The Shallow Water Equations (SWEs) for ocean applications can be discretized using finite differences, resulting in a system of time-dependent ordinary differential equations (ODEs). These ODEs can then be solved on a GPU using various time-integration schemes, which can be categorized as explicit and implicit methods. The primary aim of this thesis is to evaluate the performance of various time-integration solvers implemented on a GPU for a simplified tidal model of the North Sea. The investigation includes a comparison of explicit second-, third-, and fourth-order Runge-Kutta (RK) and multistep methods as well as several second-order implicit schemes. Moreover, a novel approach is proposed for solving the tidal model and addressing the nonlinear systems within the implicit time iterations. This approach is a combination of an implicit SDIRK2-scheme with a pseudo-time-stepping approach and a multi-level technique. All numerical schemes are implemented on the GPU using the Julia programming language. The most efficient explicit time-integration scheme was RK4. However, on a high resolution grid , the newly developed implicit solver outperformed RK4, in terms of speed.

This thesis analyzes the effectiveness of bias-aware filtering techniques, particularly the ColKF, in addressing parameter and bias estimation in data assimilation problems. The research explores the ability of this method to differentiate between the impacts of bias and parameter uncertainty, focusing on how the concept of feedback within the filtering process influences the estimation of both bias and parameters.

The study uses the Lorenz-96 model to conduct twin experiments, investigating various scenarios involving parameter estimation, bias estimation, and combined parameter and bias estimation. The experiments reveal that in a feedback filter configuration, where the bias directly influences the ODE system, the forcing parameter F of the Lorenz-96 model becomes indistinguishable from the bias. Conversely, a non-feedback filter configuration allows for the independent estimation of both the parameter and the bias.

In addition, the research highlights the challenges and considerations in implementing a flexible data assimilation framework, particularly in managing state augmentation, stochastic updates, and bias representation. It emphasizes the importance of carefully considering the feedback mechanism in bias-aware filtering, as it significantly impacts the estimation of parameters and bias.

The findings of this thesis offer valuable insights into the application of bias-aware filtering techniques in the presence of parameter uncertainty and provide a foundation for future research in developing robust and versatile data assimilation frameworks. The study encourages further exploration of these methods in real-world applications and with more complex bias structures to advance our understanding and ability to address uncertainties in dynamic systems effectively.

To optimally use wind farms, thorough understanding of wind patterns is needed. Recently, a lot of attention in the scientific community is turned to the Current FeedBack effect, where oceanic currents influence the atmosphere above. It has been shown that this also applies to tidal currents in the English Channel where the induced tidal winds have an amplitude of one-third of the underlying current. In this report focus is moved to the Dutch coast. Using a numerical integration model of a vertical grid, the horizontal wind speeds above a small area of the Dutch coast are modelled. The model is based on the 1-dimensional Navier-Stokes equations in combination with Prandtl's mixing length model to account for turbulence. The horizontal wind speeds are found to reach up to one-fourth of the amplitude of the tidal currents at a height of z = 10 m above the sea surface and 1/20 at z = 50 m. This is similar to what was found in earlier research, but a lot of assumptions were made in this model. Therefore, further research could focus on addressing some of these assumptions such that the understanding of tidal induced wind velocities can be even better understood.

Gross Primary Production (GPP) is the amount of carbon dioxide (CO2) that is fixed by an ecosystem through photosynthesis. It is a key variable to understand the carbon cycle and biodiversity conservation. In-situ measurements of GPP are possible at a local scale. To estimate GPP on a global scale, models based on remote sensing data are used. One of them is the Penman-Montheith-Leuning (PML) model, which is constructed on physical processes.

In this thesis, a sensitivity analysis of the PML model is performed for the case study of Torgnon subalpine grassland. It is defined around three aspects: the application of the PML model to Torgnon subalpine grassland, the impact of the input data on the output data, and the reliability of the calibration procedure. We found out that the PML model can be applied to the study site, but the value of the parameters presented in the literature are not optimal (R2 = 0.57 using the literature calibration and R2 = 0.94 in the optimised case).

Moreover, the model is extremely sensitive to the Leaf Area Index (LAI), and, to a lesser extent, to temperature and Photosynthetically Active Radiations (PAR). However, it is weakly dependent on the CO2 concentration of the atmosphere. The analysis of the calibration procedure showed that a simplified PML model, that does not consider the CO2 concentration and Vapour Pressure Deficit (VPD), performs similarly to the initial model. An ensemble estimation of GPP is obtained by using an ensemble of optimal parameters. It suggests that errors in the calibration principally impact the spring and summer estimations.

The topic of this thesis project is to use the particle-tracking framework to study salt intrusion.
This project was proposed by Deltares and is a small part of the SALTISolutions project, that attempts to build a digital twin model of the Rhine-Meuse Delta. From a mathematical perspective, the particle-tracking framework is inspired by the theoretical connection between partial differential equations that describes substance transport and stochastic differential equations (SDEs). The idea is to use replace the continuous substance distribution in the fluid by many particles. After tracking the particles, the consequent substance distribution can be approximated by the particles' distribution at certain time instant. There are two major achievement of this project. Firstly, different implementation of non-penetrating and flux boundary conditions for the particle-tracking framework are tested and compared. The recursion algorithm is preferred for the previous and the ``Neumann-wise'' is recommended for the latter. Secondly, the convergence order of SDE numerical schemes and their influences on the simulation of the vertical transport physics are examined by studying the one-dimensional pure diffusion test case. We see that most simple Euler scheme contaminates the stratification completely in a theoretical setting even using a small timestep, indicating that it might be worthwhile to switch to high-order schemes whenever possible. However, even if one can implement other higher order numerical scheme correctly and efficiently, which is not easy, it might be equivalently important to have enough particles and good interpolation of velocity and diffusion field in the computation domain, because they may introduces error comparable to the diffusion error. Since salt transport is already resolved by the Delft3D-FM model, it is of nonsense to use the particle-tracking framework to study transport. The one-dimensional pure diffusion test case is mainly used for verification of the method. Actually, the particle-tracking framework should be used in combination of the diagnostics timescales and tracer methods. This often requires calculation of the statistics of the particle ensemble. It will be interesting to conduct such analysis on a realistic three-dimensional test case, and this could be the field of future research.

Climate change is driving rapid transformations in the Arctic, with one of the most prominent changes being the significant decline in sea ice cover. As Arctic sea ice recedes at an alarming rate, its impact extends across various domains, necessitating a closer examination of these effects. This thesis focuses on one such domain: the relationship between Arctic sea ice and global tides. Current global hydrodynamic tidal models do not account for the energy dissipation due to sea ice nor the impact of variations in sea ice cover on tides. The seasonal fluctuations in sea ice are known to modulate tides through ice-water frictional dissipation. Given the ongoing decline in sea ice, it is imperative to develop accurate models that incorporate this dissipation. Global tidal models are crucial for several applications, including navigation and coastal flood management, highlighting the need for an efficient parameterization to account for sea ice-induced tidal dissipation.

The first research objective of this thesis was to develop a physically consistent parameterization for modeling sea ice-induced dissipation in barotropic global tide models. Chapter 2 explores the physics of air-ice-ocean interactions and the challenges of acquiring accurate sea ice drift velocities on tidal time scales. A parametric approach is introduced, which incorporates dissipation from three distinct sea ice regimes: landfast ice, drifting sea ice with internal stresses, and free-drift sea ice. The findings indicate that landfast sea ice can significantly influence the seasonal modulation of the M2 tide, particularly in regions like Hudson Bay, where it can reach up to 0.25 meters, underlining the need for further research on the long-term effects of Arctic sea ice decline.

Chapter 3 delves into the dissipation of tides caused by free drift sea ice. While this dissipation is negligible in deep, open ocean areas without wind influence, its impact in shallow water regions, such as the Spitzbergen Shelf, remains uncertain. An analysis using a beacon dataset and a physics-based ice model in the Barents Sea suggests that under low wind conditions, the dissipation from free drift sea ice is minimal, contributing only 2-3% of the bottom frictional stress.

Chapter 4 presents a new parametric approach for modeling tidal energy dissipation due to sea ice, dividing the sea ice cover into regions dominated by either Vertical Shear (VS) or Horizontal Shear (HS) energy dissipation. This approach is based on a non-dimensional Friction Number (F) that depends on sea ice thickness and concentration. The new parameterization demonstrates a stronger correlation (0.6) with altimetry data compared to current state-of-the-art methods (0.4). Additionally, it shows lower differences when compared to tide gauge observations, making it more suitable for studying the impact of sea ice decline on tides.

A significant challenge in this research was the lack of accurate, time-specific observations of tidal currents or water levels in the Arctic. To address this, the second research objective focused on developing a method for deriving tidal current constituents from GNSS buoy data, resulting in the novel ‘Model-derived fitting method’ detailed in Chapter 5. This method is evaluated through case studies, demonstrating its accuracy and robustness, especially in regions with dominant barotropic or baroclinic tidal currents.

This thesis successfully addresses key questions regarding the impact of sea ice on tides, introducing innovative parameterizations and exploring new data sources for tidal current estimation, thus advancing the understanding of Arctic tidal dynamics and ice-water interactions.

Establishing an accurate global unified vertical reference frame (VRF) is a long-standing objective of geodesy. However, that objective has still not been achieved. One particular application where the lack of such a VRF is evident, is the improvement of hydrodynamic models by assimilating total water levels acquired by tide gauges. Indeed, to facilitate a straightforward assimilation requires that both the observed and modeled water levels refer to the same vertical datum. The required accuracy is high; it is expected to be in the order of 1centimeter. The best alternative VRF for the area of interest, the northwest European continental shelf, is the European Vertical Reference Frame 2019 (EVRF2019). The EVRF2019, however, still lacks complete coverage and the required accuracy. The key reason is that it is solely based on geopotential differences from spirit leveling/gravimetry, which are not available between benchmarks separated by large water bodies. This thesis exploits model-based hydrodynamic leveling to provide these differences. The specific objective is to assess the potential of including these data in realizing of European Vertical Reference System (EVRS).

Ocean currents play a crucial role in many scientific and industrial applications. Contemporary measurement techniques are limited in spatial coverage or spatial resolution. This study presents a proof-of-concept for a new measurement principle that merges optical satellite imagery of Kelvin wakes with data from the Automatic Identification System (AIS). A case study in the Strait of Gibraltar was performed using two months of Sentinel-2 imagery, which yielded 81 visible Kelvin wakes over 25 images. For each Kelvin wake, currents were estimated in directions parallel and perpendicular to the ship's sailing line. The estimated currents were validated with respect to surface currents derived from High-Frequency Radars (HFRs) and modelled currents from the Copernicus Marine Environmental Monitoring Service (CMEMS). The results suggest that the estimated currents were highly accurate in the absence of large variations in ship course. However, the frequency of measurements is limited by satellite repeat times and Kelvin wake visibility. More research is needed to explore the potential spatiotemporal distribution of measurements.

In the realm of fluid dynamics and particle transport, the control of particle trajectories represents a formidable challenge. It would be useful to be able to optimally navigate an oceanographic float from one pre-set location to another by solely changing its buoyancy. In this thesis, a first step in discovering whether this is possible and what optimization strategy can be used is taken.
To do so, first, the physical situation is translated into a mathematical model. Then, an optimization strategy for changing the buoyancy to optimally travel to a set location is constructed. The strategy is based on gradient descent and implemented in Python. Four different definitions of an optimal trajectory to a target location are considered, those are 1) any trajectory that leads to the target location, 2) the most time-efficient trajectory, 3) the most energy-efficient trajectory, and 4) a trajectory that is both time and energy-efficient.
The optimization strategy is tested for five different starting and target locations for a small spherical float in an idealized two-dimensional linear flow field. It is concluded that it is possible to use the optimization strategy to navigate a float using buoyancy changes for all four optimization objectives, although the current implementation is not efficient enough for targets far away.
The first objective of future research should be to increase the coding efficiency. Thereafter, other steps toward a more realistic situation can be taken, such as testing for non-linear flow fields, three-dimensional fields, and bigger floats.

Extreme (still) sea levels and the possibly associated coastal floods, are generally linked to (high) tides and storm surges. The risk of coastal floods will likely intensify in the future. This is because, on the one hand, the population of coastal zones is expected to continue to grow, and, on the other hand, climate change may lead to an increase in the frequency and magnitude of extreme sea levels. Although observations suggest that on the global scale, sea level rise is the primary driver behind the increase in extreme sea levels, locally the increase in extreme sea levels may be amplified or even dominated by changes in stormsurges and tidal dynamics...

Groundwater is an essential ingredient in farming, knowledge about how this is expected to change over time can help farmers improve yields and save water. Predictions about the groundwater level can be made using a mathematical model. This model takes into account the precipitation and evaporation, the flux towards a deeper aquifer and flux to lateral open structures, with parameters for the different resistances and the storage. This model needs input data which is acquired from among others the KNMI (Koningklijk Nederlands Meteorologisch Instituut), with data about the groundwater level at the points of interest acquired from the measurements from the Water board Drenths Overijsselse Delta. The input from the model can be used to generate predictions, whilst the measurement data can be compare with the predictions to obtain more accurate predictions and calibrate the parameters in the model. Combining these factors can be done with the Kalman Filter, a mathematical tool from Data Assimilation which can be used to combine a Mathematical Model and Data into an optimal estimate. Furthermore, it is the wish to improve the parameters in the mathematical model, this causes the state to expand thereby enlarging the problem, and the parameters included in the state causes the problem to become non-linear. The Kalman Filter is only suitable for small linear models but an extension of the regular Kalman Filter can account for these problems, the Ensemble Kalman Filter. To apply all this information for groundwater modeling in a single location, first the numerical errors associated with the different model solutions are tested. It was found that a semi-analytical solution which assumed the input to stay constant over a day to produce the best result. After this the Kalman Filter is compared with the Ensemble Kalman Filter to see whether the Ensemble Kalman Filter can perform comparably in state estimation, it was found that en ensemble size of $n = 200$ this was the case. To test if the parameter calibration scheme works as desired and to test the quality of the parameters found, artificial data is created using the model with all parameters set to one. Then, the parameters are shifted to a different value and the parameter Ensemble Kalman Filter is used to try to find the original parameters back. It is found that in almost all cases the parameter calibration cause the parameter to change in the direction of one, within the first 2/3 months most change within the parameter takes place and the standard deviation of the parameters decreases. After this initial period the parameter remains more stable and the standard deviation changes little. Since the model uses multiple parameters for the resistances, the possibility of calibrating these separately was investigated. It was discovered that in the data usually one resistance parameter is lot smaller than the other, it was enough to calibrate only this parameter to account for the resistance. After this, the parameters in the model are calibrated with actual data. The model always becomes a lot closer to the measurements, and interestingly all parameter become larger than 1. Finally the quality of the predictions is tested. Here we saw that the quality improved fast, already 1/3th year was enough to find parameter far better than originally.

In recent years many automatic differentiable programming frameworks have been developed in which numerical programs can be differentiated through automatic differentiation (AD). Examples of these frameworks are Theano, TensorFlow and Pytorch. These frameworks are widely used in Machine Learning. AD also finds applications in the field of computational fluid dynamics (CFD). It is used to develop discrete adjoint CFD code for research concerning for instance sensitivity analysis, data assimilation and design optimization. However, the use of the automatic differentiable programming frameworks in the field of CFD is limited. One can find some examples in the literature on how to find a numerical solution to an initial value problem using a differentiable programming framework. In this work it will be clarified how one can implement an semiimplicit
time integration scheme for a staggered grid to simulate the propagation of long waves in water with a free surface in TensorFlow. A main advantage of the automatic differentiable programming frameworks is the user friendly application
programming interface (API) for AD. No research has been conducted to use this API in the field of CFD. In this work an example will be given how one can use TensorFlow for research concerning sensitivity analysis. AD requires a significant allocation of memory on a CPU/GPU when working with fine meshes and/or long simulations and since CPU/GPU memory is finite, the method checkpointing is
proposed to make it feasible to perform sensitivity analysis when working with fine meshes and/or long simulations. Another main advantage of the differentiable programming framework TensorFlow is the use of compute unified device architecture (CUDA) of a NVIDIA GPU in order to perform computations in parallel, which results in a significant reduction in computation time. A Benchmark will be given that indicates the computational efficiency of TensorFlow compared to a loop over grid implementation in NumPy and a Fortran CPU scalar implementation.

In the ocean resides a large amount of plastic. This has severe environmental consequences for the oceans. To be able to clean up all this plastic the location of the plastic is needed. A lot of times plastic is cleaned up at the source, but to clean up here this location needs to be known. However, what if the start location is not known and only the end location is known. This thesis looks at the following research question: Can the method of particle filtering be used to find the start location of a plastic particle of which the end location is known?. The method of particle filtering compares the end locations of the released particles and the end location of the end particle. (The end particle is the particle of which the end location is known and we want to know the start location.) The method calculates weights on the basis of this comparison for each of the released particles. Then the weights are used to calculate a probability density function that gives the likelihood of possible start locations being the right start location of the end particle. The method is applied to the MSC Zoe case, which is a container accident, and a simplification of this case. The MSC Zoe lost in this accident hundreds of containers above the Wadden Islands in the Netherlands, in these containers were bags of plastic particles. A lot of these particles washed ashore on the Wadden Islands. However, it is not known exactly where all the containers fell overboard. So the start location of the plastic particles that washed ashore is not known. The method of particle filtering applied to the simplification showed that it can indeed be used to find the likelihood of possible start locations. However, it also showed that for some values of the variables it was possible to get multiple peaks with weights that are zero in between. This is not a desired outcome for a probability density function (pdf). So a kernel estimation is used to smooth out the pdf's. It uses the weights calculated in the method of particle filtering to estimate the pdf. This gives results that also in this way the likelihood of possible start locations can be found and now without multiple peaks. The kernel estimation was also applied to the MSC Zoe case and the results were calculated for multiple end particles. The locations that came out of this were very close to a few of the possible main locations were containers fell overboard. These possible main locations came from the international investigation into the MSC Zoe accident. A simplification of this research is that the start location is found for one specific plastic particle. For future research it could be interesting to look if the method can be adapted to find the start location of concentrations of plastic particles.

Processes occurring in the near-shore region operates on a small spatial and temporal scale. Simulations of these processes have long posed challenges for computational science, and to have accurate representations require a higher resolution. This results in computationally expensive models. This project aimed to investigate the possibility of a new stochastic model, simulate these processes with higher computational efficiency, and estimate the energy density and spectral properties of waves in the near-shore region. The gist of the particle model is to discretize the energy flux into several packets of finite energy, propagating in the domain, and governed by the equations derived from the wave dynamics. These particles correspond to a particular wave component at a particular location and, therefore, are defined by these wave properties. The equations of particle motion are derived from the wave dynamics by treating energy density as probability density and the energy balance equation as a Fokker-Planck equation while the energy dissipation is modelled with exponential decay of particle energy with a location-dependent rate. An iterative approach is taken to accommodate the dissipation processes resulting from the wave interactions. These particles were treated as independent to create prospects of asynchronous computation and providing the scope of computational optimization. The phenomena of shoaling, refraction, bottom friction, and depth-induced surf breaking are included in the implementation for both monochromatic waves and irregular waves described by a two-dimensional wave spectrum. The model is tested for its performance and accuracy by comparing with the estimations from other existing models. The ability to provide control over processes in computations made SWAN a perfect candidate as a benchmark. The results showed a high degree of accuracy on comparison while the computational time was of the same order or lower to that of the SWAN model for most of the cases with a great scope of improvement. It was also observed that high computational efficiency could be achieved by sacrificing little accuracy. Additional dominant processes were identified affecting the accuracy in certain conditions by comparing the model with lab measurement data. Non-linear wave-wave interactions play an important role in the evolution of the spectrum, while diffraction becomes dominant for the flow over a shoal in two-dimension. These processes are considered as future scope of the project. The results show that with a stochastic model, it is possible to simulate real-life situations and does need further development to include additional processes and make the model computationally robust.

Satellite altimetry is an important technology used to measure sea level with high spatial and temporal resolution. Sentinel-3, a Copernicus satellite mission, offers three types of variables captured simultaneously for the first time; sea level (SSH), sea surface temperature (SST) and ocean colour (OC) variables. Sea level is measured with SAR altimetry, a technique that considerably increases spatial resolution compared to other means of observation. Altimetry measures sea level across a line that coincides with the satellite ground track, whereas SST and OC are measured on a grid. What we lack are sea level observations in-between ground tracks that would better resolve meso-scale variability. This thesis is focused on two objectives, considering previous work that has indicated associations between those variables. The first objective was to investigate the correlations among SSH, SST and OC, while the second objective was to assess to what extent inter-track sea level can be estimated using SST and OC as predictors in machine learning algorithms. Daily Sentinel-3 data over a period of eleven months were pre-processed and brought into a form that allowed for computation of metrics such as auto- and cross-correlations in the along-track direction. The focus was on the spatial scales that would enable to detect meso-scale features, such as eddies. With respect to the inter-track sea level estimation two paths were followed. In the first path, Random Forest (RF) and Multilayer Perceptron (MLP) were applied using the complete 11-month dataset as input. Moreover, RF was applied on input data that belong to each separate day. In the second path, 1D Convolutional Neural Network (CNN) was used on the complete 11-month dataset, which inherently honors the spatial dependency of the variables in contrast to the first path. Generally, the correlations between the variables were found to exist in the meso-scale but were not always strong and they depend on several other factors, such as meteorological conditions, scales included in the analysis and techniques used. All three techniques -RF, MLP and 1D CNN- that were applied on the complete 11-month dataset gave poor results. On the contrary, when RF was applied on the per-day data gave promising results that are reliable mostly in the vicinity of the ground track, although they are not based on one single global model. The results from this project suggest that there must be more research on the correlation analysis of Sentinel-3 data. It can be improved by using additional or similar techniques, such as localized cross-correlation metrics on various spatial scales. With respect to the inter-track sea level estimation, far more investigation is needed. However, there are indications that a machine learning data-driven approach could potentially work to some extent. Sentinel-3 data will become more abundant in the next years which will assist data science algorithms such as CNNs which require huge datasets.

This thesis introduces a new algorithm for optimising shipping routes within a dredging project. Highly dynamic and time-dependent hydrodynamic features influence shipping routes. Due to the complex interactions between the horizontal tide, vertical tide, stratifying forces, wind-driven forces, and limited water-depth, shipping routes were previously only optimised for large scale routes (order of 1000 km). This study presents an algorithm that can optimise shipping routes that are influenced by these small scales (order of 10 km) hydrodynamic features. This algorithm uses graph theory to solve for the time-dependent fastest path between start and destination. Graph theory searches for the optimal path through a set of nodes that are connected with edges. This study uses the time-dependent shortest path algorithm which accounts for the FIFO-criteria (Waiting criteria) and can solve the non-convex nature of the problem

The input of this algorithm is a hydrodynamic model. These models are Computational Fluid Dynamic (CFD) models that calculate currents and water levels in a specific domain. The domain is discretised into cells and nodes to calculate these hydrodynamic features. This study uses the nodes of this hydrodynamic model as the vertices of the graph. However, for some cases, the hydrodynamic model has too many nodes for the shortest path algorithm. This study presents a method for reducing the number of nodes without reducing the spatial resolution. The nodes are reduced based on a combination of the vorticity and the magnitude of the flow.

This algorithm is implemented in a python software package named Hydrodynamic Algorithm for Logistic enhancement Module (HALEM). HALEM can determine the optimal shipping route for a given hydrodynamic model. Defining different cost functions results in different optimisation purposes. This thesis presents cost functions for the fastest route, shortest route, cheapest route and least polluting route. This software is then implemented in the OpenCLSim software so that this combination of software can optimise routes of entire projects. A case study simulates a beach-nourishment at Schouwen Westkop Noord to demonstrate the practical use of HALEM and OpenCLSim. For this project, 425,500 m3 sand should be dredged offshore and pumped onto the beach. Due to the narrow gullies and tidal changes in hydrodynamic features, the routes were hard to predict. The simulation with HALEM and OpenCLSim shows an increase in the production with 21 % compared to the simulation with just OpenCLSim.

Dit onderzoek bestudeert het energieverlies van het barotroop getij aan de opwekking van intern getij. Dit energieverlies vindt plaats bij stroming van de gestratificeerde oceaan over steile topografieën, zoals ruggen in de oceaan en bij de randen van continentale platen. Zo'n 25-30% van de totale getij-energie, die wordt opgewekt door de zon en de maan gaat zo verloren.

In een wereldwijd getijmodel wordt alleen het dieptegemiddelde gedrag van de getijstroming beschouwd, waardoor de opwekking van intern getij niet expliciet gemodelleerd kan worden. Om het effect daar wel in mee te nemen, wordt het verlies van barotroop getij aan de opwekking van intern getij geparametriseerd aan de hand van variabelen, die in dat model wel meegenomen zijn.

Het onderzoek is numeriek uitgevoerd met het hydrostatisch oceaanmodel Delft3D-Flexible Mesh. In het 3D model is expliciet de opwekking van intern getij gesimuleerd en vergeleken met analytische resultaten voor de opwekking van intern getij. Daarnaast zijn deze resultaten gebruikt om de huidige geïmplementeerde parametrisering, van de opwekking van intern getij, in het 2D model te toetsen.

De expliciete simulering van de opwekking van intern getij in Delft3D-FM is succesvol gedaan. Het energieverlies van barotroop getij aan de opwekking van intern getij was in overeenstemming de literatuur. Voor smalle topografieën hoger dan (ongeveer) een halve oceaandiepte lijkt de hydrostatische aanname in het model te worden overschreden waardoor numerieke dissipatie van intern getij optreedt.

De huidige geïmplementeerde parametrisering van het verlies van barotroop getij aan de opwekking van intern getij is voor een beperkte verzameling topografieën en stratificaties getest. De resultaten geven indicaties, dat de huidige parametrisering niet in staat is om de conversie over een breder scala van topografieën in de oceanen goed te benaderen. Het voorspelbare gedrag van de conversie voor steile, superkritische topografieën wijst erop dat zo'n parametrisering wel mogelijk is.

Aanbevelingen voor verder onderzoek zijn het uitbreiden van het gebruikte model met stromingen in x- en y-richting en het effect van de Coriolis parameter. Om de parametrisering beter te testen kan het bestaande model op meer verschillende typische topografieën en stratificaties in de oceaan worden toegepast.

Globally, at each river mouth freshwater is discharged to coastal waters. At each river mouth a freshwater plume is formed. These fresh water plumes are also known as the regions of freshwater influence (or ROFI’s). Furthermore, the freshwater plume will affect local coastal water levels. In order to improve global flood forecasting, research on this topic has been conducted. Through a combination of numerical (DFlow-fm) and probabilistic (vine copula) models predictions can be made for the size- and hydraulic effect of these river plumes.

Plastic pollution is a big problem all over the world. Every year more plastic is produced, a lot of plastic litter is mismanaged and enters the ocean. It’s important to know where these plastics accumulate. With this information the problem can be quantified and the plastic litter can be cleaned up. In this project, the transport of micro plastics will be studied. These are plastic particles with a diameter smaller than 5 mm.

To model micro plastics in an accurate way, it is important to include the physical properties of plastics in a transport model. Plastic particles have an extra upwards buoyancy force in the vertical direction, this force has to be taken into account in the model. Therefore, the two-dimensional vertical behavior of plastic particles is studied in this project. Two common transport models are explored: the advection-diffusion equation and a stochastic random walk model. The properties of plastics are discussed and how the transport models can be adapted to be adequate to model micro plastics.

Micro plastics are assumed as spheres in fluid. With this assumption, the flow regime around a plastic particle is estimated with the Reynolds number. These assumptions make it possible to calculate a terminal buoyancy velocity, due to the floating character of plastic. This velocity is added in the vertical direction to
both transport models. To model the turbulence in the ocean, the eddy diffusivity coefficient is defined. This is a variable that states how turbulent the flow is, it can be described as an enhanced diffusion coefficient. The eddy diffusivity coefficient can be estimated with the model Prandlt defined. Here we used a simplified turbulence model for the tests described. In combination with Delft3D-FM the eddy diffusivity from the turbulence model in there can be used.

Both models are implemented in Matlab. The characteristics of the model match with the expected behavior of floating plastics. Plastic particles will perfectly follow the velocity field, except for the extra vertical velocity. When this term is non-zero, the particles will float. Both models have some limitations in efficiency
for modeling plastic particles. The advection-diffusion equation is not suitable for high concentration gradients. The random walk model is not suitable for big areas or long timescales. The choice between both models is depending on the sort of case that someone wants to model.

This project has been carried out at Deltares, an independent water research institute. At Deltares there is a two-dimensional horizontal model available to model particles in the ocean. In the future the existing model of Deltares and the model in this project could be combined. This combined model can be tested for
real-life situations in the ocean. With this combined model, the physical properties of plastics are included in a three-dimensional particle model.