Characterization of Positive Matrix Factorization Methods and Their Application to Ambient Aerosol Mass Spectra

Atmospheric aerosol has impacts on health, visibility, ecosystems, and climate. The organic component of submicron aerosol is a complex mixture of tens of thousands of compounds, and it is still challenging to quantify the direct sources of organic aerosol. Organic aerosol can also form from a variety of secondary reactions in the atmosphere, which are poorly understood. Real-time instrumental techniques, including the Aerosol Mass Spectrometer (AMS), which can quantitatively measure aerosol composition with high time and size resolution, and some chemical resolution, produce large volumes of data that contain rich information about aerosol sources and processes. This thesis work seeks to extract the underlying information that describes organic aerosol sources and processes by applying factor analytical techniques to organic aerosol datasets from the AMS. We have developed a custom, open-source software tool to compare factorization solutions, their residuals, and tracer-factor correlations. The application of existing mathematical techniques to these new datasets requires careful characterization of the precision in the data and the factorization models' behavior with these specialized datasets. We explore this behavior with synthetic datasets modeled on AMS data. The synthetic data factorization has predictable behaviors when solved with "too many" factors. These behaviors then guide the choice of solution for real aerosol datasets. The factor analyses of real aerosol datasets are useful for identifying aerosol types related to sources (e.g., urban combustion and biomass burning) and secondary atmospheric processes (e.g., semivolatile and low-volatility oxidized organic aerosol). We have also factored three-dimensional datasets of size-resolved aerosol composition data to explore the variability of aerosol size distributions as the aerosol undergoes processing in an urban atmosphere. This study provides evidence that primary particles are coated with condensed secondary aerosol during photochemical processing, shifting the size distribution of the primary particles to larger sizes. Application of these three-dimensional factorization techniques to other complex aerosol composition datasets (e.g., that use thermal desorption or chromatography for further chemical separation) has the potential to yield additional insights about aerosol sources and processes.