding. Contour lines with constant contour interval 50 m are also depicted. Red points show locations Fig. 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | s . Experiments with no friction 3 / 0 1 erent − η ff 100 0.02 m 3.5 9 s = 3 n / o 1 m i − t n c i m . Experiments with no friction r 90 f 0 2 8 t 0 η . cient u 0 3.0 o ffi h = 100 3.5 t 9 i s m 3 n / 80 o w n 1 i − t c i m 7 r 90 f 2 8 t 0 . u 0 3.0 o h = t i m Measurements Numerical simulation 80 2.5 w n 70 7 6 Measurements Numerical simulation 2.5 (black squares) are reported. 70 6 erence between simulated and measured (black squares) are reported. ff s s 60 3 60 3 / / 5 18 5 18 2.0 2.0 1 1 6426 6425 − 50 − 4 50 Measured runup [m] 1.5 02 m 4 40 . Distance from crater [km] 3 Measured runup [m] 1.5 Rim height of imposed wave [m] = 0 02 m 30 1.0 40 Initial wave height is 55.0m, breaking off, friction off . m 2 Distance from crater [km] n 3

55 m and no bottom friction. (Top) Runup as a function of distance

1 2 2 7 7 5 5 3 3 20 8 8 6 6 9 9 4 4

Simulation runup [m] runup Simulation

1.2 [m] Runup 1.8 2.2 1.6 1.4 3.0 2.8 2.0 2.6 2.4 = r o r r e S M R [m] Rim height of imposed wave = 0 0 30 η 1.0 Initial wave height is 55.0m, breaking off, friction off m 2 n

1 2 2 7 7 5 5 3 3 20 8 8 6 6 9 9 4 4

Simulation runup [m] runup Simulation

1.2 [m] Runup 1.8 2.2 1.6 1.4 3.0 2.8 2.0 2.6 2.4 r o r r e S M R Root mean square (RMS) error of the di Comparison of measured and simulated runups around the Karymskoye lake. Results . Experiments with no friction (red circles) and Manning coe and no bottom friction. (Top) Runup as a function of distance from crater. (Bottom) Simulated 0 η runups at 18 locations around the Karymskoyerim lake as a function of imposed amplitude of water Fig. 4. (black squares) are reported. locations. The dashed line corresponds to the simulated runups equal to the measured values. Fig. 5. are for simulation with from crater. (Bottom) Simulated runup as a function of the measured runup at 18 di = 55m

Comparison of measured and simulated runups around the Karymskoye lake. Results are for simulation Root mean square (RMS) error of the difference between simulated and measured runups at 18 locations 0 η

(red circles) and Manning coefﬁcient Fig. 5. with runup as a function of the measured runup atrunups 18 different equal locations. to The the dashed measured line corresponds values. to the simulated Fig. 4. around the Karymskoye lake as a function of imposed amplitude of water rim and no bottom friction. (Top) Runup as a function of distance from crater. (Bottom) Simulated

= 55m Comparison of measured and simulated runups around the Karymskoye lake. Results are for simulation

Root mean square (RMS) error of the difference between simulated and measured runups at 18 locations 0 η (red circles) and Manning coefﬁcient with runups equal to the measured values. Fig. 5. runup as a function of the measured runup at 18 different locations. The dashed line corresponds to the simulated around the Karymskoye lake as a function of imposed amplitude of water rim Fig. 4. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | B

north east 4 14

2 B 4 14 10 25.55 10 25.55 6 12 6 12 25.50

2 8 25.50

8 10 8

8 10

50 m and no bottom friction. 10 25.45

= 10 0 25.45 8 η

6 8 12

12 25.40 8 .) 6

12 19

6 25.40 8 and no bottom friction. .) 6 6428 6427

12 19 Distance [km] and no bottom friction. 4 Arrival times [min] 25.35 Distance [km] 4 8 4 4 Arrival times [min] 25.35 4

4 8 8 = 250m = 50m

25.30 0 8 = 250m 2 0 η 2

6 = 50m 25.30 η 0 2 0 η 2 6 η 25.25

0 36.0 s 9.0 s 18.0 s 27.0 s 0.0 s 12 10 25.25 0 0 A 18.0 s 18.0 27.0 s 36.0 s 0.0 s s 9.0 12 0 0 0 0 0 10 36.45 36.35 36.30 36.50 36.40 200 400 200 400 200 400 200 400 200 400 200 200 200 200 200

0 A

0 0 0 0 0 Wave height profiles [m] profiles height Wave

36.45 36.35 36.50 36.40 36.30 200 400 200 400 200 400 200 400 200 400

200 200 200 200 200

A bathymetry and topography proﬁle (shaded areas) along AB line in Fig. First wave arrival times for Santorini island and its surroundings. Black lines are drown Wave height profiles [m] profiles height Wave 250 m.) = 0 Fig. 7. with an interval of 2 min. Results are for simulation with Fig. 6. of Santorini. Red lines depictof the the wave height positive soon tsunami9 after km leading the distance. wave. explosion Number and The showη in explosion the each center formation ﬁgure inside shows the time Kolumbo in crater seconds lies after at the explosion. (Case with

A bathymetry and topography proﬁle (shaded areas) along AB line in Figure 2 north east of Santorini. First wave arrival times for Santorini island and its surroundings. Black lines are drown with an interval

Fig. 7. of 2 min. Results are for simulation with in seconds after the explosion. (Case with

Red lines depict the wave height soon after thewave. explosion The and show explosion the center formation inside of the the Kolumbo positive tsunami crater leading lies at 9 km distance. Number in each ﬁgure shows time Fig. 6. of 2 min. Results are for simulation with Fig. 7. in seconds after the explosion. (Case with wave. The explosion center inside the Kolumbo crater lies at 9 km distance. Number in each ﬁgure shows time Red lines depict the wave height soon after the explosion and show the formation of the positive tsunami leading Fig. 6. Maximum water elevation [m] elevation water Maximum 100 10 1 1e-01

25.50 25.50 Maximum water elevation [m] elevation water Maximum 10 1 1e-01 100 25.45 25.45 m m 25.40 25.40 m 25.55 25.55 0 0 0 5 5 5 1 2 5 5 5 5 5 5 = = = 0 0 0 25.50 25.50 η η η 25.35 25.35 25.45 25.45 m m 4 4 4 4 4 4 0 0 m m 25.40 25.40 m 0 0 0 5 5 5 5 5 1 2 5 5 5 5 5 5 = = = 0 0 0 25.30 25.30 3 1 η η η 25.35 25.35 m m = = 4 4 4 4 4 4 0 0 . Note, that the color scale is logarithmic. 5 5 0 0 0 25.30 25.30 1 3 3 3 3 3 3 3 η η η 25.25 25.25 = = 0 0 3 3 3 3 3 3 20 η η 25.25 25.25 20 Time [min] 6430 6429 Time [min] 36.45 36.35 36.45 36.35 36.40 36.30 36.50 36.40 36.30 36.50 2 2 2 2 2 2 36.45 36.35 36.45 36.35 36.50 36.40 36.30 36.50 36.40 36.30 2 2 2 2 2 2 . Note, that the color scale is logarithmic. Black thin line represents 1 1 1 1 1 1 0 25.55 25.55 η Paradisos Pori Monolithos Kamari Perissa Akrotiri . Note, that the color scale is logarithmic. Black thin line represents 25.50 25.50 0 0 0 0 0 0 1 1 1 1 1 1 2 1 1

5 5 5 2 5 5 5 4 4 0 0 0 0 0 0 4 4

15 10 10 10 10 10 0 Wave amplitude [m] amplitude Wave 25.55 25.55 η Paradisos, Pori, Monolithos, Kamari, Perissa and Akrotiri. Note, 25.45 25.45 ff erent for each location. Akrotiri Monolithos Kamari Perissa Paradisos Pori erent explosion powers. Time signals are shifted so that zero time ff ff 25.40 25.40 25.50 25.50 0 0 0 0 0 0 2 1 1 5 5 5 2 5 5 5 4 4 0 0 0 0 0 0 4 4 15 10 10 10 10 10 25.35 25.35

m Wave amplitude [m] amplitude Wave m 0 0 5 25.30 25.30 5 2 25.45 25.45 = = Results of numerical calculations of the Kolumbo explosion generating tsunami. Maximum wave 0 0 Water surface displacement registered near six coastal towns along Santorini (cf. Figure 2 for map) and η η 25.25 25.25 25.40 25.40 36.35 36.45 36.35 36.45 36.50 36.40 36.30 36.50 36.40 36.30 the original coastlines. Inundation of most east coast of Santorini is visible for all four scenarios. Fig. 9. amplitudes around Santorini for several for three different explosion powers. Time signalsa given are simulation. shifted Gauges so are that positioned zero 400 timeMonolithos, m, corresponds Kamari, 900 Perissa to m, and arrival 500 Akrotiri. time m, Note, for 500 that m, the 800 vertical m scale and is 450 different m for off each Paradisos, location. Pori, Fig. 8. Results of numerical calculations of the Kolumbo explosion generating tsunami. Maxi- Water surface displacement registered near six coastal towns along Santorini (cf. Fig. 25.35 25.35 m Black thin line representsvisible the for original all coastlines. four Inundation scenarios. of most east coast of Santorini is Fig. 9. mum wave amplitudes around Santorini for several for map) and for three di Fig. 8. corresponds to arrival time for500 a m, given 800 simulation. m Gauges and arethat positioned 450 the 400 m vertical m, o scale 900 m, is 500 di m, m 0 5 0 25.30 25.30 2 5 = = Results of numerical calculations of the Kolumbo explosion generating tsunami. Maximum wave 0 0 Water surface displacement registered near six coastal towns along Santorini (cf. Figure 2 for map) and η η 25.25 25.25 36.35 36.45 36.35 36.45 36.30 36.40 36.50 36.30 36.40 36.50 amplitudes around Santorini for several Fig. 9. the original coastlines. Inundation of most east coast of Santorini is visible for all four scenarios. Monolithos, Kamari, Perissa and Akrotiri. Note, that the vertical scale is different for each location. a given simulation. Gauges are positioned 400 m, 900 m, 500 m, 500 m, 800 m and 450 m off Paradisos, Pori, for three different explosion powers. Time signals are shifted so that zero time corresponds to arrival time for Fig. 8. . Distance zero 0 . Distance zero η 0 η

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . 0 η 7 1 0 7 1 350 1 0 60 350 1 m m m 60 m m m m 0 0 0 m 0 5 5 5 0 0 0 5 1 2 3 0 5 5 5 Akrotiri 5 1 2 3 = = = = Akrotiri 0 0 0 0 = = = = η η η η 0 0 0 0 300 η η η η 50 300 for their location). 50 2 6 1 6 0 1 1 0 · 250 1 40 2 · 250 40 2 ] ] m [ m [ 200 30 0 200 30 21 0 η 21 η 6432 6431 as a function of explosion energy registered at four 5 1 Distance [km] 5 0 1 Distance [km] 1 0 max Paradisos · Explosion energy [J] 150 20 1 Paradisos · A Explosion energy [J] 150 20 3 Pori 3 Pori Pori as a function of explosion energy registered at four different locations as a function of explosion energy registered at four different locations 10 100 10 100 Pori Monolithos Kamari Akrotiri Monolithos Kamari Akrotiri Pori Monolithos Monolithos

max max Kamari Kamari A 3 Perissa A 3 1 Perissa 1 0 0 0 1 50 0

· 1 2 5 8

6 0 4 50

· 2 5 8 6 0 4

12 15 3 10 10 20

12 15 3 10 10 20 Maximum wave amplitude [m] amplitude wave Maximum

Wave amplitude on the coast [m] coast the on amplitude Wave Maximum wave amplitude [m] amplitude wave Maximum

Wave amplitude on the coast [m] coast the on amplitude Wave for their locations). Flow depth along the original coastline of the main Santorini island for several Maximum wave amplitude 2 erent locations on the east and south coasts of Santorini (cf. Fig. ﬀ Fig. 11. di Fig. 10. Distance zero corresponds to thewise. southernmost point Distance of of the the island(cf. and six Fig. increases main counterclock- coastal towns is depicted by vertical arrows and dashed lines

Flow depth along the original coastline of the main Santorini island for several

Maximum wave amplitude

Maximum wave amplitude on the east and south coasts of Santorini (cf. Figure 2 for their location).

Fig. 10. Fig. 11. coastal towns is depicted by vertical arrows and dashed lines (cf. Figure 2 for their locations).

corresponds to the southernmost point of the island and increases counterclockwise. Distance of the six main Fig. 11. on the east and south coasts of Santorini (cf. Figure 2 for their location).

Fig. 10. coastal towns is depicted by vertical arrows and dashed lines (cf. Figure 2 for their locations). corresponds to the southernmost point of the island and increases counterclockwise. Distance of the six main