Mathematical unification of methods for hybrid life cycle assessment

Life cycle assessment (LCA) is a key method for environmental impact analysis. In this context, different methods for hybrid LCA (HLCA) have been proposed with the aim of combining bottom-up data from process-based life cycle inventories with top-down data from environmentally extended input–output tables. This is done to overcome limitations of data coverage and aggregation: Process inventory data, though detailed, may underestimate flow magnitudes or miss flows entirely, potentially underestimating environmental impacts. On the other hand, input–output data is by definition complete for intermediary flows, but highly aggregated into a small number of economic sectors and generally does not capture the use-phase of products. Combining these data sources would give a more complete picture of the environmental impact associated with products or services. Four main methods are currently recognized in literature: The integrated, tiered, matrix-augmentation and path-exchange hybrid methods. However, no consensus has emerged on the underlying mathematical differences and their applicability. Here, we propose a unifying theory of HLCA. First, we show that all methods can be expressed in the same matrix form. Using this insight, we show that instead of four, only two distinct methods exist: the tiered and the integrated methods. In particular, the matrix-augmentation method is algebraically identical to the integrated method, and the path-exchange method is the tiered method with inferred rather than compiled flows. Method names alone are therefore unreliable guides to what a study actually computes, and to whether two studies can be compared. We show how both the integrated and tiered method can be used to account for “known unknown” and “unknown unknown” data and how economic equilibrium can be maintained through balancing conditions. Finally, we offer recommendations on the optimal selection and application of each method. This constitutes an important step toward a unified methodological framework for hybrid life cycle assessment.