Review of life-cycle based methods for absolute environmental sustainability assessment and their applications

In many regions and at the planetary scale, human pressures on the environment exceed levels that natural systems can sustain. These pressures are caused by networks of human activities, which often extend across countries and continents due to global trade. This has led to an increasing requirement for methods that enable absolute environmental sustainability assessment (AESA) of anthropogenic systems and which have a basis in life cycle assessment (LCA). Such methods enable the comparison of environmental impacts of products, companies, nations, etc, with an assigned share of environmental carrying capacity for various impact categories. This study is the first systematic review of LCA-based AESA methods and their applications. After developing a framework for LCA-based AESA methods, we identified 45 relevant studies through an initial survey, database searches and citation analysis. We characterized these studies according to their intended application, impact categories, basis of carrying capacity estimates, spatial differentiation of environmental model and principles for assigning carrying capacity. We then characterized all method applications and synthesized their results. Based on this assessment, we present recommendations to practitioners on the selection and use of existing LCA-based AESA methods, as well as ways to perform assessments and communicate results to decision-makers. Furthermore, we identify future research priorities intended to extend coverage of all components of the proposed method framework, improve modeling and increase the applicability of methods.


Introduction
Life cycle assessment (LCA) is a method for estimating the environmental impacts of anthropogenic systems, such as products, companies and nations, from a 'cradle-to-grave' perspective. It covers multiple categories of environmental impact (ISO 2006a(ISO , 2006b(ISO , 2014. LCA is often used to inform decisions aimed at reducing environmental impacts, e.g. by comparing alternative products to determine which one has the better overall performance, considering, ideally, all life cycle stages (such as manufacturing and use) and impact categories (such as Climate change and Freshwater use). This has probably contributed to the globally observed incremental increase in economic value generation per unit of environmental impact (Dahmus 2014, PwC 2018. However, this increase in eco-efficiency has largely been slower than economic growth, as evidenced by the upward global trends in many indicators of environmental impact (Steffen et al 2015a), which threaten to exceed levels that natural systems can sustain at regional and planetary scales (Steffen et al 2015b). While this conclusion is not entirely new (Jevons 1866, Meadows et al 1972, Downing et al 2020, it is receiving increasing attention: a large body of academic literature related to the planetary boundaries concept has recently emerged (Downing et al 2019); the concept of climatic tipping points has strongly informed the setting of global climate targets in policy (UNFCCC 2015, IPCC 2018; companies are increasingly translating such global climate targets to the organizational level (SBT 2020); a similar approach to targetsetting for other impact categories has been called for (SBTN 2020); and popular movements are demanding drastic action to avoid the near-term depletion of a global carbon budget for the 21st century (FFF 2020) and the increasing potential for the collapse of ecosystems related to species extinction (ER 2020).
The increased focus on the finite nature of the environment has led to the emergence of several LCAbased methods for absolute environmental sustainability assessment (AESA). The core purpose of LCAbased AESA is to evaluate whether an anthropogenic system can be considered environmentally sustainable in an absolute sense for a comprehensive set of impact categories. In this context, an 'anthropogenic system' is a concept that can range in scale from a single consumer product to the global economy and comprises several interconnected anthropogenic production and/or consumption activities (Steffen et al 2015b). If this system is found to be environmentally unsustainable, absolute sustainability targets may then be calculated for future years. The word 'absolute' signals that AESA involves a comparison between the impacts of an anthropogenic system and the regional or global limits of the environment, in contrast to relative (or comparative) assessments promoted by classical LCA approaches . Box 1 contrasts relative and absolute LCA-based assessments using an illustrative example. LCA-based AESA methods are a subset of the broader category of AESA methods, some of which focus on a limited number of resources or emissions within a specific territory (Muñoz andGladek 2017, Bjørn et al 2019a). Box 1. Illustrative example of a relative and absolute environmental sustainability assessment.

Relative environmental sustainability assessment:
A diesel car and an electric train may be compared on the basis of the life-cycle impacts they cause while transporting a person 6000 km throughout a year, using a comprehensive list of impact categories. If transportation using electric train turns out to have the best environmental performance overall (for example, based on a weighted sum of impacts), it can then be identified as being more environmentally sustainable than transportation using a diesel car. The outcome of a relative assessment greatly depends on the choice of reference. For example, the electric train would perhaps not be the superior option if a bicycle was also considered in the assessment. Also, a relative assessment cannot evaluate whether any of the transportation modes performs 'well enough' to be part of an environmentally sustainable economy.

Absolute environmental sustainability assessment:
Instead of comparing the environmental impacts of different modes of transport to each other, an absolute assessment compares them to an external list of environmental carrying capacities. For example, the life-cycle climate impacts of a person's annual commuting generated by using a diesel car, an electric train and a bicycle could be compared to a share of a carrying capacity derived from the 1.5 degree climate goal of the Paris Agreement (UNFCCC 2015). This carrying capacity share could be calculated using one or more sharing principles. For example, an 'equal per capita'-principle could initially be used to assign a carrying capacity share to an individual, followed by another principle that captures the value of commuting relative to the other consumption activities in which that individual engages. It may then turn out that the bicycle is the only mode of transport whose climate impact does not exceed its assigned carrying capacity. Note that the ranking of performance between modes of transport is likely to be similar in a relative and absolute assessment (e.g. diesel car worst and bike best).
With an increasing number of LCA-based AESA methods, developers and users alike require a common framework and vocabulary as well as a comprehensive overview of existing methods and their intended use, scope, normative aspects and insights from their applications (Bjørn et al 2019a). Two recent reviews partially responded to these needs (Muñoz andGladek 2017, Faria andLabutong 2019). However, Muñoz and Gladek (2017) did not have a specific focus on methods related to LCA and several new LCA-based AESA methods have been published in the meantime, while Faria and Labutong (2019) only considered methods for the setting of future corporate greenhouse gas (GHG) emission targets. With this context, our study has four objectives: (1) to propose a framework for LCA-based AESA methods, (2) to systematically review existing methods and their applications, (3) to provide recommendations to practitioners on the use of existing methods, and (4) to identify methodological improvement needs. The remainder of this paper is structured according to these four objectives. Figure 1 displays the framework we developed for LCA-based AESA methods and sections 2.1-2.3 describe the three method components. The framework and its terminology were developed iteratively through discussions between us, considering the literature reviewed in section 3. Overall, we adopted terms that have often been used in the broader AESA literature (i.e. beyond LCA-based AESA) and that have not already been used to describe other concepts with different meanings in the LCA literature. Table 1 shows the terms resulting from this process, their definitions and similar terms identified through the LCA-based AESA literature review (see section 3). We propose to follow the standardized LCA terminology (ISO 2006a(ISO , 2006b for the elements of an AESA that also form part of classical LCA.

Estimating environmental impact
An environmental impact estimate is the modeled environmental impact of one or more elementary flows (i.e. a resource use or an emission) occurring somewhere in the life cycle of a studied anthropogenic system. An environmental impact is always quantified with the same measure and unit as the carrying capacity to which it is compared. Such a measure may describe environmental processes at the beginning A principle used to assign carrying capacity to an anthropogenic system or process Assignment principle, allocation principle, effort-sharing principle or approach of the environmental impact cause-effect chain (for Climate change, this would be a CO 2 emission equivalent) or further towards the end of this chain (an atmospheric temperature increase, in this example). As in classical LCA, the elementary flows of a studied anthropogenic system (i.e. the life cycle inventory result) are linked to their environmental impacts using the output of environmental models in the form of characterization factors (Bjørn et al 2019a). Depending on the nature of the impact category, characterization factors may be global or spatially differentiated (see figure 1). For example, characterization factors for Climate change are global, since the emission location is irrelevant for the impact, while characterization factors for Water use should generally be spatially differentiated (e.g. to the watershed level). We note that LCA-based AESA methods tend to contain a composition of impact categories that reflect the desire to protect one or two types of values. The first type is the inherent value of species and ecosystems and underpins the impact categories that relate to Ecosystem quality in the existing life cycle impact assessment (LCIA) framework . The second type is the instrumental value of natural resources and ecosystem services more widely. This second type underpins the impact categories that relate to Natural resources in the existing life cycle impact assessment (LCIA) framework . Likewise, in the planetary boundaries concept (Rockström et al 2009, Steffen et al 2015b the environment is protected due to its instrumental role in maintaining a Holocenelike Earth system, which is considered beneficial for humanity (Rockström et al 2009, Steffen et al 2015b. Acknowledging these different, but overlapping, types of values and goals underlying the two frameworks, we propose that a comprehensive AESA method should either (1) contain a set of environmental indicators that cover the impact categories related to Ecosystem quality and Natural resources in the existing LCIA framework  or (2) contain a set of environmental indicators that cover the Earth-system processes of the planetary boundaries framework (Steffen et al 2015b, Ryberg et al 2016, Chandrakumar and McLaren 2018. Figure 1 shows these two lists of impact categories. Some impact categories appear in both lists. For example, Climate change is both a concern for the stability of the Earth system and for the inherent value of species. Other impact categories in the two lists are related, but not identical. For example, the Biogeochemical flows category in the PB framework is similar to Acidification and Eutrophication in the LCIA framework, but is concerned with perturbation of natural cycles of chemical elements (nitrogen, phosphorous, silicon, etc) rather than the protection of species from those two specific environmental effects. Other impact categories only appear in one list. For example, Non-renewable resource use may negatively impact the instrumental value of resource reserves to humans, but resource depletion does not directly threaten the stability of the Earth system . Note that impact categories related to human health, commonly covered in LCA , are not relevant for AESA. This is because AESA is concerned with the potential transgression of environmental carrying capacities and not with direct human health impacts from resource use and emissions. The two lists of impact categories in figure 1 reflect the state of current scientific and methodological development and are therefore subjects to future revisions.

Quantifying carrying capacities
We define carrying capacity as: the maximum persistent impact that the environment can sustain without suffering perceived unacceptable impairment of the functional integrity of its natural systems or, in the case of non-renewable resource use, that corresponds to the rate at which renewable substitutes can be developed. The part of the definition relating to natural systems was largely adopted from Bjørn et al (2019a) (based on earlier definitions, e.g. Rees 1996, Fang et al 2015b, while the part relating to nonrenewable resource use was inspired by Daly's (1995) 'input rules' for an environmentally sustainable society. Note that in the field of population biology, carrying capacity refers to the number of individuals in a species that an environment can sustain (Sayre 2008). By comparison, a sustainable number of humans is not only dependent on the environment, but also on the average consumption and eco-efficiencies of production technologies (Chertow 2001). The carrying capacity in AESA therefore relates to the maximum sustainable total anthropogenic impact instead of the maximum number of humans.
Carrying capacity can often be expressed as a rate of emission or resource use (e.g. a fixed elementary flow equivalent per year). However, for long-lived elementary flows, such as CO 2 , and for the consumption of non-renewable resources, a time-integrated flow (e.g. between the years 2020 and 2100) may be more suitable (Rogelj et al 2019). The carrying capacity concept applies to different natural systems and at various spatial and temporal scales. For example, it can apply to the aquatic ecosystem of a particular watershed and month, or to the global climate system in the 21st century (see classification of impact categories in figure 1 as 'global' or 'regional'). Carrying capacity is an inherently normative concept, since 'perceived unacceptable impairment' and 'rate at which renewable substitutes can be developed' depend on human judgement, which can involve different ethical norms and approaches to uncertainty management (Sayre 2008, Leach 2014, Saunders 2015, Weidema and Brandão 2015. Regarding uncertainty management, the 'safe operating space' determined by a planetary boundary (Steffen et al 2015b) may be understood as a precautionary type of carrying capacity, since it is defined at a 'safe' distance from an estimated environmental threshold.

Assigning carrying capacity to an anthropogenic system
The total environmental impacts from all anthropogenic systems can be directly compared to carrying capacities in order to understand if they are environmentally sustainable or not in aggregate. When assessing a single anthropogenic system, it is necessary to assign a share of carrying capacity based on one or more sharing principles (see box 1 for an illustrative example). The choice of sharing principle is normative and different ethical norms underlie different principles. An operational AESA method allows its users to apply one or more sharing principles by formalizing it in an equation and making a link to the required data. The comparison of an anthropogenic system's environmental impact to its assigned carrying capacity allows for a judgement about the environmental sustainability of the system with respect to the impact categories considered. If the system is judged to be environmentally unsustainable (impact higher than assigned carrying capacity), methods may allow users to calculate assigned carrying capacity targets for future years. Note that the comparison of environmental impact to assigned carrying capacity is done for each environmental indicator. Aggregation of environmental impacts into a single score (e.g. through normalization and weighting steps, as per classical LCA, ISO 2006a, 2006b), is not made, as it could lead to overlooking exceedance of assigned carrying capacity for individual environmental indicators (Doka 2016, Ryberg et al 2016.

Identification of studies
We identified studies that present new LCA-based AESA methods and case studies applying existing methods. As LCA-based AESA is an emergent field, we considered both comprehensive methods and methods focusing on specific components of the framework in figure 1. We considered literature written in English in the form of peer-reviewed academic articles, conference proceedings and reports (excluding theses and dissertations). For studies presented in multiple formats (e.g. a conference paper followed by a peer-reviewed publication), only the latest version was included. The inclusion criteria were as follows: • The study must have a life cycle perspective, i.e. linking a production or consumption activity to the anthropogenic processes supporting it. This excludes studies focusing on emissions and resource use at a specific location, such as Cole et al (2014) figure 1). • Studies that apply an existing method (i.e. without modifying it in ways that have broad implications) must include a full LCA-based AESA, i.e. compare environmental impacts of one or more anthropogenic systems to assigned carrying capacities. This excludes case studies that compare the environmental impact of an anthropogenic system to unassigned carrying capacity, such as Wang et al (2019) and case studies that assign carrying capacity to an anthropogenic system without estimating its environmental impact, such as Zimmermann et al (2005).
We applied four techniques to identify studies complying with these inclusion criteria: (a) A survey of this study's authors was used to identify an initial, tentative list of studies. The procedure led to the identification of 45 studies published between 2002 and 2019, most of which were published since 2015 (see figure 2). We expect that these studies make up the vast majority of relevant studies published in peer reviewed journals and conference proceedings. Our coverage of reports outside the peer-reviewed literature may be somewhat lower, due to non-standardized indexing in literature databases and confidentiality. Table 2 presents the 45 identified studies ordered according to their year of publication and the last name of the first author. Of the 45 studies, 34 present a new method and 20 of these also present a case study applying the new method. The remaining 11 studies (45-34) apply an existing method to a case study, meaning that a total of 31 case studies (11 + 20) were covered by this review. Figure 3 maps the coverage of impact categories by the 34 studies that present a new method.

Intended applications
Ten of the 34 methods are intended for application on any anthropogenic system whilst the remaining methods are intended for specific types of systems, such as companies (9 methods), nations (7 methods) and buildings (3 methods). Most methods are intended for current conditions. This involves comparing an anthropogenic system to its assigned share of carrying capacity today. Other methods also enable, or strictly focus on, the calculation of future targets for sustainable environmental impacts. A future target can be compared to the environmental impact of a current system to understand if and how much future impact reductions are needed. Due to the long atmospheric lifetime of many GHGs, including CO 2 , methods for Climate change tend to derive future environmental impact targets from a 'peak and decline' global emission scenario that is consistent with a long-term climate goal, e.g. Rogelj et al (2018), instead of using a constant emission rate as carrying capacity. Three methods (Bendewald and Zhai 2013, Ryberg et al 2018c, Chandrakumar et al 2019a focus on target calculation in the form of cumulative GHG emissions for long-lived systems, such as buildings. Figure 3 shows that methods published before 2013 were based on the LCIA framework with 2015 being the year by which all nine LCIA impact categories (figure 1) had been addressed. Since 2015, most methods published have been PB-based and 2018 was the year in which all 9 PB-related impact categories had been collectively addressed by AESA methods. Considering all 34 methods, Climate change was the most frequently covered impact category, followed by Water use, Land-system change and Biogeochemical flows (see figure 3). The popularity of these four impact categories may be related to the fact that half of the PB-based methods are intended for studying the consumption of nations (see table 2), for which life cycle inventories are often restricted to elementary flows related to these categories (Stadler et al 2018). Most methods cover just one or two impact categories (see figure 3) and are thus far from comprehensive with respect to the framework in figure 1.

Basis of carrying capacity estimates
The carrying capacity estimates of LCIA-based methods are generally based on reviews of different literature sources, since there is no single comprehensive source that covers all impact categories. Some LCIA-based methods (such as  use planetary boundaries for the three impact categories covered in both the LCIA and PB-based frameworks (see figure 3). Early PB-based methods were based on Rockström et al (2009) whilst more recent ones refer to Steffen et al (2015b). Most PBbased methods modify one or more of the environmental indicators and boundaries proposed in the PB literature. For example, several methods use the temperature goal of the Paris Agreement (1.5-2 degrees of global warming, UNFCCC 2015) instead of the stricter PB for Climate change (1 W m −2 or 350 ppm atmospheric CO 2 , Steffen et al 2015b). Likewise, the methods of Butz et al (2018) and Meyer and Newman (2018) use 'homemade' environmental indicators with interim carrying capacities for Introduction of novel entities, for which no boundary have yet been defined in the PB science.

Spatial differentiation
Of the 34 methods, 12 allow for spatially differentiated impact assessment and/or contain spatially differentiated carrying capacity values for regional impact categories (see table 2 (2020) for Freshwater use contains a characterization factor and carrying capacity estimate for each of 11 050 watersheds. Note that many methods are spatially generic with respect to impact categories of a regional nature (in italics in figure 3). This is especially the case for methods originating in the PB framework, to which regional boundaries were introduced in 2015 (Steffen et al 2015b). None of these methods are spatially differentiated for Biogeochemical flows, Change in biosphere integrity, or Introduction of novel entities (see figure 3).

Sharing principles
The 45 reviewed studies refer to individual sharing principles with a variety of names and sometimes use a similar name for different principles. By comparing the underlying calculations, we identified a total of 10 distinct sharing principles. Table 3 gives a short description of each principle, its applicability to different types of anthropogenic systems and the number of reviewed studies applying it. The table also tentatively identifies the ethical norm underlying each principle.
The first five principles of table 2 are equally applicable to individual products, companies and sectors and to the total consumption of products by one or more individuals (e.g. during a year). These five principles span ethical norms that are egalitarian (in short: treating all people as equal), inegalitarian (in short: considering some inequalities as just) and prioritarian (in short: allowing positive discrimination for the disadvantaged) (Grasso 2012). On the other hand, the last five principles are only applicable to individual products, companies and sectors and are all based on a utilitarian ethic (in short: maximizing well-being in society) (Roemer 1996, Paavola 2001). Some principles have specific constraints in their application; for instance, Calorific content is only applicable to food products and Grandfathering is only applicable to anthropogenic systems whose existence goes back to an appropriate reference year. In many cases a principle cannot be applied alone. For example, the Equal per capita principle must be combined with another principle to be applicable to individual products, companies and sectors. This was demonstrated in the case study of Ryberg et al (2018a), who used  cover studies that are based on the LCIA-and PB framework, respectively. In the legend, the number of studies is given in parenthesis after each impact category, followed by the total number of comparisons of impact and assigned carrying capacity across these studies.
that principle to first assign carrying capacity to the total consumption of the European Union during one year and subsequently used Final consumption expenditure to arrive at an assigned share for the subset of products involved in laundry washing. All 10 principles can be applied to assess an anthropogenic system under current conditions and to define future targets. When applying principles for future target setting, parameters such as population and economic value added in the target year are often required, see Faria and Labutong (2019).
Nearly half of the 45 reviewed studies applied the Equal per capita, Grandfathering and Economic value added principles, whereas the remaining seven principle were only applied in 1-5 studies. Few studies explicitly justified their choice of sharing principles (beyond referring to older studies having applied the same principles). The difference in rate of use may reflect a combination of ease of application (e.g. in terms of required data) and perceived societal acceptability.

Case studies.
The 31 case studies identified span a wide variety of anthropogenic systems, from specific products and companies to the total consumption of nations. Most case studies can be characterized as proofs of concept, but some studies were commissioned by government entities, such as the Dutch or European environment agencies (Hoff et al 2014, Lucas and Wilting 2018a, presumably intended to inform policy. Most of the case studies cover several comparisons of anthropogenic systems and assigned carrying capacity for each of the impact categories considered. For example, the study of Brejnrod et al (2017) contains 24 comparisons for the Eutrophication impact category, due to the inclusion of (1) four anthropogenic systems (a short-life and a longlife version of two building archetypes), (2) two system boundaries (including vs. excluding energy consumption in the use phase) and (3) three environmental indicators related to impacts on soil, freshwater and ocean environmental compartments, respectively (4 * 2 * 3 = 24). The anthropogenic system has a higher impact than the assigned carrying capacity in six of that study's 24 comparisons for Eutrophication. Figure 4 shows the proportion of the aggregated number of comparisons in the 31 case studies in which impact exceeds assigned carrying capacity for the different impact categories. Supplementary material (SM) 1 (available online at stacks.iop.org/ERL/ 15/083001/mmedia) contains a detailed count for each study and a related cumulative frequency chart.
Several patterns can be observed in figure 4. There is a large difference between the proportions of comparisons in which impact exceeds assigned carrying capacity across impact categories. These differences are, overall, consistent with studies comparing total anthropogenic impacts to global carrying capacities Hauschild 2015, Steffen et al 2015b). For example, since global GHG emissions exceed the carrying capacity for Climate change, while global ozone depleting emissions by many measures are within the carrying capacity for Stratospheric ozone, it is more likely that individual anthropogenic systems are judged to be environmentally sustainable with respect to the latter impact category. There is a good agreement between the results for the three identical impact categories within the LCIA-and PBframeworks (Climate change > Water use > Stratospheric ozone depletion). Considering impact categories that are similar, but not identical, the agreement is lower: e.g. the proportions of comparisons with impacts exceeding assigned carrying capacity is substantially higher for Land-system change (PB-related) than for Land-use (LCIA-related).
The definition of planetary and regional boundaries reflect the precautionary principle (Steffen et al 2015b), which may partially explain why the scores in figure 4(b) are overall higher than the scores in figure 4(a). By contrast, the list of carrying capacities created for methods based on the LCIA framework commonly reflects a 'best estimate' approach , using average parameter values and only considering scientifically well-established impact mechanisms.
We assessed the importance of methodological choices in determining case study results (SM 2). This assessment was based on observing, within each case study, whether different methodological choices (e.g. of sharing principle) are associated with different numbers of comparisons in which impact exceeds assigned carrying capacity. In this way we found that the choice of environmental indicator (for a given impact category), sharing principle (or combination of principles) and spatial resolution appear to be most important for AESA results.
As mentioned in section 3.2.1, some AESA methods enable the calculation of future environmental impact targets. Such methods were used by 13 of the 31 case studies, in which assigned carrying capacity was calculated in one or more specific future years, most commonly for Climate change. Five of these 13 studies compare the estimated future environmental impact of one or more anthropogenic systems to future assigned carrying capacity (Girod et al 2013, Roos et al 2016, Bjørn et al 2018, Algunaibet et al 2019. These future impact scenarios were generally based on assumed specific technological innovations and behavioral changes (Girod et al 2014, Roos et al 2016 or on projections of eco-efficiency and consumer demand based on historic trends (Girod et al 2013, Bjørn et al 2018. Only Algunaibet et al (2019) took an integrated approach and used assigned carrying capacities for the year 2030 as constraints in a cost-optimization model applied to the US energy system. They found a solution that only involves exceedance of the assigned carrying capacity for one of eight environmental indicators (there was no solution with no exceedance of any assigned carrying capacity), compared to a 'business as usual' scenario in which assigned carrying capacity was exceeded for six environmental indicators.

Recommendations to practitioners on the use of existing AESA methods
This section is organized in three parts, sequenced chronologically from the perspective of a practitioner: (1) Choosing an LCA-based AESA method, (2) Performing the AESA and (3) Communicating the AESA.

Choosing a method
Below, we present four aspects that a practitioner should consider when selecting a method. These considerations are relevant for the 34 methods identified in this review (see table 2 and figure 3) as well as for future methods.

Basis in LCIA-or PB framework?
Practitioners should first consider if they need a method relating to the LCIA-or the PB framework. This decision can be based on which of the two frameworks' embedded sets of values (variants of intrinsic and instrumental values, see section 2.1) best matches the goal of the study. The decision can also be based on the more pragmatic question of whether the audience of the study is already more familiar with one framework or the other.

Coverage of impact categories, spatial differentiation and scientific robustness
Next, the practitioner should consider the coverage of impact categories and degree of spatial differentiation that best suit the study's needs, while also taking the scientific robustness of available methods into account. As in classical LCA, general good practice dictates inclusion of as many impact categories as possible to minimize the risk of 'burden shifting' (i.e. a decision leading to an increased impact in another impact category) (ISO 2006b). An exhaustive coverage of either of the two lists of impact categories in the LCA-based AESA framework (see figure 1) is currently rarely observed (see figure 3). This is due to limitations in the underlying environmental science, such as lack of environmental models for certain impact categories or unquantified planetary and regional boundaries for some Earth-system processes. When confronted with these current limitations, practitioners may restrict their choice to methods that are consistent with the goal of their study and, if needed, adapt this goal. For example, in a study of bio-based products, impact categories typically of concern in the agricultural production (such as Land use, Eutrophication and Climate Change) could be prioritized.
The review of case studies (section 3.2.6) showed that spatial differentiation can be decisive for a study's results (see SM2). In practice, application of spatially differentiated methods may depend, in part, on the resources available for constructing a spatially differentiated life cycle inventory, i.e. collecting spatial data on elementary flows contributing to regional impact categories (see figure 1). Consideration of the share of life-cycle elementary flows known to take place in regions where the carrying capacity and/or characterization factors are much higher or lower than for an average region may also be relevant. For example, a spatially differentiated assessment may be preferable for water-intensive anthropogenic systems, where most of the water consumption is known to take place in watersheds experiencing high water scarcity. However, note that many existing methods covering regional impact categories are spatially generic, e.g. eight of the 17 methods for Water use identified in this review (see figure 3).
In addition to the question of impact category coverage and spatial differentiation, the scientific robustness of these aspects is also important. Currently, a systematic comparative assessment of the scientific robustness of LCA-based AESA methods is lacking. Until this becomes available (see section 5.4), practitioners may try to judge on their own, e.g. by considering whether characterization factors have been calculated from state-of-the-art LCIA model components and whether carrying capacity estimates are well-founded in environmental science or of a more interim nature.

Sharing principle
Having chosen a method that covers environmental impact estimation and carrying capacity (see figure 1), the choice of one or more sharing principles for assigning carrying capacity to the studied anthropogenic system must be made. Many of the reviewed methods were found to apply one or more specific principles (see table 2). However, all 10 principles identified in table 3 are applicable to any of the methods. Practitioners can use table 3 to identify sharing principles that are technically applicable to the anthropogenic system they are assessing (depending, for example, on whether the system is a single product or the total consumption of an individual). In most cases, multiple sharing principles are technically applicable. In the reviewed case studies the choice of sharing principle was found to have a high influence on the results (see section 3.2.6 and SM 3). As there is generally a lack of consensus on the most appropriate principle to use, given the diversity of stakeholder perspectives, results should be calculated for multiple sharing principles.

Broader considerations
In addition to the three specific considerations above, practitioners can use method selection criteria from the broader sustainability assessment literature (Pintér et al 2012, Hauschild et al 2013, Sala et al 2015, Zijp et al 2015, for example related to: stakeholder acceptance of method; quality of method documentation; whether a method is integrated in software (which can save time for the practitioner) and whether a method will be updated in the future, thus allowing for future studies that reflect increasing scientific maturity.

Performing the LCA-based AESA
The practitioner should, as a general rule, adhere to best practice in classical LCA (ISO 2006a(ISO , 2006b. However, it is important to diverge from the predominant inventory analysis practice of expressing elementary flows in mass (or, occasionally, volume) and instead express them as an actual flowrate, i.e. a mass (or volume) per unit of time. This is necessary, since the carrying capacity in most cases relates to a rate of emissions or resource use (see section 2.2). There are different ways of incorporating time information in life cycle inventories. For example, Ryberg et al (2018a) studied the continuous activity of laundry washing in Europe and expressed all elementary flows in kg (or m 3 ) per year. Recent developments in dynamic life cycle inventory databases may also be utilized (Pigné et al 2019). Time also plays an important role in the assignment of carrying capacity, which tends to depend on variables that change on a yearly basis. Therefore, when using methods that present carrying capacity estimates per capita (e.g.  or per unit of global economic value added (e.g. Butz et al 2018), practitioners should check that the reference year used in these calculations match the reference year of the study, recalculating if necessary.

Communication to decision-makers
Since LCA-based AESA is an emerging approach within the field of environmental sustainability assessment, it is important to explain to decisionmakers how it differs from other types of assessments. For decision-makers who are familiar with classical LCA and its application for relative environmental sustainability assessment (see box 1), the focus could be on explaining the absolute nature of the assessment. This includes the ability to estimate future targets for sustainable environmental impacts (see section 3.2.6), allowing for the development of appropriate action plans.
In all cases, it is important to communicate uncertainties. For example, 11 of the 31 reviewed case studies (see table S4 in SM 2) used uncertainty propagation to evaluate the robustness of case study results. At the same time, it is important to acknowledge that some uncertainties in our understanding of natural systems, including 'unknown unknowns' , are difficult to quantify (Herrmann et al 2014, Lade et al 2020 (see section 5.2). Hence, care should be taken when interpreting AESA results. Moreover, if a study involves estimating future assigned carrying capacity, it is especially important to communicate any assumptions related to future global production and consumption. For example, if the analyst assumes a high growth rate for the global economy, this will lead to a lower assigned carrying capacity to an individual product in the future than a low, zero or negative assumed growth rate would. Also, if the analyst uses a method involving interim carrying capacity estimates or which is spatially generic for impact categories of a regional nature (see figure 3), the implications of this for the robustness of results should be addressed. As in classical LCA, it is useful to distinguish uncertainties related to engineering-and environmental science (e.g. inventory and impact assessment modeling) from those related to value judgement (e.g. the selection of a set of impact categories and the choice of sharing principle). The former can be reduced as the science matures (see section 5), while it takes societal consensus on values to manage the latter (see section 5.3).

Coverage of all framework components
The framework and related terminology presented in section 2 was the result of a comprehensive literature review (section 3) and in-depth discussions between the 20 authors of this paper; we represent a large proportion of the people currently working in the field of LCA-based AESA. We recommend that method developers use the framework and its terminology for planning, carrying out and communicating their research. For clarity and comparability, it would be helpful if method developers indicate which components of the framework (e.g. in terms of impact categories and sharing principles) are addressed by their work, as well as the components that fall out of scope. It should also be clear if a new method is intended for stand-alone use by practitioners or could be combined with one or more other existing methods.
The literature review (section 3.2) showed that there are several parts of the framework that require more attention in future LCA-based AESA method development. In terms of impact categories, figure  3 suggests that future method development could be directed to achieve a broader coverage of impact categories like Land use, Non-renewable resource use (LCIA-based) and Introduction of novel entities (PBbased). Future methods could also give greater focus to regionalization (i.e. covering spatially differentiated characterization factors and/or carrying capacities). Regionalization has the potential to identify any regional occurrences of environmental unsustainability that would be overlooked through global assessment, given the spatially uneven distribution of carrying capacity as well as environmental impacts of many elementary flows. For example, the case study of Nykvist et al (2013) found that the total land use for the production of goods and services consumed in Bangladesh was much lower than the assigned share of the global carrying capacity for Land-system change (based on the Equal per capita principle, see table 3), while total land use within Bangladesh was much higher than the carrying capacity of that region. In regionalized AESA, environmental impacts of each anthropogenic process should ideally be compared to a set of assigned carrying capacities for the region(s) affected by its elementary flows. However, the practicalities and added value to decision-makers of such assessments require exploration . In terms of assignment of carrying capacity, method developers may consider the principles identified in table 3 and their applicability as a starting point when choosing what principles to make available in a method, but should note that additional principles may be developed.

Modeling improvements
Aside from better coverage of components of the LCA-based AESA framework (section 2), the quality of the coverage should also be considered. Each component of the framework may be characterized by parameter and model uncertainty. In general, more accurate representation of a system leads to lower model uncertainty, but at the cost of increased parameter uncertainty, due to the higher number of parameters required (van Zelm and Huijbregts 2013).
State of the art LCIA methods have commonly been developed with the aim of minimizing total uncertainty by achieving a suitable compromise between model and parameter uncertainty, and LCAbased AESA can build on this in various ways: (1) characterization factors developed by classical state of the art LCIA models may be directly used in LCAbased AESA . (2) For methods based on the PB framework, some impact categories do not exist in the classical LCA literature and new LCIA models must be developed for calculating characterization factors (Ryberg et al 2016, Doka 2016). In such cases, method developers could, to the extent possible, use the same data (e.g. related to climatic conditions or physical and chemical properties of emitted substances) that underlie classical LCIA models and individual model components (such as a multimedia environmental fate model) may also be adopted. In some cases, a reduction in uncertainty may also be achieved by using other environmental indicators than those proposed in PB literature (aka 'control variables'). For example,  argued that, in the context of LCAbased AESA, the changes in precipitation and surface air temperature are more suitable environmental indicators for Land-system change than the area of forested land remaining is. (3) Uncertainties related to different parameters and modeling steps are not equally important. Developers of LCA-based AESA methods may be inspired by techniques widely used in the LCIA community to determine priorities in the quest of overall uncertainty minimization (van Zelm and Huijbregts 2013, Wender et al 2018).
Specifically for carrying capacity, it is important for method developers to be aware that carrying capacities originating in different literature sources have been estimated in response to different research questions and by using different techniques (for example, based on an understanding of a system's threshold behavior, the highest stress leading to zero (measurable) effect, or a maximum deviation from a preindustrial reference). Hence, carrying capacities are context dependent, to some extent, and not objective qualities of the environment. Also, some methods, such as Butz et al (2018), cover interim carrying capacity estimates that are in great need of further improvement. To ensure that AESA results are comparable across impact categories, method developers should aim to assemble an internally consistent list of carrying capacities, for example by developing inclusion criteria for literature estimates of carrying capacity. A related challenge is that the size of one carrying capacity may depend on whether another carrying capacity has been exceeded (Steffen et al 2015b, Lade et al 2020. For example, the exceedance of a carrying capacity for Climate change is expected to lead to significant changes in precipitation patterns, causing a change in the carrying capacity for Freshwater use due to the effect on blue water availability . The handling of such feedbacks may require an approach that integrates the modeling for several impact categories rather than modeling each causeeffect pathway in isolation. Regarding the sharing of carrying capacity, methods intended for future target setting must deal with the challenge that the economy is evolving. Prospective economic modeling should therefore be explored. Integrated assessment models may be of particular relevance, since they can be used to develop production-and consumption scenarios constrained by carrying capacities (Randers et al 2018, Rogelj et al 2018, as was partially done in the case study of Algunaibet et al (2019) (see section 3.2.6).

Applicability for decision-support
The fundamental characteristics of LCA-based AESA, compared to classical LCA used for relative environmental sustainability assessment (see box 1), offer two key motivations for decision-makers to use the approach. First, AESA can be used to evaluate whether an anthropogenic system can be considered environmentally sustainable, in an absolute sense. Second, if this is found not to be the case (as in a large proportion of the reviewed case studies, see figure 4), assigned carrying capacity can be calculated for the future and adopted as targets, e.g. in corporations Labutong 2019, Walenta 2020).
On a practical level, several actions need to be taken to make LCA-based AESA feasible for decisionsupport. Currently, AESA methods and case studies are typically only documented in the academic literature and can be hard to find, due to the historic lack of a common language. We encourage the creation of teaching materials to facilitate consistent usage of methods and sensible interpretation of results by LCA practitioners in industry, consultancy and policy settings. Likewise, a library of case studies, including any not identified in this review, could be established and maintained. In addition to being a resource for practitioners, this would form the basis of future case study reviews that build on our initial findings (section 3.2.6). It is also important for method developers to better understand the needs and experiences of potential method users. We therefore encourage the creation of a digital platform for knowledge sharing between researchers and practitioners in related fields. This would be particularly useful for method developers to better understand emergent consensus amongst stakeholders in the sharing of carrying capacity. To further qualify discussions around the use of various sharing principles, social scientists studying approaches to sharing scarce resources and the degree of societal support should be invited to join the platform.
Integration of LCA-based AESA in software is important to make its application easier. Compared to existing LCA software, LCA-based AESA requires a number of additional features: (1) management of time information for processes or elementary flows (see section 4.2), (2) spatially differentiated calculations of environmental impacts for regional categories (also a requirement for state of the art classical LCA, Mutel et al 2019), (3) spatially differentiated calculations of assigned carrying capacity for regional impact categories, and (4) links to potential databases on carrying capacities and assigned shares of carrying capacity, according to different sharing principles (elaborated in section 5.4).

Method harmonization and potential consensus building
LCA-based AESA is a new and rapidly developing field. It can be difficult for method developers to keep up with the various developments and for practitioners to identify the methods best serving their needs. The framework we propose in section 2 provides a first attempt at structuring and categorizing LCAbased AESA approaches and methods. We also align terminology encountered in the literature to bring clarity and inform harmonization efforts. The naming and characterization of sharing principles (section 3) may also contribute to near-term consensus building. In addition, the review of methods in section 3 may form the basis of a quantitative comparison of the scientific robustness of different methods, which can be used to inform method selection (see section 4.1).
As a medium-term ambition, consistency and ease of application would be improved upon the creation of complete AESA methods, developed by combining components (such as impact categories and sharing principles) of individual methods. Such an undertaking could follow the historical practice in the LCA community of creating uniform 'LCIA methodologies' , such as ReCiPe (Huijbregts et al 2017) and IMPACT World+ (Bulle et al 2019), from a selection of individual LCIA models that fulfill some common criteria. An integrated and comprehensive method often requires harmonization of its components, for example, with respect to spatial differentiation, reference conditions in LCIA modeling and naming of elementary flows.
In the longer term, more in-depth forms of method integration may be devised, inspired by the evolution of the field of classical LCA: data inputs for calculations of environmental impact, carrying capacities and assigned shares may be harmonized, for example, inspired by the processes leading to the USEtox (Rosenbaum et al 2008) or the AWARE (Boulay et al 2018) LCIA models. Also, a consensus on best practice for different methodological aspects may be sought, inspired by consensus processes for LCIA modeling, such as the one initiated by the Joint Research Centre of the European Commission (Hauschild et al 2013). This may be particularly important if agreement is to be sought on the underlying ethical norms, equations, data inputs and appropriate application for the various sharing principles ideally involving collaboration with social scientists. This could lead to the construction of databases of assigned shares of carrying capacity for different principles (expressed, for example, per unit of production), spatially and temporally differentiated where needed. As alternative to seeking a consensus on best practice, Huijbregts' (2014) proposal of using a multi-model mean for default parameter values and allowing practitioners to incorporate variance between model outputs in uncertainty analysis could also be explored.

Conclusion and outlook
This study presented the first comprehensive review of LCA-based AESA methods and their applications and proposed a method framework. These outcomes may serve as a resource for potential users to understand similarities and differences of existing methods and to choose a method and perform and communicate an assessment. Our analysis of research needs is intended to stimulate further development of the field. The study was motivated by a wish to increase the relevance of LCA for decision-support. We hope to also inspire researchers working in other fields such as Earth system science and social science to take part in ongoing efforts to improve and harmonize LCAbased AESA approaches.
The AESA approach can be used to inform action at the level of individual production and consumption activities in response to unsustainable macro-level trends. Our review of method applications found that impacts are too high in most of the covered production and consumption activities. In these cases, any historic improvement in ecoefficiency has not been large enough to decouple the environmental impacts from economic growth so that societies can operate within the regional and global limits of the environment. Building on this conclusion, it is necessary to explore what actions policymakers, the private sectors and citizens can take to drive the innovations in production and consumption that are needed to reduce impacts sufficiently.