Environ. Sci. Technol. 1986, 20,467-473
Both methods were effectivelv performed. In the case of activated carbon, the regeneration by sodium hydroxide was possible. However, phenol adsorbed was not desorbed completely. The adsorption capacity for activated carbon gradually decreased during the repetition process.
Literature Cited
Himmelstein,K. J.; Fox, R. D.; Winter, T. H. Chem. Eng. Prog. 1973,69, 65-69. Anderson, R. E.; Hansen, R. D. Ind. Eng. Chem. 1955,47, 71-75.
Chasanov, M. G.; Kunin, R.; McGarvey, F. Ind. Eng. Chem. 1956,48, 305-309.
Glossary
specific surface area, m-l concentration in liquid phase, mol/m3 c concentration at the liquid-particle interface, Ci mol/m3 CO feed concentration, mol/m3 m2/s for phemolecular diffusivity (=1.15 X D m . nol), mz/s effective surface diffusivity, m2/s particle diameter, m liquid film mass transfer coefficient, m/s amount adsorbed within a particle, mol/kg saturated amount of adsorbed phenol, mol/kg particle radius, m Reynolds number (d,pu[w) radial position in a particle, m Schmidt number [cL/(PD,)I time, s superficial fluid velocitv, m/s 2 axial position in the bed, m' void fraction of the bed €E viscosity [ =0.8019 kg/(ms) for water], kg/(m.s) CL liquid density (=995.7 kg/m3 for water), kg/m3 P PP particle density, kg/m3 Registry No. Dowex 1-X4, 9056-02-4; phenol, 108-95-2.
Pollio, F. X.; Kunin, R. Enuiron. Sci. Technol. 1967, I ,
a"
160-163.
Akahane, M.; Arai, T.; Kaneda, H.; Fujimoto, S. Nippon Kagaku Kaishi 1984, 1310-1316. Paleos, J. J . Colloid Interface Sci. 1969, 31, 7-18. Crook, E. H.; McDonnell, R. P.; McNulty, J. T. Ind. Eng. Chem. Prod. Res. Deu. 1975,14, 113-118. Farrier,D. S.; Hines, A. L.; Wang, S. W. J. Colloid Interface Sci. 1979, 69, 233-237. Kawabata, N.; Higuchi, I.; Yoshida, J. Bull. Chem. SOC.Jpn. 1981,54, 3253-3258.
Goto, S.; Goto, M.; Uchiyama, S. J. Chem. Eng. Jpn. 1984, 17, 204-205.
Hashimoto, K.; Miura, K.; Tsukano, M. J. Chem. Eng. Jpn. 1977,10, 27-34.
Dwivedi, P. N.; Upadhyay, S. N. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 157-165. Carter, J. W.; Husain, H. Trans. Inst. Chem. Eng. 1972, 50,69-75. (14) Suzuki, M.; Kawazoe, K. J . Chem. Eng. Jpn. 1975, 8, 379-382.
Received for review November 19, 1984. Revised manuscript received November 12, 1985. Accepted December 6, 1985.
Classification of Estuarine Particles Using Automated Electron Microprobe Analysis and Multivariate Techniques Paul C. Bernard and Ren6 E. Van Grieken" Department of Chemistry, University of Antwerp (U.I.A.), 8-2610 Antwerp-Wilrijk, Belgium
Doeke Eisma Netherlands Institute for Sea Research, Den Burg, Texel, The Netherlands
rn The suspended particulate matter from a series of stations in an estuary is automatically analyzed for 11 elements on a particle-by-particle basis by using electron microprobe X-ray microanalysis and an automatic image analysis system. The interpretation of the large acquired data set implies numerical multivariate analysis. The developed procedure consists of using cluster analysis on the particles of individual samples, followed by nearest centroid sorting over all samples from the study area. For the Ems estuary, the procedure provided 13 geochemically different particle types of which the relative abundance through the estuary could be followed and interpreted in terms of estuarine mixing processes. The presented methodology could be applied in other studies concerning the characterization of particle populations. Introduction
Suspended particulate matter from estuarine and marine environments is being investigated extensively in order to assess sediment processes, the interactions between sediments and the water column, and the physicochemical reactions that particles undergo. Most of the analytical methods used in this context hitherto provide the bulk composition or mineralogy of the sample. Associations between, e.g., chemical elements, mineral phases, and 0013-936X/86/0920-0467$01.50/0
morphology must then be made on a statistical basis. Alternatively, single particle analysis methods such as scanning electron microscopy (SEM) combined with X-ray analysis or electron-probe X-ray microanalysis (EPXMA) can be invoked. These directly provide the chemical and morphological characteristics of individual particles (1,2) but have the disadvantage of being enormously time consuming when performed manually. Through the automatization of computer-controlled EPXMA it has become possible to analyse several hundred particles in a relatively short time, say a few hours. This technique is increasingly being used for the analysis of atmospheric aerosol particles (3), asbestos fibers ( 4 ) ,mineral inclusions in coal samples (5), and similar applications. However, it has seldomly been used in geochemical studies on sediments and suspension particles from the aquatic environment. Only Bishop and Biscaye (6) applied an automated image analysis system to particulate matter from the nepheloid layer in the ocean and classified the particles on the basis of their Si/A1 ratio. In this paper, we report on the use of a commercially available SEM-based automatic image analysis system, the Particle Recognition and Characterization (PRC) program (7) for the study of particles throughout an estuary. Since such an automated system rapidly yields a very large data matrix, a straightforward interpretation is only possible
0 1986 American Chemical Society
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Figure 1. (a) Sampling locations in the Ems estuary. (b) Salinity and turbidity at the sampling stations.
when the individual particles are classified into particle types, necessitating combination with multivariate analysis techniques. Since most existing suitable classification methods require previous knowledge of the particle types present, a new classification scheme was developed; it involves cluster analyses on all particles of individual samples followed by a nearest centroid sorting over all samples from the study area. In this way geochemically relevant groups are obtained. The abundance of the groups can be followed through the study area, and the changes provide information about processes that influence the abundance of certain groups. To our knowledge, this is the first illustration of the capabilities of SEM-based automated image analysis combined with multivariate analysis techniques for the characterization of estuarine particles.
Experimental Section Samples and Sample Preparation. The estuary of the Ems river is located near the border of Federal Republic of Germany and The Netherlands. Suspended matter samples were collected in Nov 1982 at 10 stations in the river and throughout the estuary (Figure 1). The salinity and turbidity profile in the sampling area are shown in Figure lb. Small aliquots of water, one drop to a few milliliters, were filtered over a 47 mm diameter X 0.4 pm pore size Nuclepore membrane. Care was taken to obtain a sufficient loading for efficient analysis while maintaining a low percentage (less than 5%) of overlapping particles (8); generally the sample loading was then 50-2000 particles/mm2. After being washed and dried, the filters were vacuum coated with carbon. Instrumentation. The measurements were performed with a JEOL JXA-733 Superprobe used a t an electron energy of 20 keV and a beam current of ca. 1 nA. The magnification was 540X, allowing particles larger than 0.5-pm diameter to be analyzed. At these working conditions a maximum image resolution of 0.05 hm can be obtained. The microprobe is equipped with a 30-mm2 energy-dispersive Si(Li) detector, a wavelength-dispersive X-ray spectrometer, a secondary electron and transmission electron detector, and backscattered electron detectors (for composition and topographic viewing). The microprobe is automated with 6 Tracor Northern TN2000 system and is controlled by an LSI 11/23 minicomputer with two double-density floppy disk drives. The Tracor software was modified somewhat to obtain greater flexibility. A 9-track 800-bpi magnetic tape unit, connected as an extra bulk data storage device, allows the storage of data from many thousands of particles and provides a convenient medium for transfer of the data to a VAX 468
Environ. Sci. Technol., Vol. 20, No. 5, 1986
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Figure 2. Representation of the SEM beam scanning scheme that automatically defines the centroid of a particle.
111780 computer for additional data analysis.
Basic Measurement Methodology. In this system, the digital beam control moves the electron beam across the area to be analyzed according to a 410 x 410 point grid while monitoring the signal from the backscattered electron detector. The computer moves the electron beam according to the measuring grid until a signal above an adjustable lower threshold and below an upper limit is detected. When a particle is detected, the scan grid resolution is increased 10-fold and the particle centroid is searched. For this purpose, the particle boundary is defined as the location where the signal falls outside the selected intensity limits. Then a scan is made over the particle in a direction normal to the previous scan and starting from the midpoint between the observed particle boundaries. Such scans normal to the previous one are made subsequently until a stable midpoint position is obtained; this is taken as the centroid. This procedure is represented in Figure 2. From this point eight diagonal scans over the particle are made, and the coordinates of 16 contour points are determined. From these coordinates, the mean, maximum and minimum diameter, the area, and the circumference (or perimeter) are calculated. A shape factor is calculated as the ratio of the square of the perimeter to 4.rr times the area. An energy-dispersive X-ray spectrum is collected at the particle centroid for a preset time, e.g., 10 s. Usually the total X-ray count rate was between 500 and 2000 counts/s. The peak intensities of the K X-ray lines of Na, Mg, Al, Si, P, S, and C1 and the K a lines of K, Ca, Ti, and Fe are integrated after sub-
tracting linearly interpolated background contributions from the total counts in the spectrum regions of interest. The relative X-ray intensities and the size information are stored on a floppy disk as an object vector for each individual particle. (When the sum of the net peak intensities is below 500 counts per 10 s, the particle is not taken into account because the concentration of the detectable elements is too low for reliable interpretation of the relative X-ray intensities; this was the case for about 1% of the sized particles.) After a particle is processed, the program goes back to the search mode and moves the beam again across the grid points until the next particle is detected. To avoid reanalysis, the coordinates of the centroids of the particles are stored in the memory. After the sample area of interest has been run, the data are transferred to the mainframe computer via magnetic tape. The multivariate analysis techniques are then applied. To correct for the matrix effects in EPXMA, a matrix correction, the so called ZAF correction, is usually applied to transform the relative peak intensities into the elemental weight composition. Therefore, after the particles have been classified into groups, as will be discussed, a correction for matrix effects in EPXMA, namely, a conventional standardless ZAF correction (9),is carried out, taking into account the average composition of the group. Performing conventional ZAF corrections to the data of every individual particle before the multivariate analysis step would be more rigorous but require too much CPU time for large particle populations to be feasible in practice. Also including a ZAF correction specific for particles, e.g., the Armstrong-Buseck method (IO),would be very time consuming. Limited comparisons of these approaches indicate that applying conventional ZAF corrections to the average data from a particle group is acceptable for studies of estuarine particles. However, the exact effect of the degree of accuracy and quantification on the result of the eventual classification procedure is being studied in detail at present.
Multivariate Analysis Cluster Analysis. For each of the samples, approximately 250-300 particles were analyzed by EPXMA. Hierarchical cluster analysis methods were used to classify these particles into groups on the basis of elemental concentrations, hence, on 11variables. A classification based on the size or shape is also possible (11). Every particle i is represented in an N-dimensionalspace by an object vector x, = (xi,l,xi,2, ...,X i & , ...,x&, defined by the N-elemental X-ray intensities. The Euclidean distance coefficient is used to measure the similarity of the particles. No scale conversion is carried out in order to reduce the effect of large relative variations in the concentration results of the minor elements. The Euclidean distance coefficient dij is defined as
assuming that the N variables are orthogonal, for the particles i and j . Particles with similar composition will be close to each other in the N-dimensional space and consequently will have a small dip The Euclidean distance coefficient is calculated for every pair of objects (particles). The procedure of an hierarchical clustering is as follows; if n is the number of objects present, then (1)find the smallest element dij, (2) fuse i and j into a single group h, and (3) compute new distances d k m (mrepresents each of the remaining points). These distances replace dim and
djm. (4) Repeat for ( n- 1)cycles. With n objects present,
n(n - 1)/2 values of dLjare calculated. With increasing n, the number of required calculations rises quadratically and can become prohibitively large; this limits the number of particles that can be considered in practice. A large number of hierarchical cluster algorithms have been developed (12);they differ from each other in the way they calculate the distance dkm between a newly formed cluster and the remaining objects. To identify the optimal method for the present purposes, several were applied to the data set. The hierarchical strategies used in this study were the following: nearest neighbor (single linkage), furthest neighbor (complete linkage), group average (unweighted average linkage), simple average (weighted average linkage), and Ward’s method (error sum of squares method). Detailed descriptions of these methods are available in the literature (12). The cluster programs are incorporated in a software package recently developed by Van Espen (13). Nearest Centroid Sorting. The simultaneous classification of all the measured particles in all the samples of the study area should not be done by a hierarchical cluster analysis. Indeed, when the number of particles analyzed is, e.g., 3000, as many as 4500000 Euclidean distance coefficients have to be calculated and processed in every cycle. Therefore the “nearest centroid sorting” (14) is used. The classification rule states that an object (pattern vector) is classified to the nearest centroid of the training set (training vectors). This means that on the basis of the composition data for every particle the Euclidean distance to all the training vectors (centroids) has to be calculated. The smallest distance determines the nearest neighbor. If, e.g., 15 training vectors and 3000 particles are present, only 45 000 distances must be calculated. Of course, the classification can only be successful if proper training vectors are chosen. This is achieved by the following: (1) Cluster analysis of the composition data of the particles is performed for each individual loaded filter sample. (2) Subsequent cluster analysis of the average composition data of all the groups obtained via step 1 is performed. Hence, groups representative for the whole sample area are obtained; their average compositions are taken as the training vectors (centroids). (3) A nearest centroid sorting is performed for each particle of all samples relative to these training vectors. (4) The training vectors are replaced by the average composition of the particles which have been associated to them. Steps 3 and 4 are repeated until convergence appears and the centroids representative for the study area have been optimized. Results and Discussion Comparison of the Cluster Procedures for the Particles of One Sample. The different cluster procedures that can possibly be used for the classification of particles from one sample were compared with respect to their applicability in the context of geochemical studies on estuarine particles. The evaluation was necessarily rather intuitive and based on the experience gained: a satisfactory compromise was pursued between, on the one hand, describing the large data set using a minimum number of groups and, on the other hand, maintaining a maximum of geochemically relevant information avoiding the fusion of geochemically important groups. It appeared that Ward‘s classification method served the present purpose best. Somewhat less preferable seemed to be the furthest neighbor method closely followed by the Environ. Sci. Technol., Vol. 20,No. 5, 1986
469
simple average and by the group average method. The nearest-neighbor method was clearly the least satisfactory. Although this order can hardly be generalized, it should be mentioned that it agrees fully with the order of preference given by Massart and Kaufman (12),except for the fact that we find the furthest neighbor method to score slightly higher than expected. On the basis of this experience, it was decided to use Ward's method for the classification of the particles in the individual samples. Classification of Particles from All Samples. The objective of recognizing specific groups in a sample and following their behavior through the whole study area is not served by classification per individual samples. Indeed, due to statistical fluctuations, the groups identified by the cluster algorithms can differ in average composition from sample to sample or even for successive measurements of a finite number of particles in one sample. This is illustrated in Table I, where the cluster results are represented for two river suspension samples taken simultaneously at the same location. I t can be seen that, as far as major elements are concerned,the overall composition calculated as the weighted average of the compositions of the different groups is the same for both samples, confirming the representativeness of the sampling and validity of the chemical analyses (of course, mainly due to counting statistics, the relative differences are up to a factor of 3 for the minor elements, but since no normalization was carried out for the calculation of the dissimilarity matrix, low abundance elements have less influence on the cluster analysis results). In both samples corresponding groups with an identical composition (e.g., groups 1,4, 5, 6, and 8 in sample 1 and groups 8, 7, 4, 3, and 6 in sample 2, respectively), albeit sometimes with a different abundance, can easily be recognized. Yet, some groups that are separated in one sample are seen to merge in the other sample (e.g., groups 1 and 2 in sample 2 correspond with group 7 in sample 1). Therefore, the classification should consider simultaneously all examined particles in all samples of the study area, and application of the nearest centroid sorting method is required. Application to Suspended Particulate Material from the Ems Estuary. For each of the 10 Ems estuary samples, some 300 particles were analyzed for 11elements. For each individual sample, the results were clustered with Ward's methods, and eight groups were retained on the basis of their dissimilarity. The average elemental abundances of the 80 groups obtained for the 10 samples were clustered again with Ward's method; this provided 13 groups of average abundances. The 11 average abundances of these 13 groups were used as the training vectors in the subsequent nearest centroid sorting over all particles (-3000) from all samples. The results of this final classification are given in Table IIA, where the average composition (converted to oxides when relevant) of the optimized groups are listed, and in Table IIB, which indicates the relative abundance (particle frequency) of each group in every individual sample. The reliability (2a values) of the relative abundances of the particle types can be calculated from binomial statistics and is between 2 and 6% absolute when 300 particles are measured (25). It appears from Table IIA that 76% of the detected particles are rich in Si (>40% as SOz). Groups 13, 9, 2, and 1 probably represent quartz silt and K-, Ca- and Ferich aluminosilicates, respectively. Groups 10 and ll are calcite and/or aragonite, while groups 7 and 8 consist mostly of Fe203with a significant phosphate concentration. 470
Environ. Sci. Technol., Vol. 20, No. 5, 1986
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The low abundance groups 3,5,6, and 12 are characterized by relatively high contents of Fe and S, Ti, Ti and S, and Al, respectively. It is seen from Table IIB that the abundance of certain groups changes significantly through the Ems estuary. Figure 3 shows the particle frequency distribution with loeation for groups 7-10. Groups 7 and 8 occur at relatively high concentrations at river stations 24 and 25 but show a very low abundance from station 27, which is before the contact with saline water (Figure lb). This indicates that mixing of river suspended material with suspended material supplied from the nearshore sea takes place entirely in the freshwater tidal area, which confirms earlier results obtained by Salomons (16) based on the composition of carbonates. The inorganic particle composition as determined by EPXMA can be used as a tracer for particle origin, making it possible to evaluate the effect of mixing of material of different origin on compositional changes in the estuary and to separate the mixing effect from other effects such as deposition and mobilization. In this way EPXMA data have been used to evaluate changes in the particulate organic matter composition (17). In the Ems, the Fe- and P-containing particles (Figure 3a) probably have their origin in the peatbog areas that are being drained by the Ems river. The mineral of group 9 (an illite-type mineral?) comes inward from the outer estuary. In the outermost samples, however, group 9 is about 15% lower than further inward, which is related to an increase in the percentage 472
Environ. Sci. Technol., Vol. 20, No. 5, 1986
of group 10 (Ca rich) and of group 2. A similar shift (increase) occurs for group 13 (SiOJ between stations 28 and 30. The higher Ca mineral percentages can be caused by organic carbonate production in the estuary. The small shifts in composition, as shown by group 2, 9, and 13, cannot be related to particle formation in the estuary and are not related to a smaller or larger influx of river-supplied material, or to a particle size effect, as is indicated by the particle sizes given in Table IIA. They may therefore indicate a small third (local?) source of particulate matter (erosion?) or another form of sorting. That some sorting may take place is suggested by the fact that the higher percentages of group 9 (and the lower percentages of groups 2 and 13) occur chiefly in the area of high turbidity (Figure lb). The size of all particles that were analyzed is between 1 and 6 pm, and all have a somewhat elongated shape. This size range agrees with earlier size determinations of inorganic single suspended particles along the Dutch coast (18),but in nature most of the single mineral particles are strongly bound together by organic matter into flocs of up to a 125-pm diameter: on the order of 70% of the suspended particles are flocs and the remainder single mineral particles. Determinations by pipet analysis or by Coulter Counter give the size distribution of this mixture of flocs and single mineral particles (Figure 4). The decrease in particle size between 22 and 27, which coincides with the contact between fresh water from the river and more saline water, is probably caused by breakup of flocs because of mobilization of mucopolysaccharides that glue particles together (19). Generally, the example of the Ems estuary shows that automated individual particle analysis allows an advanced characterization of suspended particulate matter. The abundance variations of the identified particle types provide information about geochemical and physical processes that influence the distribution of certain particle types in the estuary. Acknowledgments We are grateful to L. Kaufman for critically reviewing the manuscript. Registry No. Si, 7440-21-3; Al, 7429-90-5; Ca, 7440-70-2; Fe, 7439-89-6; Mg, 7439-95-4; Na, 7440-23-5; K, 7440-09-7; Ti, 7440-32-6; Cl,, 7782-50-5; S, 7704-34-9; P, 7723-14-0.
Literature Cited (1) Dehairs, F.; Chesselet, R., Jedwab, J. Earth Planet. Sci. Lett. 1980, 49, 528-550. (2) Lambert, C. E.; Jehanno, C.; Silverberg, N.; Brun-Cotton, J. C.; Chesselet, R. J. Mar. Res. 1981, 39, 77-98. (3) Hanna, R. B.; Karchiech, K. J.; Johnson, D. L. SEM 1980, 1,323-328.
Environ. Sci. Technol. 1986, 20, 473-483
(4) Dixon, R. N.; Taylor, C. J. SEM 1979, I , 361-366. (5) Moza, A. K.; Austin, L. G. Fuel 1983, 62, 1468-1473. (6) Bishop, J. K. B.; Biscaye, P. E. Earth Planet. Sci. Lett. 1982, 58, 265-275. (7) Fritz, G. Tracor Northern Inc., 1982, TN-1912. (8) Kelly, J. F.; Lee, R. J.; Lentz, S. SEM 1980, I , 311-322. (9) Henoc, J.; Maurice, F. In “Microanalysis and Scanning Electron Microscopy;” Maurice, F.; Meny, L.; Tixier, R., Eds.; Les Editions de Physique: 1979; pp 281-317. (10) Armstrong, J. T.; Buseck, P. R. Anal. Chem. 1975, 47, 2178-2192. (11) Raeymaekers, B.; Van Espen, P.; Adams, F. Mikrochim. Acta 1984, 11, 437-454. (12) Massart, D. L.; Kaufman, L. “The Interpretation of Analytical Data by the Use of Cluster Analysis”; Wiley: New York, 1983. (13) Van Espen, P. Anal. Chim. Acta 1984,165, 31-49. (14) Anderberg, M. R. “Cluster Analysis for Application”; Academic Press: New York, 1973.
(15) Van Der Plas, L.; Tobi, A. C. Am. J . Sei. 1965,263,87-90. (16) Salomons, W. J. Sed. Petrol. 1975, 45, 440-449. (17) Eisma, D.; Bernard, P.; Boon, J. J.; Van Grieken, R.; Kalf, J.; Mook, W. G. Mitt. Geo1.-Palaeontol. Inst. Uniu. Hamburg 1984,58,397-412. (18) Eisma, D.; Kalf, J.; Veenhuis, M. Neth. J . Sea Res. 1980, 14 (2), 172-191. (19) Eisma, D.; Boon, J. J.; Groenewegen, R.; Ittekkot, V.; Kalf, J.; Mode, W. G. Mitt. Geo1.-Palaeontol. Inst. Univ. Hamburg 1983,55, 295-314.
Received for review December 26, 1984. Revised manuscript received November 4,1985. Accepted December 24,1985. P. B. is indebted to the “Instituut tot Aanmoediging van het wetenschappelijk Onderzoek i n Nijverheid en Landbouw” (I.W. O.N.L.) for financial support. This study was partially financed by the Belgian Ministry of Science Policy under Contracts 8085/10 and 84-89/69.
Source Discrimination of Short-Term Hydrocarbon Samples Measured Aloft Richard A. Wadden”
School of Public Health, University of Illinois, Chicago, Illinois 60680 Itsushi Uno and Shinji Wakamatsu
National Institute for Environmental Studies, P.O. Yatabe, Tsukuba, Ibaraki 305,Japan
rn Weighted least-squares fitting of 17 hydrocarbons was used to estimate ambient contributions from four source categories. The data set consisted of 192 samples collected from 300 to 1500 m over Tokyo, July 16-17,1981. Six runs (flights), 1-1.5 h long, spaced throughout each day, constituted chemical “snapshots” of the urban air. Vehicles contributed 7.0%, gasoline vapor 10.5%, petroleum refinery 26.0%, paint solvents 27.2%, and unexplained sources 29.3% of the total hydrocarbon concentration (based on the 17 components measured and all samples). These coefficients are only representative of the days and conditions sampled and should not be interpreted as annual emission fractions. On a run-averaged basis the correlation between refinery emissions per hour, adjusted for dispersion, and ambient concentrations of total hydrocarbon attributable to petroleum refineries was r2 = 0.899, indicating that the refinery profile was sufficiently unique to be sensed up to 70 km. The fractions for paint solvents, gasoline vapor, and unidentified sources were also consistent with wind trajectory observations. Air-quality models that link source emissions to environmental concentrations are important tools for controlling air pollution. One type of air quality model is the chemical element balance (CEB) or source-reconciliation model. This is a method to determine the relative air pollution contribution of each of the major sources of a categorical pollutant (such as total suspended particulate matter, TSP, or non-methane hydrocarbons,NMHC) from ambient measurements of the composition of the categorical pollutant at one or more receptor sites. The method requires that the composition of the categorical pollutant be known in the emissions of each source category, i.e., source fingerprints, and that the ratio of the concentration of each component to the categorical pollutant concentration be the same in the source emissions and at the receptor point. 0013-936X/86/0920-0473$01.50/0
The calculation procedure is a multivariate least-squares fit of the composition data with a specified number of source coefficients. The general equation is Y=Zp+E (1) where Y is the vector of i elemental or molecular compositions, Z is the pollution source elemental or molecular composition matrix of i components for each of j + 1 sources (including an intercept term vector of ones), p is the vector of j 1source weights or coefficients with one intercept term, and E is the vector of i errors (the difference between the measured and predicted elemental or molecular compositions). The values of p represent the fraction of the categorical component contributed by each emission source type, e.g., automobiles or oil-burning power plants. For statistical validity it is desirable to have many more components than sources. Specific values of p can be determined for each receptor sample. And a distribution of samples over a period of time will provide a distribution of values for each source coefficient. This model has been applied for TSP in a variety of locations (1-4). The method has also been used in somewhat simplified form to evaluate total hydrocarbon concentrations (THC) (5-7). (THC was defined as the sum of a number of specified “unreactive” hydracarbons in the atmosphere.) The composition of specified hydrocarbons were the elements of Y in eq 1,and corresponding source compositions were used for the values of Z. A useful approach for solving eq 1,at least for TSP, has been the weighted least-squares solution p = (Z’ C-lZ)-l(Z’ C-lY) (2)
+
where the prime and superscript minus one indicate transpose and inverse operations, respectively; is a diagonal matrix of the variances for the measurement vector Y. One necessary physical limitation is that, except for the intercept term, none of the p’s can be less than zero.
0 1986 American Chemical Society
Environ. Sci. Technol., Vol. 20, No. 5, 1986 473
