Wavelet analysis of shoreline change on the Outer Banks of North Carolina: an example of complexity in the marine sciences.

The horizontal, shore-perpendicular change in shoreline position along the Outer Banks of North Carolina is found to be a self-affine signal. We measure shoreline change by determining the horizontal change in position of the 0.8-m contour sampled from shore-perpendicular profiles spaced at 20-m intervals along the coast. The profiles are obtained from two light detection and ranging surveys performed in September 1997 and September 1998. For six selected sections of coast, wavelet analysis of the shoreline change signal indicates the signal is self-affine with a scaling exponent that varies from 1.2 to 2.1. This self-affine behavior indicates that the shoreline change signal is nonstationary with long-range persistence. A stochastic diffusion model of sediment transport replicates the observed self-affine behavior observed south of Cape Hatteras (scaling exponent between 1.2 and 1.6) whereas a random walk model replicates the signal observed north of Cape Hatteras (scaling exponent approximately 2.0). Because of the finite nature of the data set, there are limits in space and time to the power law behavior of the system. Characteristics of such systems can be described by upper-truncated power laws, which yield the upper limits of power law behavior. Applying an upper-truncated power law to the data for one section of coast, we find an upper limit of 7 km for the maximum continuous alongshore distance eroding or accreting. For the same section of coast, we find upper limits of 25 m for the maximum shore-perpendicular erosion and 11 m for the maximum shore-perpendicular accretion during the study period.