Power laws for accurate determination of landslide volume based on high-resolution LiDAR data

Abstract

Landslide volume is critical in landslide risk management due to its close association with the landslide mobility and damage to elements at risk. Limited by accessibility, site conditions and availability of equipment, directly measuring the landslide volume on site is challenging. Instead, many empirical area-volume power-law models have been developed to estimate the landslide volume. Yet the validity of these power-law models for small-scale shallow landslides is in question considering the substantial uncertainty of field-estimated landslide volume data for developing these empirical power laws. In this study, two high-resolution LiDAR-derived digital terrain models taken in 2010 and 2020 are leveraged to interpret the volumes of 1326 shallow landslides that occurred in Hong Kong during the same period. The high precision of the digital terrain models ensures the accurate interpretation of landslides and the identification of landslide source and transport areas. On the basis of the interpreted landslide characteristics, new power-law models and a multivariate distribution model are proposed to accurately estimate the volumes of small-scale shallow landslides based on easy-to-obtain landslide source features such as source area, length, width or maximum depth. The multivariate distribution model rigorously expresses the conditional probability distribution of the landslide volume and quantifies the uncertainty of volume estimation. The models therefore enhance the capability of landslide risk assessment and management.