Sensitivity coefficients for matrix-based LCA

Background, aim, and scope: Matrix-based life cycle assessment (LCA) is part of the standard ingredients of modern LCA tools. An important aspect of matrix-based LCA that is straightforward to carry out, but that requires a careful mathematical handling, is the inclusion of sensitivity coefficients based on differentiating the matrix-based formulas. Materials and methods: We briefly review the basic equations for LCA and the basic theory of sensitivity coefficients. Results: We present the complete set of sensitivity coefficients from inventory to weighting through characterization and normalization. We show the specific formulas for perturbation analysis, uncertainty analysis, and key issue analysis. We also provide an example using the ecoinvent data. Discussion: The limitations of the present approach include the restriction to small changes and uncertainties and the ignorance of correlation between input uncertainties. In contrast to common thinking, there is no restriction to normally distributed uncertainties: Every uncertainty distribution for which a variance can be defined can be submitted to the analytical uncertainty analysis. Conclusions: This paper provides a useful set of tables for a number of purposes related to uncertainty and sensitivity analysis. Recommendations and perspectives: Although the formulas derived are not simple, they are straightforward to implement in software for LCA. Once this is done, the use of these formulas can become routine practice, enabling a key issue analysis and speeding up perturbation and uncertainty analysis.