Statistical modelling of observed precipitation and its application to extreme value statistics in different spatiotemporal scales (MODEX) is a DFG-project (proposal in german).
The Gaussian distribution has many convenient properties. Consequently, climate time series are often assumed to be normal. For variables that are not well approximated by normal distributions, like precipitation, changes in the mean value can be accompagnied by changes in the spread of the distribution (scale parameter) or in the shape of the distribution. The generalized time series decomposition technique introduced (Trömel et al., 2005) provides a full analytical description of observed monthly precipitation time series. The probability density function is estimated for every time step of the observation period (every month of every year in case of monthly data) on the basis of the whole time series respectively. Consequently, probability assessments of extreme values are possible for any threshold at any time. This approach allows one to take into account instationarity of observational precipitation time series, particulary with regard to changes in different parameters (location parameter, scale parameter, shape parameter). The movie below (click on the figure) shows changes in the probability density function of the monthly precipitation time series observed in Eisenbach-Bubenbach (47.97ºN, 8.3ºE) in July during the years 1901 to 2000. Significant detected changes in the location and the scale parameter of the Gumbel distribution cause changes in the expected value, the probability for exceeding the 95th percentile and the probability for falling under the 5th percentile.