Unraveling the dynamics that scale cross‐shore headland relief on rocky coastlines: 2. Model predictions and initial tests

Abstract

We explore the behavior of a theoretical model of cross-shore headland relief caused by alongshore differences in lithology and rock strength on rocky coastlines. Results address the question of why some rocky coasts exhibit frequent headland and embayment sequences while others evolve to a flat, smooth, and sandy configuration. Main model predictions are that cross-shore headland amplitude is inversely proportional to beach sediment supply and the strength of wave energy convergence and divergence along the headland and bay, and proportional to the alongshore embayment length (or distance between headlands) and the difference between headland and bay rock strength. The coastline's initial physical properties (sea cliff height, composition, etc.) largely determine whether headlands will be persistent or transient landscape features. Model timescales over which the headland and bay reach steady state amplitude, or disappear to a flat coastline, range from 120 to 175,000 years depending on how close the initial amplitude is to steady state. In many cases, the coastline must evolve over several sea level highstands in order to reach equilibrium. A characteristic timescale (independent of initial conditions) shows that the coastline evolves most rapidly when: wave focusing is stronger; sea cliff rock is weaker or retreats faster in a given wave climate; the sea cliff retreat rate decreases rapidly as a function of beach width (i.e., the beach is very effective at dampening wave energy); and the coastline is sediment rich. Comparisons to nature suggest that our model is qualitatively capturing general rocky coastline dynamics and that modeled headland amplitudes are consistent with observed amplitudes.

Lithological controls on soft cliff planshape evolution under high and low sediment availability

“…Kitty Hawke, North Carolina, USA as discussed by Valvo et al ()), while others exhibit heterogeneous rates resulting in the formation of persistent headland and embayment features (e.g. Flamborough Head, Holderness, UK as discussed by Limber and Murray ()). The results of Figures and suggest that this change in response is governed by sediment availability.…”

“…Fronting beach volumes develop more rapidly (as shown in Figure (b)) and become the more dominant control on rates of cliff toe retreat. These results are in agreement with the exploratory model results of Limber and Murray () described earlier. The agreement supports the underlying assumptions of the latter, simpler analytical model while the quasi‐3D SCAPE model enables more detailed quantification of the cliff system, which is more appropriate for understanding specific sites.…”

“…This was supported by site comparisons for Monterey Beach, California (USA) where headlands are observed to be retreating at a higher rate than adjacent bays (Hapke and Reid, ). Finally, Limber and Murray () showed how sediment availability is also influenced by a range of additional factors. For example increasing headland width lengthens the shoreline therefore increasing sediment availability, while increasing embayment width requires greater volumes of sediment to fill pocket beaches, effectively reducing sediment availability.…”

“…The results have provided an important foundation to understanding the influence of lithological controls on coastal planshape evolution under a range of sediment conditions. However, as noted by Limber and Murray () the model greatly oversimplifies the processes occurring on rocky coastlines. Therefore, this paper describes the application of the quasi‐3D SCAPE model (Walkden and Hall, ) to help understand how varying (low) beach volumes and longshore processes may influence coastal planshape evolution on soft rock coasts.…”

A fundamental equation for describing the rate of bedrock erosion by sediment‐laden fluid flows in fluvial, coastal, and aeolian environments

“…Clastic sediment in the rocky shore zone has two contradictory effects similar to the fluvial case: to accelerate erosion working as an abrasive (the positive effect) and to halt it as a protective layer (the negative effect) (Sunamura, ). Modelling studies for the recession of coastal cliffs have been carried out, considering the positive or negative effect, or both, of beach sediment in front of sea cliffs, to illustrate the cross‐shore evolution of cliffed coasts (Castedo et al ., ; Kline et al ., ) and the alongshore development of coastline (planshape evolution) (Limber and Murray, , , ; Limber et al ., ; Carpenter et al ., ). Most of these models have adopted wave height as a surrogate for wave erosivity.…”