Frequency-size statistics of coastal soft-cliff erosion

Predicting the retreat of a coastal soft cliff is a difficult and uncertain operation, which has both theoretical and practical significance. Recession of soft cliffs occurs through a combination of processes, including slope failures and surface erosion, that are difficult to model jointly. Deterministic models for predicting coastal retreat are hampered by the complex nature of coastal erosion, which is highly nonuniform in space and episodic in time. To overcome these limitations, stochastic approaches have been proposed. These models assume distributions for the size and the time of the recession events. In this paper we investigate the frequency-size statistics of soft-cliff erosion based on two historical datasets of coastal retreat measurements at two sites in England. We find that the two datasets exhibit a similar behavior. The frequency of the recessions decreases with increasing size of the retreat. For small retreats the decrease is slow. For medium to large retreats the decrease is rapid and follows a power law. The frequency-size statistics of soft-cliff erosion is similar to the statistics of medium to large landslide areas, which are also power-law distributed. This is a significant but not conclusive result. More data are needed to confirm this finding.