Analysing the spatial patterns of erosion scars using point process theory at the coastal chalk cliff of Mesnil-Val, Normandy, northern France

Over the last decade, many cliff erosion studies have focused on frequency-size statistics using inventories of sea cliff retreat sizes. By comparison, only a few paid attention to quantifying the spatial and temporal organisation of erosion scars over a cliff face. Yet, this spatial organisation carries essential information about the external processes and the environmental conditions that promote or initiate sea-cliff instabilities. In this article, we use summary statistics of spatial point process theory as a tool to examine the spatial and temporal pattern of a rockfall inventory recorded with repeated terrestrial laser scanning surveys at the chalk coastal cliff site of Mesnil-Val (Normandy, France). Results show that: (1) the spatial density of erosion scars is specifically conditioned alongshore by the distance to an engineered concrete groyne, with an exponential-like decreasing trend, and vertically focused both at wave breaker height and on strong lithological contrasts; (2) small erosion scars (10^−3 to 10^−2 m³) aggregate in clusters within a radius of 5 to 10 m, which suggests some sort of attraction or focused causative process, and disperse above this critical distance; (3) on the contrary, larger erosion scars (10^−2 to 10¹ m³) tend to disperse above a radius of 1 to 5 m, possibly due to the spreading of successive failures across the cliff face; (4) large scars significantly occur albeit moderately, where previous large rockfalls have occurred during preceding winter; (5) this temporal trend is not apparent for small events. In conclusion, this study shows, with a worked example, how spatial point process summary statistics are a tool to test and quantify the significance of geomorphological observation organisation