Physical Interpretation of Rainfall Thresholds or Runoff-Generated Debris Flows

Rainfall thresholds for the occurrence of debris flows are commonly defined by Intensity-Duration curves (ID thresholds). Interestingly, many empirical ID thresholds show up as straight lines in a log-log plot and therefore can be expressed by power-law functions of the form I = α ⋅ Dβ, where α is the scaling coefficient and β is the exponent of the power function. The different values of α and β reflect the variability of geological and hydrological conditions in the different areas. In most cases, however, field conditions are so complex that a quantitative interpretation of the empirical rainfall threshold is impossible and the physical meaning of α and β remains obscure. In this work, we provide a physical interpretation of the rainfall thresholds that characterize an active debris flow catchment in the Eastern Italian Alps (the Dimai Basin, Belluno Province). The catchment is affected by frequent debris flows generated by surface-water runoff and has been monitored since 2010 to investigate the initiation process. Monitoring data allowed for the detection of two rainfall thresholds: a lower one that identifies the arrival of water in the initiation area (Catchment Outflow Threshold) and an upper one that identifies the initiation of debris flows by channel runoff (Debris Flow Threshold). We demonstrate that these two thresholds can be satisfactorily reproduced by a simple physically based model in which the excess rainfall is routed over the catchment using a kinematic-wave scheme. This simple analysis provides a sound explanation of the observed thresholds and can be used to develop physically based thresholds for runoff-generated debris flows.