Shoreline data analysis

Abstract

In this dissertation, shoreline response to a storm is investigated, and two new empirical models for shoreline position change, over timescales of decades to centuries, are developed and compared with earlier empirical models. The new B-spline method and regularized-ST method avoid over-fitting of data, as predictions of future shoreline position can be wildly inaccurate if based on models that over-fit. They utilize a nondiagonal data covariance matrix, with correlations estimated from the data residuals, in order to carefully estimate the uncertainty of predictions, because uncertainty is as important to shoreline managers as the predictions themselves. The first part of the dissertation investigates storm behavior at Assateague Island, MD. Earlier work showed that inclusion of a transient storm function improved statistical modeling of historical shoreline data. Here, it is found that the shoreline response to a storm has not only a transient component, as in our earlier work, but also a persistent component, and that both are required to fit the data. The B-spline and regularized-ST methods focus on reducing model parameters in the alongshore direction. The traditional single transect (ST) method uses far more parameters than necessary because it assumes that long-term erosion/accretion varies independently at each alongshore location. The new models give shoreline change rates that vary more smoothly alongshore than ST rates do, but are generally consistent with rates from prior studies. Both new models successfully address problems with earlier models, notably Gibbs effect with polynomial basis functions and noise contamination with principal component basis functions.