Due to the fractal nature of the domain geometry in geophysical flow simulations, a completely accurate description of the domain in terms of a computational mesh is frequently deemed infeasible. Shoreline and bathymetry simplification methods are used to remove small scale details in the geometry, particularly in areas away from the region of interest. To that end, a novel method for shoreline and bathymetry simplification is presented. Existing shoreline simplification methods typically remove points if the resultant geometry satisfies particular geometric criteria. Bathymetry is usually simplified using traditional filtering techniques, that remove unwanted Fourier modes. Principal Component Analysis (PCA) has been used in other fields to isolate small-scale structures from larger scale coherent features in a robust way, underpinned by a rigorous but simple mathematical framework. Here we present a method based on principal component analysis aimed towards simplification of shorelines and bathymetry. We present the algorithm in detail and show simplified shorelines and bathymetry in the wider region around the North Sea. Finally, the methods are used in the context of unstructured mesh generation aimed at tidal resource assessment simulations in the coastal regions around the UK.
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