Forecasting Shoreline Position: A Method Based on Nonlinear Shoreline Dynamics
Sandy shorelines are mobile, and traditional methods for forecasting their future position are based on linear fitting and linear extrapolation of past positions. Analysis of twenty years of mean high water (MHW) shoreline positions along four shore perpendicular transects collected by the USACE at Kitty Hawk, NC shows that sandy shoreline movement is nonlinear with self-similar (fractal) scaling. Based on the observed shoreline dynamics, a new nonlinear forecasting model is developed and applied to forecast the limits bounding the Kitty Hawk, NC shoreline position three decades into the future. The forecasting method is based on creating probability envelopes to bound the MHW positions from the start of the data records forward fifty years. The probability envelope is the (+-) standard deviation as a function of three variables: a constant equal to the value of the power spectral density when 1/period equals 1, the number of time increments, and the power scaling exponent. The forecasts are consistent with the behavior observed in the twenty-year data sets and indicate that within a 96% confidence envelope, future MHW shoreline positions should be within 14.6 m of the starting position, i.e. this is a stable-oscillatory shoreline. The forecasting method incorporates the observed stochastic dynamics of the shoreline position. In contrast, the traditional forecasting method assumes a linear trend and ignores the inherent nonlinear dynamics in the data. The traditional forecasting method applied to these four time series projects a linearly increasing mean that breaks the probability envelope eight years beyond the data and continues to increase linearly, forecasting a strongly accreting shoreline.
Barton, C. C.,
& Tebbens, S. F.
(2010). Forecasting Shoreline Position: A Method Based on Nonlinear Shoreline Dynamics. Eos, Transactions.