# Simulation of tsunami generation, propagation and coastal inundation in the Eastern Mediterranean

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Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/ doi:10.5194/os-11-643-2015 © Author(s) 2015. CC Attribution 3.0 License. Simulation of tsunami generation, propagation and coastal inundation in the Eastern Mediterranean A. G. Samaras1 , Th. V. Karambas2 , and R. Archetti3 1 CIRI– EC, Fluid Dynamics Unit, University of Bologna, Via del Lazzaretto 15/5, Bologna 40131, Italy 2 Department of Civil Engineering, Aristotle University of Thessaloniki, University Campus, Thessaloniki 54124, Greece 3 Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Viale Risorgimento 2, Bologna 40136, Italy Correspondence to: A. G. Samaras (achilleas.samaras@unibo.it) Received: 31 March 2015 – Published in Ocean Sci. Discuss.: 8 May 2015 Revised: 2 August 2015 – Accepted: 3 August 2015 – Published: 27 August 2015 Abstract. In the present work, an advanced tsunami gener- there has been a continuous effort post-2004 towards the im- ation, propagation and coastal inundation 2-DH model (i.e. provement of the tools and methods used for the assessment 2-D Horizontal model) based on the higher-order Boussinesq of coastal vulnerability to tsunami-related hazards, with nu- equations – developed by the authors – is applied to simulate merical modeling being the basis of all respective attempts. representative earthquake-induced tsunami scenarios in the Tsunami generation and propagation has been steadily Eastern Mediterranean. Two areas of interest were selected studied since the late 1980s; nevertheless, the main gap in rel- after evaluating tsunamigenic zones and possible sources in evant knowledge can be identified as to what happens when the region: one at the southwest of the island of Crete in tsunami waves approach the nearshore and run inland. The Greece and one at the east of the island of Sicily in Italy. sequence of a tsunami hitting the coast comprises a series Model results are presented in the form of extreme water el- of processes: from the tsunami generation and propagation, evation maps, sequences of snapshots of water elevation dur- to coastal-zone hydrodynamics (including surf and swash ing the propagation of the tsunamis, and inundation maps of zone dynamics), coastal inundation and wave-structure inter- the studied low-lying coastal areas. This work marks one of actions with the built environment. Regarding the modeling the first successful applications of a fully nonlinear model for part – and focusing on coastal inundation – exemplary ref- the 2-DH simulation of tsunami-induced coastal inundation; erence can be made to the work of Borrero et al. (2006), acquired results are indicative of the model’s capabilities, as who used the MOST model (Titov and González, 1997) well of how areas in the Eastern Mediterranean would be af- for tsunami generation and inundation in western Sumatra; fected by eventual larger events. Gayer et al. (2010), who used the MIKE21 Flow Model FM to simulate inundation based on roughness maps for Indone- sia; Omira et al. (2010), who applied a modified version of the COMCOT model (Liu et al., 1998) to selected cases in 1 Introduction Casablanca, Morocco; Apotsos et al. (2011), who used the Delft3D model to study inundation and sediment transport The 2004 tsunami in Southeast Asia and its devastating ef- by the 2004 SE Asia tsunami in measured and idealized fects brought to the public’s attention the long-neglected risk morphologies; and Løvholt et al. (2012), who used models tsunamis pose for coastal areas. The issue had already alerted based on the Boussinesq equations for tsunami propagation – to a certain extent – the scientific community (e.g. the re- and nonlinear shallow-water wave equations for coastal in- view of Dawson et al., 2004 for Europe); however, it is evi- undation to simulate the 2011 Tohoku tsunami. Extending to dent that the 2004 event contributed significantly to the rise coastal planning, vulnerability assessment and tsunami haz- of awareness in public authorities and policy makers, result- ard mitigation, one may refer to the work of Bernard (2005), ing in a notable shift in related research as well. Accordingly, Published by Copernicus Publications on behalf of the European Geosciences Union.

644 A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean González et al. (2009), Post et al. (2009), Kumar et al. (2010), at the southwest of the island of Crete in Greece and one Sørensen et al. (2012) and González-Riancho et al. (2014). at the East of the island of Sicily in Italy. Model results are Tsunamis in the Eastern Mediterranean have a long and presented in the form of extreme water elevation maps, se- significant history, and have attracted awareness due to the quences of snapshots of water elevation during the propa- well-established geotectonic regime of the area (i.e. Pa- gation of the earthquake-induced tsunamis, and inundation padopoulos and Chalkis, 1984; Papazachos and Papazachou, maps of the studied low-lying coastal areas. Regarding the 1998; Soloviev et al., 2000; Papadopoulos, 2003; El-Sayed inundation, in particular, this work marks one of the first suc- et al., 2004; Tinti et al., 2004; Papadopoulos and Fokaefs, cessful applications of a fully nonlinear model based on the 2005; Stefatos et al., 2006; Papadopoulos et al., 2014). The Boussinesq equations for the 2-DH simulation of tsunami- Aegean Sea and its surrounding areas, in particular, are not induced coastal inundation, thus not resorting to estimates only the most active Mediterranean regions in terms of seis- of the flooded area from simple superelevations of the water micity and tectonic movements, but their coastlines have also surface or from the spatial extension of cross-sectional run- experienced numerous tsunami events in recent, historic and up results. pre-historic times. Earthquakes and submarine slides are the two principal tsunamigenic mechanisms in the aforementioned region, al- 2 The model for tsunami generation, propagation and though volcanic eruption and collapse could not be ignored coastal inundation as a potential mechanism as well (e.g. the Late Minoan Thera event). The generation and propagation of tsunamis in the 2.1 Boussinesq equations for breaking/non-breaking Eastern Mediterranean has been numerically studied by rel- waves and tsunami generation atively few researchers, especially in comparison to the geo- tectonic regime of the area. One may refer to the work of Boussinesq-type equations are widely used for the descrip- Tinti et al. (2005), for scenarios of tsunamis of tectonic origin tion of the non-linear breaking and non-breaking wave prop- from the Algerian earthquake of 1980, the Eastern Sicily Arc agation in the nearshore or long wave propagation in the and the Western/Eastern Hellenic Arc; Salamon et al. (2007), open sea (Gobbi and Kirby, 1999; Gobbi et al., 2000; Ataie- for tsunamis generated from landslide and/or earthquake sce- Ashtiani and Najafi Jilani, 2007; Fuhrman and Madsen, narios impacting the coasts of Syria, Lebanon and Israel; 2009; Zhou and Teng, 2009; Zhou et al., 2011). Over the Lorito et al. (2008) for earthquake-generated tsunamis from years, the classical Boussinesq equations have been extended the Algeria-Tunisia, Southern Tyrrhenian, and Hellenic Arc so as to be able to include higher-order nonlinear terms, source zones; as well as of Yolsal et al. (2007) and Periáñez which can describe better the propagation of highly nonlinear and Abril (2014), covering all generation mechanisms (geo- waves in the shoaling zone. The linear dispersion character- logical faults, landslides, entry of pyroclastic flows into the istics of the equations have been improved as well, in order sea and the collapse of a volcano caldera). However, the ade- to describe nonlinear wave propagation from deeper waters quate representation of nearshore dynamics and coastal inun- (Zou, 1999). Antuono et al. (2009) and Antuono and Broc- dation remains an issue in all relevant attempts for the area. chini (2013) provide significant improvements with respect In the present work, an advanced tsunami generation, to typical Boussinesq-type models for both numerical solu- propagation and coastal inundation 2-DH model – devel- tion features (Grosso et al., 2010) and the overall flow struc- oped by the authors – is applied to simulate representa- tures; a thorough overview on Boussinesq-type models can tive earthquake-induced tsunami scenarios in the Eastern be found in Brocchini (2013). Mediterranean. Regarding the coastal hydrodynamics, the The higher-order Boussinesq-type equations for breaking nonlinear wave transformation in the surf and swash zone and non-breaking waves used in this work are the follow- is computed by a nonlinear breaking wave model based on ing (Zou, 1999; Karambas and Koutitas, 2002; Karambas and the higher-order Boussinesq equations for breaking and non- Karathanassi, 2004; Karambas and Samaras, 2014): breaking waves (Karambas and Samaras, 2014). Tsunami generation is simulated through additional time derivative ζt + ∇ (hU ) = 0, (1) terms in the continuity and momentum equations in order to represent displacements at the sea bed or surface. Inun- dation is simulated based on the dry bed boundary condi- 1 1 tion (Karambas and Koutitas, 2002); the model’s capabil- U t + ∇Mu − U ∇(U h) + g∇ζ + G (2) h h ity in representing swash zone hydrodynamics is validated 1 1 through the comparison with both two-dimensional (cross- = h∇ [∇ · (dU t )] − h2 ∇ [∇ · U t ] 2 6 shore) and three-dimensional experimental data by Syno- 1 2 1 h i lakis (1987) and Briggs et al. (1995), respectively. After eval- + d ∇ ∇ · (U t + g∇ζ ) + ∇ ∇ · d 2 U t + gd 2 ∇ζ 30 30 uating tsunamigenic zones and possible sources in the region, τb two areas of interest were selected for the applications: one − d∇(δ∇ · U )t − + E, h Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/

A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean 645 where Mu is defined as: to represent bed level changes (Mitsotakis, 2009), thus trans- forming it to: Mu = (d + ζ ) u2o + δ c2 − u2o , (3) ζt + ∇(hU ) = ζb,t , (8) and G as: where ζb is the bottom displacement; accordingly the term d 2 ∇ζb,t is added to the right-hand side of Eq. (2). For the bot- 1 2 2 2 1 2 G = ∇ d (∇ · U ) − U · ∇ U − ∇ (U · U ) (4) tom displacement function the model follows the approach 3 10 of Hammack (1973), considering two types of bed move- 1 ments: an exponential and a half-sine one. The above method − ζ ∇[∇ · (dU t )]. 2 is called active tsunami generation. The model additionally includes the option for a passive tsunami generation (i.e. the In Eqs. (1)–(4) the subscript t denotes differentiation with introduction of the aforementioned displacement directly on respect to time, d is still the water depth, U is the hori- the free surface), which is the one used in the present work zontal velocity vector U = (U, V ) with U and V being the as well. depth-averaged horizontal velocities along the x and y direc- tions, respectively; ζ is the surface elevation, h the total depth 2.2 Numerical scheme and boundary conditions (h = d + ζ ), g is the gravitational acceleration, τb = (τbx , τby ) is the bottom friction term (shear stress components ap- The numerical solution of the Boussinesq-type equations proximated by the use of the quadratic law according to Rib- (Eqs. 1 and 2) is based on the accurate higher-order numeri- berink (1998), δ is the roller thickness (determined geomet- cal scheme of Wei and Kirby (1995), who proposed a fourth- rically according to Schäffer et al., 1993). E is the eddy vis- order predictor-corrector scheme for time stepping, discretiz- cosity term (according to Chen et al., 2000), and uo is the ing the first-order spatial derivatives to fourth-order accuracy. bottom velocity vector uo = (uo , vo ) with uo and vo being The specific discretization has the advantage – over lower or- the instantaneous bottom velocities along the x and y direc- der schemes – of automatically eliminating error terms that tions respectively. In the above, Mu is the excess momen- would be of the same form as the dispersive terms and would, tum term introduced to account for energy dissipation due to therefore, need to be corrected. The scheme consists of the wave breaking; the process itself is based on a specific char- third-order in time explicit Adams–Bashford predictor step acteristic of the breaker: the presence of the surface roller, i.e. and fourth-order in time implicit Adams–Bashford corrector the passive bulk of water transported with the wave celerity. step (Press et al., 1992; Wei and Kirby, 1995). Regarding the effects of unresolved small-scale motions, Energy absorption at the open boundaries is accounted for they are parametrized applying the philosophy of the large through the introduction of artificial damping terms in the eddy simulation. The effects of subgrid turbulent processes momentum equation (Eq. 2). In particular, terms F and G are taken into account by using the Smagorinsky-type sub- are added to the right-hand sides of the momentum equation grid model (Chen et al., 2000; Zhan et al., 2003). The com- expressions along the x and y directions, respectively; the ponents of the eddy viscosity term E in Eq. (2) are defined terms are defined as (Wei and Kirby, 1995): as: F = −αr rU, (9) 1 Ex = (5) G = −αr rV , (10) d +ζ 1 where αr is the constant to be determined for the specific (νe [(d + ζ )U ]x )x + (νe [(d + ζ )U ]y + [(d + ζ )V ]x )y , run, and r is the relaxation parameter that varies from 0 to 1 2 within the specified damping zone (r =1 at the outer edges 1 Ey = (6) of the zones and decreasing down to 0 at the edges facing the d +ζ model domain) according to: 1 (νe [(d + ζ )V ]y )y + (νe [(d + ζ )V ]x + [(d + ζ )U ]y )x , i −1 for 2 r = 1 − tanh −→ i = 1, 2, 3, . . ., NN, (11) 2 with the eddy viscosity coefficient νe estimated from (Zhan with “NN” being the number of grid elements in the damping et al., 2003): zone. " #1/2 The above-described damping layer is applied along with a ∂U 2 ∂V 2 1 ∂U ∂V 2 νe = 0.25dx 2 + + + . (7) radiation boundary condition, which for principal wave prop- ∂x ∂y 2 ∂y ∂x agation direction close to the x axis is expressed by the fol- lowing (Wei and Kirby, 1995): Tsunami generation is simulated through additional terms in the continuity and momentum equations, Eqs. (1) and (2) ∂ 2ζ ∂ 2ζ cl2 ∂ 2 ζ respectively. The time derivative term ζb,t is added to Eq. (1) + cl − = 0, (12) ∂t 2 ∂t∂x 2 ∂y 2 www.ocean-sci.net/11/643/2015/ Ocean Sci., 11, 643–655, 2015

646 A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean Figure 1. Run-up and run-down of a solitary wave of H /d = 0.25 on a 1:19.85 plane sloping beach; comparison of the normalized surface elevation (ζ /d) between model results and the measurements of Synolakis (1987), at consecutive non-dimensional time instances (t 0 = t (g/d)1/2 ). where c1 = (gd)1/2 is the phase speed specified by the long- two-dimensional (cross-shore) and three-dimensional exper- wave limit. imental data by Synolakis (1987) and Briggs et al. (1995), The coast in the model can be considered either as a solid respectively. (fully or partially reflecting) boundary, or as a boundary al- Synolakis (1987) studied the run-up and run-down of lowing sea mass inland penetration and inundation. The first breaking and non-breaking solitary waves on a plane beach. case for a fully reflective boundary derives from the conser- The experiments were carried out in the wave tank facil- vative assumption expressed by: ity of the W. M. Keck Laboratories of the California In- stitute of Technology. The glass-walled tank’s dimensions ∂ζ = 0, U n = 0, (13) were 37.73 m × 0.61 m × 0.39 m (length × width × depth); ∂n the sloping beach was constructed at a 1:19.85 slope where n is the unit landward normal vector; for a partially (tan a = 1:19.85); the still water depth in the constant depth reflective boundary, it is simulated by properly adjusting the region was set to 0.2 m. The profile of the solitary wave re- value of the eddy viscosity coefficient νe (see Eq. 7) in front produced, centered at x = X1 , is given by of the coast. The second case is simulated based on the dry bed boundary condition for the simulation of run-up, as de- H ζ (x, 0) = sec h2 γ (x − X1 ), (14) scribed in detail by Karambas and Koutitas (2002). d 2.3 Model validation where H = solitary wave height and γ is defined as 1/2 The model’s capability in representing swash zone hydro- 3H dynamics was validated through the comparison with both γ= . (15) 4d Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/

A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean 647 Table 1. Tsunami run-up on a circular island: comparison of the Table 2. Tsunami run-up on a circular island: comparison of the normalized maximum run-up height (R/H ) distribution around the normalized maximum run-up height (R/H ) distribution around the island between model results and the measurements of Briggs et island between model results and the measurements of Briggs et al. (1995) for ε = 0.10; the angle α = 0 corresponds to the front al. (1995) for ε = 0.20; the angle α = 0 corresponds to the front direction of the wave approaching the island and α = π to the back direction of the wave approaching the island and α = π to the back direction. direction. Direction R/H Direction R/H a [rad] Experimental data Model results a [rad] Experimental data Model results 0 2.700 2.813 0 2.850 2.344 π/8 2.650 2.625 π/8 2.750 2.188 2π /8 2.550 2.438 2π/8 2.580 2.031 3π /8 2.100 2.250 3π/8 2.250 1.785 π/2 2.000 1.875 π/2 1.780 1.563 5π /8 1.800 1.650 5π/8 1.200 1.094 6π /8 1.700 1.500 6π/8 0.810 0.938 7π /8 1.540 1.250 7π/8 0.650 0.838 π 3.180 2.625 π 1.840 1.619 Figure 1 shows the comparison of the normalized surface elevation between model results and the measurements of Synolakis (1987) for a solitary wave of H /d = 0.28 am- plitude ratio, as a series of snapshots at consecutive non- dimensional time instances. Model predictions are in close agreement with the experimental data in both surf and swash zones. Run-up and run-down are simulated well, with the col- lapse of the bore identified in Fig. 1d, e and f, and the moment of maximum run-up in Fig. 1g. Briggs et al. (1995) studied three-dimensional tsunami run-up on a circular island. The experiments were carried out in the facilities of the US Army Corps of Engineers Waterways Experiment Station (WES) in Vicksburg, Missis- sippi. The physical model of a conical island was constructed in the center of a 30 m wide 25 m long flat bottom basin, shaped as a truncated right circular cone with a 7.2 m diam- eter at its toe and a 2.2 m diameter at its crest. The height of the cone was approximately 62.5 cm, with a beach face slope of β = 14◦ . Tsunami waves were simulated using soli- Figure 2. Tsunami run-up on a circular island: comparison of the tary waves, their surface profiles given by Eq. (14), follow- normalized maximum run-up height (R/H ) distribution around the ing the rationale of Synolakis (1987). Experiments for sym- island between model results and the measurements of Briggs et metric source lengths and a depth of d = 32 cm in the basin al. (1995) for (a) ε = 0.10 and (b) ε = 0.20; the angle α = 0 corre- sponds to the front direction of the wave approaching the island and were reproduced, for two different ratios of initial amplitude α = π to the back direction. to depth (i.e. ε = H /d), namely ε = 0.10 and ε = 0.20. Ta- bles 1, 2 and Fig. 2 show the comparison of the normal- ized maximum run-up height (i.e. run-up height to initial higher discrepancy observed only at a = π . For ε = 0.20, the wave height is R/H ) distribution around the circular island model seems to relatively underestimate run-up at the front between model results and the measurements of Briggs et part of the island, while from α = π/2 to α = π calculated al. (1995); the angle α = 0 corresponds to the front direc- R/H values are again very close to measurements. tion of the wave approaching the island and α = π to the back direction. Figure 3 shows snapshots of the free surface at different time instances for the experiment with ε = 0.20. Model predictions are in close agreement with experimental data for this test as well. For ε = 0.10, R/H values are prac- tically overlapping around the entire island, with a relatively www.ocean-sci.net/11/643/2015/ Ocean Sci., 11, 643–655, 2015

648 A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean 3 Applications in the Eastern Mediterranean 3.1 Tsunamigenic zones and sources Figure 4 shows a map of the known tsunamigenic zones in the Mediterranean Sea region along with a relative scale of their potential for tsunami generation, calculated as a con- volution of the frequency of occurrence and the intensity of tsunami events (Papadopoulos and Fokaefs, 2005; Pa- padopoulos, 2009). Sakellariou et al. (2007) summarized the possible tsunamigenic sources in the Eastern Mediterranean based on existing marine geological, bathymetric and seismic data; the results are presented in the map of Fig. 5. 3.2 Model applications In the present work, the model for tsunami generation, prop- agation and coastal inundation presented in Sect. 2 was ap- plied to two areas of interest: one at the southwest of the island of Crete in Greece and one at the East of the island of Sicily in Italy. The areas, indicated in Fig. 5, comprise the sources of the earthquake-induced tsunami scenarios and the low-lying coastal areas where inundation phenomena were studied (see also Fig. 6). Regarding the earthquake-induced tsunami scenarios, earthquakes that would generate a normalized wave ampli- tude of ζ0 = 1 m were considered; the lengths of the ma- jor and minor axes of the elliptical aftershock areas were estimated based on the empirical equations proposed by Karakaisis (1984), Papazachos et al. (1986) and Demetra- copoulos et al. (1994): log Lmajor = −2.22 + 0.57 M, (16) Lminor = Lmajor /3, (17) log ζ0 = 0.98 M − 6.92, (18) where M is the magnitude of the mainshock. It should be noted, of course, that due to the non-linearity of the studied phenomena the presented model results should not be used to estimate the absolute propagation/inundation characteristics of tsunamis with multiple or sub-multiple wave amplitudes at generation for the specific sources/areas of interest. The essence of the presented applications lies in testing the ca- pabilities of the developed model and methodology for real case scenarios of operational interest in the Mediterranean; not in replicating single tsunami events, for which, further- more, accurate inundation data would not be available. Bathymetric information was extracted by the EMOD- net Bathymetry Portal (EMODnet, 2015); shorelines by the GSHHS database (Global Self-consistent Hierarchical High- Figure 3. Tsunami run-up on a circular island: snapshots of the free resolution Geography database; NOAA/NGDC, 2015). The surface for the experiment with ε = 0.20 at: (a) t = 6.0 s, (b) t = topographic information for the coastal areas of interest were 7.5 s, (c) t = 9.0 s, and (d) t = 12.0 s. extracted by Digital Elevations Models of the NASA Shuttle Radar Topography Mission, at the best resolution available for the areas of interest (3 arc seconds for Crete and 1 arc sec- ond for Sicily; USGS/GDE, 2015). Figure 6 shows the loca- Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/

A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean 649 Figure 4. The tsunamigenic zones of the Mediterranean Sea and their respective tsunami potential (adopted from Papadopoulos and Fokaefs, 2005). Figure 5. Possible tsunamigenic sources in the Eastern Mediterranean; the black rectangles outline the two areas of interest in the present work, comprising the sources of the earthquake-induced tsunami scenarios and the low-lying coastal areas where inundation phenomena were studied (adopted from Sakellariou et al., 2007; privately processed). www.ocean-sci.net/11/643/2015/ Ocean Sci., 11, 643–655, 2015

650 A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean Figure 6. Location, elevation and selected topographic contours for the low-lying coastal areas of interest at: (a) south-southwest Crete, Figure 7. Simulated extreme water elevation (ζ /ζ0 ) for the and (b) east-southeast Sicily (base images from Google Earth, 2015; earthquake-induced tsunami scenarios at: (a) the southwest of privately processed using NASA SRTM data from USGS/GDE, Crete, and (b) the East of Sicily. 2015). tion, the elevation and selected topographic contours of the impact to adjacent coasts. Results do not indicate a signifi- low-lying coastal areas of interest where inundation phenom- cant impact to be expected for the Western coasts of Greece , ena were studied, at south-southwest Crete (Fig. 6a) and east- as – at approximately 450 km away from the tsunami source southeast Sicily (Fig. 6b). – extreme elevations do not exceed locally ζ /ζ0 = 0.2 (e.g. at the East coast of Peloponnese at y ≈ 900 km). However, and although it is stated in Sect. 3.2 that results for the simulated 4 Results and discussion scenarios should not be used to deduce the absolute charac- teristics of multiple or sub-multiple tsunamis (with regard to Figure 7 shows the simulated extreme water elevation (ζ /ζ0 ) ζ0 ), Fig. 9 is indicative of the areas to be affected by an even- for the earthquake-induced tsunami scenarios at the south- tual larger event (the same applies to Fig. 8, respectively). west of Crete (Fig. 7a) and at the East of Sicily (Fig. 7b). Se- Figure 10 shows the inundation maps of the studied low- quences of snapshots of water elevation during tsunami prop- lying coastal areas at (a) south-southwest Crete and (b) east- agation are presented in Figs. 8 and 9 for the two aforemen- southeast Sicily. The inundated areas shown in Fig. 10a and tioned scenarios, respectively. A tsunami generated at the b, where the inundation extent was more easily represented southwest of Crete (see Figs. 7a and 8) would impact most at the scale of interest, cover 3.429 and 0.641 km2 , respec- severely the adjacent coasts (as expected due to the source tively. Although for both cases inundation heights are com- proximity), with calculated extreme water elevations reach- parable, the relatively steeper slopes at the studied coasts of ing the normalized amplitude of the tsunami wave at genera- Sicily result in an overall narrower inundation zone (with the tion. The impact is expected to be significant to the East part inevitable added scale effect of the representation). Again, it of the Libyan coast as well (approx. 250 km away from the should be noted that these areas are indicative of the ones tsunami source; at x ≈ 650 km ÷ 750 km), with extreme el- to be affected by eventual larger events. Finally, regarding evations locally exceeding ζ /ζ0 = 0.4. A tsunami generated the simulation of inundation itself, Fig. 11 shows snapshots at the East of Sicily (see Figs. 7b and 9) would have a similar of the evolution of the phenomenon at the coasts of south- Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/

A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean 651 Figure 8. Sequences of snapshots of water elevation for the earthquake-induced tsunami scenario at the southwest of Crete at: (a) t = 0 s (generation), (b) t = 250 s, (c) t = 850 s, (d) t = 2000 s, (e) t = 4000 s, and (f) t = 6000 s. Figure 9. Sequences of snapshots of water elevation for the earthquake-induced tsunami scenario at the East of Sicily at: (a) t = 0 s (genera- tion), (b) t = 250 s, (c) t = 850 s, (d) t = 2000 s, (e) t = 4000 s, and (f) t = 6000 s. www.ocean-sci.net/11/643/2015/ Ocean Sci., 11, 643–655, 2015

652 A. G. Samaras et al.: Tsunami simulation in the Eastern Mediterranean Figure 10. Inundation maps of the studied low-lying coastal areas at: (a) south-southwest Crete, and (b) east-southeast Sicily for the studied earthquake-induced tsunami scenarios (see also Figs. 6–9; base images from Google Earth, 2015; privately processed using NASA SRTM data from USGS/GDE, 2015). southwest Crete for an exemplary exaggerated tsunami sce- nario (normalized wave amplitude of ζ0 = 6 m at genera- tion); it should be underlined that these results serve only to demonstrate more clearly the performance of the model at the scale of the representation, and do not relate to the sce- narios presented in the previous. Figure 11. Snapshots of the evolution of inundation at the coasts of southwest Crete (see also Fig. 6a) for an exemplary exaggerated 5 Conclusions tsunami scenario (normalized wave amplitude of ζ0 = 6 m at gen- eration), presenting: (a) the propagation of the tsunami wave to the This work presents an advanced tsunami generation, prop- nearshore; (b) the wave breaking at the lower part and the run-up agation and coastal inundation 2-DH model (developed at the upper part of the figure; (c) the run-up at the lower part and by the authors) and its applications for two representa- run-down at the upper part of the figure; and (d) the run-down at the tive earthquake-induced tsunami scenarios in the Eastern lower part of the figure. Mediterranean. The model is based on the higher-order Boussinesq equations, and its capability in representing swash zone hydrodynamics is validated through the com- Model results, presented in the form of extreme water ele- parison with both two-dimensional (cross-shore) and three- vation maps, sequences of snapshots of water elevation dur- dimensional experimental data by Synolakis (1987) and ing the propagation of the earthquake-induced tsunamis, and Briggs et al. (1995), respectively. The model is applied to inundation maps of the studied low-lying coastal areas, high- two areas of interest: one at the southwest of the island of light the model’s capabilities and are indicative of how areas Crete in Greece and one at the East of the island of Sicily in in the region would be affected by eventual larger events. It Italy. should be noted that this work marks one of the first suc- Ocean Sci., 11, 643–655, 2015 www.ocean-sci.net/11/643/2015/

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