Debris-flow volumes in northeastern Italy: Relationship with drainage area and size probability

A dataset of 809 debris flows that occurred in 537 basins in mountainous areas of northeastern Italy between the mid-19th century and 2015 is collected and analyzed. A remarkable increase in the number of events is observed in the last four decades and is mainly ascribed to more systematic data collection. The correlation between debris-flow volume and drainage basin area is obtained assuming a power-law relationship. The exponent of the power-law curve at the 50th percentile (0.67 ± 0.02) indicates negative allometry, which means that basin area grows out of proportion to debris-flow volume. In contrast, the exponents at the 98th and 99th percentiles are close to one, implying that debris-flow volumes grow linearly with basin areas. The isometric relationship between the largest debris flows and the corresponding basin areas is due to the enhanced debris supply provided by the activation of widespread sediment sources, the extent of which is proportional to the basin size. The probability density function of debris-flow volume for a subset of the collected dataset is calculated using the kernel density estimation function, which permits estimating the probability of the occurrence of debris flows that exceed a given threshold volume. The comparison with debris flows in other hydroclimatic regions shows that, although debris-flow volumes in northeastern Italy may attain high values, they are often exceeded by debris flows that occur in seismically active regions and/or are triggered by more intense rainstorms. © 2018 John Wiley & Sons, Ltd.