Multivariate Receptor Modeling for Temporally Correlated Data by Using MCMC
Park, Eun Sug, Guttorp, Peter, Henry, Ronald C., Journal of the American Statistical Association
KEY WORDS: Air pollution; Chemical species; Compositions; Dynamic models; Gibbs sampler; Kalman filter; Metropolis-Hastings algorithm; Source profile.
Multivariate receptor modeling aims to estimate pollution source profiles and the amounts or pollution based on a series or ambient concentrations of multiple chemical species over time. Air pollution data often show temporal dependence due to meteorology and/or background sources. Previous approaches to receptor modeling do not incorporate this dependence. We model dependence in the data using a time series approach so that we can incorporate extra sources of variability in parameter estimation and uncertainty estimation. We estimate parameters using the Markov chain Monte Carlo method, which makes simultaneous estimation of parameters and uncertainties possible. The methods are applied to simulated data and 1990 Atlanta air pollution data. The results show promise towards the goal of accounting for the dependence in the data.
An important problem in environmental statistics is to determine the main sources of air pollution from data obtained at a given station, or receptor. To do so, data need to contain observations on the amounts (concentrations) of different chemical compounds, or species, in the atmosphere that are received (measured) at the station. Samples of airborne pollution are subjected to extensive chemical analysis. Contributing sources leave chemical fingerprints in the sample. The amount of pollution coming from each source can be estimated if the chemical fingerprints of the sources are known. This subfield of environmental statistics is called receptor modeling.
In this article, the pollutants of concern are volatile organic compounds (VOC) observed in downtown Atlanta, GA during July and August of 1990. VOCs are important because some, such as benzene and toluene, are toxic and many react with nitrogen oxides in the air to form ozone, which can reach dangerous levels in many areas. The chemical species of interest are predominately hydrocarbons containing from 2 to 10 carbon atoms. Methane with one carbon is excluded because of its large background concentration from ubiquitous natural sources and the fact that methane is of no interest to air pollution regulators. For this reason, the total amount of VOCs in the air is commonly known as total nonmethane organic compounds (TNMOC). The VOCs in this study were determined by an innovative automated gas chromatograph (GC) that sampled the air for 50 minutes each hour and analyzed the sample in the remainder of the hour (Purdue 1991). The detector of the GC responds to the number of carbon atoms in the sample, therefore the units are in parts per billion by volume of carbon (ppbC). The mass of the VOCs in this study is dominated by carbon, so these units are proportional to mass units such as nanograms per cubic meter used for airbome particulate matter, Of the more than 1,200 hourly observations of more than 40 VOCs, a dataset of 538 observations on 38 species (37 VOC and TNMOC) measured at one location was selected (Henry, Lewis, and Collins 1994). The background concentrations of these VOCs are small compared to the very large sources in the urban center of Atlanta and can be ignored. These major sources of VOCs are three in number and all are related to gasoline and diesel fueled vehicles. Obviously, there is the tailpipe exhaust of the vehicles when being driven. However, vehicles also emit VOCs by evaporation when sitting still and when running. These evaporative emissions can be classified as two sources, one source with the composition of whole gasoline, and another source with the composition of gasoline headspace v apor. Headspace vapor is the vapor above gasoline in a container, such as a fuel tank. This vapor is enriched in the more volatile compounds in gasoline, e.g. n-butane and isopentane. Diesel fuel is much less volatile than gasoline and evaporative emissions of diesel-fueled vehicles are negligible. …