Description and Propagation of Uncertainty in Input Parameters in Environmental Fate Models


Address correspondence to Tomas Öberg, School of Natural Sciences, Linnaeus University, SE-39182 Kalmar, Sweden;


Today, chemical risk and safety assessments rely heavily on the estimation of environmental fate by models. The key compound-related properties in such models describe partitioning and reactivity. Uncertainty in determining these properties can be separated into random and systematic (incompleteness) components, requiring different types of representation. Here, we evaluate two approaches that are suitable to treat also systematic errors, fuzzy arithmetic, and probability bounds analysis. When a best estimate (mode) and a range can be computed for an input parameter, then it is possible to characterize the uncertainty with a triangular fuzzy number (possibility distribution) or a corresponding probability box bound by two uniform distributions. We use a five-compartment Level I fugacity model and reported empirical data from the literature for three well-known environmental pollutants (benzene, pyrene, and DDT) as illustrative cases for this evaluation. Propagation of uncertainty by discrete probability calculus or interval arithmetic can be done at a low computational cost and gives maximum flexibility in applying different approaches. Our evaluation suggests that the difference between fuzzy arithmetic and probability bounds analysis is small, at least for this specific case. The fuzzy arithmetic approach can, however, be regarded as less conservative than probability bounds analysis if the assumption of independence is removed. Both approaches are sensitive to repeated parameters that may inflate the uncertainty estimate. Uncertainty described by probability boxes was therefore also propagated through the model by Monte Carlo simulation to show how this problem can be avoided.