Receptor Modeling

Definitions
Model Types
Model Limitations
Multivariate Analyses
GRACE/SAFER
CMB Application and Examples
Summary
References
Table of Conversion Factors for CMB
Table of Photochemical Half-Lives of PAMS VOC

CMB Chemical mass balance
CNG Compressed natural gas
CV Coefficient of variation
GRACE Graphical ratio analysis for composition estimates
LPG Liquefied petroleum gas
LQL Lower quantifiable limit
MDL Minimum detection limit
MW Molecular weight
NMHC Nonmethane hydrocarbon
PCA Principal component analysis
SAFER Source apportionment by factors with explicit restrictions
SCE Source contribution estimate
TMB Trimethylbenzene
VOC Volatile organic compounds

• Receptor models are used to resolve the composition of volatile organic compounds (VOC) into components related to emission sources.
•  Modeling tools include:
• Principal component, factor, cluster analyses, or other multivariate statistical techniques
• Graphical ratio analysis for composition estimates (GRACE) and source apportionment by factors with explicit restrictions (SAFER)
• Chemical Mass Balance (CMB)
•  Modeling may be coupled with classification of the ambient data by wind direction, wind speed, time of day, site, season, etc.

• Many emitters have similar species composition profiles.
• Species composition profiles change between source and receptor.
• Receptor models cannot predict the consequences of emissions reductions.

 The species i-pentane, n-pentane, cyclopentane, and 2,2-dimethylbutane were found in the following source profiles: 

Bold indicates plausible sources. The profile of another likely source, jet fuel, contains only straight-chain C7 to C15 alkanes.

• Statistical procedures used to infer mix of hydrocarbon sources impacting a receptor location.
• Procedures including cluster, factor/principal component, regression, and other multivariate techniques usually available in statistical software packages.
• Literature review shows many refinements and options to these analyses.
• A drawback to these analyses is that the analyst must infer how certain statistical species groupings relate to emissions sources.
• A nice feature of these analyses is the ability to summarize a multivariate data set using a few components.

• Cluster analysis is a multivariate procedure for detecting natural groupings in data.
• The following options are available:

• To produce clusters, you must be able to compute some measure of dissimilarity between objects:

Cluster analysis performed using only the fitting species used by CMB. Samples from July, August, and September 1993 episode days were used from Galleria (Houston), TX. Single linkage method using SYSTAT (Wilkinson, 1990). Isoprene is the last species to join the cluster tree; it appears to be unrelated to the other species. Several species (e.g., acetylene to n-heptane) are tightly clustered, suggesting a common source. See Wilkinson, 1990 or other statistical texts for cluster analysis options.

Cluster analysis performed using only the fitting species used by CMB. Samples from July, August, and September 1993 episode days were used from Clinton (Houston), TX. Single linkage method using SYSTAT (Wilkinson, 1990). Note that the clustering is quite different than at the Galleria site (e.g., isoprene, dimethylpentanes). See Wilkinson, 1990 or other statistical texts for cluster analysis options.

Hierarchical tree diagram of site/time averaged fraction of NMOC for the summer SCAQS 1987 (Lurmann and Main, 1992). The 35 most abundant species were used in this analysis. Note that the dissimilarities are small indicating the sites had similar compositions.

Hierarchical tree diagram of hydrocarbon and carbonyl compounds for the summer SCAQS 1987. The site/time-averaged fractions of the most abundant 35 species were used in this analysis (Lurmann and Main, 1992). Note that the dissimilarities are larger than those in the previous example.

• Factor analysis is a method of decomposing a correlation or covariance matrix.
• Factors indicate the best associations among variables while regression lines indicate the best predictions.
• The factor model expresses the variation within and the relations among observed variables as partly common variation among factors and partly specific variation among random errors.
• Typically, the analyst may choose factor rotation, with VARIMAX rotation as the most commonly used method, to achieve a simple structure among loadings (e.g., limit components with nonzero loadings on the same variable).
• The analyst may also choose to limit the number of factors output in the analysis.

Graphical Ratio Analysis for Composition Estimates (GRACE)

• Correlations between acetylene (assumed to be emitted solely from vehicle exhaust) and other VOC are used to establish the minimum and maximum exhaust-related ratios of acetylene to other species. GRACE plots of each roadway-corrected species versus all others are also examined.

 Source Apportionment by Factors with Explicit Restrictions (SAFER)

• SAFER is a multivariate receptor model that predicts the number of sources and their composition from the ambient data. SAFER requires that these predictions be consistent with observed intercorrelations of the concentrations and with physical constraints and explicit constraints derived from GRACE.
• SAFER requires large data sets, thus, the PAMS auto-GC data are well suited for this analysis.

• GRACE/SAFER applications include Atlanta and Houston.

Ambient Data Screening

• Complete data records required.
• Species with large amounts (> 20 records) of missing data (i.e., below detection limit) were removed.
• Species with analytical problems (e.g., contamination, identification, or peak resolution problems) were removed.
• Other data cleanup included changing 0's to missing, removing outliers, and correcting for concentration offsets discovered during data QC. 

• Generate scatter plots for each species against every other species and NMHC:
• Sharply defined linear lower boundaries in the distributions (edges) should be observed. In other words, a given concentration of species A always was accompanied by a minimum concentration of species B.
• Acetylene is a common starting point (assumed to be emitted solely by vehicle exhaust).
• Determine slopes of "edges" for ratios of species A and B in a particular source.
• Assuming acetylene as a roadway source, use the ratio of species to acetylene to remove this source contribution from the data set.
• Prepare scatter plots of roadway corrected species versus other species and repeat the analysis (determine edges, ratios, etc.).
• Use these ratios as constraints in the SAFER model to finalize the composition.

The CMB model uses an effective variance least squares solution to a set of linear equations which express each measured chemical species concentration as a linear sum of products of source profile species and source contributions.

Model Input

•  Source profile species (fractional amount of species in the VOC emissions from each source type).
• Receptor (ambient) concentrations.
• Realistic uncertainties for source and receptor values. Input uncertainty is used to weigh the relative importance of input data to model solutions and to estimate uncertainty of the source contributions.

 Model Output

•  Contributions from each source type to the total ambient VOC and individual hydrocarbon species and the uncertainty.
• Performance parameters.

• Composition of source emissions are constant over the ambient and source sampling period (can tolerate substantial variabilities).
• Chemical species do not react with each other (i.e., they add linearly) (little known about this).
• All sources which may significantly contribute to the receptor have been identified and their emissions characterized (minor contributors may be omitted).
• Number of source categories £ number of chemical species (the larger the difference, the better).
• Source profiles are linearly independent (degree of independence depends on the variability of the source profile).
• Measurement errors are random, uncorrelated, and normally distributed (effects unknown).

• Assess model applicability (e.g., data from well-characterized methods, large number of species, major sources identified, source profiles available, and reasonable uncertainties attached).
• Select source profiles for potential contributors (e.g., area, natural, and point sources plus other sources identified in preliminary analyses).
• Select sources for inclusion in the CMB solution (e.g., upwind point, seasonal emitters, non-collinear profiles).
• Determine initial SCE (e.g., use variety of source profiles and fitting species combinations, determine effects on results of alternate source profiles). May need to combine similar source types due to collinearity.
• Examine model outputs and performance measures. Do spatial and temporal results make sense considering meteorology and source emission patterns?
• Check how the removal and addition of some species affects results. The source profiles need to be the most precise for the most influential species.
• Identify deviations from model assumptions (e.g., source compositions constant, all sources included, source profiles independent, etc.).
• Identify and correct model input errors (e.g., increase uncertainty of profiles, provide different composites, identify and characterize missing sources, stratify samples by meteorology).
• Verify consistency and stability of SCE (substitute different profiles for same source type, add or drop species form fit, examine source contributions to individual species).
• Evaluate results of CMB with respect to other source assessment methods (e.g., compare SCEs among nearby sites, compare source contribution variations over time with expected emissions and meteorology, apply other receptor methods and compare results, apply dispersion models and compare results).

Estimating Uncertainty in Ambient Data

s (C) = ((2MDL)² + (CV*C)²)^½

 where:

Converting Units From ppbC to mg/m³ (at 25°C)

 Handling Missing Data

• Species with > 5 percent of their values either missing or 0 should be excluded from analysis.
• For weekday averages of continuous data, set a lower limit for the number of hours required each day, e.g., 22 of 24 hours.

• Use source profile data representative of the study area during the period when ambient data were collected.
• Include ubiquitous sources such as motor vehicle exhaust, gasoline evaporation, liquid gasoline, biogenic, gasoline headspace vapor. It is possible to adjust these profiles for year by using weighting factors (i.e., apply known emission changes).
• Include natural sources such as biogenic or geogenic emissions.
• Include point sources identified in the emission inventory such as solvent use, CNG, LPG, industrial fugitives, and other sources.
• Place source data on the same basis as the ambient data (i.e., adjust for species greater than C10, oxygenates, chlorinated species, etc.).
• Unresolved species or groups (e.g., isomers of pentane) may be allocated to individual species using average ratios from similar data sets.
• Try available source profiles in sensitivity tests to determine best ones for use (minimize collinearity).

• Measurements and performance audits conducted as part of the NARSTO-Northeast study including Callahan tunnel in Boston (MA), Lincoln tunnel (NY), and a Boston federal building garage.
• Literature review. On-road vehicle exhaust profiles have been developed from measurements in the Caldecott tunnel (CA), Tuscarora tunnel (PA), Fort McHenry tunnel (MD), roadside measurement in Atlanta.
• Auto-Oil Program measurements for 1989 and 1983-1985 fleets.
• Federal Test Procedure measurements by Sigsby et al. (1987) for 1975-1982 model years.
• Texas source profiles (1993) from Fujita (1995).
• California Air Resources Board MEDS (1992).
• EPA SPECIATE.
• Analyses of ambient data (e.g., GRACE/SAFER).

• Source data should be accurate and precisely measured and uncertainty should reflect the variability expected from a number of individual emitters in the same source type. At a minimum, profiles are no more precise than the analytical techniques used to measure them.

•  Variability in measurements due to changes in operating conditions, type of source, etc. may far exceed measurement error.

• Receptor models assume relative proportions of chemical species change little between source and receptor. Hydrocarbons are photochemically reactive and most species do not strictly meet this assumption.
• Treatment of reactivity is being debated in the literature. See the reference list for methods used to take reactivity into account.

Guidelines for Selecting Species

• Literature recommends selection of species with "sufficiently long" atmospheric half-lives. Cut-offs have been made at 5, 11, and 33 hours (see table at the end of the section).
• Isoprene is the exception. Since it is the only PAMS target species directly associated with biogenic emissions, it must be used. Therefore, source contribution estimates for isoprene should be considered a lower limit because of its reactivity.
• Investigate the available source profiles: which species are the most important, which species are unique among the sources?

•  Corrected error in collinearity routines.
• Automated CMB calculations for VOC data.
• Expanded input and output format options.
• Provides additional default fitting species and source profile combinations.
• Automates decision making in individual calculations and AUTOFIT (eliminate SCEs that are negative or are lower than their standard errors).
• Automatically eliminates species from receptor site data or fitting source profiles with missing values from the fit.
• Increases usable memory.
• Expanded options in the configuration file.
• Provides a graphical interface.

• R² is used to measure the variance in the ambient species concentrations, which is explained by the calculated species concentrations via linear regression. The closer the value is to 1.0, the better the SCEs explain the measured concentrations.
• Standard error is the variance of the SCE. This should be much less than the SCE.
• Chi square (c²) is used to consider the uncertainty of the calculated species concentrations (weighted sum of squares of the differences between calculated and measured fitting species concentrations). Values < 1.0 indicate a very good fit.
• The percent mass is the percent ratio of the sum of model-calculated SCEs to the measured mass concentration. This is used to track the percent explained mass; a value near 100 percent can be misleading because poor fits can force a high percent mass.
• The t-statistic is the ratio of the SCE to its standard error. The standard error of the SCE is an indicator of the precision in the model estimates. Values < 2.0 identify model estimates that are not significantly different from 0.
• Degrees of freedom is the number of species in the fit minus the number of sources in the fit.
• The ratio of the calculated species mass (CALC) to measured species mass (MEAS) is used to identify species that are over- or under-accounted for by the model. A ratio >1.0 means that more mass for a given species was accounted for by the model than was measured in the ambient sample.
• The ratio of the residuals to the uncertainty is the signed difference between CALC and MEAS divided by the uncertainty of the difference. It is used to identify species that are over- and under-accounted for by the model.
• The normalized modified pseudo-inverse matrix (MPIN), a diagnostic output of CMB7, indicates the degree of influence each species concentration has on the contribution and standard error of the corresponding source category. MPIN is normalized such that it takes on values from -1.0 to 1.0. Species with MPIN absolute values of 1.0 to 0.5 are associated with influential species.
• Maximum source uncertainty and minimum source projection (Henry, 1992) are used to assess clusters of sources which the model cannot easily distinguish between and that are likely to be interfering with the model's ability to provide a good set of SCEs.

• Example CMB output.
• Diurnal plots of SCEs by site, month, and day-of-the-week to show temporal and seasonal variability.
• Plot investigating the wind direction and temperature dependence of SCEs.
• Pie chart showing the average source contributions for specific time of day and ozone episode.

Example results from a run of the CMB8 model using ambient data collected at the Clinton (Houston), TX site on August 17, 1993 at 0500 CST. Model performance parameters are within acceptable ranges with the exception of the T-statistic for the industrial fugitive emission source profile (PE-in_fug). (Ambient data and emission source profiles provided by E. Fujita).

Example results from a run of the CMB8 model using ambient data collected at the Clinton (Houston), TX site on August 17, 1993 at 0500 CST. Results for many of the species are provided here. Model performance parameters are within acceptable ranges for most of the important species. (Ambient data and emission source profiles provided by E. Fujita.) 

• Day of week and diurnal analyses.
• Residual VOC concentrations and graphical displays of residuals and SCEs by wind direction and time of day.
• Sensitivity of SCEs to fitting species, particularly reactive species.
• Comparison, both spatially and temporally, of relative source contributions calculated by CMB to corresponding estimates derived from local emission inventories.
• Scatter plot of predicted versus measured concentrations for the sum of the fitting species and sum of selected reactive species by site and time of day (illustrated with SCAQS data).
• Relationship between SCE (particularly the residual unexplained mass) and extent of reaction (age) of the ambient air sample (estimated by a ratio of reactive to less-reactive VOC).

Receptor models are useful for resolving the composition of volatile organic compounds into components related to emission sources. 

California Air Resources Board (1992) Modeling emissions data system. Draft report prepared by Control Strategy Modeling Section, Technical Support Division, California Air Resources Board, Sacramento, CA.

Cohen M., Ryan P.B., Spengler J.D., Ozkaynak H., and Hayes C (1989) Source receptor study of volatile organic compounds and particulate matter in Charleston, WV. Paper 89-104.3 presented at the 82nd Air & Waste Management Association Annual Meeting, Anaheim, CA, June 25-30.

Conner T.L., Collins J.F., Lonneman W.A., and Seila R.L. (1994) Comparison of Atlanta emission inventory with ambient data using chemical mass balance receptor modeling. Paper presented at the Air & Waste Management Association Emission Inventory Applications and Improvement Conference, Raleigh, NC, November 1-3.

Conner T.L., Lonneman W.A., and Seila R.L. (1995) Transportation-related volatile hydrocarbon source profiles measured in Atlanta. J. Air & Waste Manag. Assoc. 45, 383-394.

Doskey P.V., Porter J.A., and Scheff P.A. (1992) Source fingerprints for volatile non-methane hydrocarbons. J. Air & Waste Manag. Assoc., 42, 1437-1445.

Fujita E.M., Watson J.G., Chow J.C., and Magliano K.L. (1995) Receptor model and emissions inventory source apportionments of nonmethane organic gases in California's San Joaquin Valley and San Francisco Bay Area. Atmos. Environ. 29, 3019-3035.

Fujita E.M., Watson J.G., Chow J.C., and Lu Z. (1994) Validation of the chemical mass balance receptor model applied to hydrocarbon source apportionment in the Southern California Air Quality Study. Environ. Sci. Technol. 28, 1633-1649.

Gertler, A.W., Fujita E. M., Pierson W.R., Wittorff D.N. (1996a) Apportionment of NMHC tailpipe vs. non-tailpipe emissions in the Fort McHenry and Tuscarora Mountain tunnels. Atmos. Environ., Vol. 30, No. 12, pp. 2290-2305.

Gertler A.W., Sagebiel J.C., Wittorff D.N., Pierson W.R., Dippel W.A., Freeman D., and Sheetz L. (1996b) High Exhaust Emitters Project Site Characterization/Selection/Feasibility Study. Final report prepared for Coordinating Research Council, Atlanta, GA by Desert Research Institute, Reno, NV, Project No. E-5, December.

Henry R.C. (1992) Dealing with near collinearity in chemical mass balance receptor models. Atmos. Environ. 26, 933-938.

Henry R.C., Lewis C.W., and Collins J.F. (1994) Vehicle-related hydrocarbon source compositions from ambient data: the GRACE/SAFER method. Environ. Sci. Technol. 28, 823-832.

Kenski D.M. (1997) Receptor modeling for ozone prediction: an evaluation of the Lake Michigan Ozone Study data. Ph.D. Dissertation, University of Illinois, Chicago, IL.

Kenski D.M., Wadden R.A., Scheff P.A., and Lonneman W.A. (1991) Receptor modeling of VOCs in Chicago, Beaumont, and Detroit. Paper presented at the 84th Air & Waste Management Association Annual Meeting, Vancouver, B.C., June 16-21.

Kenski D.M., Wadden R.A., Scheff P.A., and Lonneman W.A. (1992) Receptor modeling of VOCs in Atlanta, Georgia. Paper no. 92-104.06 presented at the 85th Air & Waste Management Association Annual Meeting, Kansas City, MO, June 21-26.

Killus, J.P. and Moore G.E. (1991) Factor analysis of hydrocarbon species in the south-central coast air basin. Bull. Am. Meteorol. Soc., 733-743.

Lewis C.W., Conner T.L., Stevens R.K., Collins J.F., and Henry R.C. (1993) Receptor modeling of volatile hydrocarbons measured in the 1990 Atlanta Ozone Precursor Study. Paper no. 93-TP-58.04 in Proceedings from the 86th Air & Waste Management Association Annual Meeting, Denver, CO, June 14-18.

Li, C.K. and Kamens R.M. (1993) The use of polycyclic aromatic hydrocarbons as source signatures in receptor modeling. Atmos. Environ. 27a, 523-532.

Lin, C. and Milford J.B. (1994) Decay-adjusted chemical mass balance receptor modeling for volatile organic compounds. Atmos. Environ. 28, 3261-3276.

Lu Z. and Fujita E.M. (1995) Volatile organic compound source apportionment for the coastal oxidant assessment for Southeast Texas Study. Final report prepared for Texas Natural Resource Conservation Commission, Austin TX by Desert Research Institute, Reno, NV.

Magliano K.L. (1996) Descriptive analysis and reconciliation of emissions and ambient hydrocarbon data. Draft SJVAQS/AUSPEX technical topic team #5 report prepared by California Air Resources Board, Sacramento, CA.

McLaren R., Gertler A.W., Wittorff D.N., Belzer W., Dann T., and Singleton D.L. (1996) Real-world measurements of exhaust and evaporative emissions in the Cassiar Tunnel predicted by chemical mass balance modeling. Environ. Sci. Technol. 30, 3001-3009.

Mukund R., Kelly T.J., and Spicer C.W. (1996) Source attribution of ambient air toxic and other VOCs in Columbus, Ohio. Atmos. Environ. 30, 3457-3470.

NESCAUM (1995) Preview of the 1994 ozone precursor concentrations in the northeastern U.S. 5/1/94 draft report prepared by the Ambient Monitoring and Assessment Committee of the Northeast States for Coordinated Air Use Management, Boston, MA.

Pace T.G. and Watson J.G. (1987) Protocol for applying and validating the CMB model. Report prepared by Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, EPA-450/4-87-010, May.

PES (1994) Technical support for enhanced air quality modeling analysis for the purpose of the development of the 1994 ozone state implementation plan guidance. Report prepared by Pacific Environmental Services, Inc., January.

Pistikopoulos P. Masclet P., Mouvier G. (1990) A receptor model adapted to reactive species: polycyclic aromatic hydrocarbons; evaluation of source contributions in an open urban site - I. particle compounds. Atmos. Environ. 24a, 1189-1197.

Poissant, L., J.W. Bottemheim, P. Roussel, N.W. Reid, H. Niki (1996) Multivariate analysis of 1992 SONTOS data subset. Atmos. Environ., Vol. 30, No. 12, pp. 2133-2144.

Sagebiel J.C., Zielinska B., Pierson W.R., and Gertler A.W. (1996) Real-world emissions and calculated reactivities of organic species from motor vehicles. Atmos. Environ. 30, 2287-2296.

Schauer J.J., Rogge W.F., Hildemann L.M., Mazurek M.A., Cass G.R., and Simoneit B.R.T. (1996) Source apportionment of airborne particulate matter using organic compounds as tracers. Atmos. Environ. 30, 3837-3855.

Scheff P.A. and Wadden R.A. (1993) Receptor modeling of volatile organic compounds: 1. Emission inventory and validation. Environ. Sci. Technol. 27, 617-625.

Scheff P.A., Wadden R.A., Kenski D.M., Chung J., and Wolff G. (1996) Receptor model evaluation of the Southeast Michigan Ozone Study ambient NMOC measurements. J. Air & Waste Manag. Assoc. 46, 1048-1057.

Sigsby J.E., Tejada S., and Ray W. (1987) Volatile organic emissions from 46 in-use passenger cars. Environ. Sci. Technol. 21, 466-475.

Stoeckenius T.E., Ligocki M.P., Shepard S.B., and Iwamiya R.K. (1994a) Analysis of PAMS data: application to summer 1993 Houston and Baton Rouge data. Draft report prepared by Systems Applications International, San Rafael, CA, SYSAPP94-94/115d, November.

Stoeckenius T.E., Ligocki M.P., Cohen B.L., Rosenbaum A.S., and Douglas S.G. (1994b) Recommendations for analysis of PAMS data. Final report prepared by Systems Applications International, San Rafael, CA, SYSAPP94-94/011r1, February.

U.S. Environmental Protection Agency (1987) Procedures for reconciling differences in receptor and dispersion models. Report prepared by U.S. Environmental Protection Agency, Research Triangle Park, NC, EPA 450/4-87-008, May.

Venkataraman C. and Friedlander S.K. (1994) Source resolution of fine particulate polycyclic aromatic hydrocarbons using a receptor model modified for reactivity. J. Air & Waste Manag. Assoc. 44, 1103-1108.

Wilkinson L. (1990) SYSTAT: The System for Statistics. SYSTAT, Inc., Evanston, IL, Factors for PAMS hydrocarbon species to convert ppbC to mg/m³ for use in CMB. To perform the conversion, multiply the concentration value by the conversion factor. Assumes room temperature of 25°C.

Factors for PAMS hydrocarbon species to convert ppbC to mg/m³ for use in CMB. To perform the conversion, multiply the concentration value by the conversion factor. Assumes room temperature of 25°C.