Optimising 4-D surface change detection: an approach for capturing rockfall magnitude–frequency

Abstract. We present a monitoring technique tailored to analysing change from near-continuously collected, high-resolution 3-D data. Our aim is to fully characterise geomorphological change typified by an event magnitude–frequency relationship that adheres to an inverse power law or similar. While recent advances in monitoring have enabled changes in volume across more than 7 orders of magnitude to be captured, event frequency is commonly assumed to be interchangeable with the time-averaged event numbers between successive surveys. Where events coincide, or coalesce, or where the mechanisms driving change are not spatially independent, apparent event frequency must be partially determined by survey interval.

The data reported have been obtained from a permanently installed terrestrial laser scanner, which permits an increased frequency of surveys. Surveying from a single position raises challenges, given the single viewpoint onto a complex surface and the need for computational efficiency associated with handling a large time series of 3-D data. A workflow is presented that optimises the detection of change by filtering and aligning scans to improve repeatability. An adaptation of the M3C2 algorithm is used to detect 3-D change to overcome data inconsistencies between scans. Individual rockfall geometries are then extracted and the associated volumetric errors modelled. The utility of this approach is demonstrated using a dataset of  ∼  9  ×  10³ surveys acquired at  ∼  1 h intervals over 10 months. The magnitude–frequency distribution of rockfall volumes generated is shown to be sensitive to monitoring frequency. Using a 1 h interval between surveys, rather than 30 days, the volume contribution from small (< 0.1 m³) rockfalls increases from 67 to 98 % of the total, and the number of individual rockfalls observed increases by over 3 orders of magnitude. High-frequency monitoring therefore holds considerable implications for magnitude–frequency derivatives, such as hazard return intervals and erosion rates. As such, while high-frequency monitoring has potential to describe short-term controls on geomorphological change and more realistic magnitude–frequency relationships, the assessment of longer-term erosion rates may be more suited to less-frequent data collection with lower accumulative errors.