Salt marshes fronting coastal structures, such as seawalls and dikes, may offer important ecosystem-based coastal defence by reducing the wave loading and run-up levels during storms. We question (i) how the long-term salt marsh development in the Dutch Wadden Sea relates to the tidal-flat foreshore bathymetry and (ii) how the wave run-up onto dikes, which enhances the risk of dike failure, depends on foreshore bathymetry, the presence/absence of marshes, marsh vegetation properties, tidal range and wind exposure. We analysed 15 years of vegetation and bathymetry maps along the entire Dutch Wadden Sea coast, in combination with detailed process-based measurements at five locations during 3 years, to understand where salt marshes naturally form and what features determine their contribution to coastal protection. The horizontal extent of marshes along the dikes remained relatively stable over the past decade. The presence of marshes was associated with higher elevations of adjacent tidal flats (above ~0.5 m NAP), while landward-directed marsh retreat was associated with surface erosion of the fronting tidal flats. Wave run-up during storms was lower at sites with wider marshes and higher foreshore elevations. This was attributed to the marsh attenuation effect, which led to a reduction in wave heights at the dike toe. As the tidal range varies across the Dutch Wadden Sea, areas to the East with generally higher water levels experienced higher wave run-up. Synthesis and applications. We found that (i) marshes, where present, effectively protected the dikes from wave loading and (ii) the sites where marshes typically do not develop spontaneously were the most vulnerable to high wave run-up. This catch-22 problem implies that increasing reliance on nature-based coastal defences along soft-bottom coasts may require human interventions to stimulate marsh formation at the locations where it is most needed. Alternatively, ‘hard engineering’ solutions may remain necessary where implementing nature-based solutions are either too costly, unachievable, or at the expense of other ecological values, such as causing the loss of mudflats that are important for migratory birds.

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Many coastlines around the world are protected by dikes with shallow foreshores (e.g. salt marshes and mudflats) that attenuate storm waves and are expected to reduce the likelihood and volume of waves overtopping the dikes behind them. However, most of the studies to date that assessed their effectiveness have excluded the influence of infragravity (IG) waves, which often dominate in shallow water. Here, we propose a modular and adaptable framework to estimate the probability of coastal dike failure by overtopping waves (Pf). The influence of IG waves on overtopping is included using an empirical approach, which is first validated against observations made during two recent storms (2015 and 2017). The framework is then applied to compare the Pf values of the dikes along the Dutch Wadden Sea coast with and without the influence of IG waves. Findings show that including IG waves results in 1.1 to 1.6 times higher Pf values, suggesting that safety is overestimated when they are neglected. This increase is attributed to the influence of the IG waves on the design wave period and, to a lesser extent, the wave height at the dike toe. The spatial variation in this effect, observed for the case considered, highlights its dependence on local conditions – with IG waves showing greater influence at locations with larger offshore waves, such as those behind tidal inlets, and shallower water depths. Finally, the change in Pf due to the IG waves varied significantly depending on the empirical wave overtopping model selected, emphasizing the importance of tools developed specifically for shallow foreshore environments.@en

The state-of-The-Art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics-where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep ≤ 0.1) due to the increased influence of wave-induced setup and infragravity waves-which act as long-period fluctuations in mean water level-generated by nonlinear wave transformation over the foreshore.

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Coastal communities across the globe are often protected by structures, such as seawalls, levees or dikes, which allow only a safe volume of water to pass over or “overtop” them due to wave action during storms. The area seaward of these structures is often characterised by shallow, gently sloping beds referred to as foreshores. As storm waves propagate over the shallow foreshores, two notable processes occur. The first, is the attenuation of high-frequency waves that are collectively referred to as wind-sea and swell (SS), with periods less than 20 seconds. The limited water depth over the foreshore forces the SS waves to shoal and ultimately break. This shoaling and breaking, in turn, results in the second important process: the growth of infragravity (IG) waves, with periods in the order of minutes. The methods used in current practice to estimate wave overtopping are able to accurately quantify the impact of SS waves. However, they tend to neglect the influence of IG waves, which are known to play a critical role in erosion and flooding along shallow coast lines. In light of this, this dissertation aimed to develop new methods to estimate the influence of IG waves on the safety of coastal defences with shallow foreshores against wave overtopping. This aim was ultimately achieved by using state-of-art numerical models, empirical methods and field measurements to develop a suite of tools, that together, provide a framework to accurately quantify the influence of IG waves on wave overtopping. As data on shallow foreshores was limited, a numerical model (XBeach Non-hydrostatic) was first used to generate a large dataset of wave measurements at the toe of the structure for varying offshore, foreshore and structure slope conditions. The analysis, detailed in Chapter 2, revealed that the influence of IG waves increased for higher, directionally narrow-banded (long-crested) offshore waves; shallower foreshore water depths; milder foreshore slopes; and reduced vegetated cover. The combined effect of the different environmental parameters on the IG waves was then captured in an empirical model, which formed the base of the framework to follow. For determining wave overtopping, the standard approach requires the use of a wave model (often a phase-averaged model like SWAN) to estimate wave parameters at the toe, which are then used as input to the well-known formulae of the EurOtop design manual. However, this approach largely neglects the impact of IG waves. In Chapter 3, this is rectified by augmenting the traditional approach with the empirical model developed in Chapter 2 to include the effects of the IG waves on the design parameters. Considering accuracy and computational demand, the modified approach proved superior when assessing wave overtopping at dikes with shallow foreshores. This approach formed the first sub-method to estimating wave overtopping in the overall framework. Nevertheless, it is often difficult to obtain accurate estimates of wave parameters at the toe of structures with shallow foreshores. Chapter 4 offers a solution to this problem by proposing a new set of overtopping formulae that instead rely on deep-water wave parameters as input. This is done by revisiting the old but proven approach of Yoshimi Goda, now with additional data and new trend analysis techniques. The newly-derived formulae proved accurate and can be considered an alternative to the current standard (Chapter 3). Particularly, for dikes and seawalls with very and extremely shallow foreshores, where IG waves tend to dominate. This approach formed the second sub-method to estimating wave overtopping in the overall framework. Finally, in order to estimate the impact of IG waves on safety, a probabilistic method (FORM) was introduced to the framework in Chapter 5. Using the first sub-method (Chapter 3), the probability of dike failure by wave overtopping with and without IG waves was determined for dikes along the shallow Dutch Wadden Sea coast. Including the IG waves resulted in 1.1 to 1.6 times higher failure probabilities for the Dutch Wadden Sea coast, suggesting that coastal safety may be overestimated when they are neglected. This was attributed to the influence of the IG waves on the wave period and, to a lesser extent, the wave height at the structure toe. Furthermore, the spatial variation in this effect observed for the Dutch Wadden Sea highlighted its dependence on local bathymetric and offshore forcing conditions—with IG waves having greater influence on the failure probability for cases with larger offshore waves and shallower water depths. The general conclusion of the dissertation is that IG waves can have an important impact on safety. Moreover, findings indicate that the safety of existing coastal defences with shallow foreshores may be overestimated, since IG waves are largely neglected in the current practice for their design and assessment. For the case considered here (the Dutch Wadden Sea), the increase in required crest level due to the IG waves was around 2 dm with a cost in the order of M€1/per km. For shallower coastlines exposed to more energetic wave conditions, the influence of the IG waves and the corresponding safety costs are likely to be greater. This dissertation provides practitioners with a suite of tools to quantify to influence of IG waves on the safety of coastal defences with shallow foreshores against wave overtopping. Thereby, reducing the uncertainty in the overall impact of shallow foreshores and allowing dike managers to make more informed decisions when considering hazard mitigation strategies. @en

Practitioners often employ diverse, though not always thoroughly validated, numerical models to directly or indirectly estimate wave overtopping (q) at sloping structures. These models, broadly classified as either phase-resolving or phase-averaged, each have strengths and limitations owing to the physical schematization of processes within them. Models which resolve the vertical flow structure or the full wave spectrum (i.e. sea-swell (SS) and infragravity (IG) waves) are considered more accurate, but more computationally demanding than those with approximations. Here, we assess the speed-accuracy trade-off of six well-known models for estimating q, under shallow foreshore conditions. The results demonstrate that: i) q is underestimated by an order of magnitude when IG waves are neglected; ii) using more computationally-demanding models does not guarantee improved accuracy; and iii) with empirical corrections to incorporate IG waves, phase-averaged models like SWAN can perform on par, if not better than, phase-resolving models but with far less computational effort.

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Despite the widely recognized role of infragravity (IG) waves in many often-hazardous nearshore processes, spectral wave models, which exclude IG-wave dynamics, are often used in the design and assessment of coastal dikes. Consequently, the safety of these structures in environments where IG waves dominate remains uncertain. Here, we combine physical and numerical modeling to: (1) assess the influence of various offshore, foreshore, and dike slope conditions on the dominance of IG waves over those at sea and swell (SS) frequencies; and (2) develop a predictive model for the relative magnitude of IG waves, defined as the ratio of the IG-to-SS-wave height at the dike toe. Findings show that higher, directionally narrow-banded incident waves; shallower water depths; milder foreshore slopes; reduced vegetated cover; and milder dike slopes promote IG-wave dominance. In addition, the empirical model derived, which captures the combined effect of the varied environmental parameters, allows practitioners to quickly estimate the significance of IG waves at the coast, and may also be combined with spectral wave models to extend their applicability to areas where IG waves contribute significantly.

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While the significance of infragravity waves (IG) in many—often-hazardous—nearshore processes is widely-recognized, many of the empirical and numerical models used in dike safety assessments do not (directly) consider their contribution. Here, we combine physical and numerical modelling to better understand the factors that contribute to the dominance of IG waves over higher-frequency waves at the dike toe. Findings show that IG-wave dominance increases as the ratio of local water depth to offshore significant wave height decreases. Therefore, it is critical that any tool used to assess the safety of dikes fronted by very and extremely shallow foreshores accurately describe IG-wave dynamics.

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Wave run-up and dune overwash are typically assessed using empirical models developed for a specific range of often-simplistic conditions. Field experiments are essential in extending these formulae; yet obtaining comprehensive field data under extreme conditions is often challenging. Here, we use XBeach Surfbeat (XB-SB)-a shortwave-averaged but wave-group resolving numerical model-to complement a field campaign, with two main objectives: i) to assess the contribution of infragravity (IG) waves to washover development in a partially-sheltered area, with a highly complex bathymetry; and ii) to evaluate the unconventional nested-modeling approach that was applied. The analysis shows that gravity waves rapidly decrease across the embayment while IG waves are enhanced. Despite its exclusion of gravity-band swash, XB-SB is able to accurately reproduce both the large-scale hydrodynamics-wave heights and mean water levels across the 30 × 10 km embayment; and the local morphodynamics-steep post-storm dune profile and washover deposit. These findings show that the contribution of IG waves to dune overwash along the bay is significant and highlight the need for any method or model to consider IG waves when applied to similar environments. As many phase-averaged numerical models that are typically used for large-scale coastal applications exclude IG waves, XB-SB may prove to be a suitable alternative.

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The accurate prediction of extreme wave run-up is important for effective coastal engineering design and coastal hazard management. While run-up processes on open sandy coasts have been reasonably well-studied, very few studies have focused on understanding and predicting wave run-up at coral reef-fronted coastlines. This paper applies the short-wave resolving, Nonhydrostatic (XB-NH) and short-wave averaged, Surfbeat (XB-SB) modes of the XBeach numerical model to validate run-up using data from two 1D (alongshore uniform) fringing-reef profiles without roughness elements, with two objectives: i) to provide insight into the physical processes governing run-up in such environments; and ii) to evaluate the performance of both modes in accurately predicting run-up over a wide range of conditions. XBeach was calibrated by optimizing the maximum wave steepness parameter (maxbrsteep) in XB-NH and the dissipation coefficient (alpha) in XB-SB) using the first dataset; and then applied to the second dataset for validation. XB-NH and XB-SB predictions of extreme wave run-up (Rmax and R2%) and its components, infragravity- and sea-swell band swash (SIG and SSS) and shoreline setup (<η>), were compared to observations. XB-NH more accurately simulated wave transformation but under-predicted shoreline setup due to its exclusion of parameterized wave-roller dynamics. XB-SB under-predicted sea-swell band swash but overestimated shoreline setup due to an over-prediction of wave heights on the reef flat. Run-up (swash) spectra were dominated by infragravity motions, allowing the short-wave (but not wave group) averaged model (XB-SB) to perform comparably well to its more complete, short-wave resolving (XB-NH) counterpart. Despite their respective limitations, both modes were able to accurately predict Rmax and R2%.@en

Assessing the accuracy of nearshore numerical models—such as SWAN—is important to ensure their effectiveness in representing physical processes and predicting flood hazards. In particular, for application to coastal wetlands, it is important that the model accurately represents wave attenuation by vegetation. In SWAN, vegetation might be implemented either implicitly, using an enhanced bottom friction; or explicitly represented as drag on an immersed body. While previous studies suggest that the implicit representation underestimates dissipation, field data has only recently been used to assess fully submerged vegetation. Therefore, the present study investigates the performance of both the implicit and explicit representations of vegetation in SWAN in simulating wave attenuation over a natural emergent marsh. The wave and flow modules within Delft3D are used to create an open-ocean model to simulate offshore wave conditions. The domain is then decomposed to simulate nearshore processes and provide the boundary conditions necessary to run a standalone SWAN model. Here, the implicit and explicit representations of vegetation are finally assessed. Results show that treating vegetation simply as enhanced bottom roughness (implicitly) under-represents the complexity of wave-vegetation interaction and, consequently, underestimates wave energy dissipation (error > 30%). The explicit vegetation representation, however, shows good agreement with field data (error < 20%).@en