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Theor. Appl. Climatol. 87, 2939 (2007) DOI 10.1007/s00704-005-0230-4
Institute for Atmosphere and Environment, J.W. Goethe University, Frankfurt a.M., Germany
Probability change of extreme precipitation observed from 1901 to 2000 in Germany
S. Trmel and C.-D. Schnwiese
With 13 Figures
Received July 27, 2005; revised September 21, 2005; accepted October 4, 2005 Published online June 14, 2006 # Springer-Verlag 2006
Summary
A generalized time series decomposition technique is applied to monthly total precipitation data from a German station network of 132 time series covering 19012000. The decomposition technique shows that observed time series can be interpreted as a realization of a Gumbel distributed random variable with time-dependent location parameter and time-dependent scale parameter. It provides a full analytical description of the series in terms of the probability density function (PDF) for every time step of the observation period. Consequently, probability assessments of extreme values are possible for any threshold at any time.
Most of the year, an increase in the probability of exceeding the 95th percentile and a decrease in the probability of falling under the 5th percentile can be detected at several stations in the southern part of Germany. In the western part, we observe the same phenomenon in the summer months, but these changes go along with smaller magnitudes. However, climate is getting more extreme in that region in winter: Probability for both exceeding the 95th percentile and for falling under the 5th percentile is increasing. In the eastern part of Germany, increases in the probability of occurrence of relatively low precipitation in winter as well as decreases in both probabilities (>95th percentile, <5th percentile) in summer and autumn prevail.
1. Introduction
In addition to the consideration of climate changes concerning the mean value of climate elements, considerable interest has emerged in
the probability of occurrence of extreme events which can have major impacts on society, the economy, and the environment. So, an interest to estimate changes in the probability of occurrence of extreme values is obvious.
In the context of statistical analysis, Gaussian distributions have many convenient properties. Consequently, climate time series are often assumed to be normal. As stated in the central limit theorem (Storch and Zwiers, 1999) it can be a good approximation, but the theorem makes an asymptotic statement. Neglecting...