On the Evolution of Beach Shoreline According to Equilibrium Profile

Shoreline position is a key parameter of a beach state, used as a descriptor of the system response to changes in external forcings, such as sea-level rise. Changes in shoreline position are the result of hydro- and morphodynamic processes taking place in the nearshore, including feedback mechanisms. Due to this complexity, state-of-the-art methodologies aimed at reproducing the variability of the shoreline are based on several assumptions that simplify the problem. One of the most widespread methods uses a beach equilibrium profile whose shape depends only on the beach morphology (i.e., beach slope, berm) and whose location varies with sea level. Here, we derive a general equation for shoreline evolution using the equilibrium profile, and we use it to evaluate the contribution of sea-level rise to shoreline evolution under wave forcing. We also provide analytical closed-form expressions to this shoreline evolution for a 2/3-power curve equilibrium profile and for three different probability distributions of breaking wave height (corresponding to three different families commonly used to describe wave climate). Our general equation is a step forward in the computation of shoreline evolution assuming a realistic equilibrium profile (described by a range of arbitrary parameters). When used to analyze the effects of sea-level rise, it is not constrained to sea-level rises small compared to the berm height. We also provide a novel and easy way to integrate it.