Measurement error models in chemical mass balance analysis of air quality data

Abstract

The chemical mass balance (CMB) equations have been used to apportion observed pollutant concentrations to their various pollution sources. Typical analyses incorporate estimated pollution source profiles, estimated source profile error variances, and error variances associated with the ambient measurement process. Often the CMB model is fit to the data using an iteratively re-weighted least-squares algorithm to obtain the effective variance solution. We consider the chemical mass balance model within the framework of the statistical measurement error model (e.g., Fuller, W.A., Measurement Error Models, Wiley, NewYork, 1987), and we illustrate that the models assumed by each of the approaches to the CMB equations are in fact special cases of a general measurement error model. We compare alternative source contribution estimators with the commonly used effective variance estimator when standard assumptions are valid and when such assumptions are violated. Four approaches for source contribution estimation and inference are compared using computer simulation: weighted least squares (with standard errors adjusted for source profile error), the effective variance approach of Watson et al. (Atmos, Environ., 18, 1984, 1347), the Britt and Luecke (Technometrics, 15, 1973, 233) approach, and a method of moments approach given in Fuller (1987, p. 193). For the scenarios we consider, the simplistic weighted least-squares approach performs as well as the more widely used effective variance solution in most cases, and is slightly superior to the effective variance solution when source profile variability is large. The four estimation approaches are illustrated using real PM2.5 data from Fresno and the conclusions drawn from the computer simulation are validated.