Modeling risk to infrastructure due to episodic debris fan aggradation

In many mountain valleys, communities and infrastructure are exposed to high risks of damage due to debris fan aggradation. To assess such risks, two questions must be addressed: (1) What will be the extent and thickness of deposition over the fan for a given volume of debris delivered from the upstream catchment? (2) How large could debris flow volumes be for a single event or a sequence of events? In this contribution, we propose a methodology to address both questions. Its first component is a simplified model of debris fan morphology, based on assuming a fan-slope-distance relationship along paths affected by topographic obstacles like steep valley sides. Using a computationally efficient algorithm, this model can be used to reconstruct past fan volumes from terrace remnants resolved on high resolution DEM topography, and to simulate large numbers of possible future events. Its second component is a stochastic model for the evolution of fan volume framed as a form of random walk. To take into account the episodicity of debris delivery, we model this random walk as a gamma-subordinated Wiener process aka a variance-gamma process. To calibrate the model parameters, we exploit both short-term and long-term data: for the slope-distance relationship, topographic data from recent and Holocene debris-fan remnants; for the stochastic process parameters, reconstructed fan-volume changes associated with recent flood events and with older radiocarbon-dated fan surfaces. We illustrate the approach with an application to the Laonong River in southern Taiwan. In this valley, an important roadway link has been repeatedly damaged by debris-flow aggradation. To guide road and bridge reconstruction, it is essential to assess fan aggradation risk for different design alternatives on a decadal time scale or more. The model provides a basis for optimizing the layout and height of such infrastructure.