Clementine Dalelane & Thomas Deutschländer European Conference on Applications of Meteorology

1. An Analysis of Changes in the Extremes of Temperature and Precipitation based on Regional Climate Projections for Germany Clementine Dalelane & Thomas Deutschländer European Conference on Applications of Meteorology Berlin, September 12, 2011

2. A joint Project of the Working Group on „Climate Change and Civil Protection“ of the Federal German Agency Alliance Analysis of the Change • in the frequency and intensity of: • heavy precipitation events • storm events • in the duration of: • drought periods • precipitation episodes • heat waves DWD - Changes in the Extremes

3. 1. Kernel Estimator of the Point Process Intensity Functional Cluster Analysis Extreme Value Statistics DWD - Changes in the Extremes

4. Regional Climate Projections for Germany (A1B) • Models: CLM, REMO, WETTREG, STAR, HadRM, Aladin (1961-2100) • Variables: daily maximal Temperature, daily total Precipitation • Separation of the seasons (JJA, DJF) • Thresholds: 90th, 95th, 99th percentile from C20 (1961-2000) Cutting of the time series at the respective threshold Non-homogenous Poisson Point Process DWD - Changes in the Extremes

5. Nonparametric Intensity Estimation • No ex ante model selection – flexible and robust estimation • Kernel estimator known from density (Rosenblatt 1956 and Parzen 1962) and regression estimation (Nadaraya 1964) • Kernel estimator for the intensity λ(t) of a Poisson Process (Dia 1990, Mudelsee 2005) WEIGHTED MOVING AVERAGE Epanechnikov kernel with bandwidth h=3000 days DWD - Changes in the Extremes

6. Examples from CLM for q=0.99 • Estimated probability of quantile exceedance for several grid points at 10°E Temperature(Summer) Precipitation (Winter) North→South DWD - Changes in the Extremes

7. Functional Cluster Analysis • CATS algorithm (Serban & Wassermann 2005) -- Clustering After Transformation and Smoothing • Functional correlation coefficient Kernel Intensity Estimators Fourier Expansion Clustering of Fourier coefficients is equivalent to clustering of curves in time domain Set higher frequency coefficients to 0 k-means procedure DWD - Changes in the Extremes

8. Probability of Extreme Precipitation Events (DJF) • Criteria for selection of k: spatial fragmentation, discriminatory power 2 Clusters 3 Clusters 4 Clusters 5 Clusters DWD - Changes in the Extremes

9. Probability of Extreme Temperature Events (JJA) 2 Clusters 3 Clusters 4 Clusters 5 Clusters DWD - Changes in the Extremes

10. Increasing Quantiles q→1 • When data become too sparse, kernel intensity estimator no longer possible • Decomposition following Smith & Shively (1995), for u2>u1 high thresholds where G is the Generalized Pareto Distribution DWD - Changes in the Extremes

11. Generalized Pareto Distribution for extreme Temperatures (JJA) • Exponential model with time varying scale parameter with Probability of exceedance • Temporal evolution of the density Baltic sea Southwest Northeast (inland) Years 19702000203020602090Exceedance of the 0.99th percentile in kelvin (logarithmic scale) DWD - Changes in the Extremes

12. Generalized Pareto Distribution for extreme Precipitation (DJF) • Full model with time varying scale parameter and constant shape parameter with and const • Spatial distribution of the shape parameter makes no physical sense (rf. Brown 2010) • Entire modelization questionable DWD - Changes in the Extremes

13. Evaluation of the Fitted GPD Parameters Kernel intensity for u0.99 Kernel intensity for u0.9+x P(y>u0.99) from GPD with u0.9+x Temperature (Summer) Basic quantile: 90% Precipitation (Winter) Basic quantile: 90% (left) and 95% (right) • Instationary quantiles, flexible scale model, pooled shape parameter DWD - Changes in the Extremes

14. Thank you very much for your Attention DWD - Changes in the Extremes

15. Pointwise Confidence Intervals (α=0.95) • Poisson converges to Normal distribution ⇒ parametric confidence intervals Precipitation (Winter) Temperature (Summer) DWD - Changes in the Extremes