Landslide shape, ellipticity and length-to-width ratios

This paper presents a new methodology to systematically quantify the shape of landslides by their ellipticity (e(L)) and length-to-width ratio (Lambda(L)), along with variability in these measures over different geomorphic settings. Two large substantially complete triggered-event landslide inventories (source area and runout) are used: (i) 11 111 earthquake-triggered landslides (1994 Northridge, USA); and (ii) 9594 rainfall-triggered landslides (1998, Guatemala). Three methods are trialled to abstract landslide shapes to ellipses. The best method fits a convex hull to each landslide shape, approximates an ellipse with the equivalent convex hull area and perimeter, and scales this ellipse to match the original landslide area. An ellipticity index (e(L)) is used based on the intersection of the original landslide shape and the elliptical approximation. We consider an ellipse a reasonable approximation of landslide shape if e(L) >= 0.5 (>80% of landslides in each of the two landslide inventories). Landslides with e(L) < 0.5 reflect processes such as coalescence. We calculate for each landslide an ellipse length-to-width ratio (Lambda(E)), finding 1.2 <= Lambda(E) <= 15.1. The statistical distributions of Lambda(E) are examined for ten categories of landslide area (A(L)). An inverse-Gamma probability density function is found to be a good statistical model for landslide Lambda(E), with model parameters dependent on landslide area category. As landslide area A(L) increases, Lambda(E) tends to decrease for the Northridge (earthquake-triggered) inventory and increase for Guatemala (rainfall-triggered). In three additional (rainfall-triggered) landslide inventories, Lambda(E) trends are similar to Guatemala. Our findings show that (i) an ellipse is a reasonable model for >80% of landslide shapes across different geomorphic settings, (ii) those landslides significantly deviating from an ellipse can be related to landscape processes, (iii) the length-to-width ratios of ellipses are non-normally distributed, with implications for modelling landslide hazard and risk. Supporting information includes code so that the new methodology may be applied more widely. (c) 2018 John Wiley & Sons, Ltd.