Spatial scaling in geomorphology: Extrapolating micro-erosion measurements to the landform scale on shore platforms using unoccupied aerial vehicles

Downwearing rates of shore platform have been quantified with a number of ground-based techniques (such as the micro-erosion meter (MEM)), providing knowledge of the evolution of coastal landforms. However, it remains problematic to extrapolate the micro erosion results to the landform scale. This is because only a very small proportion of the platform is monitored and usually biased to flat rock surfaces. In this study, we used the shore platforms in south-eastern Australia, which has the world’s longest continual erosion records, as an example to solve the fundamental question on result extrapolation across spatial scales. Surveying using an unoccupied aerial vehicle (UAV) – post-processing kinematic (PPK) – structure-from-motion (SfM) workflow, indicates the shore platforms at Marengo and Jump Rock having similar morphology. The generated mm-scale dataset was used to contextualize 4 and 12 MEM sites into the orthomosaics and digital surface models (DSMs) at each location. By using two different methods, we assessed how these monitored surfaces were representative of the morphology of the entire platform. On average, the 4 MEM sites represented 52.2% of platform surfaces at Marengo and 73.2% with the 12 MEM sites at Jump Rock. To improve the representativeness of sampled surfaces, it was found that 20 randomly sampled MEM-size (4.33 × 10^-3 m²) surfaces could well represent (c. 90%) the landform morphology at the scale of 10⁴ m². The representativeness was only slightly improved by upscaling the surface size from original cm², to dm² (0.16 m²) and m² (1 m²) scales, implying the importance of sample number over sample size. Using the cm-scale dataset covering a larger geographic region, a bias of MEM installation was found with all 43 MEM sites concentrated at the fast-eroding upper intertidal zone. An elevation-weighted erosion rate of 0.21 mm/yr was calculated, lower than the original mean of 0.25 mm/yr provided by the MEM network. Moreover, a spatial pattern of rock surface morphology was observed across the platform with higher slope and roughness at the seaward end, suggesting more intensive wave processes and varying weathering agents compared to those surfaces further inland.