The rapid expansion of offshore wind energy, especially into intermediate depths and more non-linear wave environments, has increased the need for accurate prediction of wave-structure interactions, particularly wave run-up and the associated hydrodynamic forces on monopile foundations. These predictions are essential for ensuring the structural integrity, safety, and cost-efficiency of offshore wind turbines. Existing semi-empirical formulas are limited in their applicability, often overestimating run-up heights and failing to capture the complex non-linear interactions that occur under steep (So > 0.03) or near-breaking wave conditions typical of intermediate water depths.

This thesis presents a numerical model based on Computational Fluid Dynamics (CFD), developed using OpenFOAM and the waves2Foam toolbox, to predict wave run-up and the associated hydrodynamic forces on monopiles under varying hydrodynamic conditions. The model was validated against experimental data from de Vos et al. (2007), achieving excellent agreement with less than 5% error in peak wave run-up predictions. Following validation, the model was applied to assess the influence of scale effects, turbulence, monopile geometry, and key wave characteristics on run-up behavior and force magnitude.

The results confirm that scale effects on surface elevation and wave run-up are limited, while hydrodynamic forces show some sensitivity, particularly viscous forces in the vertical direction. Steep, high-energy waves near the breaking thresholds (So ≈ 0.04 to 0.05) produce significantly larger run-up heights and slamming forces, underlining their importance in design considerations. The geometry of the monopile also impacts localized flow patterns and wave wrapping, while turbulence contributes to increased lateral and viscous forces. However, its effect on the critical run-up at the front of the structure remains minimal.

By integrating turbulence modeling, scaling, and mesh optimization, this study establishes a robust, scalable, and accurate numerical framework for simulating complex wave-structure interactions. The model demonstrates significant improvements over existing empirical approaches, especially in intermediate water depths where non-linearity, shoaling, and breaking are present.

While the model shows excellent predictive capabilities, areas for further improvement remain. These include local mesh refinement around the monopile, higher-order discretization schemes to better capture breaking waves, and more extensive validation with recent experimental datasets. However, these enhancements would come at significant computational cost. Given the already high level of accuracy (>95%) in capturing peak wave run-up, the current model offers a practical balance between precision and efficiency. Future efforts should focus more on applying the model to irregular wave conditions and additional hydrodynamic parameters rather than fine-tuning. Researchers with greater computational resources may explore these improvements but should weigh the trade-off between added accuracy and computational expense.

The model configurations are publicly available to support future research and industry adoption: https://github.com/hiddded/MSc-thesis-wave-run-up-on-monopiles

Grass-covered dikes are a widely used measure for flood prevention. Overtopping waves can cause erosion that poses significant risks for flood safety, especially with rising sea levels and increasing storm intensities. During storm events, which involves frequent wave overtopping, erosion occurs progressively as multiple individual waves flow over the dike. This causes the dike profile to change over time as erosion holes begin to appear, which can influence the erosion potential of subsequent overtopping waves.

Current methods to estimate forces and erosion from overtopping waves rely on numerical models or analytical and empirical formulas. Numerical models are generally applicable and provide detailed spatial and temporal results, but are computationally too expensive to simulate an entire storm whilst updating the bed profile. Formulas offer quick results but lack general applicability and fail to account for the effects of erosion holes. No current method efficiently combines computational speed, detailed results and broad applicability, making it challenging to study the effects of gradually increasing erosion on overtopping waves.

This research focuses on the development of a new method that provides rapid and reliable wave overtopping simulations that can integrate erosion. This is done through surrogate modelling, which aims to create a computationally cheap model that emulates a detailed model. The foundation of this surrogate model is a Transformer-based deep learning architecture, which has proven superior in handling spatiotemporal processes.

The surrogate model is created by adapting the Vision Transformer model into a new model that can perform next-frame prediction, which involves the prediction of a next frame based on a sequence of input frames. The developed model can take an input sequence, recognize spatial and temporal patterns, and project them into a predicted future timestep. The model is trained on a dataset of overtopping wave simulations produced by the CFD software OpenFOAM. A masked loss function is applied to enhance the training process by forcing the model to focus on improving the relevant errors.

Using the trained model to generate wave overtopping simulations showed that it can accurately replicate the original CFD simulations. The surrogate model is validated against the original CFD simulations by comparing maximum values and time series for flow velocity and water depth at four different locations along the dike. The results generally show good agreement in capturing the maximum values, as well as the time of arrival and the overtopping duration. Simulating wave overtopping over an eroded dike profile showed promising results, though performance could improve with a larger and more diverse training dataset.

This research demonstrates that a Transformer-based surrogate model can effectively emulate wave overtopping simulations produced by CFD software. The surrogate model's speed and simplicity enables the simulation of a storm and updating of the bed profile. The model has not reached its full potential due to limitations in the training dataset and nuances in the simulation technique that require further refinement. However, it serves as a proof of concept that this surrogate model can provide a new tool in wave overtopping modelling, creating possibilities for new studies such as the influence of erosion on overtopping waves during storm conditions, or for probabilistic calculations that require a large number of simulations.

Rare precipitation extremes are projected to increase relatively more than common extremes under future climate change. However, it is unconfirmed whether these projected differences in relative change are observable in historical precipitation data. Therefore, this study investigated whether rare precipitation extremes have changed differently from more common ones during the period 1951 to 2010, in Western Europe. The differences in change between rare and common extremes (Drare-common) and its correlation with temperature is analysed, using daily temperature and precipitation data. The Drare-common values are calculated based on the relative change of a specific return level estimated by three methods: the Full series, the Generalized Extreme Value (GEV) and the Metastatistical Extreme Value (MEV) distribution. A correlation with daily temperature is obtained by analysing first all day temperatures and compare these with the pattern in the Drare-common values. Secondly, the temperatures at the days of the annual extremes is analysed.
The results indicate that, on average for Western Europe, historical precipitation extremes have increased in magnitude by 3.0 up to 5.4%, depending on the method. Regional variations are present in Western Europe, showing negative relative changes for the most southern regions. A Drare-common for Western Europe equal to 1.0 and 2.3%pt is obtained, for respectively the MEV and GEV method, indicating that the rarest precipitation extremes have increased more in magnitude compared to the common extremes. However, a comparison of extremes based on the time series length using the Full series indicated no difference in relative changes for return levels of 0.1 and 10 years. A statistically significant correlation between the Drare-common and temperature is obtained between the results of the GEV and Tmax and MEV method and Tmin. This correlations suggests observing a relative high Drare-common value in a region in which the change in maximum temperature is low and the change in the minimum temperature is high, depending on the method used. Analysing the temperatures during annual extremes showed an increase in both the minimum and maximum temperature on the days of the annual extremes, despite a shift from warmer to colder months in which annual extremes occur. When dividing the annual extremes into common and rare, it was concluded that a higher increase in temperature is observed during common annual extremes compared to the rare annual extremes.
It is recommended to analyse this phenomenon in more recent years. To understand the behaviour of precipitation extremes in greater depth, other driving factors causing precipitation to become extreme could be studied. Examples of these driving factors include atmospheric water vapor and the temperature in regions where precipitation is generated.

Compound floods, which can be attributed to different drivers (pluvial, fluvial, surge, tide, and waves), generate a larger flood hazard when drivers co-occur than when they occur in isolation of each other. Current compound flood risk assessments are affected by a curse of dimensionality, where a larger number of events need to be numerically simulated to understand the response of risk to drivers. This research aims to create a methodology that improves the quantification of compound flood risk by using a Treed Gaussian Process (TGP) for the case study of Charleston. A TGP can actively learn from the response of damages to drivers to reduce the number of events that need to be simulated. By comparing this approach with a state-of-the-art approach, the research shows a reduction of the computational cost by a factor of 4, an improvement in the root mean square error by a factor of 8, and an improvement in the estimate of Expected Annual Damages (EAD) by a factor of 20. This reduction in computational cost allows for the inclusion of random variables that are normally assumed constant such as the duration and time lag of drivers. A sensitivity analysis demonstrates these variables produce a statistically significant difference in the estimate of EAD, which increases its value from 172 to 219 Million USD. The research also shows the combination of events caused by drivers leading to extreme damage changes when including these additional random variables, although surge is always found to be dominant. By applying the TGP to multiple outputs, the research demonstrates the TGP is not only applicable to the case study, which shows a TGP can be implemented in current flood risk assessments.

The objective of this research is to gather more information about a possible relation between the slope angle of a rubble mound breakwater and the wave overtopping at this breakwater. The following research question is covered in this thesis: What is the influence of the slope angle of rubble mound breakwaters on wave overtopping? To answer this research question, a literature study was done and physical model tests were performed at Deltares in Delft, the Netherlands. In total, tests to five different breakwater configurations were performed, with a slope of 1:1.5, 1:2, 1:4, 1:6 and 1:8. These breakwaters were exposed to varying significant wave heights and wave steepnesses. During these tests, the amount of water from waves overtopping the structure was collected in order to determine the average wave overtopping discharge for every performed test.

Results of this study show that the slope angle has a large influence on wave overtopping at rubble mound breakwaters. It follows that the steeper the slope, the larger the wave overtopping discharge for the same dimensionless crest freeboard. This trend was captured regardless the wave steepness. This relation can be seen V both for breaking and for non-breaking wave loading. However, the dependency between the slope angle and the wave overtopping discharge appears to be larger for breaking waves than for non-breaking waves.

Furthermore, it was found that the wave steepness has a large influence on wave overtopping at rubble mound breakwaters, both for non-breaking waves and for breaking waves. In general, it can be said that the lower the wave steepness, the larger the wave overtopping discharge for the same dimensionless crest freeboard. This relation was found regardless of the slope angle of the breakwater. However, it followed that the wave steepness has a larger influence on the wave overtopping discharge at gentle slopes, like 1:6 and 1:8. It should be noted that for non-breaking waves, the influence of the slope angle and wave steepness is not present in the existing manuals, while the effects are important.

The formulas in the current guidelines to calculate the wave overtopping discharge were compared to each other and the data. These formulas were further modified based on the data gathered during the physical model tests to obtain even more accurate predictions for overtopping discharges. This resulted in the proposal of two equations to calculate the average wave overtopping discharge at permeable rubble mound breakwaters for wave loading that can be characterized as breaking waves and non-breaking waves.

Breakwaters are built in coastal zones to alter sediment transport, or protect threatened habitats and port facilities. The rising sea level is causing more water to overtop these structures. Increasing amounts of overtopping discharge can compromise the security of people, or equipment standing on the crest of breakwaters. The overtopping flow causes a peak force that drives an instability on these subjects. The flow depths and velocities depend on the hydrodynamic conditions and structure geometry. Up to date, there is limited data that characterize this flow for a wide range of wave conditions and breakwater configurations. In principle, it is possible to perform physical model tests to fill this gap, but these tests are expensive and time-consuming. Furthermore, extracting the flow depths and velocities from experiments is complex and most intrusive measuring instruments can alter the flow. An alternative or addition to physical model experiments is the use of numerical models. In the present research, a numerical model based in OpenFOAM® is used to evaluate the effects of different wave conditions and protrusion heights on the flow depths and velocities at the crest of a rubble mound breakwater.

The numerical model was validated with physical model tests performed on a rubble mound breakwater. Overall, the numerical model simulated the incident waves accurately, but overestimated the mean overtopping discharge. The overprediction of the overtopping discharge and the different methodologies of computation of the flow velocities made it difficult to validate the overtopping flow. However, the numerical model was still valuable to study the physical processes occurring during overtopping events, and the trends on the modelled flow depths and velocities when changing the wave conditions and protrusion heights.

It was determined that wave gauges and probes are the optimal methods to extract the flow depths and velocities from the numerical model. They were placed along (and over) the crest. For the specific set-up of the numerical model, it was found that the most extreme events impact the horizontal part of the crest wall in between the measuring devices. Therefore, for some instruments, the flow depths and velocities are extracted when the events are still in the air or at the moment of collision with the crest. In these cases, the trends had a different behavior than the expected one once the events are propagating attached to and along the crest. More detailed analysis and future validation are required for such circumstances.

Events associated to high exceedance probabilities showed trends aligned with the expected tendencies (for events propagating attached to the crest). This is because, these events were produced by smaller wave heights. Hence, the overtopping events collided with the horizontal part of the crest wall before the first measuring devices. For these events, it was observed that the flow depths and velocities decreased the lower the significant wave height, the larger the wave steepness, and the longer the distances from the seaward boundary. In addition, for a smaller protrusion height, more events were captured, and their flow depths and velocities were larger.