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

Abstract

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 × 10 3 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 m 3 ) 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.

Factors controlling landslide frequency–area distributions

“…Such discontinuities isolate the landslide mass from the rest of the slope. For example, Williams et al (2018) showed a rollover in frequency-size distribution of rock-falls if mapping is conducted using a low temporal resolution. Even in this situation, however, landslide margins are likely to produce smaller, continuing failures as the disturbed topography seeks equilibrium.…”

“…However, there is only one case study supporting this argument by monitoring rock-falls on a slope (Williams et al, 2018). However, there is only one case study supporting this argument by monitoring rock-falls on a slope (Williams et al, 2018).…”

“…Hypothesis 5 suggests that a lack of temporal mapping resolution causes rollover observed in rock-falls (Williams et al, 2018). Barlow et al (2012) showed the effect of temporal resolution of mapping on FADs of rock-falls.…”

“…Barlow et al (2012) showed the effect of temporal resolution of mapping on FADs of rock-falls. Williams et al (2018) went one step further by monitoring rock-falls on a slope (length~180 m and height~60 m) at approximately 1-hour intervals. Williams et al (2018) went one step further by monitoring rock-falls on a slope (length~180 m and height~60 m) at approximately 1-hour intervals.…”

“…We elaborate on the argument that lack of temporal resolution in mapping of landslides causes superimposition and coalescence of features because the landslide events that happened at different times are formed on top of each other and afterwards look like a single event (Barlow et al, 2012;Williams et al, 2018). We do so by analyzing 45 digital EQIL inventories triggered by 32 earthquakes.…”