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Two‐dimensional discrete Fourier transform analysis of karst and coral reef morphologies


Transactions in GIS

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Fourier transforms have been used in the analysis of landscapes that exhibit the influence of cyclic structures or other morphogenetic controls. Two‐dimensional Fourier transforms have been most successful when modeling features with a high frequency over the sample space. This research focuses on applications of 2D discrete Fourier transforms for karst and spur and groove coral reefs, using ArcGIS geoprocessing tools extended with Python NumPy numerical methods. Ten‐meter digital elevation data from Puerto Rico and Kentucky holokarst landscapes and five‐meter bathymetry from more unidirectional spur and groove coral reefs at Midway Atoll were analyzed. Our method identifies the dominant contributing waves in frequency space, and analyzed power contributions by 5° and 15° azimuth bins. A limiting factor in this analysis is the spatial extent of consistent morphology in the landscape. In contrast to time‐domain Fourier analysis, dominant landform frequencies can thus be of low magnitude, creating an imprecise estimate of wave morphometry and direction since this is derived from the combination of inverted x and y frequency values, and the limited frequency grain inherent in the discrete model degrades precision in the solution. Simulated karst and spur & groove landscapes were used to evaluate the grain of waveform orientation solutions.