LAUSR

Abstract Although the main driving force of debris flows is simply gravity, the dynamic processes are very complex. Kinematic uncertainties during motion make it difficult to exactly simulate debris flows. In traditional numerical simulation models of debris flows, the kinematic uncertainties are generally not considered in the Lagrangian description. In addition, the challenge of obtaining accurate simulation parameters further suggests the necessity of probabilistic modeling of debris flows. In this study, a novel statistical debris flow simulation model (Debris Flow Analyst model), is proposed in the Lagrangian description, in which the inherent stochasticity in the motion of a debris flow is described by stochastic differential equations (SDEs). In this model, the accelerations of moving debris are calculated by Newton's second law, and their locations are estimated based on Monte Carlo simulation. According to case studies, the proposed model provides results close to the analytical solution in a 1-D simulation of dam breaks in the Eulerian description and reduces some numerical oscillations. Additionally, the Debris Flow Analyst model can produce reasonable results based on a single-phase rheological model in 2-D simulations of a debris flow in Tibet and a flow-like landslide triggered by storms on 4–5 November 1993 in Hong Kong. From the theoretical perspective, our model is equivalent to the total variation diminishing (TVD) scheme in the Eulerian description. In addition, the statistical model provides a new tool to estimate kinematic uncertainties in the hazard analysis of debris flows on GIS platforms.