In times of rapid urbanization, engineering interventions in coastal systems have become more common. It is important to understand the interplay of these engineered solutions with their natural environment to minimize hazardous side effects to our ecology, economy and coastal safety. In a numerical study by Rijnsburger (2021), a flow recirculation with a diameter of 10 to 20 km - similar to an eddy - was identified in the North Sea. It remained unclear what causes the recirculation, but its location in the Rhine region of freshwater influence and near the artificial Maasvlakte headland, suggest that the recirculation could both be baroclinic or barotropic. This numerical model study is set out to understand what processes drive the recirculation. Identifying these processes is important to understand what is required to properly model the hydrodynamics along the Dutch coast, and accordingly, the spreading of sediment, pollutants and phytoplankton.

A realistic 3D hydrodynamic model was used to assess the recirculation during a validated spring-neap cycle. Our analysis shows that the recirculation has a maximum diameter of roughly 15 km during neap tide and 5 km during spring tide. The recirculation occurs in the buoyant top layer of the water column and grows offshore from its onset north of the Maasmond around HW+3 until it is overtaken by ebb tidal velocities around HW+5. This study shows that the onshore advection of negative (clockwise) vorticity water results in most water flowing back to the river mouth into an expanding clockwise recirculation, the vorticity and strength of which are strongly influenced by buoyant river outflow.
Our analysis shows that the headland is not a prerequisite for its onset. Nevertheless, two mechanisms are identified of how the headland influences the recirculation. First, during spring tide, the headland is found to ‘shelter’ the recirculation from strong ambient currents in the midfield which would otherwise hamper the recirculation. Secondly, the geometry of the river mouth influences the vorticity input in the North Sea associated with the buoyant river outflow.

To further investigate what processes influenced by the river outflow could contribute to the recirculation, a scale analysis and particle tracking study were deployed. Although, the study is not yet conclusive on what drives the onshore advection of the spinning water that flows into the recirculation, several potential processes have been identified.

For future studies that want to model the spreading of freshwater, pollutants or suspended sediment near the river mouth of the Rhine-Meuse system, this study underlines the importance of using a three-dimensional numerical model that accounts for density differences and the influence of the studied recirculation. The latter is especially important when the boundaries of the numerical domain are located close to the river mouth, due to which the influence of the recirculation is not resolved unless explicitly accounted for in the boundary conditions. This study therefore contributes to the improvement of future modelling studies of the Rhine ROFI and to our understanding of the processes that govern the hydrodynamics along the Dutch coast.

Due to climate change and human interventions, saltwater intrusion is becoming a topic of increasing concern worldwide. Salt water intrudes into the Rotterdam Waterway (RWW) by an exchange flow, where the denser sea water propagates landwards at the bottom. The main competing mechanism for this stratified exchange flow is vertical mixing, which can be realised by internal wave induced shear instabilities or wave breaking. The goal of this study is to investigate whether internal waves generated over undular bottom topography in the RWW can generate additional vertical mixing. The underlying assumption is that a decrease in stratification decreases salt intrusion.   The approach to answer the main research question is a combination of an analytical and a numerical analysis. The analytical study is based on frictionless linear theory. Internal wave behaviour is further analysed with FinLab, a finite element model which includes the non-hydrostatic processes and effects of density differences. FinLab is evaluated for the application of this study by means of a validation case.  In the analytical study, linear theory is applied to obtain a relation between the bed wave parameters and average internal wave energy density E for internal waves generated over sinusoidal bottom topography in a linearly stratified fluid. The derived expression describes that the bottom topography amplitude h0 and bed wave number kT both have a positive quadratic relation with the energy. Additionally, kTkinfluences the resonance conditions.  To validate FinLab for internal wave breaking and mixing an experiment in a wave tank, according to an example from literature, is simulated. The validation case reveals a shortcoming in the turbulent mixing parameterization. However, on scales relevant for the RWW the effect of this will not have the same significance. The validation case offers a suggestion for a subgrid closure of diffusion, where density effects are taken into account.  Numerical simulations of a 2D channel stretch with sinusoidal bottom topography, a linearly stratified fluid and a linearly varying background velocity, show generation of resonant trapped internal waves for the first two resonant modes. These occurrences correspond to the highest values of kinetic energy as function of vertical velocity averaged over the bed wave domain. The vertical buoyancy flux b is downward directed during occurrences of internal waves and becomes upward directed for increasing background flow. Vertical mixing is associated with an increase in average potential energy Ep, which is 17% higher for the base case (containing bed waves) than for a similar case without bed waves. This increase is larger when bottom shear stress increases. Richardson numbers below 0.25, associated with shear instabilities and mixing, are only observed near the bed, mainly when internal waves are present. The effect of variations in bottom topography wavelength LT and amplitude h0 on internal wave energy can be explained by the analytical formulation. The effect of bed wave parameter changes on b and relative increase in Ep can be related to the effect of the changed amount of bed friction rather than the difference in wave energy.   The first resonant mode is the most energetic, however, the average energy density found for these waves is only 0.4% to 6.7% of the potential energy anomaly (PEA); the energy required to fully mix a stratified water column. In the simulations the only mechanism that could transfer internal wave energy to turbulent kinetic energy are shear instabilities near the bed. Over the full simulation, the net vertical buoyancy transport is of negligible magnitude, where Ep shows significant increases between 6% and 99% compared to similar cases without bed waves and is enhanced during the presence of internal waves.  The main discussion point is that the quantification of vertical mixing requires improvement, particularly to determine the importance of mixing by internal wave-induced shear instabilities and by bed shear. Mixing by local shear instabilities (of which the relevant scales cannot be resolved with the current grid resolution) does not have an adequate parameterization, because density effects are not included in the turbulence closure. The bed friction parameter, which greatly influences the behaviour of the system, has to be validated. Furthermore, cases where internal waves might break in practice (e.g. at banks) were not considered. Finally, the observed internal wave energy is of small magnitude, however field measurements by Pietrzak(1991) shows that turbulence production by internal waves was significant.   

Climate change causes alterations in large scale mass transport patterns in the ocean, cryosphere and hydrology. The Gravity Recovery and Climate Experiment (GRACE) satellite mission which has been operational in the years 2002-2017 has already improved our understanding of large scale mass transport on Earth, but improvement of data quality is still needed. This will increase the quality of our current estimates of the effects of climate change on one hand and help in the validation and initiation of climate models on the other, which improves the accuracy of future predictions.

Noise in GRACE Level-2 data (monthly gravity field solutions) is caused by various reasons. The measurements themselves are already executed and their quality is fixed but better data processing algorithms and background models can reduce the current noise level. This is also relevant for the GRACE Follow On mission which might have a higher measurement precision. Over the ocean, these GRACE monthly solutions ideally only show mass exchange between continents and ocean and effects of self-attraction and loading. Therefore, the signal over the ocean is expected to consist predominantly of a linear trend and a seasonal variability. For certain oceanic regions this is not the case. In these areas still a signal variance representing interannual differences in the mass-derivative and large residuals with respect to a low-pass filtered signal are observed. This low-pass filtered signal contains only signals of a frequency lower than the semiannual cycle. These signal variance and residuals are unexpected and can be caused by inaccuracies in the currently applied oceanic background models in GRACE data processing.

For various Release 5 and Release 6 monthly solutions the noise variance, signal variance and residuals as aforementioned are estimated. The noise and signal variance are estimated by Variance Component Estimation (VCE). Additionally, numerical experiments are performed to analyze different regularization functionals and set-ups in the VCE. The oceanic regions where the largest signal variance and residuals are observed correlate. These areas are for GRACE Release 5 data the Baltic Sea, Black Sea, Arafura Sea, East Siberian Arctic Shelf, Argentine Basin and Hudson Bay. For GRACE Release 6 data a significant drop of this signal variance and residuals can be observed for the Hudson Bay and East Siberian Arctic Shelf.

Consequently, the oceanic background models for these releases are compared against each other and against the Global Tide and Surge Model (GTSM) which is a 2D hydrological model based on the Delft3D Flexible Mesh software developed by Deltares. For the whole ocean both 3/6-hourly time-series and monthly time-series are analyzed. For the shallow regions up to 200 m, the Black Sea and the Red Sea, GTSM shows significant differences with respect to the current applied oceanic background models. When comparing the oceanic background models of different releases it can be observed that the regions where the signal variance and residuals decreased for GRACE Release 6 with respect to Release 5 correlate to regions where the differences between these models is significant. This indicates that oceanic background models do significantly influence the quality of GRACE monthly solutions over the ocean.

Furthermore, it is investigated whether it can be expected that GTSM will improve the GRACE monthly solutions. For this, monthly time-series of the current applied oceanic background models are added back to the GRACE monthly solutions; consequently, by GTSM computed monthly time-series are removed. Compared to GRACE Release 5 monthly solutions, GTSM shows a reduction in the signal variance and residuals for the Hudson Bay, East Siberian Arctic Shelf, Black Sea, Baltic Sea, North Sea, Arafura Sea and certain parts of the Arctic and Southern ocean. Compared to GRACE Release 6, a reduction in the signal variance and residuals is observed for the East Siberian Arctic Shelf, Black Sea, Baltic Sea, North Sea and Arafura Sea. For these regions it is most expected that GTSM can improve GRACE monthly solutions. Since the quality of monthly solutions over the oceans is clearly influenced by the oceanic background models significant alterations in GRACE monthly solutions are expected for the shallow regions up to 200 m, Black Sea and Red Sea when applying GTSM in the GRACE data processing. Whether these will be improvements or not should be analyzed by implementing GTSM-based 3-hourly time-series in the GRACE data processing to create a new GRACE Level-2 data product.

Even though negative effects on the use of crude oil have surfaced over the past years, our energy matrix still largely relies on this energy source. The production of oil, therefore, plays an important role in our society. Unfortunately, the process of oil production is highly uncertain. There are uncertainties associated on the production strategy, e.g. where and how many wells should be drilled and how these wells should operate because of the uncertainties associated with the limited knowledge about the subsurface. In this thesis we are dealing with the uncertainty of the rock permeability distribution. Typically, rock permeabilities in the rock vary, but from the outside this can’t be perceived. If these rock permeabilities are estimated inaccurately, they will result in inaccurate pressure solutions. Then, this can lead to faulty decisions regarding the oil exploitation. To resolve this issue, a data assimilation technique may be applied to correct these model parameters based on mismatch of simulated data and observations. For this optimization technique, often gradient information is required. Since
in reservoir simulation the number of parameters generally is extremely high, computation of this information is computationally expensive. Therefore, a multiscale framework is employed to improve the
computational efficiency of the forward simulation. Multiscale methods are able to solve the model equations at a computationally efficient coarse scale and can easily interpolate this solution to the fine
scale resolution. Next, we use a Lagrangian set-up together with a multiscale framework to re-derive an efficient formulation for the derivative computation. However, as the multiscale method is prone to errors, this derivative computation formulation is recast in an iterative fashion, using a residual based
iterative multiscale method to provide control of these errors. In this thesis we show that this method generates accurate gradients. In contract to the high accuracy of the method, this method comprises a computationally heavy smoothing step. This issue can be resolved by making smart use of the Lagrange
multipliers, to re-derive an efficient iterative multiscale solution strategy. The multipliers are used to identify important domains of the region for which smoothing is required and for which regions we may neglect the smoothing. We show that the newly proposed iterative multiscale goal oriented method is computationally more efficient and we show that method is promising for efficient derivative computation, but that more work is required to fully demonstrate the benefit of this method.

Vector-based graphics are not directly compatible with the raster-based structure of dedicated graphics hardware. They suffer from a locality problem where, in order to check if a specific display pixel lies inside or outside the shape, the entire shape needs to be taken into account. This negates the advantage that the graphics pipeline’s parallel rendering structure offers. Current solutions rasterize vector graphics into a discrete raster-based texture in an extra render pass, every time the required texture resolution changes.
This work presents an approach to store vector-based shapes into discrete raster-based textures, optimized for parallel rendering. This is done by encoding the shape as piece-wise cubic Bézier curves, structured in a quad-tree. Additional data is added to remove aliasing effects in case of minification. These textures are then rendered by a custom fragment shader.
This work discusses the implementation of both the serialization and deserialization steps, as well as rendering regular vector shapes with a comparable quality.

The North Sea is known for its marine activities, which need ocean data for safe operations. The ocean surface is described using the two-dimensional wave spectrum. This ocean wave spectrum can be estimated using wave buoys, wave models or remote sensing techniques. Wave buoys and numerical models are known to contain inaccuracies, which stresses the importance of other observation techniques. The solution of this thesis is using a remote sensing technique from Sentinel-1: Synthetic Aperture Radar.

In total 11 case studies were analyzed in the North sea and 3 case studies in Portugal. Sentinel-1 SAR cross-spectra were verified and validated using wave buoy measurements and cross-spectra from simulated SAR images from OCEANSAR. In total, 6 North Sea case studies showed a positive result, where a swell peak was visible and the peak matched spectral data from wave buoys. Case studies from the Portuguese coast showed the best results, where SAR cross-spectra agreed well with buoy measurements.

Further improvements include the removal of non-linear contribution from cross-spectra, mapping of wave buoy measurements on the quasi-linear swell spectrum and calculating the full Modulation Transfer Function. This thesis showed it is possible to measure low-frequency waves in the North Sea using Sentinel-1 Synthetic Aperture Radar. SAR images lead to a better understanding of the movements of swells and provide additional information for marine activities. A combination of wave buoy data, Sentinel-1 SAR data and OCEANSAR data showed measuring swell waves is possible with this state-of-the-art remote sensing technique.