Download - Statistical Characterization of Atmospheric
-
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a Department of Environmental Engineering, Fatih University, Hadimkoy Yollu Uzere, Buyukcekmece, 34900 Istanbul, Turkeyb Department of Environmental Engineering, Yldz Technical University, Besiktas, Istanbul, Turkey
Epidemiological studies suggest that exposure to par-
ticles with an aerodynamic diameter
-
exposure may even lead to increased mortality and hos-
pitalization rates (Pope et al., 1995; EPA, 1996; Chap-
man et al., 1997). PM2.5 particles are likely to
penetrate deep into alveolar sacks of the lung. These
particles can accumulate in the respiratory system and
are associated with numerous negative health eects
(Vinitketkumnuen et al., 2002). Recently, it has been
suggested that for every 10 lg m3 increase of ne parti-cles from automotive emissions show approximately a
3% of increase in the daily mortality rate, while ne coal
combustion emissions only account for about 1%
(Laden et al., 2000).
Frequency distribution is the tabulation of raw data
obtained by dividing it into size ranges and computing
the number of data elements (or their fraction out of
the total) falling within each size range (Kenney and
Keeping, 1962). The frequency distribution of air pollu-
tant concentration data is useful in understanding the
statistical characteristics of air quality. It is a very use-
ful tool to estimate how frequently a critical concentra-
tion level is exceeded (Seinfeld and Pandis, 1998;
Wilson et al., 2002). Knowledge of the frequency distri-
bution is necessary for developing air pollutant control
2. Experimental
2.1. Sampling site and period
In this work, 86 daily aerosol samples of ne
(
-
On the other hand, the Kolmogorov Smirnov (KS)
F. Karaca et al. / Chemosphere 59 (2005) 11831190 1185collected on B37 mm Teon membrane lters with a2 lm pore size, which are recommended for gravimetricdetermination of particulate matter. The sampling ow
rate used was 1 m3 h1. Before sampling, the Teonmembrane lters were placed into a desiccator at room
temperature in open plastic Petri dishes for at least
24 h to reach a constant humidity. Afterwards, they
were weighed with a four digit sensitive balance. After
weighting, the empty lters were placed into standard
polypropylene lter holders and were put together into
a dichotomous sampler carousel. The carousel was then
carried to the sampling site in a closed plastic tray to
prevent any contamination during transportation. The
sample collection period was 24 h for all collected sam-
ples. After sampling, the lters were transferred to the
laboratory. They were placed in the desiccator again
for 24 h, and then weighted under exactly the same con-
ditions as the empty lters. For each sample, three re-
peated weight determinations were performed and the
average was reported.
2.3. Statistical analysis and probability density
functions
In order to understand the relationship between
PM2.5, PM2.510, and PM10, statistical and temporal
analysis approaches were used. Robust linear regression
model and various curvilinear models were applied and
the best-tted model was selected among them. Monthly
average variations of the PM10 and PM2.5 concentra-
tions analyzed show cyclic behaviors of the data sets.
Polynomial least square t technique was used to quan-
tify these cyclic trends. With the purpose of obtain-
ing best frequency distribution of PM2.5 and PM10data, several functions were used, namely Beta, Erlang,
Exponential, Gamma, Inverse Gaussian, Log-logistic,
Lognormal, Pearson 5, Pearson 6 and Weibull distribu-
tions. For information about the distribution functions,
one can refer to Johnson et al. (1995), Banks and Carson
(1984) and Law and Kelton (1991).
2.4. Test of the goodness of t
In this study, two tests of the goodness of t were
used to make a decision about the denition of the best
distribution function: (a) Chi-squared test, (b) Kol-
mogorov Smirnov test (KS).
Chi-squared test is a test which calculates a Chi-
square statistic that compares observed frequencies with
the expected frequencies predicted by the tted distribu-
tion (Brunk, 1960). The Chi-square test divides the range
of data into non-overlapping intervals and compares the
number of observations in each class to the number
expected based on the tted distribution. Chi-squared
statistic for this data is calculated according to Eq. (1)(Stuart and Ord, 1991).test is a statistical test of the goodness of t of the tted
cumulative distribution to the input data. The KS test
calculates the largest absolute dierence between the
cumulative distributions of the input data and the tted
distribution according to Eqs. (2)(4).
D maxD;D 2
D max in f x
; . . . i 1; . . . ; n 3
D max f x i 1n
; . . . i 1; . . . ; n 4
where D is the KS statistic, x is the value of the ith point
out of n total data points, and f(x) is the tted cumula-
tive distribution (Brunk, 1960). The KS test is used to
compute the maximum distance between the cumulative
distribution of PM2.5 and the cumulative distribution
function of the tted distribution.
3. Results and discussion
3.1. Relationship between PM2.5, PM2.510, and PM10
The annual average concentrations of PM10 and
PM2.5 were 47.1 lg m3, 20.8 lg m3 and standard devi-
ations were 32.6 lg m3, 13.6 lg m3, respectively. Theannual arithmetic mean of PM10 was found less than
the Turkish air quality standard of 60 lg m3. On theother hand, the measured PM10 value was higher than
the European Union air quality annual PM10 standard
of 40 lg m3. Turkey and European Union have notestablished an ambient air quality standard for PM2.5until the completion of this study. The measured annual
mean concentration of PM2.5 (20.8 lg m3) was higher
than the United States EPA annual PM2.5 standard of3x2 Xki1
ni npi2npi
1
where x2 is the Chi-squared statistic, n is the total num-
ber of data points, ni is the number of data points in the
ith continuous interval or ith discrete class, k is the num-
ber of intervals or classes used, and pi is the expected
probability of occurrence in the interval or class for
the tted distribution.
The resulting test statistic is then compared to a stan-
dard value of Chi squared with the appropriate number
of degrees of freedom (df) and level of signicance. In
this study, the number of degrees of freedom is taken
to be the net number of data bins [intervals, classes] used
in the calculation minus 1, because this is the most con-
servative test, that is, least likely to reject the t in error
(Stuart and Ord, 1991).15 lg m . The daily Turkish air quality standard of
-
150 lg m3 for 24-h average PM10 was exceeded twotimes and the US EPAs 24-h average PM2.5 standardwas exceeded three times during the one year study
period (86 samples).
Robust regression analyses, which are useful tech-
niques that treat the outliers, were performed to t the
results to a certain model. The outliers of data were
identied by non-linear least square robust regression
method and GaussNewton algorithm was selected as
the robust regression algorithm. After the detection
and handling of outliers, obtained results showed that
a robust tting procedure is an acceptable procedure
for our data. The scatter plot of response data versus
predictor data is illustrated in Fig. 2.
According to the obtained R-Square and error values
(Table 1), power (Robust) model (PM10 3:90 PM0:802:5 )was found to be the best model. This model has a value
of 0.80 for both, the maximum R-Square and adjusted
R-Square. This correlation indicates that PM2.5 is a con-
stant fraction of PM10 during sampling period except
June, September and October (Fig. 2). When compared
to other models, the sum of squares due to error [SSE]
and the root mean squared error (standard error)
[RMSE] values were found the lowest among other
models values with typical values of 1750 and 14.4,respectively. Plot of tted model is shown in Fig. 2
and is compared with the Power model without robust
regression techniques.
The average and standard deviation of monthly
PM2.5/PM10 ratio are 0.46 and 0.12 respectively. This ra-
tio value is very close to 0.50, and the standard deviation
is relatively small compared to the calculated ratio.
Thus, it can be suggested that the contribution of ne
and coarse particles to PM10 is equally distributed.
The lowest monthly PM2.5/PM10 ratio of 0.28 was re-
ported during June 2003 and the highest one of 0.74
Sum
due
[SSE
174
246
247
350
351
354
641
690
1186 F. Karaca et al. / Chemosphere 59 (2005) 11831190Fig. 2. Plot of power (Robust) model: PM10 3:90 PM0:802:5 forPM10 and PM2.5.
Table 1
The results of model ttings between PM2.5 and PM10
Fitted model
Power (Robust): PM10 a PMb2:5Quadratic (Robust): PM10 a PM22:5 b PM2:5 cGaussian (Robust): PM10 = a * exp(((PM2.5 b)/c)2)Linear (Robust): PM10 = a * PM2.5 + b
Cubic (Robust): PM10 a PM32:5 b PM22:5 c PM2:5 dSquare root-Y model (Robust): PM10 = (a + b *PM2.5)
2
Power-1 (Robust): PM10 a PMb2:5 cSquare root-X model (Robust): PM10 = a + b/PM2.5was found during September 2002. This indicates that
coarse particles contribute to larger portion of PM10during June and a smaller portion of PM10 during
September. During November, the contribution of both
ne and coarse particles is equal, but their observed con-
centrations are the highest among other months.
The monthly average temporal variations of PM2.5and PM10 concentrations data are shown in Fig. 3. Dur-
ing the heating season, the highest mass concentration of
PM2.5 and PM10 was reported and their variations are
closely related. The large variation of PM values during
this period with concentrations in January and February
45 times lower than those in November and December
(Fig. 3) can be explained by the prevailing meteorologi-
cal conditions during winter months in Istanbul. The
climate of Istanbul shows a transition between the Med-
iterranean and temperate climates with cool and wet
winters and warm and humid summers. The highest
amount and events of precipitation were observed for
the period of January and February during this study
and as reported by other workers (Tayanc, 2000). Scav-
enging eects of precipitation could be one of the rea-
sons for the observed low PM concentration (Basakand Alagha, 2004). In addition to that, other meteoro-
logical factors, such as surface wind speed and direction,
mixing depth and the formation of inversion layer,
might also play an important role on disturbing their
of squares
to error
]
R-square Adjusted
R-square
Root mean squared
error (standard error)
[RMSE]
9 0.80 0.80 14.4
8 0.68 0.68 17.5
5 0.68 0.68 17.6
9 0.66 0.66 17.8
0 0.66 0.65 17.9
9 0.63 0.63 18.1
4 0.57 0.56 18.8
4 0.40 0.39 20.4
-
0.50x4
+ 1.40x
02 Jan
s [Jan
2.5 2.5
n of
F. Karaca et al. / Chemosphere 59 (2005) 11831190 1187concentrations during heating season, which is common
in the sampling area due to its topography and proxi-
mity to the sea.
During wintertime, the correlation coecient be-
tween PM2.5 and PM10 was found as 0.88. This signi-
cant correlation explains that PM2.5 and PM10 have
some similar emission sources, and they were being
inuenced by the same meteorological conditions during
that period. On the other hand, the highest mass concen-
tration for PM10 was measured during the summertime
(June and July). Through this dry period, high ambient
temperature and lack of precipitation were observed. It
can be suggested that a large fraction of PM10 consists
y2.5 = -0.014x5 +
y10 = -0.0403x5
0
20
40
60
80
100
Jul-02 Aug-02 Sep-02 Oct-02 Nov-02 Dec-Month
Mon
thly
Ave
rage
[g/
m3 ]
PMPM
Fig. 3. Monthly average temporal variatioof soil-originated particles, because of re-suspension
process, which is enhanced in dry climates (Chaloulakou
et al., 2003). Furthermore, the correlation coecient be-
tween PM2.5 and PM10 was determined as 0.54. This
shows that during this period PM2.5 and PM10 are af-
fected by dierent emission sources.
The examination of the monthly average variation in
Fig. 3 shows cyclic behavior for the two time series. It is
of interest to quantify these visual impressions in the
gure. Furthermore, the computation of the magnitude
of the cycles for PM10 and PM2.5 is of particular
importance.
The data sets are clearly periodic (cycles), which sug-
gests they can be described by polynomial least squares
t according to Eq. (5).
f x c1x5 c2x4 c3x3 c1x a 5If the t does not describe the data well, it is possible to
add additional power terms with coecients until a
good t is obtained. Polynomial least squares ts were
calculated for the time series of PM2.5 (R2 = 0.59), and
for the time series of PM10 (R2 = 0.68) and are givenin Eqs. (6) and (7), respectively (Fig. 3). The goodness
of t statistics, which are sum of squares due to error
statistic (SSE) and root mean squared errors (RMSE)
were calculated for both models. SSE measures the total
deviation of the response values from the t to the re-
sponse values. SSE and RMSE values of both PM10and PM2.5 ts are calculated as 850, 322, and 14.34,
7.87, respectively.
PM10 0:0403x5 1:40x4 17:56x3 96:87x2 219x 180:9 6
PM2:5 0:014x5 0:50x4 6:41x3 36:16x2
- 6.41x3 + 36.16x2 - 81.35x + 69.65R2 = 0.59
4 - 17.56x3 + 96.87x2 - 219x + 180.9R2 = 0.68
-03 Feb-03 Mar-03 Apr-03 May-03 Jun-03 Jul-03
=1, Dec=12]
PM10PM 10
PM10 and PM2.5 concentrations (lg m3). 81:35x 69:65 7These ts appear to be reasonable to explain the similar
cyclic behavior of the examined data points. The ob-
tained ts indicate that there are two annual cycles for
each time series of PM10 and PM2.5. One of the cycles
has a peak during November and December, whereas
the other cycle peaks on June. During these peaks, maxi-
mum concentrations were observed (Fig. 3). Other
workers (Castanho and Artaxo, 2001; Laakso et al.,
2003; Gomiscek et al., 2004) reported similar particulate
matter seasonal variation behavior. Furthermore, sea-
sonal variation of PM2.5 concentrations displays high
concentrations in winter and low concentrations in sum-
mer. Until the time this study was accomplished, the
Buyukcekmece area was relaying mainly on coal and
fuel oil for heating. A natural gas supply network pro-
ject for this region was ongoing during this study. Even
though sampling site is located at least 5 km away from
any residential or industrial area, nearby industrial areas
mainly depend on fuel oil as a cheap energy source,
which adversely aects the air quality in this region as
-
PM and SO2 are considered. Therefore, we can assume
that the amount from manmade emission sources has
monthly or seasonal variations.
Alternatively, the seasonal variation of PM10 and
PM2.5 concentrations should be partially caused by
changes in the meteorological conditions. The decreased
level of PM mass concentrations during the heating sea-
son can be explained by two main meteorological fac-
tors. These are precipitation and wind speed and
direction (Orlic et al., 1999; Cheng et al., 2000).
3.2. Determination of distribution function
In this study, one-year data of PM10 and PM2.5 were
statistically analyzed and theoretical frequency distribu-
tion functions were tted and compared to the measured
data. These frequency distribution functions are Beta,
Erlang, Exponential, Gamma, Inverse Gaussian, Log-
logistic, Lognormal, Pearson 5, Pearson 6 and Weibull
distributions. Relative goodness of t, Chi-squared and
K-S tests, of the distribution functions to the PM2.5and PM10 data gave us an idea about which function
can be used to model frequency distribution of PM2.5and PM10 (Tables 2 and 3). Chi-squared values of
Log-logistic, Pearson 5, Lognormal and Inverse Gauss-
ian functions for PM2.5 produce the same value of
1.48. The KS values are 0.096, 0.101, 0.104, and 0.105,
respectively. Chi-squared values of Log-logistic, Pearson
5, Lognormal, and Inverse Gaussian functions for PM10are 0.478, 1.26, 1.26, 1.39 and KS values are 0.057,
0.067, 0.069 and 0.073, respectively. Therefore, the
Log-logistic distribution function was found to be the
most appropriate one to represent the statistical charac-
ters of PM2.5 and PM10. Computing by Pearson 5, log-
normal and inverse Gaussian distribution functions
gave approximately the same statistical eciencies.
The Log-logistic distribution is selected and equations
for PM2.5 and PM10 were calculated. Eqs. (8) and (9)
give the calculated distribution functions.
f PM2:5 3:55
PM2:5 5:3723:60
2:55
23:60 1 PM2:5 5:3723:60
3:55" #2 8
f PM10 3:18
PM10 11:7249:52
2:181
49:52 1 PM10 11:7249:52
3:18" #2 9
Table 2
Goodness of t test for PM2.5 data: maximum likelihood estimates, accuracy of t is 0.0003, level of signicance is 0.05, number of
.6
4
.470
.1
0
.74, q
1
, q =
tes, a
degrees of freedom of Chi-squared test (df) is 5
.5
4
52
4
, q =
.9
.4
.6
1.86,
1188 F. Karaca et al. / Chemosphere 59 (2005) 11831190Distribution function name Function parameters
Log-logistic min = 11.7, p = 3.18, b = 49Pearson 5 min = 26.4, a = 5.89, b = 35Lognormal min = 15.0, l = 3.96, r = 0.Inverse Gaussian min = 17.1, a = 227, b = 62.Pearson 6 min = 0.00, b = 99.4, p = 2.58Gamma min = 2.31, a = 2.17, b = 21Erlang min = 1.60, m = 2.00, b = 23Weibull min = 0.60, a = 1.45, b = 50Beta min = 0.00, max = 11635, p =
Exponential min = 0.00, b = 45.2degrees of freedom of Chi-squared test (df) is 5
Distribution function name Function parameters
Log-logistic min = 5.37, p = 3.55, b = 23Pearson 5 min = 14.8, a = 8.65, b = 27Lognormal min = 6.37, l = 3.20, r = 0Inverse Gaussian min = 7.12, a = 121, b = 28Gamma min = 0.771, a = 2.20, b = 9.2Weibull min = 1.68, a = 1.47, b = 21.3Beta min = 2.20, max = 153, p = 1
Erlang min = 1.18, m = 2.10, b = 9.9Pearson 6 min = 2.10, b = 230, p = 1.95Exponential min = 2.11, b = 19.2
Table 3
Goodness of t test for PM10 data: maximum likelihood estimaChi squared Kolmogorov Smirnov
1.48 0.096
1.48 0.101
1.48 0.104
1.48 0.105
3.14 0.110
3.14 0.113
= 12.2 3.14 0.116
8.66 0.118
24.3 8.66 0.122
15.4 0.214
ccuracy of t is 0.0003, level of signicance is 0.05, number of
Chi squared Kolmogorov Smirnov
0.48 0.057
1.26 0.067
1.26 0.069
1.39 0.073
6.52 2.96 0.082
1.39 0.083
1.39 0.083
1.39 0.095
q = 430 6.22 0.131
18.1 0.197
-
The obtained Log-logistic distribution equations for
PM10 and PM2.5 data set (86 samples) can be used to
estimate the distribution of these pollutants. Conse-
quently, one year PM2.5 and PM10 data (365 samples)
was predicted using these models. Furthermore, percen-
tiles of one-year data of PM2.5 and PM10 were also esti-
mated (Table 4). The predicted 98 percentile of PM2.5concentrations has a value of 66.3 lg m3, which is
limit of 150 lg m . As a result, the limit of 150 lg mwas exceeded 9 times within the highest 2.5& of the pre-
Table 4
Measured and predicted values by the log-logistic function for one ye
Percentiles PM2.5
Concentrations (lg m3)
Measured Predicted
10.0 7.40 7.50
20.0 12.5 10.0
30.0 12.5 13.0
40.0 16.7 16.0
50.0 16.7 19.0
60.0 20.8 23.0
70.0 25.0 26.0
80.0 28.3 32.0
90.0 41.1 42.0
97.0 62.5 60.0
97.5 62.5 64.6
98.0 63.6 66.3
F. Karaca et al. / Chemosphere 59 (2005) 11831190 1189higher than the USA 24-h average standard ofFig. 4. The relative frequency distributions of the PM2.5 and
PM10 concentrations (lg m3).dicted data set (Table 4). The relative frequency distribu-
tion (Log-logistic) of the PM2.5 and PM10 and the data
sets is illustrated in Fig. 4.
4. Conclusions
The annual arithmetic mean of PM10 was found to be
lower than Turkish air quality standard of 60 lg m3.On the other hand, this value was found to be higher65 lg m3. Accordingly, the limit of 65 lg m3 was ex-ceeded within the highest two percentile of the predicted
one-year data. This percentile corresponds to 7 days of a
year. In the same manner, the predicted 97.5& of thePM10 concentrations exceeds the 24-h average standard
3 3
ar PM2.5 and PM10 data
PM10
Concentrations (lg m3)
Measured Predicted
19.2 13.0
22.4 19.0
29.1 26.0
37.2 33.0
41.6 39.0
45.8 48.0
54.1 56.0
64.1 70.0
95.4 96.0
132 143
139 154
156 162than the European Union air quality annual PM10 stan-
dard of 40 lg m3. The annual mean concentration ofPM2.5 is higher than United States EPA annual PM2.5standard of 15 lg m3.
There is a statistically signicant relationship be-
tween PM2.5 and PM10 at the 99% condence level. In
order to explain this relationship, linear and curvilinear
models were compared. Power (Robust) model
(PM10 3:90 PM0:802:5 ) was found as the best modelwhich explains 80% of the variability in PM10.
During the heating season, the higher mass concen-
trations for PM2.5 and PM10 occurred and the correla-
tion coecient between PM2.5 and PM10 was 0.88. On
the other hand, the correlation coecient between
PM2.5 and PM10 was 0.54 for the period of June and
July, which shows that during this period PM2.5 and
PM10 may be inuenced by dierent emission sources.
The analyses for the monthly average variations
show cyclic behavior for the two time series. The numeri-
cal results indicate the presence of two cycles per year
-
for PM10. One cycle has maximum concentrations dur-
ing wintertime and the other cycle has a peak in summer
time. Main factors, which eect these cycles, can be ex-
plained by the prevailing meteorological conditions. In
600/P-95/001cF, US Environmental Protection Agency,
Oce of Research and Development, Washington, DC.
Ginn & Co., p. 261.
Castanho, A.D.A., Artaxo, P., 2001. Wintertime and summer-
and mineral dusts between 1995 and 1996. Atmospheric
Environment 34, 27712783.
Gomiscek, B., Hauck, H., Stopper, S., Preining, O., 2004.
1190 F. Karaca et al. / Chemosphere 59 (2005) 11831190time Sao Paulo aerosol source apportionment study.
Atmospheric Environment 35 (29), 48894902.
Chaloulakou, A., Kassomenos, P., Spyrellis, N., Demokritou,
P., Koutrakis, P., 2003. Measurements of PM10 and PM2.5
particle concentrations in Athens, Greece. Atmospheric
Environment 37, 649660.
Chapman, R.S., Watkinson, W.P., Dreher, K.L., Costa, D.L.,
1997. Ambient particulate matter and respiratory and
cardiovascular illness in adults: particle-borne transition
metals and the heartlung axis. Environmental Toxicology
and Pharmacology 4, 331338.
Cheng, Z.L., Lam, K.S., Wang, C.T., Chen, K.K., 2000.
Chemical characteristics of aerosols at coastal station in
Hong Kong. I. Seasonal variation of major ions, halogensBanks, J., Carson, J.S., 1984. Discrete-Event System Simula-
tion. Prentice-Hall.
Basak, B., Alagha, O., 2004. The chemical composition ofrainwater over Buyukcekmece Lake, Istanbul. Atmospheric
Research 71 (4), 275288.
Brunk, H.D., 1960. An Introduction to Mathematical Statistics.a monthly or seasonal period, we can assume that the
amount from anthropogenic emission sources is not con-
stant in the region.
Some theoretical distribution functions are selected
to t the PM10 and PM2.5 data. Their eciencies were
compared and the most representative function was de-
ned. By the help of this model, PM2.5 and PM10 data
for whole year were predicted using 86 samples set.
According to this prediction, 2.5% of the one year
PM10 data and the 2% of the one year PM2.5 data ex-
ceeded the 24 h average standard for Turkey, which is
150 lg m3, and the USA 24-h average standard of65 lg m3, respectively.
Acknowledgment
We would like to thank for the nancial support pro-
vided by Fatih University, Institute of Sciences. Project
#: P50080102.
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Statistical characterization of atmospheric PM10 and PM2.5 concentrations at a non-impacted suburban site of Istanbul, TurkeyIntroductionExperimentalSampling site and periodSampling methodStatistical analysis and probability densityfunctionsTest of the goodness of fit
Results and discussionRelationship between PM2.5, PM2.5 ndash 10, and PM10Determination of distribution function
ConclusionsAcknowledgmentReferences