A physics-based morphometric model to explain the emergence of landslide rupture geometry and to identify hillslope transience

Abstract. Like earthquakes or other rupture processes, landslide tends to universally follow some specific geometrical scaling laws and size distributions. Numerical models have attempted to explain the emergence of these universal laws, putting forward mainly the role of hillslope strength and shape. The main difficulty that models are facing is that the geometry of the surface rupture of a landslide, or of large population of landslides, is not a priori known and must often be guessed using assumptions about the rupture shape, depth, and angle. Here, we develop an analytical solution that defines an optimal rupture depth, below each point of a topography, associated with an optimal rupture angle. This defines a rupture surface that daylights downslope the rupture point. Landslides are then defined as clusters of unstable neighbours sharing the same daylight point. The geometry of the surface rupture of the landslide is then simply defined by the optimal rupture depth at each point belonging to the landslide. Applying this model, coined scaLr (slope curvature analysis for Landslide rupture) to the Central Range of Taiwan, we show it can produce landslide area-volume and area-depth relationships with power-law exponents roughly consistent with observed ones. The distribution of landslide length-to-width ratio is also consistent with the range of observed values and exhibit a distribution similar to an Inverse-Gamma. The distribution of landslide area exhibits a power-law decay for large landslides and no clear rollover is obtained despite a break in slope below a cutoff area. However, the power-law decay tends to be in the lower part of the range of observed values. Amalgamating modelled landslides does however produce more acceptable exponents, which suggests that the difference between modelled and observed landslides might partly results from inherent amalgamation in landslide catalogues. Last, we show that the optimal rupture depth also represents a morphometric index to assess landscape transience along hillslopes. In Taiwan, we tend to observe deeper expected ruptures along streams locally characterized by high river steepness as well on the aggressive side of migrating divides, as identified by the χ index. The optimal rupture depth therefore offers complementary information to fluvial metrics, such as river steepness or the χ index, and to hillslope metrics such as Gilbert’s metrics.