Unraveling the dynamics that scale cross-shore headland relief on rocky coastlines: 1. Model development

We have developed an exploratory model of plan view, millennial-scale headland and bay evolution on rocky coastlines. Cross-shore coastline relief, or amplitude, arises from alongshore differences in sea cliff lithology, where durable, erosion-resistant rocks protrude seaward as headlands and weaker rocks retreat landward as bays. The model is built around two concurrent negative feedbacks that control headland amplitude: (1) wave energy convergence and divergence at headlands and bays, respectively, that increases in intensity as cross-shore amplitude grows and (2) the combined processes of beach sediment production by sea cliff erosion, distribution of sediment to bays by waves, and beach accumulation that buffers sea cliffs from wave attack and limits further sea cliff retreat. Paired with the coastline relief model is a numerical wave transformation model that explores how wave energy is distributed along an embayed coastline. The two models are linked through genetic programming, a machine learning technique that parses wave model results into a tractable input for the coastline model. Using a pool of 4800 wave model simulations, genetic programming yields a function that relates breaking wave power density to cross-shore headland amplitude, offshore wave height, approach angle, and period. The goal of the coastline model is to make simple, but fundamental, scaling arguments on how different variables (such as sea cliff height and composition) affect the equilibrium cross-shore relief of headland and bays. The model's generality highlights the key feedbacks involved in coastline evolution and allows its equations (and model behaviors) to be easily modified by future users.