## 1. Introduction

[2] Multivariate receptor models are widely used in source apportionment of airborne particles [*Henry*, 1997, 2002; *Hopke*, 2003]. The measured chemical composition data from the samples collected at the receptor site form a matrix and this matrix can then be analyzed by UNMIX [*Henry*, 2003], PMF [*Paatero*, 1997] or other techniques to obtain two matrices representing source contribution and source profile, respectively. Recently, efforts have been made to use the methods to analyze size distribution data to identify sources [*Ruuskanen et al.*, 2001; *Wahlin et al.*, 2001; *Kim et al.*, 2004; *Zhou et al.*, 2004a, 2005].

[3] Even over a short distance (or transit time), there can be substantial changes in the size distributions of the particles emitted [*Zhu et al.*, 2002a, 2002b, 2004]. However, for the same location/transit time, the size distribution is very similar. If the size distribution coming from a source does not vary much with time, then the number concentration series measured at the receptor site have a linear relationship with the number contribution from all sources and also with their mass contributions. A previous application of multivariate receptor model with size distribution data [*Zhou et al.*, 2004a] has indicated that the number contribution of a source can be converted to its volume (mass) contribution by multiplying a constant determined by its size distribution profile.

[4] If there are linear relationships between the number concentrations and mass concentrations, it will be useful to combine the size distribution data and chemical composition data into a combined multivariate analysis. The source characteristics in both size distributions and chemical compositions may be obtained simultaneously and a better understanding of the source-receptor relationship will be provided.

[5] In this study, a small data set that includes both size distribution and composition data from the Pittsburgh Air Quality Study (PAQS) was analyzed by partial least squares (PLS) and positive matrix factorization (PMF). PLS is used to investigate the interrelationships between the number concentrations of all size intervals and the mass concentrations of all chemical species. Only if the PLS analysis can find linear relationships between the two data sets, can the two types of data can reasonably be combined and analyzed with a two-way receptor model. The results of the PMF analysis will be compared with the results in the work of *Zhou et al.* [2004b].