Accuracy of shoreline forecasting using sparse data

Sandy beaches are important resources providing recreation, tourism, habitat, and coastal protection. They evolve over various time scales due to local winds, waves, storms, and changes in sea level. A common method used to monitor change in sandy beaches is to measure the movement of the shoreline over time. Typically, the rate of change is estimated by fitting a linear regression through a time series of shoreline positions. To best manage the valuable resources within a coastal environment, accurate forecasts of shoreline position are needed. A simple way to estimate future shoreline position is to extrapolate a linear regression into the future, this method is often used to establish management guidelines like construction setback lines. A more recently developed shoreline forecasting technique utilizes the Kalman filter to assimilate shoreline data and modify the linear regression. This paper calculates the uncertainty and accuracy of both the extrapolated linear regression and Kalman filter forecasting methods for 10- and 20-year hindcasts using data collected at five diverse study areas. These data are inherently sparse (8–10 measurements per location, collected over 150 years) and are representative of the observed historical data available for the continental United States for this timeframe. Both methods produced similar results and had regionally averaged forecast accuracies of 5–16 m. We determined that the inaccuracy of the forecasts is largely due to the effects of shorter time scale variability. This variability is roughly proportional to the standard error of the linear regression, which is a useful measure of forecast uncertainty.