Toward Parsimony in Shoreline Change Prediction (II): Applying Basis Function Methods to Real and Synthetic Data

Abstract There is a need to supply coastal managers with statistically defensible hazard predictions that can be used to implement coastal setbacks and other management policies. The goal of this article is to evaluate the widely used single-transect method, as well as several new methods: t-binning, IC-binning, polynomial methods, and eigenbeaches, to identify which method(s) best predicts a 50-year eroded shoreline position. The polynomial and eigenbeach methods allow for acceleration (the rates vary with time). The methods are compared using data from nine beaches on Maui, Hawaii, and four sets of synthetic data. Evaluations of the methods are based on an information criterion, color maps of residuals, long-term (50 year) predictions, and cross-validating the most recent shoreline, which has a short-term span of 5–9 years. The newer methods identified significant rates at 74% of the transects, vs. 0% for single-transect on beaches in Maui, Hawaii. The cross-validation results showed that the polynomial and eigenbeach methods, without acceleration, best predicted the most recent shoreline. Contrary to the cross-validation results, synthetic results showed that the polynomial and eigenbeach methods with acceleration predicted the 50-year shoreline better than methods without acceleration. Nonacceleration methods predicted short-term positions better, and acceleration methods predicted long-term positions better. We conclude that the polynomial and eigenbeach methods improve the significance of the rates compared with the single-transect method.

[1]  L. Frazer,et al.  Toward Parsimony in Shoreline Change Prediction (I): Basis Function Methods , 2009 .

[2]  Robert Dolan,et al.  A new method for predicting shoreline positions from historical data , 1993 .

[3]  C. Fletcher,et al.  Longshore sediment transport rates on a reef-fronted beach: Field data and empirical models Kaanapali Beach, Hawaii , 2003 .

[4]  M. Gordon,et al.  State Coastal Program Effectiveness in Protecting Natural Beaches, Dunes, Bluffs, and Rocky Shores , 1999 .

[5]  M. Crowell,et al.  Long-term Shoreline Position Prediction and Error Propagation , 2000 .

[6]  R. Morton,et al.  Meso-scale transfer of sand during and after storms: implications for prediction of shoreline movement , 1995 .

[7]  Stephen P. Leatherman,et al.  Trends and Variability of Shoreline Position , 1998 .

[8]  Charles H. Fletcher,et al.  Mapping Shoreline Change Using Digital Orthophotogrammetry on Maui, Hawaii , 2003 .

[9]  A. McQuarrie,et al.  Regression and Time Series Model Selection , 1998 .

[10]  Bruce C. Douglas,et al.  Do Storms Cause Long‐Term Beach Erosion along the U.S. East Barrier Coast? , 2002, The Journal of Geology.

[11]  J. Rooney,et al.  Shoreline Change and Pacific Climatic Oscillations in Kihei, Maui, Hawaii , 2005 .

[12]  Charles H. Fletcher,et al.  The Predictive Accuracy of Shoreline Change Rate Methods and Alongshore Beach Variation on Maui, Hawaii , 2007 .

[13]  M. Fenster,et al.  Temporal analysis of shoreline recession and accretion , 1991 .

[14]  J. Rooney,et al.  A High Resolution , Digital , Aerial Photogrammetric Analysis of Historical Shoreline Change and Net Sediment Transport Along the Kihei Coast of Maui , Hawaii , 2008 .

[15]  Bruce C. Douglas,et al.  Considerations for shoreline position prediction , 1998 .

[16]  M. Crowell,et al.  Shoreline-position forecasting: Impact of storms, rate-calculation methodologies, and temporal scales , 2001 .

[17]  Bruce C. Douglas,et al.  On Forecasting Future U.S. Shoreline Positions: A Test of Algorithms , 1997 .