The signal of shoreline change for the Outer Banks, North Carolina is non-stationary. A baseline, west of the first line of dunes, is created for each 5 km section and shore-perpendicular profiles constructed every 20 meters in the alongshore direction. The profiles are obtained from two light detection and ranging (LIDAR) surveys performed in June 22, 2006 and July 7 and 8, 2007.
For five selected sections of coast, Fourier analysis of the shoreline change signal indicates the signal is self-affine i.e. the mean is not stationary, but changes with position along the signal (Malumud and Turcotte, 1999) with a scaling exponent that varies from 1.2 to 2.1. Four of the five selected sections of coast, Wavelet analysis of the shoreline change signal indicate the signal is self-affine with a scaling exponent that varies from 1.4 to 2.3.
The power scaling exponents extend over three orders of magnitude in length from 0.1 to 10 km.
The values of the power scaling exponent (greater than 1) indicate that the signal has no characteristic length scale and is non-stationary as the power scaling increases, low-frequency (high period) contributions dominate over high-frequency (low period) contributions. The range in power scaling exponents indicates that abrupt changes in shoreline position are less common than gradual changes over long distances (Malamud and Turcotte, 1999).