6. DATA ANALYSIS

 

MULTILINEAR METHODS FOR PHYSICAL SCIENCES

Pentti Paatero and Philip K. Hopke*

Matrix factorization methods for physical sciences ("Factor Analysis") are applicable to many problems where a number of "spectra" have been measured in similar situations or of similar samples consisting of same (perhaps unknown) constituents in different proportions. Examples: chromatographic "spectra", aerosol size distributions, compositions of environmental samples.

In this work, the factor analytic methods have been extended to solving more structured "Multilinear" models. A special program "Multilinear Engine" (ME-2) has been written. This program is easily tailored for solving models of arbitrary structure.

Based on the multilinear approach, a new model for the atmospheric source-receptor analysis is being developed. In this model, the information about wind speed and wind direction is optimally utilized. As a result, directional profiles are obtained for each source. Each profile shows how the apparent concentration of the source in question depends on wind directions. For local sources, sharply peaked directional profiles are obtained. So far, the approach has been successfully tested on measurements made at the Hyytiälä station and on simulated aerosol data, provided by the US EPA.

Co-operation with the US Environmental Protection Agency (EPA) has been started in 1999. The goal of this project is to formulate such versions of the factor analytic and/or multilinear techniques that could be used by the state and regional air protection authorities for monitoring air quality in USA. The main part of this work is performed by the Clarkson group.

In 1999, journal articles describing the application of the factor analytic methods to various measurements of pollution in the Arctic air have been published. Also, the paper describing the multilinear technique has appeared.

* Clarkson Univ., NY, USA