An Inverse Approach to Identifying Trends in Cross-Shore and Longshore Beach Behavior from Temporally Sparse Data

One-line models that are based on longshore sediment transport (i.e., Pelnard-Considère), account for alongshore continuity. Yet, can the shoreline change in a given area be explained entirely by longshore sediment transport, or is it necessary to invoke cross-shore transport? Here, we begin to address this question by using inverse methods and a statistical information criterion to select an optimal one-line model that is fitted to historical shoreline data.

Coastal processes occur over a wide range of temporal scales, and datasets that span multiple decades typically have poor temporal resolution (i.e., aerial images). To account for the sparse historical shoreline data, we constructed a simplistic shoreline change model to identify long-term behavior of a beach. Our one-line model combines a cross-shore rate to accommodate for cross-shore sediment transport with the classic Pelnard-Considère model for diffusion, as well as a longshore advection term. Inverse methods identify cross-shore rate, longshore advection, and longshore diffusivity down a sandy coastline. A technique using alongshore basis functions identifies shoreline segments where one parameter can account for cross-shore / longshore transport rates in that area. This yields model results with spatial resolution more appropriate to the temporal spacing of the data, and reduces overfitting. Because changes in historical data can be accounted for by varying degrees of cross-shore and longshore sediment transport (e.g., beach erosion can equally be explained by sand moving either off-shore or laterally), we tested a spectrum of model scenarios on the data: permitting only cross-shore sediment movement, allowing only longshore movement, and a combination of the two. The statistical information criterion determines the optimal spatial resolution and best-fitting scenario.