Shoreline Dynamics: Self-Affine Signals and Probabilistic Forecasts

Christopher C. Barton
U.S. Geological Survey

Sarah F. Tebbens
College of Marine Science, University of South Florida

Stephen M. Burroughs
Department of Chemistry and Physics, University of Tampa

The dynamics of the shoreline position at Duck, North Carolina generate a self-affine signal, a characteristic of scale invariant nonlinear systems. Persistence, a property of self-affine signals, is used to characterize internal correlations between historic mean-high-water (MHW) shoreline positions and to create forecast envelopes for probable future shoreline positions. We analyze 20-year time series derived from four transects surveyed by the U.S. Army Corps of Engineers at Duck, North Carolina. The spectral characteristics of the time series, including persistence and activity level, are determined using the Fast Lomb Periodogram. The four MHW shoreline position signals are self-affine with persistence, b, ranging between 0.8 and 0.9, indicating that each signal is stationary with weak internal correlation. This self-affine behavior indicates that changes in shoreline position arise from the collective random motion of sand grains. We use the self-affine properties of the historic record to forecast future shoreline behavior. This forecasting approach is in contrast to the traditional approach of extrapolating linear trend lines fit to historic shoreline positions, which assumes an underlying linear process with noise superimposed. Trend lines fit to the MHW shoreline signals vary depending on the subinterval considered, and therefore poorly characterize the signal and poorly predict future shoreline behavior. Using the parameters of the self-affine signal, we create forecast envelopes for probable future MHW positions. Forecast envelopes projected 50 years from the start of the record indicate that future shoreline positions will be within ±14 m of the mean MHW position of the 20-year record.

Created by Mathematica  (April 20, 2004)