Simplified representation of atmospheric aerosol size distributions using absolute principal component analysis
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 dis- tribution measurements. We illustrate the method by apply- ing it to data obtained during five field studies. Most varia- tions in the sub-micrometer aerosol size distribution over pe- riods 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 introduc- tion of a newmethod to weight the data; this preserves the or- thogonality of the components while taking the measurement uncertainties into account. We also describe a new method for identifying the approximate number of aerosol compo- nents needed to represent the measurement quantitatively. Applying Varimax rotation to the resultant components de- composes a distribution into independent monomodal dis- tributions. 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.