Modeling cliff erosion using negative power law scaling of rockfalls

We model cliff erosion using an approach based upon the negative power law scaling properties of rockfall magnitude–frequency distributions. These are derived from an extensive, high resolution, rockfall inventory for a series of sea cliffs near Staithes, North Yorkshire. A comparison between observed volumetric erosion and that produced by the model yields a statistically significant correlation. However, we note that the temporal resolution of the inventory can have an influence on results. Our data indicate that monthly inventories are capable of producing magnitude–frequency relations that model erosion in good correlation with observed events. However, for months that experience high magnitude events, seasonal inventories are more appropriate. Furthermore, increasing the return period between surveys has the effect of increasing the superimposition of rockfall events thereby reducing the slope of the power law, giving an incorrect picture of the scaling properties of rockfalls at this site. Applying observed variations in the negative power law scaling parameters to a probabilistic simulation model of cliff retreat provides a new means of assessing the most likely erosional scenarios and indicates that the current dataset may not be indicative of long term cliff evolution. This may provide a quantitative means of establishing an appropriate time window for characterizing rockfall erosion over decadal time scales.