A nonlinear, implicit one-line model to predict long-term shoreline change

We present the formulation, validation, and application of a nonlinear, implicit one-line model to simulate long-term (decadal and longer) shoreline change. The purpose of the implicit numerical method presented here is to allow large time steps without sacrificing model stability compared to explicit approaches, and thereby improve computational efficiency. The model uses a Jacobian-free Newton-Krylov solver to compute the solution to the governing equations, i.e. the shoreline position. The model is validated against an analytical solution for alongshore shoreline diffusion. The model is applied to simulate a decade of observed shoreline change at Ocean Beach (2004-2014). When wave transformation is included (implemented via SWAN and a look-up table) there is a 100% increase in the number of profiles where erosion or accretion is correctly predicted.