Topo-bathymetric behaviour of a beach controlled by a groyne field and a dune-seawall backshore

The advances in morphodynamics numerical modelling and the free availability of such updated models have made XBeach a powerful tool to predict the hydrodynamic and morphologic processes on sandy coasts. This paper addresses the impact of the sea-structure-sediments interactions in the morphological evolution of a coastal stretch which undergoes erosion and overtopping despite having a combined groyne field-dune-seawall defence scheme. Preliminary tests, tailored to conclude on the model mode-version to be applied in the case study, evidence the importance of considering the NH mode. After calibrated and validated, the model was applied for a set of cases to compute and discuss the effect of the individual defence scheme structural elements and the hydrodynamic driving factors, namely the wave energy and obliquity and the tidal range, on the morphodynamics. The results revealed that the seawall aggravates the erosion of the beach, despite being essential in the protection against overtopping and coastline retreat, and that the present configuration of the groyne field does not provide enough protection at the downdrift part of the stretch. The knowledge acquired can support the interpretation of the topo-bathymetric behaviour in similar coastal defence schemes existent worldwide.


Framework and objetives
Coastal erosion and flooding are natural coastal hazards that have been intensified by human activity and by the growing impacts of climate change on the coastal zone. They can lead to assets destruction, disruption of economic activities and, ultimately, to the loss of lives. The efforts developed in the prediction of the future evolution lead to conclude on the need for adaptation. If no adaptation measures are considered in the presence of a high emission scenario, up to 630 million people will live below the projected annual flood levels in 2100, about 2.5 times more than in 2019 (Kulp and Strauss 2019). The adaptation measures depend on the local coastal conditions and on the management strategy for the full physiographic coastal unit. Coastal defence, through either structural or non-structural solutions, traditional or new, or the combination of both, is one possible adaptation measure.
Like in many coastal stretches worldwide, mainly due to shortage of sediment supply and anthropic pressure, some of the Portuguese urbanized maritime fronts that are now seriously threatened by erosion have already been intervened with shore-normal coastline stabilization structures (groynes) and alongshore defences (seawalls), sometimes complemented with nourishment. The groynes were built at the downdrift extreme of the threatened stretches to enlarge the sandy beaches width at the groyne updrift side and, thus, protect the urbanized maritime front; the seawalls were built when the beach width was already not enough to avoid wave overtopping and flooding under extreme conditions.
With the continuous direct and indirect anthropic actions, such as the sea level rise and the increase of maritime storms frequency and severity, some of the existent defence schemes, built in the second half of the last century, when the port industry started to have a great boost, either reduced their efficacy or, in certain cases, boosted the beach vulnerability, exposing the communities to increased hazard. Since these hazards tend to aggravate for the Portuguese coast (Andrade et al. 2007), a better understanding of the wave-structure-sediment interactions (at the light of the updated scientific knowledge) and their impact in the surrounding beaches, at a wide range of time scales, is key to uphold coastal protection in the future (either through the redesign and/or elimination of the existent structures or the implementation of new ones) and, thus, to contribute to effective management plans that include adaptation measures to minimize the risks associated with coastal erosion and to benefit the surrounding beach stability.
Different methods to upgrade the knowledge on these wave-structure-sediment systems have been applied, either individually or in an integrated manner, in the last decade: theoretical process-based numerical modelling, laboratory experimentation and analytical techniques for interpretation of field and laboratory observations (Pattiaratchi et al. 2009;Razak et al. 2013;Kristensen et al. 2016). The numerical process-based model XBeach (Roelvink et al. 2009) accounts for the major hydro-morphodynamic driving processes in the surf zone and allows the sensitivity assessment of influent parameters (Trouw et al. 2012;Nederhoff 2014). Recent XBeach model applications for the present study site, located in the highly energetic Atlantic central west coast of Portugal (Oliveira et al. 2018a(Oliveira et al. , b, 2020, brought new and promising insight on the modelling capacities of the processes involved in the local sea-structure-sediments interactions. The ultimate objective of the present study is to understand how the local morphodynamics is affected by these interactions and how much these effects vary with the hydrodynamic driving factors, namely the wave energy and obliquity and the tidal range, building upon the consolidated knowledge on modelling approaches of the nearshore dynamics (Van der Hoeoven 2010; Van der Salm 2013; Van Rijn 2013).
The frequent practical limitation when applying twodimensional-horizontal (2DH) numerical modelling in the highly dynamic breaking zone, particularly models that allow several degrees of freedom (parameters estimated from field data), as is the case of XBeach, is the calibration and validation process, due to the challenge of monitoring within the zone. In the present study, the XBeach model was calibrated through a 1D (profile) modelling exercise and validated through a 2DH modelling test.
The two XBeach modes, surfbeat (SB) and non-hydrostatic (NH), are previously applied and compared, as proofof-concept, for the case of beach response in the presence of a single groyne under local average hydrodynamic forcing conditions and simplified representative geomorphologic conditions. The morphological features encountered are analysed and related to the processes taken into account in the respective mode to better understand the implications of the coastal defence scheme of Cova-Gala and their individual elements on the submerged bottom evolution.

Site description
Cova-Gala is a coastal stretch located south of the Mondego river mouth, Figueira da Foz (40°8′45" N, 8°52′42" W), in the Atlantic west coast of Portugal, with a N5° orientation coastline (Fig. 1). It is characterized by a highly energetic wave climate with large interannual and seasonal variations. The average/median statistic values of the wave regime parameters Hs (wave significant height), Tp (peak period) and Dirm (mean direction) are respectively 2.15/1.78 m, 11.6/11.4 s, and 299.5/301.2°N, being 50% of the respective parameters within the ranges of occurrence frequency 1. 31-2.64 m, 9.5-13.4 s and 289.4-312.9°N, and 40% of the Hs occurrence greater than 2 m. The reference average potential sediment drift is 1 million m 3 /year directed southwards (Oliveira 2016;Oliveira et al. 2016Oliveira et al. , 2018b. The tide regime is semi-diurnal and meso-tidal with average and maximum amplitude of about 2.2 and 3.6 m, respectively. To protect the urbanized maritime front of Cova-Gala against the erosion and flooding verified after the construction of the Mondego river mouth jetties (in the last century'60 s), a combined groyne field-dune-seawall defence scheme was built in the following decade. In 2008-2010 the river mouth's north jetty was extended 400 m and, consequently, in contrast to the sediment accumulation observed at the updrift side of the river mouth's north jetty, the southern beaches restarted to face serious erosion problems, particularly troublesome in Cova-Gala. The seawalls are located in the backshore of sandy beach cells (considering a cell as the coastal area between two consecutive groynes). Despite having a narrow berm during the summer season, when Cova-Gala has an intense recreational and bathing occupation, the cell of the 2nd seawall (counted from north to south), in Fig. 1, becomes totally submerged under storm conditions, which occur mostly between December-March (Oliveira 2016). In the recent years the beach protection has been complemented with i) regular nearshore nourishment operations performed between the 1st and 3rd groynes (also counted from north to south) and the 4-10 m contour depth (relatively to the mean sea level-MSL), using sediments dredged from the river mouth, and, in 2019, in the beach south of the 5th groyne, the area most affected by erosion, with ii) a geotextile tube revetment at the dune base, along with dune nourishment, 120 × 10 3 m 3 of sand (Oliveira et al. 2022) (Fig. 1).

XBeach model mode
Since the original development of the model, several improvements have been implemented in new releases, which resulted in the three different modes presently available. The Stationary mode solves the wave-averaged equations but neglects infragravity waves. The Surfbeat mode (SB) solves the short-wave variations on the wave group scale and the associated long waves, currents, and morphological changes are solved separately. This saves considerable computational time, at the expense of not simulating the short-wave phase. It is the most used mode when the focus is on the swash zone processes and has been extensively validated for the morphological evolution modelling of dissipative beaches, where the short waves are mostly dissipated upon reaching the shoreline. The wave-resolving Non-hydrostatic mode (NH) is more complete, solving all processes, including short and long wave motions, with a greater computational demand. It combines the non-linear shallow water equations with a pressure correction term, modelling the propagation and decay of individual waves. As a result, it accounts for wave diffraction and reflection and undertow by turning on the newly implemented reduced two-layer mode (nonhq3d). This option improves the accuracy in modelling the frequency dispersion of the NH mode due to the additional layer in comparison to the depth-averaged formulation.

Assumptions in the case study
Three assumptions were made: i) the wave diffraction and reflection are important due to the interaction of the waves with the groynes and the seawalls of the defence scheme; ii) the wave induced dynamics within the cells of the groyne field requires a 2D modelling approach; and iii) due to the local high energy wave regime, the undertow current component plays an important role. Thus, the model modes were previously tested to access the need of applying the mode with the greatest computational demand for the case study.

Model mode tests
Prior to the application of the model to the case study, it was evaluated the relative importance of the processes of diffraction, reflection and undertow currents in the surroundings of a single groyne, for the local average hydrodynamic forcing conditions and simplified representative geomorphologic conditions. The SB and NH modes of the 1.23.5526 XBeachX version were applied, for the exact same conditions, a 48-h erosive event, forced by a wave with offshore average Hs and Tp parameters, Hs = 2.15 m and Tp = 11.5 s respectively, and a theoretical obliquity of -45° (N230°), to maximize the diffraction and reflection by the groyne, as well as the longshore sediment transport. The MSL is 2.00 m above the vertical chart datum reference level (CD) and the morphological acceleration factor for the bed level updating (morfac) was set equal to 6.
The initial beach profile, considered uniform alongshore, was simplified from topo-bathymetric monitoring of Cova-Gala (Oliveira 2016). It is formed by three slopes (Fig. 2): i) 0.013 in the submerged profile, between -12 and 0 m CD; ii) 0.04 in the beach face, between 0 and 4 m CD; and iii) 0.29 for the dune, between 4 and 14 m CD. The median and 90th percentile diameter of the sediment particles size were considered d 50 = 0.30 mm and d 90 = 0.50 mm (Oliveira 2016).
A 2D absorbing-generating boundary was imposed at the offshore boundary. Neumann type wave boundaries were used for the lateral boundaries (the longshore gradient is set to zero). In the SB mode simulation, the new method implemented in XBeachX SB to derive the directional wave group energy propagation, for improving wave groupiness coherence (Roelvink et al. 2018), was used considering a bin size of 10° (single_dir). The wave direction was solved at regular intervals using the stationary solver, and then the wave energy was propagated along the mean wave direction. In the NH mode simulation, the new reduced two-layer model (nonhq3d) implemented in XBeachX NH was used, to improve the dispersive behaviour of the non-hydrostatic model by using an additional layer in comparison to the depth-averaged formulation. The remaining advanced model parameters were kept at the values recommended by the developers.
A 2D domain (x,y) of 1000 × 800 m 2 was discretized using a grid resolution dx = dy = 5 m. A 260 m long and 20 m wide groyne was set at the centre of the domain. The groyne crest level is uniform and equal to 5 m above CD and the toe of the head was set at 2 m below CD. The domain was limited by a sandy dune at the landwards boundary.

Model calibration and validation
The XBeach model contains approximately 250 parameters, several of which are relevant advanced calibration coefficients. The most influent, as proposed by the developers, are the parametrized wave asymmetry sediment component (facua) and the bed friction formulation (bedfriction) for the SB mode, and the maximum wave stepness criterium (maxbrsteep) for the NH mode (Oliveira 2022).
In the present study the XBeach model was calibrated through a 1D (profile) modelling exercise and validated through a 2DH modelling test against measured morphological data (Oliveira 2022). The best morphological performance of the NH mode was obtained with the parameters maxbrsteep = 0.4, bedfriction = manning, bedfriccoef = 0.02, facsl = 1.4, bdslpeffdir = Talmon, dilatancy = 1, gwflow = 1, gw0 = 2.22 and the default values for the remaining calibration parameters.

Beach morphodynamics tests
The morphodynamics of the defence scheme is controlled by the waves-structures-sand interactions. To best detect the effects of these interactions, the method is applied to a domain that includes only the 2nd and 3rd cells, counting from north to south, with dune and seawall, respectively, at the backshore, during short-term hydrodynamic events (Fig. 3). To avoid numerical effects from the lateral boundaries on the two central cells of interest, it was considered the dune profile for the rest of the domain, which was only used as a buffer area for spurious effects. A set of cases (Table 1), with varying hydrodynamic conditions and suppression of structures, were computed and compared to conclude on the effects of the defence scheme elements and the parameters wave height, wave obliquity and tidal range in the beach dynamics. All the cases have the same duration, 96-h. The reference case, designated as 14, is an observed storm, occurred in February/2014, known as Hercules storm (maximum Hs = 9.42 m; and wave obliquity = 10°, equivalent to direction N285°) (Fig. 4). The cases 1 to 4, 14 and 18 are considered for the testing of the effect of the driving hydrodynamic parameters in the morphodynamics. The cases 14 to 16 are considered for the testing of the effect of the defence scheme elements in the morphodynamics, respectively: existent scheme (Fig. 3); scheme without the seawall (dune instead); absence of the groynes and the seawall (dune along the full backshore).

Model mode
Both XBeachX model modes, the SB (Fig. 5) and the NH (Fig. 6), predicted the two combined impacts: i) the blocking effect on the longshore sediment transport, resulting in beach accretion in the updrift side of the groyne and erosion in the downdrift side; and ii) the cross-shore response of the beach to the erosive wave, resulting in retreat of the beach face and formation of a submerged bar. However, the SB and NH modes predicted the expected main morphological features with the following differences: • More intense erosion of the beach face, associated to the retreat of the coastline (the 2 m CD bathymetric contour), in the lee side of the groyne in the SB mode; • The formation of a smooth submerged shoal at the updrift side of the groyne, with extension until the head of the groyne, in the SB mode, distinct from the smaller and disrupted accumulation generated in the NH mode; • A submerged sandbar aligned with the incident wave direction at the downdrift side of the groyne, with development from the head towards the shore, clearly better defined, that is, narrower, higher and longer, in the NH mode; • An erosion spot at the updrift side of the groyne head, highly enhanced in the NH mode.
In synthesis, the XBeachX NH mode predicts higher bottom gradients in the surroundings of the groyne than the SB mode. The NH mode bottom features, specifically the sand accumulation with cross-shore disruptions at the updrift side of the groyne suggest the impact of groyne reflection under direct wave action; the features downdrift suggest the bottom response to the diffraction phenomenon induced by the groyne when exposed to such high energy waves with a 45° angle of attack. The results of these preliminary tests, tailored to conclude on the model mode to be applied in the case study, evidence the importance of considering the NH mode.

Effect of the defence scheme structural elements in the morphodynamics during the storm
The comparison of the morphological evolution, after the 96-h storm, between the cases existent defence scheme (14), without seawall (15) and absence of structures (16), defined in Table 1, shows: • The backshore typology, seawall or dune, forces a distinct behaviour of the sandy bottom within the cell. The seawall avoids the retreat at the top of the beach, but causes higher erosion within the cell, specifically, a larger lowering of the profile, which extends further beyond the groynes head. The higher erosion magnitude verified at the downdrift groyne is due to the obliquity of the waves, about 10° at the offshore boundary (Fig. 7 shows the map of the final morphology in case 14 subtracted from the final morphology in case 15). • The existent defence scheme causes an alongshore gradient of protection when comparing with the absence of structures (groynes and seawall): it benefits the sand accumulation in the northern stretch, including the updrift side of dune cell, but increases the erosion in the seawall cell and in the southern stretch (Fig. 8 shows the map of the final morphology in case 14 subtracted from the final morphology in case 16). • The groyne field alone, with dune in the place of the seawall, causes the alongshore gradient of protection ( Fig. 9 shows the map of the final morphology in case 15 subtracted from the final morphology in case 16) but the seawall aggravates the erosion inside its the cell (comparing Fig. 8 with Fig. 9).
Effect of the wave obliquity in the morphology of the structural defence scheme surrounding area during storms The increase of the storm waves obliquity, relative to the cross-shore direction, confirms and highlights the effect of the defence scheme in the alongshore variability of the response of the beach (Fig. 10 shows the map of the final morphology in case 18 subtracted from the final morphology in case 14). The northern stretch and the two cells benefit from accretion. The groynes have increased significantly their protective effect within 50 m at their downdrift side. At the southern part of the domain, at about 150 m south of the southern groyne, the erosion of the beach increased significantly with the increase of the storm waves obliquity. Within the cells, the updrift side of the groynes suffers more erosion due to the direct wave attack (Fig. 11).

Effect of the wave energy in the morphology of the structural defence scheme surrounding area
The cases 2, 4 and 18 were compared to evaluate the impact of the wave energy in the morphology of the surrounding area of the defence scheme. The 96-h event with Hs equal to 0.5 m showed an irrelevant impact in the morphology (not shown). Under the action of the local average wave, case 4, in Fig. 12, the beach develops an irregular alongshgore submerged bar interrupted by the groynes head, which frontal toe are focus of erosion. On the overall, the submerged bar loses robustness from north to south and the erosion at the top of the beach increases also from north to south. Both morphological features reveal the fragility of the beach system in the south part of the defence scheme. When comparing case 4 with case 18, in Fig. 11, which concerns storm waves with the same obliquity of cases 2 and 4, it can be seen that the increase of the wave height causes an increase of the magnitude of both morphological features. The larger erosion volumes extracted from the top of the beach feed the expansion of the submerged bar and the impact of both features overlaps the impact of the local erosion at the groynes head verified for the average wave, case 4.

Effect of the sea level variation in the morphology of the structural defence scheme surrounding area
When comparing case 3 ( Fig. 13) with case 4 (Fig. 12), it can be seen that, under the action of the local average wave, the tidal range enlarges significantly the cross-shore extension of the active zone of the beach. It increases the erosion at the top of the beach, not only because the wave action reaches higher topographic level but also because the submerged bar is less effective in dissipating wave energy through breaking, because the bar is slightly less robust than in case 3, computed with constant MSL, and is located further seaward. An additional feature which is intensified with the tidal range is the growth of the local erosion at the toe of the groynes head, likely due to the highest mobilization of sediments at lower sea levels.

Discussion
The preliminary numerical applications revealed the importance of the processes of diffraction, reflection and undertow currents in the surroundings of a single groyne for the average wave and the representative morpho-sedimentologic conditions of the study zone, therefore, the need to use the NH mode of the XBeachX model in the simulations designed to analyse the topo-bathymetric response of the beach controlled by the existent defence scheme. The lateral reflection of the groyne under direct oblique wave action causes the formation of cross-shore oriented bottom megaripples and thus inhibits the development of the alongshore submerged bar at the updrift side, causing, consequently, higher erosion. At the downdrift side, the impacts of diffraction by the groyne are the growth, from the head of the groyne, of a submerged shore-oriented bar, and the formation of lateral bottom megaripples less prominent than at the updrift side. Despite the seawall being essential in the defence scheme to protect against observed wave overtopping, this structure, when attacked, is responsible for the additional seabed lowering verified when comparing with the morphological evolution of this cell considering dune at the backshore (instead of seawall).
If no restrictions of the sediment supply are imposed at the lateral boundaries, that is, if the incoming sediment fluxes are equal to the waves induced sediment transport potential, the existent defence scheme decreases the protection of the stretch towards south. This situation is caused by the groynes alone but the presence of the seawall aggravates this phenomenon.
The wave obliquity, in the high energy conditions of the study site, highlights the downdrift decrease in protection in the total stretch and within the cells of 250 m length (distance between groynes), independently of the different beach backshore typology, dune or seawall, despite the groynes only partially block the longshore transport.
Under high energy conditions (for waves with Hs higher than the local average wave) the sediment fluxes mitigate the scour at the toe of the groynes head, where the submerged alongshore bar is strengthened.
The phenomenon of erosion of the toe of the groynes head, verified for the case of the local average wave, is aggravated with the tidal range. That must be due to the higher sediment fluxes around the groynes head reached during the lowest sea levels.

Conclusions
The present work provides new knowledge on the implications of modelling morphological evolution in the presence of structures through the different XBeachX modeversions available. It addresses the morphological impact of sea-structure-sediments interactions in the presence of a combined groyne field-dune-seawall defence scheme. The knowledge acquired can support the interpretation of the topo-bathymetric behaviour in similar coastal defence schemes worldwide, since besides the investigation on the effect of the defence scheme structural elements in the morphodynamics, also comparative tests have been performed to investigate on the effects of the hydrodynamic driving factors, namely the wave energy and obliquity and the tidal range.
The morphological features caused by i) the waves reflection by the seawall and by the groyne updrift side, ii) the waves diffraction by the groyne, and iii) the undertow currents demonstrate the need to apply the NH mode of the numerical model.
Under the present topo-bathymetric conditions, the seawall plays an important role to protect the maritime front against overtopping. However, it aggravates the erosion of the beach. The groynes alone are not capable of protecting the beach uniformly alongshore, despite they only partially block the longshore transport. They cause a decrease of protection downdrift that is aggravated by the seawall and the increase in wave obliquity. Under waves more energetic than the local average wave the sediment fluxes mitigate the scour at the toe of the groynes head, which, in opposition, is raised by the tide amplitude.
The coastal stretch would benefit from sand nourishment of the foreshore-backshore zone in order to guaranty, at least, a minimum width to avoid direct wave action on the seawall and the consequent trigger of erosion.