Field evidence of beach profile evolution toward equilibrium

An equilibrium framework is used to describe the evolution of the cross-shore profile of five beaches (medium grain size sand) in southern California. Elevations were observed quarterly on cross-shore transects extending from the back beach to 8 m depth, for 3–10 years. Transects spaced 100 m in the alongshore direction are alongshore averaged into nineteen 700–900 m long sections. Consistent with previous observations, changes about the time average profile in many sections are captured by the first mode empirical orthogonal function (EOF). The first EOF poorly describes sections with hard substrate (less than roughly 80% sandy bottom) and also fails near the head of a submarine canyon and adjacent to an inlet. At the 12 well-described sections, the time-varying amplitude of the first EOF, the beach state A, describes the well-known seasonal sand exchange between the shoreline and offshore (roughly between 4 and 7 m depth). We show that the beach state change rate dA/dt depends on the disequilibrium between the present state A and wave conditions, consistent with the equilibrium concepts of Wright and Short (1984) and Wright et al. (1985). Empirically determined, optimal model coefficients using the framework of Yates et al. (2009a, 2011) vary between sections, but a single set of globally optimized values performs almost as well. The model implements equilibrium concepts using ad hoc assumptions and empirical parameter values. The similarity with observed profile change at five southern California beaches supports the underlying model equilibrium hypotheses, but for unknown reasons the model fails at Duck, NC.