Investigation on the use of chemical mass balance receptor model: Numerical computations

Cheng, M.D. and Hopke, P.K., 1986. Investigation on the use of chemical mass balance receptor model: numerical computations. Chemometrics and Intelligent Laboratory Systems, 1: 33-50. The use of various numerical techniques in the chemical mass balance receptor model leads to different estimations of mass contributions by the identified sources for an ambient air quality data set. Weighted-constrained L₁ (called least absolute deviations in statistics), ordinary weighted least squares, effective variance weighted least squares, and two variants of standard linear programming methods based on the maximized allocation of aerosol mass were studied. The data sets used in this study were the simulated aerosol composition data generated by the National Bureau of Standards for the EPA workshop on mathematical and empirical receptor modeling held at Quail Roost, NC, U.S.A. in 1982. The ensemble reliability of the numerical solutions for these test data sets were evaluated. The weighted-constrained L₁ solutions were found highly stable compared to those from the least-squares methods subject to various complexities of the simulated data sets. The effective variance weighted least squares was found to be ineffective in improving the quality of aerosol mass apportionment by the chemical mass balance model. The results of the standard linear programming methods were insensitive to the lognormal random variations present in the source compositions in Set 3, but gave less precise results than those obtained with the L₁ or least squares methods.