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A size-resolved submicron organic aerosol composition dataset from a high-resolution time-of-flight mass spectrometer (HR-ToF-AMS) collected in Mexico City during the MILAGRO campaign in March 2006 is analyzed using 3-dimensional (3-D) factorization models. A method for estimating the precision of the size-resolved composition data for use with the factorization models is presented here for the first time. Two 3-D models are applied to the dataset. One model is a 3-vector decomposition (PARAFAC model), which assumes that each chemical component has a constant size distribution over all time steps. The second model is a vector-matrix decomposition (Tucker 1 model) that allows a chemical component to have a size distribution that varies in time. To our knowledge, this is the first report of an application of 3-D factorization models to data from fast aerosol instrumentation, and the first application of this vector-matrix model to any ambient aerosol dataset. A larger number of degrees of freedom in the vector-matrix model enable fitting real variations in factor size distributions, but also make the model susceptible to fitting noise in the dataset, giving some unphysical results. For this dataset and model, more physically meaningful results were obtained by partially constraining the factor mass spectra using a priori information and a new regularization method. We find four factors with each model: hydrocarbon-like organic aerosol (HOA), biomass-burning organic aerosol (BBOA), oxidized organic aerosol (OOA), and a locally occurring organic aerosol (LOA). These four factors have previously been reported from 2-dimensional factor analysis of the high-resolution mass spectral dataset from this study. The size distributions of these four factors are consistent with previous reports for these particle types. Both 3-D models produce useful results, but the vector-matrix model captures real variability in the size distributions that cannot be captured by the 3-vector model. A tracer <i>m/z</i>-based method provides a useful approximation for the component size distributions in this study. Variation in the size distributions is demonstrated in a case study day with a large secondary aerosol formation event, in which there is evidence for the coating of HOA-containing particles with secondary species, shifting the HOA size distribution to larger particle sizes. These 3-D factorizations could be used to extract size-resolved aerosol composition data for correlation with aerosol hygroscopicity, cloud condensation nuclei (CCN), and other aerosol impacts. Furthermore, other fast and chemically complex 3-D datasets, including those from thermal desorption or chromatographic separation, could be analyzed with these 3-D factorization models. Applications of these models to new datasets requires careful construction of error estimates and appropriate choice of models that match the underlying structure of those data. Factorization studies with these 3-D datasets have the potential to provide further insights into organic aerosol sources and processing

Three-dimensional factorization of size-resolved organic aerosol mass spectra from Mexico City