Modelling severe hail events over Austria using the metastatistical extreme value distribution

Knowledge about extreme values of severe hail plays an important role in engineering and insurance. The estimation of return levels of severe hail events is challenging, as hail is locally rare and documentation about hail events is not available in a unified way. For instance for the state of Austria GeoSphere provides radar based probabilities of hail (POH) and maxima of expected hail size (MEHS) that only span a period from 2010 onward.

Based on this sparse data the application of classical extreme value theory, such as Block-Maxima or Peak over Threshold might be invalid. Instead we use a version of the metastatistical extreme value distribution (MEVD), which was shown to work reasonably well in the context of extreme precipitation events, even with a rather small number of available years used for the estimation in comparison to the recurrence time. More precisely we make an assumption about the underlying probability distribution of the daily maximum POH values. The parameters of the distribution are then modeled as smooth functions of the day of the year and the year of observation, thus employing the framework of generalized additive models for location, scale and shape (GAMLSS). Furthermore we add topographic information (longitude, latitude, altitude) to our model, resulting in a full spatiotemporal model across the whole domain of Austria, from which the return values of the POH, respectively MEHS are calculated.

This framework allows for the incorporation of an arbitrary number of additional covariables, as long as they are available on the same grid as the desired output. To illustrate this we use the information of daily precipitation extremes to enrich the model with additional atmospheric information.