Application of singular-value decomposition and linear programming to analysis of aerosol mass spectra taken during the MILAGRO campaign

Description

Aerosols are known to have significant impact on climate. Many of their most important properties, such as potential to serve as cloud condensation sites and scatter light, depend on mixing state. Aerosol composition measurements were obtained using an Aerodyne mass spectrometer during flights aboard a G-1 aircraft. Results from three flights under very different field conditions were analyzed for the present study. Analysis method: Principal components analysis (PCA) and singular-value decomposition (SVD) were used for data analysis and compression and to study the evolution of aerosol mixing state as particles age downwind in the Mexico mega-city plume. The principal components define a vector space of low dimensionality and spanned by orthogonal basis vectors onto which the mass spectra are projected. Taking just three dimensions provides a resolution of any given spectrum into three orthogonal components with circa 99% variance of the projected data set explained. Building on these conventional statistical methods (PCA and SVD), we add a new analytic approach: convex polyhedral boundaries of the projected spectral data sets are obtained using linear programming methods. Uniquely defined “simplex factors” (vertices of the convex polyhedral feasible set) are analyzed and compared and contrasted with factors obtained from positive matrix factorization (PMF). In addition to their uniqueness, we show in the context of aerosol composition analysis that the simplex factors are imbued with physical and mathematical optimization properties that make them ideal factors for the representation of aerosol mixing state.