Characteristics of the size distribution of recent and historical landslides in a populated hilly region

Abstract

Despite the availability of studies on the frequency density of landslide areas in mountainous regions, frequency-area distributions of historical landslide inventories in populated hilly regions are absent. This study revealed that the frequency-area distribution derived from a detailed landslide inventory of the Flemish Ardennes (Belgium) is significantly different from distributions usually obtained in mountainous areas where landslides are triggered by large-scale natural causal factors such as rainfall, earthquakes or rapid snowmelt. Instead, the landslide inventory consists of the superposition of two populations, i.e. (i) small (b 1-2 · 10 − 2 km 2 ), shallow complex earth slides that are at most 30 yr old, and (ii) large (N 1-2 · 10 − 2 km 2 ), deep-seated landslides that are older than 100 yr. Both subpopulations are best represented by a negative power-law relation with exponents of −0.58 and −2.31 respectively. This study focused on the negative power-law relation obtained for recent, small landslides, and contributes to the understanding of frequency distributions of landslide areas by presenting a conceptual model explaining this negative power-law relation for small landslides in populated hilly regions. According to the model hilly regions can be relatively stable under the present-day environmental conditions, and landslides are mainly triggered by human activities that have only a local impact on slope stability. Therefore, landslides caused by anthropogenic triggers are limited in size, and the number of landslides decreases with landslide area.The frequency density of landslide areas for old landslides is similar to those obtained for historical inventories compiled in mountainous areas, as apart from the negative power-law relation with exponent −2.31 for large landslides, a positive power-law relation followed by a rollover is observed for smaller landslides. However, when analysing the old landslides together with the more recent ones, the present-day higher temporal frequency of small landslides compared to large landslides, obscures the positive power-law relation and rollover.

Do landslides follow landslides? Insights in path dependency from a multi-temporal landslide inventory

“…The exponent of the inverse power-law (α) for 'touching' landslides (α = 1.78) seems consistent with the most reported range of values in the literature (1.5 < α < 2.5) (Borgomeo et al 2014;Guzzetti et al 2002;Malamud et al 2004;Van Den Eeckhaut et al 2007). The other landslides (i.e.…”

“…1 < α < 1.5) ( Table 2). The small exponent of the power-law in the sub-inventories suggests that larger landslides are contributing to each sub-inventory (Borgomeo et al 2014;Van Den Eeckhaut et al 2007). The rollover (λ), which represents the size of the most frequent landslide, is larger for spatially associated landslides than for non-spatially associated landslides ('outside', Table 2).…”

Origin of the power-law exponent in the landslide frequency-size distribution

“…The rollover behaviour observed below x min can be described by a double Pareto distribution (Stark and Hovius, 2001) or by the 5 inverse Gamma distribution (Malamud et al, 2004). The different behaviour below x min is likely due to a combination of data incompleteness (Stark and Hovius, 2001), as extensively studied in the earthquake case (Mignan, 2012;Kijko and Smit, 2017), and of physical changes Malamud et al, 2004;Van Den Eeckhaut et al, 2007;Guthrie et al, 2008). However all those models provide similar estimates of α, as illustrated in Fig.…”

Using an Unmanned Aerial Vehicle-Based Digital Imaging System to Derive a 3D Point Cloud for Landslide Scarp Recognition

“…This design is sufficient to cover a relatively small to medium area. According to Van Den Eeckhaut et al [83] small landslide area are less than 0.02 km 2 in size and a medium to large landslide area size is greater than 0.02 km 2 . However, it lacks several features that are necessary to obtain a photogrammetric product, such as time synchronization between the camera and the navigation unit, control of image exposure, and the overlap and sidelap of imagery.…”

“…The image orientation (EOP) is a fundamental prerequisite parameter in any image-based reconstruction. Orienting the images was accomplished by applying the SfM approach developed by He and Habib [83]. The estimated image position and orientation and the reconstructed sparse point cloud from the UAV image dataset are shown in Figure 11.…”