1
Spectral Analysis of Boundary Layer Ozone Data from the
EUROTRAC TOR* Network
T. Cvitaš1, M. Furger2, R. Girgzdiene3, L. Haszpra4, N. Kezele1**, L. Klasinc1,
A. Planinšek5, M. Pompe6, A. S. H. Prevot2, H. E. Scheel7 and E. Schuepbach8
1
Ruđer Bošković Institute, Bijenička 54, HR-10002 Zagreb, Croatia
2
Paul Scherrer Institute, Villigen, Switzerland
3
Institute of Physics, Vilnius, Lithuania
4
Hungarian Meteorological Service, H-1675 Budapest, P.O. Box 39,
Hungary
5
Environmental Agency of Slovenia, Ministry of the Environment, Spatial
Planning and Energy of the Republic of Slovenia, Vojkova 1b, SLO-1000
Ljubljana
6
Faculty of Chemistry and Chemical Technology, University of Ljubljana,
Aškerčeva 5, SLO-1000 Ljubljana, Slovenia
7
Forschungszentrum Karlsruhe, IMK-IFU, D-82467 Garmisch-
Partenkirchen, Germany
8
*
CABO, Physical Geography, University of Berne, Switzerland
Eureka environmental project: European experiment on Transport and transformation of environmentally
relevant trace Constituents in the troposphere over Europe, subproject Tropospheric Ozone Research
**
nenad@joker.irb.hr
2
Abstract
Data obtained during many years of continuous ozone monitoring at 12 selected
EUROTRAC-TOR network stations were analyzed by applying Fourier transformation (FT).
FT averaged over the years, autocorrelation functions and FT of such functions were
calculated for each site. As expected, strong frequency signals are found for the 1 year and 1
day periods. The relative intensity of the 1 day peak can be correlated with the intensity of
local photochemical pollution as represented by a photochemical pollution index. A collective
FT spectrum for 7 European stations was calculated. This comparison confirms the existence
of a common variation in ozone volume fractions with quasi periods ranging between 7 and
44 days. These frequencies are most probably connected with quasi-cyclic synoptic scale
meteorological influences. A comparison of meteorological data from the station Zugspitze
showed similar periodicities.
Keywords: Long term ozone data; Fourier analysis, FT of autocorrelation function,
collective FT spectra, photochemical pollution index.
Introduction
Ozone concentrations in the troposphere exhibit a characteristic time variation with
pronounced diurnal cycles and seasonal behavior. The ozone diurnal and seasonal behaviors
are usually well defined for a tropospheric ozone monitoring station. This is usually
represented by statistical (e.g., average or box and whiskers graphs) [Cvitaš et al., 1995;
Cvitaš et al., 1997] and trend analysis (regression and deseasonalized techniques) [Gilbert,
1987]. Cycles with periods different from 1 day or 1 year are usually not clearly resolved in a
plot of ozone concentration against time. In the 1970s there were already observations of
3
weekend/workday dependence of air pollution data [Cleveland et al. 1974; Elkus and Wilson
1977; Cleveland and McRae 1978]. For some urban regions such 7-day cycles in ozone data
were recently confirmed [Altshuller et al. 1995; Sebold et al. 2000; Vukovich 2000; Marr and
Harley 2002)]. The spectral analysis [Marr and Harley 2002] included also NOx and VOC
data and indicated that for ozone 8-hour averages appear to be a more sensitive measure than
the 1-hour averages. There are also reports of 30-60 day atmospheric oscillations [Knutson
and Weickman 1987; Graves and Stanford 1987] and observations that stratospheric
temperature and ozone concentration exhibit similar oscillations [Pace et al. 2003]. These
cycles, which have usually significantly smaller amplitudes compared to the 1-year and 1-day
cycles, can be connected in a theoretical sense with three sources of periodic effects:
1) anthropogenic influences
2) meteorological and chemical influences
3) periodic maintenance of the instruments
It is assumed that these influences could produce cycles with periods in the range of 2 to
90 days. We consider the hebdomadal cycle as an example of anthropogenic influences which
can increase or decrease weekend ozone values by affecting the production of ozone
precursors such as VOC or NOx. On the other hand periodic patterns in maintenance of the
instruments are expected to have a period shorter than a week or two.
The aim of the present paper is to investigate this quasi-cyclic behavior of tropospheric
ozone volume fractions by looking at long term ozone monitoring data obtained at different
stations in Europe. We were mainly interested in periodicities ranging between 15 and 90
days and their correlation with meteorological variables. Here we will attempt also such
correlation of ozone with meteorological data from the EUROTRAC station Zugspitze as a
representative. If we consider long-term ozone measurements as a signal source, Fourier
4
transformation of the time domain data and the corresponding power spectrum provide a
simple way to look at these cycles [Butković et al., 2002].
Data processing
Ozone has been monitored within the EUROTRAC TOR project during the past decade in
many sites across Europe. Twelve sites of different altitudes and different pollutant levels
were selected for further analysis (Table 1.). Ozone measurements were made with
commercial UV fotometer instruments which have frequency of obtaining raw data less then
40 seconds. The raw data are than averaged into hourly or half hourly values as stated in
Table 1. Such averaged data are then used for the analysis. It is important to have sufficiently
long ozone data series for two reasons. First, because the spectral resolution increases with
frequency in the FT method, proper frequency resolution in the low frequency range (e.g., for
periods longer than 30 days) makes it important to have a long-term data set. Second, the
averaging of FT spectra improves their S/N ratio, which is possible only when a time series is
sufficiently long to facilitate splitting into several data sets without important losses in
resolution.
The stations analysed in this work are listed in Table 1. Detailed descriptions of the
stations can be found elsewhere [Cvitaš and Kley, 1994]. Seasonal variations and annual
mean ozone concentrations at these sites are described in [Scheel et al., 1997a, 1997b] and
[EUROTRAC-2 ISS, 2003].
Missing values in a given time series have to be filled in for the purpose of FT. The
number of missing values at these sites was very small and randomly distributed. After testing
several data sets using different methods (e.g., zero, average value, or the average of
corresponding values, at the same hour and day for the preceding and following years) and
comparing the results, we conclude that there is no significant difference in the main peaks of
the spectra. Therefore, the simplest solution to the problem was to use zero padding for all
5
stations. Furthermore, for better correlation analysis of the frequency peaks it is advantageous
to have the same number of data points for all stations. It could be shown that enlarging the
data sets with zeros for stations with a smaller number points up to the number for stations
with the longest record does not change the transformation quality while yielding intensities
at the same frequencies for all stations.
Results and discussion
FT spectra for the European ozone monitoring sites given in Table 1 are presented in Fig 1.
These spectra were compared by looking for the most prominent periodicities and their
possible repeatability at different sites. The criterion to select the periodicities was based on
peak intensities exceeding the x  2 value, where x is the moving average intensity for ten
consecutive points and σ is the standard deviation of for the corresponding period. In this way
certain frequency values corresponding to periods given in Table 2 could be selected
The 10-day moving average for the low frequency part of the FT spectrum covers
periods between 5 days to 1 year comprising about 500 data points. For each of these points
we calculated the standard deviation from the average, σ, of 10 neighboring points, five on
each side, and checked whether the examined point exceeds the value x  2 . The periods
corresponding to this condition were chosen as significant. This approach shows that the 1year and 1-day peak exceed the x + 2 limit but are still within the +3 limit above the
moving average curve. The periods selected in this way are given in Table 2.
Several common characteristics are worth noting:
1) All ozone data show a 1-year periodicity (seasonal cycle) as the most prominent
feature
6
2) The 1-day peak is noticeable at all sites but its intensity varies significantly which can
be attributed to the type of station in relation to local photochemical production and
transport.
3) Several other categories of frequency peaks are not as prominent, but nevertheless
they can be identified in many of the transformed data sets.
The relative importance of diurnal cycle in FT was calculated in relation to the base
peak (1 year ) for each spectrum. It was found that the relative prominence of the 24-hour
peak when compared to the 1-year peak is closely related to local photochemical pollution at a
given site. The index defined as the average ratio of the daily maximum and minimum hourly
average ozone volume fractions (set to 0.4 ppb when zero) [Cvitas and Klasinc, 1993, Cvitas
et al., 1995] was expected to correlate with the relative intensity of the 24-hour peak. This
correlation was confirmed for the rural sites only as shown in Figure 2. A quantification of the
degree of anthropogenic influences on ozone values was also given recently by analysis of 7
days, 1 day and ½ day periodicities [Audiffren et al. 2003].
The relative importance of the remaining peaks are calculated for each FT spectrum and
in Table 2 the time periods are listed corresponding to the most prominent peaks for each
station. Some peaks in the spectra correspond to exact frequencies of the second, third and
fourth harmonics of the base peak of 365.25 days. In most of the spectra, these peaks can be
found on 6, 4 and 3 month periods. These harmonic cycles appear because the 1-year period is
not purely sinusoidal. Other important peaks for each station are found to describe
approximately 40-44 day, 13-15 day, 8-11 day and 7 day quasi-cyclic behavior.
Because of the unexpected frequencies of these peaks, the question of artefacts in the
FT must be discussed [Marshal and Verdun, 1990]. The most common artefacts in FT arise
from a wrong frequency of sampling (Nyquist criterion) but, in this case, the frequency of
sampling is 1 h–1, high enough to prevent any possible fold-back peaks in the range we
7
discuss here. The other common sources of artefacts arise from the use of the sine function in
FT. As mentioned before, this type of artefacts results in harmonics and can be found in
spectra at periods of 6, 4 and 3 months; in Table 2, they are given in parentheses. Any artefact
must have a mathematically strictly-defined frequency, which provides a simple way to avoid
them.
The simplest way of testing for artefacts was to perform several FT analyses for
different time periods for each station. The position of genuine peaks should not change with
this procedure.
In addition, we tried several other methods to verify whether these periods were
genuine. In FT spectroscopic methods, averaging is a common way to improve the S/N ratio
of spectra. Due to the fact that we have limited data sets, averaging was possible by splitting
the data set into 1 year sets and then performing the FT procedure. In such a way it was
possible to average the spectra at the expense of resolution.
Another way to verify the presence of unusual periods and to overcome gaps in the data
sets was to calculate autocorrelation functions for each station and then use the
autocorrelation data for making FT. As expected, autocorrelation functions preserved the
frequencies, which were important for our investigation. The FT spectra of autocorrelation
functions are theoretically equivalent to the FT spectra of the original data.
For all of the above reasons it can be assumed that the selected peaks refer to genuine
(quasi-cyclic) behavior. These processes can be neither assigned to the maintenance of
instruments nor to local influences because these peaks are common for so many different
stations in meso-scale vicinity.
We presumed that the observed frequencies could be connected with quasi-cyclic
meteorological processes. Synoptic processes with periods between 15 and 40 days are known
in meteorology [Hies et al. 2000, Sebald et al. 2000, Marr and Harley, 2002] and such
8
processes could be the cause of observed periodicities. With this in mind we analyzed the
meteorological data for one station (Zugspitze) in the same manner. The obtained data for
ozone concentration, temperature, pressure and relative humidity are shown in Table 3. The
results indicate that there is some, but not perfect agreement for the different meteorological
parameters and the ozone concentration. There are obviously certain periodic phenomena
reflected in independently measured experimental parameters.
Differences among the European TOR stations as seen from frequency domain analysis
In order to get an overall view of the periodicities present at lower tropospheric ozone
concentrations over a longer period of time, a collective FT spectrum (Figure 3b) was
constructed by summation of the normalized equal-length FT data from 8 TOR stations
(Jungfraujoch, Zugspitze, Wank, Puntijarka, Krvavec, Preila, K-puszta, Mendrisio). The FT
data were normalized in such a way that the intensity of each peak was divided by the sum of
intensities of all peaks. The periods found in Figure 3 differ from those observed in Table 2;
this is due to the summation process, which includes the normalization procedure and which
cancels out all irrelevant peaks and improves the S/N ratio. In Figure 3a) the data for high
altitude stations and in Fig. 3c) those for low altitude stations are plotted separately. It can be
seen that periods of 20 and 32 days observable in Figure 3c disappear in Figure 3a, suggesting
that these are low-altitude station contributions. On the other hand, the 13.5 and 17.5 days
periods appearing in Figure 3a may reflect high altitude phenomena.
Main conclusions
The properties of ozone monitoring data from different ozone measuring stations can be
characterized and compared by analysing long-term ozone data in the frequency domain
obtained by the FT approach. This gives insight and information on periodicities present in
the data and the mutual relationship between monitoring sites. Thus the comparison of twelve
9
TOR2 sites by FT methods enables the detection of some common features among various
European sites. This study confirms the existence of common peaks in the frequency region
corresponding to periods mainly between 7 and 44 days, which most probably are connected
to meteorological phenomena.
Periods of 14, 20 and 199 days were found characteristic of low-altitude stations. On the
other hand, the 13.5, 17.5, 19, 44 and 175 days periods may reflect high altitude phenomena.
It would be worthwhile to examine the meteorological data in the same way. For a
better evaluation of the differences between various types of stations it would be necessary to
include long-term data from more stations.
Acknowledgements
Helpful discussions with Dr. Christophe Duroure (Paris), Dr. Anne Lindskog (Gothenburg)
and Dr. Oksana Tarasova (Moscow), as well as financial support from EUROTRAC2/TOR2,
US National Oceanic and Atmospheric Administration (NOAA) and Ministry of Science and
Technology, Republic of Croatia is gratefully acknowledged.
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Altshuler, S.L., T.D. Arcado, and D.R. Lawson, Journal of the Air and Waste
Management Association, 45, 967-972, 1995.
Audiffren N., C. Duroure, and G. Le Nir, Statistical properties of Puy de Dôme ozone
measurements. Comparison with urban site properties, in TOR-2 Final Report, edited by
EUROTRAC-2 ISS, pp 59-62, GSF, Munich, 2003.
Butković, V., T. Cvitaš., K. Džepina, N. Kezele, and L. Klasinc, Long-term ozone data
analysis, Croat. Chem. A., 75, 927-933, 2002. See also: Cvitaš, T., K. Džepina, N. Kezele,
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and L. Klasinc, Long term tropospheric ozone data analysis, MATH/CHEM/COMP,
Dubrovnik, 2000, Book of Abstracts, and IUPAC International Symposium on
Atmospheric Deposition and its Impact on Ecosystems, Tel Aviv, 2000. (Proceedings
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Cleveland, W.S., T.E. Graedel, B. Kleiner, and J.L. Warner, Science, 186, 1037-1038,
1974.
Cleveland, W.S., and J.E. McRae, Environ. Sci. & Tech., 12, 558-563, 1978.
Cvitaš, T., N. Kezele, and L. Klasinc, Boundary Layer Ozone in Croatia, J. Atmos. Chem.,
28, 125-134, 1997.
Cvitaš, T., N. Kezele, L. Klasinc, and I. Lisac, Ozone Measurements in Croatia. Pure
Appl. Chem., 67, 1450-1453, 1995.
Cvitaš, T., and D. Kley (eds), The TOR Network, EUROTRAC ISS, GarmischPartenkirchen, 1994.
Elkus, B., and K.R. Wilson, Atmos. Environ., 11, 509-515, 1977.
EUROTRAC-2 ISS (eds.) TOR-2 Final Report, GSF Munich, 2003.
Gilbert, R. O., Statistical Method for Environmental Pollution Monitoring, Van Nostrand
Reinhold, New York, 1987.
Graves, C.E., and J.L. Stanford, J. Atmos. Sci., 44, 260-264, 1987.
Hies, T., R. Treffeisen, L. Sebald, and E. Reimer, Spectral analysis of air pollutants. Part
1: elemental carbon time series, Atmos. Environ., 34, 3495 – 3502, 2000.
Knutson, T.R., and K.M. Weickmann, Mon. Wea. Rev., 115, 1407-1436, 1987.
Marr, L. C., and R. A. Harley, Spectral analysis of weekday-weekend differences in
ambient ozone, nitrogen oxide, and non-methane hydrocarbon time series in California.
Atmos. Environ., 36, 2327-2335, 2002.
Marshal, A. G., and F. R. Verdun, Fourier transforms in NMR, optical and mass
11
spectrometry, Elsevier, Amsterdam, 1990.
Pace, G., M. Cacciani, G. Calisse, A. di Sarra, G. Fiocco, D. Fua L. Rinaldi, and
S.Casadio, J. Aerosol Science, June 2003.
Pryor, S.C., and D.G. Steyn, Atmos. Environ., 29, 1007-1019, 1995.
Scheel, H. E., H. Areskoug, H. Geiss, B. Gomiscek, K. Granby, L. Haszpra, L. Klasinc, D.
Kley, T. Laurila, A. Lindskog, M. Roemer, R. Schmitt, P. Simmonds, S. Solberg, and G.
Toupance, On the spatial distribution and seasonal variation of lower-troposphere ozone
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Scheel, H. E., G. Ancellet, H. Areskoug, J. Beck, J. Bösenberg, D. De Muer, A. L. Dutot,
A. H. Egelov, P. Esser, A. Etienne, Z. Ferenczi, H. Geiss, G. Grabbe, K. Granby, B.
Gominšcek, L. Haszpra, N. Kezele, L. Klasinc, T. Laurila, A. Lindskog, J. Mowrer, T.
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Solberg, G. Toupance, C. Varotsos, and L. de Waal, Spatial and temporal variability of
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Hov, pp. 35-64, Springer, Berlin, 1997.
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12
Table 1.
Site
Country
Altitude a.s.l./m
Analyzed period
Type
(time resolution)
GarmischPartenkirchen (GAP)
Germany
740
1986 – 1999 (½ h)
urban
Izaña (IZA)
Spain
2370
1989 – 1993 (1 h)
remote
Jungfraujoch (JFJ)
Switzerland
3580
1988 – 1997 (1 h)
remote
Kollumerwaard (KOL)
Netherlands
sea level
1990 – 1995 (1 h)
rural
K-puszta (KPU)
Hungary
125
1990 – 2001 (1 h)
rural
Krvavec (KRV)
Slovenia
1720
1991 – 1994 (1 h)
remote
Mace Head (MHD)
Ireland
10
1988 – 1991 (1 h)
remote
Mendrisio (MEN)
Switzerland
350
1990 – 1999 (1 h)
rural
Preila (PRE)
Lithuania
10
1989 – 2000 (1 h)
rural
Puntijarka (PUN)
Croatia
980
1989 – 1999 (1 h)
rural
Wank (WNK)
Germany
1776
1989 – 1999 (½ h)
rural
Zugspitze (ZUG)
Germany
2937
1989 – 1997 (½ h)
remote
13
Table 2.
TOR STATION
P
E
R
ZUG
WNK
365
365
JFJ
365
(182)
(121)
146
(121)
(91)
PUN
KRV
KPU
GAP
365
365
365
175
209
102
730,
365
(182)
(121)
87
57
I
O
D
S
/
D
A
Y
44
31,
29,
24,
23
45
35,
19
48.7
36.5,
26,
19
40
28,
19
44
34,
25
17,
13
12,
13
18,
15
14
18,
14,
12
11,
10,
8
11,
10
8-10
9,11
8-11
18,
15,
14,
13
8-11
7.6,
7.3
6.9,
6.5
7
7
7
6.6
6.6
6.4
6.8,
6.5
6.9
32,
23,
20,
19
68,
57,
51
40
34,
30,
26,
22,
21
15,
13,
12
MEN
KOL
MHD
PRE
IZA
365
365
365
365
199
(182)
(121)
99,
88
66
52
28
28,
26,
34, 26
12,
15
14, 15
18,14,
12
10
9
8
8
11, 9,
8
7
7.4,
7
7
7
7
6.2
6.5
23,
20
16
11,
10
5.6
14
TABLE 3.
ZUGSPITZE
P
E
R
I
O
D
S
/
D
A
Y
OZONE
TEMPERATURE
PRESSURE
RELATIVE
HUMIDITY
365
365
365
(183)
117
365
(121)
(91)
44
31,
29,
24,
23
17,
13
11,
10,
8
6.4
73
52
34,
27,
23,
22
17,
14,
12
11, 8,5
8
7.5, 7
6.5
52, 42
28,
25,
23
16,
14,
12
9
7.5
6
(91)
67
39
29,
26,
24
21
13 -19
8-11
7.5, 7.2
6.7
15
Table headings.
Table 1. List of analyzed TOR2 stations.
Table 2. Most important periods found in FT spectra for ozone concentrations measured at 12
EUROTRAC TOR stations.
Table 3. Most important periods found in FT spectra of four experimental parameters at
Zugspitze (harmonics are given in parentheses).
16
1 year 3 month
1 month
1200
1000
800
4 days
1800
1600
1400
1200
1000
800
600
400
200
0
2 days
1.33 days
1 year
2500
3 month
1 month
14 days
1 day
2000
0
0.02
210
0.04
-1
frequency / h
102
43
400
19
23
4 days
2500
7 days
2 days
1.33 days
1 day
2000
relative intensity
1400
600
7 days
365
relative intensity
1600
relative intensity
14 days
365
relative intensity
1800
1500
1500
1000
500
0
1000
0
0.02
0.04
frequency / h-1
121
91
44 40
85
500
19
14
200
0
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0
0.001
0.002
0.003
frequency/h-1
0.004
0.005
0.006
frequency/h-1
a) K-Pusta, 1990 - 2001
b)Wank, 1989 - 1999
2000
1 year
1 month
14 days
relative intensity
1400
relative intensity
1200
1000
800
4 days
1600
1400
1200
1000
800
600
400
200
0
1.33 days
0.02
146
1600
1 day
0.04
1200
1000
800
frequency / h-1
40
110
36
26
220 121 91
400
21
2000
1800
1600
1400
1200
1000
800
24 hours
600
400
200
0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
600
frequency / h-1
121
400
2 days
1400
0
600
1800
7 days
relative intensity
1 year 3 month
relative intensity
1600
15 13.8
44
21
86
0
0.000
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0.001
0.002
c) Jungfraujoch, 1988 –1997
1 month
14 days
4 days
1400
1200
1000
1.33 days
1 year 3 month
1 month
1000
500
0
800
0.02
0.04
-1
frequency / h
183118
0.004
0.005
14 days
4 days
3000
2500
1500
0
600
3000
1 day
relative intensity
relative intensity
2000
1600
7 days
2 days
0.003
d) Zugspitze, 1989 - 1997
relative intensity
1 year 3 month
1800
relative intensity
13
frequency / h-1
frequency/h-1
2000
15
200
200
2000
1500
2 days
7 days
1.33 days
1 day
2500
2000
1500
1000
500
0
0
0.02
0.04
frequency / h-1
1000
730
64
400
42
23
18
182 86
122
500
13
39
21
15
200
0
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0
0.001
0.002
0.003
frequency/h-1
e) Mendrisio, 1990 – 1999
1 year 3 month
1 month
14 days
0.006
1 year 3 month
7 days
1 month
14 days
7 days
1800
365
4 days
3500
2500
2000
2 days
1.33 days
1 day
3000
1400
2500
2000
1500
1000
500
0
1500
0
199
1000
500
0.02
0.04
frequency / h-1
77
52
365
1600
relative intensity
relative intensity
3000
relative intensity
0.005
f) Garmisch Partenkirchen, 1986 -1999
relative intensity
3500
0.004
frequency/h-1
41 35 28 26
23
1200
1000
800
0
600
179
400
12
4 days
1800
1600
1400
1200
1000
800
600
400
200
0
2 days
1.33 days
0.02
1 day
0.04
frequency / h-1
73
40
28
26
19
14
12
200
0
0
0
0.001
0.002
0.003
frequency/h-1
0.004
0.005
0.006
0
0.001
0.002
0.003
frequency/h-1
0.004
0.005
0.006
17
g) Preila, 1989 – 2000
1 month
14 days
1400
1000
800
4 days
1600
1400
1200
1000
800
600
400
200
0
relative intensity
relative intensity
1200
7 days
2 days
1.33 days
1 year 3 month
0.02
600
14 days
1 day
4 days
1200
0.04
-1
frequency / h
800
600
7 days
2 days
1.33 days
1 day
1000
800
600
400
200
0
0
0.02
0.04
frequency / h-1
400
182 121
44
400
1 month
1000
0
251
1200
relative intensity
1 year 3 month
relative intensity
1600
h) Puntijarka, 1989 - 1999
34 31 25
14 13.5
18.5
12
8.2
7
38
85
200
200
0
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0
0.001
0.002
0.003
-1
i) Krvavec, 1991 – 2001
1 month
14 days
4 days
1200
relative intensity
relative intensity
1000
800
600
2 days
7 days
1.33 days
1 day
400
200
0.02
0.04
33
21
14 days
4 days
1000
900
800
700
600
500
400
300
200
100
0
365
700
600
frequency / h-1
56
1 month
800
800
0
122
1 year 3 month
900
0
200
1000
1000
400
0.006
600
500
0
400
7 days
2 days
1.33 days
1 day
relative intensity
1 year 3 month
0.005
j) Mace Head, 1988 - 1991
relative intensity
1200
0.004
frequency/h-1
frequency/h
0.02
frequency / h-1
182
0.04
300
36
200
13.8
15.9
12
100
0
0
0
0.001
0.002
0.003
0.004
0.005
0.006
frequency/h-1
k) Kollumerwaard, 1990 –1995
Figure 1.
0
0.001
0.002
0.003
0.004
-1
frequency/h
l) Izaña, 1989 – 1993
0.005
0.006
18
30
relative importance of FT diurnal cicle %
y = 39.644x - 46.216
R2 = 0.7922
Mace Head
25
Izana
20
Puntijarka
Krvavec
15
10
Zugspitze
5
Jungfraujoch
0
1
1.1
1.2
1.3
1.4
1.5
pollution index
Figure 2.
1.6
1.7
1.8
1.9
19
a)
8
365
sum of normalized FT spectra from five elevated and
high altitude TOR2 stations (JFJ, ZUG, WANK, PUNT, KRV)
normalised relative intensity
6
4
199
44
175 86 73
60
2
32
26
20
13.8
17.5
13.5
15
10.9
0
0
0.001
0.002
0.003
0.004
0.005
0.006
frequency/h-1
b)
10
365
sum of normalized FT spectra from eight TOR2 stations
(JFJ, ZUG, WANK, PUNT, KRV, Preila, Kpu, Mend)
normalised relative intensity
8
6
4
199
86
44
73
60
32
26
20
17.5
13.8
15
13.5
10.9
2
0
0
0.001
0.002
0.003
frequency/h-1
0.004
0.005
0.006
20
c)
4
365
sum of normalized FT spectra from three low altitude
TOR2 stations (Preila, Kpu, Mend)
normalised relative intensity
3
2
199
86
1
44
73
60
32
26
20
17.5
13.8
15
13.5
10.9
0
0
0.001
0.002
0.003
frequency/h-1
Figure 3.
0.004
0.005
0.006
21
Figure captions.
Figure 1. Fourier transformation of the ozone data for twelve TOR stations.
Figure 2. Relative diurnal to annual FT cycles vs. pollution index for less polluted TOR2
stations.
Figure 3. FT spectra obtained by summation of equal length FT data from: a) medium and
high altitude stations, b) total of 8 stations, and c) 3 low altitude stations. The numbers of days
indicated in the Figs. correspond to the frequency peak below the tip of the arrow.