1. Daily Stew Kickoff – 27. January 2011 First Results of the Daily Stew Project Ralf Lindau

2. Daily Stew Kickoff – 27. January 2011 First Steps Data: Climate stations of DWD with daily data (or even 7, 14, 21 h) Although the project is focused on weather indices and extremes, we consider initially a much easier parameter: Monthly mean temperature Derive and test methods to: Create reference time series Differences between a station and its reference are expected be zero Detect breaks Maximize the external variance by a minimum of breaks

3. Daily Stew Kickoff – 27. January 2011 DWD Climate Stations 20001900 1920 1960 1200 Stations in total, but not coexistent. 1900: 25 1940: 100 1960: 500 2000: 600

4. Daily Stew Kickoff – 27. January 2011 Kriging Approach n observations x i at the locations P i are given. Perform a prediction x 0 for the location P 0, where no obs is available. Construct the prediction by a weighted average of the observations x i. Take into account the observation errors  x i. Determine the weights i.

5. Daily Stew Kickoff – 27. January 2011 Matrix and Input Correlations The spatial autocorrelation is dervided from all available data for each of the 12 months. High correlations for monthly mean temperature.

6. Daily Stew Kickoff – 27. January 2011 Potsdam and Reference A reference for each station is created by kriging of the surrounding 16 stations. Normalized temperature anomaly in January for station Potsdam. Station and Reference seems to be nearly identical.

7. Daily Stew Kickoff – 27. January 2011 Potsdam and Reference A reference for each station is created by kriging of the surrounding 16 stations. Normalized temperature anomaly in January for station Potsdam. Station and Reference seems to be nearly identical. However, there is a difference showing a positive trend from 1930 to 2000

8. Daily Stew Kickoff – 27. January 2011 Defining breaks Breaks are defined by abrupt changes in the station-reference time series. Internal variance within the subperiods External variance between the means of different subperiods Maximize the external variance by a minimum number of breaks

9. Daily Stew Kickoff – 27. January 2011 Decomposition of Variance m years N subperiods n k members The external variance is a weighted measure for the variability of the subperiods‘ means. The internal variance contains information about the error of the subperiods‘ means. The seeming external variance has to be diminished by this error to obtain the true external variance.

10. Daily Stew Kickoff – 27. January 2011 Break Criterion The true external variance is used as criterion for breaks.

11. Daily Stew Kickoff – 27. January 2011 The first break The difference time series increase from 1930 to 2000 (as already shown) Between 1965 and 1985 the criterion reaches maximum values. More than 20% of the total variance can be explained by a break in one of these years. 1970196819691979196719781980197119721981 21.7721.7621.6721.6421.4121.3321.0720.9520.8720.77 criterion time series

12. Daily Stew Kickoff – 27. January 2011 Break Searching Method Now the first break is not simply fixed where the maximum criterion occured (1970). But combinations of two breaks are tested which contain one of the 10 best first-break candidates (10 times 100 permutations). The 10 best two-breaks combinations are used as seed for the search of three-breaks combinations.

13. Daily Stew Kickoff – 27. January 2011 19700.3197 0.3176 0.3150 0.3029 0.2968 0.2941 0.2904 0.2869 0.2857 0.2824 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19680.3296 0.3270 0.3240 0.3110 0.3039 0.3014 0.2969 0.2931 0.2911 0.2881 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19690.3232 0.3209 0.3181 0.3056 0.2991 0.2965 0.2924 0.2888 0.2872 0.2840 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19790.2821 0.2815 0.2804 0.2718 0.2686 0.2656 0.2642 0.2632 0.2621 0.2591 1930 1929 1928 1927 1925 1926 1924 1920 1923 1922 19670.3301 0.3273 0.3240 0.3106 0.3032 0.3007 0.2959 0.2919 0.2896 0.2868 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19780.2818 0.2810 0.2799 0.2710 0.2675 0.2646 0.2630 0.2617 0.2608 0.2577 1930 1929 1928 1927 1925 1926 1924 1920 1923 1922 19800.2720 0.2716 0.2707 0.2624 0.2595 0.2565 0.2553 0.2547 0.2534 0.2506 1930 1929 1928 1927 1925 1926 1924 1920 1923 1922 19710.3041 0.3023 0.3001 0.2887 0.2831 0.2804 0.2771 0.2739 0.2732 0.2697 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19720.2987 0.2971 0.2951 0.2841 0.2790 0.2761 0.2732 0.2702 0.2698 0.2662 1930 1929 1928 1927 1925 1926 1924 1923 1920 1922 19810.2654 0.2651 0.2643 0.2564 0.2537 0.2508 0.2499 0.2497 0.2497 0.2495 1930 1929 1928 1927 1925 1926 1967 1924 1968 1920 The second break

14. Daily Stew Kickoff – 27. January 2011 1 Break

15. Daily Stew Kickoff – 27. January 2011 2 Breaks

16. Daily Stew Kickoff – 27. January 2011 3 Breaks

17. Daily Stew Kickoff – 27. January 2011 4 Breaks Where to stop? The searching method is applied to a random time series to define a stop criterion

18. Daily Stew Kickoff – 27. January 2011 Random Time Series 2 breaks 30 breaks

19. Daily Stew Kickoff – 27. January 2011 Decreasing of internal variance 1 to 400 breaks within 1000 years 1 to 50 breaks within 100 years The remaining internal variance shrinks rather smoothly for a 1000 years time series. Actually, we are dealing with only a 100 years time series. Similar behaviour, but less regular. Repeat the procedure 500 times and consider the change in variance for each added break.

20. Daily Stew Kickoff – 27. January 2011 Many Breaks for many random time series In average 6% of the variance is gained by the first breaks. The 50th break gains only 0.3% The 90 and the 95 percentile remain nearly constant at a few percent. The first step is an exception as here only 100 possibilities are tested, whereas further breaks are searched from 1000 possibilities (10 candidates times 100 years). Median 90% 95%

21. Daily Stew Kickoff – 27. January 2011 Observations vs Random After 4 breaks the gained variance of the observations is comparable to that found for random time series. 4 breaks are realistic for the considered station. 95% Random 90% 50% Observations

22. Daily Stew Kickoff – 27. January 2011 Leaving out one station January February Reference from nearest 16 stations Reference without Berlin-Dahlem

23. Daily Stew Kickoff – 27. January 2011 Conclusion For monthly mean temperatures of DWD climate stations A method to create reference time series is derived. A method to detect breaks in difference time series is derived.