Dependence Structures in Modeling Disaster Dynamics

Modeling disaster events in time, severity, and location requires not only to look for the statistical distributions of these relevant quantities, but also to look for the dependencies among them. It turns out that in fact various dependencies can be observed and that ignoring these dependencies would give a completely wrong picture about the overall risk to life and property due to catastrophic events. The most obvious dependency is on time: In fact, climate change and the increase of wealth make the amount of damage per year increase, and this has to be taken into account when cat-events are modeled. However, there are numerous other dependencies: Quite obvious is the spatial dependency: Typically larger disasters have an impact on several locations. But also, the temporal dependency is observable: A disaster of type Y may trigger events of another type Z. (Think, for instance, about a heat wave, which may trigger a forest fire). There is also a possible effect of one event of type Y on the severity of a subsequent event of type Z (e.g., a preceding drought may exacerbate the effect of a subsequent flood, because the soil is not able to absorb large volumes of water). For geodynamic events, the timing between two earthquakes may influence the severity of the later event. In this paper, we review such types of dependence models and give examples based on observed data.