Statistical modelling of precipitation time series including probability assessments of extreme events Silke Trömel and Christian-D. Schönwiese Institute for Atmosphere and Environment J. W. Goethe University Frankfurt/M., Germany

Gaussian assumptions

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Modell: Gaussian distribution

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Parameter P2(t): Trends Constant annual cycle Modell: Gaussian distribution

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Parameter P2(t): Trends Constant annual cycle Modell: Gumbel distribution

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Parameter P2(t): Trends Constant annual cycle Modell: Gumbel distribution

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Parameter P2(t): Trends Constant annual cycle Modell: Weibull distribution

Statistical modelling of climate time series Parameter P1(t): Trends Annual cycle Episodic component Parameter P2(t): Trends Constant annual cycle Modell: Weibull distribution

The distance function Gaussian distribution PDF Least Squares ML Distance function ML

Different distributions and their distance functions Gaussian distribution: Least-squares : Random number Pdf Random number Distance function

Different distributions and their distance functions Weibull distribution: Frequency Precipitation [mm] Distance function Precipitation [mm] Gumbel distribution: Precipitation [mm] Pdf

Analyses of a German station network 132 time series of monthly precipitation totals, Realization of a Gumbel distributed random variable Eisenbach-Bubenbach

Example: Eisenbach-Bubenbach [47.97 o N, 8.3 o E]

The expected value

…of a Gumbel distributed random variable with time-dependent location parameter a G (t) and time-dependent scale parameter b G (t) Precipitation [mm] Pdf [1/mm]

The expected value …of a Gumbel distributed random variable with time-dependent location parameter a G (t) and time-dependent scale parameter b G (t) Precipitation [mm] Pdf [1/mm]

Germany: Changing probability of extreme events > 95th percentile January < 5th percentile January

Germany: Changing probability of extreme events < 5th percentile August > 9 5th percentile August

Trend estimates by comparison LS January Gumbel January

Conclusions The introduced generalized time series decomposition technique allows a free choice of the underlying PDF The signal is detected in two instead of one parameter of the PDF Statistical modeling of precipitation time series can be achieved The analytical description of the time series 1.allows probability assessments of extreme values for every time step during the observation period 2. provides trend estimates taking into account the statistical characteristics (of precipitation)