1. Advanced Receptor Modeling for Source Identification and Apportionment
Philip K. Hopke
Center for Air Resources Engineering and Science
Clarkson University

2. OUTLINE Background Factor Analysis Positive Matrix Factorization
Air Quality Management
Receptor Models
Factor Analysis
Positive Matrix Factorization
Applications
Summary

3. Receptor Modeling
The management of air quality involves the identification of the pollution sources, the quantitative estimation of the emission rates of the pollutants, the understanding of the transport of the substances from the sources to downwind locations, and knowledge of the physical and chemical transformation processes that can occur during that transport.

4. Receptor Modeling
All of those elements can then be put together into a mathematical model that can be used to estimate the changes in observable airborne concentrations that might be expected to occur if various actions are taken.

5. RECEPTOR MODELING

6. Receptor Modeling
Thus, other methods are needed to assist in the identification of sources and the apportionment of the observed pollutant concentrations to those sources.

7. Receptor Modeling
Receptor models are focused on the behavior of the ambient environment at the point of impact as opposed to the source-oriented models that focus on the transport, dilution, and transformations that begin at the source and follow the pollutants to the sampling or receptor site.

9. Receptor Modeling PRINCIPLE OF AEROSOL MASS BALANCE
The fundamental principle of receptor modeling is that mass conservation can be assumed and a mass balance analysis can be used to identify and apportion sources of airborne particulate matter in the atmosphere.

10. Mass Balance
A mass balance equation can be written to account for all m chemical species in the n samples as contributions from p independent sources
Where i = 1,…, n samples, j = 1,…, m species and k = 1,…, p sources

11. Receptor Modeling
The question is then what is known a priori to solve this equation.
Divide the problem into two classes
Source Profiles Known
Source Profiles Unknown

12. Mass Balance
A mass balance equation can be written to account for all m chemical species in the n samples as contributions from p independent sources
Where i = 1,…, n samples, j = 1,…, m species and k = 1,…, p sources

13. Receptor Modeling SOURCES PROFILES KNOWN Chemical Mass Balance
Multivariate Calibration Methods
Partial Least Squares
Artificial Neural Networks
Simulated Annealing
Genetic Algorithm

14. Mass Balance
However, generally we do not know source profiles and we only have the available ambient concentration data. Thus, can we deduce the number and nature of the sources and their contribution to each sample through an appropriate data analysis method?

15. Receptor Modeling SOURCES PROFILES UNKNOWN Factor Analysis
Principal Components Analysis
Absolute Principal Components Analysis
SAFER/UNMIX
Positive Matrix Factorization

16. Factor Analysis
Most factor analysis has been based on an eigenvector analysis. In an eigenvector analysis, it can be shown [Lawson and Hanson, 1974; Malinowski, 1991] that the equation estimates X in the least-squares sense that it gives the lowest possible value for

17. Factor Analysis
Thus, most factor analysis use an unrealistic unweighted least-squares fit to the data.

18. Factor Analysis
The problem can be solved, but it does not produce a unique solution. It is possible to include a transformation into the equation.
X=GTT-1F
where T is one of the potential infinity of transformation matrices. This transformation is called a rotation and is generally included in order to produce factors that appear to be closer to physically real source profiles.

19. Factor Analysis

20. Positive Matrix Factorization
Explicit least-squares approach to solving the factor analysis problem
Individual data point weights
Imposition of natural and other constraints, and
Flexibility to build more complicated models

21. Positive Matrix Factorization
The Objective Function, Q, is defined by
where σij is an estimate of the uncertainty in xij

22. IMPROVE Monitoring Network
IMPROVE: Interagency Monitoring of Protected Visual Environments
IMPROVE aerosol sampler: 4 modules
Source:

23. IMPROVE aerosol monitoring
Module A: PM2.5 on Teflon filter (UC, Davis)
Gravimetric mass
Proton Elastic Scattering Analysis (PESA) for hydrogen
Proton Induces X-ray Emission (PIXE) for Na – Mn
X-Ray Fluorescence (XRF) for Fe – Pb
Module B: denuder, PM2.5 on nylon filter (RTI)
Ion Chromatography for sulfate, nitrate, nitrite, chloride
Module C: PM2.5 on quartz filter (DRI)
Thermal Optical Reflectance (TOR) method for 8 carbon fractions
Module D: PM10 on Teflon filter

24. Carbon Analysis
As part of the IMPROVE protocol for the measurement of organic and elemental carbon (OC/EC), individual carbon fractions of OC (OC1, OC2, OC3, OC4) and EC (EC1, EC2, and EC3). In addition, the pyrolized fraction of the organic carbon (OP) is estimated

25. Carbon analysis: IMPROVE/TOR method
Source: Chow et al., 2001

26. Washington, DC monitoring site
Roof of the Natl. Capitol Region Park Police HQ
3 km NE of Ronald Reagan Washington Natl. Airport
2 km SE of Lincoln Memorial

27. Se vs. S

28. Silicon 1
NOAA HYSPLIT model was used to calculate air mass backward trajectories for days with high Si conc.
6/24 – 7/7, 1993
4/15/92
7/7/93
4/22/01 Si

29. Silicon 2 Asian dust clouds 4/6: developed over Mongolia Si
4/13: start to impact the west coast
4/9 – 4/22, 2001
4/15/92
7/7/93
4/22/01 Si

30. Fireworks contributions
July 4 fireworks contributed to high conc. of K, Pb, and Cu
7/4/92
7/4/98
7/5/00 K Pb Cu

31. OC/EC Fraction Results
A total of 718 samples collected between August 1988 and December 1997 and 35 species were used in this study.

32. OC/EC Fraction Results

33. Secondary Particles

34. Secondary Particles

35. Sulfate Factors
When the carbon thermal fractions are added to the data set, we have also extracted a third sulfate factor in addition to the winter/summer factors
This factor has been seen in data from Atlanta, GA, Washington, DC, and Brigantine, NJ.

36. Sulfate-OP Factor

37. Sulfate Factors in Washington, DC study
Summer-high: Ohio river Valley, eastern Tennessee, southern Mississippi and Alabama
OP-high: Canadian boreal fire, Central American forest fire
Winter-high: North Carolina, Midwestern areas, southeastern Texas & Louisiana

38. Sulfate Factor
With the carbon thermal fractions, the amount of carbon in the summer and winter sulfate factors drops substantially compared to analyses with total OC and EC.

39. Sulfate Factor Why is there a covariance between OP and sulfate?
Is this an indicator of secondary organic aerosol formation?
Is the secondary organic aerosol formation catalyzed by the acidity of the sulfate particles as suggested by Kamens?

40. Combustion Sources

41. Spark-Ignition in Multiple Cities

42. Diesel in Multiple Cities

43. OC/EC Fraction Results

44. OC/EC Fraction Results

45. Conclusions
We have tools to help analyze the complex compositional data being produced by the major monitoring networks in the United States.
These techniques will likely play an important role in the development of air quality management plans over the next several years.

46. Thanks To
Eugene Kim and Bilkis Begum for performing the analyses presented.
Environmental Protection Agency and the International Atomic Energy Agency for financial support.