Wave overtopping of coastal structures has been studied using physical model experiments with rubble mound breakwaters in shallow water. The mean overtopping discharge is determined for three different foreshore slopes and various hydrodynamic conditions. The hydrodynamic results confirm that energy is transferred to low-frequency waves in very shallow water and that the short waves are in phase with the lower-frequency waves in very shallow water. As a result, the extreme waves (e.g. 2% exceedance wave height) become relatively large in very shallow water due to the energy of the low-frequency waves affecting thereby the wave overtopping. To estimate the amount of energy at the low-frequency waves, an expression is derived which reasonably accurately predicts the low-frequency wave energy (RMSE of 0.06). Considering the non-dimensional overtopping discharge, the existing formulations for the non-dimensional mean wave overtopping discharge perform poorly to reasonably in shallow water with RMSLE ranging from 1.04 to 2.92. A parameter sensitivity study shows that the short-wave steepness, relative crest height and the low-frequency wave height are the most important parameters when predicting the mean overtopping discharge in shallow water. When including the short-wave steepness and relative crest height in an empirical formulation the RMSLE for the current dataset reduces to 0.69. A further increase in accuracy is found when the low-frequency wave height and 2% exceedance wave height are included (RMSLE 0.64).

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When performing physical or numerical experiments in a wave flume, it is important to distinguish between the incident and reflected wave components. Recently wave separation methods including nonlinear effects were presented which can be applied for a large range of conditions and reduces the error in the wave separation. However, these nonlinear methods also result in a complex system of equations and require more wave gauges. In this work, physical model experiments with a high spatial resolution of wave gauges were carried out to validate different wave separation methods. All tests were analysed with a Linear method, the nonlinear method described in Eldrup and Lykke Andersen (2019) (ELA method) and a Modified ELA method. In this Modified ELA method, the model complexity depends only on the condition number of the phase difference matrix making the accuracy less dependent on wave gauge positions and noise. The results show that both Nonlinear methods are always preferred over the Linear method. A detailed analysis of the number of wave gauges shows that for the same distance between first and last gauge, 6 to 8 wave gauges are required for a converged solution independently of the wave gauge position. In an ideal situation – with an ideal number of wave gauges and ideal spacing between them – the ELA and Modified ELA methods should give nearly identical results. However, for the non-ideal conditions encountered in practice, the Modified ELA is shown to be more robust.@en

Operational wave forecasting plays an important role in ensuring safe navigation and in the prediction of tidal windows for harbour approach channels. The underlying nearshore process-based wave models need to be accurate for a wide range of different conditions, from more common mild wave conditions to the occasional high energy (storm) conditions. In this work, an innovative hybrid modelling approach is proposed to improve the accuracy of operational wave forecasts. An operational wave model is combined with a machine learning model which is trained using wave measurements within the wave model domain. This hybrid modelling approach is applied to the Dutch North Sea, covering four major harbour approach channels.

The final hybrid operational wave model results in a significant average error decrease compared to just the process-based model, amounting to 21.7% for the wave energy density and 25.3% for the wave direction. The error reduction for the spectral wave parameters is even larger, with a 33.3% smaller error in spectral wave height and a 38.8% smaller error in spectral wave period. As this approach is generically applicable to spectral wave models, it contains the potential for significant improvements in operational modelling.@en

For reasons of computational efficiency, 1D XBeach cross-shore transect models are often applied on quasi alongshore-uniform coasts instead of a more computationally expensive 2DH modelling approach. In this paper we describe a practical methodology to allow 1D models to mimic infragravity wave growth observed in field conditions and represented in 2DH models and thereby significantly reduce the overestimation of infragravity wave heights near to the shore. We show that even if the coastal setting may support the 1D model assumption of alongshore uniformity in forcing and bathymetry, 1D XBeach models will overestimate infragravity wave growth relative to field conditions due to the underlying assumption of alongshore-uniform intra-wave (group) hydrodynamics common to all wave (group)-resolving models. Model analysis showed little variation in the optimum calibration value of this approach for a large range of wave forcing conditions (wave height, period and directional spread) and consistency with 2DH model results for a large range of Dutch coastal profiles. Comparison to field observations showed that the methodology significantly increased the skill of the 1D model to simulate nearshore IG wave heights. These results have implications on the ability to accurately predict the response of these coasts to energetic events, which is crucial to assess current and future flood risk and to design effective flood protection and mitigation measures.@en

A 2-layer non-hydrostatic model with improved dispersive behaviour is presented. Due to the assumption of a constant non-hydrostatic pressure distribution in the lower layer, the dispersive behaviour is improved without much additional computational time. A comparison with linear wave theory showed that this 2-layer model gives a better result for the dispersion relation and shoaling of waves in intermediate water. This means that the 2-layer model is applicable in shallow and intermediate water depths (up to relative depths kh equals 4), whereas the 1-layer model is only applicable in shallow water depths (kh smaller than 1). Three laboratory experiments, including a fringing reef and a barred beach, were used to validate the presented mode for different hydrodynamic conditions. Based on these results, it can be concluded that the 2-layer model can be applied to accurately simulate the bulk wave height and spectral properties. The low frequency wave height, the setup and in particular the second order statistics contain more scatter, but the model accurately captured the general trend. Furthermore, the model showed good results for complex bathymetries in shallow to intermediate water.

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The wave overtopping discharge during extreme storm conditions largely determines the required crest height in dike reinforcement projects. In case of future sea level rise, crest heights should be increased significantly, which potentially leads to significant costs and environmental and societal consequences. The available empirical design formulas for wave overtopping are based on data sets that show a relatively large scatter, potentially leading to inefficient design of crest level heights. In this paper a novel approach is presented in which the water depth in front of the dike is incorporated in the wave overtopping formulation leading to a lower scatter and in the case of shallow foreshores also a lower required crest height. The present approach is based on the use of an existing overtopping database (CLASH-EurOtop) and additional generated data by conducting physical experiments(Scheldt Flume of Deltares) and numerical experiments (OpenFOAM) in which the water depth was varied systematically for a variety of test conditions. Based on these three approaches, it is concluded that the wave overtopping discharge (q) is dependent on the water depth. Since this dependency is not included in the present wave overtopping formulation, this paper suggests a method to incorporate this dependency in the present existing formulas by implementing an influence factor for water depth (γd).@en

In coastal engineering context, the use of video imagery is widespread. Especially in field settings along sandy coasts, many types of data have been derived from video imagery, often using non-learning analysis techniques. Recent advances in the field of computer vision and deep learning allow for the automation of image segmentation. In this paper, these techniques are combined with video imagery of physical model tests, resulting in an innovative non-intrusive measurement technique. This technique is validated for three different applications: the measurement of surface elevation, wave run-up and bed level development. In addition to demonstrating its potential as an alternative for existing measurement instruments, it is shown that the added detail in the spatial or temporal domain provided by the technique can lead to new insights. Examples of this are the detailed analysis on the variability of the run-up height over the width of the flume and the spatial distribution of run-up velocities over the slope.@en

Quantification of human impact on water, sediment, and nutrient fluxes at the global scale demands characterization of reservoirs with an accuracy that is presently unavailable. This letter presents a new method, based on virtual dam placement, to make accurate estimations of area-volume relationships of large reservoirs, using solely readily available elevation data. The new method is based on regional similarity of area-volume relationships. The essence of the method is that virtual reservoirs are created in the vicinity of an existing reservoir to derive area-volume relationships for the existing reservoir. The derived area-volume relationships reproduced in situ bathymetric data well. An intercomparison for twelve reservoirs resulted in an average R² = 0.93. This is a significant improvement on estimates using the best existing global regression model, which gives R² = 0.54 for the same set of reservoirs.

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