SCALING IN THE RANK-ORDER STATISTICS OF CATASTROPHIC MASS FLOWS

The size distributions of many natural phenomena exhibit power-law forms. In the case of volumes of individual landslides, avalanches and related mass flows, the value of the key scaling parameter (the power-law exponent) has been inferred from regional studies of tectonically-active mountain belts and submarine basin sedimentary fill to be just less than unity. To test the relevance of this result to large scales of space and time, the statistics of the volumes of the largest mass flows known on Earth are directly examined here using rank-order statistics in the context of extreme value theory. From such an approach, the values of the scaling parameter inferred for catastrophic flows in a wide range of environments are consistent with earlier findings. These results underscore the view that mass wastage and related hazards are dominated by relatively large and infrequent events, and suggest that such processes are necessarily bounded by the largest scales of the landscape.