In quantitative risk assessment, risk is expressed as a function of hazard, elements at risk exposed, and vulnerability. Vulnerability is defined as the expected degree of loss for an element at risk as a consequence of a certain event, following a natural-scientific approach combined with economic methods of loss appraisal. The resulting value ranges from 0 (no damage) to 1 (complete destruction). With respect to torrent processes, i.e., fluvial sediment transport, this concept of vulnerability-though widely acknowledgeddid not result in sound quantitative relationships between process intensities and associated degrees of loss so far, even if considerable loss occurred during recent years. To close this gap and establish this relationship, data from three well-documented torrent events in the Austrian Alps were used to derive a quantitative vulnerability function applicable to residential buildings located on torrent fans. The method applied followed a spatially explicit empirical approach within a GIS environment and was based on process intensities, the spatial characteristics of elements at risk, and average reconstruction values on a local scale. Additionally, loss data were collected from responsible administrative bodies and analysed on an object level. The results suggest a modified Weibull distribution to fit best to the observed damage pattern if intensity is quantified in absolute values, and a modified Frechet distribution if intensity is quantified relatively in relation to the individual building height. Additionally, uncertainties resulting from such an empirical approach were studied; in relation to the data quality a 90% confidence band was found to represent the data range appropriately. The vulnerability relationship obtained allows for an enhanced quantification of torrent risk, but also for an inclusion in comprehensive vulnerability models including physical, social, economic, and institutional vulnerability. As a result, vulnerability to mountain hazards might decrease in the future.

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