Indirect identification of damage functions from damage records

TL;DR

This paper investigates how damage functions can be indirectly identified from damage records by analyzing their distributions and relating them to extreme value statistics, providing insights into damage modeling for natural disasters.

Contribution

It introduces a method to infer damage functions from damage distributions based on extreme value theory, linking damage data to specific functional forms.

Findings

Broad damage distributions suggest specific damage functions.

Power-law damage functions relate to Gumbel-distributed extremes.

Steeper damage functions correspond to Weibull-distributed extremes.

Abstract

In order to assess future damage caused by natural disasters, it is desirable to estimate the damage caused by single events. So called damage functions provide -- for a natural disaster of certain magnitude -- a specific damage value. However, in general, the functional form of such damage functions is unknown. We study the distributions of recorded flood damages on extended scales and deduce which damage functions lead to such distributions when the floods obey Generalized Extreme Value statistics and follow Generalized Pareto distributions. Based on the finding of broad damage distributions we investigate two possible functional forms to characterize the data. In the case of Gumbel distributed extreme events, (i) a power-law distribution density with an exponent close to 2 (Zipf's law) implies an exponential damage function; (ii) stretched exponential distribution densities imply power-law damage functions. In the case of Weibull (Frechet) distributed extreme events we find correspondingly steeper (less steep) damage functions.