A New Method for Predicting Shoreline Positions from Historical Data

Abstract

Shoreline rate-of-change values are routinely extrapolated into the future in order to predict the expected location of a shoreline. These rate values represent linear summaries of the processes, which have impacted the coast through time, as implicitly reflected in historical shoreline position/time data. The reliability of using linear methods for predicting future shoreline positions decreases for shorelines which behave in a nonlinear, cyclic, or chaotic manner. The goal of extrapolation is to provide the best estimate of future shoreline behavior as based on the past. Since the magnitude and direction of a long-term trend can be called into question by short-term changes, identifying the timing, persistence, and cause of a short-term change is critical for predicting a shoreline's future.

We have developed a robust linear prediction method in order to detect short-term changes in the long-term trend. This procedure identifies the linear or high-order polynomial model which best fits the data according to the Minimum Description Length (MDL) criterion. According to this method, however, only linear models are extrapolated for predictions. For non-linear models, the date at the most recent critical point is considered the approximate timing of a trend reversal. Two lines are used for extrapolation of non-linear models: One in which all pre-change data are weighted to zero i.e., old data are not believed to contribute useful information about the future) and one in which all pre-change data are assigned increasing weights (from 0 to 1) until a line is selected according to the MDL criterion. In the latter case, the old data are believed partially to contribute useful information about the future. By using a line or pair of lines for extrapolation, along with knowledge of the process-response system (if known), problems implicit in using non-linear models for predictions are avoided.

In our study, we have applied this shoreline prediction procedure to a segment of the Texas Gulf coast and the North Carolina barrier island system. Of the selected sample sites, 14% showed linear behavior according to the MDL criterion, 21% had a single change in the long-term trend (quadratic), and 65% displayed two major changes in the long-term trend (cubic).