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Chemometrics in Environmental Chemistry - Applications pp 47–86Cite as

The Mixture Resolution Problem Applied to Airborne Particle Source Apportionment

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Part of the book series: The Handbook of Environmental Chemistry ((HEC2,volume 2 / 2H))

Summary

The problem of source identification and quantitative mass apportion for airborne particulate matter commonly called receptor modeling is much the same as the spectrochemical mixture or the multivariate calibration problems commonly encountered in chemometrics. However, there are some important differences that occur for the receptor modeling problem including variability in the source profiles (corresponding to the spectral properties of the mixture components), transformation of the profiles while in transit from the emission sources to the sampling sites, and much larger errors (noise) in the sampling and analysis of the mixtures. Various mixture resolution approaches have been used including multiple linear regression (Chemical Mass Balance Model) and various type of factor analysis. The basis for these methods is presented and illustrative examples of each are given. In addition multivariate calibration methods including partial least squares, the genetic algorithm, and artificial neural networks are now being explored as ways to solve the receptor modeling problem. These methods as well as the limited applications of these approaches are also reviewed. The initial results with these methods are promising, but further development and testing are needed before they can be used as commonly as the chemical mass balance or factor analysis models.

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Abbreviations

a ij :

Gravimetric concentration of the i-th element in particles emitted by the j-th source (ng μg−1)

A :

Matrix of source profiles

α(λ):

absorptivity of a mixture at wavelength λ

C i :

Concentration of the i-th species in the mixture

ε(λ)i :

Molar extinction coefficient for the i-th compound at wavelength λ

f kj :

Mass contribution of the k-th source to the j-th sample (μm−3)

F :

Matrix of source contributions

m :

Number of species measured in the source profile or number of wavelengths at which measurements are made

n :

Number of samples

p :

Number of sources contributing to the samples or the components in the mixture

x ij :

Concentration (ng m−3) of the i-th species in the j-th ambient aerosol sample

X :

Matrix of measured ambient aerosol concentrations

z ij :

Standardized concentration (ng m−3) of the i-th species in the j-th ambient aerosol sample

Z :

Matrix of standardized measured ambient aerosol concentrations

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Authors and Affiliations

  1. Department of Chemistry, Clarkson University, Box 5810, Potsdam, NY, 13699-5810, USA

    Philip K. Hopke

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  1. Philip K. Hopke
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Editors and Affiliations

  1. Institut für Anorganische und Analytische Chemie, Friedrich-Schiller-Universität, Lessingstraße 8, D-07743, Jena, Germany

    Jürgen Einax

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Hopke, P.K. (1995). The Mixture Resolution Problem Applied to Airborne Particle Source Apportionment. In: Einax, J. (eds) Chemometrics in Environmental Chemistry - Applications. The Handbook of Environmental Chemistry, vol 2 / 2H. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49150-7_3

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  • DOI: https://doi.org/10.1007/978-3-540-49150-7_3

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