The average versus marginal debate in LCIA: paradigm regained
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COMMENTARY AND DISCUSSION ARTICLE
The average versus marginal debate in LCIA: paradigm regained Reinout Heijungs 1,2 Received: 15 September 2020 / Accepted: 21 October 2020 # The Author(s) 2020
Ten years ago, three authors put a neglected theme on the discussion agenda (Huijbregts et al. 2011). It concerns the difference between using a marginal and an average approach for assessing the effects of ecotoxic pollutants in the context of life cycle impact assessment (LCIA). The authors advocated a “paradigm shift” from marginal to average. Since then, their approach has received quite some attention (Scopus mentions mid 2020 40 citations), including a comment (Weidema 2012) and a debate paper on marginal versus average (Forin et al. 2020), commenting on an attempt to develop non-marginal factors (Boulay et al. in press). Furthermore, the debate does not seem to have been ended conclusively. The present contribution adds new fuel to the debate. Because LCA is a quantitative model, we will add a mathematical treatment to the primarily visual approach by Huijbregts et al. (2011), which has been reproduced for convenience in Fig. 1. The effect curve is described by a function f, which takes the concentration (C) of phosphorous (P) as argument, and which yields an effect (PDF, potentially disappeared fraction of freshwater macroinvertebrate species). We will assume a e ) of phosphorous, so C eP. background concentration (C Altogether, this gives the following: PDF ¼ f ðC P Þ ¼
1 1 þ 4:07C P−1:11
yielding a background effect e P ≈0:76 g ¼f C PDF
Communicatd by Matthias Finkbeiner * Reinout Heijungs [email protected] 1
Department of Operations Analytics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
2
Institute of Environmental Sciences, Leiden University, PO Box 9518, 2300 RA Leiden, The Netherlands
According to the marginal approach (a), the effect factor, EF, is given by df E Fmarginal ¼ dC P CP ¼e CP which can be worked out as E Fmarginal
1:11 4:07C P−2:11 ¼ ≈0:02 2 1 þ 4:07C P−1:11 CP ¼10
The average approach (b) yields an effect factor eP f C E Faverage ¼ eP C which further gives 1 −1:11
E Faverage
e 1 þ 4:07C P ¼ e CP
≈0:08
This makes sense, in the following two ways. First, the marginal factor tells us what the change in effect will be when a small amount of P is added on top of the background. e P ¼ 10 to 10.1, the Indeed, when we increase CP from C new result according to f changes by approximately 0.002, which neatly corresponds to 0.02 × 0.1. Second, the impact of 0.76 is entirely caused by a concentration of 10, which means a per-unit of concentration effect of approximately 0.08. Moving from the marginal approach to the average approach, as argued by Huijbregts et al. (2011), seems to better agree with long-term policy goals. In particular at the high end of the impact curve, the marginal effect approaches zero, but the environment gets very polluted. An average approach is thus worth investigating.
Int J Life Cycle Assess 1
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