Application of Principal Component Analysis to the Analysis of Atmospheric Aerosol Size Distributions

Atmospheric size distributions provide important fundamental information for studying atmospheric particle physics. To capture enough information using a distribution with reasonable resolution results in massive data sets. For example, 5-minute scans with 30 size bins produces 8640 data points per day. The complexity of such data set usually creates difficulties in data handling and interpretation. Principal Component Analysis (PCA) provides a way to reduce the dimensionality of data sets and produces a simpler yet quantitatively equivalent data set. The simplified data set usually provides an easier mean for data interpretation. In applying PCA to size distribution data, there are several important aspects that one needs to pay attention to. These include proper weighting for the data, correct selection of the number of components to extract and a rotation scheme to transform the result to simple structure for interpretation. In this poster, these important issues in applying PCA to size distribution data will be discussed. A new weighting scheme for size distribution data has been developed. This new weighting scheme allows one to fit the size distribution data more accurately without requiring too many components. Application of Varimax rotation to the eigenvectors enables one to turn the eigenvectors to a simple and physically meaningful size distribution function. As a result, a complete distribution can be broken down into a series of simple and independent distributions for easy interpretation. Furthermore, procedure on how to extract the correct number of components will be addressed. Finally, some field study measurements from Pacific 2001 and other studies held in Southern Ontario will be used as an illustration of how to make use of the rotated scores to explain some atmospheric process such as local nucleation and transport.