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Journal of Marine Science and Engineering

Article Lidar Observations of the Swash Zone of a Low- Terraced Tropical under Variable Conditions: The Nha Trang (Vietnam) COASTVAR Experiment

Luís Pedro Almeida 1,2,* , Rafael Almar 2 , Chris Blenkinsopp 3, Nadia Senechal 4, Erwin Bergsma 5 , France Floc’h 6 , Charles Caulet 6, Melanie Biausque 7, Patrick Marchesiello 2 , Philippe Grandjean 8, Jerome Ammann 6, Rachid Benshila 2, Duong Hai Thuan 9, Paula Gomes da Silva 10 and Nguyen Trung Viet 9

1 Instituto de Oceanografia, Universidade Federal do Rio Grande (FURG), Rio Grande 96203-900, Brazil 2 Laboratoire d’Etudes en Géophysique et Océanographie Spatiales (LEGOS), Université de Toulouse/CNRS/CNES/IRD, 31400 Toulouse, France; [email protected] (R.A.); [email protected] (P.M.); [email protected] (R.B.) 3 Department of Architecture and Civil Engineering, University of Bath, Bath BA2 7AY, UK; [email protected] 4 UMR 5805 EPOC, CNRS-Université de Bordeaux, CS 50023-33615 Pessac, France; [email protected] 5 Centre National d’Études Spatiales (CNES), 31400 Toulouse, France; [email protected] 6 Laboratoire Géosciences Océans-UMR 6538, CNRS-Université de Bretagne Occidentale, F-29280 Plouzané, France; france.fl[email protected] (F.F.); [email protected] (C.C.); [email protected] (J.A.) 7 School of Geography and Environmental Science, Ulster University, Coleraine BT52 1SA, Northern Ireland, UK; [email protected] 8 Laboratoire de Géologie de Lyon: Terre, Planètes, Environnement—UMR 5276, Université de Lyon, F-69622 Villeurbanne, France; [email protected] 9 Faculty of Civil Engineering, Thuyloi University, Hanoi 116705, Vietnam; [email protected] (D.H.T.); [email protected] (N.T.V.) 10 Coastal Laboratory, Federal University of Santa Catarina, Florianópolis 88040-900, Brazil; [email protected] * Correspondence: [email protected]

 Received: 12 March 2020; Accepted: 23 April 2020; Published: 26 April 2020 

Abstract: A field experiment was conducted at a tropical microtidal intermediate sandy beach with a low tide terrace (Nha Trang, Vietnam) to investigate the short-term swash-zone hydrodynamics and morphodynamics under variable wave conditions. Continuous 2D Lidar scanner observations of at the lower foreshore, subsequent run-up and swash-induced topographic changes were obtained. These data were complemented by detailed real-time kinematic GPS topographic surveys. Variable wave and tide conditions were experienced during the field experiment with relatively large (offshore significant wave height, Hs = 0.9 m to 1.3 m; peak wave period, Tp = 8 to 12 s) concomitant with spring at the beginning of the period, followed by mild wind waves (offshore Hs under 0.5 m and Tp 5 s) and neap tides. This resulted in the following morphological sequence: berm followed by rapid neap berm reformation and beach recovery within a few days. New insights into the link between intra-tidal swash dynamics and daily beach profile evolution were found using the Lidar dataset. While waves directly cause morphology changes on a wave-by-wave basis, tidal levels were found to be a key factor in determining the morphological wave-effect (accretive or erosive) due to modulated interaction between surf and swash hydro-morphodynamics.

J. Mar. Sci. Eng. 2020, 8, 302; doi:10.3390/jmse8050302 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 302 2 of 18

Keywords: swash zone; low-tide-terrace; Lidar; tide; Nha Trang—Vietnam

Highlights Nine-day detailed swash hydro-morphodynamic measurements of wave induced erosion and • recovery on a tropical beach (Nha Trang, Vietnam) with a Lidar. The wave height measured on the lower foreshore and active slope are key parameters to predict • vertical run-up on this type of intermediate beach. Tide induces a strong modulation of wave action and drives large intra- and daily changes on the • swash zone.

1. Introduction continuously adapt to wave forcing at multiple temporal [1–3] and spatial scales [4] and the morphological changes commonly observed in these environments are particularly related to the hydrodynamics of the swash zone. Swash flows are composed of two distinct phases, an upslope, landward directed flow (uprush) and a downslope, seaward directed flow (backwash). Although there is a continuum of energy in swash spectra, they are commonly divided into short wave (f > 0.05 Hz) and long wave, or infragravity, frequency bands (f < 0.05 Hz). The short wave band is normally more energetic in bore-dominated, steeper intermediate and reflective beaches [2], while swash variance in the infragravity band is typically observed on low gradient beaches [3]. Sandy beaches with a steep upper slope and flat low-tide terrace (LTT) represent one of four types of intermediate beaches [4] where the two distinct hydrodynamic regimes (reflective and dissipative) can be observed at different stages of the tide [5,6]. The wave breaker type affects the processes in the swash zone. For example, previous work [7] has suggested that the breaker type directly influences , since the amount of turbulence that reaches the bed leading to the suspension of sediment depends on the nature of breaking (e.g., plunging breaker vortices mobilize larger amounts of sediment than spilling breakers [8]). The turbulence generated by the bore collapse is advected into the swash-zone during the uprush [9], leading to a high concentration of suspended sediment. Subsequently, during the backwash, friction against the bed becomes the main source of turbulence [10]. This is enhanced in the lower swash region by the formation of backwash bores [11] and the hydraulic jump originating from the interaction between consecutive swashes [12]. The slope of the swash-zone also plays a significant role on swash-zone processes. The steeper the beach face, the more upslope transport is inhibited and more downslope transport is enhanced. The differences in forces that act during uprush and backwash lead to an asymmetry in swash velocity time-series [13,14]. If the incident wave conditions are constant, it becomes increasingly difficult to move sediment upslope on a steepening and accreting beach face and the beach slope approaches an equilibrium value. Similarly, on a flattening and eroding beach face, the slope contribution to the offshore sediment transport will progressively decrease, and the beach profile will eventually approach equilibrium [15]. On a steep LTT, however, tide-induced changes in the breaker type and swash-zone slope are expected to strongly influence swash processes, in particular the swash asymmetry [14]. Tidal modulation of breaker type (e.g., plunging breakers at high tide and spilling breakers at low tide) are known to occur on this type of beach [5,6]; however, the extent to which tidal variation affects the swash-zone hydrodynamics and, hence, the morphological response is still unclear [7]. Furthermore, although these theoretical concepts provide a basis for understanding the swash dynamics on this type of intermediate beach, the details of the process are highly complex, and limited field observations exist for validation. Most previous research on steep beaches with an LTT has been performed on mixed - beaches (MSG), where typically the upper-beach face is composed of gravel and the terrace of sand [5,16–18]. Similarities between MSG beaches and pure sandy beaches is mostly limited to the J. Mar. Sci. Eng. 2020, 8, 302 3 of 18 terrace where hydrodynamics and sediment transport mechanisms are analogous. The most landward region of the inner surf and swash zone-dynamics are controlled by factors specific to MSG beaches, including the role of the beach step [19], enhanced infiltration/exfiltration [20], the dominance of bedload transport, and strong wave reflection. Significant recent developments in techniques for remotely sensing coastal processes have made available a number of solutions, including ultrasonic altimeters, photographic techniques and Lidar, that allow simultaneous observations of water motions and bed changes in the swash-zone [21–25]. Of these technologies, Lidar has significant advantages as it provides non-intrusive, direct measurements of both water and bed surface elevation at high spatial and temporal resolution, and has minimal logistical requirements for deployment. Lidar scanners can be deployed on a frame above the swash-zone or from coastal structures such as piers to overlook the surf and swash zones [26]. Over recent years, processes in the surf and swash zones have been observed using Lidar, including more detail and with an accuracy comparable to that of other commonly used techniques [24,27–32]. In this work, we present a detailed analysis of a dataset obtained during a field experiment. Hydrodynamics and morphology measured using Lidar during a nine-day field experiment are used to assess swash asymmetry and the role of wave and tidal variability on swash-zone morphology at an intermediate low-tide terrace beach.

2. Methods

2.1. Study Area As part of the COASTVAR project (multi-scale and multi-method study of coastal variability in the of Guinea and Vietnam), a field experiment was undertaken between 26th November and 4th December 2015 at Nha Trang Beach, a sandy beach located in a semi-enclosed in southeast Vietnam (Figure1). The bay is approximately 6 km long, has an overall NE–SW coastal orientation and is partially protected from waves in the South China Sea (SCS) by a group of (Figure1). The mean sediment size varies considerably within the bay, with coarse sand in the north (D50 = 0.9 mm), reducing to medium to coarse in the south (D50 = 0.4 mm). The experiment described here was conducted in the northern part of the bay where the beach profile is characterized by a steep upper foreshore (slope 1:10) and a narrow, flat (slope 1:100) and uniform LTT, approximately 40 m wide ∼ ∼ (Figure2,[ 33,34]). The wave climate in this region is strongly influenced by the two monsoon seasons, the northeast (NM) and southwest (SM) monsoons. The NM is characterized by moderate winds (between 8 and 12 m/s) and energetic waves, typically occurring during the wet season (November to January), while the SM is characterized by mild winds and waves, between June and September [34–36]. In addition to the monsoon seasons, tropical cyclones, also known as typhoons, can produce very energetic waves in the SCS, resulting in sporadic but significant erosion and inundation hazards [37–39]. Nha Trang Beach is characterized by a mixed tide (combination of daily and semi-daily tide components) with microtidal amplitude (maximum amplitude of 1.5 m). J. Mar. Sci. Eng. 2020, 8, 302 4 of 18 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 18

FigureFigure 1. 1.Left: Left: Location Location of of Nha Nha Trang Trang bay bay and someand some important important local featureslocal features including: including: 1—Cai 1—Cai ; 2—Honestuary; Tre 2—Hon ; Tre 3—Hon island; Mieu 3—Hon island; Mieu 4—Hon island; Tam 4—Hon island. Tam The island. yellow The box yellow indicates box indicates the section the of thesection beach of selected the beach for thisselected experiment for this (zoomed experime in thent (zoomed right panel). in the Right: right Aerial panel). photograph Right: Aerial of the studyphotograph site in whichof the orange study linessite in indicate which the orange 15 cross- lines indicate transects the where15 cross-shore topographic transects surveys where were performedtopographic every surveys low tide;were in performed red is the profileevery low where tide instruments; in red is the were profile installed where (right instruments panel). were installed (right panel). 2.2. Experimental Set-up u 2.2. AExperimental range of in-situ Set- p and remote sensing instruments were deployed along a cross-shore transect of theA beach range from of in-situ the berm and crestremote to sensing depth o instrumentffshore of 15s were m (Figure deployed2). An along acoustic a cross-shore Doppler transect profilerof the beach (ADCP) from was the moored berm crest at 15 to m depth depth offshore (Figure of1) 15 and m provided (Figure 2). a completeAn acoustic characterization Doppler current of theprofiler offshore (ADCP) wave was conditions moored during at 15 m the depth experiment. (Figure 1) A and 2D Lidarprovided was a installed complete on characterization a tower located of at thethe top offshore of the wave berm conditions with an elevation during the of 3.5 experiment m to measure. A 2D inner Lidar surf was and installed swash-zone on a tower hydrodynamics located at (free-surfacethe top of the elevation berm with and an instantaneous elevation of 3.5 shoreline m to measure position, inner see surf [31,40 and]), andswash-zone morphological hydrodynamics evolution. Topographic(free-surface surveys elevation were and performed instantaneous every low shoreline tide using position, a real-time see kinematic [31,40]), GPS and system morphological (RTK-GPS) inevolution. continuous Topographic survey mode surveys along were 15 cross-shore performed transectsevery low spaced tide using by 10 a mreal-time (Figure 1kinematic). The results GPS describedsystem (RTK-GPS) in the present in continuous work are basedsurvey on mode the dataalong obtained 15 cross-shore from the transects ADCP, spaced Lidar, andby 10 topographic m (Figure survey1). The data results (only described the topographic in the present data work from are 3 of ba thesed 15 on transects the data was obtained used infrom this the manuscript—see ADCP, Lidar, Figureand topographic2). survey data (only the topographic data from 3 of the 15 transects was used in this manuscript—see Figure 2).

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Figure 2. Photograph showing the arrangement of all instruments along a cross-section of the beach Figure 2. Photograph showing the arrangement of all instruments along a cross-section of the beach (a); beach profile with instrument location and mean (MSL) indication during this experiment (a); beach profile with instrument location and mean sea level (MSL) indication during this (b); contour map of the study site topography with LIDAR profile location and two additional profiles experiment (b); contour map of the study site topography with LIDAR profile location and two used in this analysis (c). additional profiles used in this analysis (c). 2.3. Two-Dimensional Lidar 2.3.Two-Dimensional Lidar The Lidar deployed at the berm tower was a medium-range SICK LMS511 2D laser scanner (maximumThe Lidar range deployed 80 m, andat the 30 mberm at 10%tower remission). was a medium-range The Lidar emits SICK pulsed LMS511 infrared 2D laser beamsscanner (maximum(λ = 905 nm range) that 80 are m, deflectedand 30 m ontoat 10% an remission). internal mirror The Lidar rotating emits over pulsed a 190 infrared degree laser field beams of view. (λ = 905The nm) scanner that headare deflected rotates at onto 25 Hz an leading internal to anmirror angular rotating resolution over ofa 190 0.1667 degree degrees field and of theview. target The scannerdistance head is calculated rotates at using 25 Hz the timeleading of flight to an technique. angular resolution With this angular of 0.1667 resolution, degrees the and instrument the target distanceprovided is acalculated spatial resolution using the ranging time of from flight 0.01 technique. m at nadir With to 0.4 this m at angular the most resolution, distant valid the observation instrument providedpoint off shorea spatial (Figure resolution3). This spatialranging resolution from 0.01 allowed m at completenadir to coverage0.4 m at ofthe the most swash-zone distant andvalid observationcaptured wave point conditions offshore at (Figure the base 3). of theThis foreshore spatial resolution throughout allowed the experiment. complete coverage of the swash-zoneThe raw and Lidar captured data captureswave conditions both beach at the topography base of the as foreshore well as the throughout water surface, the experiment. without any distinction between the two (Figure3b). To separate the topography from the water at each cross-shore position, and over time, a moving-average time window variance filter was applied to all measurements, following the approach described in [29]. After initial data processing, the Lidar data were separated into two distinct time series: (1) beach topography (Figure3d) and (2) swash (including water depth and instantaneous shoreline evolution—Figure3c).

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FigureFigure 3. a)(a )Beach Beach profile profile the the Lidar Lidar position position shown shown as as a a red red circle circle and and theoretical theoretical projection projection of of the the differentdifferent laserlaser beamsbeams on on the the topography topography of theof the beach. beach. The The distance distance between between observations observations (black (black spots) spots)is calculated is calculated as the as horizontal the horizontal distance distance between between consecutive consecutive measurements measurements of the of the laser laser beams beams (a); (thea); the lower lower panels panels show show an example an example of raw of Lidarraw Lidar time seriestime series (b) and (b) post-processing and post-processing products: products: water waterelevation elevation (c) and (c bed) and altitude bed altitude (d) time (d) series. time series.

TheAs theraw grazing Lidar data angle captures between both the beach Lidar topograp and the targethy as decreases,well as the the water energy surface, scattered without back any to distinctionthe instrument between reduces the and two the (Figure variability 3b). ofTo the separate signal increasesthe topography [29]. This from can bethe important water at wheneach cross-shoretracking the position, water surface. and over While time, bore a frontsmoving-avera can still bege capturedtime window due tovariance their more filter normal was applied orientated to allsurface measurements, (relative to following the Lidar) the and approach the active described foam that in they[29]. produce,After initial laser data beam processing, reflections the from Lidar a datamore were horizontal separated (non-foamy) into two surfacedistinct are time weaker series: or (1) can beach be lost. topography As a result, (Figure the number 3d) and of (2) data swash gaps (includingor spikes duewater to depth erratic and returns instantane increasesous shoreline seaward withevolution—Figure the distance to3c). the Lidar. For this reason, LidarAs observations the grazing usedangle here between (both the water Lidar levels and and the bed target elevations) decreases, were the truncatedenergy scattered at a cross-shore back to thedistance instrument of 25 m reduces relative and to the the Lidar. variability of the signal increases [29]. This can be important when tracking the water surface. While bore fronts can still be captured due to their more normal 3. Results orientated surface (relative to the Lidar) and the active foam that they produce, laser beam reflections3.1. Offshore from Wave a Forcingmore horizontal (non-foamy) surface are weaker or can be lost. As a result, the number of data gaps or spikes due to erratic returns increases seaward with the distance to the Wave and tidal conditions during this experiment varied considerably (Figure4a). The first four Lidar. For this reason, Lidar observations used here (both water levels and bed elevations) were days of the experiment (27–30 November 2015) were characterized by energetic swells (narrow-banded truncated at a cross-shore distance of 25 m relative to the Lidar. energy band around 0.1 Hz—present in the wave spectra—Figure4d) with o ffshore waves recorded by 3.the Results moored ADCP having a significant wave height (Hs) between 0.9 and 1.3 m, and wave peak period (Tp) between 8 and 12 s, and spring tides (1.2 m amplitude). The following four days of the experiment 3.1.were Offshore characterized Wave Forcing by mild wind waves, with Hs under 1 m, Tp between five and eight seconds and a gradual reduction in tidal amplitude (<1 m). It is important to note that the mixed nature of the tide Wave and tidal conditions during this experiment varied considerably (Figure 4a). The first (double high tide peak) was more pronounced during spring tide conditions and gradually weakened four days of the experiment (November 27–30, 2015) were characterized by energetic swells under neap tides (Figure4a). (narrow-banded energy band around 0.1 Hz—present in the wave spectra—Figure 4d) with offshore waves recorded by the moored ADCP having a (Hs) between 0.9 and 1.3 m, and wave peak period (Tp) between 8 and 12 seconds, and spring tides (1.2 m amplitude). The following four days of the experiment were characterized by mild wind waves, with Hs under 1 m, Tp between five and eight seconds and a gradual reduction in tidal amplitude (< 1 m). It is important to note that the mixed nature of the tide (double high tide peak) was more pronounced during spring tide conditions and gradually weakened under neap tides (Figure 4a).

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Figure 4.4. Measurements of tides (blue line) and significantsignificant wave height obtained from thethe ADCPADCP moored ooffff thethe studystudy site:site: ((aa)) peakpeak wavewave period,period, ((bb)) meanmean wavewave direction,direction, andand ((cc)) normalizednormalized wavewave spectrumspectrum ((dd).).

3.2. Wave Characteristics and Run-up Observed from the Lidar 3.2. Wave Characteristics and Run-up Observed From the Lidar x The wavewave characteristicscharacteristics at the basebase ofof thethe foreshoreforeshore ((x == 25 m, see Figure2 2)) andand thethe vertical vertical run-uprun-up time-seriestime-series obtained obtained from from the the Lidar Lidar observations observations were were separated separated into into 15-minute 15-minute bursts, bursts, with with the assumptionthe assumption of tidalof tidal stationarity stationarity within within each each burst. burst. For For each each burst, burst, spectral spectral energyenergy densitydensity andand significant wave heights (Hs,LIDAR) were computed from the Lidar data at the same cross-shore location. significant wave heights (Hs,LIDAR) were computed from the Lidarp data at the same cross-shore In addition, the [41] was calculated as ξ = tanβ/ (Hs/L0), where L0 is the offshore location. In addition, the Iribarren number [41] was calculated as 𝜉=𝑡𝑎𝑛𝛽⁄(𝐻𝑠⁄)𝐿 , where L0 is wavelength measured at the ADCP and tanβ is the active foreshore slope extracted from the Lidar the offshore wavelength measured at the ADCP and tanβ is the active foreshore slope extracted from dataset (here, tan β is defined as the slope between the maximum run-up elevation and the minimum the Lidar dataset (here, tan β is defined as the slope between the maximum run-up elevation and the elevation of the run-down). The significant vertical run-up height (Rs) was calculated as four times the minimum elevation of the run-down). The significant vertical run-up height (Rs) was calculated as standard deviation of the shoreline elevation time series (R) within each 15-minute burst. four times the standard deviation of the shoreline elevation time series (R) within each 15-minute The time series of the H show a general trend similar to that of the offshore H , with initially burst. sLIDAR s larger waves up to HSLIDAR = 1.6 m that gradually decreased as the experiment progressed (Figure5). The time series of the HsLIDAR show a general trend similar to that of the offshore Hs, with The significant wave height measured at the base of the foreshore displayed a clear tidal dependence initially larger waves up to HSLIDAR = 1.6 m that gradually decreased as the experiment progressed (Figure5) indicating depth-control on wave heights as observed at other intermediate beach (Figure 5). The significant wave height measured at the base of the foreshore displayed a clear tidal sites [42] and highlighting the role of the LTT on incident wave energy dissipation in the surf zone dependence (Figure 5) indicating depth-control on surf zone wave heights as observed at other (Figure5). The significant run-up height and periods also show a strong tidal modulation, suggesting intermediate beach sites [42] and highlighting the role of the LTT on incident wave energy that mean water levels are key factors controlling swash zone hydrodynamics at Nha Trang Beach. dissipation in the surf zone (Figure 5). The significant run-up height and periods also show a strong tidal modulation, suggesting that mean water levels are key factors controlling swash zone

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 18 J. Mar. Sci. Eng. 2020, 8, 302 8 of 18 hydrodynamics at Nha Trang Beach. Calculations of energy spectral density indicate that tidal modulation of the HsLIDAR and Rs affects not only the height of the waves but also the wave periodCalculations through of wave the distribution power energy of spectralenergy densitybetween indicate the infragravity that tidal modulationand gravity of frequency the HsLIDAR bandsand (FigureRs affects 5c). not During only the low height tide, of lowe the wavesr water but levels also thefavor wave wave period breaki throughng on thethe distributiongently sloping of energy LTT, creatingbetween thevery infragravity dissipative and conditions, gravity frequency and the LTT bands acts (Figure as a 5low-passc). During filter low to tide, the lower swash-zone water levels [43], dissipatingfavor wave a breaking large part on of the the gently wave sloping energy LTT, in the creating short wave very dissipativeband (f between conditions, 0.05 and and 0.3 the Hz). LTT This acts resultsas a low-pass in a dominance filter to theof infragravity swash-zone waves [43], dissipating (f < 0.05 Hz) a that large do part not of fully the dissipate wave energy in the in surf-zone. the short waveAt high band tide, (f the between water 0.05 level and in 0.3the Hz).LTT Thisis greater results and in the a dominance terrace becomes of infragravity less efficient waves at (f dissipating< 0.05 Hz) thethat energy do not fullyof incident dissipate short in thewaves. surf-zone. A clear At indica high tide,tion theof this water modification level in the LTTin the is greaterhydrodynamic and the regimeterrace becomesis given by less the effi ratiocient between at dissipating offshore the si energygnificant of incidentwave height short measured waves. A by clear the indication ADCP and of significantthis modification wave inheight the hydrodynamic measured LIDAR regimeon the islower given foreshore by the ratio by between the Lidar off shore(Hs/HsLIDAR significant; Figure wave 6). Duringheight measured high tide byconditions, the ADCP this and ratio significant is close wave to 1 height(HsLIDAR measured is similarLIDAR to Hons) while, the lower during foreshore low tide by conditions,the Lidar (H Hs/sLIDARHsLIDAR is up; Figure to 3.56 ).times During larger high than tide H conditions,s. this ratio is close to 1 (H sLIDAR is similar to Hs) while, during low tide conditions, HsLIDAR is up to 3.5 times larger than Hs.

Figure 5. (a) Time seriesseries ofof ((aa)) HHsLIDARsLIDAR measuredmeasured on on the the lower lower foresh foreshoreore using using the the Lidar Lidar (red (red dots) with the overlap of measured tide (blue line); (b) raw verticalvertical run-up observationsobservations (black dots) and signisignificantficant vertical run-up run-up (red (red dots); (cc)) normalized normalized wave wave spectra spectra measured measured on on the the lower lower foreshore, foreshore, and; d) (d )Iribarren Iribarren number number (blue (blue dots). dots).

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Figure 6. Timeseries of the ratio between offshore significant wave height (Hs) and significant wave Figure 6. Timeseries of the ratio between offshore significant wave height (Hs) and significant wave heightFigure measured6. Timeseries on ofthe the lower ratio foreshorebetween offshoreby the Lidarsignificant (HsLIDAR wave) is heightshown (H ins ) orangeand significant and the wavetidal height measured on the lower foreshore by the Lidar (H ) is shown in orange and the tidal elevationheight measured is in blue. on the lower foreshore by the Lidar (HsLIDARsLIDAR) is shown in orange and the tidal elevation is in blue. To evaluate the effect of tide on the role of the beach profile and wave characteristics on run-up, To evaluate the effect of tide on the role of the beach profile and wave characteristics on run-up, data Towere evaluate grouped the accordingeffect of tide to onthe the tide role level, of th followinge beach profile the approach and wave pr characteristicsoposed by [44]. on Groupsrun-up, data were grouped according to the tide level, following the approach proposed by [44]. Groups were weredata weredefined grouped as low-, according mid-, and to high-tide. the tide level,The boun followingdaries theof these approach groups pr wereoposed arbitrarily by [44]. definedGroups defined as low-, mid-, and high-tide. The boundaries of these groups were arbitrarily defined as 1/3 aswere 1/3 defined (low to as mid) low-, and mid-, 2/3 and (mid high-tide. to high) The of theboun tidaldaries range of these observed groups at wereNha arbitrarilyTrang beach. defined The (low to mid) and 2/3 (mid to high) of the observed at Nha Trang beach. The significant significantas 1/3 (low run-up to mid) elevation, and 2/3 (midRs was to high)compared of the to tidal various range parameters observed commonlyat Nha Trang related beach. to Thethe run-up elevation, Rs was compared to various parameters commonly related to the run-up [44,45]. run-upsignificant [44,45]. run-up Figure elevation, 7 show sR threes was scatter compared plots ofto thevarious significant parameters vertical commonly run-up (R s)related as a function to the Figure7 shows three scatter plots of the significant vertical run-up (R s) as a function of offshore wave 0.5 0.5 0.5 ofrun-up offshore [44,45]. wave Figure characteristics 0.57 shows three ((H sscatterL0.5o) ), tanplotsβ(HsLo) of the significant and 0.5tanβ vertical(HsLIDAR Lo)run-up, where (Rs) as tan a functionβ is the characteristics ((HsLo) ), tanβ(HsLo) and tanβ(HsLIDARLo) , where tanβ is the foreshore slope foreshoreof offshore slope wave measured characteristics by the Lidar.((HsL oThe)0.5), resultstanβ(HsLo) show0.5 that and the tan verticalβ(HsLIDAR run-upLo)0.5 ,at where Nha Trang tanβ beachis the measured by the Lidar. The results show that the vertical run-up at Nha Trang beach cannot be scaled cannotforeshore be slopescaled measured by offshore by wave the Lidar. conditions The results solely, show as very that low the determination vertical run-up coefficients at Nha Trang (r2 = beach 0.43) by offshore wave conditions solely, as very low determination coefficients (r2 = 0.43) were obtained for 0.5 2 0.5 werecannot obtained be scaled for by the offshore relationship wave conditions between0.5 R solely,s and (H ass Lveryo) (Figurelow determination 7a). The0.5 ratio coefficients tanβ(HsLo) (r = 0.43)was the relationship between Rs and (HsLo) (Figure7a). The ratio tan β(HsLo) was able to explain 78% ablewere to obtained explain for78% the of relationship the variability between observed Rs and in (HthesL overtical)0.5 (Figure run-up 7a). Theobservations; ratio tanβ (HsLo)nevertheless,0.5 was of the variability observed in the vertical run-up observations; nevertheless, when Hs was replaced by whenable to H explains was replaced 78% of by the the variability HsLIDAR, the observed ratio was in able the tovertical explain run-up 88% of observations; the variability nevertheless, (Figure 7). the HsLIDAR, the ratio was able to explain 88% of the variability (Figure7). when Hs was replaced by the HsLIDAR, the ratio was able to explain 88% of the variability (Figure 7).

0.5 0.5 Figure 7. Scatter plots of the significant vertical run-up (Rs) as a function of (HsLo) (a), tanβ(HsLo) Figure 7. Scatter plots of the0.5 significant vertical run-up (Rs) as a function of (HsLo)0.5 (a), tanβ(HsLo)0.5. (b), and tanβ(HsLIDARLo) (c). The red, black and green colors are related to the low, high and mid Figure 7. Scatter plots of0.5 the significant vertical run-up (Rs) as a function of (HsLo)0.5 (a), tanβ(HsLo)0.5. (tideb), and levels tan respectively.β(HsLIDARLo) (c). The red, black and green colors are related to the low, high and mid tide levels(b), and respectively. tanβ(HsLIDAR Lo)0.5 (c). The red, black and green colors are related to the low, high and mid tide Tablelevels 1respectively. shows that overall, run-up estimations are better during high-tide for this intermediate beach,Table which 1 shows is likely that to beoverall, due to run-up the reduced estimations influence are ofbetter the LTTduring on surf-zonehigh-tide wavefor this transformation. intermediate Asbeach, a result,Table which high1 shows is correlation likely that overall,to coe beffi cientrun-updue valuesto estimationsthe were reduced obtained are influencebe fortter all during the of tested thehigh-tide parameters.LTT foron thissurf-zone Similar intermediate resultswave beach, which is likely to be due to the reduced influence of the LTT on surf-zone wave weretransformation. also observed As ata otherresult, intermediate high correlation beaches coef byficient [46,47 ].values Table 1were also indicatesobtained thatfor allHsLIDAR the testedhas a particularparameters.transformation. importance Similar As resultsa forresult, run-up were high also predictions correlation observed during atcoef otherficient low-tide intermediate values conditions, were beaches obtained when by o ff[46] shorefor and all wave [47].the height testedTable measurements1parameters. also indicates Similar are that significantly results HsLIDAR were has di alsoffaerent particular observed from the importanceat waveother heightsintermediate for measuredrun-up beaches predictions at the by base [46] during ofand the [47]. foreshorelow-tide Table (Tableconditions,1 also1 ).indicates when that offshore HsLIDAR wave has aheight particular measurements importance are for signific run-upantly predictions different duringfrom the low-tide wave heightsconditions, measured when atoffshore the base wave of the height foreshore measurements (Table 1). are significantly different from the wave heights measured at the base of the foreshore (Table 1).

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 18 J. Mar. Sci. Eng. 2020, 8, 302 10 of 18 Table 1. Statistical results of the linear regression between Rs and three different dimensional versions of an Iribarren-based relationship. Table 1. Statistical results of the linear regression between Rs and three different dimensional versions of an Iribarren-based relationship.High-tide Mid-tide Low-tide Parameter r2 RMSE (m) r2 RMSE (m) r2 RMSE (m) High-Tide Mid-Tide Low-Tide Parameter(HsLo)0.5 0.68 1.01 0.35 1.3 0.3 1.5 r2 RMSE (m) r2 RMSE (m) r2 RMSE (m) 0.5 tanβ(HsL0.5o) 0.85 0.2 0.64 0.19 0.65 0.13 (HsLo) 0.68 1.01 0.35 1.3 0.3 1.5 0.50.5 tantanβ(Hβ(HsLIDARsLoL) o) 0.880.85 0.20.2 0.770.64 0.160.19 0.650.83 0.130.07 0.5 tanβ(HsLIDARLo) 0.88 0.2 0.77 0.16 0.83 0.07 3.3. Daily Morphological Evolution 3.3. DailyThe Morphologicaldaily morphological Evolution evolution of the study site was assessed at three different locations (LidarThe profile daily and morphological transects to evolutionthe north ofand the sout studyh of sitethe wasLidar assessed profile—see at three Figure diff erent2) through locations low (Lidartide beach profile surveys and transects performed to the usin northg RTK-GPS and south (Figure of the Lidar 8). Initial profile—see surveys Figure (measured2) through on the low 27/11) tide beachshowed surveys that the performed Lidar profile using was RTK-GPS similar (Figure to the8). south Initial profile, surveys with (measured both showing on the 27 a /berm11) showed and a thatconcave the Lidar beach profile face shape. was similar On the to thenorth south profile, profile, the with berm both was showing absent, a the berm top and of athe concave profile beach was facetruncated shape. at Onthe theseawall north and profile, the beach the berm face was was characterized absent, the top by ofa steep the profile slope with was a truncated slightly convex at the seawallshape (Figure and the 8). beach It is faceimportant was characterized to note that bythe a LIDAR steep slope and withthe south a slightly profiles convex were shape located (Figure on the8). Itstraight is important section to of note Nha that Trang the bay, LIDAR while and the the north south profile profiles was were located located on the on thecurvilinear straight end section of the of Nhabay. TrangThis is bay, important while the since north the profile morphological was located resp ononse the observed curvilinear during end of the the experiment bay. This is at important the north sinceprofile the was morphological distinct from response the LIDAR observed and duringsouth profiles. the experiment While atat thethe northnorth profile profile, was the distinct lower fromforeshore the LIDAR was progressively and south profiles. eroded While and the at the top north of the profile, profile the slightly lower foreshoreaccreted, wasand progressivelyat the LIDAR erodedand south and profile, the top ofthe the initial profile berm slightly erosion accreted, was followed and at the by LIDAR the development and south profile, of a neap-berm. the initial berm The erosionerosion wasof the followed berm occurred by the development on the 28/11, of when a neap-berm. spring tides The together erosion of with the bermenergetic occurred waves on were the 28present./11, when Part spring of the eroded tides together sand was with deposited energetic landward waves were over present.the berm Part cres oft due the to eroded the overtopping sand was depositedprocesses, landwardwith the remainder over the berm being crest transported due to the on overtoppingto the LTT (Figure processes, 8). The with berm the remainderformation beingphase transportedstarted on 29/11 onto theand LTT ceased (Figure on8 ).03/12, The bermwhen formation no further phase growth started was on observed. 29 /11 and This ceased phase on 03 was/12, whencharacterized no further by growth a decrease was observed.in the tidal This range phase an wasd lowering characterized offshore by awave decrease heights. in the As tidal a result, range andreduced lowering wave o ffrun-upshore wave was heights.no longer As aable result, to reducedreach the wave pre-existing run-up was berm no longercrest leading able to reachto an theaccumulation pre-existing of berm sediment crest leading lower toon anthe accumulation foreshore (Figure of sediment 8). While lower these on the cross-shore foreshore (Figuresediment8). Whileexchanges these were cross-shore observed sediment at the LIDAR exchanges and weresouth observed profile, in at the LIDARnorth a andpersistent south profile,erosion inof thethe northlowera foreshore persistent did erosion not result of the lowerin a proportional foreshore did accumulation not result in aon proportional the top of accumulationthe profile. Since on theno topevident of the along-shore profile. Since gradient no evident in sediment along-shore transport gradient and morphological in sediment transport changes were and morphologicalnoticed during changesthe present were experiment, noticed during it is thesugg presentested that experiment, the eroded it issediment suggested was that likely the erodedtransported sediment offshore, was likelybeyond transported the limit of o fftheshore, surveys. beyond the limit of the surveys.

FigureFigure 8.8.Daily Daily low low tide tide cross-shore cross-shore beach beach profiles profiles measured measured at (a at) the (a) North, the North, (b) LIDAR (b) LIDAR and (c )and South (c) transects,South transects, the locations the locations of which of arewhich shown are shown in Figure in2 Figure. 2.

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J. Mar. Sci. Eng. 2020, 8, 302 11 of 18

3.4. Intra-Tidal MorphologicalMorphological Evolution Evolution The morphologicalmorphological evolution evolution of theof swash-zone the swash- waszone assessed was usingassessed high-frequency using high-frequency observations obtainedobservations using obtained the Lidar. using Time-averaged the Lidar. Time-avera (over 15-minged segments) (over 15-min beach segments) profiles were beach used profiles to compute were cumulativeused to compute vertical cumulative changes vertic (Figureal changes9). Inspection (Figure of 9). Figure Inspection9 shows of Figure the significant 9 shows the intra-tidal significant morphologicalintra-tidal morphological changes that changes occurred that within occurred the swash-zone: within the berm swash-zone: erosion followed berm erosion by thedevelopment followed by ofthe a development neap-berm by of the a neap-berm end of the experiment.by the end of the experiment.

Figure 9.9. BeachBeach response response measured measured using using the the Lidar, Lidar, with with the top the panel top showingpanel showing the cumulative the cumulative vertical changesvertical changes overlain overlain by the 5%, by 50%the 5%, and 50% 90% and of swash90% of inundation swash inundation lines (percentage lines (percentage that specific that specific swash locationswash location is covered is covered by water by during water a during 10 min segments);a 10 min segments); red colors red indicate colors accretion indicate while accretion blue colorswhile indicateblue colors erosion. indicate The bottomerosion. panel The presents bottom thepanel cumulative presents vertical the cumulative bed elevation vertical changes bed observed elevation on the 5% and 50% inundation lines (∆z5% and ∆z50% respectively), together with the daily-mean values. changes observed on the 5% and 50% inundation lines (Δz5% and Δz50% respectively), together with the The tidal elevation is indicated in grey. daily-mean values. The tidal elevation is indicated in grey. Intra-tidal cycles of accretion and erosion were captured by the Lidar between 27/11 and 01/12, Intra-tidal cycles of accretion and erosion were captured by the Lidar between 27/11 and 01/12, with the largest amplitude of changes around the mid-swash-zone location (∆z50% in Figure9). with the largest amplitude of changes around the mid-swash-zone location (Δz50% in Figure 9). During During these cycles, an accretion phase was observed from the low to mid tide stage of the rising tide, these cycles, an accretion phase was observed from the low to mid tide stage of the rising tide, followed by an erosive period from the mid to high-tide and falling tide stages (Figure9). The accretion followed by an erosive period from the mid to high-tide and falling tide stages (Figure 9). The phase led the formation of sand deposits that reach up to 0.5 m and were completely remobilized on the accretion phase led the formation of sand deposits that reach up to 0.5 m and were completely subsequent falling tide, resulting in minor (close to zero) net of changes over the tidal cycle. As a result, remobilized on the subsequent falling tide, resulting in minor (close to zero) net of changes over the the daily-mean cumulative vertical changes observed in the mid-swash zone are close to zero. A distinct tidal cycle. As a result, the daily-mean cumulative vertical changes observed in the mid-swash zone pattern was observed in the upper swash-zone (5% of inundation region), where negative net change are close to zero. A distinct pattern was observed in the upper swash-zone (5% of inundation was observed until 29/11; however, positive changes were observed after this. These results indicate region), where negative net change was observed until 29/11; however, positive changes were that the net vertical changes observed in the upper swash-zone were directly related to modifications in observed after this. These results indicate that the net vertical changes observed in the upper the offshore wave conditions, which were characterized by relatively large, long period waves during swash-zone were directly related to modifications in the offshore wave conditions, which were the early part of the experiment followed by smaller, shorter period waves (see Figure4d). In the mid characterized by relatively large, long period waves during the early part of the experiment followed swash, this relationship is not as clear. by smaller, shorter period waves (see Figure 4d). In the mid swash, this relationship is not as clear. 3.5. Morphological Evolution and Hydrodynamic Forcing 3.5. Morphological Evolution and Hydrodynamic Forcing The swash zone morphological evolution depends on multiple factors that act simultaneously, thus,The including swash slope,zone morphological incident wave evolution height or depends run-up characteristics. on multiple factors A multiple that act linear simultaneously, regression (Equationthus, including (1)) was slope, used incident to investigate wave height the role or of run-up four forcing characteristics. parameters A onmultiple the cumulative linear regression vertical (Equation (1)) was used to investigate the role of four forcing parameters on the cumulative vertical changes observed in the mid swash-zone (50% inundation, ∆z50%). changes observed in the mid swash-zone (50% inundation, Δz50%).

J. Mar.J. Mar. Sci. Sci. Eng. Eng.2020 2020, 8,, 302 8, x FOR PEER REVIEW 12 12of 18 of 18

Xn 𝑌=𝐶 + 𝐶𝑍 +𝜀 (1) Y = C0 + CkZk + ε (1) 1

where Y is the prediction, Z the predictor variable, n is the number of hourly observations, C0 and Ck where Y is the prediction, Z the predictor variable, n is the number of hourly observations, C and C are the non-standardized regression coefficients and ε is the residual term. The relative contribution0 k are the non-standardized regression coefficients and is the residual term. The relative contribution (as a percentage) of each forcing parameter was estiεmated from the ratio of individual variance to (as athe percentage) total following of each Equation forcing (2): parameter was estimated from the ratio of individual variance to the total following Equation (2): s S𝑆 𝑃P(Z𝑍) ==100 100 k ( (𝑘k = 1, = 2, 1,2,3, 3, 4) 4) (2) (2) S𝑆y where S is the variance of C Z and S is defined as the sum of variances of all causative components to wherek Sk is the variance ofk CkkZk andy Sy is defined as the sum of variances of all causative components ensureto ensure a total a of total 100%. of The100%. causative The causative variables variables usedin used the multiplein the multiple linear regressionlinear regression include include incident waveincident height wave at the baseheight of at the the foreshore base of (H thesLIDAR foreshore), the swash (HsLIDAR excursions), the swash variability, excursions represented variability, by the standardrepresented deviation by the of standard the vertical deviation run-up of ( σtheRz ),vertical and two run-up parameters (σRz), and that two relate parameters the foreshore that relate slope conditionthe foreshore to the concomitantslope condition vertical to the run-up concomitant spectral vertical bands (incident run-up spectral and infragravity, bands (incident expressed and by 0.5 0.5 0.5 0.5 (taninfragravity,β.Rincident) expressedand (tan βby.R (tanincidentβ.R)incidentrespectively).) and (tanβ.R Theincident predictions) respectively). based The on thepredictions computed based multiple on linearthe regressioncomputed wasmultiple able linear to explain regression 78% ofwas the able variability to explain in 78% the ∆ofz50% the observationsvariability in (Figurethe Δz50% 10 ), 0.5 includingobservations the intra-tidal (Figure cycles10), including of accretion the/ erosion.intra-tidal Results cycles show of accretion/erosion. that (tanβRinfra) Resultswas the show parameter that (tanβRinfra)0.5 was the parameter with the largest contribution0.5 (53%) followed by (tanβRincid)0.5 (38%), with the largest contribution (53%) followed by (tanβRincid) (38%), with a minor contribution from with a minor contribution from HsLIDAR and σRz. HsLIDAR and σRz.

Figure 10. (a) Predictions of the multiple linear regression model (black line) compared with the Figure 10. (a) Predictions of the multiple linear regression model (black line) compared with the cumulative vertical changes in the mid swash zone (∆z50%, red line) observed during the field experiment. cumulative vertical changes in the mid swash zone (Δz50%, red line) observed during the field (b) Scatter diagram showing the correlation between the multiple linear regression model and ∆z50% experiment. (b) Scatter diagram showing the correlation between the multiple linear regression observations. The coefficient of correlation (r2) obtained for this linear regression was 0.78. (c) Individual model and Δz50% observations. The coefficient of correlation (r2) obtained for this linear regression contributions of the forcing parameters used in the multiple linear regression expressed as a percentage. was 0.78. (c) Individual contributions of the forcing parameters used in the multiple linear regression 4. Discussionexpressed as a percentage.

4.1. Tidal Modulation of Waves and Run-Up Heights Field measurements performed at Nha Trang beach show that under relatively constant offshore wave forcing (e.g., over a full tidal cycle), wave height at the base of the foreshore and swash motions J. Mar. Sci. Eng. 2020, 8, 302 13 of 18 were distinctly different between low and high tide as the swash zone oscillated between reflective (high Iribarren number) and dissipative (low Iribarren number; Figures5 and6) conditions. As a consequence of this tidal influence on the surf and swash hydrodynamics, the use of offshore wave characteristics solely is insufficient to predict Rs ([42,48,49]—see Figure7). Present observations indicate that the lack of relationship between offshore wave characteristics and run-up is particularly evident during low tide conditions, when the LTT acts as a low-pass-filter and potentially enhances energy transfer to the infragravity band [45]. Some previous research has addressed this issue, suggesting that wave characteristics measured nearshore enable improved predictions of run-up [42]. The results presented here confirm this as using HSLIDAR in an Irribarren-type parameter resulted in better run-up estimation at Nha Trang than using offshore Hs. A similar tidal modulation has been observed on barred beaches (another type of intermediate beach) by [42,48]; however, in these cases, the spectral signature of the vertical run-up during low tide was composed of a mixture of both incident and infragravity components rather than dominated only by the infragravity band as observed at Nha Trang (Figure5). The beach slope is also seen to be a key factor that affects vertical run-up. This result is in line with the findings from [42,50] who showed that including beach slope led to significant improvements in predictions of vertical run-up on a variety of intermediate beaches. At present, there is no consistent definition of the appropriate beach slope for use in run-up predictors; however, the laboratory experiments of [50] demonstrated that surf-zone slope led to better predictions than the active foreshore slope. The main reason for this result was thought to be that surf-zone slope is more physically related to the breaking conditions (position, height and type of breaking), which directly affects the swash dynamics. Recently, the authors of [47] demonstrated that the characteristics of the nearshore , not usually accounted for in run-up predictors that use the offshore wave conditions and foreshore slope, is an important source of errors in run-up predictions, especially on barred beaches. Although the full surf-zone slope was not measured at Nha Trang, considering that this beach is a simple two-slope beach and that during the low tide conditions the Lidar was able to measure the LTT toe, it is possible that the foreshore slope observations were able to indirectly capture the tidally induced changes in the surf-zone slope. In addition to the beach slope, the results presented here show that including significant wave height at the base of the foreshore improves the vertical run-up prediction. This result is in agreement with other studies, where a clear relationship between wave run-up and bore height and celerity at collapse was observed [31,51]. Although this improvement was verified for all the tidal stages (Table1), it was more evident during low tide conditions when the most wave transformation takes place in the surf-zone leading to significant changes in the wave and run-up height. Considering the fact that the most extreme run-up excursions and potential coastal overtopping take place during high tide, our results suggest that offshore wave characteristics and foreshore slope can be used to predict extreme vertical run-up on intermediate beaches with an LTT.

4.2. Upper-Beach Erosion and Recovery

4.2.1. Daily Evolution Observations of morphological evolution in the swash-zone, including daily and intratidal measurements presented in Sections 3.3 and 3.4, showed a continuous and rapid adjustment of the beach to different tidal and wave conditions. Overall, the morphological response of the swash-zone during the experiment can be divided into two main phases: (1) berm erosion; (2) berm formation. In both cases, the morphological response was likely to be the result of a morphological adjustment to changes in water levels and an offshore wave height. Higher water levels and larger waves exposed the initial berm to overtopping and consequent erosion, while milder waves and neap tides caused a neap berm to form [52,53]. Daily low tide surveys were sufficient to describe this overall beach response, but intra-tidal Lidar observations captured more detail of the morphodynamic processes on a sandy J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 18 the initial berm to overtopping and consequent erosion, while milder waves and neap tides caused a neap berm to form [52,53]. Daily low tide surveys were sufficient to describe this overall beach response, but intra-tidal Lidar observations captured more detail of the morphodynamic processes J. Mar. Sci. Eng. 2020, 8, 302 14 of 18 on a sandy beach with an LTT. More specifically, the intra-tidal cycles of accretion and erosion observed in the mid swash-zone, during the individual tidal cycles between 27/11 and 01/12 (Figure 9).beach A similar with an morphological LTT. More specifically, response thehas intra-tidal been observed cycles on of accretionmixed coarse-grained and erosion observedbeaches with in the a sandymid swash-zone, LTT [17,18] duringand on thea pure individual gravel beach tidal [29,54] cycles betweenand associated 27/11 andwith01 the/12 cross-shore (Figure9). translation A similar ofmorphological the beach step. response Despite has some been similarity, observed onsuch mixed as the coarse-grained location in the beaches swash with where a sandy these LTT processes [17,18] occurand on (mid a pure swash), gravel beachor the [29effect,54] andof the associated tide on with lower the foreshore cross-shore wave translation height of[29], the beachimportant step. differencesDespite some related similarity, with suchenhanced as the locationinfiltration/exf in theiltration swash where processes these [17] processes and sediment occur (mid transport swash), mechanismsor the effect of make the tide a direct on lower comparison foreshore with wave previous height [29 studies], important difficult. diff Inerences addition related to this, with the enhanced mixed tideinfiltration component/exfiltration observed processes at Nha [ 17Trang] and was sediment not observed transport in mechanisms any of the previous make a direct studies comparison and may withplay an previous important studies role. di fficult. In addition to this, the mixed tide component observed at Nha Trang was not observed in any of the previous studies and may play an important role. 4.2.2. Intra-tidal profile evolution 4.2.2. Intra-Tidal Profile Evolution An accretion phase was observed between the falling tide and the peak of the first high tide. DuringAn this accretion phase, phase the run-up was observed was dominated between by the infragravity falling tide frequency and the peak motions of the and first the high swash tide. slopeDuring was this gradually phase, the decreasing run-up was (Figure dominated 11). Infragravity by infragravity swash frequency events motionsare characterized and the swash by a rapid slope wasuprush gradually phase decreasingand potentially (Figure greater 11). Infragravity ability to transport swash events sediments are characterized onto the foreshore. by a rapid Slower, uprush phaselonger-lasting and potentially backwash greater flows ability on a to gentler transport slope sediments are expected onto the to foreshore.promote deposition Slower, longer-lasting conditions (sedimentsbackwashflows have onmore a gentler time to slope settle are down, expected and to the promote low angle deposition reduces conditions the downrush (sediments flows). have In additionmore time to to this, settle and down, as andit was the observed low angle on reduces other the sandy downrush beaches flows). [55,56], In addition the lower to this, water and table as it wasposition observed during on otherthe lower sandy tidal beaches levels [55, 56enhances], the lower uprush water table position and during contributes the lower to tidalthe aggradationlevels enhances of the uprush foreshore. infiltration This and feedback contributes between to the hydrodynamics aggradation of and the foreshore.morphology This led feedback to the developmentbetween hydrodynamics of a sandy and deposit morphology in the ledmid-lower to the development swash-zoneof during a sandy this deposit period in theof time. mid-lower This accretionswash-zone phase during lasted this until period the first of time.high tide This peak, accretion and once phase the lastedtide begins until to the rise first again, high the tide erosion peak, phaseand once is initiated the tide (Figure begins to11). rise again, the erosion phase is initiated (Figure 11).

Figure 11. Cumulative vertical changes observed in the mid swash-zone (∆z50%) during the first four Figure 11. Cumulative vertical changes observed in the mid swash-zone (Δz50%) during the first four tidal cycles (a); percentage of infragravity on the vertical run-up observations (b); and slope changes (c). tidal cycles (a); percentage of infragravity on the vertical run-up observations (b); and slope changes (Anc). onshore migration of the surf and swash-zone gradually alters the hydrodynamic regime, and the run-up becomes gradually dominated by the incident band on the steepest sections of the beach. At this stage, plunging breakers and high turbulence rates are more likely to mobilize and suspend sediment into the around the break point [57]. The steeper swash-zone reduces J. Mar. Sci. Eng. 2020, 8, 302 15 of 18 the run-up asymmetry during this period of time, increasing the ability of the backwash to transport sediment offshore. As the tide rises, the swash-zone becomes steeper, reducing upslope transport and enhancing transport down the slope and erosion of the deposit. It is expected that at this time of the tide, the water table is higher in the foreshore, reducing uprush infiltration and enhancing downrush erosion [56]. This erosion phase stops at the beginning of the falling tide, when the average water level reaches its maximum on the steepest part of the beach. The falling tide is much faster than the rising phase, and few changes are observed in morphology. During gentle waves and neap tides, the swash zone slope becomes gentler (Figure 11c), favoring the conditions for deposition, and a new berm is formed. It is possible that at this stage, the morphology is approaching a new equilibrium with the dominant hydrodynamics and beach slope, resulting in limited morphological changes on the foreshore.

5. Conclusions A nine-day field experiment was conducted on Nha Trang Beach (Vietnam), a microtidal sandy beach with a low tide terrace (LTT), to study swash hydrodynamics and morphodynamics under variable wave forcing. The tide was found to play a crucial role in controlling the hydrodynamics of the surf and swash zones. Lidar observations demonstrated that significant wave height measured just seaward of the swash zone together with the foreshore active slope improves predictions of vertical run-up. Under energetic waves and spring tide conditions, the upper-beach was eroded (berm erosion). When wave energy and tidal amplitude reduced, the beach rapidly recovered, and a new berm was built on a lower part of the foreshore. The Lidar dataset has provided new insights on intra-tidal morphological changes in the mid swash-zone, with individual tidal cycles showing distinct phases of accretion and erosion. Using multiple linear regression analysis, it was possible to verify that the key factors underlying the mid swash cycles of accretion/erosion are the foreshore slope and infragravity swash motions.

Author Contributions: Conceptualization, R.A. and L.P.A. and C.B.; methodology, R.A., L.P.A., C.B., and P.G.d.S.; software, L.P.A.; validation, L.P.A.; formal analysis, L.P.A., R.A., C.B., E.B., P.G.d.S.; investigation, L.P.A., P.M., R.A., R.B., C.B., N.S., E.B., F.F., C.C., J.A., M.B., P.G., N.T.V., D.H.T., P.G.d.S.; data curation, L.P.A.; writing—original draft preparation, L.P.A.; writing—review and editing, L.P.A., P.M., R.A., R.B., C.B., N.S., E.B., F.F., C.C., J.A., M.B., P.G., N.T.V., D.H.T., P.G.d.S.; visualization, L.P.A., P.M., R.A., R.B., C.B., N.S., E.B., F.F., C.C., J.A., M.B., P.G., N.T.V., D.H.T., P.G.d.S.; supervision, R.A.; project administration, R.A. and N.T.V.; funding acquisition, R.A. and N.T.V. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Agence Nationale de la Recherché (ANR, France), grant number ANR-14-ASTR-0019 and the APC was funded by first author voucher. Acknowledgments: This work received financial support from Vietnamese (MOST2/216/QD/BKHCN-No2994) and French grant through the COASTVAR project (ANR-14-ASTR-0019). D.H.T PhD was funded by the ARTS-IRD program. The authors of this work would like to thank the support provided by all the participants present in this field experiment. The authors would like to thank the valuable contribution from the two reviewers that provided very useful suggestions to improve this manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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