Compositional Receptor Modeling
|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.