Wave run-up observations in microtidal, sediment-starved pocket beaches of the Eastern Mediterranean

Journal of Marine Systems 78 (2009) S37–S47

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Journal of Marine Systems j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j m a r s y s

Wave run-up observations in microtidal, sediment-starved pocket beaches of the Eastern Mediterranean M.I. Vousdoukas a,⁎, A.F. Velegrakis a, K. Dimou a, V. Zervakis a, D.C. Conley b a b

Department of Marine Sciences, School of Environment, University of the Aegean, University Hill, 81100, Mytilene, Greece School Earth, Ocean & Environmental Sciences, Portland Square A504, University of Plymouth, Drake Circus, Plymouth PL48AA, UK

a r t i c l e

i n f o

Article history: Received 24 January 2008 Received in revised form 4 November 2008 Accepted 22 January 2009 Available online 10 March 2009 Keywords: Wave run-up Beach dynamics Swash zone Nearshore waves Video imaging of waves Image processing

a b s t r a c t A video-based method was used to acquire wave run-up information from 3 microtidal, sediment-starved ‘pocket’ beaches on the island of Lesbos (Greece, NE Mediterranean). The results showed that the investigated beaches exhibit particular characteristics with regard to the wave run-up, compared to the sandy oceanic beaches previously studied. Run-up heights appeared to be characterised by similar frequencies to those of the nearshore waves (studied through the acquisition of high frequency wave data in the nearshore zone). Low frequency motions are introduced via the swash, but their contribution to the total run-up energy appeared to be less significant than in previous studies. Previously-proposed parameterisations were mostly found not to describe adequately the present data, whereas predictions based on previously-proposed expressions were also not satisfactory, with the possible exception of the expression of Stockdon et al. [Stockdon, H.F., Holman, R.A., Howd, P.A., Sallenger, J.A.H., 2006. Empirical parameterization of setup, swash, and runup. Coast. Eng., 53(7), 573–588], which has been obtained on the basis of extensive datasets from diverse beaches. © 2009 Elsevier B.V. All rights reserved.

where Ho is the deep water significant wave height and ξ the Iribarren number (Iribarren and Nogales, 1949; Battjes, 1974), given by:

1. Introduction An improved understanding of the swash zone processes is essential for an enhanced diagnosis/prediction of beach morphodynamics (e.g. Komar, 1998; Van Rijn, 1998) and considerable research effort has been taking place over the past years towards this objective, on the basis of laboratory (e.g. Bowen et al., 1968; Gourlay, 1992; Dibajnia, 2002) and field (e.g. Holman, 1986; Holland et al., 1995; Ruggiero et al., 2004) observations, as well as modelling (e.g. Karambas and Koutitas, 2002; Li et al., 2002; Horn, 2006). A crucial parameter of swash zone dynamics is the wave run-up height R, the accurate prediction of which is vital for the effective design of coastal protection works (e.g. Briganti et al., 2005) and beach nourishment projects (e.g. Dean, 2001), the prediction of storm wave, surge and tsunami effects (e.g. Korycansky and Lynett, 2007) and the planning of efficient coastal management schemes (e.g. Munoz-Perez et al., 2001; Xue, 2001; Kroon et al., 2007). An early effort to parameterize the run-up height was by Hunt (1959), who suggested the following relationship: R = Ho n

ð1Þ

n=

β ðHo =Lo Þ1 = 2

ð2Þ

where β is the beach slope and Lo is the deep water wavelength. Several studies followed, aiming to generate predictive run-up formulae and determine relationships (if any) between wave heights, beach slopes and the Iribarren number. Holman (1986) measured wave run-up through video imagery and suggested the following expression for the 2% exceedence of the peak run-up height (R2%): R2k = ð0:83n + 0:2ÞHo

ð3Þ

while Douglass (1992), using the same dataset, proposed an independent of the beach slope relationship for the maximum runup height Rmax: Rmax 0:12 = qffiffiffiffiffi Ho Ho

ð4Þ

Lo

⁎ Corresponding author. Faculdade de Ciências do Mar e do Ambiente. Universidade do Algarve, Campus de Gambelas, 8005 - 139, Faro, PORTUGAL. Tel.: +351 289 800900; fax: +351 289 706972. E-mail addresses: [email protected] (M.I. Vousdoukas), [email protected] (A.F. Velegrakis), [email protected] (K. Dimou), [email protected] (V. Zervakis), [email protected] (D.C. Conley). 0924-7963/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmarsys.2009.01.009

There have been other similar studies, which have related wave runup to wave and beach slope parameters (e.g. Guza and Thornton, 1982; Raubenheimer et al.,1995; Raubenheimer and Guza,1996). For example, Nielsen and Hanslow (1991) proposed the parameter (β Ho Lo)1/2 as a

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Fig. 1. Location of the experimental sites. Coordinates in degrees.

control, whereas Ruessink et al. (1998) and Ruggiero et al. (2004) suggested a linear relationship between the run-up height and ξ, after studying beaches under highly dissipative conditions. The most recent and extensive analysis (Stockdon et al., 2006) combined information from 10 different field sites and reached to the following relationships: 0

 i1 = 2 1 Ho Lo 0:563β2 + 0:004 C + A ðall dataÞ 2 h

1=2 B R2k = 1:1@0:35βðHo =Lo Þ

morphology (e.g. see Velegrakis et al., 2005). Although most of these beaches are currently under erosion (e.g. EUROSION, 2004) and likely to be particularly vulnerable to extreme wave run-ups, no relevant studies have been carried out yet. Thus, the objective of this contribution is to present/discuss the results of a video-based, wave run-up study, carried out in the microtidal, sediment-starved beaches of the NE Mediterranean Sea (Greece), which are exposed mostly to locally-generated short waves.

ð5Þ 1=2

R2k = 0:043ðHo Lo Þ

dissipative beaches ðnb0:3Þ

ð6Þ

An interesting development regarding the acquisition of wave runup information has been the use of video-based techniques, which over the recent years have been shown to be an effective tool in coastal research (e.g. Erikson et al., 2005; Holman and Stanley, 2007; Velegrakis et al., 2007), as they provide non-intrusive, low-cost measurements in the energetic nearshore zone. Thus, while earlier studies used mostly in situ sensors (e.g. electrical wires) for run-up observations (e.g. Hunt, 1959; Baldock et al., 1997; Baldock and Holmes, 1999), video-based techniques have recently become dominant in similar efforts (e.g. Ruggiero et al., 2004; Gorman and Coco, 2005; Stockdon et al., 2006). Most of these techniques use ‘time-stack’ images (e.g. Aagaard and Holm, 1989; Holland and Holman, 1993), which allow the acquisition of time-series of run-up excursion lengths, through the application of edge detection algorithms or manual digitization, which can be then translated into run-up heights, if the beach profile is known. Previous run-up studies (upon which parameterisations have been based) have mostly taken place on sandy beaches exposed to oceanic wave and tidal conditions (e.g. Holman and Guza, 1984; Ruggiero et al., 2001; Erikson et al., 2005; Stockdon et al., 2006). However, there are many regions (e.g. the Mediterranean Sea), where the geological history, absence of oceanic swell, extreme storm waves and tides and particular climatic conditions have resulted in the formation of beaches with different characteristics, i.e. in the formation of narrow, sediment-starved ‘pocket’ beaches, fronted by seabeds with irregular

Fig. 2. Examples of the experimental layout in (a) Varia beach and (b) Haramida beach. Note that the camera was monitoring the wave run-up behind the instrument platform (the same cross-section).

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2. Study area Field observations were obtained from 3 narrow ‘pocket’ beaches of Lesbos Island (NE Aegean Sea, Greece), located along the SE coast of the island (see Fig. 1). The area is characterized by a microtidal regime, with the tidal range of the open sea beaches not exceeding 0.3 m (Tsimplis, 1994). Kanoni and Varia beaches are NE facing beaches with a relatively low wave regime due to the protection offered by the Asia Minor coast (Fig. 1); in comparison, the south facing Haramida beach is affected by the southerly and southeasterly waves generated in the E. Aegean Sea which, in some cases, can reach offshore wave heights (Hs) of up to 1.8 m. However, despite the low wave regime (particularly that of the Kanoni and Varia beaches), all three beaches have undergone severe erosion and are often completely inundated under moderately high wave conditions. 3. Methods 3.1. Data acquisition The experiments took place in May 2007, on neaps. Beach elevation was measured using standard levelling techniques for the sub-aerial and shallow marine section of the beach (depths less than 1.5 m) and a diver equipped with a pressure sensor (accuracy ± 0.02 m) for the deeper, offshore, waters. The distance from the onshore reference point of the beach profiles was measured with the use of a taut,

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calibrated rope, stabilized on the bed all along the measured crosssection of the beach. The levelling work took place immediately before and after the observations. In addition, surficial sediment samples were collected from the ‘dry’, onshore profile, the swash and the offshore zones. As the mud content of the sediment samples was negligible (less than 1% of the sample’s weight), the grain size distribution was determined by dry sieving and the grain size parameters were estimated according to Folk (1980). Synchronised (Nortek Vector) ADV, pressure and optical backscatter (OBS) sensors, were placed in the shallow nearshore waters to acquire high frequency (16 Hz) hydrodynamic (and sediment resuspension) information (see Fig. 2). The sensors were mounted on an aluminium cubic frame, which was positioned in a way that its effects on the flow were minimised (e.g. see Voulgaris and Meyers, 2004; Verney et al., 2007). The East/North/Up coordinate system was used to take into account flow-induced tilting/displacement and burst duration was set to 300 or 600 s (depending on the experimental site), with ‘sleep-mode’ intervals of 300 s. For the wave run-up observations, JVC GR-D270E video cameras were used; these were placed at elevated positions to obtain information from the highest point of view possible. For the synchronization of the video cameras with the sensors of the instrument platform, the clock of a laptop computer (synchronized with the other deployed sensors) was videotaped on the screen for few seconds. Given that the frame capturing frequency was 29.97 frames/s, the maximum synchronisation error was found not to exceed 1/29.97 s which, for the purpose of this study, was considered acceptable.

Fig. 3. Steps of the wave run-up video technique. Each frame is transformed into binary format and after several processing steps, the position of the incident bores (gray line) and the upper run-up limit (white line) is estimated.

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Observations at the Varia beach were obtained in two consecutive days, as a significant deterioration in the light conditions due to heavy clouding did not allow their conclusion in the first day, whereas only one burst of observations was obtained in Haramida beach due to instrumentation malfunction. During the observations, the beachface of the investigated beaches was characterized by accumulations of Posidonia oceanica fragments, originated from the extensive sea grass meadows found offshore; these accumulations had to be removed prior to the experiments to allow discernible video observations. However, still significant amounts of P. oceanica fragments existed both in the water and the beach. 3.2. Data analysis 3.2.1. Swash motion tracking The wave run-up observations were obtained using a video-based technique which, in addition to cross-shore run-up observations, can also provide 2-D information on the upper run-up limit and the position of the propagating bores. Video capturing took place in desktop PCs, using Adobe Premier software, whilst the processing of the videos was carried out with specially-developed MATLAB codes. In order to translate image space scales to real world dimensions, image rectification procedures were followed, consisting of two steps: (a) calibration of the camera's intrinsic parameters and (b) translation of the camera field of view to real world coordinates. Lens distortion consists of several constituent distortions, with the geometric distortion being the most significant. There are several approaches for camera calibration procedures (Heikkilä and Silvén, 1997; Tsai et al., 2001; Erikson et al., 2005). In the present study, the Heikkilä and Silvén (1997) approach was followed, using a 1 × 1 m dotted board (dot radius ∼ 2 cm and distance between two neighbouring centers ∼ 10 cm) as reference to estimate the correction parameters (Zhang, 2002). Image rectification methods range from cumbersome and highly accurate explicit techniques to simplified implicit approaches (e.g. Thormodsgard and Lillesand, 1987; Holland and Holman, 1997; Coxeter, 2003). For the present study, an implicit approach was considered more suitable, according to which the frame plane coordinates of the image are transformed to real world coordinates, using a perspective transformation matrix P (Hartley and Zisserman, 2006). The latter is estimated through a non-linear iteration ‘calibration’ procedure which takes into account ‘control points’ of known positions in both coordinate systems (Holland and Holman, 1997). Thus, it was necessary to identify (three or more) points on the camera's field of view and measure accurately their actual coordinates, using a Differential GPS. The geo-rectification accuracy is controlled by several parameters, such as the spatial distribution of the control points, the landscape and the projected area (see also, Vousdoukas, 2008; Vousdoukas, submitted for publication). In our case, the maximum error was estimated to be less than 10 cm. Following geo-rectification, each frame was processed in order to identify the upper run-up limit. As the present contribution focuses on the analysis of the field observations, only a brief overview of the used processing techniques is provided here (see also Fig. 3); a more detailed description of these techniques can be found in Vousdoukas (2008). A pre-processing of the video is necessary to normalize pixel intensities (i.e. to take into account changes in luminance) and ‘clean’ the image from ‘noise’ linked to the presence of litter on the beach and distortions due to the non-simultaneous refreshing of lines in the PAL system (e.g. see Chapman and Chapman, 2000; Erikson and Hanson, 2005). The run-up measurements were based on the tracking of the foam formed due to wave breaking. The foam areas were identified on each frame, which had been previously converted into binary format to reduce processing times. The upper run-up limit was identified by implementing a motion detection algorithm, and further processing was restricted on the image area found offshore of the upper limit. Bore

Table 1 Wave statistics, Iribarren number and set-up for each site, based on the sea surface elevation time series from the ADV pressure sensor. Site

D

Hs

Ho

Lo

T

LADV

ξsz

ηs

V1 V2 Kan Har

0.88 0.79 1.02 1.85

0.24 0.32 0.08 0.29

0.26 0.33 0.09 0.30

10.3 12.9 3.5 18.5

2.6 2.9 1.5 3.4

6.9 7.5 3.3 12.2

0.46 0.45 0.13 0.37

0.05 0.07 0.01 0.05

Key: V1, Varia beach, first day of observations; V2, Varia beach, second day of observations; Kan, Kanoni beach; Har, Haramida beach; D, water depth; Hs , significant wave height; Ho, offshore significant wave height; Lo, offshore wave length; T, wave period; LADV, wavelength at the point of the measurement; ξsz, Iribarren number (considering surf zone beach slopes); ηs, wave set up estimated through Eq. (8). Length/height units in m and time units in s. Mean values of all bursts from each site are shown.

propagation tracking was also possible (see Fig. 3), following the filtering of the smaller features on the binary image (bores are larger structures than foam), even though such information was not used in the present study. The measurements were then validated ‘manually’, by re-creating the obtained videos with the addition of the traced upper run-up limit and bore fronts. The time series of the upper run-up limit were also projected on time-stack images, and they were validated visually as well as through comparison with series obtained by ‘manual’ processing of the time-stack images (e.g. see Holman and Stanley, 2007). 3.2.2. Wave run-up estimation All processing took place in MATLAB. The processing product was time series of longshore ‘profiles’ of the upper swash front in a Ny × Nt matrix format (where is the Ny number of cross-sections (defined by the long-shore spatial resolution) and Nt the number of measurements). Since everything was geo-referenced (in metric dimensions), each column of the matrix corresponded to a time-series of the swash excursion length, at a specific cross-section. The results were 2-D, but given that wave measurements were obtained from one beach profile in each experimental site, only the corresponding run-up time series was used. The discrete heights of the wave run-up (R) were estimated, using the uppermost position of each swash event. R is usually defined as a discrete-in-time variable, that contains the local maxima of the sealevel time series η(t); η(t) can be decomposed into (i) the maximum wave set-up ηs and (ii) swash-induced, water level fluctuations S(t) (e.g. see, Stockdon et al., 2006): ηðt Þ = ηs + Sðt Þ

ð7Þ

As the instrument platform was located offshore of the breaking zone and the burst duration was short (300–600 s), set-up measurements could not be obtained; thus, ηs was estimated, following (e.g. Holman, 2001): ηs = 0:45Ho n

ð8Þ

where Ho. Information on the deep water wave conditions was, therefore, essential for the estimation of the wave set-up. Sea surface elevation data, obtained by the instrument platform pressure sensor, were processed to derive the nearshore wave time series (e.g. see Tucker and Pitt, 2001). Zero-crossing values were obtained and spectral analysis was used to estimate the wave parameters (Table 1). The deep water wave conditions were then estimated using linear wave theory, according to: Ho = Hs

   0:5 C 2kh 4π 1+ 2 sinhð2khÞ gT

ð9Þ

where Ho is the deep water significant wave height, Hs is the significant wave height at the platform position, C the wave celerity,

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Fig. 4. Beach profiles from Varia (a), Kanoni (b) and Haramida (c) beaches. The location of the instrument platform is also shown. Note that the observations from the Varia beach were obtained in two days (V1, V2) and the instrument platform was repositioned at the second day of observations. Arrows: location of the longshore bars at Kanoni beach (b) and the beachrock platform (c).

h the depth at the platform location, g the gravitational acceleration, and T and k the wave period and wave number, respectively. Swash-induced vertical fluctuations were estimated by translating the run-up excursion lengths to elevations, using the corresponding beach profiles. Tidal contributions on the water-level fluctuations were not considered, due to the limited tidal range of the area (less than 5 cm on neaps) and the short duration of the bursts. At all experimental sites, the beach profiles were found to be stable, during the duration of the experiments (due, probably, to the short duration of the field observations and the mild wave conditions). Beach slope, although an important parameter in swash zone studies, can not always be easily defined, given the irregular morphology of natural beaches. Previous studies have used either the foreshore beach slope βs (e.g. Stockdon et al., 2006), or the surf zone beach slope βsz (e.g. Holman and Sallenger, 1985; Nielsen and Hanslow, 1991). The former can be estimated in the swash zone, i.e. in the section of the foreshore defined by z = ηs ± 3 · σ(S(t)), where ηs is the mean sea level and σ(S(t)) the standard deviation of the swashinduced water level variation S(t). The latter can be estimated by considering the profile section between the breaking point and the upper run-up limit. In the present study, the foreshore beach slope βs is used for the run up parameterization in the following sections; similarly, the Iribarren number ξs is also related to the foreshore slope. The surf zone beach slope βsz (and the related Iribarren number ξsz) is used only to classify the beaches (e.g. Komar, 1998) according to their longer term conditions. As a result, when ξ and β symbols without subscripts appear in the text, they correspond to the foreshore values. 4. Results 4.1. Beach morphology and hydrodynamics All three investigated beaches are characterised by small lengths and very limited widths. Varia beach is a 600 m long, NE facing beach, bounded by rock promontories and backed by a 3 m high seawall; its

width is very limited, being less than 10 m along its entire length (∼8 m at the experimental site during the observations, see Fig. 4a). During the time of observations, the beachface had a slope (βs) of 0.21 and consisted of poorly-sorted coarse sediments with a mean grain size of −1.2 φ; however, offshore of the wave breaking zone, the sediments were found to be much finer, consisting of well-sorted sands (mean grain size of 2.86 φ and sorting of 0.3 φ) at the position of the instrument platform. Kanoni beach is also a narrow, ‘pocket beach’, backed by a coastal road, with the width of its subaerial section never exceeding 20 m. At the location and time of the video observations, the width of the subaerial beach was ∼ 18 m, with its highest elevation being a little more than 1 m (Fig. 4b); the slope (βs) was estimated as 0.11. Two low longshore bars were observed at ∼ 10 and ∼30 m from the coastline. The sediments of the submarine section of the beach were found to be quite homogenous, with a mean grain size of 2.39 φ and a sorting of 0.55 φ; in comparison, the swash zone sediments were coarser (and less well sorted), with a mean grain size of 0.35 φ. Kanoni beach can be considered generally as dissipative, as the Iribarren number ξsz (the surf zone estimated on the basis of the distance of the offshore bars, see Fig. 4) was estimated as b0.3. Finally, the south facing Haramida beach had a width of around 20 m and a beachface slope (βs) of 0.16, while its swash zone consisted of poorly-sorted coarse sediments (mean size −1.4 φ) during the time of the observations. Submerged beachrock outcrops (e.g. Vousdoukas et al., 2007) were observed at ∼15 m from the coastline (Fig. 4c); the seabed offshore of these outcrops was found to be covered by wellsorted sands (mean grain size of 2.06 φ and sorting of 0.5 φ at the location of the instrument platform). P. oceanica meadows were found in the nearshore waters of all investigated beaches (offshore of water depths of ∼2 m); these may influence the local nearshore hydrodynamics and sediment dynamics (e.g. Clarke and Kirkman, 1989; Yang et al., 2001; Keulen and Borowitzka, 2003; Paling et al., 2003). During all experiments, the wave conditions were mild (see, for example, Fig. 5), particularly at the Kanoni beach. Moreover, during the

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Fig. 5. Hydrodynamic conditions at Haramida beach (water depth of 1.85 m): (a) cross-shore flow velocity at 0.1 m from the seabed; (b) longshore flow velocity at 0.1 m from the seabed; (c) sea-surface elevation fluctuations (waves); (d) optical backscatter signal at 0.1 m from the seabed; and (e) swash zone sea level (η(t), see Section 3.2.2). Note that the wave run-up heights, although synchronised with the remainder of the data shown, do not correspond to the same wave events, due to the distance between the platform and the coastline (∼30 m).

duration of observations, the data showed negligible low frequency sea level changes, suggesting the absence of significant tidal motions (the experiments in these microtidal beaches also took place on neaps). At all sites, negligible mean flows were observed (Fig. 5a and b), probably due to the low energy of the incident waves and the position of the platform outside the breaking zone, i.e. in the wave refraction zone (Komar,1998). The measured flow velocities (at ∼0.1 m from the bed) in the crossshore direction did not exceed 0.7 m/s, while in the longshore direction rarely exceeded 0.4 m/s for all experimental sites. Sediment resuspension events, which were mostly associated with wave groups, were observed at all sites (see Fig. 5). Estimation of the deep water wave parameters, on the basis of the recorded sea surface elevation information, showed mild offshore wave conditions during the observations (Table 1). During the Kanoni beach experiment, deep water waves were found to be the least energetic, with wave heights Ho ranging (depending on the burst) between 0.07 and 0.11 m, wave lengths Lo between ∼ 3–5 m and periods between T ∼ 1.3–1.8 s. In comparison, the offshore wave regime at the Varia and Haramida beaches was more energetic (Ho ∼ 0.24–0.34 m; Lo ∼ 10–19 m and T ∼ 2.6–3.4 s). Generally, the wave parameters for each set of observations did not show significant changes between bursts, as the ‘sleep-mode intervals’ were of small duration (300 s). From these deep water wave characteristics and the surf zone beach slopes βsz (equal to 7.2, 2 and 4.7% for Varia, Kanoni, Haramida, respectively), the Iribarren numbers ξsz shown in Table 1 are estimated, showing that Kanoni is the only dissipative beach.

conditions (e.g. limited swash zone widths and the not consistent beach textures/colours). The performance of video-based technique is controlled by (i) the accuracy of the transformation of the screen scale (in pixels) to real dimensions (in m) and (ii) the performance of the

4.2. Wave run-up Comparison between the results from the automated video technique and those obtained ‘manually’ was found to be satisfactory (Fig. 6), with the RMS errors for the excursion lengths ranging between 0.048 and 0.11 m for all bursts and locations. The results showed that the employed approach can provide good quality wave run-up information, even when applied in relatively unfavourable

Fig. 6. Comparison of the ‘automatically’ obtained time series with those obtained ‘manually’ for the horizontal maximum run-up excursion limit (RMS error of 0.056 m) for a Kanoni beach burst.

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Fig. 7. Wave run-up excursion lengths, validated on time-stack images from (a) Varia, (b) Kanoni and (c) Haramida beaches. Note that only sections of the bursts are shown for better display.

run-up tracking algorithm. The scaling errors are mostly related to the image projection from three to two dimensions. In the present study, both the performance of the geo-referencing and the tracking algorithm was found to be very satisfactory (Fig. 6), which was compared to manual measurements, as well as with timestack images (Holman and Stanley, 2007). The longest maximum run-up excursion lengths were observed in Varia (mean of bursts ∼ 3.145 m), while in Kanoni and Haramida they were much shorter (1.89 and 2.20, respectively) (see Fig. 7); these differences can be mostly attributed to the different wave conditions prevailing during the time of the observations in each of the experimental sites (Table 1). Moreover, the run-up motions at the dissipative Kanoni beach differed from those at the other sites (see, for example, Fig. 7); discernible low frequency motions were present at this site, despite the very mild wave regime. 2% exceedence run-up heights R2% rarely exceeded 0.3 m, with the highest values observed at the Varia beach (V1) and the lowest at the Kanoni beach (Table 2). At Haramida beach, although the offshore wave heights were comparable to those of the Varia beach (Table 1), run-up heights were found to be significantly reduced; this is, probably, due to the higher nearshore relief and the coarser nature of the swash zone sediments of Haramida beach (see Section 4.1), which are likely to have resulted in increased wave energy dissipation and swash zone percolation. This observation highlights the significance of the beach morphological and sedimentological character and suggests that predictions on the basis of empirical expressions derived from observations obtained from sandy, sediment-rich oceanic beaches may not predict satisfactory the run-up at sediment-starved, coarse-grained beaches (see also Section 5). The run-up and swash statistics (Table 2) showed standard deviations between ∼0.03–0.06 and kurtosis and skewness values ranging between ∼2.4 and 4.3 and ∼ −0.8 and 0.3 respectively. The distributions were found to be negatively-skewed (shorewards) at Varia and Haramida beach (see also Stockdon et al., 2006), whereas, at Kanoni beach, these were positively skewed. The cumulative probability density function (PDF) of the continuous swash height series (Fig. 8a, b and c) appeared to be in good

agreement with the Gaussian distribution with Pearson correlation coefficients higher than 0.997. Similar comparison for the PDFs of the 2% exceedence run-ups (Fig. 8d, e and f) resulted in lower correlation values (0.938–0.98), reflecting the not entirely Gaussian nature of the swash (see also Table 2); these results are comparable to those obtained in previous studies (e.g. Holland and Holman, 1997; Gorman and Coco, 2005; Stockdon et al., 2006). Comparison between the wave and swash height spectra (Fig. 9), showed a good agreement with regard to the locations of the significant peaks. This is interesting in the case of the Haramida beach (Fig. 9c and f) the nearshore zone of which is characterised by the presence of submerged beachrock outcrops. Vousdoukas et al. (2007) have shown that the presence of such outcrops in the shallow nearshore zone may result in a shift of the wave energy frequency downstream of the outcrop, due to wave-outcrop interactions. It appears, however, that such a shift (if at all present in this case) did not affect significantly the swash motions. Low frequency swash motions (0.005 Hz b freq b 0.1 Hz) have been a particular topic of discussion (e.g. Mase, 1988; Watson and Peregrine, 1992; Erikson et al., 2006). These have been suggested to be either the result of infragravity motions (e.g. Huntley et al., 1977; Guza and Thornton, 1982; Holland et al., 1995), or the effect of wave groups (Baldock et al., 1997; Baldock and Holmes, 1999; Brocchini and Gentile, 2001). The results of the present study appear to be different to those reported previously (e.g. Holman and Guza, 1984; Mase, 1988;

Table 2 Statistical moments of the run-up heights (mean of all bursts in each site). Site

MnR

StdR

KurtR

SkR

StdS

KurtS

SkS

R2%

V1 V2 Kan Har

0.22 0.23 0.09 0.17

0.04 0.03 0.05 0.03

3.19 3.80 2.42 4.09

− 0.57 0.06 0.26 − 0.25

0.06 0.06 0.04 0.04

2.89 4.26 2.73 2.96

− 0.24 − 0.81 0.15 − 0.21

0.26 0.25 0.11 0.19

Key: MnR, StdR, KurtR, and SkR refer to the mean, standard deviation, kurtosis and skewness of the wave run-up height R, respectively; The subscripts 2%, and S denote the 2% exceedence wave run-up height value and the swash induced sea-level fluctuation, respectively.

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Fig. 8. Cumulative probability density (PDF) distributions for the swash height S (a, b and c) and the run-up R series (d, e and f) for bursts from the Varia (a, d), Kanoni (b, e) and Haramida (c, f) beaches. Dashed lines show the Gaussian distributions.

Baldock and Holmes, 1999; Erikson et al., 2006), as the contribution of the low-frequency motions to the total spectral density of run-up heights (Fig. 9 and Table 3) was found to be relatively low. Nevertheless, the swash height time series showed higher levels of energy contributions from the low frequencies, compared to those of

the waves (Table 3 and Fig. 9), particularly for the series from dissipative Kanoni beach; at this site, the low frequency contributions were found to be the most significant (∼ 28%). Swash heights in this beach were also found to be associated with low frequencies (in the vicinity of the infragravity band); in comparison, the low frequency

Fig. 9. Spectral density of the estimated swash height (a, b and c) and sea-level (d, e and f) time series from the Varia (a, d), Kanoni (b, e) and Haramida (c, f) beach observations. The dashed lines correspond to the data obtained during the second day of the experiment at Varia beach (V2).

M.I. Vousdoukas et al. / Journal of Marine Systems 78 (2009) S37–S47 Table 3 Contribution of infragravity (0.005 Hz b freq b 0.1 Hz) and incident frequencies (freq N 0.1 Hz) to the total variance of the swash height and sea-level time series. Location Varia Kanoni Haramida Mean

Run-up height (%)

Sea level (%)

Infragravity

Incident

Infragravity

Incident

19.1 47.4 34.2 33.6

80.9 52.6 65.8 66.4

0.9 0.7 1.2 0.9

99.1 99.3 98.8 99.1

The results from the two experiments in Varia beach have been combined for the purpose of this table.

contributions to the total variance were found to be limited (b15%) at the Haramida and Varia sites, with swash also appearing to be associated with higher frequencies than those of the Kanoni beach. The swash height spectra drop-off slopes (Fig. 9) were of the order of 2–3, i.e. slightly reduced compared to those observed in previous studies (e.g. Guza and Thornton, 1982; Ruessink et al., 1998; Erikson et al., 2006). In comparison, the drop-off slopes of the wave spectra were much higher, ranging between 6 and 8. Such drop-off rates may suggest saturated nearshore/swash zone conditions, under which, an increase of the deep water significant wave height Ho does not necessarily result in an increase in the contribution of the incident frequencies to the swash motion spectra (e.g. Raubenheimer and Guza, 1996; e.g. Ruggiero et al., 2004). Saturated conditions have been found to be mostly associated with wave groups (see Holland et al., 1995; Raubenheimer et al., 1995). In our case, however, the source of the low frequency motions could not be resolved, since for the precise identification of standing waves (e.g. Huntley et al., 1977; Raubenheimer et al., 1995) or wave groups (Baldock et al., 1997), wave measurements at several points along a beach cross-section are required. It must be noted however, that given the mild wave conditions prevailing during our field observations, saturation of the nearshore zone is considered unlikely and the observed frequency bands contributions could be mostly attributed to depth attenuation of the very short incident waves. To provide some quantitative information on the contribution of the incident and infragravity components in relation to the dimensional Iribarren number β (Ho Lo)1/2 (e.g. Guza and Thornton, 1982; Stockdon et al., 2006), linear regression was used (see Fig. 10). The fit for the incident component was better (R = 0.6, p = ∼0.03) than that of the infragravity component which in addition was not significant for 95% confidence interval (p = ∼ 0.8). The fitting was repeated after excluding the beachface slope from the Iribarren number, but again the correlation was poor (R = 0.15, p = ∼0.9). The incident component linear fitting coefficients (slope = 0.58, b = 0.08) were found to be close to those estimated by Stockdon et al. (2006) (slope = 0.75, b = 0). However, this was not the case for the infragravity contributions for which an almost zero or negative slope is estimated, in contrast to other similar studies. This can be mostly due to the fact that in the present measurements the infragravity contributions are not shown to be as high as in other related studies (see also Table 3) and therefore cannot be properly modelled.

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the exception of the general expression of Stockdon et al. (2006) (i.e. Eq. (5)) which resulted in RMS errors of ∼0.04 m; this is, probably, due to the fact that the Stockdon et al. (2006) expression was derived from an extensive dataset obtained from diverse sites and conditions. Six (6) parameters, Hoξ, (Ho Lo)1/2, Ho (Ho/Lo)− 1/2 and (β Ho Lo)1/2 as well as the Stockdon et al. (2006) and Holman (1986) parameterisations, were fitted linearly against the R2% run-up heights observed during the present investigation (Fig. 11 and Table 4). Following the fitting, the general performance of the expressions improved (RMS b 0.05 m, see Table 4), with the Stockdon et al. (2006) expression still giving the best results. Considering the predictions with regard to the individual beaches of the present investigation, RMS errors were the lowest for the Kanoni beach (0.02 to 0.04 m, depending on the parameterization) and the highest for the Haramida beach (0.03 to 0.11 m). The unfavourable comparisons between the present data set and the previously proposed parameterisations can be mostly attributed to the particular environmental conditions of the investigated beaches. The protected beaches of the NE Aegean are generally characterised by locally-generated short waves (with small heights and periods rarely exceeding 3 s) and limited fetch (generally less than 20 miles) and, consequently, of much shorter swash zones than those previously studied. Thus, as scale-effects are likely, the parameterisations proposed for beaches affected by much more energetic wave regimes (including oceanic swell) may not perform well in such conditions. In addition the beach morphology and, particularly, the sedimentology of the investigated, sediment-starved

5. Discussion The results of the present investigation were used to test previously proposed parameterizations/expressions of the wave runup (Hunt, 1959; Holman, 1986; Synolakis, 1987; Douglass, 1992; Ruggiero et al., 2001; US Army Corps of Engineers, 2002; Stockdon et al., 2006). Predictions of run-up heights, based upon previously proposed parameterizations/expressions and the wave parameters and beach slopes estimated from the present field data (Table 1) did not show good agreement with our run-up observations, with

Fig. 10. Scatter plots comparing the incident (a) and infragravity (b) contributions to the swash height with the dimensional Iribarren number (βsHo Lo)1/2. In (c) the beachface slope is excluded from the parameter to give slightly better fit for the infragravity component. The linear fit coefficients are included in the plots. Key: ‘.’ Varia Day 1; ‘+’ Varia Day 2; ‘⁎’ Kanoni; ‘Δ’ Haramida.

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M.I. Vousdoukas et al. / Journal of Marine Systems 78 (2009) S37–S47

Fig. 11. Scatter plots of the 2% exceedence of the run-up height series (R2%) against the parameters Ho ξ, (Ho Lo)1/2, Ho (Ho /Lo)− 1/2 and (βsHo Lo)1/2 and the Stockdon et al. (2006) (St06) and Holman (1986) (Hol86) parameterisations. Line corresponds to linear fit model for each case (see Table 4 for the coefficients of the linear fitting and corresponding RMS errors).

beaches are also different. Their swash zones are generally characterised by poorly-sorted, coarse sediments and extensive P. oceanica meadows are present in the nearshore waters. Moreover, layers of deposited sea-grass fragments are often found buried within the beach sediments. These layers can influence significantly the porous properties of the beach and, thus, the water infiltration/exfiltration and pore pressure dynamics, processes that control the hydrodynamics and morphodynamics of the swash zone (e.g. Horn, 2006; Masselink and Russell, 2006). Finally, the different methodologies used to obtain field observations could also be a factor responsible for the observed discrepancies. For example, video-based observations take place in a spatiallydiscrete domain, controlled by the real distance per pixel ratio, which can be different for each experimental site. On the other hand, data obtained from electrical wires take place in a spatially-continuous domain and in that case measurements can also be affected by the height from the bed. Sampling frequencies/errors are also likely to vary between video-based studies, whereas the combination of time series of run-ups and sea-levels (waves) is not always a straightforward exercise, as the former are in a Lagrangian and the latter in an Eulerian reference frame (e.g. Baldock et al., 1997). Such effects are minimised in the case that run-up excursion lengths (and the resulting heights) are small, as it was the case in the present study, but may be significant in beaches with long swash zones. 6. Conclusions The study showed that the video-based approach employed can provide good quality wave run-up information in the particular conditions of the narrow, sediment-starved beaches of the E. Mediterranean. The results showed that these beaches exhibit particular characteristics with regard to the wave run-up compared to the sandy oceanic beaches previously studied; these differences may be attributed to the particular wave regime and sedimentological characteristics. Although run-up heights appeared to be characterised by frequencies similar to those of the nearshore waves, there was still

an introduction of low frequency motions to the swash (particulary in the case of the dissipative beach). On the other hand, their contribution to the total run-up energy appeared to be less than that found in previous studies. Wave run-up heights were also found to be influenced significantly from the swash zone sedimentology and/or the nearshore bed morphology, indicating that run-up predictions on the basis of empirical expressions derived from observations obtained from the sediment-rich oceanic beaches may not be appropriate in this case. Tests regarding the ability of previously-proposed parameterisations to fit the present data resulted in a mixed picture (particularly for the beach with the most irregular relief and coarser swash zone sediments); Douglass (1992) and Stockdon et al. (2006) parameters appeared to perform better than the rest. Finally, comparison between the present observations and predictions based on previously proposed expressions was also not satisfactory, with the possible exception of the Stockdon et al. (2006) expression, which has been obtained on the basis of extensive datasets from diverse beaches. This also suggests a differential behaviour of the investigated beaches, compared to those previously studied, and highlights the need to be careful when applying empirically-derived expressions for the prediction of wave run-ups.

Table 4 Coefficients (slope, offset) and corresponding RMS errors (m), related to the linear fitting of the run-up heights observed in the present investigation with previously proposed parameters (see also Fig. 11).

Slope Offset RMS error

Ho ξ

(Ho Lo)1/2

Ho (Ho/Lo)− 1/2

Stock06

Hol86

(β Ho Lo)1/2

0.43 0.09 0.03

0.07 0.09 0.09

0.53 0.09 0.03

0.63 0.08 0.02

0.07 0.09 0.10

0.20 0.07 0.03

Key: R2%, 2% exceedence for the run-up height; Ho, deep water significant wave height; Lo, offshore wavelength; ξ, the Iribarren number; β, the beach slope. Stock06 and Hol86 refer to the Stockdon et al. (2006) and Holman (1986) parameters, respectively.

M.I. Vousdoukas et al. / Journal of Marine Systems 78 (2009) S37–S47

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