Wave overtopping at rubble mound structures is one of the most important phenomena affecting the hydraulic performance of these coastal structures. In addition to the design of coastal structures, also the climate adaptation of coastal structures has become more important due to sea level rise. Adding a crest wall to an existing structure, increasing the height of a crest wall, adding a berm, or increasing the width or height of a berm, can be effective measures to account for effects of sea level rise. For this purpose, the individual effects of a crest walls and a berm need to be predicted, but also the combination of both (see for instance Van Gent, 2019, and Van Gent and Teng, 2023).

Wave overtopping estimates are generally based on physical modelling in wave flumes and wave basins. Numerical modelling of wave overtopping provides additional opportunities to examine wave overtopping for a wide variety of structure geometries. The combination of physical modelling with numerical modelling is referred to as hybrid modelling. To provide design guidelines for rubble mound structures with a crest wall and for structures with a berm in the seaward slope, Van Gent et al (2022) provides design guidelines based on physical model tests. Numerical modelling provides opportunities to examine wave overtopping at structures with a crest wall and a berm to further extend guidelines for the design and (climate) adaptation of rubble mound structures. In Irías Mata and Van Gent (2023) guidelines based on physical modelling have been extended based on numerical modeling with OpenFOAM to examine the influence of several aspects such as the wave steepness, crest wall and recurved parapet, berm, and structure slope on wave overtopping at rubble mound breakwaters. Although the present work focusses on wave overtopping, also forces on crest walls have been examined using the applied numerical model, see for instance Jacobsen et al, 2018, and Irías Mata et al, 2023.

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.

The design of crest walls is often based on empirical formulations, physical model tests, numerical models and a fair amount of expert judgement. The present work validates the prediction of wave induced forces on the front face of crest walls on top of composite breakwaters in the numerical model OpenFOAM. The results show that OpenFOAM is able to capture the shape and order of magnitude of the force events caused by non-breaking and heavily breaking waves. In addition, a calibrated model predicts the highest wave induces forces caused by breaking waves with errors lower than 20%.