Modeling PCB dechlorination in aquatic sediments by principal component based factor analysis and positive matrix factorization

Anaerobic PCB dechlorination in aquatic sediments is a naturally occurring process that reduces the dioxin-like PCB toxicity. The PCB biphenyl structure is kept intact but the number of substituted chlorine atoms is reduced, primarily from the para and meta positions. Flanked para and meta chlorine dechlorination, as in process H/H', appears to be more common in-situ than flanked and unflanked para, and meta dechlorination as in process Q. Aroclors that are susceptible to these reactions include 1242, 1248, 1254, and 1260. These dechlorination reactions have recently been modeled by a least squares method for Ashtabula River, Ohio, and Fox River, Wisconsin sediments. Prior to modeling the dechlorination reactions for an ecosystem it is desirable to generate overall PCB source functions. One method to determine source functions is to use loading matrices of a factor analytical model. We have developed such models based both on a principal component approach including nonnegative oblique rotations, and positive matrix factorization (PMF). While the principal component method first requires an eigenvalue analysis of a covariance matrix, the PMF method is based on a direct least squares analysis considering simultaneously the loading and score matrices. Loading matrices obtained from the PMF method are somewhat sensitive to the initial guess of source functions. Preliminary work indicates that a hybrid approach considering first principal components and then PMF may offer an optimum solution. The relationship of PMF to conventional chemical mass balance modeling with or without some prior knowledge of source functions is also discussed.