Mathematical Modeling of Basal Coastal Cliff Erosion in Uniform Strata: A Theoretical Approach

Abstract

This article utilizes the general assumption that cliff erosion is dependent on the strength of wave assailing forces and the resistance of the cliff material. It considers the possibility of understanding and describing coastal cliff erosion processes, particularly basal erosion, through a mathematical analysis of one of the clearest manifestations of its action, i.e., the development of the basal cliff notch through mechanical wave action. It analyzes profile change through time, assuming a cliff composed of uniform strata. Deterioration of the cliff is expressed by means of the erosion function, which in this study is related to the cliff erosion rate. An equation, termed the Belov, Davies, Williams (BDW) equation, has been formulated for a moving surface, and this is proposed as a mathematical model of cliff profile change. Explicit solutions of the BDW equation are found for both steady state and time‐dependent erosion rates. In both cases, it is assumed that wave erosion intensity decreases exponentially with height. Solutions obtained showed that cliff retreat, related to basal notching, depends upon the erosion intensity and magnitude of the geophysical parameters. The model predicted the occurrence of cliff basal notching, the depth of which is comparable to field observations and can be applied to other locations. It is believed the approach and model has the potential to be developed further for other structural contexts such as locations with a variable lithology.