Statistically simulated time series of wave parameters are required for many coastal and offshore engineering applications, often at the resolution of approximately 1 h. Various studies have relied on autoregressive moving-average (ARMA) processes to simulate synthetic series of wave parameters in a Monte Carlo sense. However, accurately representing inter-series dependencies has remained a challenge. In particular, the relationship between wave height and period statistics is complex, due to the limiting steepness condition. Here, we present a new simulation method for joint time series of significant wave height, mean zero-crossing periods and a directional regime variable. The latter distinguishes between northern and southwestern waves. The method rests on several model components which include renewal processes, Fourier series with random coefficients, ARMA processes, copulas and regime-switching. A particular feature is a data-driven estimate for a wave height-dependent limiting wave steepness condition which is used to facilitate copula-based dependence modeling. The method was developed for and applied to a data set in the Southern North Sea. For this site, the method could simulate time series with realistic annual cycles and inter-annual variability. In the time series data, the bivariate distribution of significant wave height and mean zero-crossing period was well represented. An influence of the directional regime on the bivariate distribution could also be modeled. However, the influence was not as strong in simulated data as in observed data. Finally, simulated series captured duration and inter-arrival time of storm events well. Potential applications for output of the simulation method range from the assessment of risks to the planning and budgeting of operations in coastal and offshore environments.

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Infragravity (hereafter IG) waves are surface ocean waves with frequencies below those of wind-generated “short waves” (typically below 0.04 Hz). Here we focus on the most common type of IG waves, those induced by the presence of groups in incident short waves. Three related mechanisms explain their generation: (1) the development, shoaling and release of waves bound to the short-wave group envelopes (2) the modulation by these envelopes of the location where short waves break, and (3) the merging of bores (breaking wave front, resembling to a hydraulic jump) inside the surfzone. When reaching shallow water (O(1–10 m)), IG waves can transfer part of their energy back to higher frequencies, a process which is highly dependent on beach slope. On gently sloping beaches, IG waves can dissipate a substantial amount of energy through depth-limited breaking. When the bottom is very rough, such as in coral reef environments, a substantial amount of energy can be dissipated through bottom friction. IG wave energy that is not dissipated is reflected seaward, predominantly for the lowest IG frequencies and on steep bottom slopes. This reflection of the lowest IG frequencies can result in the development of standing (also known as stationary) waves. Reflected IG waves can be refractively trapped so that quasi-periodic along-shore patterns, also referred to as edge waves, can develop. IG waves have a large range of implications in the hydro-sedimentary dynamics of coastal zones. For example, they can modulate current velocities in rip channels and strongly influence cross-shore and longshore mixing. On sandy beaches, IG waves can strongly impact the water table and associated groundwater flows. On gently sloping beaches and especially under storm conditions, IG waves can dominate cross-shore sediment transport, generally promoting offshore transport inside the surfzone. Under storm conditions, IG waves can also induce overwash and eventually promote dune erosion and barrier breaching. In tidal inlets, IG waves can propagate into the back-barrier lagoon during the flood phase and induce large modulations of currents and sediment transport. Their effect appears to be smaller during the ebb phase, due to blocking by countercurrents, particularly in shallow systems. On coral and rocky reefs, IG waves can dominate over short-waves and control the hydro-sedimentary dynamics over the reef flat and in the lagoon. In harbors and semi-enclosed basins, free IG waves can be amplified by resonance and induce large seiches (resonant oscillations). Lastly, free IG waves that are generated in the nearshore can cross oceans and they can also explain the development of the Earth's “hum” (background free oscillations of the solid earth).

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Shallow foreshores in front of coastal dikes can reduce the probability of dike failure due to wave overtopping. A probabilistic model framework is presented, which is capable of including complex hydrodynamics like infragravity waves, and morphological changes of a sandy foreshore during severe storms in the calculations of the probability of dike failure due to wave overtopping. The method is applied to a test case based on the Westkapelle sea defence in The Netherlands, a hybrid defence consisting of a dike with a sandy foreshore. The model framework consists of the process-based hydrological and morphological model XBeach, probabilistic overtopping equations (EurOtop) and the level III fully probabilistic method ADIS. By using the fully probabilistic level III method ADIS, the number of simulations necessary is greatly reduced, which allows for the use of more advanced and detailed hydro- and morphodynamic models. The framework is able to compute the probability of failure with up to 15 stochastic variables and is able to describe feasible physical processes. Furthermore, the framework is completely modular, which means that any model or equation can be plugged into the framework, whenever updated models with improved representation of the physics or increases in computational power become available. The model framework as described in this paper, includes more physical processes and stochastic variables in the determination of the probability of dike failure due to wave overtopping, compared to the currently used methods in The Netherlands. For the here considered case, the complex hydrodynamics like infragravity waves and wave set-up need to be included in the calculations, because they appeared to have a large influence on the probability of failure. Morphological changes of the foreshore during a severe storm appeared to have less influence on the probability of failure for this case. It is recommended to apply the framework to other cases as well, to determine if the effects of complex hydrodynamics as infragravity waves and morphological changes on the probability of sea dike failure due to wave overtopping as found in this paper hold for other cases as well. Furthermore, it is recommended to investigate broader use of the method, e.g., for safety assessment, reliability analysis and design.@en

Overwash hydrodynamics datasets are mixed in quality and scope, being hard to obtain due to fieldwork experimental difficulties. Aiming to overcome such limitations, this work presents accurate fieldwork data on overwash hydrodynamics, further exploring it to model overwash on a low-lying barrier island. Fieldwork was performed on Barreta Island (Portugal), in December 2013, during neap to spring-tides, when significant wave height reached 2.64 m. During approximately 4 hours, more than 120 shallow overwash events were measured with a video-camera (at 10 Hz), a pressure transducer (at 4 Hz) and a current-meter (at 4 Hz). This high-frequency fieldwork dataset includes runup, overwash number, depth and velocity. Fieldwork data along with information from literature were used to setup XBeach model in non-hydrostatic mode. The baseline model had variable skills over the duration of the overwash each 30 minutes. The baseline model was forced to simulate overwash with different nearshore morphology, grain-size and lagoon water level. An average decrease of about 30% overwash was obtained due to changes in the nearshore episode, performing better during the rising tide than during the falling tide. Model average number of events RMSE (root-mean-square-error) was 7 events morphology, mostly a small vertical growth of the submerged bar. The coarser and finer grain-sizes tests produced an 11% change in overwash, with less overwash on the coarser barrier. Changing lagoon water levels had a reduced effect on overwash hydraulics.@en

Aquatic vegetation in the coastal zone attenuates wave energy and reduces the risk of coastal hazards, e.g., flooding. Besides the attenuation of sea-swell waves, vegetation may also affect infragravity-band (IG) waves and wave setup. To date, knowledge on the effect of vegetation on IG waves and wave setup is lacking, while they are potentially important parameters for coastal risk assessment. In this study, the storm impact model XBeach is extended with formulations for attenuation of sea-swell and IG waves, and wave setup effects in two modes: the sea-swell wave phase-resolving (nonhydrostatic) and the phase-averaged (surfbeat) mode. In surfbeat mode, a wave shape model is implemented to capture the effect of nonlinear wave-vegetation interaction processes on wave setup. Both modeling modes are verified using data from two flume experiments with mimic vegetation and show good skill in computing the sea-swell and IG wave transformation, and wave setup. In surfbeat mode, the wave setup prediction greatly improves when using the wave shape model, while in nonhydrostatic mode (nonlinear) intrawave effects are directly accounted for. Subsequently, the model is used for a range of coastal geomorphological configurations by varying bed slope and vegetation extent. The results indicate that the effect of wave-vegetation interaction on wave setup may be relevant for a range of typical coastal geomorphological configurations (e.g., relatively steep to gentle slope coasts fronted by vegetation). @en