Direct Treatment of Uncertainty: I—Applications in Aquatic Invertebrate Risk Assessment and Soil Metabolism for Chlorpyrifos

Abstract

Environmental processes are wrought with uncertainty. Therefore, an efficient means to propagate uncertainty is advantageous, especially if regulatory decisions are based upon any research or data analysis where uncertainty is present. The Deterministic Equivalent Modeling Method (DEMM) propagates parametric uncertainties in model input parameters to output predictions. DEMM is used to calculate uncertainty in output parameters based upon the direct effect of every uncertain input parameter. Rather than sampling input distributions and running hundreds or thousands of model calculations as in Monte Carlo or Latin Hypercube Sampling, DEMM carries a representation of each distribution throughout the calculation of the dependent variable. An overview of DEMM is provided. Once DEMM algorithms are established using symbolic mathematical software program(s), and the dependent variable expansion hypothesized, then the additional overhead required to set up and solve algebraic or differential systems is small. Examples of DEMM using literature values for chlorpyrifos (a widely used insecticide) effects and fate illustrate DEMM's capability for uncertainty propagation. Determination of chlorpyrifos risk quotients for invertebrates (algebraic system) and chlorpyrifos metabolic fate in soil (differential equation system) are presented. These examples illustrate DEMM methodology on problems of interest in environmental fate and risk assessment. Multiple data sets and field/laboratory observations for chlorpyrifos were assembled and utilized with DEMM to propagate uncertainty in output predictions. Chlorpyrifos environmental fate (environmental degradation and metabolite formation/degradation) and risk for aquatic invertebrates, with uncertainty characterized using DEMM are discussed.