**Spatial Variability of Beach Impact from Post-Tropical Cyclone Katia (2011) on Northern Ireland's North Coast**

#### **Giorgio Anfuso 1,\*, Carlos Loureiro 2,3, Mohammed Taaouati 4, Thomas Smyth <sup>5</sup> and Derek Jackson <sup>6</sup>**


Received: 17 March 2020; Accepted: 9 May 2020; Published: 13 May 2020

**Abstract:** In northern Europe, beach erosion, coastal flooding and associated damages to engineering structures are linked to mid-latitude storms that form through cyclogenesis and post-tropical cyclones, when a tropical cyclone moves north from its tropical origin. The present work analyses the hydrodynamic forcing and morphological changes observed at three beaches in the north coast of Northern Ireland (Magilligan, PortrushWest's southern and northern sectors, andWhiterocks), prior to, during, and immediately after post-tropical cyclone Katia. Katia was the second major hurricane of the active 2011 Atlantic hurricane season and impacted the British Isles on the 12–13 September 2011. During the Katia event, offshore wave buoys recorded values in excess of 5 m at the peak of the storm on the 13 September, but nearshore significant wave height ranged from 1 to 3 m, reflecting relevant wave energy dissipation across an extensive and shallow continental shelf. This was especially so at Magilligan, where widespread refraction and attenuation led to reduced shore-normal energy fluxes and very minor morphological changes. Morphological changes were restricted to upper beach erosion and flattening of the foreshore. Longshore transport was evident at Portrush West, with the northern sector experiencing erosion while the southern sector accreted, inducing a short-term rotational response in this embayment. In Whiterocks, berm erosion contributed to a general beach flattening and this resulted in an overall accretion due to sediment influx from the updrift western areas. Taking into account that the post-tropical cyclone Katia produced £100 m (\$157 million, 2011 USD) in damage in the United Kingdom alone, the results of the present study represent a contribution to the general database of post-tropical storm response on Northern European coastlines, informing coastal response prediction and damage mitigation.

**Keywords:** wave energy; Hurricane Katia; longshore transport; dissipative

#### **1. Preamble: Katia Cyclone Description**

Hurricane Katia's formation was instigated by a wide low-pressure system on the 28th of August 2011, offshore of the western coast of Africa (Figure 1). The low pressure system moved westward and, on 29 August, acquired sufficient convective intensity to be designated as a tropical depression when it was located about 695 km southwest of the south westernmost Cape Verde Islands (https://www.nhc.noaa.gov, accessed on 18 April 2020). The depression moved to the west-northwest for the next 24 h and gradually strengthened, becoming a tropical storm on 30 August about 787 km southwest of the Cape Verde Islands. The cyclone maintained a west-northwest trajectory at around 27.8 km h−<sup>1</sup> for the next two days and steadily strengthened to reach hurricane intensity on the Saffir-Simpson Hurricane Wind Scale by 1 September when it was located about 2176 km east of the Leeward Islands. After achieving hurricane status, Katia turned northwest and continued to strengthen and reached hurricane category 4 status on 5 September with wind peak intensity of 220 km h−<sup>1</sup> and a central low pressure of 942 mb when the hurricane was located about 870 km south of Bermuda. Such extreme conditions lasted one day only and the hurricane then slowed down and gradually turned north-east on 9 September (Figure 1). After this, the wind field expanded and weakened. When Katia was located about 650 km northwest of Bermuda, it turned toward the east-northeast and increased in speed, to approximately 92 km h<sup>−</sup>1, arriving over the cold sea-surface temperatures (22 ◦C) of the North Atlantic Ocean. The combination of cold water and strong vertical wind shear favoured the quick transition from a hurricane status into a powerful post-tropical low-pressure system by 1200 UTC 10 September when it was located about 463 km south-southeast of Cape Race, Newfoundland. On 11 September, Katia cyclone, a large and powerful post-tropical storm, turned north-east towards the northern British Isles with an average velocity of 85 km h<sup>−</sup>1. The post-tropical cyclone reached the northern coast of Scotland on 12 September and produced sustained gale-force winds across most of the British Isles and hurricane-force wind gusts in Scotland, Northern Ireland, and northern England with average wind speed from 101 to 188 km h−<sup>1</sup> with peak values of 212 km h−<sup>1</sup> recorded in North Wales. On the 13 September the cyclone continued north-eastward and dissipated over the North Sea. In Europe, the post-tropical cyclone Katia impacted numerous locations, downing trees, bringing down power lines, and leaving thousands without electricity. In the United Kingdom the storm was responsible for two deaths and caused approximately £100 m (\$157 million 2011 USD) in damage [1].

**Figure 1.** Track of Katia cyclone obtained from NOAA [1].

#### **2. Introduction**

Coastal development continues to increase and some 50% of the world's coastline is currently under pressure from excessive development [2,3], mainly in the form of tourism, one of the world's largest industries [4,5]. In Europe, the rapid expansion of urban artificial surfaces in coastal zones during the 1990–2000 period [6], has occurred in the Mediterranean and South Atlantic areas, namely Portugal (34% increase) and Spain (18%), followed by France, Italy and Greece. Ireland, a more peripheral holiday beach destination, has also had significant development of urban artificial surfaces in the coastal zones. In Northern Ireland, in 2018, 2.8 million visitors and over 2 million Northern Ireland residents took an overnight trip to the region, spending an unprecedented £968 million, £42 million more compared with 2017 [7].

Activities related with tourism can be significantly affected by the impacts of storms and hurricanes, producing damages to recreational and protective structures, with associated reduction of beach width and general aesthetics [8]. Over the past century, several storms and hurricanes have caused vast economic loses along with large numbers of deaths along the world's coastlines [9]. According to Dolan and Davis [10], the most powerful storms that have struck the Atlantic coast of USA, occurred on the 7–9 March 1962 (the "Ash Wednesday" storm), 7–11 March 1989, and on the 28 October–1 November 1991 (the "All Hallows' Eve").

Morton and Sallenger [11] investigated hurricanes and tropical cyclones that impacted the Gulf of Mexico and the Atlantic coast of USA, evaluating damages and washover penetration linked to hurricanes Carla (1961), Camille (1969), Frederic (1979), Alicia (1983) and Hugo (1989). According to Sallenger [12], the greatest coastal changes are recorded when the beach system completely submerges in an inundation regime: it can take place locally on a barrier island, incising a new inlet, as happened during Hurricane Isabel (2003) in North Carolina, Charley and Ivan in Florida (2004), and Katrina (2005) in Alabama. Additionally, inundation can submerge tens of kilometres of coast as occurred on the Bolivar Peninsula (TX, USA) during hurricane Ike (2008) and in Louisiana during Rita and Katrina events in 2005.

In northern Europe, damages to coastal structures, beach erosion and flooding inundation are often associated with mid-latitude (or extratropical) storms that form through cyclogenesis in the mid-latitude westerly wind belt and, secondly, post-tropical cyclones that form when a tropical cyclone moves north from its tropical origin [13].

In terms of the effects of mid-latitude storms, Bonazzi et al. [14] reconstructed spatial maps of peak gust footprints for 135 of the most important damaging events in 15 European countries in the past four decades, i.e., 1972–2010. The most important storms were 87J, Daria, Vivian, Anatol, Lothar, Martin, Erwin/Gudrun, Kyrill, Emma, Klaus and Xynthia. They observed 64% of events used in their analysis occurred during North Atlantic Oscillation positive phase (NAO+) months and their inter-annual variability, described by the NAO, modulated the main orientation of the storm tracks and the frequency of storm events.

On the Atlantic edge of Europe, Anfuso et al. [15] characterized, using the Storm Power Index [10], the distribution of storms in the Gulf of Cadiz during the 1958–2001 period and, highlighted particularly stormy years, e.g., years characterized by more storms and extended storm durations. Rangel-Buitrago and Anfuso [16] and Anfuso et al. [15] also observed the most powerful stormy years in Cadiz occurred every 5–6 years (e.g., in 1995–1996, 2002–2003, 2009–2010) with a 7–8-year periodicity recorded by Ferreira et al. [17] and Almeida et al. [18] in Faro (Southern Portugal).

The energetic conditions recorded in the Cadiz Gulf area during the 1995–1996 period also corresponded with similar weather conditions observed over the same period in Wales (UK) by Phillips [19] and Phillips and Crisp [20]. Dodet et al. [21] highlighted a highly unusual sequence of extratropical storms over the 2013–2014 winter period along Europe's Northeast Atlantic region, incorporating wave analysis over the period 2002–2017 for the northwest of Ireland, the Bay of Biscay and west of Portugal and beach erosion/recovery in five beaches in SW England, Brittany and the Bay of Biscay (France) that were surveyed on a monthly basis for more than 10 years. That winter recorded

the most energetic conditions along the Atlantic coast of Europe since at least 1948 [22] resulting in most of western Europe' coastlines being severely impacted [23–25] albeit with the exception of beaches in NW Northern Ireland (this field site).

Santos et al. [26] examined waves around UK that exceeded the 1 in 1-year return level analysed from 18 different buoy records for the period from 2002 to mid-2016, de-clustered into 92 distinct storm events. The majority of events were observed between November and March, with large inter-annual differences in the number of events per season associated with the West Europe Pressure Anomaly. The 2013/2014 storm season represented an outlier in terms of the number of wave events, their temporal clustering and return levels.

The strength and position of extratropical cyclones is influenced largely by the pattern of atmospheric circulations over the North Atlantic Basin, which, in turn, are reflected in the signal and strength of the North Atlantic Oscillation Index [27]. However, Atlantic tropical cyclones that move northward from the tropics and undergo extratropical transition may also cause high-impact weather events in Western Europe [28]. Tropical cyclones generated in the Atlantic basin drift westward at tropical latitudes within the easterly Trade winds, and migrate northward affecting the east coast of the US. Usually once every 1–2 years, these cyclones move eastward undergoing extratropical transition and reach western Europe as post-tropical storms often with hurricane force-winds [29]. In Northwest Ireland, the earliest reported high-magnitude event was the 'Night of the Big Wind', which was probably the tail-end of a hurricane reported in January 1839. Cooper and Orford [30] described the occurrence and impacts of post-tropical cyclones on the British Isles using historical and contemporary information. Examining the period between 1922 and 1998, they identified nine major tropical cyclones that traversed the Atlantic and impacted the British Isles. MacClenahan et al. [31] identified Hurricane Debbie (September 1961) as the largest storm that impacted Ireland during the second half of the 20th Century. Recently, Guisado-Pintado and Jackson [32,33] described the effects of the post-tropical Storm Ophelia (2018) and Storm Hector (2019) in Ireland's NW Donegal coast.

The post-tropical cyclone Katia impacted the British Isles during the 12–13 September 2011 causing £100 m (\$157 million, 2011 USD) in damage. The present work analyses what, if any, morphological changes occurred during the Katia cyclone in three beaches in the north coast of Northern Ireland, taking into account that storm-induced waves persisted until the 15 September, a couple of days after the cyclone dissipation. The importance of the present study lies in the necessity of understanding and predicting morphological changes associated with the impacts of hurricanes and intense post-tropical storms that, while infrequent, can sometimes have significant impacts on exposed coastal areas of the British Isles and cause relevant economic losses [30]. The behaviour of these coastal systems can be greatly affected in the future due to observed and modelled changes in frequency and intensity of extreme storms, and particularly the poleward migration of the maximum intensity of tropical cyclones as a result of global climate changes [34]. There is also concern that a possible change in hurricane tracks could lead to such destructive events impacting more frequently Southern European coasts, resulting in potentially more dramatic responses [35,36]. The results of the present study contributes to our understanding of beach and coastal response to post-tropical storm events along the coast of Northern Ireland and adds information to the general database of storm response on coastlines of this nature, informing damage mitigation and coastal response prediction.

#### **3. Study Area**

This paper examines the morphological change in three sandy beach sites, Magilligan Strand, Portrush (West Strand) and Whiterocks (eastern section of Curran Strand) (Figure 1, Table 1). These beaches are located on a high wave energy, microtidal, 20 km section of Northern Ireland's northern coastline [37,38]. Magilligan Strand, the most westerly beach studied, is part of a 10 km long, dissipative beach that stretches from Magilligan Point in the west to Downhill in the east. The area of beach monitored at Magilligan has been accreting since 1980 [39] and is backed by large dunes, approximately 10 m in height, which are densely vegetated with *Ammophila arenaria*.


**Table 1.** Main attributes of selected sites.

West Strand (Portrush) is an 850 m long, concave shaped beach bounded by basalt headlands to the northeast and southwest. Two sectors have been investigated within this pocket beach, one at the northern and one at the southern part and respectively noted as 'Portrush southern' and 'Portrush northern' sectors. The beach has undergone significant development beginning in 1825 when a jettied harbour was constructed against the north eastern headland [40]. In the 1960s, a promenade and car park were constructed on the dune complex behind the beach and a recurved seawall constructed on the back beach replaced the natural foredune. This development resulted in significant lowering of the beach surface elevation [41].

Whiterocks beach is located at the easternmost extremity of Curran Strand and is the most easterly study site investigated. Curran Strand is a 3 km long beach constrained by a basalt headland to the west and chalk cliffs to the east. The beach is convex in shape due to the sheltering effect of the Skerries islands located approximately 1.5 km offshore, however wave refraction around the islands produces high energy waves at the eastern extremity of the beach. The section of beach monitored at Whiterocks is backed by chalk boulders and a single steep vegetated foredune ranging from 6–25 m in height behind which a golf course has been constructed.

High-resolution multibeam bathymetric data for this coastline, collected in the framework of the Joint Irish Bathymetric Survey completed in September 2008, demonstrates an irregular and dynamic configuration of the continental shelf and shoreface of the North Coast of Northern Ireland, with tidal banks and sand waves indicating complex flow patterns and active sediment transport pathways (Figure 2). The substratum of the shelf and shoreface of this coastal area is predominantly composed of fine to medium sand sediments, with most exposed bedrock and stony outcrops close to the shore [42]. A wide and relatively flat shoreface extends for over 6 km with depths of less than 15 m offshore Magilligan beach, flanked by the Tuns Bank, a large ebb-delta associated with the Foyle River. The shoreface of Portrush beach is much narrower and steep, with a relatively linear configuration and reaching depths in excess of 18 m approximately 1.2 km seaward of the beach. The offshore shelf and shoreface at Whiterocks presents a complex configuration, influenced by the presence of the Skerries islands and their influence on wave, tidal and sediment transport fluxes. The most exposed section of Whiterocks shoreface is relatively similar to Portrush beach, reaching depths in excess of 20 m approximately 2 km seaward of the beach.

**Figure 2.** Location map with used grid for wave propagation and offshore buoys.

#### **4. Methodology**

A beach monitoring program was undertaken to investigate the impacts of storm Katia by surveying beach morphology before, during and after the storm. Surveys were conducted at Magilligan from 7 to 14 September 2011 while surveys at Portrush West Strand (at two sectors) and at Whiterocks beach took place between the 12 and 15 September 2011. Beach morphological changes were determined through topographic surveys extending from the back beach to low water level using a differential GPS (Trimble 4400) with 1–3 cm accuracy. Survey data were used to quantify the impact of Katia on beach morphology and volumetric changes at each sector. Cross-shore profiles were also extracted and their vertical morphological variability analysed to identify the main active zones [43,44].

Morphological and volumetric variations were compared with nearshore wave forcing to assess the process-response relationships in the monitored beaches, using the nearshore wave power, wave steepness and alongshore wave energy flux. These parameters have been extensively used for exploring morphological changes in wave-dominated beaches and found to be relevant indicators to understand beach erosion and accretion [45]. Here, we computed wave forcing indicators based on shallow water wave parameters obtained from high-resolution nearshore wave modelling using SWAN [46,47]. SWAN was implemented using a nested modelling scheme and forced in the western and northern boundaries with observed wave parameters measured at the M4 offshore buoy (55◦ N, 10◦ W), maintained by the Irish Marine Institute, and the Blackstones buoy (56◦03' N, 7◦03' W) operated by CEFAS (Figure 2). Waves were initially propagated over a large-scale computational grid with a resolution of 250 m and using the 2018 EMODnet bathymetry dataset [48] that extended from the buoy locations all the way into the north coast region (Figures 2 and 3a), in order to obtain the boundary conditions for a finer resolution run focused on the study area (Figures 2 and 3b). The model was run with an hourly timestep from 00:00 on the 7 September 2011 to 23:00 on the 16 September 2011. The nested nearshore wave runs were performed using a 5 m high-resolution computational

domain, implemented with a detailed bathymetric grid based on JIBS multibeam dataset for the North Coast (Figure 2). The nearshore runs were performed for the exact same time period indicated above, using wave spectra obtained from the large-scale run. The nested runs considered variable water levels obtained from the hourly records of Portrush Tide Gauge. SWAN was implemented in third generation, 2D stationary mode, using a JONSWAP spectral shape to represent the wave field, directional discretization in regular classes of 5◦ and frequency discretization in 33 logarithmic distributed classes between 1 and 0.03 Hz. Following Loureiro et al. [49] and Matias et al. [50], SWAN runs used default parameters for wave growth, whitecapping dissipation, depth-induced breaking according to the β-kd model for surf-breaking [51], triad and quadruplet wave-wave interactions. Outputs from SWAN provided wave conditions for the nearshore area in each survey site, extracted for a single point in front of the beach in 4 to 5 m water depth.

**Figure 3.** Modeled wave heights (m) for peak offshore storm conditions (**a**) and nearshore wave heights (m) (**b**) during above offshore wave conditions.

Based on SWAN outputs, wave forcing indicators for analyzing process-response relationships were computed assuming the shallow water approximations for linear wave theory following Komar [52]. Wave power (Ps) provides an indication of the rate at which energy is transferred by moving waves and is widely recognized as an important parameter for exploring wave-induced morphological change in sandy beaches (e.g., [45,52]). Wave power was computed according to:

$$\mathbf{P}\_s = \mathbf{E} \mathbf{C}\_K \tag{1}$$

where E is wave energy, computed according to:

$$\mathbf{E} = \text{(1/8)} \text{ } \text{ọ g } \text{H}\_{\text{\textquotesingle}}{}^{2} \text{ } \tag{2}$$

where ρ is water density (1025 kg/m3), g gravitational acceleration (9.81 m/s) and Hs is nearshore wave height. Wave group velocity (Cg), was also obtained using the shallow water approximation:

$$\mathbf{C}\_{\mathbb{K}} = \sqrt{\mathbf{g} \, \text{h}} \tag{3}$$

where h is the water depth. Wave steepness (Ls) was determined according to:

$$\mathbf{L}\_{\sf s} = \mathbf{T} \cdot \mathbf{\sqrt{g \ h}}\tag{4}$$

where T is the nearshore wave period.

Recognizing the importance of wave direction in combination with wave energy in driving longshore sediment transport and alongshore variable morphological changes during energetic conditions, particularly along indented or embayed coastlines (e.g., [45,53]), the alongshore component of the wave energy flux was also computed according to Komar's [52] approximation, given by:

$$P\_1 = P\_\text{s} \text{ sin } \alpha\_\text{b} \text{ cos } \alpha\_\text{b} \tag{5}$$

where α<sup>b</sup> is the wave breaking angle, determined according to the nearshore wave direction and beach orientation.

Wave steepness, obtained from the ratio of wave height (Hs) with wave length (Ls) was also computed for analyzing process-response relationships, considering the established association among high steepness waves (H/L > 0.02), offshore sediment transport and beach erosion in contrast to low steepness waves (H/L < 0.02), that are associated with onshore sediment transport and beach accretion [54].

#### **5. Results**

#### *5.1. Wave Energy Spatial and Temporal Distribution*

Wave conditions differed significantly between the offshore location where the wave records were obtained in the western coasts of Ireland and Scotland, and the nearshore areas adjacent to the monitored sites on the north coast of Northern Ireland (Figure 3).

Storm waves generated by the Katia post-tropical cyclone lasted until the 15 September, two days after the cyclone dissipated. Significant wave heights ranged from 1 to 3 m in the nearshore region, while offshore the wave buoys recorded values in excess of 5 m at the peak of the storm on 13 September 2011. Significant wave attenuation across the wide and irregular shelf and shoreface of Northern Ireland is evident from the exposed open ocean locations of the buoys to the relatively sheltered north coast area (Figures 2 and 3a,b). Considering in higher detail the variability within the north coast high resolution grid (Figure 3b), it is observed that wave heights also change significantly between the western, more protected area, towards the eastern more exposed one. Water levels recorded during the storm at Portrush's tidal gauge and modelled wave characteristics in each investigated site are presented in Figure 4. Maximum water levels were recorded on the 13 September 2011 (Figure 4a), with a storm surge effect ranging between 0.2 and 0.5 m induced by the low atmospheric pressure during the passage of the storm on the 13 September. Nearshore wave heights, even during the most energetic period of the storm, recorded between the 13 and 14 September and shown in Figures 3 and 4b, are relatively low, ranging from around 0.8 m in Magilligan to around 1.6 m in Portrush.

**Figure 4.** Water levels (**a**) at the Portrush tide gauge were reported as values above Ordnance Datum Malin (equivalent to Mean Sea Level). Wave height (**b**), wave steepness (**c**), wave power (**d**), wave direction (**e**) and alongshore wave energy flux (**f**) at different investigated sites.

This pattern is confirmed by the comparison of the time series for the different sites of interest; wave heights during storm Katia were not considerably high, having undergone significant attenuation and dissipation as they propagated through the shallow and irregular shelf of the north coast of Ireland. This is particularly noticeable for Magilligan, fronted by a wide and shallow shoreface, and Whiterocks, partially protected by the Skerries islands, while the more exposed Northern and Southern sectors of Portrush experienced more energetic conditions. Wave steepness (Figure 4c) displays significant spatial variability, while temporal changes largely reflected the variation in wave height during the surveyed period (Figure 4b). Lowest values were recorded in the most sheltered location, Magilligan, where the steepness ranged from ca. 0.002, during less energetic conditions (i.e., 11–12 September) to ca. 0.007 during more energetic conditions (i.e., 8–10 and 13–15 September periods). Steeper waves were observed at Portrush southern sector (Figure 4c), with values of ca. 0.015 and 0.025 for less and more energetic conditions, respectively. Such an increase in wave steepness, on the order of 0.05, from lower to moderate steepness conditions, was also observed in the other study sites (Figure 4c).

Spatial and temporal variability in wave power also reflected the changes in nearshore wave height, with distinct differences recorded among the different surveyed locations. The lowest values were observed at Magilligan whilst the highest were found at Portrush southern sector (Figure 4d). The dependence of nearshore wave power on water depth is particularly evident in Portrush southern sector, with clear temporal variation associated with the tide-induced changes in water level during the most energetic wave conditions. The influence of wave direction on morphological changes experienced in the four beaches during the storm, explored through the angle of approach and alongshore wave energy flux, indicate that relevant southward fluxes were experienced in the

more exposed Portrush Northern and Southern sectors, while at Whiterocks alongshore fluxes were easterly directed. In Magilligan, waves arrived fully refracted and shore normal, inducing negligible alongshore wave energy fluxes (Figure 4e,f).

#### *5.2. Morphological and Volumetric Beach Changes*

#### 5.2.1. Magilligan

During the 7–10 September 2011, the beach showed limited elevation changes (on the order of 5–10 cm), which were largely uniform along both the cross-shore, i.e., along the dry beach and the foreshore and the longshore direction (Figure 5a). Volumetric variation indicates some general beach erosion (Table 2). The survey carried out on the 14th, i.e., after the most energetic waves impacted the beach (Figure 4b,d), showed longshore uniform erosion in the dry beach, with vertical erosion of ca. 10 cm, and an equivalent accretion at the central part of the beach according to a beach pivoting mechanism. Volumetric changes reflected a general, very small, accretion (Figure 5b, Table 2), with an alongshore uniform pattern consistent with the shore normal waves that impacted this beach during the storm (Figure 4e,f).

**Figure 5.** (**a**) Profile 2 evolution and (**b**) 3D morphological changes at Magilligan.


**Table 2.** Volumetric variation (m3) between surveys and at the end of the monitoring program.

#### 5.2.2. Portrush, Southern Sector

During the initial phases of the storm, the beach presented very small morphological and volumetric changes (Figure 6 and Table 2) with a shore normal directed energy flux (Figure 4f). A uniform accretion along the cross-shore profile of ca. 10 cm was recorded on the 14 September (Figure 6a) and corresponded with a volumetric increase of 512.3 m<sup>3</sup> (Table 2). This was linked to the sediment supply from the Portrush northern sector due to northerly approaching waves that induced a southward directed flux (Figure 4f). During the last stages of the storm, approximately 5 cm of vertical erosion was observed in different parts of the profile, especially in the central and lower parts (Figure 6a and Table 2) probably due to the reduction of sediment inputs availability from the northern sector. Overall, from the 12 to 15 September, the beach presented a vertical accretion of 10–15 cm especially in the central-upper part (Figure 6b) associated with a volumetric accretion of 123.9 m3, likely due to sediment supplied from the northern sector that recorded erosion (Figure 7). The uppermost part of the beach showed different behavior, as its dynamic is strongly affected by a backing concave concrete seawall.

**Figure 6.** (**a**) Profile 2 evolution and (**b**) 3D morphological changes at Portrush Southern Sector.

**Figure 7.** (**a**) Profile 2 evolution and (**b**) 3D morphological changes at Portrush Northern Sector.

#### 5.2.3. Portrush, Northern Sector

The main morphological and volumetric changes were recorded in the first stages of the storm, i.e., on the 13th September (Figure 7a and Table 2). A well-developed berm, 20–30 cm in height present along the whole sector investigated, was completely eroded with a sediment loss of approximately 432.6 m3 (Table 2). The berm was essentially transported southward to feed the southern sector of this pocket beach and, to a lesser extent, the middle and lower part of the profile (Figure 7a). This is the result of a relevant (2000 N/s) southward directed wave energy flux, forced by northerly approaching waves observed during that period (Figure 4e,f). In the following surveys only very small changes, of few centimetres, were observed. Overall, the beach recorded 30–35 cm of vertical erosion (Figure 7a,b) along the upper part, through the erosion of the berm, which corresponded to a volumetric change of <sup>−</sup>233.3 m<sup>3</sup> (Table 2).

#### 5.2.4. Whiterocks

Prior to the storm, the beach presented a well-developed berm, ca. 30–40 cm in height (Figure 8a). During the first stages of the storm, on the 13 September, relevant morphological changes took place linked to the erosion of the berm and the landward and seaward transport of the eroded sand according to a process of beach flattening—but no net erosion was recorded (Table 2), this indicating a supply of sediments from the western part of Curran strand driven by eastward alongshore wave energy fluxes under low energy westerly approaching waves (Figure 4e,f). No relevant morphological changes took place in following days and accretion was recorded along all the profile (Figure 8a and Table 2). Overall, at the end of the storm, the beach recorded a volumetric accretion of 632.2 m<sup>3</sup> visible on the dry beach and at the lower foreshore (Figure 8b).

**Figure 8.** (**a**) Profile 2 evolution and (**b**) 3D morphological changes at Whiterocks.

#### **6. Discussion**

The Northern and Western coasts of Ireland are classified as high-energy coastlines and are often affected by energetic storms and the tail-end of a small number of Atlantic Hurricanes [32,33,55–57]. The effects of some of these events have been described by different authors [32,55–60], but the specific impacts of a recent post-tropical cyclone on Northern Irish beaches have not been investigated so far.

Coastal morphological changes investigated in this paper were related to the effects of the post-tropical cyclone Katia that impacted the coast of Northern Ireland from the 12 to the 15 September 2011 with sustained winds of ca. 95 km h−<sup>1</sup> and offshore waves in excess of 5 m in height. The cyclone originated as a tropical depression over the eastern Atlantic on 29 August, strengthened into a tropical storm the following day and than developed into a hurricane by 1st September, becoming a Category 4 hurricane with winds of 225 km h−<sup>1</sup> by 4 September moving eastward towards the east coast of USA and downgraded to a post-storm cyclone one day before reaching the British Isles on the 12–13 September 2011.

The earliest reported high-magnitude event in the Northwest of Ireland was the 'Night of the Big Wind', which was probably the tail-end of a hurricane that hit Ireland in January 1839. More recently, an analysis of instrumental storm records since the 1950s [60], identified Hurricane Debbie as the largest storm that impacted Ireland during the second half of the 20th Century [31,60,61]. Hurricane Debbie moved west across the Atlantic still maintaining hurricane-force winds and affecting Ireland in September 1961, with winds of up to 181 km h−<sup>1</sup> for more than 5 h along the west of Ireland [60]. Furthermore, Guisado-Pintado and Jackson [32,33] mentioned the effects of Hurricane Charley (1986), which was considered a post-tropical storm when it reached the south coast of Ireland, and described in detail the effects of the extratropical storm Ophelia. This event, re-classified as a "post-tropical" storm but being previously a Category 3 hurricane [61], reached the western coast of Ireland on the 16 October 2017, triggering a nationwide severe weather warning and causing substantial coastal flooding.

During storm Katia, offshore wave buoys recorded values in excess of 5 m at the peak of the event but nearshore significant wave height ranged from 1 to 3 m, reflecting relevant wave energy reduction linked to a variety of dissipation processes, that is: although offshore conditions in the exposed Atlantic section of the coast were very energetic, when waves propagate and refract to reach the study areas (Figure 2), they dissipate significant amounts of energy due to bottom friction, refraction and diffraction along the wide, shallow and irregular shelf and shoreface, and indented coastline [56]. This was particularly noticeable at Magilligan, as this area is protected towards the west by a resistant rocky headland and the shoreline is situated on the lee side of the Innishowen Peninsula that prevents the arrival of large amounts of wave energy from the SE, SW or NW quadrants [57]. Finally, at Magilligan, because of the wide shoreface adjacent to it and its long-term association with a large ebb-delta (Tuns Bank), bottom friction dissipation and refraction are more significant than at other sites examined here and the waves arrived almost perfectly shore parallel. This leads to a very small angle of approach and minimal alongshore wave energy fluxes. As a result, at Magilligan, there was limited wave forcing over the whole period, both in terms of wave height and power, but also reduced wave steepness

and almost insignificant alongshore fluxes. Specifically, with respect to other locations, wave power observed here was the lowest (i.e., 5 <sup>×</sup> 103 kW m−<sup>1</sup> during the peak of the storm), much smaller than what was observed during the last phases of Ophelia storm (20 <sup>×</sup> <sup>10</sup><sup>3</sup> kW m<sup>−</sup>1) [32]. As a result, only minor morphological changes were recorded at Magilligan with erosion of the upper beach and flattening of the foreshore, a trend similar—but with much smaller vertical morphological variations—to the one observed at Five Finger Strand in NW Ireland [32].

Less significant nearshore wave refraction favoured higher (compared to Magilligan) wave height and wave power values in Portrush and Whiterocks. Wave power ranged from 10 to 20 <sup>×</sup> <sup>10</sup><sup>3</sup> kW m−<sup>1</sup> and presented a clear longshore component, predominantly southward at both Portrush sectors and eastward at Whiterocks. Hence, longshore transport was evident at Portrush sectors that are included within a morphological sediment cell [9] enclosed by a harbour, in the northern end, and a headland in the southern end. The northern sector presented erosion while the southern sector accreted, probably from a point of pivoting in beach planform located in between the two sectors as observed at other morphological cells [9,62], which is consistent with a short-term rotational response identified in small embayments in various other settings [63–65] and in other studies of large embayed beaches [66–68].

At Whiterocks, a trend similar to the one noted at Portrush was observed. Berm erosion took place by means of a general beach flattening and this resulted in an overall accretion due to an influx of sediment from the western section of the beach.

Overall, storm Katia produced relatively limited impacts on the beaches of the north coast of Northern Ireland. This was also noted by Guisado-Pintado and Jackson [32] and Cooper et al. [56] that indicated that, to have a relevant impact on dissipative beaches of Northern Ireland, storms need to be directed onshore and coincide with high tide, rendering storm duration and offshore intensity of less importance. Katia, which reached approximately 96 km h−<sup>1</sup> presented much lower intensity that Debbie (181 km h<sup>−</sup>1), but was marginally higher than Ophelia (gusts of 74 km h−1) and had a longer duration than the previous events. This was not reflected in terms of morphological changes since during Katia the storm track and prevailing wind directions, which are relevant aspects in determining storm damages [23], were from the SW and W directions, while the beaches investigated are mainly exposed to N, NW and NE quadrants. Interestingly, this was also the case for previous hurricane/post-tropical cyclones Debbie and Ophelia. As observed by Cooper et al. [56], Northern Irish coasts facing NE and N are more susceptible to lower magnitude and longer duration storms, characterised by short sea waves, from a northerly direction. Further, as reported by Cooper et al. [56] and Guisado-Pintado and Jackson [32,33] and confirmed by this study, morphological changes produced on the coast were very localized and dependant on nearshore wave propagation driving cross and alongshore energy fluxes, since the volume and direction of transport during storm impact was highly site-specific. A similar trend, i.e., changes in the direction of longshore transport and morphological and volumetric (positive/negative) modalities of beach response to storms impacts, was recorded in SW England during the 2013–2014 storm winter season [69]. At Magilligan and Whiterocks, erosion processes did not greatly affect the dry beach and did not impact at all on the frontal dunes since this depends on storm peak coincidence with high tidal levels [32,56,65]. As observed by Cooper et al. [56] at Magilligan, the formation of the local dune escarpment is relatively rare and is typically associated with storms that occur at or close to high tide, with predicted tidal elevations of 2.1 m (high spring tide). During Katia storm, maximum water elevation was 1.4 m (high neap tide). The upper beach in Portrush, which is backed by a concrete concave seawall, experienced more relevant vertical changes, especially at the southern sector where the upper beach connects directly with the seawall and the backshore is inexistent.

#### **7. Conclusions**

Despite offshore wave buoys values in excess of 5 m wave height at the peak of the post-tropical cyclone Katia on the 13 September 2011, nearshore significant wave height ranged from 1 to 3 m. This was due to the dissipation processes experienced by waves as they propagate and refract along

a shallow and irregular shelf and shoreface to reach the studied coastal sectors. Such propagation process produced a very small angle of approach and minimal alongshore wave energy fluxes at Magilligan and, as a result, this location only recorded minor morphological changes with erosion of the upper beach and flattening of the foreshore. More limited nearshore wave refraction favoured higher waves at Portrush and Whiterocks, leading to increased wave power with a clear longshore component, ranging from southward at both Portrush sectors to eastward at Whiterocks. Longshore transport at Portrush favoured erosion in the northern sector and accretion in the southern sector, which is consistent with a short-term rotational response. At Whiterocks, a trend similar to the one noted at Portrush was observed, i.e., an overall accretion due to an influx of sediment from the western section of the beach.

Katia post-tropical cyclone, as other similar events—e.g., hurricane Debbie and post-tropical cyclone Ophelia, produced moderate impacts in the beaches investigated because the storm track and prevailing wind directions were from the SW and W directions, while the monitored beaches are mainly exposed to N, NW and NE quadrants. Overall, it is not possible to predict a general and homogeneous response of the north coast of Northern Ireland to such kind of events because morphological changes produced are very site-specific and dependant on water level during the storm and, especially, wave transformation across the shelf and shoreface that controls the volume and direction of sediment transport and hence, beach morphological response.

**Author Contributions:** Conceptualization, G.A., C.L. and D.J.; methodology, T.S. and C.L.; software, M.T.; investigation, G.A. and T.S.; resources, D.J.; data curation, C.L. and M.T.; writing—original draft preparation, G.A.; writing—review and editing, C.L., D.J. and T.S.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This work is a contribution to the Andalusia (Spain) PAI Research Group RNM-328. Carlos Loureiro contribution is developed in the framework of H2020 MSCA NEARControl project, which received funding from the European Union's Horizon 2020 Research and Innovation programme under the Marie Skłodowska-Curie grant agreement No. 661342.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Tsunami Propagation and Flooding in Sicilian Coastal Areas by Means of a Weakly Dispersive Boussinesq Model**

#### **Carlo Lo Re \*, Giorgio Manno and Giuseppe Ciraolo**

Department of Engineering (DI), University of Palermo, Viale delle Scienze, Bd. 8, 90128 Palermo, Italy; giorgio.manno@unipa.it (G.M.); giuseppe.ciraolo@unipa.it (G.C.)

**\*** Correspondence: carlo.lore@unipa.it; Tel.: +39-238-965-24

Received: 27 April 2020; Accepted: 15 May 2020; Published: 19 May 2020

**Abstract:** This paper addresses the tsunami propagation and subsequent coastal areas flooding by means of a depth-integrated numerical model. Such an approach is fundamental in order to assess the inundation hazard in coastal areas generated by seismogenic tsunami. In this study we adopted, an interdisciplinary approach, in order to consider the tsunami propagation, relates both to geomorphological characteristics of the coast and the bathymetry. In order to validate the numerical model, comparisons with results of other studies were performed. This manuscript presents first applicative results achieved using the weakly dispersive Boussinesq model in the field of tsunami propagation and coastal inundation. Ionic coast of Sicily (Italy) was chosen as a case study due to its high level of exposure to tsunamis. Indeed, the tsunami could be generated by an earthquake in the external Calabrian arc or in the Hellenic arc, both active seismic zones. Finally, in order to demonstrate the possibility to give indications to local authorities, an inundation map, over a small area, was produced by means of the numerical model.

**Keywords:** tsunami propagation; tsunami flooding; sicilian coast; coastal hazard

#### **1. Introduction**

In the study of the tsunami propagation phenomenon is very important to model the wave frequency dispersion because of its significant role during wave transformation from deep to intermediate waters. During the propagation to the shore, dispersive waves refract, shoal, due to coastal bathymetry morphology. Long waves have an high impact on surf-zone dynamics, sediment transport and beach erosion. In the Mediterranean sea, the effects of tsunamis on the coasts could be similar to the effects of large storms [1,2] and the detailed modeling of the shoreline movement is important in order to avoid big uncertainties [3]. Tsunamis are huge waves generated by earthquakes, submarine volcanic eruptions or landslides. In very deep oceanic waters tsunami do not dramatically increase in height. But as the waves travel onshore, they increase in height as the bathymetry gradually decrease, becoming potentially destructive (e.g., the tsunami in Indian Ocean in December 2004, or in Japan in March 2011). Usually the tsunami were modelled as solitary waves and obliviously the shoaling, breaking, and run-up are phenoma of major interest for researcher [4–9]. The high computational power of modern computers and parallel computing make it possible to solve more and more complex fluid dynamics problems. Indeed, it is possible to solve 3D Reynolds Averaged Navier–Stokes (RANS) equations and use methods like Smoothed Particle Hydrodynamics (SPH) or Volume Of Fluids (VOF) [10–12]. Unfortunately, 3D tsunami modeling requires high computational efforts that are not consistent with practical purposes. To overcome this problem we used the weakly dispersive model described by [4,13]. This kind of approach, also called the non-hydrostatic Non Linear Shallow Water Equations (NLSWE) method, usually solves, in the horizontal coordinates and

time, free surface motion with a single value function. This requires a much lower vertical resolution than 3D methods. Moreover, the used model has an accurate modeling technique of wetting/drying processes [4,13]. The Western Ionian area, due to the clash between the African and Eurasian tectonic plates, is exposed to a high seismic risk causing possible tsunamis whose origin is directly related to earthquakes. In particular, the Greek and Italian (Calabrian and Sicilian ones) coastal areas are among the most exposed sites to such a hazard. These coastal areas, have a strong anthropization which makes them more vulnerable [14]. In order to plan actions useful for risk mitigation, it is necessary to produce flooding and exposure maps that can be used for prevention and protection purposes. In the last decades, due to the recent tsunami disasters, researchers developed numerical models of increasingly quality. Ref Samaras et al. [15], to simulate the effects of a tsunami striking the Greek and Sicilian coasts, used two-dimensional Boussinesq equations with a high order of approximation. Ref Schambach et al. [16] used a non-hydrostatic three-dimensional model coupled with a non-linear and dispersive two-dimensional model to simulate the propagation of a tsunami on the coast, generated by the earthquake struck the city of Messina on 28th December 1908. Ref Mueller et al. [17] used, instead, the well-known Cornell Multi-grid Coupled Tsunami model (COMCOT), which solves the NLSWE in spherical and Cartesian coordinates, to analyze the effects of scenarios of a flood near the Maltese coasts. The same two-dimensional model was adopted by [18] to examine the characteristics of an earthquake-induced tsunami in the south of the province of Bali (Indonesia). In this paper, we present preliminary results regarding hypothetical strike of an earthquake induced tsunami on Sicilian coast. Furthermore, an inundation map, over a very small area, was produced by means of the weakly dispersive Boussinesq model [4,13].

#### **2. Materials and Methods**

Many Mediterranean coastal areas are potentially exposed to the tsunami risk [15]. Specifically, the Sicilian coasts are highly exposed, because they have morphological characteristics able to enhance flooding effects and because they are densely populated and plenty of infrastructure. One of the most exposed Sicilian coastal area, to probable tsunami events, is the Ionian Mediterranean area [19]. In fact, two important tectonic structures are located in this area, the external Calabrian Peloritano Arch and the Hellenic Arch; both originated due to the clash between the Eurasian Plate and the African Plate, Figure 1).

**Figure 1.** Possible seismic sources in the Ionian Sea. The data-set is taken from the DISS Working Group [20], Caputo and Pavlides [21].

The tectonic structure of this area includes also several smaller plates [19] making more difficult the analysis of earthquake-induced tsunami (Figure 1). The outer Calabrian Arc has impressive deep reverse fault systems (Figure 1), with a predominantly NW-SE direction [14,22], which could originate earthquakes with significant magnitudes [23]. The Hellenic Arc (about 1000 km long) is also one of the most seismically active areas near Greece (Figure 1). This structure consists of three main elements: an outer area (South) consisting of three ocean tranches, an intermediate area with an island arc and a North area characterized by a volcanic islands arc [24]. The coastal area of study was the South of the Ionian Sicilian coast. The coast is articulated with low and rocky coastlines and with sandy beaches, with a slight slope and variable width, delimited by small promontories. This area, depicted in Figure 2 was used for numerical test adopting a weakly dispersive numerical model (see Section 2.1). The location chosen as a case study is Marzamemi (from the Arabic marsa for port and memi for small), a little coastal village on the Sicilian Ionian area (Italy). This village was selected because it falls into specific typologies: (a) it has a big exposure to seismic areas that can cause tsunamis; (b) the coast has a flat topography (at about 300 m from the coastline altitudes ranging between 1 and 6 m above sea level); (c) in this coastal sector, the continental shelf is tight (about 17 km) and it is engraved by little canyons; (d) despite being a fishing village, Marzamemi is densely populated both during the summer and during the international frontier film festival; (e) it is a site of archaeological-industrial interest because, in its main square, an old tuna factory is still present. Figure 2 shows an overview of studied coastal area, a magnification of the promontory area of Marzamemi and the boundaries of the numerical domain. The village develops on the promontory northward the small fishery port, this promontory is partially exposed to the wave action. In particular, the shoreline of the promontory northern part is preceded by the rocky shelf that has small water depths (about 0.2 m).

**Figure 2.** The case study area. The red rectangle shows the Marzamemi promontory, the yellow dash-dot line highlights the boundaries of the numerical model.

#### *2.1. The Numerical Model*

The numerical model here adopted is a weakly dispersive Boussinesq type of model ([4,13]), which is a depth integrated model derived from the incompressible continuity and averaged Navier-Stokes Reynolds momentum equations. Generally, a good numerical model for water waves should guarantee a balance between the frequency dispersion and nonlinearity and the Boussinesq type of models are ones of the most suitable. Basically, the governing equations include a non-hydrostatic pressure term in order to better reproduce the frequency dispersion than the classical hydrostatic model (NLSWE). The model dispersive properties were achieved by adding the non-hydrostatic pressure component in the governing equations. In the *z* momentum equation, both the vertical local and convective acceleration terms were kept. The numerical solver has shock capturing capabilities and easily addresses wetting/drying problems. The governing equations are written in a conservative form, this property guarantees that the models can properly simulate discontinuous flows (e.g., breaking, hydraulic jumps, and bores) [25–27]. In the following are listed the non-hydrostatic depth-integrated continuity and momentum equations:

$$\frac{\partial h}{\partial t} + \frac{\partial (lIh)}{\partial x} + \frac{\partial (Vh)}{\partial y} = 0 \tag{1}$$

$$\frac{\partial(\mathcal{U}h)}{\partial t} + \frac{\partial(\mathcal{U}^2h)}{\partial \mathbf{x}} + \frac{\partial(\mathcal{U}Vh)}{\partial y} = -gh\frac{\partial h}{\partial \mathbf{x}} - gh\frac{\partial z\_b}{\partial \mathbf{x}} - \frac{1}{2}\frac{\partial(q\_bh)}{\partial \mathbf{x}} - q\_b\frac{\partial z\_b}{\partial \mathbf{x}} - \frac{g n^2(\mathcal{U}h)\sqrt{(\mathcal{U}h)^2 + (Vh)^2}}{h^{7/3}} \tag{2}$$

$$\frac{\partial(Vh)}{\partial t} + \frac{\partial(LVh)}{\partial x} + \frac{\partial(V^2h)}{\partial y} = -gh\frac{\partial h}{\partial y} - gh\frac{\partial z\_b}{\partial y} - \frac{1}{2}\frac{\partial(q\_bh)}{\partial y} - q\_b\frac{\partial z\_b}{\partial y} - \frac{gn^2(Vh)\sqrt{(llh)^2 + (Vh)^2}}{h^{7/3}} \tag{3}$$

$$\frac{\partial(Wh)}{\partial t} + \frac{\partial(LIWh)}{\partial x} + \frac{\partial(VWh)}{\partial y} = q\_b \tag{4}$$

where *U*, *V* and *W* are the depth-integrated velocity components in the *x*, *y* and *z* coordinates. *Uh*, *Vh* and *Wh* are the specific flow rate components. *qb* = *q*ˆ*b*/*ρ*, *q*ˆ*<sup>b</sup>* is the dynamic pressure and *n* is the Manning coefficient. Indeed, the total pressure was decomposed by means of:

$$p = \rho g(H - z) + \mathfrak{q} \tag{5}$$

Figure 3 shows the definition scheme of the adopted variables, the subscript *b* refers to bottom.

**Figure 3.** Definition scheme of the adopted variables.

The governing equations Equations (1)–(5) are a system of Partial Differential Equations in the unknown variables *h*, *Uh*, *Vh*, *Wh* and *qb*. The solution of the system of equation was performed using the fractional time step procedure [13]. The governing equations were solved using a fractional time step procedure, where a hydrostatic problem and a non-hydrostatic problem are sequentially solved. The dynamic pressure terms in the momentum equations are neglected when solving the hydrostatic problem and were kept in the non-hydrostatic problem. Furthermore the hydrostatic problem was

solved by a prediction-correction scheme, in the corrector step of the hydrostatic problem, a large linear system for the unknown water levels and dynamic pressures is solved.

#### **3. Validation of the Numerical Model**

#### *3.1. The Carrier and Greenspan Numerical Solution*

In order to validate the numerical model two comparisons with the results of other authors were performed. A test to propagates a sinusoidal wave train incident an inclined plane was performed. Ref Carrier and Greenspan [28] proposed an analytical solution derived by the Airy's approximation of the NLSWE. This analytical solution became a standard test for run-up and run-down modelling. A sinusoidal wave, 0.006 m height and a period of 10 s, was used to force the weakly dispersive Boussinesq model. The wave train propagates in a numerical flume with a water depth of 0.5 m and a slope of 1:25. The envelope of the free surface, computed by the weakly dispersive Boussinesq model at different time steps, was plotted in Figure 4 superimposed with the analytical solution of [28]. Figure 4b shows a magnification of an intermediate time step identified with a black circle in Figure 4a.

**Figure 4.** (**a**) Envelope of free surface of sine wave run-up on a planar beach. Comparison between the weakly dispersive model (blue dotted lines) and Carrier and Greenspan [28] analytical solution (continuous red lines). (**b**) A zoom of the surface elevation near the planar beach at an intermediate time step.

Figure 5 shows the oscillations of the run-up (*R*), compared to the analytical solution of Carrier and Greenspan [28], nevertheless, the slight underestimation of the maxima of *R* the result of the non-hydrostatic weakly dispersive model are very good. The proposed model shoreline horizontal velocity was also compared with the analytical solution Figure 6. The horizontal shoreline velocity is almost the same both in the numerical and in the analytical solution.

**Figure 5.** Shoreline vertical motion *R* of sine wave run-up on a planar beach. Comparison between adopted model (blue dotted lines) and the analytical solution by Carrier and Greenspan [28] (continuous red lines).

**Figure 6.** Shoreline velocity of monochromatic wave run-up on a planar beach. Comparison between adopted model (blue dotted lines) and the analytical solution by Carrier and Greenspan [28] (continuous red lines).

#### *3.2. The Fringing Reef Experiment*

The second test case was the solitary wave propagation over a reef. The wave transformation over an idealized fringing reef highlights the model's capability in resolving nonlinear dispersive solitary waves, considering also wave breaking. The experiments results used for the comparison were carried out at the O.H. Hinsdale Wave Research Laboratory of Oregon State University where a model of a flat dry reef was used to represent a real fringing reef [5,6]. The numerical model replicated the real flume that was 48.8 m long, 2.16 m wide, and 2.1 m high. The computational grid was simply built with equilateral triangles of edge length equal to 0.08 m. The total number of triangles was 55,550 and the nodes were equal to 28,813 and the time step was *dt* = 0.02 s. Figure 7 shows the numerical domain and the surface elevation at *t* <sup>∗</sup> = *t* · *g*/*h*<sup>0</sup> = 55.1 and the red line shows a local zoom of the triangular mesh.

**Figure 7.** The numerical domain and the triangular equilateral mesh used in the flat reef run-up test. The red box highit a magnified area of the mesh. The surface elevation correspond to *t* ∗ = 55.1.

A solitary wave with a dimensionaless wave height of *H*/*h*<sup>0</sup> = 0.5 was generated at the inlet of numerical flume and a Manning coefficient *n* = 0.012 was adopted to reproduce the roughness of the bottom of the flume. In Figure 8 are shown the model results compared to the measured data [5] at 13 dimensionaless time steps *t* <sup>∗</sup> = *t* · *g*/*h*0.

**Figure 8.** Surface elevations of solitary wave over a flat reef with *H*/*h*<sup>0</sup> = 0.5 and 1:5 slope. Solid blue lines are the weakly dispersive model results and the red triangles are measured data. Each subplot shows the results at a dimensionaless time step.

The solitary wave becomes steeper as it propagates over the slope and it rises over the coral reef shoals without breaking into a typical plunge.

In the dimensionless time step *t* ∗= 64.3, the numerical model shows a draw-down in front of the flat reef, that produces a back-reflected wave (Figure 8). Instead, the high-speed water sheet over the reef quickly runs up. The numerical model accurately replicated the physics of the phenomenon at each time step (Figure 8). Moreover, the numerical model well reproduces the solitary wave propagation over the edge reef as shown in Figure 9. The time series refers to a point far 22 m from the wavemaker as described in [29], once more the agreement with the numerical model is good.

**Figure 9.** Time series of the surface elevation at edge of the reef. The blue line is the numerical model results the red circles are the measurements by [29].

#### **4. Results and Discussions of a Real Case of Tsunami Propagation**

In order to make an inundation map of a small interest area a numerical model was used in the case study of Marzamemi (see Section 2).

A triangular mesh was built using the code proposed by Engwirda [30]. The unstructured mesh has the following characteristics: 11,714 triangles, 5990 nodes (see Figure 10a). The triangles size was determined by means of a density function related to bathymetry, making larger triangles in deeper waters.

**Figure 10.** The Marzamemi numerical domain. (**a**) The used triangular mesh, (**b**) the bathymethry of the studied area, the color bar shows the elevation in meters above mean water level. In the subplots the coordinate origin are E = 510,569 m; N = 4,066,207 m; WGS84-UTM33N reference system.

The bathymetry of the model was obtained from regional digital bathymetric charts whereas digital elevation model was built by the regional topographic maps at 1:10,000 scale (see Figure 10b). The two lateral sides of the domain were walls with a free slip condition, in the bottom was calculated a friction term using the Manning's roughness coefficient equal to 0.012 s/m1/3 see Equations (2) and (3). The adopted time step was Δ*t* = 0.2 s and the incoming tsunami wave was simulated as 2 m height solitary wave. The propagation of a tsunami wave and the subsequent flooding areas are shown in Figure 11 in which each subplot shows the surface elevation (above Mean Water Level (MWL)) in a specific time after the start of the simulation. At the initial time step a solitary wave, 2 m height, was generated in the eastern domain side, about 500 m far from the coastline. This wave is linked to a possible earthquake with a return period of about 2000 years [31], neglecting a statistical study regarding catastrophic events. The earthquake-induced tsunami is related to a hypocentral point near to seafloor and the fault mechanism is reverse. In particular, it was taken into account, as a potential tsunami source, an earthquake about 200 km far from the coast. It is important to point out that in this manuscript we are presenting a preliminary study. Analysis of tsunami propagation in the Ionian sea area including statistical studies about earthquake-induced tsunami hazard are ongoing.

**Figure 11.** Water surface elevation. The origin of coordinate axis is E = 510,569 m; N = 4,066,207 m; WGS84 UTM33N reference system.

Figure 11 reports the water surface elevation at several time steps. The water elevation was calculated regarding the initial condition (still water level), thus it coincides with the water depth where the points originally were dry. In the subplot (a) of Figure 11, the tsunami propagation at time *t* = 12 s is shown. In this time the wave is about 300 m far from the coastline and its shape begins to change due to the frequency dispersion. Simultaneously, the wavefront starts to rotate as a result of the change of bathymetry, at the *t* = 24 s, in Figure 11b, it is clearly distinguishable the refraction process. At *t* = 36 s Figure 11c, the wave reaches the coast near the most exposed stretch in which there is the main square of the village of Marzamemi. In Figure 11d, *t* = 48 s, it is described the shoaling of the tsunami and the initial flooding inside the main streets of the village reaching the wave an elevation of 2 m. In this time the northern part of the village is not yet flooded. In the next subplot, (e) *t* = 54 s, a complete inundation of the main square and the littoral promenade is shown although with small water depth (20–40 cm). At same time step, it is possible to see the wave breaking over the seawall that should protect the habitations and the road infrastructure. The last time step, (f) shows the flooding of the whole studied coastal area. A magnification of the last time step of the simulation is shown in Figure 12 with the *x* and *y* coordinates in the local reference system and the water height measured above the MWL. At *t* = 65 s, the church and the ancient tuna factory, XV century, were flooded.

**Figure 12.** Magnification of subplot (f) of Figure 11. The red lines shows the MWL the color bar shows the water level above the MWL.

#### **5. Concluding Remarks**

In this paper, preliminary studies regarding the tsunami flooding hazards were presented. The tsunami is an highly nonlinear and dispersive wave and it must be modeled using appropriated numerical model. Indeed, the adopted Boussinesq type of model, in its category of depth integrated, guarantees a balance between the frequency dispersion and non-linearity. Moreover, it was possible, by means of the Delaunay mesh grid, to have very detailed results with a minor computational cost. As a consequence of this, the model better assess the coastal flooding hazard. The numerical model was validated through the analytical solution of Carrier and Greenspan [28] and with the experimental study presented by Roeber et al. [5]. The comparisons with the numerical model show excellent agreements. Finally, it was applied the numerical modeling procedure to a real case in order to perform the propagation of the tsunami and to evaluate its impact on the coast and the subsequent coastal flooding. To assess both the possibility of coastal flooding and their extent, an earthquake, that cause a tsunami, was generated off the Ionian coast (return period c.a. 2000 years).The results of the tsunami propagation show that the extent of the flooded areas is about 100 m inward the shoreline. All roads near the shoreline, including the historic village square, are flooded. The water levels, although not extremely high, could cause dangers mainly in the periods of the year when the population density grows considerably. These results, although preliminary, highlight the extreme fragility of this coastal site. For this reason, further numerical modeling is ongoing, taking into account also the structural response of the buildings inside the village of Marzamemi. This preliminary investigation is the basis for further studies that are already underway, their results will be useful for civil protection agencies in order to project emergency management plans.

**Author Contributions:** Data curation, C.L.R. and G.M.; Formal analysis, C.L.R. and G.M.; Methodology, C.L.R., G.M., and G.C.; Software, C.L.R. and G.M.; Supervision, G.C.; Geological and geomorphological supervision, G.M.; Hydarulic modelling C.L.R.; Writing—original draft, C.L.R., G.M. and G.C.; Writing—review & editing, C.L.R., G.M. and G.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by SIMIT THARSY Tsunami Hazard Reduction System C1-3.2-5-INTERREG V-A Italia-Malta.The APC was funded by SIMIT THARSY.

**Acknowledgments:** We thank our scientific responsible, Goffredo La Loggia, for assistance to tasks development during the project SIMIT-THARSY.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
