Abstract
Abstract. When a natural hazard event like an earthquake affects a region and generates a natural catastrophe (NatCat), the following questions arise: how often does such an event occur? What is its return period (RP)? We derive the combined return period (CRP) from a concept of extreme value statistics and theory – the pseudo-polar coordinates. A CRP is the (weighted) average of the local RP of local event intensities. Since CRP's reciprocal is its expected exceedance frequency, the concept is testable. As we show, the CRP is related to the spatial characteristics of the NatCat-generating hazard event and the spatial dependence of corresponding local block maxima (e.g., annual wind speed maximum). For this purpose, we extend a previous construction for max-stable random fields from extreme value theory and consider the recent concept of area function from NatCat research. Based on the CRP, we also develop a new method to estimate the NatCat risk of a region via stochastic scaling of historical fields of local event intensities (represented by records of measuring stations) and averaging the computed event loss for defined CRP or the computed CRP (or its reciprocal) for defined event loss. Our application example is winter storms (extratropical cyclones) over Germany. We analyze wind station data and estimate local hazard, CRP of historical events, and the risk curve of insured event losses. The most destructive storm of our observation period of 20 years is Kyrill in 2002, with CRP of 16.97±1.75. The CRPs could be successfully tested statistically. We also state that our risk estimate is higher for the max-stable case than for the non-max-stable case. Max-stable means that the dependence measure (e.g., Kendall's τ) for annual wind speed maxima of two wind stations has the same value as for maxima of larger block size, such as 10 or 100 years since the copula (the dependence structure) remains the same. However, the spatial dependence decreases with increasing block size; a new statistical indicator confirms this. Such control of the spatial characteristics and dependence is not realized by the previous risk models in science and industry. We compare our risk estimates to these.
Highlights
The combined return period (CRP) is related to the spatial characteristics of the natural catastrophe (NatCat)-generating hazard event and the spatial dependence of corresponding local block maxima
We extend a previous construction for maxstable random fields from extreme value theory and consider the recent concept of area function from NatCat research
After a natural hazard event such as a large windstorm or an earthquake has occurred in a defined region and results in a natural catastrophe (NatCat), the following questions arise: how often does such a random event occur? What is the corresponding return period (RP, called recurrence interval)? Before discussing this issue, we underline that the extension of river flood events or windstorms in time and space depends on the scientific and socioeconomic event definition
Summary
After a natural hazard event such as a large windstorm or an earthquake has occurred in a defined region (e.g., in a country) and results in a natural catastrophe (NatCat), the following questions arise: how often does such a random event occur? What is the corresponding return period (RP, called recurrence interval)? Before discussing this issue, we underline that the extension of river flood events or windstorms in time and space depends on the scientific and socioeconomic event definition. As we will show by a combination of existing and new approaches from stochastic and NatCat research, the concept of CRP is strongly related to the spatial association/dependence between the local event intensities, their RPs, and corresponding block maxima, such as annual maxima. Previous opportunities and approaches for a risk estimate are the conventional statistical models that are fitted to observed or re-analyzed aggregated losses ( called as-if losses) of historical events, as used by Donat et al (2011) and Pfeifer (2001) for annual sums The advantages of such simple models are the controlled stochastic assumptions and the small number of parameters; the disadvantages are high uncertainty for widely extrapolated values and limited possibilities to consider further knowledge. We expect that the reader is familiar with statistical and stochastic concepts such as statistical significance, goodness-of-fit tests, random fields, and Poisson (point) processes (Upton and Cook, 2008)
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