oab

la

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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matter outdoors. Chemosphere 49, 10091043.

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