A statistical method to predict debris flow deposited volumes on a debris fan

The present paper aims to give a useful methodology to predict the debris volume G_s associated to a debris flow and deposited on the basin's terminal fan in the alpine region. Predicting the occurrence and the magnitude of a debris flow is often a very difficult task, as it is necessary to consider the variability of the geological, hydraulic and pluviometric factors connected to the beginning, propagation and deposition of a debris flow. These factors are not easily quantifiable, as well as their influence on the debris volumes deposited on the debris fan. Even if some useful mathematical (and deterministic) relations have been proposed by some authors to predict the likely debris volumes, they do not seem to take into account the high variability of the influencing factors. For these reasons a statistical investigation of the relationship between Gs and the basin area A has been undertaken. By means of well known statistical methodologies and by using a sample of about two hundred data (referred to the alpine region), a new criterion is proposed, in the present paper, for the prediction of a probable Gs value. For a given basin, this value is obtained on the basis of a statistical risk degree arbitrarily chosen. A probabilistic methodology is also proposed, which, when results of an accurate survey are not available for a particular basin, may provide a rational basis for a first hazard zonation and the design of mitigative measures.