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.

Alpine hazards such as debris flow, floods, snow avalanches, rock falls, and landslides pose a significant threat to local communities. The assessment of the vulnerability of the built environment to these hazards in the context of risk analysis is a topic that is growing in importance due to global environmental change impacts as well as socioeconomic changes. Hence, the vulnerability is essential for the development of efficient risk reduction strategies. In this contribution, a methodology for the development of a vulnerability curve as a function of the intensity of the process and the degree of loss is presented. After some modifications, this methodology can also be used for other types of hazards in the future. The curve can be a valuable tool in the hands of local authorities, emergency and disaster planners since it can assist decision making and cost-benefit analysis of structural protection measures by assessing the potential cost of future events. The developed methodology is applied in two villages (Gand and Ennewasser) located in Martell valley, South Tyrol, Italy. In the case study area, buildings and infrastructure suffered significant damages following a debris flow event in August 1987. The event caused extensive damage and was very well documented. The documented data were used to create a vulnerability curve that shows the degree of loss corresponding to different process intensities. The resulting curve can be later used in order to assess the potential economic loss of future events. Although the validation process demonstrated the reliability of the results, a new damage assessment documentation is being recommended and presented. This documentation might improve the quality of the data and the reliability of the curve. The presented research has been developed in the European FP7 project MOVE (Methods for the Improvement of Vulnerability Assessment in Europe).

Vulnerability assessment for elements at risk is an important component in the framework of risk assessment. The vulnerability of buildings affected by torrent processes can be quantified by vulnerability functions that express a mathematical relationship between the degree of loss of individual elements at risk and the intensity of the impacting process. Based on data from the Austrian Alps, we extended a vulnerability curve for residential buildings affected by fluvial sediment transport processes to other torrent processes and other building types. With respect to this goal to merge different data based on different processes and building types, several statistical tests were conducted. The calculation of vulnerability functions was based on a nonlinear regression approach applying cumulative distribution functions. The results suggest that there is no need to distinguish between different sediment-laden torrent processes when assessing vulnerability of residential buildings towards torrent processes. The final vulnerability functions were further validated with data from the Italian Alps and different vulnerability functions presented in the literature. This comparison showed the wider applicability of the derived vulnerability functions. The uncertainty inherent to regression functions was quantified by the calculation of confidence bands. The derived vulnerability functions may be applied within the framework of risk management for mountain hazards within the European Alps. The method is transferable to other mountain regions if the input data needed are available.

In the European Alps, the concept of risk has increasingly been applied in order to reduce the susceptibility of society to mountain hazards. Risk is defined as a function of the magnitude and frequency of a hazard process times consequences; the latter being quantified by the value of elements at risk exposed and their vulnerability. Vulnerability is defined by the degree of loss to a given element at risk resulting from the impact of a natural hazard. Recent empirical studies suggested a dependency of the degree of loss on the hazard impact, and respective vulnerability (or damage-loss) functions were developed. However, until now, only little information is available on the spatial characteristics of vulnerability on a local scale; considerable ranges in the loss ratio for medium process intensities only provide a hint that there might be mutual reasons for lower or higher loss rates. In this paper, we therefore focus on the spatial dimension of vulnerability by searching for spatial clusters in the damage ratio of elements at risk exposed. By using the software SaTScan, we applied an ordinal data model and a normal data model in order to detect spatial distribution patterns of five individual torrent events in Austria. For both models, we detected some significant clusters of high damage ratios, and consequently high vulnerability. Moreover, secondary clusters of high and low values were found. Based on our results, the assumption that lower process intensities result in lower damage ratios, and therefore in lower vulnerability, and vice versa, has to be partly rejected. The spatial distribution of vulnerability is not only dependent on the process intensities but also on the overall land use pattern and the individual constructive characteristics of the buildings exposed. Generally, we suggest the use of a normal data model for test sites exceeding a minimum of 30 elements at risk exposed. As such, the study enhanced our understanding of spatial vulnerability patterns on a local scale.

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