Aspects of risk assessment in power-law distributed natural hazards

Risk assessment is mainly based on certain scenarios involving an event of a certain size which is thought to be characteristic for the considered type of hazard. However, many natural hazards extend over a wide range of event sizes, and some of them are even free of characteristic scales. An expression for the risk taking into account various event sizes is derived, and its implications on risk assessment for earthquakes, forest fires, landslides, and rockfalls are discussed. Under simple assumptions on the damage as a function of the event size, it turns out that the total risk is governed by either the small number of large events or the majority of small events. The distinction between these two classes depends on both the power-law exponent of the event size distribution and the damage function. For earthquakes, forest fires, and rockfalls, the total risk is mainly constituted by the largest events, while results are non-unique for landslides.