A nonlinear model is developed to study the time-dependent relationship between the alongshore variability of a sandbar, a(t), and alongshore-averaged sandbar position, x_c(t). Sediment transport equations are derived from energetics-based formulations. A link between this continuous physical representation and a parametric form describing the migration of sandbars of constant shape is established through a simple transformation of variables. The model is driven by offshore wave conditions. The parametric equations are dynamically coupled such that changes in one term (i.e., x_c) drive changes in the other (i.e., a(t)). The model is tested on 566 days of data from Palm Beach, New South Wales, Australia. Using weighted nonlinear least squares to estimate best fit model coefficients, the model explained 49% and 41% of the variance in measured x_c and a(t), respectively. Comparisons against a 1-D horizontal (1DH) version of the model showed significant improvements when the 2DH terms were included (1DH and 2DH Brier skill scores were —0.12 and 0.42, respectively). Onshore bar migration was not predicted in the 1DH model, while the 2DH model correctly predicted onshore migration in the presence of 2DH morphology and allowed the bar to remain closer to shore for a given amount of breaking, providing an important hysteresis to the system. The model is consistent with observations that active bar migration occurs under breaking waves with onshore migration occurring at timescales of days to weeks and increasing 2DH morphology, while offshore migration occurs rapidly under high waves and coincides with a reduction in 2DH morphology.
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