Inferences on weather extremes and weather-related disasters: a review of statistical methods

The study of weather extremes and their impacts, such as weather-related disasters, plays an important role in climate-change research. Due to the great societal consequences of extremes - historically, now and in the future - the peer-reviewed literature on this theme has been growing enormously since the 1980s. Data sources have a wide origin, from century-long climate reconstructions from tree rings to short databases with disaster statistics and human impacts (30 to 60 yr). In scanning the peer-reviewed literature on weather extremes and impacts thereof we noticed that many different methods are used to make inferences. However, discussions on methods are rare. Such discussions are important since a particular methodological choice might substantially influence the inferences made. A calculation of a return period of once in 500 yr, based on a normal distribution will deviate from that based on a Gumbel distribution. And the particular choice between a linear or a flexible trend model might influence inferences as well. In this article we give a concise overview of statistical methods applied in the field of weather extremes and weather-related disasters. Methods have been evaluated as to stationarity assumptions, the choice for specific probability density functions (PDFs) and the availability of uncertainty information. As for stationarity we found that good testing is essential. Inferences on extremes may be wrong if data are assumed stationary while they are not. The same holds for the block-stationarity assumption. As for PDF choices we found that often more than one PDF shape fits to the same data. From a simulation study we conclude that both the generalized extreme value (GEV) distribution and the log-normal PDF fit very well to a variety of indicators. The application of the normal and Gumbel distributions is more limited. As for uncertainty it is advised to test conclusions on extremes for assumptions underlying the modeling approach. Finally, we conclude that the coupling of individual extremes or disasters to climate change should be avoided