Parametric wave growth in a frequency integrated wave model

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Waves in coastal waters play a role in forecasting storm conditions, as boundary conditions for the assessment of coastal risk and in coastal structure design. Assessment of their impact can be made through numerical modeling. In a forecasting context, the CPU time of the wave model is decisive in its suitability. Recent years wave model approaches have been to describe both linear and non-linear generation, dissipation and transfer processes in the wave spectrum explicitly. This resulted in computationally demanding tools. Such models are very suitable for research purposes or for design and assessment if time is available, but are rather heavy tools for forecasting applications on larger scales. Parametric models describe the wave spectrum through characteristics in a smaller solution space compared to spectral models, which makes them potentially faster solvers. In this thesis the suitability for forecasting of a spectrally integrated approach to the wave action balance is investigated. The stationary wave drivers from the storm impact assessment model XBeach were taken as a starting point. A second balance equation was identified to model the evolution of the mean period. In estuaries and behind shoals, locally generated waves can be dominant over offshore wave conditions. As part of the project, a wave generation mechanism is developed for the modified wave drivers based on prediction relations for growth of wind-waves under fetch-limited conditions. The two-equation approach was discretized and tested in a 1D Matlab model and the solution was proven to converge towards the literature prescribed growth curves for total wave energy and mean wave period. This approach was then implemented in the unstructured Frequency Integrated wave drivers in D-Flow FM. The implementation has been verified through semi-1D test cases and showed convergence behavior equal to the Matlab model. A hindcast of a 1982 storm in the Haringvliet was performed to compare the model skill of the unstructured frequency integrated model (FIM-FM) to the spectral wave model SWAN. In this hindcast the model skill of FIM-FM is comparable to SWAN for significant wave height and mean wave period for all locations apart from directly behind a shoal. Depth and wave height dependence of bottom friction coefficients should be studied in more validation cases to improve the prediction of wave steepening over shoals. Further research should also look into the iterative method in the solver for stationary solutions of the model equations to realize faster CPU time of a stationary problem. Although not established in this thesis, faster CPU time compared to a spectral model like SWAN should be possible based on the reduction of the solution space.