A simple equilibrium model for predicting shoreline change

Abstract

This contribution describes the development, calibration and verification of a 1-D behaviour-orientated shoreline prediction model. The model primarily encapsulates shoreline displacement forced by wave-driven cross-shore sediment transport. Hysteresis effects are shown to be important and are included in the model, whereby present shoreline change is influenced by past hydro-/morpho-dynamic conditions. The potential magnitude of shoreline change increases with incident wave power and the degree of disequilibrium. The latter disequilibrium term (Ωeq−Ω) is expressed in terms of the time-evolving equilibrium (Ωeq) and instantaneous (Ω) dimensionless fall velocities and dictates the direction of shoreline movement. Following Wright et al. (1985) the equilibrium fall velocity is defined as a function of the weighted antecedent conditions and is a proxy for the evolving beach state. The decay rate of the weighting function used to compute Ωeq is a model free parameter determined by calibration against measured data, which physically reflects the degree of observed ‘memory’ of the system. The decay in amplitude of this weighting function with time is controlled by a ‘memory decay’ term (ϕ), where the weighting reaches 10%, 1% and 0.1% at ϕ, 2ϕ and 3ϕ days prior to the current calculation time. The model is applied to two multi-year (6+ years) data sets incorporating hourly wave and weekly shoreline measurements, from two contrasting energetic sites in SE Australia. The first is the relatively dissipative, straight Gold Coast (QLD) and the second is a more intermediate embayed beach at Narrabeen (NSW). The model shows significant skill at hindcasting shoreline change at both sites, predicting approximately 60% of the total shoreline variability. The Gold Coast shoreline is dominated by a strong seasonal signal. Conversely, at the Narrabeen embayment, shoreline variability (and morphology) is more dynamic, responding at storm frequency. Evidence suggests that there is a strong coherence between the shoreline position and morphodynamic state and that both have response times characterised by ϕ. It is hypothesised that optimised ϕ values in the shoreline model physically relate to the efficiency of sediment exchanges between the shoreface and offshore bars and the prevalence of one- or two-dimensional horizontal circulation. The general success of this new shoreline model for hindcasting the observed shoreline behaviour at two distinctly different open-coast sites suggests that this approach may be suitable for broader application.