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This study developed a semi-empirical equilibrium-based shoreline change model, which was a nonlinear mixed-effect model allowing for random effects at equilibrium foreshore profiles. Using the model, the long-term uncertainties of equilibrium foreshore profiles, which were derived from such incompleteness of the model equation and latent variables unconsidered in the model were investigated. The model was applied to the longitudinal sandy beach profile data obtained at the Hasaki coast of Japan. The result showed that the uncertainties had the equilibrium foreshore profiles move parallel to the cross-shore direction, which resulted in foreshore deposition and erosion over several years and the slope of the equilibrium foreshore profile grew steeply with time by the uncertainties.

Uncertainty Estimation of Equilibrium Beach Profile by Nonlinear Mixed-Effect Model with Long-term Measured Data