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# First Results of the Daily Stew Project

First Results of the Daily Stew Project. Ralf Lindau. 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

## First Results of the Daily Stew Project

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

2. 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 Daily Stew Kickoff – 27. January 2011

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

4. Kriging Approach • n observations xi at the locations Pi are given. • Perform a prediction x0 for the location P0 , where no obs is available. • Construct the prediction by a weighted average of the observations xi. • Take into account the observation errors Dxi. • Determine the weights li. Daily Stew Kickoff – 27. January 2011

5. 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. Daily Stew Kickoff – 27. January 2011

6. 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. Daily Stew Kickoff – 27. January 2011

7. 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 Daily Stew Kickoff – 27. January 2011

8. 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 Daily Stew Kickoff – 27. January 2011

9. Decomposition of Variance m years N subperiods nk 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. Daily Stew Kickoff – 27. January 2011

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

11. 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. criterion time series Daily Stew Kickoff – 27. January 2011

12. 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. Daily Stew Kickoff – 27. January 2011

13. The second break • 0.3197 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 1968 0.3296 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 1969 0.3232 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 1979 0.2821 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 1967 0.3301 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 1978 0.2818 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 1980 0.2720 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 1971 0.3041 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 1972 0.2987 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 1981 0.2654 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 Daily Stew Kickoff – 27. January 2011

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

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

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

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

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

19. Decreasing of internal variance 1 to 400 breaks within 1000 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. 1 to 50 breaks within 100 years Daily Stew Kickoff – 27. January 2011

20. 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). 95% 90% Median Daily Stew Kickoff – 27. January 2011

21. Observations 95% Random 90% 50% 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. Daily Stew Kickoff – 27. January 2011

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

23. 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. Daily Stew Kickoff – 27. January 2011

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