Probabilistic delineation of debris-flow routing pathways in cones and fans within a Monte Carlo framework

Debris flow phenomena are difficult to predict because their occurrence depends on multiple factors (e.g. availability of sediment, volume, and rainfall intensity, as well as slope conditions before an intense rainfall event, etc.). When they occur, debris flows can significantly modify the topographic surface of conical-shaped fans and cones via erosion and deposition phenomena.
This contribution aims, for the first time, to use a Monte Carlo approach to simulate the most probable avulsion paths of debris flows and define those conveying a certain drainage area with a minimum occurrence probability. We rely upon various digital terrain models (DEM) available for the Fiames area (Cortina d'Ampezzo, BL), covering approximately 1.6 km² , and the average local elevation and the standard deviation of each cell of the domain are evaluated. We then generate N=2000 Monte Carlo realizations of possible topographic (equiprobable) surfaces, according to the geostatistical procedure known as Sequential Gaussian Simulations (SGSIMs). On each topographic surface obtained, the optimal drainage network is extracted using algorithms that guide the flow, by gravity, along the directions of maximum slope, as commonly used in hydrology. It is therefore possible to obtain as many drainage networks as there are simulated topographies. The ensemble of drainage networks (networks) is used to obtain the most probable network, extracted from the average topographic surface among the simulated ones.
Furthermore, we set a threshold on the drainage area variable, thus it is possible to calculate the probability of having, in a domain's location, a flow conveyance (per unit of area) higher than the threshold one. Finally, it is possible to (at least preliminarily) evaluate the probability of existing infrastructure vulnerability by appraising the probability that they are located along possible drainage routes or not. The presented approach moves the analysis of avulsion paths within the probability space. It can be validated by verifying the correspondence between a part of the probable (synthetic) pathways with those that historically occurred. Furthermore, it allows us to define routes and (synthetic) triggering points different from the historical ones.