Geological record of marine tsunami backwash: The role of the hydraulic jump

Tsunamis are marked by distinct phases of uprush during coastal inundation and backwash when tsunami water recedes. Especially in the case of a steep coastal profile, the return flow may operate in a Froude‐supercritical regime, eroding the flooded area and transporting large volumes of sediment seawards. Important sediment accumulation occurs when the supercritical flow goes through a hydraulic jump where it becomes subcritical upon deceleration. An inferred example in coarse‐grained, mixed carbonates from the Lower Pleistocene on Rhodes (Greece) is described, with offshore bars up to 10 m long with scour‐and‐fill structures and steep antidune stratification. In finer‐grained sandy depositional systems such structures may be much longer, up to hundreds of metres. It is suggested here that, analogous to some turbidite beds, the apparent lack of structures or the presence of faint stratification that is common for graded sand layers within marine tsunamiites may in fact consist of extremely low‐angle, landward‐dipping backset‐strata that formed under a landward‐migrating hydraulic jump during the basinward retreat of tsunami water. Numerical simulations that focus on the internal stratification of backwash‐generated offshore bars support this hypothesis. The recognition of such deposits in the sedimentary record enlarges the toolbox for assessing the past frequency of tsunamis in coastal areas.

Numerical simulations offer a powerful tool that complements the understanding of tsunamigenic sediment transport dynamics Apotsos et al., 2011a;Gusman et al., 2012;Kihara et al., 2012;Ranasinghe et al., 2013;Sugawara et al., 2014), demonstrating that the backwash current normally operates in a Froudesupercritical flow regime (Simpson & Castelltort, 2006;Weiss, 2008;Apotsos et al., 2011b;Yamazaki et al., 2011;Jiang et al., 2015), which is consistent with observations from laboratory flume experiments (Yoshii et al., 2017) and calculations of flow parameters of real-world tsunamis (Bahlburg & Spiske, 2012). Rapid deceleration of the supercritical flow, e.g. upon reaching the sea or running over a slope break (Yamazaki et al., 2011), forces the transition to subcritical conditions accompanied by high rates of suspension fallout (Apotsos et al., 2011b) and the formation of a hydraulic jump (Simpson & Castelltort, 2006;Weiss, 2008;Yamazaki et al., 2011;Jiang et al., 2015). While supercritical backwash may transport large amounts of sediment, the transition from the supercritical return flow to the sluggish, landward-migrating hydraulic jump may be the most important element of deposition of tsunami sediment transported seawards.
This study discusses marine tsunamigenic backwash and presents a process-based analysis of an inferred tsunami deposit from the Lower Pleistocene on Rhodes Island (Greece). A set of diagnostic features for recognizing high-energy, marine backwash deposits in the geological record is presented. Part of the studied outcrop is interpreted as being the result of tsunamis on the basis of their position within decimetric, bioturbated higherfrequency, storm-induced beds. The inferred tsunami beds have larger volumes (metre-scale thickness), they lack bioturbation in the basal and central part, and are associated with higher-energy conditions indicated by the presence of backset-beds (antidune cross-bedding). In particular, the supercriticality of tsunami-backwash currents and the transition to subcriticality accompanied by a hydraulic jump and large-scale deposition of sediment are considered here. This has been a largely ignored criterion of tsunamigenic depositional processes.

GENERAL TSUNAMI CHARACTERISTICS
Generation by disturbance of the water column Tsunamis are generated in four ways (Sugawara et al., 2008;Bourgeois, 2009). Earthquakes lie at the origin of most: 90% worldwide and 75% in the Mediterranean Sea (Sugawara et al., 2008;Sørensen et al., 2012). Volcanic eruptions (e.g. Santorini and Krakatoa, Latter, 1981;Cita & Aloisi, 2000) and (subaqueous) landslides (e.g. Storegga and Hawaii, Bondevik et al., 1997;Ward, 2001;McMurtry et al., 2004;Puga-Bernab eu et al., 2013)  have been caused by bolide-water impacts (Ward & Asphaug, 2000;Kharif & Pelinovsky, 2005), the most famous undoubtedly being the asteroid impact at the Cretaceous-Palaeogene boundary (Smit et al., 1996), suggested to have induced a mega-tsunami, exceeding 150 m in height, which travelled as far as 300 km inland (Matsui et al., 2002), leading to backwash over a period of hours or even days (Lawton et al., 2005). Scheffers and Kelletat (2003) report over 50 historical occurrences worldwide of run-up heights of more than 10 m, with five exceeding 100 m, during the last 400 years. Numerical modelling on the basis of a synthetic earthquake database by Sørensen et al. (2012) reveals a probability of close to 100% for a tsunami wave run-up exceeding 1 m to occur somewhere along the Mediterranean coast every 30 years.

Propagation from deep into shallow water
Deep-water tsunami waves have very long wavelengths (exceeding 100 km) and propagate at hundreds of km/h (Joseph, 2011). Tsunami wave periods range from 10 min to 1 h, that is, some 100 times longer than the period of wind-induced waves (Weiss & Bahlburg, 2006;Fujiwara, 2008). Tsunami waves slow down when they reach shallower water, while wave amplitude and current velocity (uniform throughout the water column) increase (Sugawara et al., 2008;Joseph, 2011), in agreement with eyewitness accounts and video footage of a landward moving 'wall of water' (Tappin et al., 2012). Such bores move over a basal boundary layer where most of the shear stress is generated, capable of transporting virtually all grain sizes (Pickering et al., 1991;Weiss, 2008). This produces a distinctive flow style (Dawson, 1994) characterized by (i) a widespread uprush associated with coastal impact, (ii) a quasi-stillstand when the current stagnates and (iii) a vigorous backwash during water retreat, each stage lasting many minutes or longer. This cycle can be repeated multiple times as a consequence of the tsunami wave train, with hydraulic energy generally decreasing with each new incursion (Sugawara et al., 2008), although this is not always the case (Nanayama & Shigeno, 2006). Shiki and Yamazaki (1996) pointed out that tsunamis generated very close to the hypocentre of an earthquake are generally marked by only a few pulses. In certain cases, the backwash of the second wave stopped the propagation of the following waves (Lavigne et al., 2009).

Inundation of onshore area
The process of tsunami wave impact at the shore is essentially similar to that of normal waves at the beach (Butt & Russell, 1999;Young et al., 2010), characterized by rapid flow acceleration as the wave front passes (Apotsos et al., 2011b). Associated erosion may extend up to hundreds of metres inshore, and much farther along river beds (Ontowirjo et al., 2013). Tsunami run-up velocities may be as high as 10 to 18 m s À1 (35 to 65 km h À1 ; Reimnitz & Marshall, 1965;Tsutsumi et al., 2000;Bryant & Nott, 2001), in particular in narrow channels and near headlands (Cherniawsky et al., 2007). The erosional phase is followed by a depositional phase during gradual deceleration until the point of maximum inundation is reached (Apotsos et al., 2011b). Tsunamis are thus both depositional and erosional agents (Dawson, 1994). Whether erosion or deposition predominates depends largely on the erosion capacity of the backwash current (Umitsu et al., 2007). As a consequence of flow deceleration, deposits formed by the onshore tsunami uprush are typically graded, and thin and fine landwards (Hindson & Andrade, 1999;Nanayama et al., 2000;Gelfenbaum & Jaffe, 2003;Goff et al., 2004;Tuttle et al., 2004;Moore et al., 2006;Fujino et al., 2010;Bahlburg & Spiske, 2012) and are commonly capped by organic-rich mud layers laid down during tsunami stillstand at maximum inundation (Tuttle et al., 2004;Morton et al., 2007;Fujiwara, 2008). Large, occasionally imbricated boulders located hundreds of metres onshore have also been ascribed to the energetic uprush phase (Goto et al., 2007;Frohlich et al., 2009;Maouche et al., 2009). The inland propagation after coastal impact is thus well beyond the normal position of the shoreline, up to hundreds of metres for steep coastal areas (generally coarse-grained) and up to kilometres where the coastal gradient is low (fine-grained) (see compilation by Scheffers & Kelletat, 2003). Tsunami wave energy, height and velocity are considerably reduced in the presence of coastal vegetation, e.g. by flow resistance in mangrove forests (Teh et al., 2009) or as a result of energy loss due to tree breaking (Thuy et al., 2012), and is therefore a focus of tsunami-impact mitigation programmes.

Backwash from inundated onshore areas into shallow-marine waters and beyond
Bottom friction, percolation of water into the ground and energy loss due to the run-up eventually cause the cessation of the landward advance of tsunamis. As a consequence of the wave retreating faster than the receding water (Yamazaki et al., 2011), a subsequent reverse flow develops after a short period of stagnation (Dawson & Stewart, 2008), while tsunami water near the shoreline starts to retreat before the maximum inundation height is reached and the wave front continues to move onshore (Apotsos et al., 2011b). Resulting tractive backwash currents become concentrated towards topographic lows (Einsele et al., 1996;Le Roux & Vargas, 2005 2012; Fujiwara & Tanigawa, 2014) and might locally erode bed rock platforms (Aalto et al., 1999). Coastal relief can cause the backwash to flow obliquely to the shoreline. Such local factors have different effects on each of the sub-units of a tsunami deposit (Fujino et al., 2006), potentially resulting in high lateral variability in the associated sediment. Similarly, rebound from coastal cliffs influences the distribution of the backwash deposit (Massari & D'Alessandro, 2000).
Numerical simulations show that the erosion capacity of the backwash depends on the amount of water onshore, which is a function of tsunami wave height (Fagherazzi & Du, 2008) and the slope of the bed (Apotsos et al., 2011b). Along high-relief coastlines, tsunami backwash is accelerated due to gravity, gaining transport potential and the ability to generate net offshore transport especially in the case of well-erodible substrates (MacInnes et al., 2009). As a consequence, backwash-generated erosion rates achieved seawards of the shoreline (on parts of the sea floor that are normally below sea-level) are potentially much higher than onshore (Pritchard & Dickinson, 2008;Apotsos et al., 2011b;Li et al., 2012). Accordingly, several field surveys show that tsunamis were net depositional on low-relief coastlines (Gelfenbaum & Jaffe, 2003;Kurian et al., 2006), whereas tsunamis flowing over high-relief coastlines generated net offshore transport (MacInnes et al., 2009).
Modelling and calculations demonstrate that the backwash develops into a supercritical flow, also on low-gradient coasts (Simpson & Castelltort, 2006;Weiss, 2008;Apotsos et al., 2011b;Bahlburg & Spiske, 2012;Jiang et al., 2015;Yoshii et al., 2017). Rapid deceleration upon entering the sea invokes high settling rates of suspended sediment that may lead to the formation of hyperpycnal flows (Coleman, 1968;Le Roux & Vargas, 2005;Weiss, 2008), particularly where coastal funnelling of receding tsunami water occurs. Coleman (1968) suggested a link between coastal funnelling and the formation of submarine canyons, generating and expanding pathways for turbidity currents. Some authors have questioned whether the deposits of self-sustained tsunamigenic density flows, which have lost a direct connection with the tsunami backwash, should be considered 'tsunamiites' (Shanmugam, 2006;Weiss, 2008). Such self-sustained density flows are beyond the scope of this study.

EXAMPLE OF MARINE BACKWASH DEPOSITS ON RHODES ISLAND
In the following section a candidate for marine tsunamibackwash deposits in coarse-grained, mixed carbonates from the Lower Pleistocene on Rhodes Island (Greece) is described (Fig. 1). The exposures enable a process-based analysis of high-energy event deposits in an otherwise low-energy shallow-marine environment. These deposits, previously studied by Hansen (1999), form part of the Cape Arkhangelos Calcarenite facies group of the Rhodes Formation. The depositional setting adhered to in this study is strongly based on the work of Hansen (1999), however, his Facies C, D and E are here combined and reinterpreted together.

Depositional setting
Rhodes Island is located in the Aegean Sea on the eastern reach of the Hellenic Arc, a chain of forearc islands north of the Hellenic subduction zone (Fig. 1). On the east coast of Rhodes, Plio-Pleistocene extensional grabens developed in Mesozoic meta-limestones (Hanken et al., 1996). The Lower Pleistocene Cape Arkhangelos Calcarenite discussed here was deposited in an E-W trending basin, bounded to the N and NE by a steep, cliffed headland of the meta-limestone 'basement', and to the S and W by Pliocene siliciclastics (Hansen, 1999). In a small embayment near Kallithea Springs (Fig. 1), a temperate carbonate platform developed during the Early Pleistocene. During its build-up phase, the platform was greatly influenced by the input of siliciclastic sediment, which was gradually replaced by biogenic debris as the platform matured. Skeletal production rates eventually exceeded the creation of accommodation space and excess carbonate sediment was occasionally transported seawards and deposited on the sloping front of the prograding wedge that separated the upper and lower shoreface, leading to the formation of the "giant-scale foresets" of Facies E of Hansen (1999). The generally very well-sorted clinoform foresets are 5 to 100 cm thick and up to 12 m high with a variable dip (5 to 40°) of 10 to 15°on average ( Fig. 2), consisting of cross-bedded and bioturbated decimetric packstone and grainstone beds (Hansen, 1999). Sediment is composed of fine-grained to medium-grained skeletal sand of dominantly rhodalgal origin and of ca 10% lithic components (Fig. 3). Centimetre-scale rhodolith fragments occur sporadically.

Scour-and-fill structures
The succession of clinoform foresets contains more than 20 spoon-shaped scour-and-fill structures some 10 to 80 m wide (Hansen, 1999) with variable longitudinal dimensions, occurring at various stratigraphic positions. Outcrop conditions impede the detailed mapping of all scour-and-fill structures. The studied exposure displays two such, broadly similar structures each made up of three sub-units (Figs 3 and 4). The lower scour-and-fill structure (Unit 1) is exposed over 25 m in approximately palaeoflow-parallel direction. It is up to 5 m thick and has an erosional base with steep side walls and up to 3 m of local relief (Figs 4 and 5). Unit 1 is overall fining upwards with much coarser sediment than the clinoform foresets (Fig. 3). In contrast to the locally intensely bioturbated packstones and grainstones of the clinoform foresets, Sub-units 1 and 2 and the lower part of Sub-unit 3 are devoid of bioturbation, which only affected the upper part of Sub-unit 3. The proportion of sub-angular to rounded lithic components ranges from as much as 2/3 at the base to about 1/4 at the top of Unit 1. The skeletal composition is invariably dominated by rhodalgal fragments, making up 20 to 30% of the bioclastic grains (Fig. 3). Each sub-unit is described in more detail:

Sub-unit 1
Backset-bedded conglomerate. Backset-beds (Davis, 1890) within this sub-unit are up to 20 cm thick and dip up to 50°(exceeding the angle of repose indicating rapid covering) in a landward direction. They have sigmoidal shapes with a convex-up seaward end and a concave-up base where each backset-bed truncates the underlying one, generating the erosion surface that floors the entire scourand-fill structure of Unit 1 (Fig. 4). Individual backsetbeds are poorly sorted, while grain size decreases seawards yet remaining within the conglomerate range. As a result of the seaward-fining trend within individual backsetbeds, Sub-unit 1 is fining upwards. The decrease in grain   size is accompanied by a reduction in the proportion of lithic components, decreasing from ca 2/3 at the base to 1/3 at the top of the sub-unit. In exposures perpendicular to the palaeoflow, Sub-unit 1 displays lenticular geometries marked by numerous reactivation surfaces (Fig. 6).

Sub-unit 2
Wavy-bedded grainstone. This sub-unit consists of undulating, centimetric planar bedding that truncates the top of Sub-unit 1. The bedding is similar to that produced by upper plane-flow, but develops vertically into low-angle foreset cross-bedding towards the top of Sub-unit 2. The sediment is composed of well-sorted, coarse sand of which ca 1/5 is of lithic origin. Locally, internal truncations occur (Fig. 4).

Sub-unit 3
Cross-bedded rudstone. The low-angle foreset cross-bedding of the upper part of Sub-unit 2 passes vertically into the much steeper cross-bedding of the more voluminous Sub-unit 3. In both sub-units, cross-bedding dips uniquely in seaward direction. The moderately sorted rudstones form decimetric sets that together reach over 3 m in thickness. The granule-size sediment in Sub-unit 3 is for ca 1/4 composed of lithic fragments. The upper half is generally affected by vertically intensifying bioturbation.

Process interpretation
Each scour-and-fill unit was deposited from an overall waning, seaward-directed flow that went through a series of distinct hydrodynamic conditions and deposition of associated sub-units (Fig. 7): (1) hydraulic jump depositing coarse-grained backset-beds, (2) sheet-flow generating upper plane bedding and (3) highly depositional subcritical flow leading to the aggradational stacking of subaqueous dunes. The high proportion of lithic components in the scour-and-fill structures, when compared to that in the clinoform foresets, attests to a sediment source near the shoreline (or on land) mixed with shallow-marinederived skeletal grains. This matches well with an origin from a very strong marine backwash event following coastal inundation. Backwash-generated erosion left a substantial imprint in the sedimentary record. The erosion surface at the base of Unit 1 is the result of rapid alternations of erosion and deposition: First, an individual backset-bed was 'dumped' during the depositional phase. Then, during the intermittent erosion phase, part of the clinoform foreset and part of the landward side of the backset-bed just deposited were eroded. Prolonged repetition of these two alternating phases generated the backset-beds of Sub-unit 1, which is thus floored by a composite erosion surface (Fig. 4) (cf. Dietrich et al., 2016;Slootman et al., 2016) that formed as a result of the intrinsic, high-frequency pulsating nature of the supercritical backwash current rather than due to the impact of the landward-migrating wave(s). Thus, the composite erosion surface at the base of Subunit 1 formed as the result of high basal shear stresses in a supercritical flow that ran down the bathymetric break separating the upper and lower shoreface. Where this surface flattened and the flow decelerated and thickened, a convex-up antidune was created under stationary wave conditions (Fig. 7). The generation of such an obstacle resulted in the vertical growth of a standing wave until oversteepening and subsequent breaking occurred, resulting in the formation of a hydraulic jump (cf. Alexander et al., 2001;MacDonald et al., 2009;Cartigny et al., 2014;Slootman, 2016). Alternatively, the initial sediment mound was deposited directly from the hydraulic jump by suspension fallout due to the rapid loss of traction (cf. MacDonald et al., 2009). The hydraulic jump migrated upstream and upslope by the continued deposition of locally very steep backset-beds (Sub-unit 1) that formed by the massive settling of coarse sediment directly downstream of the jump (Fig. 7) (cf. Massari, 1996). The length and inclination of the slope over which the supercritical flow accelerated thereby progressively decreased and, as a result, so did the intensity of the hydraulic jump (decreasing difference between Froude numbers at either side of the jump). This induced the transition to subcritical flow conditions throughout the slope and upper-stage plane-bed formation (Sub-unit 2). Further gradual decrease in hydraulic energy led to relatively sustained flow conditions with high rates of sediment fallout from the sediment-laden flow and the formation of subaqueous dunes (Sub-unit 3). Bioturbation of the upper half of Subunit 3 started after deposition. At this location, the event deposit consists of only one waning-flow deposit. If the event was associated with multiple waning-flow phases, these did not leave a sedimentary imprint at this particular location.
Earlier interpretations of the studied deposits on Rhodes by Hansen (1999) proposed sediment-laden underflows to have been generated as storm or floodinduced currents that accelerated down the clinoform foresets, creating a chute-and-pool bedform (Sub-unit 1) that evolved into plane beds (Sub-unit 2) and HCS as the current waned. This led Hansen (1999) to invoke major storms or hurricanes as the formative events of the scourand-fill structures. An argument opposing such interpretation is the gradual transition between Sub-units 2 and 3, which shows that the aggradational dunes (Sub-unit 3) are part of the event deposits. In other sections, Hansen (1999) interpreted channel fills and conglomeratic crossbedding as two additional facies, which are here for a large part included in Sub-unit 1 and to a lesser extent in Sub-unit 2. This illustrates the apparent ambiguity of marine backwash deposits. Likewise, cross-bedding suggested to originate from subaqueous dunes during tsunami uprush elsewhere (Nanayama & Shigeno, 2006) may indeed consist of steep backset-bedding deposited from a landward-migrating hydraulic jump during tsunami backwash such as proposed for the studied outcrops on Rhodes. Antidune structures have been described from deepwater tsunami-induced deposits (Shiki & Yamazaki, 1996;Smit et al., 1996;Ishihara et al., 2014;Slootman et al., 2016). In such deep-water environments, however, the generation of antidunes is no longer a direct result of tsunami backwash but is controlled by the morphodynamics of self-sustained supercritical density flows. Shallow-marine backwash deposits, on the other hand, have been reported to include HCS (Fujiwara et al., 2000;Fujino et al., 2006), antidune stratification (Massari & D'dro, 2000;Lawton et al., 2005) or both (Fujiwara & Kamataki, 2007). In addition, large-scale (up to 50 m wavelength) scour-and-fill structures were reported from some tsunamiites, which were in most cases characterized by smaller, superimposed scours at their base and underlain by soft-sediment deformation structures interpreted as the result of mega-hummocks formed by the combined effects of wave motion and backwash flow (Rossetti et al.,  Stippled lines indicate (erosional) subordinate set boundaries within sub-units (reactivation surfaces). Sub-unit 2 overlies Sub-unit 1. Sub-unit 3 is not exposed here. Note that the backset-bedding of Sub-unit 1 and the wavy bedding of Sub-unit 2 look like hummocky cross-stratification (HCS), but are here confidently interpreted as hydraulic jump-related and antidune-related deposits, respectively, on the basis of flow-parallel exposures. See Fig. 1 for location (N36Á375734°E28Á237209°). 2000; Fujino et al., 2006;Puga-Bernab eu et al., 2007) or, alternatively, as large-scale antidunes generated by supercritical backwash currents (Massari & D'Alessandro, 2000). The structures discussed in this study reveal the potential of the marine backwash-generated hydraulic jump in producing scour-and-fill and/or antidune structures. A more general applicability of the proposed model is investigated through a comparison with numerical simulations.

Comparison with numerical simulations of tsunami backwash
Numerical simulations can provide insight into flow processes associated with tsunami impact, uprush and backwash (Weiss, 2008;Xiao et al., 2010;Apotsos et al., 2011a,b;Gusman et al., 2012;Kihara et al., 2012;Ranasinghe et al., 2013;Sugawara et al., 2014;Jiang et al., 2015). Yamazaki et al. (2011) modelled the 2009 Samoa Tsunami in the South Central Pacific, focusing on the effect in Pago Pago Harbour located in an L-shape embayment fringed with reefs along its shores. Water depth over the ca 1 km long reef flat is about 10 m, increasing to 30 m over a distance of 500 m from the reef edge. The tsunami first exposed the shallow reef flats and then flooded the low-lying coastal areas in the vicinity of the harbour. Some 10 min later, the water retreated seawards and flowed supercritically over the reef edge generating a waterfall that plunged into a hydraulic jump until the next wave arrived. Simpson and Castelltort (2006) and Jiang et al. (2015) incorporated sediment transport dynamics into their numerical studies to investigate the morphological evolution of the substrate during tsunamis. Both studies document supercritical backwash and the deposition of an offshore bar associated with a hydraulic jump, although neither provided details on the internal structure of the bedform. Whereas Jiang et al. (2015) simulated their scaled laboratory experiments, Simpson and Castelltort (2006) presented a tsunami of real-world dimensions using the one-dimensional form of the shallow-water equations (see Data S1) to compute the depth-averaged flow velocity and water depth while tracking the evolution of the substrate that evolved in response to erosion and deposition. The authors considered a typical coastal profile consisting of an initially planar, low-angle (0Á2°) ramp of erodible material with a constant grain size of 4 mm that is partially emerged (Fig. 8A), which was then forced with a series of successively weaker tsunami waves (period of 15 min) arriving from the seaward end of the model (Fig. 8B through K).
To clarify the internal architecture of the backwashgenerated offshore bar, the simulations of Simpson and Castelltort (2006) were repeated without changing their parameters. Tracking the topography at regular time intervals of 30 sec produced the stratification in the model (close-up in Fig. 8L). The results serve to illustrate the conceptual formative process rather than to reconstruct marine backwash in the Rhodes setting. Results show that after inundation ( Fig. 8C and D), the backwash of the model tsunami is capable of transporting large quantities of sediment from the near-shore into the offshore zone as the water from each surge retreats. The sediment is initially deposited in a convex-up structure (Fig. 8E) onto which sigmoidal backset-beds accrete under a hydraulic jump at the transition between the supercritical part (at the landward side) and the subcritical part (at the seaward side) of the backwash current (Fig. 8F). The erosional concave-up bases of backset-beds deposited during the first backwash phase together form the large-scale, concave-up composite erosion surface that floors the offshore bar. Successive impact, uprush and backwash ( Fig. 8G through K) did (in this case) not significantly affect the structures formed by the first tsunami cycle.
The numerically produced sedimentary structures display similarities to Sub-unit 1 in the investigated deposits, but failed to generate the wavy bedding and/or cross-bedding of Sub-units 2 and 3. In addition, the dimensions in the simulations greatly differ from those observed in outcrop. On Rhodes, the steepest backset-bed dips about 50°. In the simulations, the steepest backset-beds do not exceed a dip of 0Á3°. Related to this is the difference in length between the Rhodes and model backset-beds: a few metres versus a few hundreds of metres, respectively. Such discrepancies derive indirectly from a difference in the steepness of the sea floor (ca 10 to 15°on Rhodes and only 0Á2°in the model). A steeper sea floor leads to an increased velocity and a reduced thickness of the supercritical flow, augmenting the Froude number. The intensity of the hydraulic jump is a function of the difference in Froude number at either side of the transition. Strong jumps on steep sea floors occur over a shorter distance and are accompanied by a greater difference in flow depth between the incoming and outgoing flow. This enables the rapidly deposited fallout sediment on the steep slope to build a topographically higher bedform with backsetbeds that are steeper than those associated with weaker hydraulic jumps on low-inclination sea floors. An additional effect is caused by grain-size variations. Settling velocity during tractionless suspension fallout directly downstream of the hydraulic jump increases with increasing particle diameter. This results in an enhanced sedimentation rate over a shorter distance, which thus contributes to deposition of steeper backset-beds and the formation of a bedform with shorter length and greater amplitude on steep sea floors. Therefore, backset-stratification might only be clearly apparent in coarse-grained sediment deposited under high sedimentation rates. In finer-grained systems, and in particular in exposures with limited spatial extent, such structures may remain largely unnoticed. Field investigations by  revealed low-angle backset-stratification in apparently structureless and faintly stratified Bouma Ta and Tb intervals in turbidites, deposited over large-scale bedforms (10s to 100s m wavelength) that formed in association with hydraulic jumps in turbidity currents . Laboratory and field observations (Postma et al., 2009) demonstrated that local soft-sediment deformation within such deposits forms due to an upward-oriented pressure gradient under the hydraulic jump (see also Slootman, 2016). Therefore, while interpreting apparently structureless or faintly stratified tsunami deposits that unveil only a fining-upward signature (Takashimizu & Masuda, 2000;Fujiwara et al. 2000;Fujino et al., 2006;Fujiwara & Kamataki, 2007), it should be considered that such deposits may have originated from a hydraulic jump during tsunami backwash, producing seemingly horizontal stratification due to the extremely low angle of the backset-beds.

Storms or tsunamis?
How can tsunami backwash deposits be discriminated from rip-current deposits generated by major storms? Tsunami features are not exclusive and a significant overlap exists between sedimentary signatures produced by cyclones and storms, including erosion surfaces, anomalously coarse sand layers, imbricated and exotic boulders, chaotic bedding, normal and inverse grading, and multiple fining-upward units (see review by Shanmugam, 2012). The repeated alternation of landward and seawarddirected currents is stressed by several authors as a main   characteristic of tsunami-induced flows (Takashimizu & Masuda, 2000;Fujiwara, 2007;Massari et al., 2009), however, in situ surveys of multiple gravity flow events demonstrate that these can also be generated during a single storm event (Puig et al., 2004). According to Morton et al. (2007), storm inundation is gradual and prolonged, marked by the impact of numerous waves onto the shore and no significant return flow until after the main flooding. In contrast, the Early Pleistocene carbonate ramp of Rhodes was affected by sudden seaward flows carrying near-shore-derived sediment (with dominantly lithic composition) mixed with shallow-marine skeletal debris. In addition, the geographical position of the island was and is within a major tsunamigenic zone, which has the greatest tsunami hazard record of the Mediterranean region, owing to the presence of nearby seismogenic faults in the Hellenic subduction zone (Lorito et al., 2008). Considering well-documented historical events (Papadopoulos & Fokaefs, 2005), the statistical probability of Rhodes being struck by tsunamis exceeding several metres in height is once every few centuries (Sørensen et al., 2012). The recurrence period of tsunamis on Rhodes is about 500 yr for tsunamis with a run-up height of 3 m and 5000 yr for run-ups 10 m high (Sørensen et al., 2012). The frequency of severe storm events, on the other hand, is much higher than this (Trigo et al., 1999;Camuffo et al., 2000;Leckebusch et al., 2006;Nissen et al., 2010). Hence, it is tempting to explain the clinoform foresets as the consequence of storm-induced offshore transport, and to assign tsunamis as the cause of marine backwash events that led to the generation of large-scale scour-and-fill structures.

CONCLUSION
This study stresses the potential of supercritical marine tsunami-backwash to imprint the depositional record, in particular with respect to the deposition of sediment from a hydraulic jump at the transition from supercritical to subcritical flow. Such deposits contain backset-bedding in concave-up depressions floored by composite erosion surfaces. On steep sea floors and with coarse sediment, such backset-beds build a bedform up to several metres high and of the order of 10 m long. In environments in which the coarsest grain size is sand, bedforms may be much longer and less high. As a result, the internal architecture may appear structureless or horizontally laminated due to the extreme length and very low angle of backset-beds, leaving the fining-upward signature as the only recognizable feature in typical exposure dimensions. In the view of supercritical backwash, wavy stratification is best explained as antidune stratification and not as HCS. Tsunami hazard assessment benefits from the enhanced understanding of all aspects of tsunamis. Improving the ability to recognize tsunami deposits and associated processes enables a potentially vast archive of ancient tsunamiites in the geological record to be consulted.