Department of Chemical Engineering, Amir Kabir University ofTechnology (Tehran Polytechnic), Tehran, Iran
Iran Meteorological Organization
Atomic Energy Organization of Iran, Tehran, Iran
Abstract
Over the recent years, Target Transformation Factor Analysis (TTFA) has beenwidely applied to various cases of environmental source resolution. As amultivariate receptor model, this form of factor analysis allows the determinationof actual elemental source profiles. The analysis seeks to identify groups ofsamples with similar characteristics. Additionally, this technique identifies thecorrelation that exists between the data and utilizes them over the set ofmeasured elements of different samples. This is practically accomplished on amatrix called correlation matrix. TTFA also permits the direct calculation of thecontribution of each source to each sample. As an attempt to evaluate the qualityof particulate matters in the Tehran metropolitan are, TTFA was applied on a setof existing data, collected during a period from March 1994 to February 1995.Elemental concentrations were determined by means of Instrumental NeutronActivation Analysis (INAA) and Atomic Absorption. Due to lack of datarepresenting actual source profile, unique test vector method was used. Theobtained results addressing the source identification, estimation of source profileand source contributions are discussed.
Air pollution in major cities and industrial area has emerged as the most seriousproblem that that threats the human and other forms of life on earth. Suspendedparticulate matters, containing poisonous elements, are known as importantpollutants that could cause enormous and varied adverse health effects.In recent decades there has been a large influx of people from the rural areas intoTehran resulting in large increases in the population and the intensification ofindustrial activities. This together with the complex and unorganized trafficnetworks, the high average age of the cars, the use of lead in petrol, the specifictopography and the prevailing meteorological conditions has resulted in adramatic decrease in the quality of the air, containing high level of pollutants.
The intention of the authors was a through study of particulate matters, and themethods used to identify and determine the main sources of pollution and thecontribution of particulate of matters to this pollution as measured at givenreceptors.In the course of this study different receptor models were studied, developed andutilized on a few sets of limited data existing on particulate matters and therelated elemental composition in the Tehran atmosphere.To begin with. Chemical Mass Balance (CMB) was studied and applied.However, to use this method data such as knowledge of major sources withknown source profile is required which is usually not available. Therefor, morecomplex and advanced models, which require less data, had to be used. Themodel used in this study is factor analysis and its specific feature called " TargetTransformation Factor Analysis " (TTFA). This model is essentially very similarto CMB and provides the necessary means that overall knowledge ofinvestigators of the probable major sources could be well utilized in determiningthe best profiles of actual element concentrations [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
2 Description of Data
The applied data was provided by Inin Atomic Energy Organization, whichincluded data gathered during the period from March 1994 until February 1995.Stationary samplers were installed at ten presumed-important locations of Tehran(The map of city of Tehran metropolitan area, showing the locations of 10sampling stations, may be found in [11]). Designed and built by GammaIrradiation Center (GIC), each high volume air sampler used consisted of asuction motor, a calibrated gas meter, a filter holder, a timer and otheraccessories. The samplers had a variable flow rate (normally 10 nf/hr) and thefilters used for air sampling were Whatman-41 with a diameter of 12.5 cm. Thesampling was performed twice a week on Monday and Thursday during theperiod 8 AM to 4 PM, and the air volume that passed through each filter was 40-50 m".The originally collected filters were cut into four equal parts. One part was usedfor the detection of Pb, Ni, Fe and Mn with Atomic Absorption Spectroscopy
(AAS). The second part was used to determine the short half life (SHL) of Al,Ca, Mg, V, Ti and the third part was used for long half life (LHL) of Sb, Ce, Co,Cr, Cs, Fe, Sc, Se, Zn by means of Instrumental Neutron Activation Analysis(INAA).For atomic absorption analysis, the measurement of the absorbency was carriedout with a COBC Model 920 spectrometer. Atomic absorption of the fourelements of Fe, Mn, Ni and Pb was performed at the wavelength of 327, 279.5,232 and 217 nm, respectively.The selection was based on the elemental toxicity and also on the basis on lowactivation cross section or low density of the gamma lines of the N A A methodimpractical.For AAS analysis, efficiencies greater than 90% for Pb and more than 85% forother elements were observed. Relative standard errors for the variability test fora given sample was less than 5%. For INAA, efficiencies in the range of 80-90%were observed, and the variability test was similar to that of AAS.Assessment of the results for the 21 elements expressed using the two techniquesproduced the following results with the concentration in unit of pig/nf.
Figure 1. Observed elemental concentrations
Out of the twenty-one elements measured in each sample, a majority of elementswere metallic. Unfortunately, experiments for the determination of carbon, sulfurand silisium were not carried out. The data pertaining to the concentration ofcarbon, sulfur and silisium can be used to identified the contribution of thefollowing sources respectively; residual fuel oil, wood and road; sulfates andincinerators; soil and sand blast. It is important to note that out of ten samplingstations, station number 3 was located in Atomic Energy Organization, in Tehran
downtown. Due to its specific and representative location (not being close tomajor potential sources) and also since it was one of the best operated samplingstation that could yield the most complete set of data, the data collected at thisstation was chosen to be utilized with the developed TTFA program.
3 Mathematical Background
The objective of TTFA is to resolve the ambient data set into sourcecontributions given by the matrix equation:
JT = AF (1)
Where X is the data matrix that contains m rows of properties (elements) each
observed f? cases. The n columns of X are therefor the n samples each
constituting a sample of m -dimensional property vector. A is a matrix ofdimension m x p , containing the concentration profile vectors for each of p
sources and, F , a p x n matrix, contains the contribution of each source in F
to X . The goals of a factor analysis are: (1) to determine p , the number of
independent sources that contribute to the system, (2) to determine the sourceprofile matrix A and (3) to calculate F which is the contribution of each sourceto each sample. In the simplest form this study is an analysis of the relationsbetween the eigensolutions for X'X and XX' , which represent, respectively,variation among both observations and properties.The first step in the analysis is the constructing correlation matrices. Two type of
correlation (about origin) can be written. In Q-mode analysis the basis is CQ the
correlation between samples over elements, and in R-mode analysis the basis is
Cfl , the correlation between elements over samples [7]. We define the
'correlation' matrices CQ and C# ,
(2)
where
Vl = Diag(X'X) (3)
and
(5)
as you can see the matrices are scaled to unit diagonal. The direction of scaling isthe same as the direction of matrix multiplication in each method. The rest ofanalysis is the same for the two methods.The correlation matrix is next diagonalized by finding a matrix such that
Where A is a diagonal matrix of eigenvalues arranged in decreasing order of
magnitude and Q contains the associated eigenvectors. Depending on whether
the R- or Q-mode correlation matrix is analyzed, the values of A and Fmatrices can be calculated as follows [7]:
Q-mode
(7)
R-mode
F*=Q»V?X . (10)
In the next step, the number of resolvable sources is determined. In the absenceof error, the eigenvalues beyond the true number of independent sources becomezero, except for calculational errors. Because the data contains noise, the choicebecomes more difficult. Several approaches have been suggested in the literature.A large relative decrease in the magnitude of eigenvalues is one indicator of thecorrect number of factors. In another test the reproduced data using the firstp eigenvalues were compared point -by-point with the original data, and an
average error, Chi-square and Exner value [12] were calculated as the indicatorof agreement between the reproduced and original data. The number ofindependent sources was determined from examination of these indicators.After the truncation of A and F matrices to only p remained factors, it is
necessary to interpret their nature. The A matrix produced by diagonalizationcan not be directly associated with actual source profiles, since it is one of aninfinite number of mathematically equivalent matrices that will diagonalize thecorrelation matrix. In order to relate this abstract matrix to one with physicalsignificance, it is necessary to geometrically realign the factor axes with axesthat represents real source emission concentration profiles. Such physicallysignificant axes called test vectors are derived from existing knowledge of therelative elemental composition of actual source materials. The realignmentprocedure called target transformation involves finding a rotation vector r ,which by the weighted least-square minimization of error between b and the
rotated axes of A . The weighted target transformation rotation is given by
Where W, die weight matrix, is a diagonal matrix that can have as its diagonalelements the inverse of the variance of elemental concentrations, or inverse ofthe square of the average error of determination for the concentration values [6].In addition to source profile test vectors, uniqueness test vectors, having thevalue for one element set to 1.0 and those of other elements set to 0.0, areanalyzed for all elements [13]. The test vector predicted by the uniqueness testcan then be used as a normalized source concentration profile that have not beenmeasured. These unique test vectors can be obtained using an iterative procedure
until the average percent error decreases less than 10"̂ . In each iteration a new bobtained as follows:
6 = ̂ r (12)
The identified sources were then used to calculate the corresponding masscontributions using a weighted least-square method [6].
4 Computer Implementation
TTFA was carried out using the computer program called NIVAR, developed bythe authors. This program has been written in MATLAB® 5.2 environment, andit can perform calculations in Q- and R-mode. NIVAR consist of severalfunctions for diagonalization, determination of correct number of independentsources, target transformation and error estimation.The Jack-Knifing method was used to calculate the error associated with thereproduction data from the results of Target Transformation Factor Analysis[14]. NIVAR is an interactive program, and the user can select specific options,such as, the mode of calculations, uniqueness test for elements, source profileiteration, Jack-Knifing error estimation and generation of various kinds of plotsof final and intermediate results.
5 Results and Discussions
Target transformation factor analysis of Q-mode was applied to the set of datafrom station number 3. This included 110 samples, which were analyzed for 18elements. In the data set, there were days for which, due to some fielddifficulties, no sample analysis was recorded.In order to have enough sample for 18 elements it was decided to assign averagevalues of concentrations to theses days with no recorded data which leaded to amatrix of 18 rows and 110 columns representing concentration of elements (injig/iff*) for each sample.It has to be mentioned that the nature of elements originally analyzed was 21,which included the main 18 elements together with Co, Ce and Cs. Once TTFAwas implemented on all 21 elements, the unjustifiable result was obtained.During the course of so many attempts with TTFA model, authors realized thatinclusion of Co, Ce and Cs would introduce disturbances in source profiles of
justifiable sources (i.e. the one which could be interpreted easily as a commonsource such as soil, residual fuel oil, etc.).Additionally, another effect of the inclusion of 21 elements in the calculationswas that non-interpretable singular sources, such as source with only Co asindicator element, would be obtained. Due to their undesirable effects on sourceprofiles of main sources and on producing imaginary or non physicallyinterpretable sources (such as source with only Co as its indicator element),attempt was made to eliminate Co, Ce and Cs from the calculation.The selected data set was then fed to the developed software NIVAR toimplement the required calculation according to TTFA model.The first step was to determine the minimum number of factors requiredrepresenting the observed variance of the data set. For each number of (assumed)retained factors, the Chi-square value, Exner function value, RMS error and theaverage arithmetic percent error give an indicator of the point-by-point errorbetween the original data and the data reproduced with that number of factors.According to Hopke et al. [8], an indicator parameter should show a smaller rateof decrease once the proper number of factors has been used. This approach wasused in this study, too. But, for some reason, which could be due to errors in dataset, no clear decreasing trend in the indicator parameters was observed.
Table 1. The eigenvalue, chi-square, Exner value andaverage percent error for the first twenty vectors
Instead, another approach was introduced in which the introduced error related toeach vector was calculated by removing the relevant vector and retaining the restof the vectors. In this way error associated with omitting the given vector isestimated. Therefore, the minimum number of required vectors will bedetermined once a minor error (for example 1%) is reached in the sequence oferror estimation for each vector. The results of the tests that determined theminimum number of required factors are given in Table 1.It should be noted that obtained values for Chi-square shows a non-interpretabletrend while from those values obtained for Exner, average percent error andRMS it can easily be realize that the appropriate number of factor is 7. In thedata set, nature and identity of sources was determined by means of a targettransformation analysis. Since no test vectors of different sources was availablefor Tehran, the unique test method was used to determine source profiles. Table2 lists the source vectors, which were derived from the uniqueness test.Commonly, the calculated source vectors should be compared with the actualsource profile, so that extent of overlapping can be evaluated. However, due tothe lack of existing actual source profile for Tehran metropolitan, the comparisoncould not be done. This test vectors are scaled to the absolute rather than tonormalized concentrations. Normalized test vectors can be used if the totalsample weight is known. The vectors would then be scaled to the absoluteconcentrations with scaling factors calculated, from both the source contribution
Table 2. The resulted source vectors (gr/gr)Element
and the total weight of sample, by means of a multiple regression analysis.The seven test vectors which produced the best overall agreement were; soil,residual fuel oil, refuse incinerator, iron and steel industries, automobile, cementand an unknown source with Cr, Sc as major elements.Index elements for each of the sources was found from source profile derived byTTFA. The calculated source profile for soil showed large factor loading for K,Na, Fe and Mn. Moreover the calculated source profiles for the residual fuel oilrefuse incineration, iron and steel industries, automobiles and cement has a largefactor loading for V, As-K-Na, Mn-Fe, Pb-Br and Ca respectively. Once, TTFAmethod is applied on an originally singular crustal source it could be furthersubdivided or differentiated into two sources of soil and limestone or cement. Infact this shows the superiority of TTFA over other factor analysis procedures.The high calcium loading was assumed to be attributed to cement plants aroundthe sampling site (station 3).Regarding differentiation of sources as mentioned above attention must be paidto cases where indicator elements of separating sources happened to be verysimilar. Arsenic (As), would be needed to clearly differentiate the contributionsof soil and coal-burning power plant. However, arsenic can not explicitlydifferentiate the contributions of refuse incineration, and coal related sources.More information and reliable data on other elements would be needed so thatsource differentiation could be well implemented. Unfortunately, lack of data on
Figure 2. Average percent contribution of each source
Important elements (such as C, Si, S) caused more complexity and vagueness inthe matter of source identification. It is important to know that different errors,such as analytical errors, sampling errors, sample preparation errors, numericalerrors and most importantly errors accompanied inherently with unique testvector method resulted in introduction of errors in calculated results and,consequently, in insufficient source resolution. However, the presented resultsare the best result could possibly be obtained given the scarcity of informationabout sources in Tehran and using factor analysis.As could be inferred from Table 2 the unknown source with indicator elementsof (Sc, Cr) is not clear and no physical source representing it was found. Finally
average percent contribution of each source to the total average mass is given inFigure 2. This information can be utilized by decision-makers to define andimplement the most effective pollution prevention scenarios.
Acknowledgement
This research was supported in part by Iran Meteorological Organization and theResearch Office of Amir-Kabir University of Technology. The data set wasprovided by Iran Atomic Energy Organization.Authors gratefully acknowledge the provided supports from all above-mentionedinstitutes.
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