Atmospheric Environment 38 (2004) 4667–4673

ARTICLE IN PRESS

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doi:10.1016/j.at

Comparison between Conditional Probability Function andNonparametric Regression for Fine Particle Source Directions

Eugene Kima, Philip K. Hopkeb,*aDepartment of Civil and Environmental Engineering, Clarkson University, Box 5708, Potsdam, NY 13699, USA

bDepartment of Chemical Engineering, Clarkson University, Box 5708, Potsdam, NY 13699, USA

Received 18 March 2004; accepted 26 May 2004

Abstract

The objective of this study is to examine the use of conditional probability function (CPF) and nonparametric

regression (NPR) to identify directions of PM2.5 (particulate matter p2.5mm in aerodynamic diameter) sources using

data collected from multiple monitoring sites across the US NPR has been used on cyclohexane data from Houston, TX

and correctly showed the direction of the source. In recent source apportionment studies using positive matrix

factorization (PMF), ambient PM2.5 compositional data sets from 24-h integrated samples including eight individual

carbon fractions collected at four monitoring sites, Atlanta, GA, Washington, DC, Brigantine, NJ, and Seattle, WA,

were analyzed identifying 10–11 sources. To analyze local point source impacts from various wind directions, CPF and

NPR were calculated using the source contributions estimated from PMF coupled with wind direction measured on

site. The comparison between CPF and NPR demonstrated that both methods agreed well with the locations of known

local point sources. CPF was simpler and easier to calculate than NPR. In contrast, NPR provided PM2.5

concentrations and associated uncertainties. This study indicates that both methods can be utilized to enhance source

apportionment study of ambient PM2.5.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Conditional probability function; Nonparametric regression; Positive matrix factorization; Source apportionment; Source

direction

1. Introduction

Since US Environmental Protection Agency promul-

gated new national ambient air quality standards for

airborne particulate matter less than 2.5 mm in aero-

dynamic diameter (PM2.5), advanced source apportion-

ment methods for PM2.5 are required for the source-

specific community epidemiology as well as in the

implementation planning process for attaining the air

quality standards. Positive matrix factorization (PMF)

(Paatero, 1997) has been used to assess PM2.5 source

ing author. Fax: +1-315-268-6654.

ess: hopkepk@clarkson.edu (P.K. Hopke).

e front matter r 2004 Elsevier Ltd. All rights reserve

mosenv.2004.05.035

contributions (Ramadan et al., 2000; Polissar et al.,

2001; Song et al., 2001; Lee et al., 2002; Kim et al.,

2003).

In recent source apportionment studies using PMF

method, ambient PM2.5 compositional data sets of daily

integrated samples including eight individual carbon

fractions collected at four monitoring sites, Atlanta,

GA, Washington, DC, Brigantine, NJ, and Seattle, WA,

were analyzed identifying 10–11 sources. In these

studies, a method is needed to find the directions of

high values of PMF estimated source contributions that

are likely to be related with the directions of sources.

The conditional probability function (CPF) has been

successfully used to analyze point source impacts in

d.

ARTICLE IN PRESSE. Kim, P.K. Hopke / Atmospheric Environment 38 (2004) 4667–46734668

these four studies as well as other source apportionment

studies (Kim et al., 2003, 2004a; Zhou et al., 2004;

Begum et al., 2004). Nonparametric regression (NPR)

has been tested using cyclohexane data from Houston,

TX and correctly pointed in the direction of the source

(Henry et al., 2002).

The objective of this study is to explore the use of

CPF and NPR to identify directions of PM2.5 sources

using data collected at multiple motoring site across US.

To analyze source impacts from various wind directions,

CPF and NPR are calculated using source contributions

estimated from PMF coupled with wind direction

measured on sites. The CPF values for each source are

compared with corresponding NPR results.

2. Experiment

2.1. Sample collection and chemical analysis

Atlanta PM2.5 samples were collected at the South-

Eastern Aerosol Research and CHaracterization

(SEARCH) (Kim et al., 2003; Hansen et al., 2003)

monitoring site located in Atlanta, GA. Daily integrated

PM2.5 samples were collected using the particulate

composition monitor (PCM, Atmospheric Research

and Analysis, Inc.) that permits simultaneous sampling

on a 3-stage filter pack (Teflon, Nylon, and cellulose

filter), a Nylon filter, and a quartz filter.

The PM2.5 samples from Washington, DC, Brigan-

tine, NJ, and Seattle, WA were collected on Wednesdays

and Saturdays at the Interagency Monitoring of

Protected Visual Environments (IMPROVE) (Malm

et al., 1994) monitoring site. Integrated 24-h PM2.5

samples were collected on Teflon, Nylon, and quartz

filters. The quartz filters collected by both SEARCH and

IMPROVE studies were analyzed via the thermal optical

reflectance (TOR) method (Chow et al., 1993) for eight

temperature resolved carbon fractions (OC1-OC4, EC1-

EC3) (Desert Research Institute, Reno, NV).

For the Atlanta study, 529 daily samples collected

between August 1998 and August 2000 were used. A

total of 718 samples collected between August 1988 and

December 1997 and 910 samples collected between

March 1992 and May 2001 were used for the Washing-

ton, DC and Brigantine studies, respectively. For the

Seattle study, 384 samples collected between March

1996 and February 2000 were analyzed. Detailed filter

analyses and summaries of PM2.5 speciation data used in

these PMF analyses are provided in Kim et al. (2004b,c)

and Kim and Hopke (2004a,b).

2.2. Source apportionment

The general receptor modeling problem can be stated

in terms of the contribution from p independent sources

to all chemical species in a given sample as follows

(Miller et al., 1972; Hopke, 1985)

xij ¼Xp

k¼1

gikfkj þ eij ; ð1Þ

where xij is the jth species concentration measured in the

ith sample, gik is the particulate mass concentration from

the kth source contributing to the ith sample, fkj is the

jth species mass fraction from the kth source, eij is

residual associated with the jth species concentration

measured in the ith sample, and p is the total number of

independent sources. PMF provides a solution that

minimizes a weighted sum of squared residuals (Paatero,

1997; Polissar et al., 1998). PM2.5 compositional data

measured in Atlanta, GA, Washington, DC, and

Brigantine, NJ were analyzed using PMF2, and those

measured in Seattle, WA was analyzed using more

flexible multivariate modeling tool, the multilinear

engine (Paatero, 1999).

The application of PMF depends on the estimated

uncertainties for each of the data values. The uncer-

tainty estimation provides a useful tool to decrease the

weight of missing and below detection limit data in the

solution. The procedure of Polissar et al. (1998) was

used to assign measured data and the associated

uncertainties. The final PMF solutions were determined

by experiments with different number of sources with

the final choice based on the evaluation of the resulting

source profiles as well as the quality of the species fits.

The 11–, 10 –, 11– and 11-source models provided the

most physically reasonable source profiles for the

Atlanta, Washington, DC, Brigantine, and Seattle

studies, respectively. A summary of the PMF resolved

average source contributions to PM2.5 mass concentra-

tions at four monitoring sites used in this study is shown

in Table 1.

2.3. Conditional probability function

CPF (Ashbaugh et al., 1985) analyzes point source

impacts from varying wind directions using the source

contribution estimates from PMF coupled with the wind

direction values measured on site (Kim et al., 2003). The

CPF estimates the probability that a given source

contribution from a given wind direction will exceed a

predetermined threshold criterion.. The same daily

contribution was assigned to each hour of a given day

to match to the hourly wind data. The CPF is defined as

CPFDy ¼mDy

nDy; ð2Þ

where mDy is the number of occurrence from wind sector

Dy that exceeded the threshold criterion, and nDy is the

total number of data from the same wind sector. In this

study, 24 sectors were used (Dy ¼ 15�). Calm wind

(o1m s�1) periods were excluded from this analysis due

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Table 1

The PMF resolved average source contributions (mgm�3) to PM2.5 mass concentrations at four monitoring sites

Average source contribution (standard error)

Atlanta, GAa Washington, DCb Brigantine, NJc Seattle, WAd

Secondary sulfate aerosol 2.2 (0.10)

Secondary sulfate aerosol (carbon-low) 8.3 (0.3)

Secondary sulfate aerosol (summer-high) 7.7 (0.3) 5.4 (0.2)

Secondary sulfate aerosol (winter-high) 1.1 (0.03) 0.6 (0.02)

Secondary sulfate aerosol (carbon-rich) 1.0 (0.03) 1.9 (0.07) 0.7 (0.02)

Diesel emissions 1.8 (0.07) 0.3 (0.01) 0.4 (0.01) 1.9 (0.10)

Gasoline vehicle 1.1 (0.04) 3.8 (0.1) 1.4 (0.04) 0.8 (0.06)

Nitrate-rich secondary aerosol 1.4 (0.06) 1.6 (0.06) 0.6 (0.03) 0.4 (0.02)

Airborne soil 0.5 (0.02) 0.3 (0.02) 0.4 (0.02) 0.6 (0.03)

Incinerator 0.7 (0.02) 0.2 (0.01)

Aged sea salt 0.4 (0.01) 0.8 (0.03) 0.7 (0.03)

Oil combustion 0.3 (0.01) 0.1 (0.005) 0.2 (0.02)

Sea salt 0.5 (0.03) 0.3 (0.04)

Wood smoke 1.1 (0.04) 1.4 (0.09)

Paper mill 0.2 (0.01)

Metal processing 0.6 (0.03) 0.1 (0.005)

Railroad traffic 0.4 (0.01)

Cement kiln/carbon-rich 0.3 (0.01)

Bus maintenance facility/highway traffic 0.3 (0.02)

aKim et al., 2004b.bKim and Hopke, 2004a.cKim and Hopke, 2004b.dKim et al., 2004c.

E. Kim, P.K. Hopke / Atmospheric Environment 38 (2004) 4667–4673 4669

to the isotropic behavior of wind vane under calm

winds. From tests with several different percentile of the

fractional contribution from each source, a threshold

criterion of the upper 25 percentile was chosen to define

the directionality of the sources. The sources are likely

to be located to the direction that have high conditional

probability values.

2.4. Nonparametric regression

NPR (Hardle, 1990) is a regression model without

parameters since it estimates the expected value of

concentration given wind direction. To find the direc-

tions of peaks in the ambient concentrations, Henry et al.

(2002) suggested NPR using a Gaussian kernel as a

nonsubjective alternative to the usual bar chart method

that is highly dependent on the location and size of Dy:NPR produces statistical confidence intervals as well as

estimates of the location of peaks, and is able to separate

closely located peaks. NPR was applied to the hourly

measured cyclohexane data from two sites in Houston,

TX. The triangulation of the peak directions estimated

from two sites correctly pointed to the source (Henry

et al., 2002).

The average concentration over a sliding window of

width Dy centered at y is generalized to use Dy as a

smoothing parameter.

%Cðy;DyÞ ¼Pn

i¼1 Kððy� WiÞ=DyÞCiPni¼1 Kððy� WiÞ=DyÞ

; ð3Þ

where Wi is the measured wind direction and Ci is the

measured concentration for the ith sample, and n is the

total number of samples. To give different weights to the

measurements, a Gaussian kernel function, K(x), is used

and defined as

KðxÞ ¼1ffiffiffiffiffiffi2p

p expð�0:5x2Þ: ð4Þ

This function gives maximum weight to the measure-

ments near y: Henry et al. (2002) defined Dy in terms of

the full width of the peak in kernel function measured at

the point where the curve has fallen to half of its

maximum value. The optimal Dy is the one that

minimize the sum of squared difference (V ðDyÞ) betweenthe measured concentration and the estimated concen-

tration leaving out one observation.

V ðDyÞ ¼Xn

j¼1

ðCj � %CjðWj ;DyÞÞ2; ð5Þ

ARTICLE IN PRESS

Fig. 2. Comparison between (a) CPF and (b) NPR plots for the

oil combustion in Seattle, WA.

E. Kim, P.K. Hopke / Atmospheric Environment 38 (2004) 4667–46734670

where

%CjðWj ;DyÞ ¼

Piaj KððWj � WiÞ=DyÞCiP

iaj KððWj � WiÞ=DyÞ: ð6Þ

The confidence intervals in the estimated concentra-

tions are based on the asymptotic normal distribution

(Hardle, 1990) and defined as

S2ðyÞ ¼Ck %sðyÞnDy %fðyÞ

; ð7Þ

where

Ck ¼1ffiffiffiffiffiffi2p

p ; ð8Þ

%fðyÞ ¼ ðnDyÞ�1Xn

i¼1

Ky� Wi

Dy

� �; ð9Þ

%s2ðyÞ ¼ ðn %fðyÞÞ�1Xn

i¼1

Ky� Wi

Dy

� �ðCi � %Cðy;DyÞÞ2: ð10Þ

In this study, the same daily contribution deduced by

PMF was assigned to each hour of a given day as Ci in

Eq. (3) to match to the hourly wind data. Calm winds

were also excluded from this analysis.

3. Results and discussion

To determine the optimal Dy for the calculation of

NPR, a variety of angular intervals were tested. The

final Dy for each of the forty-three source contributions

to particle mass at the four monitoring sites ranged from

3� to 14�. These values were determined based on the

evaluation of the measured concentrations and the

estimated concentrations leaving out one observation

(Eq. (5)).

Fig. 1. Location of the monitoring site in Seattle, WA. The

Beacon Hill monitoring site in Seattle is denoted by %.

The comparison between CPF and NPR demon-

strated that both methods agreed well with the locations

of known local point sources. Fig. 1 shows the locations

of the Seattle monitoring site and the Port of Seattle,

which is located about 5 km northwest of the site. It is a

major containerized cargo port with large marine oil

combustion sources. Fig. 2 presents the CPF and NPR

Fig. 3. Location of the monitoring site in Brigantine, NJ. The

monitoring site is denoted by %.

Fig. 4. Comparison between (a) CPF and (b) NPR plots for the

sea salt in Brigantine, NJ.

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Table 2

Pearson correlation coefficients between CPF values and NPR values

Pearson correlation coefficient

Atlanta, GAa Washington, DCb Brigantine, NJc Seattle, WAd

Secondary sulfate aerosol 0.96

Secondary sulfate aerosol (carbon-low) 0.47

Secondary sulfate aerosol (summer-high) 0.72 0.91

Secondary sulfate aerosol (winter-high) 0.95 0.97

Secondary sulfate aerosol (carbon-rich) 0.21 0.95 0.95

Diesel emissions 0.58 0.91 0.96 0.80

Gasoline vehicle 0.59 0.93 0.93 0.69

Nitrate-rich secondary aerosol 0.93 0.98 0.94 0.93

Airborne soil 0.86 0.82 0.87 0.95

Incinerator 0.97 0.97

Aged sea salt 0.95 0.95 0.72

Oil combustion 0.94 0.85 0.99

Sea salt 0.96 0.96

Wood smoke 0.88 0.73

Paper mill 0.78

Metal processing 0.91 0.81

Railroad traffic 0.75

Cement kiln/carbon-rich 0.82

Bus maintenance facility/highway traffic 0.72

aKim et al., 2004b.bKim and Hopke, 2004a.cKim and Hopke, 2004b.dKim et al., 2004c.

E. Kim, P.K. Hopke / Atmospheric Environment 38 (2004) 4667–4673 4671

plots for the oil combustion source in which the

calculated values are displayed in terms of a polar scale.

The radial axis has units of mgm�3, and inner and outer

lines denote the 95% confidence intervals in the NPR

plot. In Fig. 2, both the CPF and NPR plots indicate oil

combustion contributions from the direction of the Port

of Seattle. Fig. 3 shows the location of the Brigantine

monitoring site and Fig. 4 shows CPF and NPR plots

for sea salt. Both plots in Fig. 4 indicates sea salt

contributions from the direction of Atlantic Ocean that

is located south and east of the Brigantine site.

Table 2 shows the Pearson correlation coefficients for

the values from CPF against those from NPR for four

monitoring sites. To match the 24 angular sectors used

for the CPF, the 24 NPR values corresponding to the

middle of each 24 angular sectors used for the CPF were

only used without averaging NPR values or changing Dyfor the correlation analysis. Table 2 indicates high

correlations (r2 ¼ 0:7220:99) between CPF and NPR

estimations for local point sources. Regional secondary

sources as well as traffic sources show good correlations

(r2 ¼ 0:7220:98), except for two secondary sulfate

aerosols (r2 ¼ 0:47 and 0:21), gasoline vehicle

(r2 ¼ 0:59), and diesel emissions (r2 ¼ 0:58) in Atlanta,

GA. The CPF and NPR plots of these four Atlanta

sources are compared in Fig. 5 showing similar trends

although they have poor correlations. The source

directions of north and southeast for carbon-low

secondary sulfate, southeast for gasoline vehicles, and

south and northeast for the diesel emissions are shown

in both CPF and NPR plots. The poor correlations

for the four sources may be due to the poorly defined

directionality of secondary and traffic sources.

4. Conclusion

The CPF and NPR were compared for the usefulness

in identifying directions of PM2.5 sources using source

contributions at four monitoring sites across US:

Atlanta, GA, Washington, DC, Brigantine, NJ, and

Seattle, WA. The comparison between CPF and NPR

demonstrated that both methods agreed well with the

locations of known local point sources. CPF is simpler

and easier to calculate than NPR. In contrast, NPR

provided smoothed PM2.5 concentrations and associated

uncertainties for 360 wind sectors. In this study, NPR

was tested using a variety of PM2.5 source contributions

for the first time, and demonstrates that both methods

can be utilized to enhance source apportionment study

of ambient PM2.5.

ARTICLE IN PRESS

Fig. 5. The comparison between (a) CPF and (b) NPR plots for

Atlanta, GA.

E. Kim, P.K. Hopke / Atmospheric Environment 38 (2004) 4667–46734672

Acknowledgements

We would like to thank Dr. Ronald Henry for

providing his script for the NPR calculation. This work

was supported by the United States Environmental

Protection Agency (US EPA)’s the Science to Achieve

Results (STAR) program under Grant R83107801.

Although the research described in this article has been

funded by the US EPA, the views expressed herein are

solely those of the authors and do not represent the

official policies or positions of the US EPA.

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