About the return period of a catastrophe

Abstract. To understand catastrophes like earthquakes stochastically, their return period (RP) should be quantified for the concerned region. Measures such as event magnitudes or indexes are less helpful for this purpose. We derive the combined return period (CRP) from the pseudo-polar coordinates of extreme value theory. The CRP is the (weighted) mean of local RPs and is again an RP; other metrics do not provide such testable reproductivity. We demonstrate CRP’s opportunities on extratropical cyclones (winter storms) over Germany, including validation and bias correction of local RP estimates. Furthermore, we introduce new estimation methods for the RP of an event loss (risk curve) via CRP-scaling of historical storm fields. For high RP, the resulting event losses of the German insurance market are higher in the case of max-stable dependence. The latter means the same dependence level between local maxima of a year as of a decade. However, spatial dependence is not stable but decreases by increasing period. Such control of spatial dependence is not realized by previous risk models from science and industry. Our loss estimates for RP of 200 years are also significantly smaller than those of European regulation's standard model.