Long-term Shoreline Position Prediction and Error Propagation

Abstract

Beach erosion necessitates forecasting future shoreline positions for effective coastal management. Simple forecast methods, such as end-point rate and linear regression have been proposed in the coastal literature and are widely used. However, the matter of the error of forecasts has largely been neglected. If measurement errors and a linear trend of erosion were the only factors determining shoreline position, making predictions of future shoreline positions and their associated confidence intervals would be easy using linear regression. Unfortunately, real and sometimes enduring fluctuations of beach width occur that are much larger than the measurement uncertainty. Wintertime fluctuations of up to several 10's of meters are well-known; most investigators for this reason do not use winter shoreline positions to study long-term shoreline behavior. An individual great storm can cause beach erosion amounting to scores of meters requiring a decade or more for recovery. Using shoreline position data in linear regressions without considering storm-caused erosion and subsequent beach recovery may yield inaccurate predictions of future position resulting from the underlying erosion, and greatly inflated estimates of uncertainty (e.g., 95% confidence intervals). A case study of shoreline position change in Delaware is presented to show how consideration of knowledge other than shoreline positions alone can lead to useful results for shoreline position forecast errors. It is also demonstrated that modern, more accurate survey measurement techniques can be helpful in improving the quality of forecasts even if the inherent variability of shoreline position indicators remains at the level of many meters.