Detecting Discontinuities in Air and Precipitation Data Across Europe

1. Detecting Discontinuities Marco Giannitrapani 1 Marian Scott 1 Adrian Bowman 1 Ron Smith 2 ( 1=University of Glasgow, 2= CEH of Edinburgh ) Valencia, 9-11 April 2003

2. What is a “discontinuity”? A discontinuity is an “abrupt-change” in mean level. Temporary change Permanent change Why are we interested in detecting discontinuities? • It is necessary to identify any discontinuities to understand the cause of the change: • Emission changes. • Change in laboratory. • Weather effects. • Something else…. • If possible, it is so necessary to correct the series before doing any trend analysis, if not, to analyse each “sub-trend” separately.

3. DATA ANALYSED • Weekly means of the natural logarithm of the daily data for: • SO2 • SO4 in air • SO4 in precipitation (corrected and not for the sea-salt) • Across Europe

4. Austria (4) Croatia (2) Czech Republic (2) Denmark (6) Finland (7) France (12) Germany (19) Latvia (2) Lithuania (2) Netherlands (7) Norway (12) Poland (5) Slovakia (4) Sweden (8) Switzerland (5) United Kingdom (10)

5. PRELIMINARY ANALYSIS Daily data have shown the presence of two kind of seasonal cycles “Day within the week” “Week within the year” Difference between week and weekend days. Difference between seasons of the year. de-seasonalised data

6. Theory of the Discontinuity Test The test used was proposed by Bowman and Pope (1997): At each data point x1, x2,…, xnwe observe the data y1, y2,…, yn where: yi = g(xi)+ei for i = 1,… ,n. (where g is a smooth function) The test statistic is based on the difference between the left (gl(xi)) and the right (gr(xi)) smooths, where: Left Smoother Right Smoother where kh(the kernel smoother) is the normal density function in z with mean xjand standard deviation h; I{} is the indicator function. Criteria for detection is given by |gl(xi) - gr(xi)| > 3 standard errors.

7. First Example of Discontinuity Plot of SO2

8. First Example of Discontinuity

9. First Example of Discontinuity Plot of SO2

10. First Type of Discontinuity First Example of Discontinuity

11. First Example of Discontinuity

12. First Example of Discontinuity

13. First Example of Discontinuity

14. First Example of Discontinuity

15. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

16. Second Type of Discontinuity Second Example of Discontinuity

17. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

18. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

19. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

20. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

21. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

22. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

23. Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected

24. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

25. Third Type of Discontinuity Third Example of Discontinuity

26. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

27. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

28. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

29. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

30. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

31. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

32. Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected

33. Final Remarks • The test can be used to identify whether changes in trend have occurred. • Once a discontinuity is detected, the series should be corrected before interpreting the trend, or doing any analysis. If it is not possible to do any corrections, then it becomes necessary, to treat each sub-trend separately. • This version of the test requires estimation of the correlation and of the variance of the data. These have been computed on the basis of the weekly means after removing any trend and seasonality. • Because of the edge bias in smoothers, fifty "testing points" at the start and fifty at the end of the series have been excluded.

34. Conclusions • A slight steadily decreasing trend can be noted, which seems more pronounced for SO2. • However, the rate of decrease is not constant over the entire time period, and discontinuities represent a common feature. • In particular, several “temporary” discontinuities have been identified. • There are strong arguments for not fitting a single (and simple) trend function. • Some data present still peculiar features that need to be revisited.