The use of constrained least-squares to solve the chemical mass balance problem

Abstract A form of weighted least-squares regression is commonly used for solving the chemical mass balance problem. In the presence of measurement error and collinearity between source profiles, this approach can produce physically impossible negative values to provide the best fit to the data. As sources cannot produce a contribution to ambient particulate loadings smaller than zero, a mathematical method that constrains the solution to be greater than or equal to zero ensures physically meaningful results. Two non-negative least-squares routines reported to work well for severe collinear regression problems have been incorporated into a program for solving the CMB problem. Their utility has been initially tested with the simulated data sets created for the U.S. EPA's Quail Roost II workshop by the National Bureau of Standards. The results of these tests are presented here and compared with ordinary weighted and effective variance least-squares results. In general, the constrained least-squares method provided better results than the unconstrained techniques.