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Methodology and results for O3 data
In order to better understand the temporal fluctuations of the atmospheric ozone content, the Rao and Zurbenko technique (RZ) is applied (Eskridge et al., 1997; Meghan et al., 1998) to the long ozone time series of Vigna di Valle and Arosa, and to the Italian Brewer data sets. The different time scales involved can be separated, allowing to identify the effective ozone trend.
Following the RZ method, the Brewer ozone time series can be splitted in a long-term component (time period greater than 2 years), a seasonal component (time period below 2 years but greater than 1 month), a short-term component (time period below 1 month, related to weather patterns, which we call high frequency ozone). The two remaining terms of turbulence and instrumental error may be considered negligible here, giving a contribute only when single daily ozone data are considered. From the analysis, it seems that meteorological factors affect Rome data more than Ispra’s (Casale et al., 2000). On the other hand, the seasonal term plays a significant role in explaining Ispra variability compared to Rome.The same RZ analysis can be applied to the monthly ozone time series of Vigna di Valle and Arosa. After filtering all cyclical variations smaller than the 11 years solar cycle, the decline is singled out starting from 1970s for Arosa (2.20%/10 years) and from 1980s for Vigna di Valle (4.98%/10 years).
In order to characterize the O3 trend, a well-known advanced statistical methodology is applied to the long time series of yearly and monthly mean values (low frequency ozone) to ascertain the internal structure of the series. Therefore simple randomness of the series is tested against serial correlation and against trend. The trend analysis is used in a sequential way and completed by a change point search procedure. For this purpose, as suggested by Sneyers, Mann?Kendall-Sneyers trend tests (MKS) are used (Sneyers, 1990; Sneyers, 1992).
The tests are non parametric (distribution free) having optimal power relative to the corresponding parametric ones. The trend test is applied in a progressive sequential onward and backward way in order to avoid false conclusions due to the eventual existence of compensating internal trends. A Pettitt test (1979) completes the analysis showing the possible abrupt character of climate instability. The change point is estimated in the case of series divided by one such point into two sub-series with or without trend. A significance level of 95% is chosen to interpret the results. Under this condition, the hypothesis of trend is accepted or rejected at the level of 5%, depending on whether probability is <5% or >5%.
Tables 1 and 2 show the MKS, Pettitt and RZ analysis’ results. The column "Zurbenko" in Table 2 indicates the slope of regression line of the long term component obtained by using the RZ technique, cross-checking the validity of the trend. The trend slope is determined from around 1970 at Arosa and from around 1980 at Vigna di Valle (see column "year" in Table 2).
Table 1. Summary of the statistical tests on O3 on yearly basis. The trend is expressed as %/10years
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Yearly |
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Yearly |
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Yearly |
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VV: Vigna di Valle; AR: Arosa; prob: probability <5%
Table 2. Results of Pettitt’s test on O3. The third column (Pettitt) indicates the "change point" year;
the last three columns report the trends before and after the change point and the RZ results
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left trend %/10 years |
right trend %/10 years |
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VV: Vigna di Valle; AR: Arosa
It is pointed out on yearly basis, by means of MKS methodology (Table 1), the existence of a negative trend of 0.63% every ten years, in the period 1927-1999, and 1.76%/10 years in the period 1958-99 at Arosa. A negative trend of 1.57% every ten years, from 1958 to 1999, is estimated at Vigna di Valle. By means of Pettitt test, the "change point" year is estimated (Table 2): around 1983 at Vigna di Valle and around 1978 at Arosa. A significant decreasing trend of ?1.09% every 10 years at the first site and ?3.2%/10 years at the second one is detected from the change point on.
The same method of analysis applied to the yearly mean amount is extended on monthly basis. Table 3 and 4 present a summary of monthly ozone trends estimated in the period 1958-1999 (VV) and 1927-1999 (AR) considering respectively the whole record time period and that from the change point. The reported probability (<5%) refers solely to the significant negative trends
Table 3. Summary of the statistical tests on O3 on monthly basis. The sign + indicates significant positive trend; the sign - indicates significant negative trend; a blank cell indicates no trend
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Trend (%/10 years) |
Probability (%) |
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VV (1958-1999) |
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AR (1927-1999) |
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Table 4. Summary of the statistical tests on monthly basis on O3 at the right of the change point. The sign + indicates significant positive trend; the sign - indicates significant negative trend; a blank cell indicates no trend
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Trend (%/10 years) |
Probability (%) |
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VV (1958-1999) c.p. 1983 |
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AR (1958-1998) c.p. 1979 |
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c.p.: change point
These results are in accordance with recent studies on ozone decline by Bojkov and Fioletov (1995) Bojkov et al. (1998) and the last WMO Scientific Assessment of Ozone Depletion (1999).