2004 Progress Report: Development of Advanced Factor Analysis Methods for Carbonaceous PM Source Identification and Apportionment

EPA Grant Number: R831078
Title: Development of Advanced Factor Analysis Methods for Carbonaceous PM Source Identification and Apportionment
Investigators: Hopke, Philip K. , Henry, Ronald C. , Paatero, P. , Spiegelman, C.
Institution: Clarkson University
Current Institution: Clarkson University , Texas A & M University , University of Helsinki , University of Southern California
EPA Project Officer: Chung, Serena
Project Period: October 1, 2003 through September 30, 2006 (Extended to December 31, 2006)
Project Period Covered by this Report: October 1, 2003 through September 30, 2004
Project Amount: $450,000
RFA: Measurement, Modeling, and Analysis Methods for Airborne Carbonaceous Fine Particulate Matter (PM2.5) (2003) RFA Text |  Recipients Lists
Research Category: Air , Air Quality and Air Toxics , Particulate Matter

Objective:

Carbonaceous particles are becoming a larger fraction of fine particle aerosol because of the controls on precursor gases that lead to sulfate and nitrate formation. Accurate source identification and apportionment will be important for developing effective control strategies for areas found to be out of attainment of the PM2.5 standard. In addition, there is increasing interest in epidemiological studies to relate adverse health effects to apportioned source contributions. The objective of this research project is to combine the best features of the two advanced factor analysis models, UNMIX and Positive Matrix Factorization (PMF), and to test the effectiveness of this improved factor analysis methodology by analysis of the data developed in the various Supersites, with an emphasis on data from the New York City Supersite and other data from New York State.

Progress Summary:

During Year 1 of the project, we made progress in several areas, including the development of a new geometrical view of factor analysis in either the source profile or the contribution space. The results of this view are presented in a paper in press by Henry. This work recognizes that singular value decomposition of the data leads to two sets of eigenvectors. One set of eigenvectors spans a space in which source compositions are points and source contributions are hyperplanes. This space is shown to be dual to the space spanned by the second set of eigenvectors of the data, in which source compositions are hyperplanes and source contributions are points. The analytical formulae for this duality are given. Finally, the duality principle is applied to greatly increase the computational speed of the UNMIX multivariate receptor model.

The prior work by Ronald Henry on edges in the data and as a guide in UNMIX has led to the recognition that edges in the source contribution space observed in PMF analyses of data can be used as diagnostics to help guide the rotations. Edges in the plots of two vectors of the source contribution matrix suggest that additional rotations should be applied to rotate that edge toward the appropriate axis. This approach is described by Paatero, et al. (2005) and is illustrated with an example from Dhaka, Bangladesh.

To further assist with the identification of local sources, the use of the conditional probability function and nonparametric regression has been compared by Kim and Hopke (2004). Both of these methods have their utility in relating the resolved source contributions to the direction of the sources through the available local wind direction data.

Another aspect of the problem of rotational ambiguity is the use of expanded models to resolve factors. This approach uses two sets of modeling equations. We are exploring if the use of the additional equations begins to provide a measure of identifiability in the solution. This work is in its early stages, but it appears that there may be conditions under which the resulting equations provide unique solutions. Such a result would substantially enhance the utility of factor analysis methods.

Future Activities:

We will continue working on an approach to determine the uncertainties in the resolved source profiles and contributions, including both sampling and measurement uncertainties as well as rotational ambiguities. This approach involves bootstrapping and the arbitrary pulling of values in both positive and negative directions. Such an approach will not be valid for highly time-resolved data in which there is substantial serial correlation. For such situations, the bootstrapping will need to be modified to blocks of data that preserve a sufficient amount of the serial correlation as to be for a valid measure of the uncertainties.

We will continue to explore various kinds of data to ascertain the utility of expanded models to resolve additional sources and potentially reduce the rotational ambiguity in the resulting solutions.


Journal Articles on this Report : 2 Displayed | Download in RIS Format

Other project views: All 37 publications 21 publications in selected types All 21 journal articles
Type Citation Project Document Sources
Journal Article Henry RC. Duality in multivariate receptor models. Chemometrics and Intelligent Laboratory Systems 2005;77(1-2):59-63. R831078 (2004)
R831078 (2005)
R831078 (Final)
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  • Journal Article Paatero P, Hopke PK, Begum BA, Biswas SK. A graphical diagnostic method for assessing the rotation in factor analytical models of atmospheric pollution. Atmospheric Environment 2005;39(1):193-201. R831078 (2004)
    R831078 (2005)
    R831078 (Final)
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  • Supplemental Keywords:

    PM2.5, receptor models, positive matrix factorization, PMF, UNMIX, advanced factor models, bootstrap, rotational ambiguity, source resolution, source apportionment, fine particle aerosol, sulfate, carbonaceous particles, nonparametric regression, NPR, nitrate, sulfate and nitrate formation,, RFA, Scientific Discipline, Air, Ecosystem Protection/Environmental Exposure & Risk, particulate matter, Air Quality, air toxics, Environmental Chemistry, Air Pollution Effects, Monitoring/Modeling, Environmental Monitoring, Engineering, Chemistry, & Physics, Environmental Engineering, carbon aerosols, air quality modeling, particle size, atmospheric particulate matter, health effects, particulate organic carbon, atmospheric dispersion models, atmospheric measurements, model-based analysis, aerosol particles, atmospheric particles, mass spectrometry, chemical characteristics, PM 2.5, emissions monitoring, environmental measurement, positive matrix factorization, motor vehicle emissions, air quality models, airborne particulate matter, air sampling, carbon particles, air quality model, emissions, diesel exhaust, thermal desorption, particulate matter mass, ultrafine particulate matter, mobile sources, PM2.5, aersol particles, modeling studies, aerosol analyzers, measurement methods, chemical speciation sampling, particle size measurement, carbonaceous particulate matter

    Progress and Final Reports:

    Original Abstract
  • 2005 Progress Report
  • 2006
  • Final Report