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.