In the present work, an advanced tsunami generation, propagation and coastal inundation 2-DH model (i.e. 2-D Horizontal model) based on the higher-order Boussinesq equations – developed by the authors – is applied to simulate representative earthquake-induced tsunami scenarios in the Eastern Mediterranean. Two areas of interest were selected after evaluating tsunamigenic zones and possible sources in the region: one at the southwest of the island of Crete in Greece and one at the east of the island of Sicily in Italy. Model results are presented in the form of extreme water elevation maps, sequences of snapshots of water elevation during the propagation of the tsunamis, and inundation maps of the studied low-lying coastal areas. This work marks one of the first successful applications of a fully nonlinear model for the 2-DH simulation of tsunami-induced coastal inundation; acquired results are indicative of the model's capabilities, as well of how areas in the Eastern Mediterranean would be affected by eventual larger events.

The 2004 tsunami in Southeast Asia and its devastating effects brought to the public's attention the long-neglected risk tsunamis pose for coastal areas. The issue had already alerted – to a certain extent – the scientific community (e.g. the review of Dawson et al., 2004 for Europe); however, it is evident that the 2004 event contributed significantly to the rise of awareness in public authorities and policy makers, resulting in a notable shift in related research as well. Accordingly, there has been a continuous effort post-2004 towards the improvement of the tools and methods used for the assessment of coastal vulnerability to tsunami-related hazards, with numerical modeling being the basis of all respective attempts.

Tsunami generation and propagation has been steadily studied since the late 1980s; nevertheless, the main gap in relevant knowledge can be identified as to what happens when tsunami waves approach the nearshore and run inland. The sequence of a tsunami hitting the coast comprises a series of processes: from the tsunami generation and propagation, to coastal-zone hydrodynamics (including surf and swash zone dynamics), coastal inundation and wave-structure interactions with the built environment. Regarding the modeling part – and focusing on coastal inundation – exemplary reference can be made to the work of Borrero et al. (2006), who used the MOST model (Titov and González, 1997) for tsunami generation and inundation in western Sumatra; Gayer et al. (2010), who used the MIKE21 Flow Model FM to simulate inundation based on roughness maps for Indonesia; Omira et al. (2010), who applied a modified version of the COMCOT model (Liu et al., 1998) to selected cases in Casablanca, Morocco; Apotsos et al. (2011), who used the Delft3D model to study inundation and sediment transport by the 2004 SE Asia tsunami in measured and idealized morphologies; and Løvholt et al. (2012), who used models based on the Boussinesq equations for tsunami propagation and nonlinear shallow-water wave equations for coastal inundation to simulate the 2011 Tohoku tsunami. Extending to coastal planning, vulnerability assessment and tsunami hazard mitigation, one may refer to the work of Bernard (2005), González et al. (2009), Post et al. (2009), Kumar et al. (2010), Sørensen et al. (2012) and González-Riancho et al. (2014).

Tsunamis in the Eastern Mediterranean have a long and significant history, and have attracted awareness due to the well-established geotectonic regime of the area (i.e. Papadopoulos and Chalkis, 1984; Papazachos and Papazachou, 1998; Soloviev et al., 2000; Papadopoulos, 2003; El-Sayed et al., 2004; Tinti et al., 2004; Papadopoulos and Fokaefs, 2005; Stefatos et al., 2006; Papadopoulos et al., 2014). The Aegean Sea and its surrounding areas, in particular, are not only the most active Mediterranean regions in terms of seismicity and tectonic movements, but their coastlines have also experienced numerous tsunami events in recent, historic and pre-historic times.

Earthquakes and submarine slides are the two principal tsunamigenic mechanisms in the aforementioned region, although volcanic eruption and collapse could not be ignored as a potential mechanism as well (e.g. the Late Minoan Thera event). The generation and propagation of tsunamis in the Eastern Mediterranean has been numerically studied by relatively few researchers, especially in comparison to the geotectonic regime of the area. One may refer to the work of Tinti et al. (2005), for scenarios of tsunamis of tectonic origin from the Algerian earthquake of 1980, the Eastern Sicily Arc and the Western/Eastern Hellenic Arc; Salamon et al. (2007), for tsunamis generated from landslide and/or earthquake scenarios impacting the coasts of Syria, Lebanon and Israel; Lorito et al. (2008) for earthquake-generated tsunamis from the Algeria-Tunisia, Southern Tyrrhenian, and Hellenic Arc source zones; as well as of Yolsal et al. (2007) and Periáñez and Abril (2014), covering all generation mechanisms (geological faults, landslides, entry of pyroclastic flows into the sea and the collapse of a volcano caldera). However, the adequate representation of nearshore dynamics and coastal inundation remains an issue in all relevant attempts for the area.

In the present work, an advanced tsunami generation, propagation and coastal
inundation 2-DH model – developed by the authors – is applied to simulate
representative earthquake-induced tsunami scenarios in the Eastern
Mediterranean. Regarding the coastal hydrodynamics, the nonlinear wave
transformation in the surf and swash zone is computed by a nonlinear
breaking wave model based on the higher-order Boussinesq equations for
breaking and non-breaking waves (Karambas and Samaras, 2014).
Tsunami generation is simulated through additional time derivative terms in
the continuity and momentum equations in order to represent displacements at
the sea bed or surface. Inundation is simulated based on the

Boussinesq-type equations are widely used for the description of the non-linear breaking and non-breaking wave propagation in the nearshore or long wave propagation in the open sea (Gobbi and Kirby, 1999; Gobbi et al., 2000; Ataie-Ashtiani and Najafi Jilani, 2007; Fuhrman and Madsen, 2009; Zhou and Teng, 2009; Zhou et al., 2011). Over the years, the classical Boussinesq equations have been extended so as to be able to include higher-order nonlinear terms, which can describe better the propagation of highly nonlinear waves in the shoaling zone. The linear dispersion characteristics of the equations have been improved as well, in order to describe nonlinear wave propagation from deeper waters (Zou, 1999). Antuono et al. (2009) and Antuono and Brocchini (2013) provide significant improvements with respect to typical Boussinesq-type models for both numerical solution features (Grosso et al., 2010) and the overall flow structures; a thorough overview on Boussinesq-type models can be found in Brocchini (2013).

The higher-order Boussinesq-type equations for breaking and non-breaking
waves used in this work are the following (Zou, 1999; Karambas and Koutitas, 2002;
Karambas and Karathanassi, 2004; Karambas and Samaras, 2014):

In Eqs. (

Regarding the effects of unresolved small-scale motions, they are
parametrized applying the philosophy of the large eddy simulation. The
effects of subgrid turbulent processes are taken into account by using the
Smagorinsky-type subgrid model (Chen et al., 2000; Zhan et al., 2003).
The components of the eddy viscosity term

Tsunami generation is simulated through additional terms in the continuity
and momentum equations, Eqs. (

The numerical solution of the Boussinesq-type equations (Eqs.

Energy absorption at the open boundaries is accounted for through the
introduction of artificial damping terms in the momentum equation (Eq.

Run-up and run-down of a solitary wave of

The above-described damping layer is applied along with a radiation boundary
condition, which for principal wave propagation direction close to the

The coast in the model can be considered either as a solid (fully or
partially reflecting) boundary, or as a boundary allowing sea mass inland
penetration and inundation. The first case for a fully reflective boundary
derives from the conservative assumption expressed by:

The model's capability in representing swash zone hydrodynamics was validated through the comparison with both two-dimensional (cross-shore) and three-dimensional experimental data by Synolakis (1987) and Briggs et al. (1995), respectively.

Synolakis (1987) studied the run-up and run-down of breaking and
non-breaking solitary waves on a plane beach. The experiments were carried
out in the wave tank facility of the W. M. Keck Laboratories of the
California Institute of Technology. The glass-walled tank's dimensions were
37.73 m

Figure 1 shows the comparison of the normalized surface elevation between
model results and the measurements of Synolakis (1987) for a solitary
wave of

Tsunami run-up on a circular island: comparison of the normalized
maximum run-up height (

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,
Mississippi. 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 diameter 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

Tsunami run-up on a circular island: comparison of the normalized
maximum run-up height (

Tsunami run-up on a circular island: comparison of the normalized
maximum run-up height (

Tsunami run-up on a circular island: snapshots of the free surface
for the experiment with

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 convolution of the frequency of occurrence and the intensity of tsunami events (Papadopoulos and Fokaefs, 2005; Papadopoulos, 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.

In the present work, the model for tsunami generation, propagation and coastal inundation presented in Sect. 2 was applied 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 amplitude of

The tsunamigenic zones of the Mediterranean Sea and their respective tsunami potential (adopted from Papadopoulos and Fokaefs, 2005).

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).

Bathymetric information was extracted by the EMODnet Bathymetry Portal (EMODnet, 2015); shorelines by the GSHHS database (Global Self-consistent Hierarchical High-resolution Geography database; NOAA/NGDC, 2015). The topographic information for the coastal areas of interest were 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 second for Sicily; USGS/GDE, 2015). Figure 6 shows the location, the elevation and selected topographic contours of the low-lying coastal areas of interest where inundation phenomena were studied, at south-southwest Crete (Fig. 6a) and east-southeast Sicily (Fig. 6b).

Location, elevation and selected topographic contours for the
low-lying coastal areas of interest at:

Simulated extreme water elevation (

Figure 7 shows the simulated extreme water elevation (

Sequences of snapshots of water elevation for the
earthquake-induced tsunami scenario at the southwest of Crete at:

Sequences of snapshots of water elevation for the
earthquake-induced tsunami scenario at the East of Sicily at:

Inundation maps of the studied low-lying coastal areas at:

Snapshots of the evolution of inundation at the coasts of
southwest Crete (see also Fig. 6a) for an exemplary exaggerated tsunami
scenario (normalized wave amplitude of

Figure 10 shows the inundation maps of the studied low-lying coastal areas
at (a) south-southwest Crete and (b) east-southeast Sicily. The inundated
areas shown in Fig. 10a and b, where the inundation extent was more
easily represented at the scale of interest, cover 3.429 and 0.641 km

This work presents an advanced tsunami generation, propagation and coastal inundation 2-DH model (developed by the authors) and its applications for two representative earthquake-induced tsunami scenarios in the Eastern Mediterranean. The model is based on the higher-order Boussinesq equations, and its capability in representing swash zone hydrodynamics is validated through the comparison with both two-dimensional (cross-shore) and three-dimensional experimental data by Synolakis (1987) and Briggs et al. (1995), respectively. The model is applied 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.

Model results, presented in the form of extreme water elevation maps, sequences of snapshots of water elevation during the propagation of the earthquake-induced tsunamis, and inundation maps of the studied low-lying coastal areas, highlight the model's capabilities and are indicative of how areas in the region would be affected by eventual larger events. It should be noted that this work marks one of the first successful applications of a fully nonlinear model based on the Boussinesq equations for the 2-DH simulation of tsunami-induced coastal inundation, thus not resorting to estimates of the flooded area from simple superelevations of the water surface or from the spatial extension of cross-sectional run-up results. Similar attempts can constitute the basis of a more detailed coastal flooding risk assessment and mitigation along the coasts of the Eastern Mediterranean.

Renata Archetti acknowledges the financial support of the Italian Flagship Project RITMARE (SP3-WP4-AZ2). The authors would like to thank the Handling Topic Editor Prof. Lakshmi Kantha and the three anonymous referees for their constructive comments and suggestions. Edited by: L. Kantha

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