Toward Parsimony in Shoreline Change Prediction (I): Basis Function Methods

Single-transect methods of shoreline change prediction are unparsimonious, i.e., they tend to overfit data by using more parameters than necessary because they assume that both signal and noise at adjacent transects are independent. Here we introduce some new methods that reduce overfitting by expressing change rate as a linear sum of basis functions. In the method of IC-binning, the basis functions are boxcars—an information criterion is used to assign contiguous alongshore locations into bins within which change rate is constant; the resulting rate is discontinuous but may be useful for beach management. In the polynomial method, the basis functions are polynomials in alongshore distance, and the change rate varies continuously along the beach. In the eigenbeaches method, the basis functions are the principal components of the matrix of shorelines. To choose the number of basis functions in each method, and to compare methods with each other, we use an information criterion. We apply these new methods to shoreline change on Maui Island, Hawaii, briefly here, and in more detail in a companion paper. The polynomial method works best for short beaches with rates that vary slowly in the alongshore direction while eigenbeaches works best for shorelines that are long, or have rates that vary rapidly in the alongshore direction. The Schwarz information criterion and the AICu version of the Akaike information criterion performed well in tests on real data and noisy synthetic data.