Anderson, T.R. and Frazer, L.N., 2014. Toward parsimony in shoreline change prediction (III): B-splines and noise handling.
The traditional single-transect method for predicting long-term shoreline change uses far more parameters than necessary because it assumes that erosion/accretion (change) rates at adjacent alongshore positions (transects) are independent. Such overfitting can cause poor predictions of future shoreline location, so recent work has modeled change rates as linear sums of polynomials, or linear sums of principal components. Here we introduce an alternative method that uses linear sums of B-splines. As in earlier work, an information criterion is used to identify the optimal number of basis functions. The local nature of B-spline models makes them less susceptible to the Gibbs effect than polynomial models, and their smoothness makes them more robust to noise than principal components regression. We also compare three noise-handling techniques by examining their effects on the posterior probability density functions of rates. We find that noise handling affects both predicted rate and its uncertainty, and that correlated noise is best addressed by iteratively constructing a full covariance matrix from data residuals. We illustrate our procedure using synthetic data and shoreline data from Assateague Island and Ocean City, Maryland.