A UNIFIED THEORY FOR AEROSOL SOURCE APPORTIONMENT MODELS (RECEPTOR MODELS, REGRESSION)

A stochastic source apportionment model has been developed with explicitly included random variables to account for the measurement errors in the source and ambient/receptor data, and to simulate the linear source-receptor relationship. Using this model, a variety of quantitative source apportionment problems can be solved if the fundamental hypothesis of a mass balance for receptor models holds. This hypothesis is the single assumption needed in the development of the stochastic receptor model. The source compositions can be either constant or random values and the linear source-receptor relationship is a weak assumption for the success of the stochastic receptor model.; To solve the general stochastic model and various simplified forms of it, a number of numerical techniques were examined. The solution techniques examined include unweighted least squares (LS), L(,1), and minimax, the ordinary and the effective variance weighted least squares, the weighted, constrained L(,1) (WCL(,1)) and secondly weighted, constrained L(,1) (W2CL(,1)), the method of maximization of the sum of source contributions (SLIP(k), k = 0 or 3). The effects of measurement errors and collinearity on the precision and accuracy of these solution techniques were investigated using simulated data. The simulated data were generated by Monte-Carlo techniques.; The structure and magnitude of measurement errors in the source and ambient/receptor data and the strength of collinearity in the source matrix were exactly known in these numerical experiments. The effects of constant and variational source compositions on the accuracy and precision of source estimates were examined separately. The effective variance weighted least squares method yielded negligible improvement on the accuracy and precision for the source contributions over the ordinary weighted least squares method. The weighted L(,1) (WCL(,1) and W2CL(,1)) schemes yielded less accurate and precise estimates than the weighted LS (OWLS and EVWLS) methods, presumably because the measurement errors are normally distributed. SLIP 3 estimator failed to improve the estimated source contribution for SLIP 0 estimator.