Research Summary

Compositional Receptor Modeling
Dean Billheimer
Air quality management is a difficult problem with important consequences for human and environmental health. The difficulties arise primarily from problems with pollution measurement and transport: identification of sources, estimation of emission rates, physical transport of substances, and physical and chemical transformation processes occurring during transport (Hopke,~1999). Source apportionment, or receptor, models address these issues by analyzing pollution concentrations measured in ambient air. Observations are composed of a convex mixture of chemical species originating from an unknown number of different sources. Typically, individual source chemical profiles are not known. Receptor models aim to estimate the chemical profiles of the sources, and to characterize the mixing process.

While a number of modeling methods have been developed to address the source apportionment problem, they fail to address important characteristics of air pollution receptor data. First, no methods have been developed that incorporate covariate information in the modeling framework. Both environmental (e.g., wind speed and direction) and anthropogenic (e.g., weekly commuting patterns) factors contribute to observed variation. Quantitative techniques for evaluating such factors would provide powerful tools for air quality management. Second, most methods assume observations are mutually independent. (Indeed, only Park, et~al.,~2000 have attempted to account for serial dependence.) As with other atmospheric data, one anticipates temporal dependence between multiple observations from a single site, and spatial dependence for a network of samplers. While correlation complicates evaluation of inherent variability, it can be used to benefit prediction.

I propose to extend the compositional modeling approach outlined in Billheimer~(2000) to develop statistical methods that:

1) incorporate covariate information in modeling mixing proportions,
2) incorporate temporal correlation structure for multiple observations at a single site
3) incorporate spatial correlation structure to improve estimation from a network of sites.

Each of these extensions can be effected by means of a hierarchical statistical model of the mixing process. Inclusion of covariates and dependence structure will provide important tools for improving prediction and reducing unexplained variation of receptor data.