HR: 14:55h
AN: NG12A-06 INVITED     [PDF]
TI: An Approach for Forecasting Shoreline Stability Based on Fractal Persistence
AU: * Barton, C C
EM: barton@usgs.gov
AF: U.S. Geological Survey, 600 4th St., South, St. Petersburg, FL 33701 United States
AU: Tebbens, S F
EM: tebbens@marine.usf.edu
AF: College of Marine Science, University of South Florida, 140 7th Ave., South, St. Petersburg, FL 33701 United States
AU: Burroughs, S M
EM: sburroughs@ut.edu
AF: Department of Chemistry and Physics, University of Tampa, Tampa, FL 33606 United States
AU: Morton, R A
EM: rmorton@usgs.gov
AF: U.S. Geological Survey, 600 4th St., South, St. Petersburg, FL 33701 United States
AU: Dismukes, J S
EM: jdismukes@usgs.gov
AF: U.S. Geological Survey, 600 4th St., South, St. Petersburg, FL 33701 United States
AB: Persistence is a fractal measure of the degree of internal correlation in the stochastic portion of a self-affine time series. We use persistence to characterize internal correlations between shoreline positions and then to forecast a probability envelope bounding future shoreline positions. The envelope is the standard deviation determined as a function of three variables: the number of time increments, N; the activity level determined from the power spectral density; and persistence. The persistence of a 20-year time series of the mean-high-water (MHW) shoreline positions is calculated for four profiles surveyed by the U.S. Army Corps of Engineers at the Field Research Facility (FRF), Duck, NC. The four MHW shoreline time series signals are nonlinear and self-affine with persistence values ranging between 0.8 and 0.9, which indicates that the shoreline position is weakly internally correlated, slightly non-stationary, and has highly varying trends at all time scales sampled. Forecast envelopes based on the 20-year record are extrapolated to 50 years from the start of the record. The forecast envelopes are controlled by the persistence and activity level measured from the 20-year time series and by the initial shoreline position. The forecasts describe the 20-year data sets well and indicate that within a 96% confidence envelope, future decadal MHW shoreline excursions should be within $\mp$ 14.6m of the initial position in 1981. We also applied the traditional method of characterizing and forecasting future positions by fitting linear trend lines to the historic shoreline positions and extrapolating to forecast future positions. The traditional method results in a linearly increasing mean that breaks the envelope eight years into the future and continues to increase, forecasting net accretion indefinitely into the future for a shoreline that has been oscillatory-stable for the past 150 years. We find the traditional method to be a poor representation of the observed pattern of change in shoreline position and a poor basis for extrapolating future shoreline positions.
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3220 Nonlinear dynamics
DE: 4546 Nearshore processes
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting