Forecasting seasonal to multi-year shoreline change

Abstract

This contribution details a simple empirical model for forecasting shoreline positions at seasonal to interannual time-scales. The one-dimensional (1-D) model is a simplification of a 2-D behavioural-template model proposed by Davidson and Turner (2009). The new model is calibrated and tested using five-years of weekly video-derived shoreline data from the Gold Coast, Australia. The modelling approach first utilises a least-squares methodology to calibrate the empirical model coefficients using the first half of the dataset of observed shoreline movement in response to known forcing by waves. The model is then verified by comparison of hindcast shoreline positions to the second half of the observed shoreline dataset. One thousand synthetic time-series of wave height and period are generated that encapsulate the statistical characteristics of the modelled wave field, retaining the observed seasonal variability and sequencing characteristics. The calibrated model is used in conjunction with the simulated wave time-series to perform Monte Carlo forecasting of the resulting shoreline positions. The ensemble-mean of the 1000 individual five-year shoreline simulations is compared to the unseen shoreline time-series. A simple linear trend forecast of the shoreline position was used as a baseline for assessing the performance of the model. The model performance relative to this baseline prediction was quantified by several objective methods, including cross-correlation ( r), root mean square (RMS) error analysis and Brier Skill tests. Importantly, these tests involved no prior knowledge of either the wave forcing or shoreline response. The new forecast model was found to significantly improve shoreline predictions relative to the simple linear trend model, capturing well both the trend and seasonal shoreline variabilities observed at this site. Brier Skill Scores (BSS) indicate that the model forecasts based on unseen data were rated as ‘excellent’ (BSS = 0.83), and root mean square errors were less than 7 m (≈ 14% of the observed variability). The standard deviations of the 1000 individual simulations from ensemble-averaged ‘mean’ forecast were found to provide a useful means of predicting the higher-frequency (individual storm) shoreline variability, with 98% of the observed shoreline data falling within two standard deviations of the forecast position.