Analytical Uncertainty Propagation in Life Cycle Inventory and Impact Assessment: Application to an Automobile Front Panel

Background, aim, and scope Uncertainty information is essential for the proper use of Life Cycle Assessment (LCA) and environmental assessments in decision making. So far, parameter uncertainty propagation has mainly been studied using Monte Carlo techniques that are relatively computationally heavy to conduct, especially for the comparison of multiple scenarios, often limiting its use to research or to inventory only. Furthermore, Monte Carlo simulations do not automatically assess the sensitivity and contribution to overall uncertainty of individual parameters. The present paper aims to develop and apply to both inventory and impact assessment an explicit and transparent analytical approach to uncertainty. This approach applies Taylor series expansions to the uncertainty propagation of lognormally distributed parameters. Materials and methods We first apply the Taylor series expansion method to analyze the uncertainty propagation of a single scenario, in which case the squared geometric standard deviation of the final output is determined as a function of the model sensitivity to each input parameter and the squared geometric standard deviation of each parameter. We then extend this approach to the comparison of two or more LCA scenarios. Since in LCA it is crucial to account for both common inventory processes and common impact assessment characterization factors among the different scenarios, we further develop the approach to address this dependency. We provide a method to easily determine a range and a best estimate of a) the squared geometric standard deviation on the ratio of the two scenario scores, "A/B", and b) the degree of confidence in the prediction that the impact of scenario A is lower than B (i.e., the probability that A/B75%). For the aluminum panel, the electricity and aluminum primary production, as well as the light oil consumption, are the dominant contributors to the uncertainty. The developed approach for scenario comparisons, differentiating between common and independent parameters, leads to results similar to those of a Monte Carlo analysis; for all tested cases, we obtained a good concordance between the Monte Carlo and the Taylor series expansion methods regarding the probability that one scenario is better than the other. Discussion The Taylor series expansion method addresses the crucial need of accounting for dependencies in LCA, both for common LCI processes and common LCIA characterization factors. The developed approach in equation (8), which differentiates between common and independent parameters, estimates the degree of confidence in the prediction that scenario A is better than B, yielding results similar to those found with Monte Carlo simulations. Conclusions The probability distributions obtained with the Taylor series expansion are virtually equivalent to those from a classical Monte Carlo simulation, while being significantly easier to obtain. An automobile case study on an aluminum front end panel demonstrated the feasibility of this method and illustrated its simultaneous and consistent application to both inventory and impact assessment. The explicit and innovative analytical approach, based on Taylor series expansions of lognormal distributions, provides the contribution to the uncertainty from each parameter and strongly reduces calculation time.