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.

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.

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.

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.

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.

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.