Multilinear Model for Spatial Pattern Analysis of the Measurement of Haze and Visual Effects Project WANNA CHUEINTA, † PHILIP K. HOPKE,* ,† AND PENTTI PAATERO ‡ Departments of Chemistry and Chemical Engineering and Center for Air Resources Engineering and Science, Clarkson University, Potsdam , New York 13699-5708, and Departm ent of Physical Sciences, University of Helsinki, Helsinki, Finland A multilinear model was developed for the analysis of the spatial patterns and possible sources affecting haze and its visual effects in the southwestern United States. The data from the project Measurement of Haze and Visual Effects (MOHAVE) collected during the late winter and mid- summer of 1992 at the monitoring sites in four states (i.e., California, Arizona, Nevada and Utah) were used in the study. The three-way data array was analyzed by a four- product-term model. This study makes a direct effort to include wind patterns as a component in the model in order to obtain the information of the spatial patterns of source contributions. The solution is computed using the conjugate gradient algorithm with applied non-negativity constraints. For the winter data set, reasonable solutions contained six sources and six wind patterns. The analysis of summer data required seven sources and seven wind patterns. The ME results are compared to the prior single- species empirical orthogonal function analysis results and prior work describing the transport pathways. Introduction Project MOHAVE (Measurement of Haze and Visual Effects) was primarily designed to estimate the contribution of Mohave Power Plant to the haze observed at Grand Canyon National Park. The project operated a large area network consisting of monitoring, modeling, and data assessment with participantsfrom government,industry,and academia. The field measurement part ofthe project was conducted in 1992. Samples were collected for approximately 30 d in the winter and 50 d in the summer at about 30 locations in a four-state region of the southwestern United States that covered southern California,southern Nevada,southwestern Utah, and Arizona. Data assessment and modeling efforts have been undertaken by many research groups and have led to numerous reports and papers (e.g., refs 1-6). The objective of this paper was to investigate the ap- plication of a multilinear receptor model to identify and apportion the contributions and spatial patterns of particle sources that impacted the haze and visual effects in the southwestern United States by use of the chemical composi- tion data of fine particle samples from project MOHAVE. To model the full set of compositional data over the complete spatial domain, it is necessary to use a multilinear model to incorporate location,species,and time.Previousstudieshave used trilinear (7) and three-way factor analysis models (8). On the basis of this experience, the proposed model was specified as a four-product-term that included wind pattern factor in the modelin an attempt to obtain the sensible spatial patterns of source contributions corresponding to the wind or transport patterns. The mathematical tool called the multilinear engine (ME-2)was used to solve the problem (9). ME-2 is a versatile program that can be used for solving a wide variety of multilinear models. The specific features of ME-2 include individual data point weighting and non- negativity constraints. Materials and Methods Data Description. The field samplingofthe MOHAVEproject was performed in two phases. The first phase (winter) was in January-February1992.The second phase (summer)was in July-September 1992.Figure 1is a map ofthe area showing locations of the Mohave Power Plant (MOPP) and the monitoringsites across the region ofthe southwestern United States that included California, Nevada, Utah, and Arizona. The network consisted of about 30 sites. Two of these monitoring sites, Hopi Point (HOPO) near the main visitor center at the south rim and Meadview (MEAD) near the far western end of the Grand Canyon National Park (GCNP), were considered as the key receptor sites representative of the GCNP. Table 1 lists the codes and the locations of all of the sampling sites. The IMPROVE sampler consists of a size selective inlet, a cyclone to provide a particle size cutoff based on the flow rate, collection substrates, a critical orifice that provides the proper flow rate for the desired particle size cutoff, and a vacuum pump (10, 11). One or more independent module was used to collect fine particles (equivalent aerodynamic diameter, EAD <2.5 μm) onto different types of filters appropriate for the various chemicalanalyses.The Teflo filter samples were analyzed for fine mass by gravimetric analysis (12),for light absorption coefficient bylaser integratingplate method (13), for H by proton elastic scattering analysis (14), and for trace elements by particle-induced X-ray emission (14). Quartz filters were analyzed for organic and elemental carbon (OC and EC) by thermal optical reflectance (15). Ion *Correspondingauthor telephone: (315)268-3861;fax: (315)268- 4410; e-mail: hopkepk@clarkson.edu. † Clarkson University. ‡ University of Helsinki. FIGURE 1. Project M OHAVE site map. Environ. Sci. Technol. 2004, 38, 544-554 544 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 2, 2004 10.1021/es026356n CCC: $27.50  2004 American Chemical Society Published on Web 11/25/2003