Sarah F.Tebbens*^†, Stephen M.Burroughs*^‡, and Eric E.Nelson*

*College of Marine Science, University of South Florida, St. Petersburg, FL 33701; and ^‡Department of Chemistry and Physics, University of Tampa, Tampa, FL 33606

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 ˜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.

If one measures the length of a coastline by walking calipers along the coast and counting the number of steps necessary, the measured length increases as the opening of the calipers decreases (1, 2). The relationship between the number of steps and caliper width is a power law and the scaling exponent is the fractal dimension of the coastline (2). Although virtually all coastlines are fractal over some range of length scale, the change of shoreline position with time has not been previously examined. With the application of light detection and ranging (LIDAR) technology to surveys of coastal beaches, it is now possible to obtain high-resolution topography for hundreds of kilometers of beach in a single day. This article examines the pattern of shoreline change between two LIDAR surveys of the Outer Banks, NC collected in September 1997 and September 1998.

This work examines shoreline change along the Atlantic coast of the North Carolina Outer Banks from Cape Lookout to Oregon Inlet (Fig. 1). We divide the study region into three areas based on strike of the coast and dune stabilization history. Area 1 includes the region south of Ocracoke Inlet, which is nearly undeveloped with low-lying (generally less than 5 m) dunes and wide beaches. Areas 2 and 3 are north of Ocracoke Inlet. The dunes in areas 2 and 3 were actively stabilized by Works Progress Administration and Civilian Conservation Corps workers beginning in 1937 (3). A continuous vegetated line of dunes was created from Ocracoke inlet to the Virginia state line with dune heights ranging from 3 to 8 m and dune base widths of 25–100 m. The dunes were then planted with grass, trees, and shrubs. Stabilization efforts continued at irregular intervals throughout areas 2 and 3 until the mid-1970s (3). Since that time, stabilization efforts have decreased but have not completely stopped in the more-developed regions, particularly north of Cape Hatteras (area 3). Area 2 is the dune-stabilized region south of the bend at Cape Hatteras, where the coast strikes roughly northeast. Area 3 is north of Cape Hatteras, where the coast strikes roughly north-south.

During the study interval, there were five storms during which wave heights over 4 m were recorded at Diamond Shoals Light off Cape Hatteras (Fig. 1). In area 1, the dunes are sufficiently low-lying that the largest storm waves during the study interval apparently washed over the island (4). In areas 2 and 3, it appears that the largest storm waves reached the dunes and were reflected back toward the ocean (4).

This study examines LIDAR data collected by using the National Aeronautics and Space Administration (NASA) Airborne Topographic Mapper (ATM) as part of a collaborative project between NASA, the National Oceanographic and Atmospheric Administration, and the U.S. Geological Survey. The ATM can survey beach topography along hundreds of kilometers of coast in a single day with data densities that far exceed traditional survey technologies. Each swath is typically 375 m wide and continuous along the aircraft flight line. The aircraft pitch, roll, and heading were obtained with an inertial navigation system. The position of the aircraft was determined by using a kinematic global positioning system (5).

The LIDAR instrument transmits light to a target where it is reflected/scattered back to the instrument (e.g., ref. 6). The travel time is measured and used to determine the distance to the target, from which a topographic map can be created with a vertical accuracy of roughly 15 cm (7). The footprint of the laser is about 0.5 m, with a geographic (i.e., latitude and longitude) location accuracy of roughly 1 m (7).

In September 1997 and 1998, Airborne Topographic Mapper LIDAR surveys were conducted along major portions of the