Abstract
The overall subject of this thesis is the massive parallel application of the extreme value analysis (EVA) on climatological time series. In this branch of statistics one strives to learn about the tails of a distribution and its upper quantiles, like the so-called 50 year return level, an event realized on average only once during its return period of 50 years. Since most studies just focus on average statistics and it's the extreme events that have the biggest impact on our life, such an analysis is key for a proper understanding of the climate change. In there a time series gets separated into blocks, whose maxima can be described using the generalized extreme value (GEV) distribution for sufficiently large block sizes. But, unfortunately, the estimation of its parameters won't be possible on a massive parallel scale with any available software package since they are all affected by onceptional problems in the maximum likelihood fit. Both the logarithms in the negative log-likelihood of the GEV distribution and the theoretical limitations on one of its parameters give rise to regions in the parameter space inaccessible to the optimization routines, causing them to produce numerical artifacts. I resolved this issue by incorporating all constraints into the optimization using the augmented Lagrangian method. With my implementation in the open source package **climex** it is now possible to analyze large climatological data sets. In this thesis I used temperature and precipitation data from measurement stations provided by the German weather service (DWD) and the ERA-Interim reanalysis data set and analyzed them using both a qualitative method based on time windows and a more quantitative one relying on the class of vector generalized linear models (VGLM). Due to the climate change a general shift of the temperature towards higher values and thus more hot and less cold extremes would be expect. Indeed, I could find the cation parameters of the GEV distributions, which can be thought of as the mean event size at a return period of approximately the block size of one year, to increase for both the aily maximum and minimum temperatures. But the overall changes are far more complex and dependent on the geographical location as well as the considered return period, hich is quite unexpected. E.g. for the 100 year return levels of the daily maximum temperatures a decrease was found in the east and the center of Germany for both the raw series and their anomalies, as well as a quite strong reduction for the raw series in the very south of Germany. The VGLM-based non-stationary EVA resulted in significant trends in the GEV parameters for the daily maximum temperatures of almost all stations and for about half of them in case of the daily minima. So, there is statistically sound evidence for a change in the extreme temperatures and, surprisingly, it is not exclusively towards higher values. The analysis yielded several significant trends featuring a negative slope in the 10 year return levels. The analysis of the temperature data of the ERA-Interim reanalysis data set yielded quite surprising results too. While in some parts of the globe, especially on land, the 10 year return levels were found to increase, they do in general decrease in most parts of the earth and almost entirely over the sea. But since we found a huge discrepancy between the results of the analysis using the station data within Germany and the results obtained for the corresponding grid points of the reanalysis data set, we can not be sure whether the patterns in the return levels of the ERA-Interim data are trustworthy.
