Extreme Value and Trend Analysis Based on Statistical Modelling of Precipitation Time Series

Abstract

Application of a generalized time series decomposition technique shows that observed German monthly precipitation time series can be interpreted as a realization of a Gumbel-distributed random variable with time-dependent location parameter and time-dependent scale parameter. The achieved complete analytical description of the series, that is, the probability density function (PDF) for every time step of the observation period, allows probability assessments of extreme values for any threshold at any time. So, we found in the western part of Germany that climate is getting more extreme in winter. Both the probability for exceeding the 95th percentile and the probability for falling under the 5th percentile are increasing. Contrary results are found in summer. The spread of the distribution is shrinking. But in the south, relatively high precipitation sums become more likely and relatively low precipitation sums become more unlikely in turn of the twentieth century.