Payer, Tilman (2007): Modelling extreme wind speeds. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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### Abstract

Very strong wind gusts can cause derailment of some high speed trains so knowledge of the wind process at extreme levels is required. Since the sensitivity of the train to strong wind occurrences varies with the relative direction of a gust this aspect has to be accounted for. We first focus on the wind process at one weather station. An extreme value model accounting at the same time for very strong wind speeds and wind directions is considered and applied to both raw data and component data, where the latter represent the force of the wind in a chosen direction. Extreme quantiles and exceedance probabilities are estimated and we give corresponding confidence intervals. A common problem with wind data, called the masking problem, is that per time interval only the largest wind speed over all directions is recorded, while occurrences in all other directions remain unrecorded for this time interval. To improve model estimates we suggest a model accounting for the masking problem. A simulation study is carried out to analyse the behaviour of this model under different conditions; the performance is judged by comparing the new model with a traditional model using the mean square error of high quantiles. Thereafter the model is applied to wind data. The model turns out to have desirable properties in the simulation study as well as in the data application. We further consider a multivariate extreme value model recently introduced; it allows for a broad range of dependence structures and is thus ideally suited for many applications. As the dependence structure of this model is characterised by several components, quantifying the degree of dependence is not straight forward. We therefore consider visual summary measures to support judging the degree of dependence and study their behaviour and usefulness via a simulation study. Subsequently, the new multivariate extreme value model is applied to wind data of two gauging stations where directional aspects are accounted for. Therefore this model allows for statements about the joint wind behaviour at the two stations. This knowledge gives insight whether storm events are likely to be jointly present at larger parts of a railway track or rather occur localized.