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Fractal analysis of coastal drifter trajectories Mason, Edward Alexander


Surface drifter observations in coastal oceans display turbulence, but this turbulence often varies in space and it is difficult to attribute the levels of turbulence to different oceanographic processes by the typical means of studying ocean variability. In this study, I lean on an idea from chaos theory to characterise the different levels of turbulence observed, fractal dimension. Previous studies present many methods that can be used to determine fractal dimension of large-scale drifter tracks, here I present the three most popular in the literature on this matter. In this study, I first ask the question, which method is optimal for calculating fractal dimension? And secondly, I aim to determine what fractal dimensions can be expected of coastal drifter trajectories and how useful these quantities are for understanding ocean processes. To address these motivating questions, I first modify the three methods to better suit modern data (in which sources of uncertainty can play a big role) and test them on sets of known fractal dimension to determine their accuracy. Then I apply each method to drifter observations in three coastal ocean settings (the Salish Sea, the St. Lawrence, and the northern British Columbia ( BC ) continental shelf) and consider the magnitudes of fractal dimensions and how dimensions of differing magnitudes relate to different oceanographic/turbulent processes. The results of this study show that the box counting method is the most applicable method and that fractal dimensions computed by this method fall between 1 and 1.5, a range wider than those suggested by historical studies of large-scale processes. Finally, fractal dimensions are shown to be insightful metrics that can be used to determine the processes acting on the water but not in all cases. This work bridges the gap in knowledge between an historical technique and modern data, and provides scope for further exploration as to its applications.

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