Abstract: Coastal erosion is a major problem for shorelines everywhere in the world. In order to mitigate beach stability problems it is necessary to determine the equilibrium shape of the beach planform. Current equilibrium planform shape equations are only valid under certain simplifications; for instance, they are unable to predict the effect of nearshore islands and/or rocky bottoms, as well as the effect of several diffraction points. The aim of this paper is to present a new process-based shape equation that is able to overcome those limitations and estimate the static equilibrium shoreline of complex bathymetry beaches. The equation is based on the hypothesis that a pocket beach gets its static equilibrium planform when the mean surf-zone longshore velocity averaged over a period of time is null () in every point along the beach. Based on this hypothesis, the direction of the shoreline that nulls the mean surf zone longshore velocity along the beach is evaluated. Therefore, the shape equation is based on the longshore current velocity formula. The new equilibrium shape equation is applied to two Spanish beaches, namely Milagro beach and Cala Millor beach. Milagro beach has a very smooth bathymetry and the parabolic shape equation developed by Hsu and Evans (1989) is able to predict the equilibrium shoreline. Cala Millor is more complex: it has some rock outcrops along the beach and the parabolic shape equation does not work. The equilibrium shape equation presented in this paper simulates the equilibrium shoreline of both beaches successfully with a high R2 (around 0.96) between the modelled shoreline and the real shoreline in both case studies.

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