Atmospheric Chemistry and Physics www.atmos-chem-phys.net 1680-7316 1680-7324 7 3 2007 10.5194/acp-7-875-2007 http://www.atmos-chem-phys.net/7/875/2007/ http://www.atmos-chem-phys.net/7/875/2007/acp-7-875-2007.html http://www.atmos-chem-phys.net/7/875/2007/acp-7-875-2007.pdf 875 886 2007-02-16 Simplified representation of atmospheric aerosol size distributions using absolute principal component analysis T. W. Chan M. Mozurkewich mozurkew@yorku.ca Department of Chemistry and Centre for Atmospheric Chemistry, York University, Toronto, Ontario, Canada now at: Environment Canada, Toronto, Ontario, Canada Principal component analysis provides a fast and robust method to reduce the data dimensionality of an aerosol size distribution data set. Here we describe a methodology for applying principal component analysis to aerosol size distribution measurements. We illustrate the method by applying it to data obtained during five field studies. Most variations in the sub-micrometer aerosol size distribution over periods of weeks can be described using 5 components. Using 6 to 8 components preserves virtually all the information in the original data. A key aspect of our approach is the introduction of a new method to weight the data; this preserves the orthogonality of the components while taking the measurement uncertainties into account. We also describe a new method for identifying the approximate number of aerosol components needed to represent the measurement quantitatively. Applying Varimax rotation to the resultant components decomposes a distribution into independent monomodal distributions. Normalizing the components provides physical meaning to the component scores. The method is relatively simple, computationally fast, and numerically robust. The resulting data simplification provides an efficient method of representing complex data sets and should greatly assist in the analysis of size distribution data. Barthelmie, R. J. and Pryor, S. C.: Implications of Ammonia emissions for fine aerosol formation and visibility impairment – a case study from the Lower Fraser Valley, British Columbia, Atmos. Environ., 32, 345–352, 1998. Birmili, W., Wiedensohler, A., Heintzenberg, J., and Lehmann, K.: Atmospheric particle number size distribution in central Europe: statistical relations to air masses and meteorology, J. Geophys. Res., 106, 32 005–32 018, 2001. Buhamra, S. S., Bouhamra, W. S., and Elkilani, A. S.: Assessment of air quality in ninety-nine residences of Kuwait, Environ. Technol., 19, 357–367, 1998. Cattell, R. B.: The Scree test for the number of factors, J. Multiv. Behav. Res., 1, 245–276, 1966. Chan, T. W. and Mozurkewich, M.: Application of absolute principal component analysis to size distribution data: Identification of particle origins, Atmos. Chem. Phys., 7, 887–897, 2007. Cheng, M. T. and Tsai, Y. I.: Characterization of visibility and atmospheric aerosols in urban, suburban, and remote areas, The Science of the Total Environment, 263, 101–114, 2000. Cochran, R. N. and Horne, F. H.: Statistically weighted principal component analysis of rapid scanning wavelength kinetics experiments, Anal. Chem., 49, 846–853, 1977. Comrey, A. L. and Lee, H. B.: A first course in factor analysis (2nd edition), Lawrence Erlbaum Associates, Hillsdale, N. J., 1992. Ferre, L.: Selection of components in principal component analysis: A comparison of methods, Comput. Stat. Data Anal., 19, 669–682, 1995. Hotelling, H.: Analysis of a complex of statistical variables into principal components, J. Educ. Psychol., 24, 417–441, 1933. Jackson, J. E.: A user's guide to principal components, Wiley-Interscience, New York, 1991. Jolliffe, I. T.: Principal component analysis, Chapter 1. Springer-Verlag, New York, 1986. Keenan, M. R. and Kotula, P. G.: Accounting for Poisson noise in the multivariate analysis of ToF-SIMS spectrum images, Surf. Interface Anal., 36, 203–212, 2004. Keiding, K., Sørensen, M. S., and Pind, N.: A receptor model for urban aerosols, based on oblique factor analysis, Anal. Chim. Acta, 193, 295–307, 1987. Knutson, E. O. and Whitby, K. T.: Aerosol classification by electric mobility: apparatus, theory, and applications, J. Aerosol Sci., 6, 443–451, 1975. Li, S. M.: A Concerted effort to understand the ambient particulate matter in the Lower Fraser Valley: The Pacific 2001 air quality study, Atmos. Environ., 38, 5717–5894, 2004. Mäkelä, J. M., Koponen, I. K., Aalto, P., and Kulmala, M.: One-year data of submicron size modes of tropospheric background aerosol in southern Finland, J. Aerosol Sci., 31, 595–611, 2000. Maynard, A. D. and Maynard, R. L.: A derived association between ambient aerosol surface area and excess mortality using historic time series data, Atmos. Environ., 36, 5561–5567, 2002. Mönkkönen, P., Koponen, I. K., Lehtinen, K. E. J., Hämeri, K., Uma, R., and Kulmala, M.: Measurements in a highly polluted Asian mega city: observations of aerosol number size distribution, modal parameters and nucleation events, Atmos. Chem. Phys., 5, 57–66, 2005. Mozurkewich, M., Chan, T. W., Aklilu, Y. A., and Verheggen, B.: Aerosol particle size distributions in the Lower Fraser Valley: evidence for particle nucleation and growth, Atmos. Chem. Phys., 4, 1047–1062, 2004. Paatero, P. and Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, 5, 111–126, 1994. Peters, A., Skorkovsky, J., Kotesovec, F., Brynda, J., Spix, C., Wichmann, H. E., and Heinrich, J.: Associations between mortality and air pollution in Central Europe, Environmental Health Perspectives, 108, 283–287, 2000. Schwartz, S. E.: The whitehouse effect – shortwave radiative forcing of climate by anthropogenic aerosols: an overview, J. Aerosol Sci., 27, 359–382, 1996. Schwela, D.: Exposure to environmental chemicals relevant for respiratory hypersensitivity: global aspects, Toxicol. Lett., 86, 131–142, 1996. Spurny, K. R.: Aerosol chemistry and its environmental effects in Aerosol chemical processes in the environment, edited by: Spurny, K. R., pp. 3–21, Lewis Publishers, New York, 2000. Thurston, G. D. and Spengler, J. D.: A quantitative assessment of source contributions to inhalable particulate matter pollution in metropolitan Boston, Atmos. Environ., 19, 9–25, 1985. Twomey, S.: Aerosols, clouds and radiation, Atmos. Environ., 25A, 2435–2442, 1991. Wang, S. C. and Flagan, R. C.: Scanning Electrical Mobility Spectrometer, Aerosol Sci. Technol., 13, 230–240, 1990. Whitby, K. T.: The physical characteristics of sulfur aerosol, Atmos. Environ., 12, 135–159, 1978.