Matrix-based Methods for Regionalized Life Cycle Assessment

We develop a comprehensive computational framework for matrix-based regionalized life cycle assessment (LCA). When life cycle inventories and impact assessment methods have different spatial scales, spatial allocation is needed to map inventory locations to impact assessment spatial units. We review spatial allocation based on intersected areas and existing background emissions, and propose using additional spatial inventory data as a third type of allocation, which we call extension tables. Extension tables allow for detailed maps of individual processes, or even separate maps for specific process emissions — a significant improvement over the assumed uniform spatial density of process datasets. Extension tables can also be applied to existing process datasets. New LCA matrix formulae are developed for all three forms of spatial allocation, and these formulae allow for the expression of results on multiple spatial scales. As the final calculation result is a matrix, instead of a single value, the most damaging processes, emissions, and spatial units for every spatial scale used can be easily identified and combined. A case study of ecosystem damage due to freshwater consumption from irrigation of cotton in the United States is used to illustrate the different approaches. We implement our framework in an accessible open-source software package, including multiple additional examples.