The Importance of Monitoring Interval for Rockfall Magnitude‐Frequency Estimation

Abstract

Rockfalls commonly exhibit power law volume‐frequency distributions, where fewer large events are observed relative to more numerous small events. Within most inventories, the smallest rockfalls are the most difficult to detect and so may not be adequately represented. A primary challenge occurs when neighboring events within a single monitoring interval are recorded as one, producing ambiguity in event location, timing, volume, and frequency. Identifying measurement intervals that minimize these uncertainties is therefore essential. To address this, we use an hourly data set comprising 8,987 3‐D point clouds of a cliff that experiences frequent rockfalls. Multiple rockfall inventories are derived from this data set using change detections for the same 10‐month period, but over different monitoring intervals. The power law describing the probability distribution of rockfall volumes is highly sensitive to monitoring interval. The exponent, β, is stable for intervals >12 hr but increases nonlinearly over progressively short timescales. This change is manifested as an increase in observed rockfall numbers, from 1.4 × 103 (30 day intervals) to 1.4 × 104 (1 hr intervals), and a threefold reduction in mean rockfall volume. When the monitoring interval exceeds 4 hr, the geometry of detected rockfalls becomes increasingly similar to that of blocks defined by rock mass structure. This behavior change reveals a time‐dependent component to rockfall occurrence, where smaller rockfalls (identifiable from more frequent monitoring) are more sensitive to progressive deformation of the rock mass. Acquiring complete inventories and attributing discrete controls over rockfall occurrence may therefore only be achievable with high‐frequency monitoring, dependent upon local lithology.

Emergent characteristics of rockfall inventories captured at a regional scale

“…Following pointwise change detection, the data belonging to each individual rockfall event were grouped using the clustering algorithm DBSCAN (Density-Based Spatial Clustering of Applications with Noise), developed by Ester et al (1996). Contiguous points of change were assumed to belong to a single event, although the influence of rockfall scar coalescence has been recognized at intervals beneath the annual timescales used here (Barlow et al, 2012;Williams et al, 2019). DBSCAN is the most commonly used single-scan clustering technique and defines clusters based on the local density of points.…”

“…We recognize that our distributions (captured annually), as opposed to previous local scale monitoring (captured monthly), could be prone to under-sampling and other biases, such as the threshold that was set for the minimum detectable change (0.10m) during data processing, as well as differences in the way that cloud-to-cloud comparison methods identify and treat insignificant change. Previous research has demonstrated the relative stability and reliability of power laws fit to rockfall volume probability distributions at monitoring intervals >12hours (Williams et al, 2019). We therefore consider that any bias in the data collected most likely relates to rockfalls that were not captured (e.g.…”

“…Although the length of time over which rockfall frequency estimates are made is known to exert a profound influence on β (Barlow et al, 2012;Williams et al, 2019), the length scale, L, over which power laws can be applied remains poorly constrained. It is also apparent that many previously reported observations do not indicate whether power laws derived on a site-specific basis (e.g.…”

“…Such data require methods that are able to retain the 3D character of the data while also being able to measure rockfall volumes that can span over six orders of magnitude, and over spatial extents that can exceed~10 6 m 2 . These settings could include, but are not limited to, a length of coastline (for example, Teixeira, 2006;Rosser et al, 2007;Marques, 2008;Lim et al, 2010;Young et al, 2011;Barlow et al, 2012;Rohmer and Dewez, 2013;Kuhn and Prüfer, 2014;Williams et al, 2018Williams et al, , 2019, cut slopes along a transport corridor (for example, Bunce et al, 1997;Hungr et al, 1999;van Veen et al, 2017), or on montane, alpine or arctic rock walls (for example, Dussauge-Peisser et al, 2002;Malamud et al, 2004;Santana et al, 2012;Messenzehl and Dikau, 2017). Without data obtained at these scales, it remains difficult to assess whether rockfalls are truly scale invariant across all the possible volumes of a given distribution, to put limits on modelled power laws of rockfall magnitude and frequency, and therefore to test whether rockfalls can be considered stochastic phenomena.…”

Remote thermal detection of exfoliation sheet deformation

“…High spatio-temporal resolution monitoring of rock cliffs using terrestrial laser scanning (TLS) point clouds (e.g., Abellán et al 2009Abellán et al , 2010Rosser et al 2013;Royán et al 2014Royán et al , 2015Kromer et al 2015aKromer et al , 2018Stock et al 2018) has shown that it is possible in some cases to detect precursor deformations below centimetric scale and to monitor them over time until failure. In addition to obtaining a more comprehensive rockfall inventory and a more realistic volume-frequency relationship (Barlow et al 2012;van Veen et al 2017;Williams et al 2018Williams et al , 2019, near real-time TLS surveys offer new opportunities to better anticipate failure (Eitel et al 2016;Kromer et al 2015bKromer et al , 2017. These systems also help to better understand the influence of environmental factors on rockfall triggering (Jaboyedoff and Derron 2005).…”