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

Abstract

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.

Alongshore variability in wave energy transfer to coastal cliffs

“…Klein and de Menezes, 2001;Sallenger et al, 2002;Bowman et al, 2009), which is also observed in numerical modelling studies of coastal change (e.g. Limber and Murray, 2011;Limber et al, 2014). Few studies, however, have examined the alongshore variability of wave energy transfer and erosion on low-sediment, rock coasts.…”

“…The focussing of wave energy and erosion around rock coastlines is controlled by prevailing wave and current directions (Carter et al, 1990), the availability and distribution of sediment (Sunamura, 1976(Sunamura, , 1982Limber and Murray, 2011), coastline planform and foreshore geometry (e.g. Klein and de Menezes, 2001;Bowman et al, 2009;Hapke et al, 2009;Limber and Murray, 2011;Limber et al, 2014), coastal bathymetry (e.g. Trenhaile, 1987;Komar, 1997), and relative rock strength and the resistance to wave energy transfer (Sunamura, 1977(Sunamura, , 1992.…”

“…Limber and Murray, 2011;Limber et al, 2014). In general, alongshore variations in shallow water bathymetry result in nearshore refraction of waves: the convergence of waves focuses energy onto headlands, and divergence disperses energy as waves enter bays (e.g.…”

“…Trenhaile, 1987;Komar, 1997). Wave energy transfer to the coastline is therefore determined by the degree to which the coastline projects seaward and is thus more exposed to incoming waves and greater energies (Carter et al, 1990;Limber et al, 2014).…”

Machine learning components in deterministic models: hybrid synergy in the age of data

“…An additional benefit is the direct coupling of models to data, especially valuable for exploratory models (Murray, 2003). Several studies have already used this approach, embedding machine learning components directly in models (e.g., Jain and Srinivasulu, 2004;Corzo et al, 2009;Limber et al, 2014) or during model calibration Hulscher, 2002, 2003;Ruessink, 2005). The focus of this article is on machine learning components that are directly embedded within physics-based models.…”