Is mainstream LCA linear?
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LCI METHODOLOGY AND DATABASES
Is mainstream LCA linear? Reinout Heijungs 1,2 Received: 10 March 2020 / Accepted: 12 August 2020 # The Author(s) 2020
Abstract Purpose It is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. Here we study the meaning of the term linear, and in relation to that, the question if LCA is indeed linear. Methods We explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Each of them is defined in accessible terms and illustrated with examples. Results We analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined. Discussion and conclusions Despite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear. We discuss a few of such cases. We also discuss a few practical implications for practitioners of LCA and for developers of new methods for LCI and LCIA. Keywords LCA . Life cycle assessment . Linear models . Nonlinear models . Linearity
1 Purpose We often read statements concerning the linearity of LCA. As an example, below are a few quotations from articles in The International Journal of Life Cycle Assessment: & & & &
“Linear models such as... LCA” (Yang 2017; Yang and Heijungs 2018) “At the heart of LCA methodology, default assumptions lie in the strict linearity between inputs and outputs” (Gibon and Schaubroeck 2017) “Unlike conventional LCA, [our] life cycle inventory... relies on complex nonlinear calculations” (Di Lullo et al. 2020) “The reduction of model uncertainties in the inventory analysis through the use of nonlinear modeling” (Huijbregts 1998)
& & &
“The LCA model scaled linearly” (Villares et al. 2017) “The first adaptation necessary for LCA... is to permit nonlinear relationships in the inventory models” (Geyer et al. 2010) “LCA, in effect, assumes linearity of all concentrationresponse functions: all impact indices are proportional to the emitted quantities” (Spadaro and Rabl 1999)
Apparently, many authors seem to agree that mainstream LCA, or at least mainstream LCI, is linear. However, saying that LCA is linear is one thing, but it is another how such authors arrive at that conclusion, and what they mean by it. In this paper, we will study two questions: & &
Question 1: what does it mean when we say that LCA is linear? Question 2: is it true that mainstream LCA is indeed linear?
Communicated by: Yi Yang * Reinout Heijungs [email protected] 1
Department of Supply Chain Analytics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
2
Institute of Environmental Sciences, Leiden University, PO Box 9518, Leiden 2300 RA, The Netherlands
Answers to these two questions may induce new questions, such as the following: & & &
Is it bad th
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