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This study investigates the detection of discontinuities in air and precipitation data across Europe and explores the need for identifying and correcting these discontinuities before trend analysis. Weekly means of SO2, and SO4 in air and precipitation data from multiple countries in Europe were analyzed. The study proposes a test for identifying discontinuities based on the difference between left and right smooths. The preliminary analysis reveals the presence of seasonal cycles and a variety of discontinuities in the data. Further analysis and corrections are necessary before interpreting trends in the data.
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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
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.
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
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)
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
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.
First Example of Discontinuity Plot of SO2
First Example of Discontinuity Plot of SO2
First Type of Discontinuity First Example of Discontinuity
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Second Type of Discontinuity Second Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
Third Type of Discontinuity Third Example of Discontinuity Plot of SO4 in precipitation not corrected
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.
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.