domain: sdv sde

text:
Antoine Esnouf

Keywords: Life Cycle Assessment, Life Cycle Inventory, Life Cycle Impact Assessment method, Representativeness, Angular distance, Dimension reduction, Biofuel Analyse du cycle de vie, Inventaire du Cycle de Vie, Méthode d'Évaluation de

The Life Cycle Assessment framework (LCA) is a multi-criteria approach aiming to assess all the potential environmental impacts of any human activities. Within a standardized framework, a human activity is described throughout its values chain: from raw material extraction, through materials processing, distribution, use stages, to waste management. Then, all emission flows to the environment as well as all resource consumption flows, all defined as elementary flows, are quantified in a Life Cycle Inventory result (LCI). Translation of LCI results into a reduced number of scores that each has an environmental meaning is carried out at the Life Cycle Impact Assessment (LCIA) phase using LCIA methods. However, the holistic nature of LCA, which has induced the development of many different LCIA methods with quite a few environmental impact categories each, can make the LCIA method and impact categories selection challenging for LCA practitioners. By benefiting from a huge compilation of LCI results within cumulated LCI database, the present work develops the Representativeness Index (RI) that assesses, from a geometrical point of view, the appropriateness of LCIA methods and their impact categories for any LCI result. This innovating approach relies on the contextualization of LCI results and impact categories regarding a database and on an angular measurement within a vector space. The relevance of the RI results is tested by analysing RI trends from an entire database and by applying it to a biofuel study case.

Lay abstract / Résumé pour le grand public Antoine Esnouf / PhD dissertation / 2018 XIII Lay abstract / Résumé pour le grand public

Human activities affect the environment through natural resources consumptions and polluting substances emissions. By quantifying these consumptions and emissions, also called elementary flows, Life Cycle Assessment is a standardized tool that evaluates the potential environmental impacts of a product throughout its life cycle. The translation of a product description into environmental impacts is then compulsory in order to be able to study and compare products on a limited number of indicators and not on all the identified flows. To this end, potentially disturbed environmental mechanisms have been modelled and improved over the past few decades. However, the choice of environmental indicators may not be obvious among all the proposed one, whereas this step is crucial for an environmental analysis. This thesis proposes the development of an innovative metric to support this choice and to question the relevance of the selected indicators.

Les activités humaines interviennent sur l'environnement à travers la consommation de ressources naturelles et l'émission de 1.3.1. LCI results and LCI results database ...................................................................... 1.3.2. Impact categories and LCIA methods ..................................................................... 1.4 3.2.1. RI methodology .................................................................................................... 3.2 3.3.1. Illustrative example .............................................................................................. 3.3.1.1. LCIA 4.2.1. RI methodology .................................................................................................... 4.2.2. Fields of activity study .......................................................................................... 4.3 4.3.1. Study of the ILCD .................................................................................................. 4.3.1.1. Global 6.2.1. Standardization .................................................................................................. 6.2.2. Decorrelation ..................................................................................................... 6.2.3. Regionalization,variability and other perspectives .............................................. 6.3. GENERAL The amount of the 𝑥 th elementary flow for the 𝑖 th product (𝑖 = 1, … , 𝑚; 𝑥 = 1, … , 𝑛) j the j-th characterization model of a LCIA method

Tables -Supplementary Information

Figures

Figures Figures -Main

Figures -Supplementary Information

𝐪 𝑗

The vector of characterization factors of the 𝑗 th impact category within G*: an impact category vector (𝑗 = 1, … , 𝑝). It is also the impact category vector transferred from G* to G

𝑞 𝑥,𝑗

The characterization factor of the 𝑗 th impact category for the 𝑥 th elementary flow (𝑗 = 1, … , 𝑝; 𝑥 = 1, … , 𝑛) G*

Dual space of the G vector space, i.e. the ℝ n vector space of all the linear forms 𝑞 𝑗 ∶ G→ℝ 𝐐 LCIA method matrix composed of a set characterization vectors of 𝑝 impact categories ℎ 𝑗,𝑖 LCIA result of the i th product on the 𝑗 th impact category

(

Additional definitions:

Elementary flow intensity: after the standardization procedure (Chapter 2), the intensity refers to the contribution of the elementary flow on the norm of its LCI result vector.

Elementary flows with the highest intensities lead the direction of the vector; it is through these dimensions that the LCI result distinguished itself from the LCI result database.

Elementary flow pattern: the pattern of a LCI result refers to how the elementary flow intensities are distributed within a LCI result.

French extended abstract (résumé étendu)

Résultats

La méthodologie est testée sur quatre mix électriques issus de la base de données ecoinvent 3.1 pour 18 méthodes de calcul. Les résultats ont mis en évidence des différences de représentativité entre les méthodes de calcul pour chacun des inventaires étudiés (Figure 1). Cela montre l'intérêt potentiel de l'utilisation d'un tel indice pour discuter de l'adéquation de la méthode de calcul choisie pour un inventai re donné.

Résultats

Les distributions des IRs de la méthode de calcul de l'ILCD montrent des différences entre domaines d'activités (Figure 3). Cette méthode permet de bien représenter les résultats d'ICV des domaines d'activités de la production de machines et matériels de transport, de la production d'électricité ou encore de la construction. Par contre, le domaine de l'agriculture et de la sylviculture, par exemple, ne semble pas être globalement bien représenté.

This first chapter presents the context of the theoretical development of the thesis.

A bibliographical review addresses the selection of LCIA method and impact category in LCA. Then, it introduces the research question, the objectives and the general structure of the thesis.

Context

The thermo-industrial revolution that broke out in the XIX th century has brought countless positive transformations in the way of life and needs of a large part of mankind. Mainly due to coal, oil and gas exploitation, our modern industrialized society can provide a huge diversity of products and services that support, or set a valuable background for, the welfare, the education, the mobility, the freedom ,the creativity and the happiness of its own people. However, human development is nowadays facing both limited natural resources [START_REF] Meadows | The Limits to Growth[END_REF] and limited assimilation capacity of the major biogeochemical cycles [START_REF] Hoekstra | Humanity's unsustainable environmental footprint[END_REF]. Overexploitation of energy, land, soil fertility, water and material combined with anthropic emissions that tend to modify current natural balances rise major environmental and social challenges. This led the United Nations to adopt 17 Sustainable Development Goals in 2015 for human societies (see Figure 5, United Nations, 2015). Apprehending and measuring the human pressure on the environment is then necessary to reduce humanity's environmental footprint if we want to achieve some of the Sustainable Development Goals one day. Among environmental impact assessment approaches, the Life Cycle Assessment (LCA) framework is one of the most suitable one.

Life Cycle Assessment

LCA is a standardized and internationally recognized approach for environmental evaluation (ISO, 2006a(ISO, , 2006b)). This decision-making tool quantifies the potential environmental marginal impacts of a product or a service within all its value s chain. LCA is a multi-criteria assessment that covers the potential impacts of the studied system on a set of environmental impact categories: from natural resource consumptions (energy, water, land…), as well as on ecosystem quality (eutrophication, eco -toxicity…) and human health (particulate matter, toxicity…). LCA allows identifying the life cycle stages that need to be focused on, i.e. the environmental "hot-spot", to mitigate the environmental burden of the whole system. Having a holistic point of view of the impacts over the whole system, LCA can prevent burden shifting from an environmental impact category to another, or from a life cycle stage to another. This assessment is realized on the basis of a functional unit, that is associated with a measurable referenced flow, an d that reflects the function(s) fulfilled by the product(s) or service(s): comparison of systems that have the same functional unit is then possible.

In the four-step framework of LCA, beginning with the goal and scope and ending with the interpretation, the two main steps on which the presented work will focus on are the Life Cycle Inventory procedure (LCI) and the Life Cycle Impact Assessment (LCIA) (see Figure 6). The LCI procedure describes the studied production system throughout its values chain (from raw material extraction, through materials processing, production, distribution and use stages, to waste management, e.g. disposal or recycling) and quantifies within a LCI result all emission flows to the environment as well as all resource consumption flows (all defined as elementary flows). At the LCIA level, elementary flows are translated in terms of category indicators. Elementary flows are multiplied by a Characterization Factor (CF), quantifying to what extend they contribute to a given environmental impact category, based on cause-effect chains, also called environmental impact pathways. These impact categories (at midpoint level) can be assessed through their damages (at endpoint level) and further aggregated into three area of protection: Resources, Ecosystems quality and Human health.

Data structure in LCA

LCA is a framework that allows translating elementary flows from a human activity into a reduced number of scores that each has an environmental meaning. LCA handles datasets that model human activities (LCI results and its elementary flows) and model environmental mechanisms (impact category and its CF).

LCI results and LCI results database

Sets of LCI results are gathered within LCI results databases. Each stage of a Life Cycle is modelled by a structure called "Unitary process" (see Figure 7). It inventories the technological inputs and outputs (the technology matrix) and the elementary flows (the intervention matrix) of that specific stage. The technology matrix links all unit ary process of a LCI database between each other: it represents the human activities network. A n aggregated LCI ("System process") consists in the quantification of all elementary flows over an entire process tree. It results from the computation of a final demand vector (product), the technology matrix and the intervention matrix [START_REF] Heijungs | The Computational Structure of Life Cycle Assessment[END_REF]. Both unitary and system process databases (the second type is obtained from the first one) can be used depending on the aim of each LCA study. A system process database can be seen as a set of aggregated LCI results representing all modelled human activities that belong to numerous fields of activity (for example: agriculture and forestry, electricity power generation or machinery and transport equipment…).

Figure 7. Technical and environmental system in LCA Emission flows to the environment and resource consumption flows are the elementary flows of a LCI result. They reflect the intervention of human activities with the environment. Each elementary flow is expressed within an emission or an extraction unit that is common for the entire LCI result database. A dimension is defined by its unit, an environmental compartment and a sub-compartment where the substance is emitted: the fossil CO2 emission (substance), kg (unit), to air (compartment), urban air close to ground (sub-compartment).

The number of dimensions observed in a LCI result database depends on the environmental interventions took into account by developers. Each LCI result is a vector that can be localized in a linear space by the value of its elementary flows taken on each dimension of the database.

Impact categories and LCIA methods

The impact categories (at midpoint, endpoint and damage level) are the criteria used to characterize, assess and compare production systems. For each impact category (e.g. climate change, particulate matter or resource depletion…), a category i ndicator is defined (e.g. CO2 equivalent, PM2.5 equivalent or antimony equivalent …). Elementary flows of a LCI result are converted into a corresponding amount of the category indicator by means of CFs: CF units are expressed in indicator unit equivalents per unit of elementary flow. CF values result from the modelling of environmental mechanisms . For a given environmental mechanism, all related CFs form the characterization model of its corresponding impact category. The environmental relevance and the scientific validity of the characterization models are constantly challenged to update the best practice [START_REF] Bare | Critical Analysis of the Mathematical Relationships and Comprehensiveness of Life Cycle Impact Assessment Approaches[END_REF][START_REF] Hauschild | Identifying best existing practice for characterization modeling in life cycle impact assessment[END_REF][START_REF] Jolliet | Global guidance on environmental life cycle impact assessment indicators: impacts of climate change, fine particulate matter formation, water consumption and land use[END_REF][START_REF] Rack | Life Cycle Impact Assessment -where we are, trends, and next steps: a late report from a UNEP/SETAC Life Cycle In itiative workshop and a few updates from recent developments[END_REF][START_REF] Udo De Haes | Best available practice regarding impact categories and category indicators in life cycle impact assessment[END_REF].

LCIA methods are associated to ready-to-use sets of impact categories (EC-JRC, 2010a; [START_REF] Hauschild | Identifying best existing practice for characterization modeling in life cycle impact assessment[END_REF]. Quite a few impact categories and LCIA methods are now available for LCIA. Figure 8 provides an overview of major LCIA methods published since 2000: each LCIA method is composed of 10 to 20 different impact categories. During the goal and scope definition phase, the selection of a LCIA method and impact categories is one of the crucial steps for LCA practitioners. They often choose a LCIA method (or a subset of impact category proposed by a LCIA method) according to (i) existing guidelines bearing the latest update of LCIA methods, (ii) the context and the decision maker needs defined in the goal and scope definition phase, (iii) the modelling choice of the impact categories belonging to a method (the intended purpose, the problem or damage-oriented approach, the covered impacts, the regional and temporal validity of the method…) but also (iv) the habits and the expertise of the LCA practitioner (EC-JRC, 2011; [START_REF] Guinée | Selection of Impact Categories and Classification of LCI Results to Impact Categories[END_REF]ISO, 2006aISO, , 2006b;;[START_REF] Rosenbaum | Selection of Impact Categories, Category Indicators and Characterization Models in Goal and Scope Definition. Chapter 2: Goal and Scope Definition in Life Cycle Assessment[END_REF].

Concerning the selection of impact categories, the main requirements addressed by the ISO are:

-"the selection […] shall reflect a comprehensive set of environmental issues related to the product system being studied taking the goal and scope into consideration"

-"Value-choices and assumptions made during the selection […] should be minimized"

For LCA practitioners, the selection has been facilitate by the development of ready -touse default lists of impact categories (i.e. the LCIA methods presented in Figure 8) [START_REF] Guinée | Selection of Impact Categories and Classification of LCI Results to Impact Categories[END_REF]. Differences between these LCIA methods are due to the modelling choice of the environmental issues, the substance coverage, the relative ranking of the reference substance or are due to different spatial or time scales [START_REF] Owsianiak | IMPACT 2002+, ReCiPe 2008 and ILCD's recommended practice for characterization modelling in life cycle impact assessment: a case study-based comparison[END_REF].

Traditionally, midpoint methods have been defined by their focus o n the following five impact categories: stratospheric ozone depletion, global warming, acidification, eutrophication, and smog formation [START_REF] Bare | Critical Analysis of the Mathematical Relationships and Comprehensiveness of Life Cycle Impact Assessment Approaches[END_REF]. Other environmental concerns complete LCIA methods to up to 20 impact categories, as for example: toxicity categories, land occupation, pesticides into soil, energy resources, ionizing radiation...

Following the aim of being holistic, such large sets of impact categories can however challenge the LCIA method and impact categories selection and subsequently the efficiency of environmental regulation (as product eco-design, decision making or environmental labelling) [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF]. [START_REF] Guinée | Selection of Impact Categories and Classification of LCI Results to Impact Categories[END_REF] suggests that "it might be useful to distinguish between different types of default lists per specific sector".

Paying high attention to impact categories consistency and double counting, relevant impact categories could also come from different LCIA methods [START_REF] Rosenbaum | Selection of Impact Categories, Category Indicators and Characterization Models in Goal and Scope Definition. Chapter 2: Goal and Scope Definition in Life Cycle Assessment[END_REF].

During the result interpretation phase

In addition to the selection of a LCIA method and impact categories during the goal and scope definition stage, a focus on a few impact categories can be carried out on LCIA results. The following paragraphs propose an overview of practical procedures that select the LCIA results that are worthwhile focusing on. These procedures determine the relevance from: (i) clear environmental distinctions between alternatives, (ii) exte rnal valuations or (iii) from redundancies between impact category results.

In comparative LCA and following the LCIA step, impact categories exclusion from interpretation (i) is sometimes carried out based on an empirical threshold value applied on the LCIA result differences: for instance, no clear conclusions can be done from LCIA results with less than 20% difference for a human toxicity indicator. By quantifying uncertainties, exploration of the relative importance of impact categor ies through the magnitude of differences between LCIA results can lead to promising tool s in comparative LCA [START_REF] Mendoza Beltran | Quantified Uncertainties in Comparative Life Cycle Assessment: What Can Be Concluded?[END_REF].

Within the ISO recommendation, existing practices for normalization and weighting (ii) use external valuation of impact categories that might guide LCA practitioners on a reduce subset of LCIA results to interpret. Valuation factors allow aggregating or comparing impact category results. Other weighting procedures are currently under development. On the basis of decision makers' preferences, surveys of public opinion, willingness to pay (implying monetarization of environmental issues) and expert's knowledges, the relative importance of impact categories (i.e. weighting) is also explored using Multi-Criteria Decision Analysis (MCDA) and Linear Programming. However, all these procedures might be criticized due to the subjectivity of the weighting, inconsistency of monetarization approaches and safeguard subjects [START_REF] Cortés-Borda | On the use of weighting in LCA: Translating decision makers' preferences into weights via linear programming[END_REF][START_REF] Prado-Lopez | Stochastic multi-attribute analysis (SMAA) as an interpretation method for comparative life-cycle assessment (LCA)[END_REF].

Other studies tackle this problem through redundancies (iii) that can be observed within LCIA results on specific case studies (few numbers of LCI results with the same functional unit). Using Principal Component Analysis (PCA) combined with uncertainty analysis or multi-objective optimization, these studies reveal impact category results relationships that lead to impact category grouping [START_REF] Basson | An integrated approach for the consideration of uncertainty in decision making supported by Life Cycle Assessment[END_REF][START_REF] Bava | How can farming intensification affect the environmental impact of milk production?[END_REF][START_REF] Chen | Environmental assessment of trout farming in France by life cycle assessment : using bootstrapped principal component analysis to better de fi ne system classi fi cation[END_REF][START_REF] De Saxcé | Assessment and improvement of the appropriateness of an LCI data set on a system level -Application to textile manufacturing[END_REF][START_REF] Mouron | Management influence on environmental impacts in an apple production system on Swiss fruit farms: Combining life cycle assessment with statistical risk assessment[END_REF][START_REF] Pozo | On the use of Principal Component Analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains[END_REF] .

In the same context but applied on large sets of LCI results, [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF] proposed a procedure using PCA over a large range of products and LCIA methods (all the LCIA results of 135 impact categories for 976 LCI results from ecoinvent database 3.1) to select the impact categories explaining the major part of the variance in the product ranking. Other studies that apply multivariate statistical analysis or multi -linear regression on LCIA results of LCI results from different fields of activity focus on revealing redundancies between impact categories [START_REF] Huijbregts | Is Cumulative Fossil Energy Demand a Useful Indicator for the Environmental Performance of Products[END_REF]Pascual-González et al., 2016[START_REF] Guinée | Selection of Impact Categories and Classification of LCI Results to Impact Categories[END_REF][START_REF] Steinmann | Resource Footprints are Good Proxies of Environmental Damage[END_REF]. The objectives of these studies were to predict LCIA results from a reduced number of proxy impact categories, and then focus the interpretation on this reduce set of selected impact categories.

Objectives

We saw that the selection of worthwhile impact categories is carried out at two diff erent stages of the LCA framework: the goal and scope definition phase and the LCIA result s interpretation. The present work tends to take into consideration the ISO requirement of having a "comprehensive set of environmental issues related to the product system" with a mathematical point of view. LCI results databases provide a huge compilation of human activities and LCIA methods provide a wide diversity of potential environmental indicator. With the general aim of improving the selection procedure of LCIA methods and impact categories by analysing LCI database, the research question of the thesis is:

By exploring LCI results through their standardized elementary flow trends, is it possible to assess by a systematic approach the relative relevance of LCIA methods and their respective impact categories for LCA studies?

The Figure 9 presents the global structure of the thesis. After the introduction (Chapter 1), the Chapter 2 defines and presents the theoretical development of the Representativeness Index (RI), established for the first time in this thesis. RI is a proximity measurement developed to explore, within a standardized vector space, the relationships between LCI results and LCIA methods through an angular distance. Within the standardized vector space, the representativeness can then be defined as the similarity between the LCI result vector and the impact category vector through the enviro nmentally concerning dimensions. The relative adequacy of LCIA methods for LCI results is then analyzed.

Chapter 3 proposes a tool based on the RI methodology to guide impact categories selection for LCA studies. The links between the global RIs of LCIA me thods, the RIs of their impact categories and the dimensions that support RI values are examined.

Chapter 4 analyses RI results among large sets of LCI results based on fields of activity.

We explore if the RI methodology puts forward distinct LCIA methods and environmental issues while analysing datasets based on subtypes of products and activities.

Chapter 5 applies the RI methodology on the LCA of the production of biofuel from cellulosic macro-algae. First, an inventory of the system designed in the Green AlgOhol project is presented and a contribution analyses is carried out with the ILCD method. For the ILCD method, RIs of the whole system and sub-parts of the values chain are analyzed.

A screening of classic LCIA methods and their impact categories is performed through their RIs.

Finally, a discussion about the scientific and practical relevance of the main outcomes of the thesis, along with future research perspectives to address their identified shortcomings, is provided in Chapter 6. This chapter presents the theoretical development of the Representativeness Index. A geometric formalization of the LCA framework is proposed and the proximity measurement, on which the PhD work is based to explore the relationships between LCI results and LCIA methods, is defined. The relative adequacy of classic LCIA methods for four electricity mix production LCIs is analyzed.

Introduction

The LCA methodology provides a standardized and commonly used framework to quantify the environmental impacts of human activities (ISO, 2006b(ISO, , 2006a)). In the fourstep framework of the LCA, beginning with the goal and scope and ending with the interpretation, the main steps are the Life Cycle Inventory procedure (LCI) and the Life Cycle Impact Assessment (LCIA). The LCI procedure describes a production system throughout its values chain and the LCI result quantifies all emission flows to the environment as well as all resource consumption flows (all defined as elementary flows). At the LCIA level, by means of linear-weighted aggregations using Characterization Factors (CFs), elementary flows are translated in terms of environmental impacts such as climate change, depletion of resources, acidification, ionizing radiation or human toxicity... LCIA methods are associated to ready-to-use sets of impact categories (EC-JRC, 2010b). Impact categories of LCIA methods rely on the characterization models of the environmental issues. The environmental relevance and the scientific validity of the characterization models are constantly challenged to update the best practice [START_REF] Bare | Critical Analysis of the Mathematical Relationships and Comprehensiveness of Life Cycle Impact Assessment Approaches[END_REF][START_REF] Hauschild | Identifying best existing practice for characterization modeling in life cycle impact assessment[END_REF][START_REF] Huijbregts | ReCiPe2016: a harmonised life cycle impact assessment method at midpoint and endpoint level[END_REF][START_REF] Jolliet | Global guidance on environmental life cycle impact assessment indicators: impacts of climate change, fine particulate matter formation, water consumption and land use[END_REF][START_REF] Rack | Life Cycle Impact Assessment -where we are, trends, and next steps: a late report from a UNEP/SETAC Life Cycle In itiative workshop and a few updates from recent developments[END_REF][START_REF] Udo De Haes | Best available practice regarding impact categories and category indicators in life cycle impact assessment[END_REF]. The use of different LCIA methods may then lead to disparate results [START_REF] Dreyer | Comparison of Three Different LCIA Methods: EDIP97, CML2001 and Eco-indicator 99[END_REF][START_REF] Monteiro | Life-cycle assessment of a house with alternative exterior walls: Comparison of three impact assessment methods[END_REF][START_REF] Owsianiak | IMPACT 2002+, ReCiPe 2008 and ILCD's recommended practice for characterization modelling in life cycle impact assessment: a case study-based comparison[END_REF][START_REF] Pizzol | Impacts of "metals" on human health: a comparison between nine different methodologies for Life Cycle Impact Assessment (LCIA)[END_REF]. [START_REF] Owsianiak | IMPACT 2002+, ReCiPe 2008 and ILCD's recommended practice for characterization modelling in life cycle impact assessment: a case study-based comparison[END_REF] showed that disagreements in LCIA results are mainly due to differences in the underlying characterization model, in substance coverage, in relative ranking of the reference substance or due to different spatial or time scales. LCA practitioners often choose a LCIA method (or a subset of impact category proposed by a LCIA method) according to (i) existing guidelines bearing the latest update of LCIA methods, (ii) the context and the user needs guided by the goal and scope of the LCA study, (iii) the modelling choice of the method (the intended purpose, the problem or damage-oriented approach, the covered impacts, the regional and temporal validity of the method…) but also (iv) the habits and the expertise of the LCA practitioner (EC-JRC, 2011;ISO, 2006b;[START_REF] Laurent | Review of LCA studies of solid waste management systems -Part II: Methodological guidance for a better practice[END_REF].

From a data analysis point of view, LCIA reduces the complexity of systems described at LCI result level from several hundred variables (high-dimensional dataset of elementary flows, which makes it difficult to fully apprehend the comparison), to a reduced number of criteria for which systems are described by their performance on a few environmental impact categories (low-dimensional dataset, allowing an easier comparison). LCIA can be viewed as a dimensional reduction technique, inherently linked with information losses, but where each of the resulting dimensions has an environmental meaning.

The aim of this work is to help practitioners select the most appropriate LCIA method with regard to the studied LCI results. The selection of impact categories was examined over a large range of products and impact categories by [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF]. Based on the maximum amount of variance of results from the impact categories, Principal Component Analysis has highlighted an optimal set of impact categories derived from different LCIA methods. In this paper, a Representativeness Index (RI) is proposed to assess how LCI result information can be captured by the LCIA methods and their own impact categories. This RI does not measure the relevance of the environmental model behind the LCIA methods. It rather offers the possibility to obtain an objective appraisal of LCIA methods with additional information on the completeness representation of inventory results they actually perform and can contribute to LCIA result interpretation. This paper is organized as follows: in Section 2.2, the RI is defined and the algorithm developed from a geometric representation of LCA is presented. This approach is illustrated in Section 2.3 on classic LCIA methods for several electricity mix productions from the ecoinvent database [START_REF] Moreno Ruiz | Documentation of changes implemented in ecoinvent Data 3.0[END_REF]. Finally, representativeness of impact categories are presented for two electricity mixes through a single LCIA method in order to deepen the interpretation of the RIs.

Material and method

The proximity relationship between a LCI result and impact category vectors can be studied thanks to the geometrical interpretation of LCA methodology. The proximity measurement -also called Representativeness Index (RI) in the following -is defined and adjusted according to the impact category vector as well as to vector sub-spaces generated by sets of impact category vectors (LCIA methods). The implementation is then presented.

Geometrical representation of LCA methodology

2.2.1.1. Life Cycle Inventories result LCI result is classically defined in LCA as an inventory vector resulting from the computation of the final demand vector, the technology matrix and the intervention matrix [START_REF] Heijungs | The Computational Structure of Life Cycle Assessment[END_REF]. This aggregated LCI result consists in the quantification of n elementary flows, resulting from emissions into the environment and resource extractions, over the whole process tree (the involved life cycle steps). This aggregated LCI result belongs to a G space of n dimensions where n is the number of different elementary flows. The visualization of LCI result in a vector space generated by an elementary flow basis has previously been suggested by [START_REF] Heijungs | The Computational Structure of Life Cycle Assessment[END_REF] and Le [START_REF] Téno | Visual data analysis and decision support methods for nondeterministic LCA[END_REF].

Therefore any LCI result can be localized in this ℝ n vector space either as a simple data point gi or as a data vector gi with n coordinates 𝑔 𝑥,𝑖 (𝑥 ∈ {1, 2, … , 𝑛}). The norm of the LCI result vector is directly linked to the reference flow of its functional unit (e.g. the norm of one kilogram of a given product is one thousand times greater than t he norm of one gram of the same given product). The direction of the LCI result depends on the relative proportion of the elementary flows. As a simple illustration, Figure 11.a. represents two LCI, 𝐠 1 and 𝐠 2 , described by two elementary flows (i.e. into a 2dimensional space, here NO2 and NH3 gas emissions).

Impact categories

The impact categories are the environmental issues used to characterize, assess and compare production systems. For each impact category (e.g. climate change, particulate matter or resource depletion…), a category indicator is defined (e.g. CO 2 equivalent, PM 2.5 equivalent or antimony equivalent). Elementary flows of the LCI result are converted into a corresponding amount of the category indicator by means of CFs. CF values result from the modelling of environmental concerns and, for a given environmental concern, all related CFs form the characterization model of its corresponding impact category. A j characterization model is then a qj function that associates a gi LCI vector to a hj,i onedimensional impact result expressed as a category indicator:

𝑞 𝑗 ∶ { 𝐺 → 𝐻 𝐠 𝑖 → ℎ 𝑗,𝑖 ℎ 𝑗,𝑖 = 𝑞 𝑗 (𝐠 𝑖 ) = ∑ 𝑞 𝑥,𝑗 × 𝑔 𝑥,𝑖 𝑛 𝑥 =1 (1)
Where 𝑞 𝑥,𝑗 is the CF for x-th elementary flow.

In mathematical terms, the linear-weighted aggregation performed by an impact category corresponds to a linear form that maps a G vector space to a scalar. The G* dual space is the n-dimensional vector space of all the linear forms 𝑞 𝑗 ∶ 𝐺 → ℝ. Independently of their environmental meaning, all the characterization models determined by their CFs 𝑞 𝑥,𝑗 (𝑥 ∈ {1, 2, … , 𝑛}) belong to the dual space. LCI result and characterization models belong to G and its G* dual space, respectively. According to the Fréchet-Riesz theorem, a linear form 𝑞 𝑗 of G* can be represented by a unique vector within G. The characterization model of an impact category can therefore be associated with a vector 𝐪 𝑗 of the G space using the CFs as coordinates. As a simple illustration, Figure 11.b. shows two impact categories, particulate matter formation (𝐪 1 ) and acidification (𝐪 2 ), in the inventory result space. For the sake of simplification, the term "characterization model of impact categories" will from now on be referred to as the "impact category vector". Also, the same notation 𝐪 𝑗 will be applied for the impact category vector transferred from G* to G.

Geometric interpretation of Life Cycle Impact Assessment

By representing LCI results and impact category vectors in the same vector space, the LCIA result 𝑞 𝑗 (𝐠 𝑖 ) (or ℎ 𝑗,𝑖 ) is then assimilated to the scalar product 〈𝐪 𝑗 , 𝐠 𝑖 〉 between the 𝐠 𝑖 LCI vector and the 𝐪 𝑗 impact category vector. Figure 11.c. represents the orthogonal projections OI of two 𝐠 1 and 𝐠 2 LCI result vectors on the two 𝐪 1 and 𝐪 2 impact category vectors. The coordinates and the norm of OIj,i are easily related to the value ℎ 𝑗,𝑖 of the impact result (i.e. the scalar product of 𝐪 𝑗 with 𝐠 𝑖 ):

𝑶𝑰 𝑗,𝑖 = 〈𝐪 𝑗 , 𝐠 𝑖 〉 ‖𝐪 𝑗 ‖ 2 . 𝑐 𝑗 = ℎ 𝑗,𝑖 ‖𝐪 𝑗 ‖ 2 . 𝐪 𝑗 (2) ‖𝑶𝑰 𝑗,𝑖 ‖ = 〈𝐪 𝑗 , 𝐠 𝑖 〉 ‖𝐪 𝑗 ‖ = ℎ 𝑗,𝑖 ‖𝐪 𝑗 ‖ (3) Figure 11.c.
shows LCIA results visualized through LCI result projections on the impact category axis. Projections of the LCI results on impact category vectors are closer to the 𝐠 1 and 𝐠 2 LCI result for the particulate matter (I1,1 and I1,2) than for the acidification category (I2,1 and I2,2). This implies that, if only one impact category has to be studied as in the example presented in Figure 11, particulate matter would be the most appropriate choice from a data analysis point-of-view to represent the LCI result produced information. Obviously, this does not provide any information regarding th e possible environmental drawbacks of the particulate matter concern compared to the acidification concern. If an inventory and its projection are superimposed, the associated impact categories capture all the elementary flow information. On the contrary, a large distance between an inventory and its projection implies that the corresponding impact category poorly reflects the LCI result data.

Definition of a Representativeness Index

The directions of LCI result vectors in the G space are driven by the elementary flows and the directions of impact category vectors are driven by the modelled harmfulness of elementary flows for the environmental concerns. By measuring the proximity between a LCI vector and an impact category vector or between a LCI vector and a vector sub-space generated by a LCIA method (a set of LCI vectors), the faithfulness of LCIA results in representing the LCI result can be assessed. It would then be possible to select suitable impact category vectors or a suitable LCIA method according to the studied LCI results.

The developed RI is first presented for a LCI result with an impact category vector and secondly with a LCIA method.

RI of an impact category

Measuring the distance between multidimensional data sets is common in data analysis techniques [START_REF] Leskovec | Mining of Massive Datasets[END_REF]. The most common measurement between two vectors is the Euclidean distance. It can be used to measure the proximity between the extremity of 𝐠 𝑖 and the extremity of 𝐪 𝑗 or the extremity of 𝐠 𝑖 and Ij,i. However, the Euclidean distance is sensitive to the norm of ‖𝐠 𝑖 ‖. Considering two LCI results pointing in the same direction but bearing different norms, the Euclidean distances measured with the same impact category vector would then be different, despite the fact that their elementary flows are similarly represented. To measure the distance between directions, the angular cosine distance hence appears as the most convenient metric to RI.

Defining αj,i as the angle formed by the directions of LCI 𝐠 𝑖 and the impact category vector 𝐪 𝑗 (see 2-dimensional space example Figure 11.d.), RI is defined as:

𝑅𝐼(𝐪 𝑗 , 𝐠 𝑖 ) = |cos(𝛼(𝐪 𝑗 , 𝐠 𝑖 ))| = | 〈𝐪 𝑗 , 𝐠 𝑖 〉 ‖𝐪 𝑗 ‖.‖𝐠 𝑖 ‖ | (4)
Because 𝐠 𝑖 and -𝐠 𝑖 are identically represented by an impact category, the absolute value of the angular cosine is used. When the RI is close to one, LCIA results carry the major part of the LCI result information (the projection of 𝐠 𝑖 on 𝐪 𝑗 is close to 𝐠 𝑖 ); conversely, when RI tends towards zero, the LCIA result does not handle the inventory correctly.

RI of a LCIA method

Considering Q as a LCIA method, Q defines a non-orthogonal multidimensional subspace generated by its p impact vectors 𝐪 𝑗 (𝑗 ∈ {1, … , 𝑝}). As previously performed on a single impact category, the projection of a LCI vector can be done on a LCIA method subspace and the proximity between the LCI and the sub-space can be measured.

In Figure 12, considering a vector space generated by three elementary flows (unit vectors are not presented for reasons of clarity), a 2-dimensional sub-space Q generated by a LCIA method comprising two impact categories 𝐪 1 and 𝐪 2 is plotted. The LCIA result of 𝐠 1 includes I1,1 and I2,1, the results from each impact category. The orthogonal projection of 𝐠 1 on Q (𝐠 1 ,Q) is the part of the inventory which is captured by the LCIA method. The unrepresented part can be measured by the angle 𝛼 𝑸,𝑖 formed by 𝐠 𝑖 and 𝐠 𝑖 ,Q, and collected by the RI (eq 5). The RI of the method is an assemblage of the RIs from its different impact categories (see Chapter 3).

𝑅𝐼(𝐐, 𝐠

𝑖 ) = |cos (𝛼 𝐐,𝑖 ) | = √ 1 -( ‖𝐠 𝑖 -𝐠 𝑖,𝐐 ‖ ‖𝐠 𝑖 ‖ ) 2 (5)
If the elements of Q are independent and orthogonal, 𝐠 𝑖 ,Q can be considered as the result of the least squares regression 𝐠 𝑖 ,Q = Qy where y is the projection of 𝐠 𝑖 in the Q subspace.

The distance 𝐠 𝑖 𝐠 𝑖 ,Q=‖𝐠 𝑖 -𝐠 𝑖,𝐐 ‖ can then be easily defined as the residual (𝐠 𝑖 =Qy+𝐠 𝑖 𝐠 𝑖 ,Q).

The impact categories of LCIA methods are obviously dependent; many emissions have more than one environmental drawback, thus implying that the characterization factors cover several impact categories. In order to employ the residual of a least squares approach to determine 𝐠 𝑖 𝐠 𝑖 ,Q, the subspace of the Q LCIA method must be expressed with independent vectors: these are a set of orthogonal vectors 𝐐 ⊥ which can be obtained through a Gram-Schmidt process.

Pretreatment

In LCI results databases, elementary flows are quantified using several units (e.g. kilograms, Becquerel or Joules). In many cases, when a same unit is used, elementary flows present different orders of magnitude (e.g. within ecoinvent, fossil carbon dioxide emissions to the atmosphere are close to 1 kg for most of the LCI results while benzene emissions to surface water are close to 1 µg). A pre-treatment is necessary, if all elementary flows are assured to equally discriminate LCI results within a database and hence if the dependence between measurement units and orders of magnitude and representativeness must be avoided. Classic approaches include min-max normalization, decimal scaling or z-score (most commonly used, optimal for Gaussian distribution).

Unfortunately, the first two techniques are sensitive to the presence of outliers while zscore is not appropriate for lognormally distributed data [START_REF] Qin | What distribution function do life cycle inventories follow?[END_REF]. Preference is given to the scaling of dimensions according to their geometric mean (the mean of the logarithms) because it transforms elementary flows into a common numerical range:

𝑔 ̃𝑥,𝑖 = 𝑔 𝑥,𝑖 √ ∏ 𝑔 𝑥,𝑙 𝑚 𝑙=1 𝑚 , ∀𝑖 ∈ {1, … 𝑚}, 𝑥 ∈ {1, … 𝑛} (6)
CF units are expressed in kg indicator equivalents per kg of elementary flow; therefore to keep consistent with the units, CFs become:

𝑞 ̃𝑥,𝑗 = 𝑞 𝑥,𝑗 × √∏ 𝑔 𝑥,𝑙 𝑚 𝑙=1 𝑚 (7)
The standardization of impact categories transforms them in such way that high standardized CFs correspond to dimensions that are significant for the impact category and for the whole database. The LCIA method sub-spaces are then orthogonalised through a Gram-Schmidt process. RIs of LCIA methods regarding each LCI result are finally calculated using the results of a least squares regression. To determine the RIs of impact categories, the same procedure is followed except that orthogonalisation is not required. LCIA methods are ranked according to their RIs over the entire ecoinvent 3.1 database "allocation at the point of substitution" [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF]. This version of the database was released in 2014. This database comprises 11,276 aggregated LCI result vectors that are described through 1,869 elementary flows (the intervention matrix). The vector space G therefore has 1,869 dimensions. [START_REF] Hauschild | Spatial differentiation in Life Cycle impact assessment -The EDIP2003 methodology[END_REF][START_REF] Jolliet | IMPACT 2002+: A new life cycle impact assessment methodology[END_REF]NIST, 2007;[START_REF] Steen | A systematic approach to environmental priority strategies in product development (EPS). Version 2000 -General system characteristics[END_REF][START_REF] Steen | Environmental Assessment of Products and Material Systems A systematic approach to environmental priority strategies in product development ( EPS ). Version 2000 -General system characteristics[END_REF]. The CF nomenclature was transferred from the SimaPro nomenclature to the ecoinvent elementary flows nomenclature with the assistance of the ecoinvent centre that provides us a translation file.

Overview of the approach and implementation

Based on the studied ecoinvent database, electricity production mixes serve as an illustrative example. Four inventories referring to the market production of 1 kWh of high voltage electricity are used. The market version of these LCI results models the aggregated environmental flows of electricity production mixes, transmission networks and electricity losses during transmission. The Chinese and French mixes were chosen because of the prevailing production of hard coal and nuclear power, respectively (see Annex A Figure S 3). The German mix and the area covered by the Northeast Power Coordinating Council (NPCC, North-eastern North America, U.S. only) were analysed because of the diversity of the power supplies that do not individually exceed 34% of the mix.

Implementation was conducted with Python 2.7 on a Jupyter Notebook (formerly IPython Notebook, [START_REF] Perez | IPython: A System for Interactive Scientific Computing[END_REF] and using the numerical computation libraries SciPy, Pandas, Matplotlib. The implemented procedure is available upon request from the first author.

Results and discussion

This section firstly presents the results on the representativeness of LCIA methods for each of the studied LCI results. Secondly, RIs are compared between the different LCI results in order to assess the LCIA method that would be most suitable for comparison.

Finally, the RIs of the impact categories within a LCIA method are investigated.

RI analysis of each LCI result

The RI results of the eighteen LCIA methods, analysed using the procedure described in Figure 13, are presented in Figure 14. Along the x-axis, LCIA methods are simply sorted in alphabetical order. illustrates that the information from the high standardized elementary flows of a LCI result can be well represented by a LCIA method with a small number of impact categories.

Considering the French mix production, Ecological Scarcity outranges all other methods. For the other methods, three main groups can be distinguished. The first group cons ists of 8 LCIA methods with RIs ranging from 0.09 to 0.10. The second and third groups include 4 LCIA methods with RIs ranging from 0.014 to 0.018 and from 0.003 to 0.006 respectively. The RI for the EPD method stands on its own between the second and thir d groups.

RIs for the NPCC mix production show a similar trend when compared to the French mix production: Ecological Scarcity also represents this LCI result well and the same first group of LCIA methods is observed around 0.05. However, no group can be distinguished here within the lower RIs showing a gradual decrease for the remaining methods.

Finally, the German mix production shows 4 groups of LCIA methods with EDIP, ILCD and the three ReCiPe Midpoint methods as the most representative LCIA methods wit h RIs close to 0.075.

This illustrative example demonstrates how RIs present differences for each LCI result.

When analysing one specific LCI result, it is possible to determine the most appropriate and representative LCIA method. This study also reveals a set of LCIA methods with equivalent RIs (3 groups for the French mix and 4 groups for the German mix). The methods that constitute a group can be similar in one way or another (similar environmental concerns taken into account within the methods, or simil ar characterization models, for example). RIs values can be related to the number of impact categories but this has not been observed for all the four LCI results analysed in the illustrative example (see Annex A Figure S 5).

Comparison of RIs of LCIA methods

The purpose of LCA is to be used as a comparison approach; and for a couple of LCI results, both RIs must be investigated (see Figure 15). The most representative LCIA methods for two LCI results get high and similar RIs which localise them close to the first bisector. For example, when comparing the Chinese and the French mix productions (upper left chart), the Ecological Scarcity RI is high for the French mix but distant from the first bisector. This implies that with this LCIA method, the Chinese mix could be underrepresented compared to the French mix, and this could weaken result interpretation.

A set of methods (The ReCiPe mid., the ReCiPe end. imp., the ILCD and the Impact 2002+) seems to be a good compromise to compare these two LCI results according to their representativeness. The impact 2002+ might be better for comparing the Chinese and NPCC mixes. The EPD method could be noteworthy for the comparison between the Chinese and German mixes. The Ecological Scarcity method could be relevant for the French and the NPCC representativeness. To compare RIs from more than two of these LCI results is more challenging although the methods that are the most representative of all the LCI results are the ILCD and ReCiPe Midpoint. Results presented in this figure could therefore be decisional support information very easy to understand for the choice of the most representative LCIA method.

Analysing RIs of impact categories

This work focuses on the representativeness of the LCIA method and not on the impact categories to study. However, to fully understand the links between impact category RIs and LCIA method RIs, Figure 16 presents the impact category RIs of the ReCiPe mid. I. method for the Chinese and the French production mixes. This LCIA method appeared as one of the most representative methods for both of them. RIs are here determined for each impact separately. The same information on elementary flows can be represented by different impact categories due to correlations between impact categories. For the Chinese production mix, the first three main impact categories that represent the inventory are particulate matter formation, the terrestrial acidifica tion and climate change.

These three environmental concerns are assessed in most of the LCIA methods, which is why this LCI result is quite well represented (Figure 14). The results are quite consistent, given that this production mix is driven by hard coal production.

For the French production mix, the RI of the ionizing radiation category is higher. Within this method, only one impact category represents the main part of the LCI result. As a consequence, the analysis of the environmental impact of this LCI result might not be relevant if methods that do not take this environmental concern into account are used, such as Bees, CML-IA or Traci methods.

The present focus on Chinese and French mixes implies that for certain LCI result such as the Chinese mix, several impact categories are needed to reach an acceptable representativeness of the elementary flows. On the contrary, the French mix is globally mono-criterial with the ionizing radiation category that outranges the representation of this LCI result compared to the other impact categories.

Conclusions

This work provides a first step in the representation of LCI results by LCIA methods from an algebraic point of view. With the RI measurement, the relevance of LCIA methods used to study the environmental profile of one production system or several production systems within their own database can be compared. Neither the scientific nor the environmental relevance of the LCIA method model is assessed here. The case study shows how LCIA methods can be discriminated on the basis of the information of the studied LCI results that they represent. It reveals that some LCIA methods with a small RI overlooked the main environmental issues of the LCI results. After adapting the implementation and resolving the database nomenclature issues, this methodology could be used by LCA practitioners to compare the adequacy of their own LCI result with the different LCIA methods. Additionally to the practitioner's knowledge, justifications towards the LCIA method could partly rely on RIs. Results suggest also that the representativeness of impact categories can be variable within a single LCIA method. A LCA study that focuses on a small set of representative impact categories, and not on a complete LCIA method, could lead to further relevant conclusions and interpretations of the environmental results. The RI could then be part of the solution of the impact category selection. Finally, the application of this methodology to specific fields of activity (see Chapter 4) or to compare the global suitability of methods for different LCI results databases, could lead to the establishment of generic guidelines on the use of LCI A methods or impact categories to analyse given LCI results. These guidelines could rely on descriptive statistics of the RIs across different fields of activity.

Chapter 3: A tool to guide the selection of impact categories for LCA studies by using the Representativeness Indexes The previous chapter consisted on the presentation of the RI measurement and its application for LCIA methods selection. This measurement is here used for the selection of impact categories that are worthwhile to focus on. A study case on two electricity mix production LCI results is proposed to present the potential benefits of such measurement for LCA practitioners. The links between the global RIs of LCIA methods and the RIs of their impact categories raised orthogonal issues and an algorithm is then proposed to overcome it. Finally, an interpretation of the standardization proc edure leads to study LCI result patterns and defines environmentally critical dimensions.

Introduction

While the main goal of the Life Cycle Assessment (LCA) framework is to quantify and assess all the potential environmental impacts of human activities (ISO, 2006b), the study of results over a too wide range of environmental impacts can become inefficient and lead to unclear conclusions [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF]. To obtain those environmental impact results, the LCA framework is structured in four phases where the Life Cycle Inventory (LCI) phase is one of the key one; it describes a product, a process or an activity throughout its value chain and quantifies its system-wide emissions and resource extractions. An LCI database (of which ecoinvent [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF] is a prime example) contains a large number of unit processes, each of which specifies the inputs and outputs (such as electricity, plastic, fossil resources and pollutants) of activities (such as rolling steel or driving a truck). Those LCI unit process databases allow LCA practitioners modelling the whole value chain of their study in reasonable time. The result of an LCI is a list of quantified emissions and resource extractions, collectively indicated as elementary flows, aggregated over all (up to thousands) unit processes that make up the system. In a cumulated LCI database, the entries are not the unit processes but rather the system-wide elementary flows, for each included product. From the LCI result, the Life Cycle Impact Assessment (LCIA) phase then translates these elementary flows in terms of environmental impacts. Different LCIA methods are available , often with a name, such as ReCiPe [START_REF] Goedkoop | ReCiPe 2008: A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level[END_REF], Traci [START_REF] Bare | TRACI 2.0: the tool for the reduction and assessment of chemical and other environmental impacts 2.0[END_REF] and ILCD (EC-JRC, 2010a). Each LCIA method consists of a number of environmental impact categories (such as global warming and ecotoxicity) and proposes Characterization Factors (CFs) to quantitatively link the elementary flows to these impact categories. There are often ten or more such impact categories within each LCIA method (EC-JRC, 2010b). Although aiming at being holistic, such large sets of impact categories can challenge the efficiency of environmental regulations (like product eco-design, decision making or environmental labelling). Further modelling the impacts into so-called endpoint damage levels could resolve the issue related to large sets. However, due to uncertainties, all models which are presently available are still classified as "interim" [START_REF] Hauschild | Identifying best existing practice for characterization modeling in life cycle impact assessment[END_REF].

A reduction in the number of impact categories, by selecting the most relevant impact categories to focus on, would enable more effective environmental optimization. For comparative LCA, existing practices for normalization and weighting use external valuation of impact categories that might guide LCA practitioners on a reduced subset of LCIA results to interpret [START_REF] Lautier | Development of normalization factors for Canada and the United States and comparison with European factors[END_REF]. However, these procedures are increasingly discouraged [START_REF] Prado-Lopez | Stochastic multi-attribute analysis (SMAA) as an interpretation method for comparative life-cycle assessment (LCA)[END_REF]. By quantifying the uncertainties, exploration of the relative importance of impact categories through the magnitude of differences between LCIA results can produce promising tools for comparative LCA [START_REF] Mendoza Beltran | Quantified Uncertainties in Comparative Life Cycle Assessment: What Can Be Concluded?[END_REF].

Some authors used Principal Component Analysis (PCA), combined with uncertainty analysis or multi-objective optimization [START_REF] Mouron | Management influence on environmental impacts in an apple production system on Swiss fruit farms: Combining life cycle assessment with statistical risk assessment[END_REF][START_REF] Pozo | On the use of Principal Component Analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains[END_REF] to deal with the large number of environmental indicators. Sometimes, PCA was also applied on LCIA results with technical indicators to reveal the relationships between those indicators [START_REF] Basson | An integrated approach for the consideration of uncertainty in decision making supported by Life Cycle Assessment[END_REF][START_REF] Bava | How can farming intensification affect the environmental impact of milk production?[END_REF][START_REF] Chen | Environmental assessment of trout farming in France by life cycle assessment : using bootstrapped principal component analysis to better de fi ne system classi fi cation[END_REF][START_REF] De Saxcé | Assessment and improvement of the appropriateness of an LCI data set on a system level -Application to textile manufacturing[END_REF] . [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF] applied PCA over a large range of products and LCIA methods (all the LCIA results of 135 impact categories for 976 products provided by ecoinvent) to select impact categories. In order to deal with impact category units and the wide orders of magnitude of LCIA results due to the high diversity of reference flows , they proposed to apply a product ranking. An alternative approach was a log-transformation on LCIA results prior to using a multi-linear regression [START_REF] Steinmann | Resource Footprints are Good Proxies of Environmental Damage[END_REF]. As comment to this last article, Heijungs (2017) noticed that the reference flow values of the studied LCIA results affect the outcomes of their work. He suggested standardizing the LCIA results by their energy footprint to be free of the default reference flow. This emphasizes the need to address data heterogeneity.

Other studies that apply multivariate statistical analysis or multi -linear regression on LCIA results of products from ecoinvent focus on revealing correlation or alleged redundancies between impact categories [START_REF] Huijbregts | Is Cumulative Fossil Energy Demand a Useful Indicator for the Environmental Performance of Products[END_REF]Pascual-González et al., 2016[START_REF] Guinée | Selection of Impact Categories and Classification of LCI Results to Impact Categories[END_REF][START_REF] Steinmann | Resource Footprints are Good Proxies of Environmental Damage[END_REF]. The objectives of these studies were to predict LCIA results from a reduced number of proxy impact categories. All these approaches work on the impact category results alone, and do not consider LCI information and its translation to impact categories.

By translating the elementary flows in terms of impact categories, LCIA can be considered to be a dimension reduction technique: LCIs are described by LCI results with more than a thousand variables (elementary flows) while LCIA results are a much smaller number of environmental indicators. The remaining dimensions, which all have an environmental meaning, may not all be necessary for dealing with the main environmental issues of the studied product. As the environment is disturbed and even damaged by such diverse substance emissions or resource utilizations from different human activities, all impact categories should be covered, but some of them may not be essential for the conclusion of one particular product, for instance, because they are strongly correlated with other impact categories.

The Representativeness Index (RI) was recently proposed by [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF] to provide a relative measure of the discriminating power of LCIA methods. The RI is meant to explore the relative relevance of each impact category belonging to a LCIA method for a specific product. It does not assess the relevance of the environmental model behind impact categories of the LCIA methods, but it is an aid to LCA practitioners, so they might focus on a reduced number of impact categories that best represent the elementary flows associated with a particular product. Moreover, by studying the links between the RI of an entire LCIA method and the RIs of its constituent impact categories, some issues have been raised on the correlation of the representativeness of impact categories [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF].

The aim of this paper is to further develop the potential benefits of the RI methodology and to discuss representativeness issues regarding non-orthogonal (i.e. dependent) impact categories, and ways to solve such issues. We also developed an operational tool to calculate RIs as a downloadable Python package from an open access deposit.

The present paper is organized as follows: in Section 2, the standardiz ation of the vector space where the LCA study takes place and the proximity relationship between an LCI vector and LCIA method subspaces (or impact category vectors) is briefly revisited as it is the same framework as that explained in [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF]. The algorithm of orthogonalization of impact categories to avoid redundancy issues within a LCIA method is presented. The approach is illustrated and discussed in Section 3 on the ILCD method for two products results from the cumulated ecoinvent database [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF]. Main tendencies of RI results over the cumulated LCI database are then explored. The main representative dimensions that support most of the RI values are then determined. Finally, results from the decorrelation algorithm are analysed over the entire cumulated LCI database.

Material and method

3.2.1. RI methodology

Standardization and definition of an inner product

As proposed by several authors [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF][START_REF] Heijungs | The Computational Structure of Life Cycle Assessment[END_REF][START_REF] Téno | Visual data analysis and decision support methods for nondeterministic LCA[END_REF] the vector space where the LCA framework takes place is generated by a basis that represents the n elementary flows that are included in the study. The result of the LCI phase, for the 𝑖 th product, can be described as a vector 𝐠 𝑖 (see Figure 18. a.). However, each component 𝑥 of such an LCI result vector, so the elementary flows 𝑔 𝑥,𝑖 that form 𝐠 𝑖 , has its own accounting unit (e.g. kilogram, Becquerel, joule...), and within this vector space, no consistent inner product (which induces a norm) can be defined [START_REF] Heijungs | The Computational Structure of Life Cycle Assessment[END_REF]. In this perspective, it is useful to recall that the vector spaces that are usual ly employed in the engineering disciplines refer to 3-dimensional Euclidean space, in which vectors have a magnitude and a direction, and concepts such as angle and distance make sense. In non-metric vector spaces, vectors are more abstractly considered to be 𝑛-tuples, for which such concepts are not defined [START_REF] Gentle | Matrix Algebra[END_REF]. In order to be able to measure distances or angles between vectors, we here extend the studied vector space with an inner product after a standardization step.

Among the diversity of possible standardizations (min-max, z-score…), the geometric mean of each elementary flow over all products is used in the present work for two reasons. First, the geometric mean is robust to extreme values. Secondly and more importantly, this choice allows our approach being free of the reference flow values of LCI results (i.e. the issue emphased by [START_REF] Heijungs | Comment on "Resource Footprints are Good Proxies of Environmental Damage[END_REF] about [START_REF] Steinmann | Resource Footprints are Good Proxies of Environmental Damage[END_REF] approach; see the section 2.1.2. and Annex B -1 for details). Defining 𝐺x as the geometric mean of the 𝑥 th elementary flow, so

𝐺 𝑥 = exp ( 1 𝑚 ∑ ln|𝑔 𝑥,𝑖 | 𝑚 𝑖=1 ) (1)
he 𝑥 th standardized elementary flows 𝐠 ̃𝑥,𝑖 of the 𝑖 th LCI result is:

𝑔 ̃𝑥,𝑖 = 𝑔 𝑥,𝑖 𝐺 𝑥 (2)
Note that we used the absolute value in equation 1 to allow for cases where the values are negative.

Within this standardized vector space and given two LCI result vectors 𝐠 ̃1 and 𝐠 ̃2, we can define the inner product of these vectors as:

〈𝐠 ̃1, 𝐠 ̃𝟐〉 = ∑ 𝑔 ̃𝑥,1 𝑔 ̃𝑥,2 𝑛 𝑥=1 (3)
Next, we define the norm or Euclidean length of a vector 𝐠 ̃𝑖 as

‖𝐠 ̃𝑖‖ = √〈𝐠 ̃𝑖, 𝐠 ̃𝑖〉 (4)
Finally, this allows us to define the angle 𝛼 between two LCI vectors, say, 𝐠 ̃1 and 𝐠 ̃2, indicated by 𝛼 1,2 , as

𝛼 1,2 = arccos ( 〈𝐠 ̃1, 𝐠 ̃2〉 ‖𝐠 ̃1‖‖𝐠 ̃2‖ ) (5)
Within the standardized vector space, the LCI result of each product has then its own vector direction and norm (see Figure 18.a.).

The norm of a standardized LCI result vector still depends on the magnitude of the reference flow of the product, while the direction of the vector doesn't. This justifies the proposed definition based on the angle between vectors (see part 2.1.2).

Regarding impact categories, the consequences of unit amounts of the different elementary flows are summarised by their characterization factors (CFs), the numbers 𝑞 𝑥,𝑗 . CFs are conversion factors used to assess the elementary flows in terms of impact category results. The collection of CFs of one impact category therefore defines a vector within the elementary flow vector space (according to the Fréchet -Riesz theorem, see [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF] section 2.1.2). Figure 1.a. illustrates this for two impact categories, where the vector of CFs is denoted as 𝐪 ̃1 and 𝐪 ̃2, after standardization (see below).

Because we work with standardized elementary flows, the CFs should be standardized as well to maintain unit consistency:

𝑞 ̃𝑥,𝑗 = 𝑞 𝑥,𝑗 𝐺 𝑥 (6)
In this way, by standardizing the impact categories, we can depict the vectors 𝐪 ̃𝑗 into the same standardized vector space. It reveals the main dimensions that contribute to each of the modelled environmental issues.

The LCIA step of the LCA framework translates the LCI result 𝐠 𝑖 into a quantified LCIA result ℎ 𝑗,𝑖 . The scalar ℎ 𝑗,𝑖 is the amount of impacts on the 𝑗 th impact category for the 𝑖 th product using a linear transformation:

ℎ 𝑗,𝑖 = ∑ 𝑞 𝑥,𝑗 𝑔 𝑥,𝑖 𝑛 𝑥=1 (7)
The LCIA result of a standardized LCI result vector 𝐠 ̃𝑖 with a standardized impact category 𝐪 ̃𝑗 equals to the previous LCIA result ℎ 𝑗,𝑖 of the unstandardized vectors:

ℎ ̃𝑗,𝑖 = 〈𝐪 ̃𝑗, 𝐠 ̃𝒊〉 = ∑ 𝑞 𝑥,𝑗 𝐺 𝑥 𝑔 𝑥,𝑖 𝐺 𝑥 𝑛 𝑥=1 = ℎ 𝑗,𝑖 (8)
We extend the definition of the inner product of two standardized LCI vectors, say, 〈𝐠 ̃1, 𝐠 ̃2〉 to the inner product of two standardized impact categories, say, 〈𝐪 ̃1, 𝐪 ̃2〉, and to the inner product of a standardized LCI vector and a standardized impact category 〈𝐪 ̃𝑗, 𝐠 ̃𝑖〉 (previously used in equation 8 for the definition of the LCIA result ℎ ̃𝑗,𝑖 ). This also allows us to define the norm of an impact category, ‖𝐪 ̃𝑗‖, the angle between two impact categories, 𝛽, and the angle (𝛾 𝑗,𝑖 ) between an LCI vector 𝐠 ̃𝑖 and an impact category vector, 𝐪 ̃𝑗. This finally allows us to define the representativeness index RI between an LCI vector and an impact category, as discussed in the next section.

RI between a LCI result and an impact category

Within a standardized vector space, the representativeness index (RI) proposed by [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF] is a measure between a standardized LCI result (𝐠 ̃𝑖) vector and an impact category vector (𝐪 ̃𝑗). In order to be free of the norm of the different vectors, it is based on the angle 𝛾 𝑗,𝑖 between an LCI result vector and an impact category vector. The RI of an LCI result 𝐠 ̃𝑖 for the impact category 𝐪 ̃𝑗 is:

𝑅𝐼 𝑗,𝑖 = 𝑅𝐼(𝐪 ̃𝑗, 𝐠 ̃𝑖) = |cos(𝛾 𝑗,𝑖 )| = | 〈𝐪 ̃𝑗, 𝐠 ̃𝑖〉 ‖𝐪 ̃𝑗‖‖𝐠 ̃𝑖‖ | = | 𝐡 𝑗,𝑖 ‖𝐪 ̃𝑗‖‖𝐠 ̃𝑖‖ | (9)
The higher the values of the RI, the better the impact category represents the main dimensions of the LCI result vector (i.e. the direction), relatively to the cumulated LCI database. Within the standardized vector space, the representativeness index can then be interpreted as a measure of similarity between the standardized LCI result vector and the standardized impact category vector.

RI between a LCI result and a LCIA method

In addition to the RI between an LCI result and an impact category, we define the RI between an LCI result and an entire LCIA method consisting of a collection of impact categories. An LCIA method can be regarded as a sub-space of the standardized vector generated by the impact categories. The LCIA method is written as a matrix 𝐐, consisting of the 𝑝 different impact categories that belong to that method:

𝐐 = ( 𝐪 1 ⋯ 𝐪 𝑝) (10)
Because we decided to work in standardized space, we effectively work with

𝐐 ̃= (𝐪 ̃1 ⋯ 𝐪 ̃𝑝) (11)
The RI of the entire LCIA method is then defined, for LCI result 𝐠 𝑖 , as

𝑅𝐼 𝑖 = 𝑅𝐼(𝐐 ̃, 𝐠 ̃𝑖) = √∑(𝑅𝐼(𝐪 ̃j, 𝐠 ̃𝑖)) 2 𝑝 𝑗=1 (12)

Correlation and decorrelation

The impact category vectors of the LCIA method are in general not orthogonal, that is, the angle 𝛽 between some of the (standardized) impact category vectors is not 90 degrees.

This also implies that for an LCIA method, subsets of non-orthogonal impact category vectors can be observed for which the impact category vectors are correlated with each other. The effect of this is an over-or under-representation of the LCI result vector by those impact category vectors. It relies on the fact that RIs of the non -orthogonal impact category vectors for the LCI result vector will assess and represent the LCI res ult vector through the same main elementary flows. Indeed, the main direction of a LCI result vector can be close to the main direction of two (or more) non-orthogonal impact category vectors, which lead to an over-representation, or at the opposite, both impact category vectors miss this main direction even if their characterization factors are not null on the main dimensions of the LCI result vector, which then lead to an under -representation. At the LCIA method level, this over or under-representation can be solved by an orthogonalization procedure of the impact category vectors 𝐪 ̃𝑗 [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF]. This procedure is based on the well-known Gram-Schmidt process [START_REF] Arfken | Mathematical Methods for Physicists[END_REF]. The Gram-Schmidt process returns a new set of standardized perpendicular vectors, which will be denoted here as 𝐪 ̃𝑗 ⊥ (see Figure 18.b.). Similar to equation 11, we can pack these vectors for the entire LCIA method in one matrix, 𝐐 ̃⊥. Using the angle 𝛾 𝑗,𝑖 ⊥ between an LCI result vector 𝐠 ̃𝑖 and an orthogonalized impact category vector 𝐪 ̃𝑗 ⊥ , this in turn can serve to calculate a new RI of a LCIA method, similar to equations 9 and 12:

𝑅𝐼 𝑗,𝑖 ⊥ = 𝑅𝐼(𝐪 ̃𝑗 ⊥ , 𝐠 ̃𝑖) = |cos(𝛾 𝑗,𝑖 ⊥ )| (13)
and

𝑅𝐼 𝑖 ⊥ = 𝑅𝐼(𝐐 ̃⊥, 𝐠 ̃𝑖) = √∑(𝑅𝐼 𝑗,𝑖 ⊥ ) 2 𝑝 𝑗=1 (14)
The procedure that is proposed to take into account the over or under-representation for the RIs of impact category belonging to the same LCIA method is schematized in Figure 19. The upper part describes the steps that are needed to obtain 𝑅𝐼 𝑖 and 𝑅𝐼 𝑖 ⊥ that are needed to take out the consequences of the correlations between impact category vectors.

The lower part describes the iterative loop developed in section 2.1.5. that is needed to solve the consequences triggered by the order dependency of the impact category that is inherent in the Gram-Schmidt process.

The Gram-Schmidt process allows obtaining a set of orthogonal impact category vectors from one LCIA method and thus allows determining its 𝑅𝐼 𝑖 ⊥ . But the order of processing the different 𝐪 ̃𝑗 vectors in 𝐐 ̃ determines the RIs of the standardized and orthogonalized vectors. With the Gram-Schmidt iterative process, the first treated vector is not modified (and its RIs will not be different between 𝐪 ̃1 and 𝐪 ̃1 ⊥ ) while the next vectors are orthogonalized paying regard to the previously handled vectors (and there will be differences between the RIs of 𝐪 ̃𝑗 and 𝐪 ̃𝑗 ⊥ (for 𝑗 = 2, … , 𝑝)). Because of that, the orthogonalized impact category vectors that result from the Gram-Schmidt process cannot be directly used to look at the RIs of 𝐠 ̃𝑖 for uncorrelated impacts due to this order dependency.

To solve the problem of order-dependency we define a unique order of treatment of the impact categories. Instead of applying Gram-Schmidt to the usual order 𝑗 = 1, … , 𝑝, we first sort the impact category vectors, and apply the Gram-Schmidt process to the vectors arranged in that new order. This order is determined by using the correlation matrix of the impact category vectors belonging to 𝐐 ̃ (see Figure 19). This makes sense because the correlation coefficient of two vectors is equivalent to the cosine of the angle between these vectors [START_REF] Gniazdowski | Geometric interpretation of a correlation[END_REF], which in turn is equal to the RI as defined above. For each impact category, the sum of the squares of all its correlation coefficients (𝑆𝑆𝑅) is calculated:

𝑆𝑆𝑅 𝑗 = ∑ (𝑟(𝐪 ̃𝑗, 𝐪 ̃𝑙)) 2 𝑝 𝑙=1 (15)
This includes the trivial case 𝑙 = 𝑗, for which 𝑟 = 1, but because it doesn't affect the ranking we can leave it in. The order of impact categories is determined by ranking these sums 𝑆𝑆𝑅 𝑗 in descending order. The first impact category to be processed is then the one which has the highest 𝑆𝑆𝑅, and the maximal correlation with the other impact categories.

The over-or under-representation of an LCI result vector by a set of impact category vectors corresponds to the difference between the RIs measured by the non -orthogonal impact categories and the RIs measured by the orthogonalized impact categories. Based on the determination of those differences, a decorrelation algorithm is proposed in the next section. This algorithm allows distributing the over-or under-representation between the non-orthogonal impact categories (iteration loop in Figure 19). From the 𝑅𝐼 𝑗,𝑖 ⊥ determined for a LCIA method after the Gram-Schmidt process, the over-or under-representation need to be quantified and distributed over the subset of nonorthogonal impact categories. For the LCI vector 𝐠 ̃𝑖 and the impact category 𝐪 ̃𝑗, the RI of the orthogonalized impacts (𝑅𝐼 𝑗,𝑖 ⊥ ) is compared to the original one (𝑅𝐼 j,i ). Their distance 𝑑 𝑗,𝑖 (as defined in equation 14) is interpreted as the over-or under-representation of 𝐠 ̃𝑖 expressed by the impact category 𝑗 and that is redundant or missing regarding the categories that have been previously processed given the order of the impact categories used in the Gram-Schmidt process:

𝑑 𝑗,𝑖 = √ (𝑅𝐼 𝑗,𝑖 ) 2 -(𝑅𝐼 𝑗,𝑖 ⊥ ) 2 (16)
The over-or under-representation 𝑑 𝑗,𝑖 of the impact category 𝐪 ̃𝑗 has to be distributed over the other non-orthogonal impact categories. For this purpose, each 𝑑 𝑗,𝑖 is treated iteratively with the same order that is used for impact categories in the Gram -Schmidt process. Let Θ 𝑗 be the subset of the category vectors 𝐪 ̃𝑡 that are correlated to 𝐪 ̃𝑗, Θ 𝑗 = {𝐪 ̃𝑡|𝑡 ∈ {1, … , 𝑝}, 𝑟(𝐪 ̃𝑡, 𝐪 ̃𝑗) ≠ 0}. 𝑅𝐼 𝑡,𝑖,𝑗 is the RIs modified by the decorrelation process of the LCI result vector 𝐠 ̃𝑖 for the impact category 𝐪 ̃𝑡 during the 𝑗 th iteration. For the first impact category treated 𝑑 1,𝑖 = 0 (𝑅𝐼 1,𝑖 ⊥ is equal to 𝑅𝐼 1,𝑖 because 𝐪 ̃1 is not modified by the Gram-Schmidt process, so 𝐪 ̃1 ⊥ = 𝐪 ̃1). Consequently, the results 𝑅𝐼 𝑡,𝑖,1 of 𝐠 ̃𝑖 for these categories 𝐪 ̃𝑡 are the original RIs that are obtained from equation 9:

𝑅𝐼 𝑡,𝑖,1 = 𝑅𝐼 𝑡,𝑖 (17)
Let 𝑆 𝑖 = ∑ (𝑅𝐼 𝑡,𝑖,1 ) 2 𝑝 𝑡=1 the sum of the squares of 𝑅𝐼 𝑡,𝑖,1 . For the following iterations (𝑗 = 2, … , 𝑝), all the 𝑅𝐼 𝑡,𝑖,𝑗 will share the over or under-representation measured by 𝑑 𝑗,𝑖 :

𝑅𝐼 𝑡,𝑖,𝑗 = √ (𝑅𝐼 𝑡,𝑖,𝑗-1 ) 2 -(𝑑 𝑗,𝑖 ) 2 × (𝑅𝐼 𝑡,𝑖,1 ) 2 𝑆 𝑖 (18)
At the end of the iteration procedure, all the resulting decorrelated RIs, 𝑅𝐼 𝑗,𝑖 decorr = 𝑅𝐼 𝑡,𝑖,𝑝 , of 𝐠 ̃𝑖 for the impact category vectors of an LCIA method obtained through this algorithm are free from the consequences of the order of the impact category used within the Gram-Schmidt process.

Material

The methodology is applied to the cumulated LCI result version of the ecoinvent 3.1 "allocation at the point of substitution" database [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF]. This version of the cumulated LCI database was released in 2014. It comprises 11,206 LCI result vectors that are described through 1,727 elementary flows (the intervention matrix). The elementary flows vector space therefore has 1,727 dimensions. Compared to [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF], the same matrix was used although certain elementary flows and LCI results were removed from the cumulated LCI database. Indeed, considering that the analysis is applied to LCI results, the 70 LCI results that have only less than 30 referenced elementary flows are set aside. 142 elementary flows were also not taken into account due to the low number of LCI results that take value on them.

The ILCD V1.05 (EC-JRC, 2010a) is the studied LCIA method. It was extracted from the SimaPro 8.1.1.16 software to analyse the most recent and operational version. The CF nomenclature was transferred from the SimaPro nomenclature to the ecoinvent elementary flows nomenclature with the assistance of the ecoinvent centre.

Implementation was conducted with Python 2.7 on a Jupyter Note -book [START_REF] Perez | IPython: A System for Interactive Scientific Computing[END_REF] (formerly IPython Notebook) and using numerical computation libraries SciPy (V 0.16.0), Pandas (V 0.17.1) and Matplotlib (V 1.5.0). Python is an open -source programming language which is increasingly used in data sciences and in LCA framework as in Brightway2 [START_REF] Mutel | Brightway: An open source framework for Life Cycle Assessment[END_REF]).

An operational tool written with Python 3.6 was also developed. It is available from an online deposit hosted on github.com with the DOI: 10.5281/zenodo.1068914. The package allows to apply the methodology on LCI result excel files (system process) exported from SimaPro and modelled within the ecoinvent 3.1 "allocation at the point of substitution" database (further development needs to be done to apply the methodology to other cumulated LCI databases and to cumulated LCI result files exported from other software). Three outputs can be obtained per LCI result: RIs of LCIA methods, RIs of their impact category vectors and RIs of decorrelated categories. Almost all the multi -criteria LCIA methods can be analysed. Standardization is applied with geometric means of elementary flows after a nomenclature translation from ecoinvent to SimaPro.

Based on the studied cumulated LCI ecoinvent database, the LCI results of the Chinese and the German electricity production mixes serve as an illustrative example of the presented work. The two LCI results refer to the market production of 1 kWh of high voltage electricity. The market version of these LCI results models the elementary flows of electricity production mixes, transmission networks and electricity losses during transmission.

Results and discussion

3.3.1. Illustrative example 3.3.1.1. LCIA results analysis with respect to RIs A comparison of LCIA results from the Chinese and the German electricity mixes points to a number of noteworthy elements evidenced by the impact categories RI results (see Figure 20). The upper bar-chart typically illustrates the results of a comparative LCA study, the lower chart represents the outputs of the python package (see data in Annex B -6). For the German mix, ten impact category results are higher than for the Chinese mix, out of the sixteen impact categories of the ILCD method. Germany is two -fold higher for 9 categories: Ozone depletion, Toxicities (cancer and non-cancer effects), Ionizing radiations (human health and ecosystems), Freshwater eutrophication, Ecotoxicity and both Resource depletions. The German mix also uses a higher proportion of land area, but the gap is smaller (China is only 21% lower than Germany on this impact category). Contrasting LCIA results are observed for particulate matter, photochemical ozone formation, acidification and terrestrial eutrophication where China is five times higher than Germany. The same observation can be made for climate change and marine eutrophication but with a lower difference (compared to China, German impacts are lower by 41% and 63% respectively).

The global RIs of the ILCD method are 0.113 for the Chinese and 0.0285 for the German mix. The Chinese mix has a better overall representation with this LCIA method because its RI of method is higher. Using impact category RIs from Figure 20, this high overall RI of the method comes from high impact category RI results on particulate matter, acidification, photochemical ozone formation, climate change and terrestrial eutrophication (in decreasing order of contribution). During interpretation, the focus must, in priority, be put on this reduced set of impact category vectors.

The main representative impact categories for the German mix are ionizing radiation (HH), freshwater eutrophication, climate change, water resource depletion and human toxicity (non-cancer effect). The RIs of these LCIA results are two to three times higher for these impact categories (see Figure 20) and they should be looked at first and foremost for the result interpretation.

The environmental issues highlighted for this comparative LCA study are not the same for both LCI results. Given the contextualization of LCI results and impact categories from the cumulated LCI database, the use of 𝑅𝐼 𝑗,𝑖 and 𝑅𝐼 𝑗,𝑖 ⊥ guides the LCA practitioner in the interpretation of the main representative impact categories for each LCI result.

Example of decorrelation on two LCI results

Results from the decorrelation of impact category RI results obtained for the two previously studied LCI results are presented in the Figure 20. Using the 𝑅𝐼 𝑗,𝑖 , the equation 12 results in 0.137 and 0.0293, respectively for the Chinese and the German mixes, while the overall RIs of the ILCD method are 0.113 and 0.0285 (see above). These differences show the dependences between the impact category vectors, which are removed by the presented algorithm.

Six impact category RIs are particularly affected by decorrelation ( see Figure 20). The algorithm lowers the representativness index of the Chinese mix for the particulate matter, acidification, photochemical ozone formation, and terrestrial eutrophication categories.

The climate change and marine eutrophication categories are affected to a lesser extent.

The decorrelation of the German mix RIs does not affect its representativeness index on any particular impact category. Orthogonalized results do not modify the previous interpretations.

Global trends of impact category RIs over the cumulated LCI database

The ordered distribution of the impact category RIs of the entire cumulated LCI database indicates that their values rapidly decrease below 0.1, reaching 10 -2 to 10 -5 (see Figure 21). These low values result from the high-dimensional vector space in which the study takes place. The ranges of impact category RI values are globally similar when the different impact categories are compared. In an analogous manner, these impact categories represent the different LCI results of the cumulated database, in terms of quantity of information. They all seem relevant for a large number of LCI results. However, all impact categories are probably not compulsory for the analysis of a single LCI result, as observed in the previous illustrative example. Considering a given LCI result and a single impact category, Annex B -3 illustrates how the impact category RI result relies on the best compromise between elementary flows and CFs. This value is highly driven by one dimension (elementary flow or CF), which is, most of the time, the one with the highest CF of the impact category (see Annex B -8 and 9). These high standardized CFs are the environmentally critical dimensions of the database for the studied impact categories. According to the resulting LCI result patterns (see Annex B -2), most of the main elementary flows are probably not involved in the RI value: i.e., they do not correspond to these high standardized CFs. These high CFs point to the dimensions and support most of the RI values. However, only one dimension per category cannot explain all of the RI values and, depending on each LCI result, a combination of dimensions (high elementary flow or high CF) is obviously essential (see Annex B -3).

For 11 206 ecoinvent LCI results, their representative dimensions, the dimensions which provide 95% of their RI values, were determined (see Annex B -9). A combination reaching a maximum of 10 dimensions is obtained for land use: a combination of 10 or less dimensions provides 95% of all the RI values ( Finally, the RI values per number of dimensions per combination were investigated.

Results for the Climate change category are presented in Figure 22 (similar figures are presented in Annex B -4 for the other impact categories). As previously observed in Table 1 (column 1), 7 dimensions is the maximal amount of representative dimensions per combination. A slight decrease in RI values is observed when the number of required dimensions increases for this impact category (this is also observed for almost all impact categories).

Most of the LCI results that only require one dimension to reach 95% of their RI present a high RI value. These LCI results have a very high intensity for the same dimension that drives the impact category vector. When more dimensions are required within 95% of the value, the RI values decrease. Using Annex B -9, the same representative dimensions that are generally found to be involved (due to high CFs) although LCI results have a lower intensity for these dimensions.

These analyses reveal that only a few dimensions out of the entire cumulated LCI database provide values for a large part of the RIs. They are the most critical and representative dimensions through which the modelled human activities in ecoinvent impact most of the time on the environmental issues of the ILCD. The high RIs reveal the LCI results that have high standardized elementary flow values on these critical dimensions. The lower RIs therefore provide insights on the elementary flow values of the LCI results on these critical dimensions.

3.3.4. Decorrelation of impact category RIs within a LCIA method 3.3.4.1. Correlation matrix of impact categories Table 2 presents the correlation matrix of the impact categories (after standardization).

Based on their correlation, five different subsets of intercorrelated categories (i.e. Θ 𝑗 ) are labelled from A to E and described in Table 3. Some impact categories feature in two subsets.

0 0 0 0 1.2e-3 0 0 0 0 0 MEP 0 0 0 0 0 1 4.4e-1 1.5e-1 1.2e-2 4.3e-1 0 0 0 0 0 TEP 0 0 0 0 0 4.4e-1 1 3.
4e-1 2.7e-2 9.7e-1 0 0 0 0 0 AP 0 0 0 0 0 1.5e-1 3.5e-1 1 3.3e-1 4.5e-1 0 0 0 0 0 PMP 0 0 0 0 0 1.2e-2 2.7e-2 3.3e-1 1 6.7e-2 0 0 0 0 0 POFP 4.0e-9 1.4e-8 2.6e-7 6.2e-11 1.2e-3 4.3e-1 9.7e-1 4.5e-1 6.7e-2 1 0 0 0 0 0 The Photochemical ozone formation (within subset C) has a particular position because it correlates with the two subsets A and B which do not have any elementary flows in common. This category is the one with the highest SSR (eq. 15) and is therefore the first one to be processed by the algorithm. Consequently, the orthogonalization of one subset A or B does not affect the orthogonalized RI of the other subsets through Photochemical ozone formation relationships. However, the Photochemical ozone formation is affected by both subset A and B.

IRE 0 0 0 0 0 0 0 0 0 0 1 5.7e-1 0 0 0 IRHH 0 0 0 0 0 0 0 0 0 0 5.7e-1 1 0 0 0 MFRDP 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 WRDP 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 LU 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 FWEP 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The two ionizing radiation impact categories (subset D) are only correlated with each other. Impact categories that do not correlate with any other are gathered in subset E.

The correlation coefficients point out that subsets B and D present very high correlations (between 1.17 × 10 -2 and 4.44 × 10 -1 ) in comparison to subset A (from 1.40 × 10 -13 to 5.32 × 10 -1 ). The Photochemical ozone formation potential also presents higher correlation coefficients with subset B (up to 9.66 × 10 -1 ) than with subset A (up to 1.24 × 10 -3 ). The nitrogen oxide dimensions dominate the CFs on subset B. This observation is critical for the Photochemical ozone formation category (see Annex B -8).

Excepting for the high chromium VI and Zinc CFs that relate both human toxicities and freshwater ecotoxicity impact categories, the dimensions on which the correlations of the subset A are based do not correspond to the dimensions associated with major CFs for these impact categories. This can explain the low correlation indexes within this subset.

Consequences of decorrelation over the cumulated LCI database

Orthogonalized impact category RI values are obtained by applying the algorithm to all 11206 ecoinvent LCI results. To determine the global trends of the redistribution of the representativeness of impact categories for all LCI results, the distribution of the ratio Results imply that the major part of the redistribution slightly decreases the RI values from 𝑅𝐼 𝑗,𝑖 to 𝑅𝐼 𝑗,𝑖 decorr (between 0 and 20%). Obviously, impact categories that do not correlate with any other impact category do not show any change (subset E). For subsets A, B and C, a decrease is the main tendency but high increases are observed for some inventories, with a 95% percentiles up to 80% (reaching 300% for extreme values). High values are correlated between the impact categories of these 3 subsets (see SI.A.2). However, for the major part of the impact category RIs (negative modifications down to 20%), the correlation appears to be less obvious. Nevertheless, the modifications remain low for each subset. The wide RI redistribution of the photochemical ozone formation (first impact category treated by the algorithm) is triggered by the orthogonalization from the other two subsets that form another "profile" on Figure 23.

As for subset D, the distribution of the modifications in impact category RI is very restricted. This could be explained by the fact that only two impact categories belong to this subset. No correlation of the redistribution with the other subsets is observed (see Annex B -5).

The increase of RI values for 𝑅𝐼 𝑗,𝑖 decorr is triggered by the high 𝑅𝐼 𝑗,𝑖 ⊥ which is observed for several subsets. A LCI result with an high value on an elementary flow, which is not associated to a high CF of any impact categories, can be highlighted by the orthogonalization step and thus lead to an increase in the RI value. The orthogonalization of the impact category redirects the vector towards a secondary elementary flow (see Figure 18.b). When LCI results have a high value on this second elementary flow, their 𝑅𝐼 𝑗,𝑖 ⊥ tend to increase compared to 𝑅𝐼 𝑗,𝑖 . Most of the LCI results characterized by higher 𝑅𝐼 𝑗,𝑖 ⊥ originate from agricultural production.

Dimensions such as NMVOC (non-methane volatile organic compounds), ammonia, nitrate or ethene seem to represent the main secondary dimensions that trigger the increase of RIs for the A, B and C subsets when the CFs from the orthogonalized impact categories are analysed. Most of the LCI results characterised by RI increases originate from agricultural production. This is mainly related to ammonia and nitrate dimensions. The redistribution of extra information from the secondary dimension should provide the impact categories of the subset with an increase that finally allows their 𝑅𝐼 𝑗,𝑖 decorr to comply with the RI of the LCIA method.

Conclusions

This work completes the RI methodology previously developed [START_REF] Esnouf | Representativeness of environmental impact assessment methods regarding Life Cycle Inventories[END_REF] by focusing on the appropriateness of impact categories. We propose a freely downloadable operational tool for RI calculation and have applied this methodology to an illustrative example. The impact category RIs have proven that interpretations of LCIA results can be deepened. They can assist practitioners by orientating their analysis towards relevant impact categories. Analyses were also carried out over all LCI results of the cumulated LCI database to extract global RI trends. The same approach could also be used for other ecoinvent versions, cumulated LCI databases or specific fields of activity. Moreover, the cumulated LCI database trends were used here to standardize the impact categories. Other types of standardization, for example, based on the global elementary flows of a geographical area or economic sector, could relate the RI methodology. Finally, a focus on the standardized elementary flows that provide the value of the impact category RIs for each LCI result could be interesting to trace the main directions that are linked to each impact category.

An algorithm proposing a solution for correlation issues was developed and implemented within the operational tool. Redundant information was spread out according to the original impact category RI. Further work could focus on other types of algorithms where the whole impact category subset would not be affected by the modification of RIs. Only the impact categories with elementary flows affected by orthogonalization would be affected. Based on the RI methodology and taking into account the consistency of impact categories, relevant impact categories could also derive from different LCIA methods, thus enabling the development of composite LCIA methods.

Chapter 4: Representativeness of impact categories in LCA according to fields of activity In this chapter, we explore if the RI methodology puts forward distinct LCIA methods and environmental issues while analysing relatively homogeneous datasets based on subtypes of products and activities. Analysis of RIs of all impact categories from classic LCIA methods shows interesting trends that could lead to provide guidelines for LCA practitioners regarding the 14 studied fields of activity.

To avoid redundancy in the thesis between chapters, this chapter is not fully formatted as a publishable article. Reminders on context and method will be added so that the article can be read independently.

Introduction

Life Cycle Assessment (LCA) is an interesting approach to assess and compare all the potential environmental impacts of human activities (ISO, 2006a(ISO, , 2006b)). The elementary flows linked to the different productions of products or services constitute Life Cycle Inventories (LCI) result. LCI results are then translated in term of environmental impact through the Life Cycle Impact Assessment (LCIA). However, a large number of LCIA methods has been developed over the past decades and offer a wide choice of environmental indicators [START_REF] Hauschild | Identifying best existing practice for characterization modeling in life cycle impact assessment[END_REF]. Each of them has its own specificities, characterization models, spatial and time scales [START_REF] Owsianiak | IMPACT 2002+, ReCiPe 2008 and ILCD's recommended practice for characterization modelling in life cycle impact assessment: a case study-based comparison[END_REF] which can puzzle LCA practitioners when a LCIA method and its impact categories have to be chosen during the goal and scope definition phase of their studies.

LCI results databases as ecoinvent 3.1 [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF] However, these works focus on the LCIA results and do not handle the LCI result vector space. The Representativeness Index (RI) presented in Chapter 2 assesses the appropriateness of a LCIA method and each of its impact categories for any given LCI result. For a studied LCI result, the RI measurement relies on the contextualization of the LCI result (see Chapter 3) and the impact categories and (at the elementary flow and the characterization factor level) in regard of its database from which the studied LCI result is modelled. The angular proximity between a LCI result and the impact categories is the measure of relevance of the impact category (see Chapter 2 and 3).

The previous chapters provide RI results for specific case studies using four and two LCI results. This chapter focuses on the RI results by segregating LCI results based on their field of activity. With a systematic approach, we explore if the RI methodology puts forward distinct environmental issues per field of activity. Before the modeling of a LCI result, these results can provide to the LCA practitioner a first estimation of the main representative impact categories associated to the involved processes. It will be on the main dimensions of these categories that the modeling effort will have to be done. Then once the LCI result is modelled and its main representative impact categories obtained, it can bring elements of discussion by comparing the representative impact categories of the studied LCI results and the representative impact categories of the field of activity.

This paper is organized as follows: in Section 4.2, the developed measurement from the RI methodology is briefly reminded and the LCI results grouping procedure per field of activity is presented. In Section 4.3, the results of the global RI of the ILCD method are presented, followed by the analysis of the RI distributions of its 16 impact categories. Finally, RI results between fields of activity are compared with enlarging the analysis to 18 LCIA methods which gather 232 impact categories.

Material and method

RI methodology

The present work takes place within the same formalization of the LCA framework as described in Chapter 2. For each LCI result and regarding the frame of reference of the LCI results database, the RI measurement assesses the intensity of each of its elementary flows and compares this intensity to the critical dimensions of a set of impact cate gories. This assessment allows revealing the representative impact categories (or the representative LCIA methods) regarding a LCI result. In this chapter, we study the same version of the ecoinvent database [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF] [START_REF] Bare | TRACI 2.0: the tool for the reduction and assessment of chemical and other environmental impacts 2.0[END_REF][START_REF] Frischknecht | Swiss Eco-Factors 2013 according to the Ecological Scarcity Method[END_REF][START_REF] Goedkoop | ReCiPe 2008: A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level[END_REF][START_REF] Guinée | Handbook on Life Cycle Assessment[END_REF][START_REF] Hauschild | Spatial differentiation in Life Cycle impact assessment -The EDIP2003 methodology[END_REF][START_REF] Jolliet | IMPACT 2002+: A new life cycle impact assessment methodology[END_REF]NIST, 2007;[START_REF] Steen | A systematic approach to environmental priority strategies in product development (EPS). Version 2000 -General system characteristics[END_REF][START_REF] Steen | Environmental Assessment of Products and Material Systems A systematic approach to environmental priority strategies in product development ( EPS ). Version 2000 -General system characteristics[END_REF]

Fields of activity study

The modelled activities are divided into 14 fields of activity using the International Standard Industrial Classification of All Economic Activities (ISIC) (United Nation, 2008). This classification proposes different level of grouping: section, division, group and class. For example, the activity of wheat grain production is referred to Section A 0111. It belongs to the Section A 'Agriculture, forestry and fishing', division 01 'Crop and animal production, hunting and related service activities', group 011 'Growing of non-perennial crops', and class 0111 'Growing of cereals (except rice), leguminous crops and oil seeds'.

The present study analyses the RI measurement regarding 9,622 LCI results of the ecoinvent database with a referenced ISIC number. Here, the section level of the classification was used (see Table 3). A splitting with the division code was applied when activities gathered by a section were considered too diversified (see Section C and D) and when the generated subgroups were big enough to determine valuable descriptive statistics. Details of the division level belonging to each field of activity are provided in Annex C -1. Subdivisions of Section C "Manufacturing" were needed due to the large range of products covered. These subdivisions were based on the ISIC division level and led to six consistent sets of LCI results (regarding the fields of activity) with enough LCI results each. Section D was split in three to separate the energy carriers (electricity and heat) of the natural gas manufacturing and supply division. The subdivision of Section H led to three subgroups where air and water transports were put aside because of being constituted of only ten LCI results each. Sections not taken into account due to low numbers of LCI (which limit the calculation of descriptive statistics) represent a total of 176 LCI results: manufacture of furniture, air and water transports, telecommunications, real estate activities, architectural and engineering activities, office support activities.

Descriptive statistics are determined on the RI distributions of each field of act ivity regarding the ILCD method and its different impact categories. Fields of activity are analysed through common non-parametric descriptors as median (range of the median is assessed by its order of magnitudes and its width) and inter -quartiles. This allows comparing the representativeness between fields and between impact categories.

Considering medians as a good indicator of the RI distribution over LCIA method and impact category, basic correlation analyses are finally performed between median values of several fields of activity. The median values of other multi -criteria LCIA methods, that represent a total of 232 impact categories, are finally studied (see details in Annex C -2). Impact categories related to the same environmental issue are grouped. For example, all impact categories assessing metal, fossil, abiotic, mineral depletion or energy resources but from different LCIA methods are put together within the environmental issue "Resources and energy use". In line with the main categories proposed in the ILCD documentation (EC-JRC, 2011), 12 groups of environmental issue are then created (see Table 4). The goal is to uncover similitude and difference on the RI results of environmental issues from different LCIA methods. RI distributions show clear distinction and uncover the differentiations of the fields of activity from the database. The medians range from 10 -1 to 10 -3 and with considering the larger of the inter-quartiles (from 7 to 3.35 × 10 2 ), an evaluation of the relative appropriateness of the ILCD method between fields of activity can be possible. Gathering all the studied LCI results, the database ranges in the middle of the ranking as it would have been expected. The impact categories of the ILCD represent well the Machinery and transport equipment (MATE) and, at the opposite, the LCI results of the Agriculture and Forestry (AF) products seem not to be very intensive on the representative dimensions of those impact categories. The inter-quartiles show a relatively high variability between fields. It can reveal the high or low heterogeneity of the LCI results pattern within a field. This value is discussed after when analysing impact category RIs.

As an illustrative example, let us consider an electricity production from anaerobic digester feed with dedicated agricultural productions (the biomass is produced for energetic purpose). This system takes place mainly in the agricultural sector. If it is put in front of an electricity mix, two activity sectors are involved in the comparison. The ranges of RIs highly differ between both sectors, if the electricity one is well represented, agricultural activities are often poorly represented by the ILCD (see Figure 24). Potential advantages of the anaerobic digestion system should be interpreted cautiously because of the potential misrepresentation of this sector: conclusions should consider relevant impact categories for the agricultural sector (see below) in priority.

Distribution of RIs of impact categories per field of activity

Figure 25 presents results of the 16 impact categories for three fields of activity and the whole database: the Agriculture and Forestry (AF), the Electricity Power Generation (EPG) and the Steam and Air Conditioning Supply (SACS). These three fields of activity were chosen because of dissimilar results distributions observed on their global RIs (Figure 24). RIs of impact categories allow uncovering the interesting ones that support the global RIs of the ILCD. Descriptive statistics and figures related to all the other fields of activity are provided in Annex C -4.

Median values range from 10 -3 to 10 -5 for AF. These values are globally higher for the EPG and the SACS fields: ranging from 10 -2 to 10 -3 and from 10 -2 to 10 -4 respectively. The database gets average values from 10 -3 to 10 -4 . As already observed on global RI distributions, studying the ranges of the median values shows clear distinctions between these fields of activity. LCI results related to EPG and SACS are globally better represented by these impact categories than AF. These LCI results are more intensive on dimensions that are also targeted by the impact categories.

The ratio between the minimal and the maximal median values are not similar between fields of activity (also see data in Annex C -4). This ratio is very low for EPG (maximal median being 12 times greater than the minimal), the AF obtain a lager ratio (48 times) which is even greater for SACS (88 times). A high ratio shows that a clear distinction between high and low representative impact categories could be made. Some impact categories are more representative of the intensive elementary flows of the concerned LCI results than others impact categories. This ratio is finally not very contrasted (3.7 times) when analysing the whole database: all the impact categories are relevant for at least some LCI results. Regarding the inter-quartiles, their distributions are quite variable between fields of activity but are similar within each field of activity. SACS has very narrow distributions (maximum of inter-quartiles: 6.8) while AF has very large ones for all impact categories (maximum of inter-quartiles: 564). The variability of inter-quartiles observed on the global RIs of the LCIA method (Figure 24) was similar of these results. A high variability obtained for AF can be interpreted by the fact that the intensities of these LCI results on the critical dimensions are more variable than for SACS. It reveals a high or low heterogeneity on the LCI results patterns within each field of activity. When the interquartiles are large, it might be interesting to study sub-divisions of field separately, assuming that inter-variabilities between sub-parts are larger than intra-variabilities of them. Indeed, the overlapping inter-quartiles can be an issue for the selection of representative impact categories per field and RIs per LCI result might be more relevant to study than studying RI distributions.

Based on the median values, impact category ranking reveal interesting results. Focusing on the first impact categories, this ranking reveals the environmental issues that are most of the time considered as relevant by expert when studying LCI results belonging to the respective fields of activity. The land use, the marine and terrestrial eutrophication and the acidification indicators are put forward for the AF. This gives the key concerns for the electricity from anaerobic digestion system to focus on, in addition to climate change, photochemical ozone formation and acidification, which are targeted by the EPG. For this field, the very low rank of resource depletion can be surprising but it is due to the fact that this ILCD indicator gives higher importance on indium (a critical mineral raw material) and other mineral than on fossil fuels. Within the SACS field, a high number of heat productions from wood resources are actually present. This can explain why the land use ranks first for this field. The intensities of LCI results on CFCs used for cooling productions might also be responsible for the ozone depletion rank. Terrestrial eutrophication and particulate matter are put forward due to emissions related to steam and heat production (nitrogen oxides, particulates, sulfur dioxide). The number of interesting impact categories per field of activity seems to depend on the ratio bet ween the maximal and the minimal median value and the overlapping of inter -quartiles between impact category RIs. As the ratio of extreme medians is small for the whole database while inter-quartiles are very large, the impact category ranking (Figure 25.d.) may not be meaningful and point out that all categories are needed.

Knowing the field of activity of a LCI result, medians and inter-quartiles of RIs determined from the other studied LCIA method might lead to support the selection and provide guidelines toward the 18 LCIA methods and the main impact categories As previously carried out with LCIA methods, relationships between impacts categories regarding different fields of activity are investigated here with correlation analysis on median values of RIs, (see Figure 27). First of all and without considering the environmental issue groups, the correlations of impact categories between fields of activity (low for MATE -AF, Figure 27.a. and high for construction -MATE, Figure 27.d.) are similar to the correlations of LCIA methods. This demonstrates that LCI results

patterns from related fields of activity tend to be similar. On the contrary, two fields that are very distinct lead to a dispersed cloud of points. The localizations itself of the clouds of points are also the same as observed for LCIA methods (high RIs for MATE and low RIs for AF), but impact category RIs get smaller values than global RIs of LCIA method.

Those observations are direct consequences of the links between the value of the global RIs of LCIA method and impact category RIs (see Chapter 3).

Regarding the environmental issue groups, the acidification, the particulate matter, the ozone depletion, the photochemical ozone formation, the climate change and the ionizing radiation groups show very similar behaviors regarding the distributions of their representation of fields of activity. Medians of these groups are very close. It reveals the potential strong correlations of impact categories that model similar environmental issues from different LCIA methods [START_REF] Steinmann | Resource Footprints are Good Proxies of Environmental Damage[END_REF].

The eutrophication group is segregated in two parts (see blue dots in Figure 27.a. and Figure 27.b.). This division is mainly due to the grouping of marine and terrestrial eutrophication (nitrogen as limiting factor for the ecosystem) with freshwater (phosphate as limiting factor) within the same environmental issue group.

The human toxicity group, the eco-toxicity, the land use and the resources energy use groups show much more dispersed median values. The characterization models behind the impact categories grouped by these environmental issues are very different. As a consequence, the standardized impact categories have different environmentally critical dimensions: their vectors point to different dimensions. For example, the critical dimensions of resource and energy use impact categories are very distinct: indium, copper, nickel, chromium, cadmium, crude oil and natural gas. They show a wide dispersion (black dots in

Conclusion

This paper presents an exploration of the representativeness of LCI results grouped by fields of activity regarding LCIA methods and impact categories. Segregation of LCIA methods and impact categories based on RIs of fields of activity can be possible. We show that, for group of LCI results, some indicators are more relevant to study due to a better representation of the LCI results patterns within the group. Land use, eutrophications and acidification are the best representative impact categories for Agriculture and Forestry products while climate change, photochemical ozone formation and acidification are relevant for Electricity Power Generation processes. Similitude of representativeness of impact categories from different LCIA methods was also observed as in other papers.

However, a limitation of this analysis is due to the relatively high inter -quartiles that are sometimes obtained and thus, the localization of impact categories might not only be resumed by the median value. The global distributions are also interesting whi le medians and inter-quartiles avoid overlapping distribution within a field of activity. More homogeneous groups might be sometimes more relevant to obtain stronger conclusions.

Another limitation is the redundancy among products within the ecoinvent data base. Indeed, within a field of activity, some LCI results from different market or area are very similar. The electricity power generation sector is one of the main sectors affected by this issue. The high number of LCIs that model electricity production mix probably heavily pulls the standardization of the database and the impact category in function of their LCI results patterns. RI distributions might be affected by the over -representation of several LCI results. Fields of activity with very distinct LCI results patterns from the main ones (as Agriculture and Forestry) might endure it by obtaining relatively low RIs. [START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF] carried out a more drastic LCI result selection before any pretreatment by using only global market product and by discarding LCIs with high pattern similarity.

This work can finally lead to carry out screening of the representativeness of all the impact categories provided by the different LCIA methods regarding the LCI result being studied by a LCA practitioner. Selection of representative impact categories from different LCIA methods and related to different environmental issues could provide relevant composite LCIA method per field of activities.

Chapter 5: Life Cycle Assessment of a biofuel production from cellulosic macro-algae: key aspects for the environmental concerns This chapter applies the RI methodology on the LCA of the production of biofuel from cellulosic macro-algae. First, an inventory of the system developed within the Green AlgOhol project (ANR-14-CE05-0043) is presented and a contribution analysis is carried out with the ILCD method. Then, RIs of the whole system and sub-part of the values chain are studied for the ILCD method. Finally, a RIs screening of classic LCIA methods and their impact categories is performed. This chapter is not fully formatted as a publishable article to avoid repetitions and will be improved to be read independently.

Introduction

Providing the world in truly sustainable energy is one of the major concerns that our society has to face during the decades to come. Switching from fossil fuel to biofuel is considered as a promising potential alternative. Among feedstock, new biomasses l ike algae receive increasing attention as a potential renewable source for biorefinery to produce materials, chemicals or energy [START_REF] Pandey | Statistical analysis of the ecoinvent database to uncover relationships between life cycle impact assessment metrics[END_REF]. All algae have a potential high biomass yield but compared to microalgae, macro-algae can potentially be cultivated in offshore cultivation systems or in simple open raceway systems, and due to their structure, the biomass concentration is made easier by just being harvested [START_REF] Collet | Recommendations for Life Cycle Assessment of algal fuels[END_REF][START_REF] Collet | Lifecycle assessment of microalgae culture coupled to biogas production[END_REF]. While micro-algae have metabolic storage pathways based on lipids, macroalgae are natural producers of starch and unlignified cellulose [START_REF] Hughes | Biogas from Macroalgae: Is it time to revisit the idea?[END_REF].

New alternatives to conventional energy carrier have to be an improvement from an environmental perspective. Several environmental analysis with Life Cycle Assessment (LCA) were carried out for biofuel productions from macro-algae such as biodiesel [START_REF] Aresta | Utilization of macro -algae for enhanced CO2 fixation and biofuels production: Development of a computing software for an LCA study[END_REF], methane through an anaerobic digestion process [START_REF] Cappelli | Co-digestion of Macroalgae for Biogas Production: An LCA-based Environmental Evaluation[END_REF][START_REF] Langlois | Life cycle assessment of biomethane from offshore-cultivated seaweed[END_REF][START_REF] Pilicka | Life Cycle Assessment of Biogas Production from Marine Macroalgae: a Latvian Scenario[END_REF][START_REF] Seghetta | Seaweed as innovative feedstock for energy and feed -Evaluating the impacts through a Life Cycle Assessment[END_REF] or ethanol through a fermentation process [START_REF] Aitken | Life cycle assessment of macroalgae cultivation and processing for biofuel production[END_REF][START_REF] Alvarado-Morales | Life cycle assessment of biofuel production from brown seaweed in Nordic conditions[END_REF][START_REF] Brockmann | Environmental assessment of bioethanol from onshore grown green seaweed[END_REF]. These studies show the potential of this kind of biomasses for energetic purpose but point out the need of an efficient design of the system face to inputs of the cultivation step (fertilizer, electricity consumption…).

Brown and red seaweeds are already widely used as food and feedstock for biorefinery processes (mainly for agar, carrageenan, and alginates extraction, [START_REF] Bixler | A decade of change in the seaweed hydrocolloids industry[END_REF]. However green macro-algae represent a minor part of the actual algae production. Species like Chaetomorpha sp. are an interesting biofuel feedstock with the ease of production and high similar cellulose content to that of land-based biomass [START_REF] Schultz-Jensen | Pretreatment of the macroalgae Chaetomorpha linum for the production of bioethanol--comparison of five pretreatment technologies[END_REF].

To tackle the potential of this kind of biofuel production system, this study assesses the environmental performance of a hypothetical system of ethanol production from onshore cultivated green seaweed (Chaetomorpha sp.) and its use in a passenger car. All the values chain is considered for this prospective LCA study to uncover the main contributing production steps of the Life Cycle Inventory result (LCI) on environmental indicators. The Representativeness Index (RI) presented in the previous chapter is then used on this LCI result to test the representativeness of the selected LCIA method (in the goal and scope definition phase of the LCA study) and its respective impact categories. Moreover, the representativeness of these environmental indicators is determined on subsystems of the LCI result. Finally, a screening over other LCIA methods is performed to explore RI results on other environmental indicators.

System definition and inventory

Goal and scope, and functional unit

The goal of the analysis is the evaluation of the potential environmental impacts caused by bioethanol production from cellulosic macro-algae (Cheatomorpha sp.) and its combustion in a passenger car. In a cradle-to-grave perspective, environmental performance is assessed using the standardized LCA methodology. All the steps of the values chain are included: from the algal cultivation to the final use to power a passenge r car. This LCI result is assessed to determine the main contributors to the environmental impact of the system. The functional unit of the system is to drive 100 km in a passenger car (medium size). The LCA software Simapro 8.1 has been used for the model ing. The ecoinvent database V.3.1 "allocation at the point of substitution" was used for background processes [START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF]. The characterization of environmental impacts is based on the LCIA method ILCD 2011. Recommended by the European Union (EC-JRC, 2011), the selected LCIA method assesses the environmental impacts at a midpoint level. Due to inconsistencies between the water impact assessment method and ecoinvent v.3.1 database, this impact has been removed from the assessment method.

Life cycle inventory

Figure 28 shows the main steps of the system. System starts from the algal cultivation in open raceways: this step needs a supply of water from the sea and uses up fertilizers.

After the harvesting, algae are conveyed to the ethanol production plant. This second main step is composed by pre-treatments and enzymatic hydrolysis of the biomass, and an alcoholic fermentation. Post-treatments (distillation and purification) are then carried out to provide ethanol inline with distribution and use constraint. System ends w ith the final use to power a passenger car. Based on laboratory scale data, the growth rate of Chaetomorpha is estimated to be 10 g DM /m²/day with an initial density of 0.5 kg DM/m². The dr y weight of the grown algae is assumed to be 20%. Algae cultivation is carried out in open raceways where water is mixed by a paddle wheel. Four raceways are considered in this cultivation system. They are all excavated and lined with an EPDM liner of 1.14 mm. A large raceway (5,000m²) is dedicated to the growth period of algae. Every week 350 kg of DM of algae are transferred from the large raceway to a small raceway (three open raceways of 1,500 m² each) for a batch of starvation. Two weeks of starvation is needed to stress algae to increase their carbohydrate content (estimation to up to 50% of DM). A cultivation season of 28 weeks is assumed but there are only 23 weeks where a full production is considered: the first 5 weeks are needed to get a minimal quantity of algae to start starvation procedures. Only nitrogen and phosphate are added to seawater during the growth period: ammonium sulfate and phosphate (ecoinvent market processes). Additional details on the infrastructure and industrial amenities can be found in [START_REF] Brockmann | Environmental assessment of bioethanol from onshore grown green seaweed[END_REF].

Ethanol production

After the harvest, algae are transported over 60 km by lorry to the ethanol production site.

The pre-treatment and the enzymatic hydrolysis of biomass are achieved to make the carbohydrates accessible during the bacterial fermentation step. The pre-treatment and the enzymatic hydrolysis are modelled using the ASPEN software to define infrastructure, industrial amenities, electricity and heat (confidential data, French Petroleum and New Energies Sources Institute, IFP Energies Nouvelles). The enzymatic production is modelled from the ASPEN model proposed at an industrial scale level by NREL [START_REF] Davis | Process Design and Economics for the Conversion of Lignocellulosic Biomass to Hydrocarbons : Dilute-Acid and Enzymatic Deconstruction of Biomass to Sugars and Biological Conversion of Sugars to Hydrocarbons Process Design and Economics for the Conversion[END_REF][START_REF] Humbird | Process Design and Economics for Biochemical Conversion of Lignocellulosic Biomass to Ethanol Process Design and Economics for Biochemical Conversion of Lignocellulosic Biomass to Ethanol[END_REF]. Cellulase is produced through an aerobic fermentation process by Trichderma reesei. Glucose needed as input is provided by hydrolyzation of maize starch [START_REF] Dunn | Energy consumption and greenhouse gas emissions from enzyme and yeast manufacture for corn and cellulosic ethanol production[END_REF] and nitrogen is provided from corn steep liquor [START_REF] Mu | Comparative life cycle assessment of lignocellulosic ethanol production: Biochemical versus thermochemical conversion[END_REF]. After the enzymatic hydrolysis of the algal biomass, a solid-liquid separation step is operated. To obtain a full overview of the whole system with an ecodesign perspective and a complete mass balance, neither allocation nor substitution was taken into account. It remains obvious that co-product management rules will have to be used for comparison to conventional fuel.

Ethanol is obtained through an anaerobic fermentation process of the sweet solution obtain after the solid-liquid separation. The ethanol production is based on the model proposed by NREL. 63% of the carbon of the sweet solution is considered to be transformed into ethanol by Zymomona mobilis.

Ethanol purification

Distillation, rectification and dehydration of the fermented solution are based on the NREL model. Distillation allows reaching a concentration of 37% of ethanol; rectification increase the titration to 92.5% and then the dehydration makes the titration reaching a suitable value of 99.7% for combustion in an engine. Distribution to service stations is based on a process inventoried in ecoinvent database that takes i nto account freight by lorry and train.

Ethanol combustion

The model of the combustion of ethanol in a passenger car is based on the ecoinvent process 'transport, passenger car, medium size, petrol, EURO 5' for Europe. Fuel consumption is changed for ethanol consumption based on their low heating value: 42.5 MJ/kg for petrol and 28.1 MJ/kg for ethanol [START_REF] Jungbluth | Life cycle inventories of bioenergy[END_REF]: ethanol consumption is then 9.4 kg over 100km. Emissions strictly linked to petrol evaporation (PAH, benzene, toluene, ethene, propene…) and heavy metal emissions per kilogram of petrol used are removed of the inventory. Carbon dioxide, carbon monoxide and methane emissions are considered as biogenic. Other flows (road use, car maintenance, and tire and brake emissions) are not modified considering that the fuel type would not modify them.

Applying the RI methodology

RIs of the ILCD method and its corresponding impact categories are determined for the modelled LCI. The script provided on the online deposit was used (Chapter 3).This analysis tests the representativeness of the selected environmental issues during the goal and scope of the LCA study. Further investigations are conducted on RIs of subsystems of the LCI. Aggregated LCI result of the following four subsystems are obtained from SimaPro: macro-algae production and production, purification and combustion of ethanol. Representativeness of the ILCD method and its impact category are determined for those four aggregated LCI results.

Finally, a screening of the global RIs of other classic LCIA methods and the RIs of their respective impact categories is carried out to check if other indicators tackle a better representation of the LCI result and its subsystems than the ILCD impact categories.

Results and discussion

Contribution analysis

The results of the contribution analysis are shown in Figure 29. Onshore production and transport of the harvested algae (macro-algae production) contribute for more than 40% to the overall environmental burden for all impact categories, except resource depletion. This LCI step has its major contributions on land use and ionizing radiations categories.

The electricity needed to move water and the production of the raceways (excavation and linen use) are the steps that are involved in most this contribution (see Annex D -1).

Figure 29. Process contribution analysis

Ethanol production impacts exceed 20% for seven impacts, being the second largest contributor for each. The most contributive step for ethanol production is the pretreatment and enzymatic hydrolysis step. The heat provided by steam production from natural gas is the environmental hotspot for this process on climate change and ozone depletion. Cooling of the solution is the hotspot on the ionizing radiations. An interesting result is the contribution of starch from conventional maize which is use for cellulase production: human toxicity (non-cancer effects), terrestrial and marine eutrophication are effected to up to 10% by this agricultural step. Chapter 5: Life Cycle Assessment of a biofuel production from cellulosic macro -algae: key aspects for the environmental concerns Ethanol purification obtains its major contribution on climate change and ozone depletion with around 20% of the environmental burden. Like for pre-treatments, heat production is the process that triggers this result.

Ethanol combustion is the main contributor to resource depletion often the second contributors (for six impacts). Car production is the final step that obtained non -negligible contributions on most of categories. Resource depletion is dominated by indium, tantalum, cadmium and nickel use while chromium VI, copper and zinc emissions drive human toxicities and ecotoxicity results. Being set as biogenic carbon, the carbon dioxide emitted by ethanol combustion does obviously not appear in climate change result.

The major optimization that could be obtained would be on the cultivation step.

Increasing yield growth of Chaetomorpha and limiting water movements and transfers are the main parameters that would decrease the environmental burden of this step.

RI results

RIs of the ILCD

For the entire LCI result, the global RI of the ILCD is 7.75 x 10 -5 . This value is quite low regarding the distributions obtained in Chapter 4. The environmentally critical dimensions of this LCIA method do not target the highest standardized elementa ry flow of the LCI result.

Figure 30 presents RI results of the non decorrelated impact categories of the ILCD. As for the global RI of the LCIA method, the impact category RIs are relatively low. The RI methodology reveals that most of the elementary flows on which this LCI result is intense are not on dimensions targeted by the impact categories of the ILCD. The ionizing radiation HH, the land use and the resource depletion categories are the impact categories that are put forward. The first standardized elementary flows of the LCI result are captured by those three impact categories. The environmental burden on those impact categories is due to the electricity that powers the system and the land used by raceways (Annex D -1). Because the algae production step is the one that most use those processes, its optimization seems to be the highest priority in order to decrease the environmental burden of this scenario. The global RIs of the ILCD method are presented in Table 5 for four subsystems of the LCI result. The first three subsystems, macro-algae production and ethanol production and purification, obtain higher RIs than the entire LCI result. Ethanol production has the highest RI that range close to the median of the RIs of the database (Chapter 4). By extracting subsystems, the LCI results obtain totally different elementary flow patterns: their elementary flow intensities are different from the original LCI result. If a global system can be poorly represented by an assessment method, subparts, considered separately, can be well grasped. Ethanol combustion remains misrepresented by ILCD with a RI of the same order of magnitude than the entire one.

Table 5. RI values of the ILCD method for each subsystem of the biofuel production from macro-algae system. RI Macro-algae production subsystem 2.71 x 10 -4 Ethanol production subsystem 7.09 x 10 -3 Ethanol purification subsystem 2.63 x 10 -3 Ethanol combustion subsystem 2.32 x 10 -5

Full system 7.75 x 10 -5

Looking at the RIs of impact categories (see Figure 31), similar trends than the ones observed for global RIs are obtained: ethanol production and purification have very high RIs compared to the other two steps and to the entire LCI result (Figure 31.a). The three most representative impact categories for ethanol production are the two ionizing radiations and ozone depletion. This subsystem has a very different elementary flow pattern compared to the entire LCI result. The potential diminution of the LCA contribution of this particular subsystem would have to be carried out through th ese three impact categories. Globally, analysing impact category RIs of subsystem put forward the same impact categories that the most representative of the entire LCI result. Magnitudes of the RIs are however deeply modified from a subsystem to another due to different elementary flow patterns. Climate change occupies a singular position by being at the 8 th position for the entire LCI result and being ranked second most representative impact category for the ethanol purification.

Macro-algae is the main contributive step of the whole system for most of the impa cts (Figure 29), but it is not the best represented by ILCD (Figure 31.a). This points out the need of focusing the attention in this step for the improvement of the system and of the assessment.

Considering the ILCD method, the eight impact categories that best represent the environmental issues of the studied system and its subsystems are: ionizing radiation HH, land use, resource depletion, ozone depletion, ionizing radiation E, freshwater ecotoxicity, marine eutrophication and climate change. The interpretation and the ecodesign improvement should preferentially be focused on this subset of the ILCD method.

LCIA methods screening

The ILCD method was selected by the goal and scope of the LCA study. We here explore if other classic LCIA methods best represent the LCI and tackle differently the elementary flows patterns of the studied LCI result and its four subsystems. Results of the global RI of LCIA methods are presented in Figure 32.

RIs of the full system are quite low comparing to its subsystems as it was observed for ILCD in part 5.3.2.2. Splitting subsystems allows revealing environmental flow patterns specific of the different steps. Proximities of LCIA methods regarding these subsystems are very different. While studying the entire LCI result would be more relevant with a ReCiPe method, the three last subsystems are putting forward other LCIA method: Ecological Scarcity, EPS and EDIP. Screening of impact category RIs for the entire system and the four sub-systems is proposed in Annex D -2. Urban land occupation is the impact category that provides the larger part of RI values of ReCiPe methods. Raceways are modelled to occupy industrial area, the aggregated entire LCI use this elementary flow with high intensity and this impact category considered this dimension with high priority. This land use impact category is more specific than the one belonging to the ILCD methods and it targets intense elementary flows of our LCI result. In addition to the land use issue assessed by several categories, toxicities and ionizing radiations impacts are the other representative environmental issues for this LCI result. This screening could be a tool to inform practitioners that on impact category from other LCIA methods; their LCI results are well represented in term of the elementary flow pattern and the critical dimension of the concerned impact category.

Conclusions

The environmental hotspots of the production of ethanol from onshore cultivated seaweed were assessed using the LCA methodology. The study reveals that the main contributive step was the algae production on almost all impact categories. It is through its land occupation and its electricity consumption that this step impact on the environment. Y ield growth of the studied algae and its cultivation system were the main parameters that could trigger a diminution of the environmental burden of the values chain.

The second objective of this study was to apply an innovative measurement, the RI, to assess the relevance of the environmental indicators used by a LCA. This measurement put forward ionizing radiations, land use and resource depletion as the most representative impact categories of this LCI result. Classic environmental study of transport system always focuses on climate change, fossil fuel depletion and particulate matter issues. However, contextualizing our LCI results within the frame of a large database, the main environmental concerns of our system were on different one. This study case sh ows the great interest that this methodology could provide to LCA practitioners to support them on eco-design projects.

Chapter 6: General discussion and conclusion

The major aim of this thesis was to develop metrics to assess the relevance of a LCIA method and/or a subset of impact categories with respect to the studied systems. The objective was to fully tackle impact categories to the ISO requirement that requests that a "comprehensive set of environmental issues related to the product system" should be analysed. The work leads to the formalization of the LCA framework from a geometric viewpoint and the development of a Representativeness Index per LCIA method and impact category. Neither the scientific nor the environmental relevance of the LCIA method models is assessed here but the approach shows how the LCI result information is caught by the LCIA. In this chapter, it is proposed to review the outcomes of the the sis, to point out their potentials and limitations, and to guide future research efforts to improve and deepen the exploratory approaches developed.

Main outcomes of the thesis

There were two kinds of outcomes regarding the developed RI measurement: t he approach principles and the corresponding practical aspects.

Methodological outcomes

First, the study provides an operational methodology to assess the appropriateness of LCIA method and impact categories while carrying out a LCA (Chapter 2 and 3 ). This methodology is based on a geometric formalization of the LCA framework. Indeed with a norm and a direction, LCI results and impact categories are considered as vector and can be localized in the same vector space. The LCIA phase of a LCI result is then a classic scalar product and can be visualized with an orthogonal projection. The developed RI measurement relies on the angular distance observed between a LCI result vector and each impact categories, or between a LCI result vector and a multi-dimensional sub-space generated by a set of impact categories. The relevance of indicators used to study an environmental profile can be compared with the RI measurement.

Environmentally critical dimensions are also put forward for all possible impact categories. Then, the developed angular measurement provides an interesting insight on the elementary flows intensity over the critical dimensions determined for the impact category (and subsequently the critical dimensions of the corresponding LCIA method).

The standardization procedure determines the elementary flow intensities of each LCI by confronting it with the frame of reference of the LCI database context (a set of LCI result representing the "world" through the modelled activities). The critical dimensions therefor reveal the main problematic dimensions, according to the "world" representation, regarding the modelled environmental mechanisms. By providing additional information based on LCI results, justifications towards the choice of a LCIA method and its decorrelated impact categories can rely on RIs. This innovative methodology assists the practitioner's knowledge by giving an objective overview of his LCI results regarding the human activities modelled and regarding the critical dimensions of each impact categories.

Practical results

Secondly, the main practical outcome of the thesis is an operational tool written in Python 3.6 for RI calculation. The corresponding code is made available from an online deposit (Chapter 3). It allows LCA practitioners to calculate RIs for their own LCI result (ecoinvent 3.1, at point of substitution, for this first version, next improvements should increase the number of databases).

Other practical outcomes have been obtained by confronting the measurement to large sets of LCI results (Chapter 4). By exploring RI results among homogeneous sets of LCI results grouped by their field of activity, it shows contrasted representativeness results of LCIA methods and impact categories. Results are particularly interest ing for impact categories that are known to endure environmental pressure from specific fields of activity, and then that are put forward by the RI measurement. For instance, land use, eutrophications and acidification were determined as the best represent ative impact categories for agriculture and forestry products while climate change, photochemical ozone formation and acidification seemed to be the most relevant impact categories for electricity power generation processes. The RI gives an objective justi fication to emphasis interpretation of LCA results on some environmental issues by field of study.

Finally, the RI methodology is applied in Chapter 5 on a case study from the Green AlgOhol project: the modelling of a biofuel production from cellulosic macroalgae. First, an environmental contribution analysis is presented. Then, RI analyses of the entire values chain complete the study and investigation of RIs of four sub -parts of the LCI result lead to three main impact categories (ionizing radiation human health, land use and resource depletion) potentially complemented with five others. A screening of RI results (global RIs of LCIA methods and RIs of impact categories) is finally achieved to prospect RIs on other LCIA methods. This shows how RI contributes to an ecodesign approach by adding information on the relevance of assessment criteria for the improvement process.

Limitations and perspectives of the Representativeness Index

Standardization

As for the most of quantitative multicriteria approaches, the variability of studied dimensions, in term of units and magnitudes, forces to free of them by standardization. The Representativeness methodology presented here therefore depends on standardization by the geometrical mean determined over an entire database. Due to disparities observed among the number of LCI results per field of activity (for instance ecoinvent database has 2,788 LCI results for the electricity power generation and only 280 LCI results for the mining and quarrying field), the standardized elementary flows are obviously oriented according to the features of the most represented fields of activity. Because of some sectors are overrepresented in the database compared to the "real world", the standardization procedure in the RI computation involves that the geometric means of elementary flows do not truly reflect the real elementary flow trends of all the interventions of the techno-sphere with the environment.

Regarding this limit, several research perspectives can be suggested:

-Suppressing overlaps among products can be a first way to limit the number of LCI results within overrepresented fields. Indeed, very similar LCI results (electricity productions from coal from different countries, chemical products with very similar process or modelled with the same proxies...) are present in LCI results databases and might perturb elementary flow trends;

-Standardization using data from input-output databases could also overcome this issue (e.g. EXIOBASE for I-O table with environmental data). Market information between sectors of activity could be used to "weight" them in the standardization procedure. The RI of a LCI result will then face its elementary flow intensities in relation to the territory to which it belongs to and regarding the local environmentally critical dimensions;

-The standardization procedure could also be carried out using elementary flow trends from fields of activity. The issues raised by the number of LCI results per field might be overcome this way if the number of LCI results per field still allows determining a representative geometric mean. However, a standardization intrafield of activity only make LCI result distinguished from their field; inter-field comparison cannot be done. This way, RIs might respond to another specific research question.

Decorrelation

The algorithm of decorrelation proposed in Chapter 3 presents some limitations. Ind eed, to deal with overrepresentation and underrepresentation issues, the procedure focuses on the impact category level which generates artifacts and inconsistencies within the decorrelated RIs. Impact categories that are not linked through the dimensions that trigger a potential representation issue might in fact be affected by the decorrelation. To avoid this kind of inconsistency, sharing of the redundant information could be manage by focusing further developments at the dimension level.

Regionalization, variability and other perspectives

Facing the development of the regionalization of LCI results and LCIA methods, LCA data structure might be deeply affected in the future. Detailed data at regional level can multiply the number of dimensions that have to be managed (regionalization involves potential different CFs per substance, compartment and sub-compartment). Obviously, the studied vector space will be larger. Such modifications of the vector space will lead to adapt the RI methodology. The "curse of dimensionality" associated with highdimensional spaces [START_REF] Leskovec | Mining of Massive Datasets[END_REF], which manifests itself by having almost any two vectors to be almost orthogonal, may bring unintuitive RI results. The very low RI results that are currently obtained (from 10 -2 to 10 -5 ) is already a consequence of the high number of dimensions of the LCA vector space.

When carrying a LCA study, LCI result and elementary flow variabilities and uncertainties can be described. Those variabilities can generate a huge number of different LCI results. The current RI methodology developed in this PhD work didn't face the issue of variability in LCA and how to take it into account from an operational point of view. However, the variability observed for a given elementary flow over a database i s often higher than the variability of this elementary flow determined for a given LCI result.

The RI results obtained for a large set of LCI results (whole database or fields of activity) could then not be deeply affected by taking into account the variab ility of the LCI results. Moreover, RI values of one LCI result can be determined for extreme bounds of the variability of its elementary flows. The link between the variability and the variation of the RI should still be investigated in details.

The direct implementation within LCA dedicated software, the use of different databases and the multiple versions of those databases (which imply a dedicated ad hoc standardization process), but also inconsistencies in the nomenclatures and the structures of the different databases, are practical limitations for the full operationalization of the methodology. The current Python implementation can facilitate the future use of the code given that it is a free license language that is already used in other LCA framewo rk (e.g. Brightway2).

Concerning LCI results databases, the RI methodology has to be tested on other versions of the ecoinvent database and other LCI results databases. Comparing RI results from different databases could guide LCA practitioners on a specific database; even if this choice would still be mainly led by the different rules supervise the development of a database (as for example the system boundaries rules regarding the co -product management).

Finally, this approach could initiate screening of impact categories from up-to-date LCIA methods to generate composite LCIA methods per LCI result. This perspective would have to deal with orthogonalization issues and focus on the complementarity of impact categories to limit representativeness issues among the selected ones. Moreover, the number of impact categories per optimized subsets could be challenging to determine. Specific default lists of impact categories could be proposed per fields of activity through such global analysis of a database.

General conclusion

Selection of a LCIA method and relevant impact categories for decision support is one of the decisive steps when assessing the environmental burden of human activities with the LCA framework. The selection has to be taken during the goal and scope definition phase and a focus on several impact category results can be done during the interpretation phase. Having an overview of LCI result database, this PhD thesis proposed to question the relevance of a chosen LCIA method and the different impact categories with the development of an innovative metric. This work was led by the following general research question: "By exploring LCI results through their standardized elementary flow trends, is it possible to assess by a systematic approach the relative relevance of LCIA methods and their respective impact categories for LCA studies?"

Using LCI results and a geometric formalization of the LCA methodology, the theoretical basis of the RI measurement was developed in Chapter 2. The RI is an angular distance between a LCI result and a LCIA method. The relevance of LCIA methods was analysed to support LCA practitioner decision. To illustrate the feasibility of such a procedure, the RI measurement was applied on four electricity mix productions case studies. LCIA methods were then discriminate regarding their RI.

The Chapter 3 deepened the analysis at the impact category level to screen, for a LCI result, which indicators are worthwhile focusing on within a LCIA method. A comparative LCA study could then benefit from the RI measurement when interpreting LCIA results. Correlation among impact categories raised representativeness issues that were resolved with the development of an orthogonalization algorithm. A python package was also developed in parallel of this Chapter to provide an operational tool for LCA practitioners.

Finally, Chapter 4 and 5 explored the RI measurement possibilities over a wide range of LCI results segregated by their field of activity and over a case study obtained from the Green AlgOhol project. Field of activity analyses showed different RI trends regarding impact categories that could lead to general guidelines. Splitting an entire LCI result from its main values chain steps uncovers that different impact categories could be focused on for each of them.

Chapter 6 aimed at proposing possible routes for further developments of the RI measurement. LCA practitioners could benefit from such a decision tool but its appropriation still faces challenges.

LCA is a multicriteria decision support. If many works deal with the choice of the indicators (to avoid redundancy, to simplify the decision or to facilitate the interpretation of results), very few studies are focused on the representativeness of the inventory. The questions "What is the part of the initial information that I assess in my analysis?" and "How the impact categories are relevant in front of the technical system?" are issues that are poorly addressed in LCA studies. The RI measurement defined in this PhD provides objective and quantitative answers to these questions and contribute to a more efficient interpretation of LCA results.

One of the great features of the LCA approach is the structuration of the environmental assessment process. The environmental concerns of a human activity are tackled through two aspects: practitioner models activities (LCI: procedure to obtain LCI results) and methods developers provide assessment tools (LCIA methods) for environmental purposes. The work presented in this PhD contributes to a better consistency between these two steps to ensure an efficient assessment. compartment) to the ecoinvent nomenclature. The other three steps are needed in this order to deal with CFs that are only characterized for "unspecified" sub -compartment in SimaPro, while the ecoinvent nomenclature does not have "unspecified" but only the specified sub-compartments. For example, ecoinvent can have "surface water" and "ocean" sub -compartments for the "water" compartment and no "unspecified" sub-compartment, while an impact category only has CF for the "unspecified" sub-compartment. The procedure will apply the same CF from the "unspecified" to the "surface water" and "ocean" sub -compartments and will delete, at the end, the "unspecified" sub-compartments. Annex B: Supplementary Information -Chapter 3

Annex B-1: Inventory standardization regardless of reference flow

The following development presents the advantages of using the geometric means to standardize elementary flows. The choice of the geometric means is interesting for the calculus of the RI regarding the specific format of the data used. Indeed, each LCI result (which is a compilation of elementary flows) is associated with a reference flow that corresponds to the quantity of product or service provided. Referenced flows are expressed in various units (kg of product, kWh generated, t.km transported…) which obviously raise inconsistency while studying sets of LCI results or a global database. However, using the geometric mean and an angular distance allow obtaining RIs independent from the value of each reference flow.

Let consider a cumulated LCI database DB composed of m LCI results described over n elementary flow dimensions. For homogenisation of elementary flows, the standardization consists here in dividing the elementary flows of each elementary flow by their respective geometric mean.

The expression of the geometric mean 𝐺 𝑥 over a certain elementary flow 𝑥 using all the LCI results of the cumulated LCI database DB (with a total of 𝑚 LCI results) is:

𝐺 𝑥 = √∏ 𝑔 𝑥,𝑖 𝑚 𝑖=1 𝑚 (SI.1)
To present why the geometric mean is interesting to use regarding the specificity of LCI result data on their reference flow, we consider another cumulated LCI database DB * composed of exactly the same LCI results except for the "a" LCI result which is different by its reference flow: it is set δ times higher than in DB. Taking a transportation LCI as an example, this factor could be 1 000 times for this human activity described for 1 t.km (in DB * ) instead of 1 kg.km (in DB). All the elementary flows of this LCI are 1 000 higher in DB * than in DB whereas they model the same activity. We have The same reasoning can be easily extended to more than one different reference flows between DB and DB * . This shows that the standardization by the geometric mean allows to RIs being independent of the reference flows used in databases.

Annex B-2: Standardizations and LCI patterns

The aim of Annex B -1 is to explain the meaning of the standardization. Focus is put on the elementary flow level, which is the core of the information contained by LCI results. Firstly, all data analysis procedures require a pretreatment step to homogenize the data. Each procedure depends on the question and on the structure of the analysed data.

For homogenisation of elementary flows, the standardization consisted in dividing the elementary flows of each dimensions by their respective geometric mean. The set of geometric means summarizes the global trend of the cumulated LCI database over each dimension: it is the average LCI result of a database.

By standardizing each LCI result by the set of geometric means, the dimensions where they are particularly intensive regarding the rest of the LCI results can be revealed. For each standardized LCI result, a division by their norms can be made in order to determine and compare the standardized elementary flows from different LCI results without any influence of their reference flows. In any case, this normalisation is part of the calculus of RIs (cf. equations 4 of the chapter 2 and 3). It is required here for exactly the same reason as the influence of the reference flow value. Standardized elementary flows therefore follow the same numerical range and have a maximal value of 1. The high standardized elementary flows guide the orientation of the LCI result vector. For each LCI result of the cumulated LCI database, we determined the number of different dimensions where the standardized elementary flows allow for 95% of the norm to be reached (i.e. the number of dimensions that assembles the principal information on the direction). We then split the LCI results according to their number of dimensions and plot, with a maximum of 20 dimensions, the These two figures accumulate the results of the standardized elementary flows of 7660 different LCI results. The other LCI results need more than 20 different dimensions to reach 95% of their norm. They reveal flow patterns on LCI results where the two extremes are: either a very intensive LCI result on one precise standardized elementary flow while all the other standardized elementary flows present a very low weight on the norm; or the LCI result information is totally spread out over all the dimensions with equal and relatively low standardized elementary flows. With a database such as ecoinvent 3.1, built with 1727 dimensions, the standardized elementary flows of LCI results that are equally spread over all dimensions have a value of 1 √1727 ⁄ = 2.41 × 10 -2 . Such a LCI result is in fact the standardized average LCI result of the database with, before being standardized, the geometric means as elementary flows. This value is also the minimum value that the highest elementary flow of an LCI result could reach. This LCI result, however is not observed because the maximal number of dimensions needed for 95% of the norm is 640 dimensions. For 2299 LCI results, the main direction of the vectors is dominated by one dimension ( ). For the first observation (i), the difference in information per elementary flows between groups that need 50 or 51 dimensions is low compared to the groups that only need 1 or 2 dimensions. The number of LCI result per group covers the high numbers of dimensions. The second observation (ii) implies that when the information covers a high number of dimensions, elementary flow values tend to 1 √𝑛 ⁄ (where n is the number of dimensions). Some LCI results still present a strong heterogeneity with a very high first elementary flow (although less than 0.95) with lower extra elementary flows that are needed for 0.95 to be reached, as demonstrated in Figure S 7 where high extreme values of elementary flows are observed when a high number of dimensions is needed.

Concerning the impact categories, the CF values express the modelled dangerousness of elementary flows towards environmental concerns. Expressed in kg of environmental indicator equivalents per kg (or Bq or J) of elementary flow, the standardization is app lied by multiplying the CFs by the geometric means of the cumulated LCI database (expressed in kg or Bq or J of elementary flow). Considering one impact category, all its standardized CFs have the same unit: indicator equivalent. This standardization brings forth the key dimensions where the LCI results of the cumulated LCI database have a globally high contribution on each impact category: it is the LCA results of the average LCI result of the database. Standardized impact categories reveal the critical dimensions that are characterized by the modelled environmental issues as well as the dimensions that highly contribute to the impact categories by taking into account the global trend observed over the cumulated LCI database. The standardized impact category vectors are given in Annex B -7.

Annex B-3: RI results according to standardized elementary flows and CFs

The RI of a LCI result for an impact category is the cosine of the angle between a standardized LCI result vector and a standardized impact cate gory vector. The representativeness of an impact category regarding a LCI result relies on the direction of the two vectors, which depends on the similarity between the standardized elementary flows and the standardized CFs. An impact category is representative of a LCI result if the dimensions for which the LCI result distinguished itself from the cumulated LCI database are those for which the database produces a high global impact (cf. Annex B -1). From a database point of view, high RIs reveal LCI results that strongly emit for dimensions that are globally high contributors towards the concerned impact categories.

In other words, when a LCI result emits above the average of the database for one or several dimensions and when the standardized CFs of these dimensions are also very high for an impact category, it should be sufficiently relevant to study this LCI result through this category with regard to all modelled product.

Considering the global trend of the cumulated LCI database, emissions of the LCI result are high for one or several dimensions that are also, globally, the strongest contributors to the impact category.

The RI values (from all LCI results of ecoinvent for one impact category) plotted as a function of the elementary flow that is the first contributor of the RI, suggests these values are correlated, as illustrated in This excel file presents the result sheets obtained from the developed Python scritp. It is available from an online deposit with the DOI: 10.5281/zenodo.1068914. The package allows to apply the methodology on LCI excel files (system process) exported from SimaPro and modelled within the ecoinvent 3.1 database "allocation at the point of substitution" (further development have to be done to apply the methodology on other database and on LCI files exported from other software).

Three outputs can be obtained: global RIs of LCIA methods, RIs of their impact categories and RIs of the decorrelated RIs. Almost all the multi -criteria LCIA methods can be analysed. RIs of LCIA methodology and impact categories (orthogonalized or not) can be obtained.

Only RIs of the impact categories of the ILCD Mid+ V1.05 are presented.

Results are from the analyses of the Chinese and the German electricity mix production. For example in Table S 22, there are 4194 different LCIs which have the elementary flow "carbon dioxide, fossil to air non-urban air or from high stacks" that appear in the combination of three elementary flows that are needed to get up to 95% of the value of their Climate Change RIs. This elementary flow is also the one that is the most frequent within all RIs: it is present within 28% of all combinations.

  . SELECTION OF LCIA METHODS AND IMPACT CATEGORIES ............................................................1.4.1. During the goal and scope definition phase ........................................................... 1.4.2. During the result interpretation phase .................................................................. 1.5. OBJECTIVES .................................................................................................................... CHAPTER 2: REPRESENTATIVENESS OF ENVIRONMENTAL IMPACT ASSESSMENT METHODS REGARDING LIFE CYCLE INVENTORY RESULTS ....................................................................... CONTENTS OF CHAPTER 2......................................................................................................... 2.1. INTRODUCTION ............................................................................................................... 2.2. MATERIAL AND METHOD.................................................................................................

  2.4. CONCLUSIONS ................................................................................................................. CHAPTER 3: A TOOL TO GUIDE THE SELECTION OF IMPACT CATEGORIES FOR LCA STUDIES BY USING THE REPRESENTATIVENESS INDEXES .......................................................................... CONTENTS OF CHAPTER 3......................................................................................................... 3.1. INTRODUCTION ............................................................................................................... 3.2. MATERIAL AND METHOD....................................................................................................

  RESULTS AND DISCUSSION ..................................................................................................

  . RESULTS AND DISCUSSION ..................................................................................................

5. 2

 2 .2.1. Macro-algae production ............................................................................................. 5.2.2.2. Ethanol production .................................................................................................... 5.2.2.3. Ethanol purification ................................................................................................... 5.2.2.4. Ethanol combustion ................................................................................................... 5.2.3. Applying the RI methodology ................................................................................ 5.3. RESULTS AND DISCUSSION .................................................................................................. 5.3.1. Contribution analysis ............................................................................................ 5.3.2. RI results .............................................................................................................. 5.3.2.1. RIs of the ILCD ........................................................................................................... 5.3.2.2. RIs of the ILCD impact category regarding the four LCI result subsystems ..................... 5.3.2.3. LCIA methods screening ............................................................................................. 5.4. CONCLUSIONS ................................................................................................................. CHAPTER 6: GENERAL DISCUSSION AND CONCLUSION ........................................................... CONTENTS OF CHAPTER 6 ......................................................................................................... 6.1. MAIN OUTCOMES OF THE THESIS .......................................................................................... 6.1.1. Methodological outcomes ..................................................................................... Environmentally critical dimensions are also put forward for all possible impact categories. Then, the developed angular measurement ....................................................................... 6.1.2. Practical results .................................................................................................. 6.2. LIMITATIONS AND PERSPECTIVES OF THE REPRESENTATIVENESS INDEX ..........................................

  CONCLUSION ....................................................................................................TablesTables -Main Chapters TABLE 1. DESCRIPTIVE VALUES FOR THE ANALYSIS OF THE MAIN DIMENSIONS OF RIS ...................................... TABLE 2. CORRELATION MATRIX OF IMPACT CATEGORIES OF THE ILCD METHOD, ON THE BASIS OF 11206 PRODUCTSFROM ECOINVENT. ................................................................................................................ TABLE 3. NUMBER OF INVENTORIES PER FIELDS OF ISIC ACTIVITY .............................................................. TABLE 4. NUMBER OF IMPACT CATEGORIES PER ENVIRONMENTAL ISSUES .................................................... TABLE 5. RI VALUES OF THE ILCD METHOD FOR EACH SUBSYSTEM OF THE BIOFUEL PRODUCTION FROM MACRO-ALGAE SYSTEM. ............................................................................................................................

  ..................................................................................... TABLE S 7. MAIN CFS OF OZONE DEPLETION ..................................................................................... TABLE S 8. MAIN CFS OF HUMAN TOXICITY, CANCER EFFECTS ................................................................ TABLE S 9. MAIN CFS OF HUMAN TOXICITY, NON-CANCER EFFECTS ......................................................... TABLE S 10. MAIN CFS OF PARTICULATE MATTER ............................................................................... TABLE S 11. MAIN CFS OF IONIZING RADIATION HH ........................................................................... TABLE S 12. MAIN CFS OF IONIZING RADIATION E (INTERIM) ................................................................TABLE S 13. MAIN CFS OF PHOTOCHEMICAL OZONE FORMATION ........................................................... TABLE S 14. MAIN CFS OF ACIDIFICATION ........................................................................................ TABLE S 15. MAIN CFS OF TERRESTRIAL EUTROPHICATION .................................................................... TABLE S 16. MAIN CFS OF FRESHWATER EUTROPHICATION ................................................................... TABLE S 17. MAIN CFS OF MARINE EUTROPHICATION ......................................................................... TABLE S 18. MAIN CFS OF FRESHWATER ECOTOXICITY ......................................................................... TABLE S 19. MAIN CFS OF LAND USE .............................................................................................. TABLE S 20. MAIN CFS OF WATER RESOURCE DEPLETION .....................................................................

  RIS OF HUMAN TOXICITY, NON-CANCER EFFECTS .....................................................................................................................................

  .....................................................................................................................................

  Figures -Main Chapters

FIGURE 1 .

 1 FIGURE 1. IRS GLOBAUX DES METHODES DE CALCUL POUR LES QUATRE MIX ELECTRIQUES...................................

FIGURE 2 .

 2 FIGURE 2. RESULTATS D'ACV ET D'IRS DES MIX DE PRODUCTION ELECTRIQUE CHINOIS ET ALLEMAND. LES ECARTS ENTRE LES IRS ORIGINAUX ET DECORRELES (COULEURS FRANCHES) SONT REPRESENTES PAR DES COULEURS PASTEL. ............................................................................................................................... FIGURE 3. DISTRIBUTIONS DES IRS GLOBAUX DE LA METHODE DE CALCUL DE L'ILCD EN FONCTION DES DOMAINES D'ACTIVITE ......................................................................................................................... FIGURE 4. REPRESENTATION SCHEMATIQUE DE LA CHAINE DE VALEURS ETUDIEE ............................................ FIGURE 5. THE SUSTAINABLE DEVELOPMENT GOALS TO END POVERTY, PROTECT THE PLANET AND ENSURE PROSPERITY FOR ALL (UNITED NATIONS, 2015) ........................................................................................... FIGURE 6. FRAMEWORK OF THE ILCD LCIA METHOD, LINKING ELEMENTARY FLOWS TO MIDPOINT AND ENDPOINT INDICATORS, EXTRACTED FROM HAUSCHILD ET AL. (2013) .............................................................. FIGURE 7. TECHNICAL AND ENVIRONMENTAL SYSTEM IN LCA ................................................................... FIGURE 8. LCIA METHODS PUBLISHED SINCE 2000 (COUNTRY/REGION OF ORIGIN IN BRACKETS), EXTRACTED FROM ROSENBAUM (2017) ............................................................................................................ FIGURE 9. STRUCTURE OF THE THESIS ................................................................................................ FIGURE 10. GRAPHICAL ABSTRACT OF CHAPTER 2 ................................................................................. FIGURE 11. GEOMETRICAL REPRESENTATION OF LCA: A) TWO LCI VECTORS G1 AND G2 PLOTTED IN A TWO DIMENSIONAL INVENTORY SPACE (NO2 AND NH3 GAS EMISSIONS IN AIR) ; B) IMPACT CATEGORY VECTORS FOR PARTICULATE MATTER FORMATION (Q1) AND ACIDIFICATION (Q2); C) LCA RESULTS; D) ANGULAR DISTANCES BETWEEN INVENTORIES AND IMPACT CATEGORY VECTORS. ............................................................... FIGURE 12. VISUALISATION OF LCIA RESULTS AND MEASUREMENT OF THE COSINE DISTANCE WITHIN A 3-DIMENSIONAL SPACE ............................................................................................................. FIGURE 13. SCHEMATICS OF THE PROCEDURE ...................................................................................... FIGURE 14. RI OF LCIA METHODS FOR FOUR ELECTRICITY MIX PRODUCTIONS ............................................... FIGURE 15. COMPARISON OF LCIA METHOD RIS (NUMBERS INDICATE THE CORRESPONDING OVERLAPPED POINTS) FIGURE 16. RIS OF THE IMPACT CATEGORIES OF THE RECIPE MID. I. METHOD FOR THE CHINESE AND FRENCH ELECTRICITY MIX PRODUCTIONS ................................................................................................ FIGURE 17. GRAPHICAL ABSTRACT OF CHAPTER 3 ................................................................................. FIGURE 18. A) REPRESENTATION OF TWO STANDARDIZED LCI RESULT VECTORS G1 AND G2 (IN BLUE), TWO STANDARDIZED IMPACT CATEGORY VECTORS Q1 AND Q2 (IN RED), AND THE FOUR OF THE ANGLES ΓJ, I USED TO MEASURE RIS. THE VECTOR SPACE IS SPANNED BY TWO BASIS VECTORS (E1 AND E2) REPRESENTING STANDARDIZED ELEMENTARY FLOWS, SUCH AS CO2 AND NOX. B) ILLUSTRATION OF THE CORRELATION ISSUE AND Q2 ⊥, THE ORTHOGONAL VERSION OF Q2 (SEE BELOW). ........................................................... FIGURE 19. SCHEMATICS OF THE PROPOSED ALGORITHM ........................................................................

FIGURE 20 .

 20 FIGURE 20. LCIA RESULTS (EXPRESSED RELATIVE TO THE HIGHEST VALUE) AND IMPACT CATEGORY RIS FOR THE LCI RESULTS OF THE CHINESE AND GERMAN ELECTRICITY MIXES FROM THE ILCD METHOD. BRIGHT COLOURS CORRESPOND TO DECORRELATED RIS RIJ, IDECORR WHILE PASTELS COLOURS INDICATE THE PART REMOVED FROM THE ORIGINAL RIS BY THE DECORRELATION PROCEDURE, DJ, I. ...................................................

FIGURE S 1 .

 1 FIGURE S 1. SCHEMATICS OF THE FULL PROCEDURE, FROM EXPORTATION OF DATA TO RI CALCULATION ............. FIGURE S 2. STANDARDIZATION OF FOUR ILLUSTRATIVE LCI RESULTS IN TWO DIMENSIONS (BOXPLOTS SHOW THE DISTRIBUTION OF THE WHOLE DATABASE) ................................................................................. FIGURE S 3. ELECTRICITY MIX PRODUCTION FROM THE 4 STUDIED COUNTRIES. THESE MIXES WERE EXTRACTED FROM THE ECOINVENT 3.1"ALLOCATION AT THE POINT OF SUBSTITUTION" VERSION. .................................... FIGURE S 4. REPRESENTATIVENESS INDEX (RI) OF LCIA METHODS FOR THE 4 STUDIED ELECTRICITY MIX PRODUCTIONS. FOR EACH MIX PRODUCTION, LCIA METHODS DECREASE IN ORDER OF RIS. ..................... FIGURE S 5. RELATIONSHIP BETWEEN RI SCORES OF THE 18 LCIA METHODS FOR THE 4 STUDIED LCIS AND THE NUMBER OF IMPACT CATEGORY PER LCIA METHOD. .................................................................... FIGURE S 6. NUMBER OF LCI RESULT PER NUMBER OF DIMENSIONS THAT ASSEMBLE 95% OF THEIR PRINCIPAL

  𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) 𝐺 𝑥 Geometric mean of 𝑔 𝑥,𝑖 for the 𝑥 th elementary flow (𝑥 = 1, … , 𝑛) 𝐠 ̃𝑖 Standardized form of 𝐠 𝑖 (using the geometric mean) (𝑖 = 1, … , 𝑚) 𝐪 ̃𝑗 Standardized form of 𝐪 𝑗 (using the geometric mean) (𝑗 = 1, … , 𝑝) 𝐐 ̃ LCIA method matrix consisting of standardized impact vectors 𝐪 ̃𝑗 𝛾 𝑗,𝑖 Angle between 𝐪 ̃𝑗 and 𝐠 ̃𝑖 (𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) 𝐪 ̃𝑗 ⊥ Orthogonalized form of 𝐪 ̃𝑗 (from a Gram-Schmidt process) (𝑗 = 1, … , 𝑝) 𝐐 ̃⊥ LCIA method matrix consisting of orthogonalized impact vectors 𝐪 ̃𝑗 ⊥ 𝑅𝐼 𝑗,𝑖 Representativeness index of 𝐪 ̃𝑗 for 𝐠 ̃𝒊 (𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) 𝑅𝐼 𝑖 Representativeness index of LCI-result 𝐠 ̃𝒊 for all impact categories (𝑖 = 1, … , 𝑚) 𝑅𝐼 𝑗,𝑖 ⊥ Ortohogonal representativeness index of 𝐪 ̃𝑗 ⊥ for 𝐠 ̃𝒊 (𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) 𝑅𝐼 𝑖 ⊥ Orthogonal representativeness index of LCI-result 𝐠 ̃𝒊 for all orthogonalized impact categories (𝑖 = 1, … , 𝑚) 𝑅𝐼 𝑗,𝑖 decorr Decorrelated representativeness index of 𝐪 ̃𝑗 for 𝐠 ̃𝒊 (𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) 𝑆𝑅𝑅 𝑗 Sum of squared correlation coefficients of 𝐪 ̃𝑗 and all other 𝐪 ̃-vectors (𝑗 = 1, … . , 𝑝) Θ 𝑗 A set of impact category vectors that are correlated to 𝐪 𝑗 and belonging to 𝐐 (𝑗 = 1, … , 𝑝) 𝑆 𝑖 Sum of squared RIs over 𝑡 = 1, … , 𝑝 (𝑖 = 1, … , 𝑚) 𝑘 Iteration round (𝑘 = 2, … , 𝑝) 𝑅 𝑡,𝑖,𝑘 RI result of the 𝐪 ̃𝑡 for 𝐠 ̃𝑖 and treated during the iteration 𝑘 (𝑡 = 1, … , 𝑝; 𝑖 = 1, … , 𝑚; 𝑘 = 2, … , 𝑝) 𝑑 𝑗,𝑖 Distance between 𝑅𝐼 𝑗,𝑖 and 𝑅𝐼 𝑗,𝑖 ⊥ (𝑖 = 1, … , 𝑚; 𝑗 = 1, … , 𝑝) Ij,i Projection of the 𝐠 ̃𝑖 LCI vector on the 𝐪 ̃𝑗 impact category vector 𝛼 𝑗,𝑖 Angle formed by the directions of 𝐠 ̃𝑖 LCI and the impact category vector 𝐪 ̃𝑗 |cos(𝛼 𝑗,𝑖 )| Absolute value of the angular cosine of 𝛼 𝑗,𝑖 〈𝐱, 𝐲〉 Inner product of vectors 𝐱 and 𝐲 ‖𝐱‖ Norm (Euclidean length) of vector 𝐱 Glossary Antoine Esnouf / PhD dissertation / 2018 XXVII

Figure 1 .

 1 Figure 1. IRs globaux des méthodes de calcul pour les quatre mix électriques Lors d'une comparaison de plusieurs résultats d'ICV avec une méthode donnée, ces indices montrent les potentielles différences de représentativité. Une méthode peut être adéquate pour l'un des résultats d'ICV mais ne pas représenter les principales problématiques environnementales pour un autre.

Figure 3 .

 3 Figure 3. Distributions des IRs globaux de la méthode de calcul de l'ILCD en fonction des domaines d'activité

Figure 4 .

 4 Figure 4. Représentation schématique de la chaîne de valeurs étudiéeLe travail d'inventaire se base sur des données de laboratoire obtenues dans le cadre du projet, de simulations de productions industrielles (logiciel Aspen) et i ssues de la littérature. La modélisation de l'ICV utilise la base de données ecoinvent 3.1. La méthode de calcul utilisée pour déterminer les impacts potentiels est la méthode de l'ILCD. Une analyse des contributions environnementales est alors menée.

Figure 5 .

 5 Figure 5. The sustainable development goals to end poverty, protect the planet and ensure prosperity for all (United Nations, 2015)

Figure 6 .

 6 Figure 6. Framework of the ILCD LCIA method, linking elementary flows to midpoint and endpoint indicators, extracted from Hauschild et al. (2013)

Figure 8 .

 8 Figure 8. LCIA methods published since 2000 (country/region of origin in brackets), extracted from Rosenbaum (2017)

Figure 10 .

 10 Figure 10. Graphical abstract of Chapter 2

Figure 11 .

 11 Figure 11. Geometrical representation of LCA: a) Two LCI vectors 𝐠 𝟏 and 𝐠 𝟐 plotted in a two dimensional inventory space (NO2 and NH3 gas emissions in air) ; b) impact category vectors for particulate matter formation (𝐪 𝟏 ) and acidification (𝐪 𝟐 ); c) LCA results; d) angular distances between inventories and impact category vectors.

Figure 12 .

 12 Figure 12. Visualisation of LCIA results and measurement of the cosine distance within a 3-dimensional space

Figure 13

 13 Figure 13 summarizes the full procedure to compute the RI of LCIA methods. Data cleaning is only presented in Figure S 1 of Annex A as it is carried out before the standardization step (data cleaning indeed mainly deals with the nomenclature of elementary flows). Both datasets (LCIA methods and LCI results) are first standardized using the geometric mean of each dimension. The consequences of the LCI result standardization on the directions are illustrated in Figure S 2 of the Annex A.The LCIA method sub-spaces are then orthogonalised through a Gram-Schmidt process. RIs of LCIA methods regarding each LCI result are finally calculated using the results of a least squares regression. To determine the RIs of impact categories, the same procedure is followed except that orthogonalisation is not required.

Figure 13 .

 13 Figure 13. Schematics of the procedure

Figure 14 .

 14 Figure 14. RI of LCIA methods for four electricity mix productions The Chinese mix production appears to be well represented by several LCIA methods, where the two most suitable are the ILCD and ReCiPe_end_imp_I. For this electricity mix, RIs decrease gradually from 0.11 to 0.03 with ReCiPe_end_dam_E. (see Annex A Figure S 4 for ordered method by decreasing RI values). However, this decrease in RIs is not correlated with the number of impact categories per method: although the 3 ReCiPe_end_dam methods (H, I and E) are each composed of 3 damage indicators and the Ecological Scarcity comprises 18 impact categories, they all get equivalent RIs. This

Figure 15 .

 15 Figure 15. Comparison of LCIA method RIs (numbers indicate the corresponding overlapped points)

Figure 16 .

 16 Figure 16. RIs of the impact categories of the ReCiPe mid. I. method for the Chinese and French electricity mix productions

Figure 17 .

 17 Figure 17. Graphical abstract of Chapter 3

Figure 18

 18 Figure 18. a) Representation of two standardized LCI result vectors 𝐠 ̃𝟏 and 𝐠 ̃𝟐 (in blue), two standardized impact category vectors 𝐪 ̃𝟏 and 𝐪 ̃𝟐 (in red), and the four of the angles 𝜸 𝒋,𝒊 used to measure RIs. The vector space is spanned by two basis vectors ( 𝐞 𝟏 and 𝐞 𝟐 ) representing standardized elementary flows, such as CO2 and NOx. b) Illustration of the correlation issue and 𝐪 ̃𝟐 ⊥ , the orthogonal version of 𝐪 ̃𝟐 (see below).

Figure 19 .

 19 Figure 19. Schematics of the proposed algorithm

Figure 20 .

 20 Figure 20. LCIA results (expressed relative to the highest value) and impact category RIs for the LCI results of the Chinese and German electricity mixes from the ILCD method. Bright colours correspond to decorrelated RIs 𝑹𝑰 𝒋,𝒊 𝐝𝐞𝐜𝐨𝐫𝐫 while pastels colours indicate the part removed from the original RIs by the decorrelation procedure, 𝒅 𝒋,𝒊 .

Figure 21 .

 21 Figure 21. Range of RI values of the ILCD impact categories regarding the LCI results of ecoinvent. Figured are: the median (black dot), the first and third quartile (black segment). Impact categories are classified according to their median.

Figure 22 .

 22 Figure 22. Boxplot of RI distributions according to the amount of dimensions per combination to represent 95% of the information.

  𝑅𝐼 decorr -𝑅𝐼 𝑅𝐼 are analysed for each impact category; see Figure 23. Distributions of the ratio are based on the original RI values and the orthogonalized RI values of the impact categories (see equations 16 and 18). For one LCI result, all the RIs of the impacts categories with a similar belonging to the subsets obtain the same ratio (while each LCI result is associated to a unique ratio). That means with the ILCD method that five group are done: Impact categories only in subset A, only in subset B, in A, B a nd C (i.e. the Photochemical ozone formation category), in D and in E.

Figure 23 .

 23 Figure 23. Analyses of the different redistribution of RI values. Ordinate refers to the belonging of the impact categories. Shown are: the median (large dot), the first quartile (left end of line), the third quartile (right end of line), and the 5% and 95% percentiles (small dots).

  decorr -RI original) / RI original

  4.3.1.1. Global RIs of the ILCD per field of activity Global RIs of LCI results regarding the ILCD method are first analysed. The RI distributions per field of activity and over the database are presented in Figure 24 (data are provided in Annex C -3). A ranking is applied from the median of RI values.

Figure 24 .

 24 Figure 24. Global RI distributions for fields of activity and the whole database (black dots are the medians, first and third quartiles are represented b y the bars. Fields of activity are classified according to their median)

Figure 25 .

 25 Figure 25. RI distributions for three fields of activity and the whole database (black dots are the medians, first and third quartiles a re represented by the bars. Impact categories are classified according to their median)

Figure 26 Figure 26 .

 2626 Figure 26.a. shows a sparse cloud of points. The LCIA methods represent with very different manners the information from the MATE and AF fields. As already seen with the ILCD method, the MATE gets globally higher RIs than the AF. The dispersion indicates that LCIA methods target different environmental issues that are more or less representative of the MATE or the AF. On the contrary, other comparisons obtain better correlations: Processed Biobased product -AF (Figure 26.b.); Electronic and electrical equipment -MATE (Figure 26.c.); Construction -MATE (Figure 26.d.). Correlations of global RI results on these fields reveal possible similitude on LCI results patterns from different fields (similitude inter field) and links within their respective value s chain.

  Figure 27.c. and Figure 27.d.), seemingly segregated into two groups for the resource and energy use (mineral and fuels), regarding the representation within each field of activity.

Finally, being groupedFigure 27 .

 27 by environmental issues, the impact categories show similar ranking as observed in section 3.1.2. regarding each field of activity. Land use and eutrophication groups stand out for AF; and climate change, resource and energy use and photochemical ozone formation groups are put forward for EPG. Comparison of the medians of impact category RIs

Figure 28 .

 28 Figure 28. Schematic representation of the values chain

Figure 30 .

 30 Figure 30. RI results of the entire LCI result

  Figure 31. a) RI results of the ILCD impact categories (ranking by decreasing RIs of the whole LCI result). b) Normalization by the highest RI is applied for each LCI result due to the different magnitude.

Figure 32

 32 Figure 32. a) RI results of the classic LCIA methods (ranking by decreasing RIs of the whole LCI result). b) Normalization by the highest RI is applied for each LCI result due to the different magnitude.

Figure S 1 .

 1 Figure S 1. Schematics of the full procedure, from exportation of data to RI calculation Data cleaning of LCIA methods takes place in four steps. The first is a translation of the SimaPro nomenclature of elementary flows(substance, compartment and subcompartment) to the ecoinvent nomenclature. The other three steps are needed in this order to deal with CFs that are only characterized for "unspecified" sub -compartment in SimaPro, while the ecoinvent nomenclature does not have "unspecified" but only the specified sub-compartments. For example, ecoinvent can have "surface water" and "ocean" sub -compartments for the "water" compartment and no "unspecified" sub-compartment, while an impact category only has CF for the "unspecified" sub-compartment. The procedure will apply the same CF from the "unspecified" to the "surface water" and "ocean" sub -compartments and will delete, at the end, the "unspecified" sub-compartments.

Figure S 2 .

 2 Figure S 2. Standardization of four illustrative LCI results in two dimensions (boxplots show the distribution of the whole database)

Figure S 3 .Figure S 4 .

 34 Figure S 3. Electricity mix production from the 4 studied countries. These mixes were extracted from the ecoinvent 3.1"allocation at the point of substitution" version.

Figure S 5 .

 5 Figure S 5. Relationship between RI scores of the 18 LCIA methods for the 4 studied LCIs and the number of impact category per LCIA method.

  Figure S 6. The standardized elementary flow distributions are also presented in Figure S 7.

Figure S 6 .

 6 Figure S 6. Number of LCI result per number of dimensions that assemble 95% of their principal information

  Figure S 6). Obviously, Figure S 7 indicates that the values of the standardized elementary flows are above 0.95. Through the value of one elementary flow, these LCI results distinguish themselves significantly, regarding the average LCI result of the database. Figure S 6 reveals that half of the LCI results of the database only need 5 or less dimensions, to comprise up to 95% of the norm. When more dimensions are needed, (i) the number of LCI result per group of number of dimensions decreases (Figure S 6), and (ii) the elementary flow values are lower (Figure S 7

  Figure S 8 for climate change. The major trend of the RI is driven by its first contributor. Considering these particular first elementary flows and their related CFs, the values of their multiplications have also been plotted (black dots): this represents the part of the RI that is provided by the first contributor.

Figure S 8 .

 8 Figure S 8. RI values as a function of their first elementary flow contributors (red dots) and parts of the RI provided by the first contributor (black dots). The Figure S 8 illustrates that only a few dimensions support the first elementary flows for this impact category. This small number of dimensions, represented by straight black lines, is essentially determined by the higher CFs of the impact category. Very few first

Figure S 9 .

 9 Figure S 9. RI values as a function of the rank of the first elementary flow contributorRIs between 10 -4 and 10 -6 that are related to very high first elementary flows (1 to 0.1) highlight dimensions that have low CFs. Only very few LCI results use these dimensions as first elementary flows contributing to their RI. The value of the RI is provided by the best compromise between high CFs and high elementary flows. However, values of high CFs that endorse the global impact of the database on the environmental issue, most often bear more weight on the RI values. RIs provide an interesting insight on the intensity of the elementary flow of each of the studied LCI results over the critical dimensions determined for the impact category. For one LCI result, the impact category that has the highest RI is the impact category with best compromise between high elementary flow intensities and high CFs.

Figure S 10 .Figure S 14 .

 1014 Figure S 10. RI distributions for Climate Change, Ozone depletion, Human toxicities cancer and non-cancer effects

Figure S 15 .Figure S 20 .

 1520 Figure S 15. Distributions of impact category RIs for Sections A, B and C (Section C: Processed Biobased products)

Table of

 of CONTENTS OF CHAPTER 1......................................................................................................... 1.1. CONTEXT ....................................................................................................................... 1.2. LIFE CYCLE ASSESSMENT .................................................................................................... 1.3. DATA STRUCTURE IN LCA...................................................................................................

contents

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  ... .3. RESULTS AND DISCUSSION ..................................................................................................

2.2.1. Geometrical representation of LCA methodology .................................................

.. 2.2.1.1. Life Cycle Inventories result ........................................................................................ 2.2.1.2. Impact categories ....................................................................................................... 2.2.1.3. Geometric interpretation of Life Cycle Impact Assessme nt ........................................... 2.2.2. Definition of a Representativeness Index ............................................................... 2.2.2.1. RI of an impact category ............................................................................................. 2.2.2.2. RI of a LCIA method .................................................................................................... 2.2.3. Pretreatment .......................................

................................................................ 2.2.4. Overview of the approach and implementation ..................................................... 2.2.5. Material............................................................................................................... 22.3.1. RI analysis of each LCI result ................................................................................. 2.3.2

. Comparison of RIs of LCIA methods ....................................................................... 2.3.3. Analysing RIs of impact categories ........................................................................

  .2.1.2. RI between a LCI result and an impact category ........................................................... 3.2.1.3. RI between a LCI result and a LCIA method .................................................................. 3.2.1.4. Correlation and decorrelation ..................................................................................... 3.2.2.5. Decorrelation algorithm of impact category RIs ...........................................................

.1.1. Standardization and definition of an inner product ...................................................... 3

3

.2.3. Material............................................................................................................... 3.3.

  results analysis with respect to RIs ...................................................................... 3.3.1.2. Example of decorrelation on two LCI results ................................................................3.3.2. Global trends of impact categoryRIs over the cumulated LCI database .................. 3.3.3. Contribution analyses of impact category RIs through elementary flow and CF values .. 3.3.4. Decorrelation of impact category RIs within a LCIA method ................................... CONTENTS OF CHAPTER 4 ......................................................................................................... 4.1. INTRODUCTION ............................................................................................................... 4.2. MATERIAL AND METHOD ....................................................................................................

3.3.4.1. Correlation matrix of impact categories....................................................................... 3.3.4.2. Consequences of decorrelation over the cumulated LCI database ................................. 3.4. CONCLUSIONS .................................................................................................................

Table of contents Antoine Esnouf / PhD dissertation / 2018 XVII CHAPTER 4: REPRESENTATIVENESS OF IMPACT CATEGORIES IN LCA ACCORDING TO FIELDS OF ACTIVITY ............................................................................................................................

  RIs of the ILCD per field of activity ................................................................... 4.3.1.2. Distribution of RIs of impact categories per field of activity ......................................... 4.3.2. Exploring RI distributions within other LCIA methods ............................................. 4.3.2.1. Comparison of RIs of LCIA methods ............................................................................ 4.3.2.2. Comparison of RIs of environmental issues modelled within LCIA methods ................... 4.4. CONCLUSION ..................................................................................................................

CHAPTER 5: LIFE CYCLE ASSESSMENT OF A BIOFUEL PRODUCTION FROM CELLULOSIC MACRO-ALGAE: KEY ASPECTS FOR THE ENVIRONMENTAL CONCERNS .................................................. CONTENTS OF CHAPTER 5 ......................................................................................................... 5.1. INTRODUCTION ............................................................................................................... 5.2. SYSTEM DEFINITION AND INVENTORY ..................................................................................... 5.2.1. Goal and scope, and functional unit ...................................................................... 5.2.2. Life cycle inventory ...............................................................................................

TABLE S 1

 S . GLOBAL RIS OF LCIA METHODS .......................................................................................TABLE S 2. RIS OF THE ILCD IMPACT CATEGORIES ............................................................................... TABLE S 3. DECORRELATED RIS OF THE ILCD IMPACT CATEGORIES .......................................................... TABLE S 4. ELEMENTARY FLOWS SUPPORTING IMPACT CATEGORY RIS FOR THE CHINESE ELECTRICITY MIX ........... TABLE S 5. ELEMENTARY FLOWS SUPPORTING IMPACT CATEGORY RIS FOR THE GERMAN ELECTRICITY MIX .......... TABLE S 6. MAIN CFS OF CLIMATE CHANGE .

TABLE S 21

 S . MAIN CFS OF MINERAL, FOSSIL AND RENEWABLE RESOURCE DEPLETION ...................................TABLE S 22. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF CLIMATE CHANGE ........................... TABLE S 23. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF OZONE DEPLETION ......................... TABLE S 24. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF HUMAN TOXICITY, CANCER EFFECTS ..... TABLE S 25. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN

TABLE S 26

 S . OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF PARTICULATE MATTER ......................TABLE S 27. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF IONIZING RADIATION HH ..................TABLE S 28. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF IONIZING RADIATION E (INTERIM) .......TABLE S 29. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF PHOTOCHEMICAL OZONE FORMATION .. TABLE S 30. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF ACIDIFICATION............................... TABLE S 31. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF TERRESTRIAL EUTROPHICATION .......... TABLE S 32. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF FRESHWATER EUTROPHICATION .......... TABLE S 33. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF MARINE EUTROPHICATION ................ TABLE S 34. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF FRESHWATER ECOTOXICITY ................ TABLE S 35. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF LAND USE ..................................... TABLE S 36. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF WATER RESOURCE DEPLETION ............ TABLE S 37. OCCURRENCES OF THE MAIN ELEMENTARY FLOWS IN RIS OF MINERAL, FOSSIL AND RENEWABLE RESOURCE DEPLETION .......................................................................................................... TABLE S 38. NUMBER OF LCI PER DIVISION.......................................................................................

	Tables

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TABLE S

 S 39. IDENTIFICATION KEY FOR IMPACT CATEGORIES CLASSIFICATION ...............................................TABLE S 40. CLASSIFICATION OF IMPACT CATEGORIES BY ENVIRONMENTAL ISSUES ....................................... TABLE S 41. RIS MEDIANS OF LCIA METHODS PER FIELDS OF ACTIVITY (1) ................................................ TABLE S 42. RIS MEDIANS OF LCIA METHODS PER FIELDS OF ACTIVITY (2) ................................................ TABLE S 43. RIS INTER-QUARTILES OF LCIA METHODS PER FIELDS OF ACTIVITY (1) ...................................... TABLE S 44. RIS INTER-QUARTILES OF LCIA METHODS PER FIELDS OF ACTIVITY (2) ...................................... TABLE S 45. DESCRIPTIVE STATISTICS OF RI DISTRIBUTIONS OF THE ILCD IMPACT CATEGORIES PER FIELD OF ACTIVITY

Glossary Frequent acronyms and abbreviations:

	AF	Agriculture and Forestry
	CF	Characterization Factor
	EPG	Electricity Power Generation
	HH	Human Health
	ILCD	International Reference Life Cycle Data System
	LCA	Life Cycle Assessment
	LCI	Life Cycle Inventory
	LCIA	Life Cycle Impact Assessment
	MATE	Machinery and transport equipment
	PCA	Principal Component Analysis
	RI	Representativeness Index
	SACS	Steam and Air Conditioning Supply
	Main variables, parameters and notations
	Vectors and matrices are distinguished from scalar by being written in bold, matrices are
	moreover capitalized.
	𝑚	Number of products in LCI database
	𝑛	Number of elementary flows
	𝑝	Number of impact categories in a LCIA method
	G	ℝ n vector space where each dimension refers to an elementary flow
	i	the i-th product of the cumulated LCI database
	𝐠 𝑖	LCI result vector of the 𝑖 th product (𝑖 = 1, … , 𝑚)
	𝑔 𝑥,𝑖

6. Chapitre 2. Représentativité des méthodes de calcul d'impacts environnementaux au regard des résultats d'ICVs

  XIXème siècle, la révolution thermo-industrielle a permis à une large partie de l'humanité de transformer radicalement son mode de vie et ses besoins. Principalement par l'exploitation du charbon, du pétrole et du gaz, la société industrielle s'est construite En comparant via l'ACV plusieurs systèmes qui remplissent la même fonction, l'ACV est un outil clé pour l'aide à la décision.Le cadre méthodologique de l'ACV suit quatre grandes étapes : définition des objectifs et du champ d'étude, procédure d'inventaire des flux du cycle de vie, évaluation des impacts potentiels et interprétation. Ce travail de thèse se concentre sur les deux principales en reliant les résultats de l'inventaire et l'évaluation des impacts potentiels.Pour obtenir un résultat d'Inventaire du Cycle de Vie (ICV), les flux de matières et d'énergies (les flux élémentaires), prélevés ou émis dans l'environnement, sont recensés et quantifiés depuis l'étape d'extraction des matières premières jusqu'au traitement du produit en fin de vie. Lors de la phase d'Évaluation de l'Impact du Cycle de Vie (ECVI), le résultat d'ICV est traduit sous forme d'indicateurs environnementaux sur un ensemble de catégories d'impact. Les flux élémentaires sont multipliés par des facteurs de caractérisation (FCs). En se basant sur une chaîne de causalités, ces FCs modélisent les conséquences de chaque flux vis-à-vis des problématiques environnementales. de certains résultats de catégories d'impact est effectué lors de l'interprétation. Afin de réduire le nombre de résultats de catégories d'impact à interpréter, différentes méthodes de sélection ont été développées comme ne considérer une différence entre les alternatives qu'à partir d'un certain seuil (ordre de grandeur de 20%), utiliser des valeurs de normalisation ou pondération, ou encore étudier les redondances observées entre résultats de catégories d'impact.Objectif et organisation de la thèseCe travail de thèse propose de prendre en considération d'un point de vue mathématique les exigences de l'ISO par rapport à la sélection de catégories d'impact qui doivent « refléter un ensemble complet de problèmes environnementaux liés au système de De même, les FCs sont standardisés en les multipliant par ces moyennes géométriques. Cette standardisation permet de contextualiser les résultats d'ICV et les catégories d'impact par rapport à la base de données étudiée.

	Contexte et objectifs généraux Objectif du chapitre
	Ce chapitre pose les fondements méthodologiques de la mesure de représentativité
	L'évolution de nos activités développée durant la thèse. Formalisant l'ACV avec un point de vue géométrique, l'IR est
	défini afin d'évaluer la part d'information des systèmes analysés représenté e par les
	méthodes de calcul d'impact. L'IR est une mesure d'adéquation entre résultat d'ICV et
	méthodes d'impact, il n'apporte aucune information sur la validité scientifique des
	modèles mis en oeuvre dans les méthodes.
	〈𝐪 𝑗 ,𝐠 𝑖 〉 ‖𝐪 𝑗 ‖.‖𝐠 𝑖 ‖ |	𝑅𝐼(𝐐, 𝐠 𝑖 ) = √ 1 -( ‖𝐠 𝑖 -𝐠 𝑖,𝑸 ‖ ‖𝐠 𝑖 ‖ )
	Le Chapitre 5 applique cette méthodologie sur l'ACV d'une production de carburant à
	partir de macro-algue cellulosique. Ce cas d'étude se base sur l'inventaire obtenu da ns le
	cadre du projet Green AlgOhol (ANR-14-CE05-0043) dans lequel s'inscrit cette thèse.
	L'enjeu est de contribuer à une démarche d'écoconception en apportant une information
	sur les critères regardés.

Au pour fournir une diversité de produits et de services qui améliorent (ou constituent une base utile pour l'amélioration) le bien-être de sa population, son éducation, sa mobilité, ses libertés, sa créativité et son bonheur. Face à cette situation idéalisée, le développement humain est aujourd'hui confronté à la fois à des ressources naturelles limitées

[START_REF] Meadows | The Limits to Growth[END_REF]

et à une capacité d'assimilation limitée des grands cycles biogéochimiques

[START_REF] Hoekstra | Humanity's unsustainable environmental footprint[END_REF]

. L'utilisation excessive d'énergie, des terres, de la fertilité des sols, de l'eau et autres matériaux, associée aux émissions anthropiques qui tendent à modifier les équilibres naturels actuels, ont engendré des défis environnementaux et sociaux majeurs. La pérennité de nos activités est questionnée face aux nombreux enjeux comme ceux identifiés par les Nations Unies à travers les 17 objectifs de développement durable des sociétés humaines

(United Nations, 2015)

. Mesurer la pression des activités humaines sur l'environnement est alors nécessaire pour réduire notre empreinte environnementale. Une métrique est indispensable pour chercher à remplir ces objectifs de développement durable. Parmi les approches d'évaluation des impacts sur l'environnement, l'analyse du cycle de vie (ACV) est un outil normalisé

(ISO, 2006a(ISO, , 2006b

) et reconnu internationalement.

L'Analyse du Cycle de Vie L'ACV est une méthode dite « orientée produit » qui permet de quantifier les impacts marginaux potentiels d'un produit, d'un service ou d'un système sur l'ensemble de sa chaîne de valeurs (son cycle de vie). Cette analyse environnementale relève d'une approche multicritère en calculant des impacts tant sur l'épuisement des ressources naturelles (eau, énergie primaire…), sur la qualité des écosystèmes (eutrophisation, écotoxicité…) que sur la santé humaine (toxicité, particules…). L'ACV permet ainsi d'identifier les étapes d'un cycle de vie qui peuvent être améliorées dans le but de diminuer sa charge environnementale, tout en limitant les transferts de pollution vers une autre étape ou vers une autre problématique environnementale. Cette évaluation environnementale est réalisée sur la base de la fonction rendue par le produit, service ou système évalué.

Des résultats d'ICV déjà modélisés sont regroupés au sein de bases de données qui regroupent un nombre important d'activités humaines (environ 10,000 activités pour les bases les plus récentes). Celles-ci sont d'une grande aide pour les praticiens ACV en leur évitant de tout modéliser à chaque nouvelle étude : ils peuvent utiliser des résultats déjà obtenus pour de nombreux sous-systèmes (comme un mix de production électrique dans un pays donné ou un transport maritime par exemple).

Les catégories d'impact (les enjeux environnementaux) sont regroupées à travers des méthodes de calcul, une dizaine d'entre elles sont proposées par la littérature. Chaque méthode propose d'étudier les résultats d'ICV à travers un ensemble de 10 à 20 catégories d'impact. Les principales différences qui existent entre méthodes viennent des modèles de caractérisation des mécanismes environnementaux utilisés pour le calcul des FCs, des flux élémentaires pris en compte ou encore des différences d'échelles temporelles et spatiales considérées.

Sélection des méthodes d'impacts

Lors d'une étude ACV, le choix de la méthode de calcul et des catégories d'impact est primordial pour le praticien. Ce choix dépend de nombreux facteurs comme les exigences de la problématique de l'étude définie dans les objectifs, les recommandations internationales ou d'experts, ou encore les connaissances et les habitudes du praticien.

Le caractère holistique de l'ACV, qui a entraîné la production de nombreuses catégories d'impacts différentes, peut rendre difficile le choix de la méthode et des catégories d'impact à étudier. Ainsi, la sélection des méthodes de calcul et des catégories d'impact est tout d'abord réalisée lors de la phase de définition des objectifs et du champ d'étude , puis un approfondissement produits étudié ». En bénéficiant d'une vision globale des tendances des flux élémentaires au sein d'une base de données de résultats d'ICV, la méthodologie développée permet d'évaluer, au sein d'un espace vectoriel standardisé, la pertinence relative du choix de la méthode de calcul et des catégories d'impact par rapport aux résultats d'ICV obtenus lors d'une ACV. Le Chapitre 2 présente le développement méthodologique d'un Indice de Représentativité (IR). Suite à une formalisation vectorielle de l'ACV, cette métrique est utilisée pour explorer les distances entre résultat d'ICV et méthodes de calcul au sein de l'espace vectoriel d'étude. L'adéquation des méthodes peut ainsi être comparée pour chaque résultat d'ICV. En se basant sur l'IR, le Chapitre 3 propose un outil de sélection de catégories d'impact au sein d'une méthode de calcul. Les liens entre l'IR global d'une méthode et l'ensemble des IRs des catégories d'impact de cette même méthode sont approfondis. Une analyse des dimensions, sur lesquelles chaque IR se base, a permis de déterminer des dimensions dites environnementalement critiques pour chaque catégorie d'impact. Une analyse des résultats d'IRs est réalisée dans le Chapitre 4, en regroupant les résultats d'ICV par grands domaines d'activité. Ceci permet d'explorer la diversi té de ces secteurs et de dégager des tendances dans leur représentation. Les potentialités et des perspectives de l'approche sont enfin présentées au Chapitre Méthodes L'interprétation géométrique de l'ACV permet de définir un espace vectoriel généré par les dimensions associées à chaque flux élémentaire d'une base de données. Chaque résultat d'ICV peut être localisé au sein de cet espace. De la même façon, les catégories d'impact d'une méthode de calcul sont localisées grâce à leur FCs. Le calcul des résultats d'impacts est alors assimilé à un produit vectoriel entre le vecteur de résultat d'ICV et chaque vecteur de catégorie d'impact. Les directions des résultats d'ICVs et des catégories d'impact sont déterminées par les flux élémentaires et les FCs. Afin de s'affranchir des normes de chaque vecteur, l'IR se base sur la mesure du cosinus de l'angle formé entre le résultat d'ICV et chaque catégorie d'impact ou le sous espace vectoriel généré par l'ensemble des catégories. Ainsi, un fort IR révèlera une forte proximité entre ces vecteurs. Ce chapitre se focalise sur les IRs globaux des méthodes de calcul et non les IRs des catégories d'impact. Les expressions mathématiques de la métrique développée pour un résultat d'ICV 𝐠 𝑖 et une catégorie d'impact 𝐪 𝑗 puis une méthode de calcul Q sont alors : 𝑅𝐼(𝐪 𝑗 , 𝐠 𝑖 ) = |cos(𝛼 𝑗,𝑖 )| = | 2 Où 𝛼 𝑗,𝑖 est l'angle entre les vecteurs 𝐠 𝑖 et 𝐪 𝑗 ; et 𝐠 𝑖,𝑸 le projeté orthogonal de 𝐠 𝑖 sur l'hyperplan généré par les catégories d'impact de Q.

Etant donnée la diversité des unités et des ordres de grandeur des flux élémentaires au sein d'une base de données telle qu'ecoinvent 3.1

[START_REF] Wernet | 01_Heavy metals into soil Eco_Scarc_2013_V1.01_Mineral resources EDIP_2003_V1.05_Resources (all) EPD_2013_V1.01_Abiotic depletion (optional) EPS_2000_V2.08_Crop growth capacity EPS_2000_V2.08_Depletion of reserves EPS_2000_V2.08_Wood growth capacity ILCD_Mid+_V1.05_Mineral, fossil & ren resource depletion Impact_2002+_V2.12_Mineral extraction Impact_2002+_V2.12_Non-renewable energy ReCiPe_End_E_V1.11_End_Fossil depletion ReCiPe_End_E_V1.11_End_Metal depletion ReCiPe_End_H_V1.11_End_Fossil depletion ReCiPe_End_H_V1.11_End_Metal depletion ReCiPe_End_I_V1.11_End_Fossil depletion ReCiPe_End_I_V1.11_End_Metal depletion ReCiPe_Mid_E_V1.11_Fossil depletion ReCiPe_Mid_E_V1.11_Metal depletion ReCiPe_Mid_H_V1.11_Fossil depletion ReCiPe_Mid_H_V1.11_Metal depletion ReCiPe_Mid_I_V1.11_Fossil depletion ReCiPe_Mid_I_V1.11_Metal depletion TRACI_2.1_V1.02_Fossil fuel depletion BEES_V4.05_Eutrophication CML-IA_baseline_V3.02_Eutrophication EDIP_2003_V1.05_Aquatic eutrophication EP(N) EDIP_2003_V1.05_Aquatic eutrophication EP(P) EDIP_2003_V1.05_Terrestrial eutrophication EPD_2013_V1.01_Eutrophication ILCD_Mid+_V1.05_Freshwater eutrophication ILCD_Mid+_V1.05_Marine eutrophication ILCD_Mid+_V1.05_Terrestrial eutrophication Impact_2002+_V2.12_Aquatic eutrophication ReCiPe_End_E_V1.11_End_Freshwater eutrophication ReCiPe_End_H_V1.11_End_Freshwater eutrophication ReCiPe_End_I_V1.11_End_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Freshwater eutrophication ReCiPe_Mid_E_V1.11_Marine eutrophication ReCiPe_Mid_H_V1.11_Freshwater eutrophication ReCiPe_Mid_H_V1.11_Marine eutrophication ReCiPe_Mid_I_V1.11_Freshwater eutrophication ReCiPe_Mid_I_V1.11_Marine eutrophication TRACI_2.1_V1.02_Eutrophication BEES_V4.05_Acidification CML-IA_baseline_V3.02_Acidification EDIP_2003_V1.05_Acidification EPD_2013_V[END_REF]

, une standardisation des flux d'inventaires est nécessaire afin d'harmoniser les plages des valeurs des flux élémentaires sur chaque dimension. Ces plages de valeurs étant sur des échelles logarithmiques nettement différentes, leurs moyennes géométriques sont utilisées pour diviser chaque flux de chaque inventaire.

Chapitre 3. Un outil d'aide à la sélection des catégories d'impact lors d'une ACV

  Une courte analyse des IRs des catégories d'impact de la méthode ReCiPe midpoint Individualiste est finalement présentée pour le mix chinois et français. Avec des IRs similaires de méthode, cette analyse montre les disparités qui existent sur les IRs des catégories d'impact. Ces IRs de catégories d'impact font l'objet d'une étude plus approfondie dans le Chapitre 3.Les résultats du cas d'étude de ce chapitre ont montré que le mix chinois est mieux représenté par l'ILCD et que les problématiques environnementales mises en avant par les IRs sont pour la plupart différentes entre les deux résultats d'ICVs (Figure2). En effet, le mix chinois obtient des IRs élevés pour les particules fines, l'acidification, la formation d'ozone photochimique, le changement climatique et l'eutrophisation terrestre. Concernant le mix électrique allemand, les catégories d'impact sur lesquelles se concentrer sont les radiations ionisantes (HH), l'eutrophisation des eaux douces, le changement climatique, l'utilisation des ressources en eau et la toxicité humaine (hors cancers). L'utilisation des IRs permet de guider le praticien sur les principales catégorie s d'impact à interpréter et de nuancer des résultats obtenus sur l'ensemble des catégories de la méthode.

	Objectif du chapitre
	Le Chapitre 2 ayant présenté l'IR et l'ayant appliqué aux méthodes de calcul, le
	Chapitre 3 propose l'utilisation de cette métrique pour aider au choix des résultats de
	catégories d'impact pertinents dans une méthode sur lesquels approfondir l'interprétation
	d'une ACV. L'IR est ici un outil d'aide à la réduction du nombre de catégories d'impact à
	étudier afin de faciliter la prise de décision. Un ensemble de scripts, écrit en langage
	Python, est proposé au téléchargement via un dépôt en ligne (DOI:
	10.5281/zenodo.1068914) pour permettre le calcul de l'IR de méthode et de catégories
	d'impacts.
						sous-représentativité des
	catégories d'impact. Pour résoudre ces problèmes de représentativité, un algorithme de
	décorrélation des IRs a été développé.
	Méthodes
	Les liens entre l'IR global d'une méthode et l'ensemble des IRs des catégories d'impa ct
	de cette même méthode sont ici approfondis. En effet, du fait d'une non orthogonalité
	parfaite des catégories standardisées, il peut exister une différence entre la somme des
	carrés des IRs de catégories d'impact et le carré de l'IR global de la méthode de calcul.
	Un algorithme de décorrélation des IRs de catégories d'impact est ainsi proposé afin que
	les valeurs obtenues correspondent à l'IR global de la méthode utilisée.
	Cet algorithme est tout d'abord appliqué à deux mix électriques (Allemagne et Chin e)
	issus de la base de données ecoinvent 3.1 pour la méthode de calcul de l'ILCD. Les IRs
	obtenus sont alors mis en relation avec les résultats d'ACV de ces résultats d'ICVs.
	En considérant l'ensemble des résultats d'ICV de la base de données, une analyse des
	distributions des résultats des IRs de catégories d'impact est réalisée. Les corrections des
	IRs obtenues par l'algorithme de décorrélation sont aussi analysées sur tous ces résultats
	d'ICVs. Ce chapitre propose finalement une interprétation des indice s en s'appuyant sur
	les valeurs des flux élémentaires et des FCs qui fournissent la plus grande partie de la
	Le Chapitre 2 a fait l'objet d'un article publié dans la revue Science of the Total valeur des IRs.
	Environment,	Volume	621,	Avril	2018,	Pages	1264-1271
	(https://doi.org/10.1016/j.scitotenv.2017.10.102)

L'étude des IRs des catégories d'impact par rapport à l'IR global d'une méthode a mis en évidence que les corrélations entre catégories d'impact standardisées d'une même méthode peuvent amener une sur-représentativité ou une Résultats

Figure 2. Résultats d'ACV et d'IRs des mix de production électrique chinois et allemand.

	l'origine de la valeur des IRs. Ces dimensions seraient des dimensions critiques d'un
	point de vue environnemental pour la base de données étudiée. Grâce à l a prise en compte
	des tendances des flux élémentaires sur toute la base de données, les catégories les plus
	représentatives des intensités d'un résultat d'ICV sont donc les plus pertinentes à étudier.
	Le Chapitre 2 a fait l'objet d'un article publié dans la revue Science of the Total
	Environment,	Volume	658,	Mars	2019,	Pages	768-776
	(https://doi.org/10.1016/j.scitotenv.2018.12.194)
	Les écarts entre les IRs originaux et décorrélés (couleurs franches) sont représentés par
	des couleurs pastel.
	L'algorithme de décorrélation des catégories n'entraîne pas de modifications des
	conclusions obtenues sur les IRs originaux. La détermination des dimensions qui
	soutiennent les valeurs des IRs a permis d'apporter à ces résultats d'intéressantes
	discussions complémentaires.
	Sur l'ensemble des résultats d'ICV de la base de données, l'analyse des dimensions
	représentatives a mis en évidence que ce sont principalement les dimensions a yant des
	FCs importants, et non les flux élémentaires majoritaires, qui sont le plus fréquemment à

Chapitre 4. Représentativité des catégories d'impact en fonction des domaines d'activité

	Objectif du chapitre
	Ce chapitre se propose d'explorer les tendances des résultats d'IRs en regroupant les
	résultats d'ICV par grands domaines d'activité. Cette étude permet de tester comment
	cette métrique met en avant des méthodes d'impacts (et des catégories d'impact) en
	fonction des domaines d'activités où les inventaires se placent.
	Méthodes
	En se basant sur la classification internationale de normalisation en industrie, pour toutes
	les branches d'activité économique (International Standard Industrial Classification,
	ISIC), 9 622 résultats d'ICV provenant de quatorze grands domaines d'activité ont pu être
	étudiés. Les IRs sont étudiés à travers leur distribution (médiane et interquartile) pour les
	différentes méthodes d'impacts et leurs catégories.

Chapitre 6. Discussion et conclusion générale

	Résultats L'un des principaux atouts de l'approche ACV vient de la structuration qu'elle apporte.
	Les enjeux environnementaux d'une activité humaine sont abordés à travers deux aspects :
	L'étude des impacts montre que la production des algues est la principale étape L'objectif principal de la thèse était le développement d'une métrique permettant les chaînes de valeurs (ICV) sont modélisées par les praticiens et les développeurs de
	contributrice pour 13 des 15 catégories d'impact. C'est notamment à cause de l'électricité d'évaluer la pertinence du choix d'une méthode de calcul et des catégories d'impact méthodes fournissent des outils d'évaluation (méthodes ACVI) qui modélisent des
	utilisée pour mettre en mouvement l'eau dans les bassins et la construction mêm e des associées. Ce travail a ainsi abouti au développement d'un indice de représentativité où mécanismes environnementaux. Les travaux présentés dans cette thèse contribuent à une
	bassins que ce système impacte sur l'environnement. Les autres étapes de la chaîne de l'ACV est abordée comme une projection géométrique. meilleure cohérence entre ces deux étapes afin de contribuer à une meilleure pertinence et
	valeurs affectent les catégories sans dépasser 20% de l'impact global du système, excepté efficacité des évaluations environnementales.
	pour l'étape de combustion (liée à la construction du véhicule) dont la part monte à plus
	de 30% pour les toxicités et l'écotoxicité, l'eutrophisation de l'eau douce et l'utilisation En bénéficiant de l'étude globale de bases de données de résultats d'ICV, la mise en
	de ressources naturelles. perspective de chaque résultat d'ICV et la contextualisation des catégories d'impact par
	rapport à cette base ont permis de considérer d'une manière innovante la sélection
	Le calcul des IRs de l'ILCD a permis de mettre en évidence la forte représentativité des d'indicateurs environnementaux. Ce travail de thèse ouvre plusieurs perspectives.
	radiations ionisantes, de l'utilisation de surface terrestre et de ressources naturelles.
	L'obtention des IRs des quatre sous-systèmes a montré qu'étendre l'analyse à cinq autres Concernant la standardisation utilisée et du fait de la constitution même des bases de
	catégories d'impacts supplémentaires permettrait d'avoir une meilleure repr ésentativité de données de résultats d'ICV, la surreprésentation de certains domaines d'activité (par
	l'ensemble du résultat d'ICV. Les trois premiers sous-systèmes, la production de macro-exemple, ecoinvent possède plus de 2788 résultats d'ICV de production d'électricité mais
	algues et la production et la purification de l'éthanol, obtiennent des IR s plus élevés que ne rassemble que 280 résultats d'ICV d'extraction minière) peut orienter les tendances
	l'ensemble de résultats d'ICV. La production d'éthanol a l'IR le plus élevé qui se des flux élémentaires vers ces mêmes domaines. L'utilisation de bases de données
	rapproche de la médiane des IRs de la base de données (chapitre 4). Si un système global « input-output » pourrait fournir des valeurs de standardisation qui reflèteraient les
	peut être mal représenté par une méthode d'évaluation, les sous -parties, considérées tendances d'émissions du « monde réel » avec une meilleure fidélité. Cela permettrait de
	séparément, peuvent être bien appréhendées. La combustion de l'éthanol reste mal prendre en compte les importances relatives des secteurs d'activité entre eux, en fonction
	représentée par l'ILCD avec un IR du même ordre de grandeur que celui de l'ensemble. des flux monétaires échangés.
	La production des macro-algues est la principale étape contributive de l'ensemble du Le partage d'informations surreprésentées ou sous-représentées par l'algorithme de
	système pour la plupart des impacts, mais ce n'est pas l'étape la mieux représentée par décorrélation du Chapitre 3 prend en compte les corrélations entre les vecteurs de
	l'ILCD. Ceci souligne la nécessité de focaliser l'attention dans cette étape pour catégories d'impact puis les valeurs des IRs originaux. Cette procédure peut entra iner des
	l'amélioration du système et de l'évaluation. résultats où des IRs sont modifiés sans que les dimensions associées qui engendrent ces
	problèmes de représentativité ne soient celles sur lesquelles les vecteurs de catégories
	Finalement, en étendant l'analyse des IRs à d'autres méthodes de calcul et leurs sont corrélés. Une perspective intéressante serait donc de baser la ré partition de
	catégories d'impacts, l'ILCD n'était pas forcement la méthode la plus représentative de ce l'information redondante de représentativité sur l'étude des dimensions et non des
	résultat d'ICV. En effet, à travers des catégories comme par exemple l'utilisation de catégories d'impact.
	surface urbaine ou la comptabilisation des émissions de pesticides, des méthodes comme
	ReCiPe ou Ecological scarcity pourraient amener une représentation plus précise des flux La régionalisation et l'étude de la variabilité en ACV sont des domaines qui n'ont pas été
	élémentaires problématiques de l'inventaire au regard de la base de données. abordés au regard de la méthodologie développée. Le détail des données au niveau
	régional va augmenter le nombre de dimensions au sein des bases de données, ce qui
	nécessitera des adaptations de la méthodologie des IRs. Les liens entre la variabilité en
	ACV et la variabilité au niveau des IRs devront aussi être étudiés en détail.
	Enfin, en élargissant le calcul des IRs sur l'ensemble des catégories d'impact mises à
	disposition par les méthodes de calcul, la création de « méthodes composites » qui
	concentrent des indicateurs environnementaux pertinents au regard du résultat de l'ICV
	pourrait être une aide précieuse pour un praticien menant une étude d'écoconception.

Contents of Chapter 1 1

  .1. CONTEXT ....................................................................................................................... 1.2. LIFE CYCLE ASSESSMENT .................................................................................................... 1.3. DATA STRUCTURE IN LCA................................................................................................... SELECTION OF LCIA METHODS AND IMPACT CATEGORIES ............................................................ OBJECTIVES ....................................................................................................................

	1.3.1. LCI results and LCI results database ......................................................................
	1.3.2. Impact categories and LCIA methods .....................................................................
	1.4. 1.4.1. During the goal and scope definition phase ...........................................................
	1.4.2. During the result interpretation phase ..................................................................
	1.5.

  .2.1. RI of an impact category ............................................................................................. 33 2.2.2.2. RI of a LCIA method .................................................................................................... 34 2.2.3. Pretreatment ....................................................................................................... 35 2.2.4. Overview of the approach and implementation ..................................................... 36 2.2.5. Material............................................................................................................... 36 2.3. RESULTS AND DISCUSSION .................................................................................................. 38 2.4. CONCLUSIONS ................................................................................................................. 41

	Chapter 2: Representativeness of Contents of Chapter 2
	environmental impact assessment
	methods regarding Life Cycle Inventory
	results

Figure 9. Structure of the thesis 2.1. INTRODUCTION ............................................................................................................... 29 2.2. MATERIAL AND METHOD.................................................................................................... 30 2.2.1. Geometrical representation of LCA methodology ................................................... 30 2.2.1.1. Life Cycle Inventories result ........................................................................................ 30 2.2.1.2. Impact categories ....................................................................................................... 31 2.2.1.3. Geometric interpretation of Life Cycle Impact Assessment ........................................... 32 2.2.2. Definition of a Representativeness Index ............................................................... 33 2.22.3.1. RI analysis of each LCI result .

................................................................................ 38 2.3.2. Comparison of RIs of LCIA methods ....................................................................... 39 2.3.3. Analysing RIs of impact categories ........................................................................ 40

  The LCIA methods are extracted from the SimaPro 8.1.1.16 software to analyse the most recent and operational version. Single-criteria and supersede methods are not considered; only current multi-criteria methods are selected, which represents eighteen classic LCIA

	methods: ILCD V1.05, CML-IA baseline V3.02, TRACI 2.1 V1.02, BEES+ V4.05,
	Impact 2002+ V2.12, Ecological Scarcity 2013 V1.01, EPD system 2013 V1.01, EPS
	2000 V2.08, EDIP 2003 V1.05 and ReCiPe V1.11 midpoint (mid), endpoint at impact
	level (end-imp) and aggregated at damage level (end-dam) for egalitarian perspective (E),
	hierarchist perspective (H) and individual perspective (I) version (Bare, 2011; EC-JRC,
	2010a; Frischknecht and Sybille, 2013; Goedkoop et al., 2009; Guinée et al., 2001;

Contents of Chapter 3 3

  .1. INTRODUCTION ............................................................................................................... 3.2. MATERIAL AND METHOD.................................................................................................... Standardization and definition of an inner product ...................................................... 3.2.1.2. RI between a LCI result and an impact category ........................................................... 3.2.1.3. RI between a LCI result and a LCIA method .................................................................. 3.2.1.4. Correlation and decorrelation ..................................................................................... 3.2.2.5. Decorrelation algorithm of impact category RIs ........................................................... 3.2.3. Material............................................................................................................... 3.3. RESULTS AND DISCUSSION .................................................................................................. 3.3.1. Illustrative example .............................................................................................. 3.3.1.1. LCIA results analysis with respect to RIs ...................................................................... 3.3.1.2. Example of decorrelation on two LCI results ................................................................ 3.3.2. Global trends of impact category RIs over the cumulated LCI database ..................

	3.2.1.1.

3.2.1. RI methodology .................................................................................................... 3.3.3

. Contribution analyses of impact category RIs through elementary flow and CF values .. 3.3.4. Decorrelation of impact category RIs within a LCIA method ................................... 3.3.4.1. Correlation matrix of impact categories....................................................................... 3.3.4.2. Consequences of decorrelation over the cumulated LCI database ................................. 3.4. CONCLUSIONS .................................................................................................................

Table 1 .

 1 Table1, column 1) with a global average of 3.17 dimensions (column 4). Considering Climate change, a combination of maximum seven different dimensions is sufficient to obtain 95% of the RI values and its average number of representative dimensions is 3.37. This impact category has a total of 62 non null CFs, although only half of them are present within the representative dimensions of the database: 31 dimensions are present at least in one combination to reach 95% of a single RI. However, most LCI results possess the same representative dimensions, which are obviously strongly related to the higher CFs of the concerned impact category (see Annex B -9). Considering Resource depletion, almost all of its dimensions are present in at least one RI. Conversely, Toxicities and Ionizing radiations present the highest differences between numbers of non-null CF values and numbers of representative dimensions (see Table1), which shows that it is almost always the same dimensions that drive the RI value. Descriptive values for the analysis of the main dimensions of RIs

	Impact category	maximal number of representative dimensions per LCI	number of different dimensions for 95% of the RIs	number of dimensions with CF ≠ 0	average number of representative dimensions
	Climate change	7	31	62	3.37
	Ozone depletion	8	14	19	3.10
	Human toxicity, cancer
	effects	6	46	218	2.49
	Human toxicity, non-
	cancer effects	8	64	434	3.36
	Particulate matter	7	19	26	4.24
	Ionizing radiation HH	4	9	56	2.00
	Ionizing radiation E
	(interim)	5	6	25	1.60
	Photochemical ozone
	formation	8	59	130	4.28
	Acidification	8	11	13	4.54
	Terrestrial
	eutrophication	6	10	11	3.15
	Freshwater
	eutrophication	6	9	11	2.18
	Marine eutrophication	7	16	25	3.36
	Freshwater ecotoxicity	7	94	624	3.37
	Land use	10	66	76	4.63
	Water resource
	depletion	3	3	3	1.97
	Mineral, fossil & ren
	resource depletion	8	80	92	3.11

Table 2 .

 2 Correlation matrix of impact categories of the ILCD method, on the basis of 11206 products from ecoinvent.

		FWET HTC HTNC ODP	CCP	MEP	TEP	AP	PMP POFP	IRE	IRHH MFRDP WRDP	LU	FWEP
	FWET	1	5.3e-1 9.5e-2 2.9e-11 1.4e-13	0	0	0	0	4.0e-9	0	0	0	0	0
	HTC 5.3e-1	1	1.0e-2 2.0e-7 6.0e-11	0	0	0	0	1.4e-8	0	0	0	0	0
	HTNC 9.5e-2 1.0e-2	1	1.4e-7 2.9e-11	0	0	0	0	2.6e-7	0	0	0	0	0
	ODP 2.9E-11 2.0e-7 1.4e-7	1	9.1e-5	0	0	0	0	6.2e-11	0	0	0	0	0
	CCP 1.4e-13 6.0e-11 2.9e-11 9.1e-5	1

Table 3 .

 3 Definition of subsets of impact categories and their abbreviations.

					Member of subset
	Impact category	Abbreviation
			A	B	C	D	E
	Freshwater ecotoxicity	FWET	X		X
	Human toxicity, cancer effects	HTC	X		X
	Human toxicity, non-cancer effects	HTNC	X		X
	Ozone depletion	ODP	X		X
	Climate change	CCP	X		X
	Marine eutrophication	MEP		X	X
	Terrestrial eutrophication	TEP		X	X
	Acidification	AP		X	X
	Particulate matter	PMP		X	X
	Photochemical ozone formation	POFP	X	X	X
	IRE Ionizing radiation E (interim)	IRE				X
	Ionizing radiation HH	IRHH				X
	Mineral, fossil &
	renewable resource depletion	MFRDP				X
	Water resource depletion	WRDP				X
	Land use	LU				X
	Freshwater eutrophication	FWEP				X

  INTRODUCTION ............................................................................................................... 69 4.2. MATERIAL AND METHOD.................................................................................................... 70 4.2.1. RI methodology .................................................................................................... 70 4.2.2. Fields of activity study .......................................................................................... 71 4.3. RESULTS AND DISCUSSION .................................................................................................. 73 4.3.1. Study of the ILCD .................................................................................................. 73 4.3.1.1. Global RIs of the ILCD per field of activity .................................................................... 73 4.3.1.2. Distribution of RIs of impact categories per field of activity .......................................... 74 4.3.2. Exploring RI distributions within other LCIA methods ............................................. 77 4.3.2.1. Comparison of RIs of LCIA methods ............................................................................. 77 4.3.2.2. Comparison of RIs of environmental issues modelled within LCIA methods ................... 79 4.4. CONCLUSION .................................................................................................................. 81

	Contents of Chapter 4
	4.1.

  gather a wide diversity of human activity models as for example from wheat grain production to high -speed train transport. Several studies already proposed to test statistical procedures, as selection or redundancy of indicators, by sampling LCI results depending on their field of activity.

[START_REF] Huijbregts | Is Cumulative Fossil Energy Demand a Useful Indicator for the Environmental Performance of Products[END_REF]

classified around 1218 LCI results segregated through four fields of activity from the ecoinvent database V. 1.2: energy production, material production, transport and waste treatment. Environmental impact scores were then analysed with linear regression to explore correlation with a fossil energy based indicator. Fields of activity proposed by the ecoinvent database V.2 were analysed by

Pascual-González et al. (2016)

to uncover the relationships between environmental indicators.

[START_REF] Steinmann | How Many Environmental Impact Indicators Are Needed in the Evaluation of Product Life Cycles?[END_REF]

carried out a principal component analysis on 976 LCIA results of "cradle to gate" LCI results segregated in seven product types. Distinct distributions on principal component scores were obtained per product category. Two product categories (oil and electricity) from ecoinvent, that gather a total of 231 LCIA results, were studied by

[START_REF] Pascual-González | Combined use of MILP and multi-linear regression to simplify LCA studies[END_REF]

with a combination of multi-linear regression and mixedinteger linear programming to predict impact category results. Results showed that working with homogeneous set of LCI results leads to different sets of LCIA metrics and different number of LCIA metrics needed to predict the other ones.

  as in the previous chapters.

	Firstly, global RIs of the ILCD methods (EC-JRC, 2011) are determined for the LCI
	results of different fields of activity. RIs are then measured for its impact categories
	regarding each LCI result. Secondly, the study is enlarged to other multi-criteria methods:
	CML-IA baseline V3.02, TRACI 2.1 V1.02, BEES+ V4.05, Impact 2002+ V2.12,
	Ecological Scarcity 2013 V1.01, EPD system 2013 V1.01, EPS 2000 V2.08, EDIP 2003
	V1.05 and ReCiPe V1.11 midpoint (mid), endpoint at impact level (end -imp) and
	aggregated at damage level (end-dam) for egalitarian perspective (E), hierarchist
	perspective (H) and individual perspective (I) version.

Table 3 .

 3 Number of inventories per fields of ISIC activity

	Field of activity	Number of LCI results
	Section A, Agriculture and forestry	632
	Section B, Mining and quarrying	280
	Section C, Processed Biobased product	482
	Section C, Chemicals and Plastics	1494
	Section C, Other non-metallic mineral products	285
	Section C, Metals and metal products	564
	Section C, Electronic and electronical equipment	355
	Section C, Machinery and transport equipment	355
	Section D, Electricity power generation	2788
	Section D, Manufacture of gas	90
	Section D, Steam and air conditioning supply	407
	Section E, Sewerage and Waste treatment	1150
	Section F, Construction	561
	Section H, Transport land	179
	total	9622

Table 4 .

 4 Number of impact categories per environmental issues

	Environmental issue	number of categories
	Land occupation/transformation	21
	Climate change	17
	Resources and energy use	27
	Eutrophisation	20
	Acidification	15
	Ozone depletion	14
	Photochemical oxidant formation	11
	Particulate matter formation	12
	Ecotoxicity	47
	Human toxicity	28
	Ionising radiation	14
	Water depletion	6
	total

  4.3.2. Exploring RI distributions within other LCIA methods 4.3.2.1. Comparison of RIs of LCIA methods We extended the global RI analyses to other LCIA methods. Comparison of median values from the distributions of global RIs per field of activity regarding 18 LCIA methods are presented in Figure 26. Biplots reveal the relative appropriateness of each LCIA method regarding the different fields of activity and allow visualizing correlations. Through the different environmental indicators measured within each LCIA method, relevance of LCIA methods differs for a given field of activity.The Ecological Scarcity method (ECO_Scarcity) is ranked as the best LCIA method to use for most of the fields. It is mainly due to the high number of impact cate gories that is measured by this LCIA method. By aggregating information through 3 indicators, the ReCiPe damage methods are the last representative LCIA methods.

Contents of Chapter 5 5

  .1. INTRODUCTION ............................................................................................................... 85 5.2. SYSTEM DEFINITION AND INVENTORY .................................................................................... 86 5.2.1. Goal and scope, and functional unit ...................................................................... 86 5.2.2. Life cycle inventory ............................................................................................... 86 5.2.2.1. Macro-algae production ............................................................................................. 87 5.2.2.2. Ethanol production ..................................................................................................... 88 5.2.2.3. Ethanol purification .................................................................................................... 88 5.2.2.4. Ethanol combustion ................................................................................................... 89 5.2.3. Applying the RI methodology ................................................................................ 89 5.3. RESULTS AND DISCUSSION .................................................................................................. 90 5.3.1. Contribution analysis ............................................................................................ 90 5.3.2. RI results .............................................................................................................. 91 5.3.2.1. RIs of the ILCD ............................................................................................................ 91 5.3.2.2. RIs of the ILCD impact category regarding the four LCI result subsystems ...................... 92 5.3.2.3. LCIA methods screening .............................................................................................. 94 5.4. CONCLUSIONS ................................................................................................................. 96

  The expression of the geometric mean G * x for DB * is then:The norm of 𝐠 ̃𝑖 * is linked to the norm of 𝐠 ̃𝑖 as follows

	‖𝐠 ̃𝑖 * ‖ =	1 √𝛿 𝑚	× ‖𝐠 ̃𝑖‖	(SI.7)
	Similarly, with the standardized Characterization Factors
	𝑞 ̃𝑥,𝑗 = 𝑞 𝑥,𝑗 × 𝐺 𝑥 , and 𝑞 ̃𝑥,𝑗 * = 𝑞 𝑥,𝑗 × 𝐺 𝑥 *	(SI.8)
	and using equation (SI.4), we obtain the following relations:
	𝑞 ̃𝑥,𝑗 * = √𝛿 𝑚	× 𝑞 ̃𝑥,𝑗 , and ‖𝐪 ̃𝑗 * ‖ = √𝛿 𝑚	× ‖𝐪 ̃𝑗‖	(SI.9)
	With equation 10, we have the development of 𝑅𝐼(𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * ) using DB *
	𝑅𝐼(𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * ) = | ‖𝐪 ̃𝑗 * ‖ × ‖𝐠 ̃𝑖 * ‖ 〈𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * 〉 |	(SI.10)
	With 〈𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * 〉 = ∑ (𝑞 ̃𝑥,𝑗 * × 𝑔 ̃𝑥,𝑖 * ) 𝑛 𝑥=1	and equations (SI.6-SI.9), this is rewritten
	𝑅𝐼(𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * )= |	∑ 𝑛 𝑥=1 √𝛿 ( √𝛿 m m ×‖𝐪 ̃𝑗‖× ×𝑞 ̃𝑥,𝑗 × √𝛿 m 1 √𝛿 m ×‖𝐠 ̃𝑖‖ ×𝑔 ̃𝑥,𝑖 ) 1	|	(SI.11)
	And finally after simplification
	𝑅𝐼(𝐪 ̃𝑗 * , 𝐠 ̃𝑖 * ) = 𝑅𝐼(𝐪 ̃𝑗, 𝐠 ̃𝑖)	(SI.12)
	Moreover, concerning the 𝐠 𝒂
	𝑅𝐼(𝐪 ̃𝑗 * , 𝐠 ̃𝑎 * ) = | ∑ (𝑞 ̃𝑥,𝑗 × 𝛿 × 𝑔 ̃𝑥,𝑎 ) 𝑛 𝑥 ‖𝐪 ̃𝑗‖ × 𝛿 × ‖𝐠 ̃𝑎‖ |	(SI.13)
	𝐠 𝑖 * = 𝐠 𝑖 , and 𝐠 𝒂 * = 𝛿 × 𝐠 𝑎 which equals to 𝑅𝐼(𝐪 ̃𝑗, 𝐠 ̃𝑎).	(SI.2)
	where 𝑖 ∈ {1, … , 𝑚}, 𝑖 ≠ 𝑎. 𝐺 𝑥 * = √𝛿 × 𝑔 𝑥,𝑎 𝑚 × √ ∏ 𝑔 𝑥,𝑖 𝑚 𝑖=1 𝑖≠𝑎 𝑚	(SI.3)
	𝐺 𝑥 * = √𝛿 𝑚	× 𝐺 𝑥	(SI.4)
	Within DB and DB * , a standardized x elementary flow is then:
	𝑔 ̃𝑥,𝑖 =	𝑔 𝑥,𝑖 𝐺 𝑥	, and 𝑔 ̃𝑥,𝑖 * =	𝑔 𝑥,𝑖 𝐺 𝑥 *	(SI.5)
	From equation SI.2 and SI.3, we have:
	𝑔 ̃𝑥,𝑖 * =	1 √𝛿 𝑚	× 𝑔 ̃𝑥,𝑖	(SI.6)

Table S

 S

	1. Global RIs of LCIA methods
	LCIA method	Chinese electricity	German electricity
		mix production	mix production
	ILCD_Mid+_V1.05	1.13E-01	2.72E-02
	ReCiPe_Mid_E_V1.11	9.02E-02	3.29E-02
	ReCiPe_Mid_H_V1.11	9.19E-02	3.68E-02
	ReCiPe_Mid_I_V1.11	1.03E-01	3.66E-02
	ReCiPe_End_E_V1.11_Damage	3.92E-02	1.74E-02
	ReCiPe_End_H_V1.11_Damage	5.93E-02	1.36E-02
	ReCiPe_End_I_V1.11_Damage	7.15E-02	1.21E-02
	ReCiPe_End_E_V1.11_End_	1.04E-01	3.31E-02
	ReCiPe_End_H_V1.11_End_	1.06E-01	3.70E-02
	ReCiPe_End_I_V1.11_End_	1.16E-01	3.69E-02
	CML-IA_baseline_V3.02	8.88E-02	2.76E-02
	TRACI_2.1_V1.02	8.25E-02	1.91E-02
	Impact_2002+_V2.12	8.67E-02	3.11E-02
	Eco_Scarc_2013_V1.01	8.68E-02	8.81E-02
	EPD_2013_V1.01	7.63E-02	1.77E-02
	EPS_2000_V2.08	1.22E-01	1.18E-02
	EDIP_2003_V1.05	9.52E-02	5.94E-02
	BEES_V4.05	1.01E-01	2.08E-02

Table S 2. RIs of the ILCD impact categories ILCD, Impact category Chinese electricity mix production

 S

			German electricity
			mix production
	Climate change	3.54E-02	8.02E-03
	Ozone depletion	1.99E-03	5.32E-03
	Human toxicity, cancer effects	3.40E-03	4.22E-03
	Human toxicity, non-cancer effects	7.35E-03	6.44E-03
	Particulate matter	9.77E-02	1.24E-03
	Ionizing radiation HH	5.50E-03	1.75E-02
	Ionizing radiation E (interim)	1.84E-03	5.95E-03
	Photochemical ozone formation	4.43E-02	2.68E-03
	Acidification	6.42E-02	2.20E-03
	Terrestrial eutrophication	3.79E-02	2.41E-03
	Freshwater eutrophication	7.57E-03	1.57E-02
	Marine eutrophication	1.74E-02	1.20E-03
	Freshwater ecotoxicity	3.12E-03	4.48E-03
	Land use	4.33E-03	1.24E-03
	Water resource depletion	6.12E-17	1.49E-08
	Mineral, fossil & ren resource	5.84E-04	7.06E-04
	depletion

Table S 3. Decorrelated RIs of the ILCD impact categories ILCD, Impact category Chinese electricity mix production

 S The following tables correspond to the analysis of the elementary flows that contribute the most to RIs of both of the studied LCI. The LCIA method used is the ILCD. RIs are determined with the database under the ecoinvent elementary flow nomenclature and not with the simapro elementary flow nomenclature. Elementary flows supporting impact category RIs for the Chinese electricity mix Elementary flows supporting impact category RIs for the German electricity mix Main standardized Characterization Factors per impact category of the ILCDThe following tables correspond to the main CFs for each impact category of the ILCD obtained after the standardization procedure. Only the first eight CFs per impact category are presented due to the high number of CFs.

				Annexes Annexes Annexes Annexes Annexes
	German electricity mix production 7.56E-03 5.02E-03 3.97E-03 Annex B-7: RI description per LCI through the main elementary flows Climate change 3.53E-02 Ozone depletion 1.99E-03 Human toxicity, cancer effects 3.40E-03 LCI: electricity, high voltage//[CN] market for electricity, high voltage Global RI of the method: 1.13E-01 Table S 4. Impact category Elementary flows Dimension contribution of the RI Impact category RI Std elementary flow value particulate matter particulates, < 2.5 um to air urban air close to ground 7.65E-02 9.74E-02 8.60E-02 sulfur dioxide to air urban air close to ground 1.66E-02 8.15E-02 acidification sulfur dioxide to air urban air close to ground 4.32E-02 6.40E-02 8.15E-02 nitrogen oxides to air urban air close to ground 1.27E-02 5.96E-02 sulfur dioxide to air non-urban air or from high stacks 7.56E-03 9.98E-03 photochemical ozone formation nitrogen oxides to air urban air close to ground 3.55E-02 4.41E-02 5.96E-02 sulfur dioxide to air urban air close to ground 5.54E-03 8.15E-02 terrestrial eutrophication nitrogen oxides to air urban air close to ground 3.66E-02 3.78E-02 5.96E-02 climate change carbon dioxide, fossil to air urban air close to ground 2.53E-02 3.53E-02 3.66E-02 methane, fossil to air non-urban air or from high stacks 5.00E-03 5.22E-02 carbon dioxide, fossil to air non-urban air or from high stacks 4.07E-03 6.01E-03 marine eutrophication nitrogen oxides to air urban air close to ground 1.63E-02 1.74E-02 5.96E-02 water resource depletion water, river to natural resource in water 5.62E-03 9.46E-03 5.81E-03 water, well, in ground to natural resource in water 3.76E-03 1.47E-02 freshwater eutrophication phosphate to water ground-, long-term 6.58E-03 7.55E-03 6.73E-03 phosphate to water ground-9.67E-04 4.49E-03 human toxicity, non-cancer effects zinc, ion to water ground-, long-term 1.93E-03 7.33E-03 2.27E-03 arsenic, ion to water ground-, long-term 1.93E-03 3.77E-03 mercury to air urban air close to ground 1.71E-03 6.74E-02 zinc to air urban air close to ground 7.76E-04 3.87E-02 lead to air urban air close to ground 3.91E-04 5.23E-02 ionizing radiation hh radon-222 to air low population density, long-term 4.41E-03 5.48E-03 5.38E-03 carbon-14 to air non-urban air or from high stacks 8.83E-04 1.54E-03 land use transformation, to industrial area to natural resource land 2.25E-03 4.33E-03 8.21E-03 transformation, from unspecified to natural resource land 2.02E-03 1.16E-02 transformation, to dump site to natural resource land 1.89E-03 4.95E-02 occupation, dump site to natural resource land 9.10E-04 3.64E-02 transformation, to mineral extraction site to natural resource land 7.42E-04 1.04E-03 human toxicity, cancer effects chromium vi to water ground-, long-term 2.95E-03 3.39E-03 2.99E-03 freshwater ecotoxicity zinc, ion to water ground-, long-term 1.39E-03 3.11E-03 2.27E-03 copper, ion to water ground-, long-term 5.94E-04 7.68E-04 nickel, ion to water ground-, long-term 3.69E-04 4.46E-03 chromium vi to water ground-, long-term 2.74E-04 2.99E-03 LCI: electricity, high voltage//[DE] market for electricity, high voltage Global RI of the method: 2.85E-02 Table S 5. Impact Elementary flow Dimension Impact category Std elementary or from high stacks ozone depletion ethane, 1,2-dichloro-1,1,2,2-tetrafluoro-, cfc-114 to air non-urban air or from high stacks 2.89E-03 5.37E-03 2.12E-02 methane, 1.53E-03 1.16E-02 eutrophication term nitrogen oxides to air non-urban air or from high stacks 7.33E-04 2.54E-03 nitrogen oxides to air urban air close to ground 1.76E-04 6.45E-04 nitrate to water ground-1.38E-04 1.23E-02 to natural resource land particulate matter sulfur dioxide to air non-urban air or from high stacks 3.84E-04 1.25E-03 1.44E-03 particulates, < 2.5 um to air urban air close to ground 3.09E-04 3.48E-04 particulates, < 2.5 um to air 2.46E-04 9.06E-04 Annex B-8: Table S 6. Main CFs of Climate Change vanadium, ion to water ground-, long-term 1.97E-04 2.15E-03 ozone depletion methane, bromotrifluoro-, halon 1301 to air non-urban air or from high stacks 9.28E-04 1.99E-03 9.49E-04 ethane, 1,2-dichloro-1,1,2,2-tetrafluoro-, cfc-114 to air non-urban air or from high stacks 8.58E-04 6.27E-03 ionizing radiation e (interim) carbon-14 to air non-urban air or from high stacks 1.54E-03 1.84E-03 1.54E-03 cesium-137 to water ocean 2.17E-04 4.51E-03 mineral, fossil & ren resource depletion nickel, 1.98% in silicates, 1.04% in crude ore, in ground to natural resource in ground 1.66E-04 5.82E-04 9.31E-04 indium, 0.005% in sulfide, in 0.003%, pb, zn, ag, cd, in ground to natural resource in ground 1.60E-04 1.65E-04 uranium, in ground to natural resource in ground 8.63E-05 4.57E-03 coal, hard, unspecified, in ground to natural resource in ground 4.54E-05 4.68E-02 category contribution of the RI RI flow value ionizing radiation hh radon-222 to air low population density, long-term 1.46E-02 1.76E-02 1.78E-02 carbon-14 to air non-urban air or from high stacks 2.63E-03 4.60E-03 freshwater eutrophication phosphate to water ground-, long-term 1.41E-02 1.58E-02 1.45E-02 phosphate to water ground-1.68E-03 7.79E-03 climate change carbon dioxide, fossil to air non-urban air or from high stacks 6.25E-03 8.09E-03 9.23E-03 carbon dioxide, fossil to air urban air close to ground 1.09E-03 1.58E-03 methane, fossil to air non-urban air or from high stacks 4.89E-04 5.10E-03 water resource depletion water, river to natural resource in water 5.21E-03 7.37E-03 5.39E-03 water, well, in ground to natural resource in water 2.14E-03 8.38E-03 human toxicity, non-cancer effects zinc, ion to water ground-, long-term 2.82E-03 6.49E-03 3.32E-03 arsenic, ion to water ground-, long-term 2.79E-03 5.44E-03 mercury to air non-urban air or from high stacks 3.97E-04 9.22E-03 ionizing radiation e (interim) carbon-14 to air non-urban air or from high stacks 4.59E-03 6.00E-03 4.60E-03 cesium-137 to water ocean 7.76E-04 1.62E-02 iodine-131 to air non-urban air 3.52E-04 3.89E-01 bromochlorodifluoro-, halon 1211 to air non-urban air or from high stacks methane, bromotrifluoro-, halon 1301 to air non-urban air or from high stacks 5.59E-04 5.72E-04 freshwater ecotoxicity zinc, ion to water ground-, long-term 2.03E-03 4.52E-03 3.32E-03 copper, ion to water ground-, long-term 7.73E-04 9.99E-04 nickel, ion to water ground-, long-term 7.04E-04 8.50E-03 chromium vi to water ground-, long-term 3.58E-04 3.91E-03 vanadium, ion to water human toxicity, cancer effects chromium vi to water ground-, photochemical ozone formation nitrogen oxides to air non-nitrogen oxides to air urban air nmvoc, non-methane volatile nitrogen oxides to air sulfur dioxide to air non-urban marine nitrate to water ground-, long-1.30E-03 2.51E-03 1.45E-03 crop, non-irrigated, intensive transformation, from annual 2.45E-03 2.20E-02 air or from high stacks 1.40E-04 1.44E-03 to natural resource land transformation, to annual crop 3.44E-03 4.38E-02 unspecified 1.77E-04 4.09E-04 to natural resource land crop, non-irrigated, extensive urban air or from high stacks transformation, from annual 5.84E-03 6.92E-02 unspecified origin to air non-to natural resource land organic compounds, 2.19E-04 1.11E-03 crop, non-irrigated, extensive transformation, to annual 5.85E-03 6.85E-02 close to ground 3.84E-04 6.45E-04 to natural resource land crop, non-irrigated, intensive urban air or from high stacks 1.60E-03 2.70E-03 2.54E-03 transformation, to annual 9.25E-03 1.87E-02 crop to natural resource land long-term 3.86E-03 4.25E-03 3.91E-03 land use transformation, from annual 9.29E-03 2.13E-03 3.08E-02 close to ground ground-, long-term 3.27E-04 3.57E-03 terrestrial eutrophication nitrogen oxides to air non-1.65E-03 2.43E-03 2.54E-03 non-urban air or from high stacks Dimension Climate Std elementary flow rank 19 21 21 26 107 26 21 26 47 30 141 26 144 80 132 222 306 243 24 45 29 193 440 115 97 38 48 624 271 306 833 224 271 Std elementary 157 373 730 1247 345 914 1491 1056 316 670 138 440 216 672 1705 211 41 flow rank 222 543 308 448 404 888 524 517 424 610 514 405 543 284 1 1286 610 1044 420 576 909 154 914 55 1436 22 1000 24 1247 730 187 576 120 592 730 urban air or from high stacks nitrogen oxides to air urban air close to ground 3.96E-04 6.45E-04 1247 particulates, < 2.5 um to air 8.31E-05 6.40E-04 1249 change nitrogen oxides to air ammonia to air non-urban air acidification sulfur dioxide to air non-urban nitrogen oxides to air non-sulfur dioxide to air urban air nitrogen oxides to air urban air 1.37E-04 6.45E-04 1247 to natural resource in ground close to ground 1.86E-04 3.51E-04 1485 1.04% in crude ore, in ground nickel, 1.98% in silicates, 8.45E-05 4.74E-04 1379 urban air or from high stacks 5.70E-04 2.54E-03 730 ground ground to natural resource in air or from high stacks 1.09E-03 2.21E-03 1.44E-03 914 0.003%, pb, zn, ag, cd, in depletion indium, 0.005% in sulfide, in 1.91E-04 1.96E-04 1718 or from high stacks 1.31E-04 9.12E-03 406 & ren resource resource in ground mineral, fossil uranium, in ground to natural 2.85E-04 7.12E-04 1.51E-02 299 unspecified 1.83E-04 4.09E-04 1436 unspecified sulfur dioxide to air urban air close to ground 7.17E-05 3.51E-04 1485 carbon dioxide, fossil to air urban air close to ground 6.92E-01 carbon dioxide,	Std CF value 8.90E-01 2.04E-01 5.30E-01 2.12E-01 7.58E-01 5.95E-01 6.80E-02 6.14E-01 6.92E-01 9.57E-02 6.77E-01 2.73E-01 9.67E-01 2.55E-01 9.77E-01 2.15E-01 8.50E-01 5.13E-01 2.54E-02 2.00E-02 7.46E-03 8.19E-01 5.73E-01 2.74E-01 -1.75E-01 3.82E-02 2.50E-02 7.12E-01 9.87E-01 6.12E-01 7.74E-01 8.28E-02 Std CF value 1.37E-01 1.32E-01 2.88E-01 2.73E-01 1.12E-02 2.68E-01 8.90E-01 2.72E-01 9.16E-02 9.16E-02 9.78E-01 1.37E-01 9.99E-01 4.80E-02 1.78E-01 9.75E-01 1.89E-02 9.70E-04 8.19E-01 5.73E-01 9.77E-01 2.15E-01 6.77E-01 6.92E-01 9.57E-02 9.67E-01 2.55E-01 8.50E-01 5.13E-01 4.31E-02 9.99E-01 4.80E-02 9.04E-04 9.78E-01 6.12E-01 7.74E-01 8.28E-02 9.16E-02 8.96E-01 -1.11E-01 9.72E-02 7.86E-02 4.33E-01 -8.43E-02 1.98E-01 8.55E-02 5.95E-01 4.95E-01 6.28E-01 -3.02E-01 9.87E-01 9.16E-02 6.48E-01 1.30E-01 6.14E-01 2.12E-01 5.30E-01 1.78E-01 2.24E-01 7.58E-01 9.75E-01 1.44E-02 1.89E-02 4.47E-01 2.04E-01	Std CF rank 0 3 1 3 0 1 6 1 0 3 1 Std CF rank
	Human toxicity, non-cancer effects	7.34E-03		6.07E-03
	Particulate matter Antoine Esnouf / PhD dissertation / 2018 Antoine Esnouf / PhD dissertation / 2018 Antoine Esnouf / PhD dissertation / 2018 Antoine Esnouf / PhD dissertation / 2018	7.89E-02	136	8.19E-04 131 133 135 137	Antoine Esnouf / PhD dissertation / 2018
	Ionizing radiation HH	5.43E-03		1.72E-02
	Ionizing radiation E (interim)	1.82E-03		5.85E-03
	Photochemical ozone formation	3.57E-02		1.53E-03
	Acidification	5.19E-02		1.45E-03
	Terrestrial eutrophication	3.06E-02		1.59E-03
	Freshwater eutrophication	7.57E-03		1.57E-02
	Marine eutrophication	1.41E-02		7.92E-04
	Freshwater ecotoxicity	3.12E-03		4.22E-03
	Land use	4.33E-03		1.24E-03
	Water resource depletion	6.12E-17		1.49E-08
	Mineral, fossil & ren resource	5.84E-04		7.06E-04
	depletion

fossil to air non-urban air or from high stacks

		6.77E-01
	carbon dioxide, fossil to air unspecified	2.32E-01
	methane,

fossil to air non-urban air or from high stacks

		9.57E-02
	dinitrogen monoxide to air urban air close to ground	1.09E-02
	methane, fossil to air urban air close to ground	8.05E-03
	methane, fossil to air unspecified	7.05E-03
	dinitrogen

monoxide to air non-urban air or from high stacks

	5.88E-03
	Table S 7. Main CFs of Ozone depletion

Dimension Ozone depletion methane, bromotrifluoro-, halon 1301 to air non-urban air or from high stacks

	9.78E-01
	ethane, 1

,2-dichloro-1,1,2,2-tetrafluoro-, cfc-114 to air non-urban air or from high stacks 1.37E-01 methane, bromochlorodifluoro-, halon 1211 to air non-urban air or from high stacks

	1.32E-01
	methane,

tetrachloro-, r-10 to air urban air close to ground

		5.57E-02
	methane, dichlorodifluoro-, cfc-12 to air urban air close to ground	5.39E-02
	ethane, 1,1,2-trichloro-1,2,2-trifluoro-, cfc-113 to air unspecified	2.86E-02
	methane, chlorodifluoro-

, hcfc-22 to air non-urban air or from high stacks

	Table S 8. Main CFs of Human toxicity, cancer effects
	Dimension	Human
		toxicity, cancer
		effects
	chromium vi to water ground-, long-term	9.87E-01
	chromium vi to water surface water	1.51E-01
	chromium to air non-urban air or from high stacks	3.58E-02
	nickel, ion to water ground-, long-term	2.27E-02
	arsenic, ion to water ground-, long-term	1.77E-02
	chromium, ion to water surface water	4.55E-03
	chromium, ion to water unspecified	3.88E-03
	chromium vi to soil unspecified	3.56E-03
	Table S 9. Main CFs of Human toxicity, non-cancer effects
	Dimension	Human toxicity,
		2.46E-02
	methane, chlorodifluoro-, hcfc-22 to air urban air close to ground	1.70E-02

non-cancer effects zinc, ion to water ground-, long-term 8.50E-01 arsenic, ion to water ground-, long-term

		5.13E-01
	mercury to air unspecified	6.20E-02
	zinc to air non-urban air or from high stacks	5.99E-02
	mercury to air non-urban air or from high stacks	4.31E-02
	arsenic, ion to water surface water	3.25E-02
	lead to air non-urban air or from high stacks	3.03E-02
	zinc to air unspecified	2.96E-02

Annexes

Antoine Esnouf / PhD dissertation / 2018 139

oxides to air non-urban air or from high stacks

	Table S 10. Main CFs of Particulate matter
	Dimension	Particulate
		matter
	particulates, < 2.5 um to air urban air close to ground	8.90E-01
	particulates, < 2.5 um to air non-urban air or from high stacks	2.72E-01
	sulfur dioxide to air non-urban air or from high stacks	2.68E-01
	sulfur dioxide to air urban air close to ground	2.04E-01
	particulates, < 2.5 um to air unspecified	1.30E-01
	sulfur dioxide to air unspecified	5.58E-02
	nitrogen oxides to air urban air close to ground	1.69E-02
	nitrogen 1.66E-02
	Table S 11. Main CFs of Ionizing radiation HH
	Dimension	Ionizing
		radiation HH

radon-222 to air low population density, long-term 8.19E-01 carbon-14 to air non-urban air or from high stacks 5.73E-01 radon-222 to air non-urban air or from high stacks

	Table S 12. Main CFs of Ionizing radiation E (interim)
	Dimension	Ionizing radiation
		E (interim)
	carbon-14 to air non-urban air or from high stacks	9.99E-01
	cesium-137 to water ocean	4.80E-02
	hydrogen-3, tritium to water surface water	1.48E-02
	hydrogen-3, tritium to water ocean	1.12E-02
	antimony-124 to water surface water	8.08E-03
	cobalt-60 to water surface water	4.78E-03
	cesium-137 to water surface water	3.39E-03
	cobalt-58 to water surface water	3.27E-03
	Table S 13. Main CFs of Photochemical ozone formation
	Dimension	Photochemical
		ozone formation
	nitrogen
		2.33E-02
	cesium-137 to water surface water	1.07E-03
	cobalt-60 to water surface water	7.42E-04
	uranium-234 to air non-urban air or from high stacks	6.04E-04
	iodine-129 to air non-urban air or from high stacks	4.60E-04
	radium-226 to water surface water	3.76E-04

oxides to air non-urban air or from high stacks 6.28E-01 nitrogen oxides to air urban air close to ground

		5.95E-01
	nitrogen oxides to air unspecified	4.33E-01
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air non-urban air or from high stacks

	1.98E-01

sulfur dioxide to air non-urban air or from high stacks

	9.72E-02
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air unspecified

		7.66E-02
	sulfur dioxide to air urban air close to ground	6.80E-02
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air urban air close to ground

	Annexes
		6.48E-02
	Antoine Esnouf / PhD dissertation / 2018	141

nitrogen oxides to air non-urban air or from high stacks 6.48E-01 nitrogen oxides to air urban air close to ground

	Table S 14. Main CFs of Acidification Table S 16. Main CFs of Freshwater eutrophication
	Dimension Dimension	Acidification Freshwater
	sulfur dioxide to air non-urban air or from high stacks	7.58E-01 eutrophication
	sulfur dioxide to air urban air close to ground phosphate to water ground-, long-term	5.30E-01 9.77E-01
	nitrogen oxides to air non-urban air or from high stacks phosphate to water ground-	2.24E-01 2.15E-01
	nitrogen oxides to air urban air close to ground phosphate to water surface water	2.12E-01 2.10E-03
	sulfur dioxide to air unspecified phosphorus to water surface water	1.58E-01 1.98E-03
	nitrogen oxides to air unspecified phosphorus to soil agricultural	1.55E-01 1.33E-03
	ammonia to air unspecified phosphorus to soil industrial	2.43E-02 4.23E-04
	ammonia to air urban air close to ground phosphate to water ocean	9.99E-03 1.45E-04
	phosphorus to water ocean	3.73E-05
	Table S 15. Main CFs of Terrestrial eutrophication
	Table S 17. Main CFs of Marine eutrophication
	Dimension	Terrestrial
	Dimension	eutrophication Marine
		eutrophication
		6.14E-01
	nitrogen oxides to air unspecified	4.47E-01
	ammonia to air unspecified	5.45E-02
	ammonia to air urban air close to ground	2.24E-02
	ammonia to air non-urban air or from high stacks	1.44E-02
	nitrogen oxides to air lower stratosphere + upper troposphere	1.78E-05
	nitrate to air unspecified	1.14E-05

nitrate to water ground-, long-term 8.96E-01 nitrogen oxides to air non-urban air or from high stacks

		2.88E-01
	nitrogen oxides to air urban air close to ground	2.73E-01
	nitrogen oxides to air unspecified	1.99E-01
	nitrate to water ground-	1.12E-02
	nitrate to water surface water	9.37E-03
	ammonium, ion to water ground-, long-term	7.18E-03
	ammonium, ion to water surface water	6.71E-03

Annexes

Antoine Esnouf / PhD dissertation / 2018 143

, to mineral extraction site to natural resource land 7.12E-01 transformation, to annual crop, non-irrigated, intensive to natural resource land

	Table S 18. Main CFs of Freshwater ecotoxicity
	Dimension	Freshwater
		ecotoxicity
	copper, ion to water ground-, long-term	7.74E-01
	zinc, ion to water ground-, long-term	6.12E-01
	vanadium, ion to water ground-, long-term	9.16E-02
	chromium vi to water ground-, long-term	9.16E-02
	nickel, ion to water ground-, long-term	8.28E-02
	antimony to water ground-, long-term	3.67E-02
	arsenic, ion to water ground-, long-term	1.81E-02
	chromium vi to water surface water	1.40E-02
	Table S 19. Main CFs of Land use
	Dimension	Land use
	transformation4.95E-01
	transformation, to industrial area to natural resource land	2.74E-01
	transformation,

to annual crop, non-irrigated, extensive to natural resource land

	Table S 20. Main CFs of Water resource depletion
	Dimension	Water resource
		depletion
	water, river to natural resource in water	9.67E-01
	water, well, in ground to natural resource in water	2.55E-01
	water, lake to natural resource in water	8.34E-03
	Table S 21. Main CFs of Mineral, fossil and renewable resource depletion
	Dimension	Mineral, fossil & ren
		resource depletion
	indium, 0
		8.55E-02
	transformation, to annual crop to natural resource land	7.86E-02
	occupation, forest, intensive to natural resource land	7.45E-02
	transformation, to dump site to natural resource land	3.82E-02
	transformation, to traffic area, road network to natural resource land	3.72E-02

.005% in sulfide, in 0.003%, pb, zn, ag, cd, in ground to natural resource in ground

	9.75E-01
	nickel, 1

.98% in silicates, 1.04% in crude ore, in ground to natural resource in ground

	1.78E-01
	cadmium, 0

.30% in sulfide, cd 0.18%, pb, zn, ag, in, in ground to natural resource in ground 1.17E-01 silver, ag 9.7e-4%, in mixed ore, in ground to natural resource in ground 3.11E-02 copper, 0.99% in sulfide, cu 0.36% and mo 8.2e-3% in crude ore, in ground to natural resource in ground 2.74E-02 lead, 5.0% in sulfide, pb 3.0%, zn, ag, cd, in, in ground to natural resource in ground

	2.67E-02
	silver, 0

.007% in sulfide, ag 0.004%, pb, zn, cd, in, in ground to natural r esource in ground

	2.16E-02
	tantalum, 81

.9% in tantalite, 1.6e-4% in crude ore, in ground to natural resource in ground

  For each impact categories, the following tables reference the main representative elementary flows based on an occurrence analysis. These elementary flows are the ones that most often provide 95% of the RI values for each LCI. The columns corresp ond to the number of different elementary flows per combination. Table are limited to the first eight main elementary flows.

	Annexes
	Annex B-9: Occurrence of representative elementary flows
		2.14E-02
	Antoine Esnouf / PhD dissertation / 2018	145

fossil to air non-urban air or from high stacks

  Table S 22. Occurrences of the main elementary flows in RIs of Climate Change

	Elementary flow	1	2	3	4	5	6	7	total	% of total
										occurrence
	carbon dioxide, 329	783	4194	4619	556	42	123	10646 28%
	carbon dioxide, fossil to air urban air close to ground	203	812	4209	4630	556	42	123	10575 56%
	carbon dioxide, fossil to air unspecified	18	61	2962	4327	504	42	123	8037	77%
	methane,

fossil to air non-urban air or from high stacks

	2	124	799	3503	223	5		4656	90%
	dinitrogen monoxide to air urban air close to ground	12	75	458	222	21	50	838	92%
	dinitrogen

monoxide to air non-urban air or from high stacks

	24	125	279	233	34	123	818	94%
	methane,

fossil to air urban air close to ground

	141	278	178	28	1	626	96%
	methane,

non-fossil to air non-urban air or from high stacks

	8	11	25	168	177	12	112	513	97%

Table S 23.

 S Occurrences of the main elementary flows in RIs of Ozone Depletion

	Elementary flow	1	2	3	4	5	6	7	8	total	% of total
											occurrence
	methane,

bromotrifluoro-, halon 1301 to air non-urban air or from high stacks

	1681	2095	2593	2199	1275	772	66	19	10700 31%
	ethane, 1

,2-dichloro-1,1,2,2-tetrafluoro-, cfc-114 to air non-urban air or from high stacks

	128	653	1944	2088	961	760	65	19	6618	50%
	methane,

bromochlorodifluoro-, halon 1211 to air non-urban air or from high stacks

		118	533	2070	2074	929	738	66	19	6547	69%
	methane, tetrachloro-, r-10 to air urban air close to ground	45	532	529	1090	916	605	62	19	3798	80%
	methane, dichlorodifluoro-, cfc-12 to air urban air close to ground	26	156	411	754	978	770	66	19	3180	89%
	methane,

chlorodifluoro-, hcfc-22 to air non-urban air or from high stacks

			170	114	370	439	291	27	19	1430	93%
	methane, chlorodifluoro-, hcfc-22 to air urban air close to ground	2	2	131	62	419	476	62	19	1173	96%
	ethane, 1

,1,2-trichloro-1,2,2-trifluoro-, cfc-113 to air unspecified

	41	208	67	131	192	206	43	19	907	99%

  Table S 24. Occurrences of the main elementary flows in RIs of Human toxicity, cancer effects

	Elementary flow	1	2	3	4	5	6	total	% of total
									occurrence
	chromium vi to water ground-, long-term	808	5005	4502	837	34	3	11189 40%
	chromium vi to water surface water	3	4384	4364	834	33	3	9621	75%
	chromium to air non-urban air or from high stacks	2		2839	471	27	3	3342	87%
	arsenic, ion to water ground-, long-term		374	307	209	6		896	90%
	chromium, ion to water surface water		10	438	298	22		768	93%
	chromium, ion to water ground-		27	192	247	22		488	94%
	chromium, ion to water unspecified		38	253	61			352	96%
	chromium vi to soil unspecified		86	154	57	1		298	97%

  Table S 25. Occurrences of the main elementary flows in RIs of Human toxicity, non-cancer effects Table S 27. Occurrences of the main elementary flows in RIs of Ionizing radiation HH

	Elementary flow	1	2	3	4	total	% of total
							occurrence
	radon-222 to air low population density, long-term	98	11029 45	10	11182 50%
	carbon-14 to air non-urban air or from high stacks	19	11029 45	10	11103 100%
	uranium-234 to air non-urban air or from high stacks			30	10	40	100%
	radon-222 to air non-urban air or from high stacks	3	2	6		11	100%
	thorium-230 to air non-urban air or from high stacks				8	8	100%
	polonium-210 to air urban air close to ground			5		5	100%
	uranium-238 to water surface water			4		4	100%
	radium-226 to water ocean				2	2	100%

14 to air non-urban air or from high stacks

  Table S 28. Occurrences of the main elementary flows in RIs of Ionizing radiation E (interim)

	Elementary flow	1	2	3	4	5	total	% of total
								occurrence
	carbon-5155	5687	65	270	29	11206 62%
	cesium-137 to water ocean		5686	65	270	29	6050	96%
	hydrogen-3, tritium to water surface water		1	44	270	29	344	98%
	antimony-124 to water surface water				270	29	299	100%
	carbon-14 to water surface water					29	29	100%
	iodine-

131 to air non-urban air or from high stacks

	21	21	100%

Table S 29.

 S Occurrences of the main elementary flows in RIs of Photochemical ozone formation

	Elementary flow	1	2	3	4	5	6	7	8	total	%

of total occurrence nitrogen oxides to air non-urban air or from high stacks

		28	364	1364 3679 3556 1334 152	4	10481 22%
	nitrogen oxides to air urban air close to ground	82	315	792	3439 3549 1332 131	4	9644	42%
	nitrogen oxides to air unspecified	6	275	947	3142 3395 1323 151	4	9243	61%
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air non-urban air or from high stacks

		15	114	647	2102 2744 1157 137	4	6920	76%
	sulfur dioxide to air non-urban air or from high stacks	6	145	222	766	1166 686	40		3031	82%
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air unspecified

	8	165	196	529	1262 581	53	2794	88%
	nmvoc,

non-methane volatile organic compounds, unspecified origin to air urban air close to ground

		106	290	376	979	776	123	4	2654	93%
	sulfur dioxide to air urban air close to ground	28	112	440	616	374	20		1590	97%

  Table S 30. Occurrences of the main elementary flows in RIs of Acidification

	Elementary flow	1	2	3	4	5	6	7	8	total	% of total
											occurrence
	sulfur dioxide to air non-urban air or from high stacks	65	430	1525	2066	3426	2811	277	2	10602 21%
	sulfur dioxide to air urban air close to ground	13	261	1267	1959	3417	2811	277	2	10007 40%
	nitrogen oxides to air non-urban air or from high stacks	5	377	520	1384	2945	2760	277	2	8270	57%
	nitrogen oxides to air urban air close to ground	41	242	768	961	2735	2734	277	2	7760	72%
	sulfur dioxide to air unspecified	2	24	299	520	2810	2690	270	2	6617	85%
	nitrogen oxides to air unspecified	1	48	349	944	1319	2377	273	2	5313	95%
	ammonia to air non-urban air or from high stacks	78	88	61	233	149	228	58	2	897	97%
	ammonia to air urban air close to ground		62	67	80	138	268	95	2	712	99%

to air non-urban air or from high stacks

  Table S 31. Occurrences of the main elementary flows in RIs of Terrestrial eutrophication

	Elementary flow	1	2	3	4	5	6	total	% of total
									occurrence
	nitrogen oxides 344	1039	5034	3786	287	10	10500 30%
	nitrogen oxides to air urban air close to ground	198	685	4920	3787	288	10	9888	58%
	nitrogen oxides to air unspecified	74	553	4819	3722	288	10	9466	85%
	ammonia to air unspecified	24	97	120	2435	95	10	2781	93%
	ammonia to air urban air close to ground		83	155	1045	271	10	1564	97%
	ammonia to air non-urban air or from high stacks	50	256	161	373	211	10	1061	100%
	nitrogen oxides to air lower stratosphere + upper troposphere			10				10	100%
	nitrate to air unspecified		1	1				2	100%

Table S 32.

 S Occurrences of the main elementary flows in RIs of Freshwater eutrophication Occurrences of the main elementary flows in RIs of Marine eutrophication

			Annexes
	Table S 33. Elementary flow	1	2	3	4	5	6	7	total	% of total
										occurrence
	nitrate to water ground-, long-term	575	1317	2126	5315	744	243	35	10355 27%
	nitrogen oxides to air non-urban air or from high stacks	81	662	1854	5199	728	243	35	8802	51%
	nitrogen oxides to air urban air close to ground	139	493	1473	5238	739	236	35	8353	73%
	nitrogen oxides to air unspecified	58	273	768	5000	635	242	35	7011	92%
	nitrate to water ground-	113	221	253	201	162	51	14	1015	94%
	ammonium, ion to water surface water	11	69	89	110	248	206	35	768	96%
	nitrate to water surface water	1	50	133	138	196	189	35	742	98%
	ammonium, ion to water ground-, long-term	18	58	59	28	80	1	21	265	99%
	Elementary flow	1	2	3	4	5	6	total	% of total
									occurrence
	phosphate to water ground-, long-term	253	9352	971	573	31	8	11188 46%
	phosphate to water ground-		9167	928	571	31	8	10705 90%
	phosphorus to water surface water		61	339	564	31	8	1003	94%
	phosphate to water surface water	5	67	220	507	20	8	827	97%
	phosphorus to soil agricultural	7	51	349	67	11	8	493	99%
	phosphorus to water ground-		1	30	3	31	8	73	100%
	phosphate to water ocean	2		42	5			49	100%
	phosphorus to soil industrial	3	1	30				34	100%
	Antoine Esnouf / PhD dissertation / 2018			149

  Table S 34. Occurrences of the main elementary flows in RIs of Freshwater ecotoxicity

	Elementary flow	1	2	3	4	5	6	7	total	% of total
										occurrence
	copper, ion to water ground-, long-term	98	3546	2386	2194	2396	312	43	10975 29%
	zinc, ion to water ground-, long-term	40	3530	2293	2166	2399	306	43	10777 58%
	chromium vi to water ground-, long-term		26	591	1131	2211	265	39	4263	69%
	vanadium, ion to water ground-, long-term	13	46	407	909	1825	211	38	3449	78%
	nickel, ion to water ground-, long-term		11	496	696	1861	237	40	3341	87%
	antimony to water ground-, long-term		12	374	119	260	52	2	819	89%
	antimony to water surface water			83	56	219	38		396	90%
	chromium vi to water surface water		12	44	62	103	113	2	336	91%

Table S 35.

 S Occurrences of the main elementary flows in RIs of Land use

	Elementary flow	1	2	3	4	5	6	7	8	9	10	total	% of total
													occurrence
	transformation, to mineral extraction site to natural resource land	493	418	715	1449	1648	1623	1406	640	40	2	8434	16%
	transformation,

to annual crop, non-irrigated, intensive to natural resource land

		1	404	706	849	1661	1784	1403	646	39	2	7495	31%
	transformation, to industrial area to natural resource land	13	473	549	832	1333	1329	863	570	22	2	5986	42%
	transformation, from annual crop to natural resource land		269	459	546	1274	1325	1296	624	38	2	5833	53%
	transformation, from unspecified to natural resource land	62	295	432	669	1213	1180	770	493	14	2	5130	63%
	transformation, from mineral extraction site to natural resource land	9	87	116	241	343	589	447	329	19	2	2182	68%
	transformation,

from annual crop, non-irrigated, intensive to natural resource land

	193	212	168	53	315	485	373	20	2	1821	71%
	transformation,

to annual crop, non-irrigated, extensive to natural resource land

	116	35	49	462	589	287	34	2	1574	74%

  Table S 36. Occurrences of the main elementary flows in RIs of Water resource depletion

	Elementary flow	1	2	3	total	% of total
						occurrence
	water, river to natural resource in water	987	9458	688	11133 51%
	water, well, in ground to natural resource in water	62	9443	688	10193 97%
	water, lake to natural resource in water	9	19	688	716	100%

.005% in sulfide, in 0.003%, pb, zn, ag, cd, in ground to natural resource in ground

  Table S 37. Occurrences of the main elementary flows in RIs of Mineral, fossil and renewable resource depletion

	Elementary flow	1	2	3	4	5	6	7	8	total	% of total
											occurrence
	indium, 02596	5034	2149	558	289	27	3	10656 31%
	nickel, 1

.98% in silicates, 1.04% in crude ore, in ground to natural resource in ground

	36	896	4508	1622	491	207	4	7764	53%
	cadmium, 0

.30% in sulfide, cd 0.18%, pb, zn, ag, in, in ground to natural resource in ground

			1415	3869	1104	189	59	1	6637	72%
	uranium, in ground to natural resource in ground	100	87	540	587	125	57	4	1500	76%
	silver,

ag 9.7e-4%, in mixed ore, in ground to natural resource in ground

	18	600	430	213	6	3	1270	80%
	copper, 0

.99% in sulfide, cu 0.36% and mo 8.2e-3% in crude ore, in ground to natural resource in ground

	21	39	314	456	210	2	1042	83%
	tantalum, 81.

9% in tantalite, 1.6e-4% in crude ore, in ground to natural resource in ground

	12	71	241	317	16	123	1	781	85%
	carbon,

organic, in soil or biomass stock to natural resource in ground

  RIs medians and inter-quartiles of LCIA methods per field of activity

			Annexes
	Annex C: Supplementary Information -Chapter 4 Annex C-3:
	Annex C-1: Number of LCI per division
	Table S 38. Number of LCI per division
	Field of activity	Division Name of division		Number
					of LCIs
	Section A, Agriculture	1	Crop and animal production, hunting
	and forestry		and related service activities
		2	Forestry and logging
	Section B, Mining and	5	Mining of coal and lignite
	quarrying	6	41 Extraction of crude petroleum and	98	154	273	13	579	87%
			natural gas
		7	Mining of metal ores
		8	Other mining and quarrying
		9	Mining support service activities
	Section C, Processed	10	Manufacture of food products
	Biobased product	13	Manufacture of textiles
		16	Manufacture of wood and of products of
			wood and cork, except furniture;
			manufacture of articles of straw and
			plaiting materials
		17	Manufacture of paper and paper
			products
		18	Printing and reproduction of recorded
			media
		19.0	Biobased chemicals
	Section C, Chemicals Antoine Esnouf / PhD dissertation / 2018 19.1	Manufacture of coke and refined	157
	and Plastics		petroleum products
		20	Manufacture of chemicals and chemical
			products
		22	Manufacture of rubber and plastics
			products
	Section C, Other non-	23	Manufacture of other non-metallic
	metallic mineral		mineral products
	products
	Section C, Metals and	24	Manufacture of basic metals
	metal products	25	Manufacture of fabricated metal
			products, except machinery and
			equipment
	Section C, Electronic
	and electronical
	equipment

  Table S 41. RIs medians of LCIA methods per fields of activity (1) Table S 42. RIs medians of LCIA methods per fields of activity (2) RIs inter-quartiles of LCIA methods per fields of activity (1)

					Annexes
	LCIA method Table S 43. LCIA method	Section Section	Section Section	Section Section	Section D_Steam Section	Section Section C_Other	Section Section	Section Section
		C_Machinery A_Agriculture	D_Electricity B_Mining and	D_Manufacture C_Processed	and air C_Chemicals and	E_Sewerage and non-metallic	F_Construction C_Metals and	H_Transport C_Electronic and
		and transport and forestery	power quarrying	of gas Biobased	conditioning Plastics	Waste mineral	metal products	land electronical
		equipment	generation	product	supply	treatment products		equipment
	LCIA method BEES BEES	Section 2.38E-02 2.62E+02	Section 5.12E-02 1.33E+02	Section 3.39E-02 7.74E+01	Section 6.15E-03 2.21E+02	Section C_Other 8.80E-03 1.58E+01	Section 1.58E-02 1.86E+01	Section 1.61E-02 5.50E+01
	CML-IA CML-IA	A_Agriculture and forestery 7.98E-02 2.86E+02	B_Mining and quarrying 4.52E-02 1.76E+02	C_Processed Biobased 3.19E-02 5.88E+01	C_Chemicals and Plastics 1.14E-02 1.71E+02	non-metallic mineral 9.79E-03 1.86E+01	C_Metals and metal products 5.79E-02 2.64E+01	C_Electronic and electronical 1.67E-02 1.74E+02
	ECO_Scarcity ECO_Scarcity	8.23E-02 2.62E+01	7.83E-02 1.82E+02	product 4.60E-02 2.75E+01	8.03E-02 3.49E+02	products 2.53E-02 1.03E+01	6.81E-02 2.17E+01	equipment 5.80E-02 4.67E+01
	BEES EDIP EDIP	1.67E-04 6.33E-02 7.00E+01	6.52E-03 4.11E-02 1.31E+02	3.45E-04 3.07E-02 2.38E+01	9.73E-04 3.12E-02 2.47E+02	1.42E-02 1.26E-02 1.44E+01	9.05E-03 4.51E-02 2.34E+01	1.29E-03 2.86E-02 7.52E+01
	CML-IA EPD EPD	2.90E-04 4.42E-02 4.35E+02	1.07E-02 3.10E-02 1.89E+02	8.43E-04 1.93E-02 5.78E+01	1.93E-03 9.20E-03 1.48E+02	1.69E-02 7.39E-03 1.48E+01	1.65E-02 4.05E-02 2.68E+01	5.74E-03 1.37E-02 1.66E+02
	ECO_Scarcity EPS EPS	4.93E-03 6.28E-02 1.47E+02	1.38E-02 2.91E-02 7.91E+01	1.88E-02 2.49E-02 4.89E+01	2.63E-03 2.64E-02 1.12E+02	2.14E-02 2.91E-03 1.21E+01	2.06E-02 5.21E-02 1.61E+01	4.25E-03 2.53E-02 6.89E+01
	EDIP ILCD ILCD	1.36E-03 5.22E-02 6.29E+01	8.37E-03 5.07E-02 1.27E+02	1.59E-03 2.45E-02 5.19E+01	1.89E-03 1.98E-02 2.91E+02	1.61E-02 8.20E-03 1.71E+01	1.10E-02 4.01E-02 1.84E+01	2.72E-03 1.73E-02 7.79E+01
	EPD Impact_2002+ Impact_2002+	2.03E-04 3.29E-02 5.26E+01	3.77E-03 5.73E-02 2.02E+02	3.85E-04 5.91E-02 3.01E+01	8.56E-04 9.02E-02 3.49E+02	1.31E-02 1.02E-02 1.63E+01	8.20E-03 3.36E-02 2.28E+01	5.38E-03 3.67E-02 5.71E+01
	EPS ReCiPe_end_dam_E ReCiPe_end_dam_E	1.29E-03 1.26E-02 3.86E+02	1.13E-02 1.85E-02 2.05E+02	1.07E-03 2.60E-02 1.14E+02	1.51E-03 5.17E-03 2.68E+02	1.46E-02 1.79E-03 2.88E+01	1.24E-02 1.18E-02 2.19E+01	4.67E-03 7.49E-03 1.10E+02
	ILCD ReCiPe_end_dam_H 9.82E-03 1.11E-03 ReCiPe_end_dam_H 1.54E+02	4.45E-03 1.97E-02 1.48E+02	1.17E-03 2.60E-02 1.07E+02	1.13E-03 2.90E-02 2.10E+02	1.50E-02 8.09E-04 3.08E+01	9.12E-03 7.28E-03 2.95E+01	2.12E-03 7.36E-03 6.37E+01
	Impact_2002+ ReCiPe_end_dam_I ReCiPe_end_dam_I	3.66E-03 1.34E-02 1.82E+02	1.14E-02 2.19E-02 9.12E+01	3.41E-03 2.56E-02 7.79E+01	1.53E-03 1.54E-02 1.99E+02	1.65E-02 7.38E-04 2.84E+01	9.76E-03 8.48E-03 3.48E+01	2.67E-03 9.22E-03 5.49E+01
	ReCiPe_end_dam_E ReCiPe_end_imp_E ReCiPe_end_imp_E	9.03E-05 4.02E-02 1.17E+02	2.68E-03 4.53E-02 1.00E+02	1.59E-04 4.55E-02 8.90E+01	3.54E-04 1.04E-01 3.86E+02	8.33E-03 7.67E-03 1.31E+01	3.46E-03 4.45E-02 3.43E+01	7.30E-04 4.18E-02 3.35E+01
	ReCiPe_end_dam_H 3.04E-04 ReCiPe_end_imp_H 3.99E-02 ReCiPe_end_imp_H 3.74E+01	2.36E-03 5.57E-02 1.10E+02	3.51E-04 5.75E-02 8.87E+01	4.05E-04 1.04E-01 3.30E+02	9.60E-03 1.75E-02 1.30E+01	2.95E-03 4.34E-02 3.32E+01	6.30E-04 4.48E-02 1.62E+01
	ReCiPe_end_dam_I ReCiPe_end_imp_I ReCiPe_end_imp_I	2.92E-04 4.81E-02 2.54E+01	2.73E-03 5.42E-02 1.10E+02	3.66E-04 5.32E-02 6.92E+01	4.32E-04 1.03E-01 3.21E+02	1.00E-02 1.76E-02 1.50E+01	3.29E-03 4.43E-02 3.45E+01	8.97E-04 4.54E-02 1.60E+01
	ReCiPe_end_imp_E ReCiPe_mid_E ReCiPe_mid_E	1.34E-03 4.03E-02 1.26E+02	1.20E-02 7.26E-02 1.10E+02	2.65E-03 4.32E-02 1.02E+02	1.36E-03 1.05E-01 3.89E+02	1.67E-02 1.23E-02 1.34E+01	1.12E-02 4.36E-02 2.69E+01	4.20E-03 5.29E-02 3.35E+01
	ReCiPe_end_imp_H ReCiPe_mid_H ReCiPe_mid_H	1.51E-03 3.99E-02 4.30E+01	1.30E-02 7.55E-02 1.11E+02	4.56E-03 5.48E-02 9.87E+01	1.88E-03 1.05E-01 3.25E+02	1.68E-02 1.77E-02 1.34E+01	1.06E-02 4.34E-02 2.72E+01	3.78E-03 5.29E-02 1.65E+01
	ReCiPe_end_imp_I ReCiPe_mid_I ReCiPe_mid_I	1.81E-03 4.81E-02 4.46E+01	1.18E-02 7.52E-02 1.10E+02	4.46E-03 5.28E-02 1.02E+02	1.91E-03 1.05E-01 3.49E+02	2.04E-02 1.77E-02 1.51E+01	1.45E-02 4.43E-02 2.57E+01	3.75E-03 5.16E-02 1.64E+01
	ReCiPe_mid_E TRACI TRACI	1.10E-03 1.72E-02 2.04E+02	1.12E-02 3.03E-02 1.53E+02	2.65E-03 3.42E-02 5.57E+01	1.39E-03 8.69E-03 2.82E+02	1.69E-02 6.33E-03 2.23E+01	1.06E-02 1.20E-02 1.65E+01	4.20E-03 1.32E-02 8.11E+01
	ReCiPe_mid_H	1.42E-03	1.31E-02	5.06E-03	1.80E-03	1.72E-02	1.06E-02	3.80E-03
	ReCiPe_mid_I	1.42E-03	1.18E-02	4.58E-03	1.80E-03	2.07E-02	1.52E-02	3.96E-03
	TRACI	1.57E-04	3.34E-03	2.57E-04	7.53E-04	1.18E-02	7.47E-03	9.50E-04
	Antoine Esnouf / PhD dissertation / 2018		159

  Table S 44. RIs inter-quartiles of LCIA methods per fields of activity (2) RIs distributions per field of activity for the ILCD method The Table S 45 presents descriptive statistics of RI distributions of the ILCD impact categories per field of activity. The respective RI distributions are plotted on the following figures. Table S 45. Descriptive statistics of RI distributions of the ILCD impact categories per field of activity

					Annexes
	LCIA method BEES CML-IA ECO_Scarcity EDIP EPD EPS Annex C-4: Field of activity Section C_Machinery and transport equipment 7.21E+00 1.20E+01 1.03E+01 1.13E+01 1.02E+01 8.46E+00	Section D_Electricity power generation 6.81E+00 1.32E+01 1.06E+01 9.83E+00 1.31E+01 1.84E+01 median Ratio	Section D_Manufacture of gas 5.57E+00 6.81E+00 4.20E+00 6.92E+00 1.08E+01 5.57E+00 median	Section D_Steam and air conditioning supply 1.80E+00 1.65E+00 1.77E+00 2.83E+00 1.55E+00 2.52E+00 median Quartile	Section E_Sewerage and Waste treatment 1.06E+01 1.84E+01 3.36E+01 1.89E+01 2.04E+01 2.71E+00 Qaurtile	Section F_Construction 9.36E+00 1.42E+01 8.39E+00 1.19E+01 1.52E+01 8.80E+00	Section H_Transport land 9.43E+01 1.78E+02 6.03E+02 6.89E+01 1.72E+02 2.37E+02
	ILCD		1.23E+01	1.15E+01 c mean geometri	7.19E+00 and median median max max	1.60E+00 min	1 min	1.20E+01 3 max	8.33E+00	3.35E+02
	Impact_2002+	9.15E+00	1.80E+01	min	5.78E+00	2.27E+00		3.51E+00	7.68E+00	5.19E+02
	ReCiPe_end_dam_E Database	1.34E+01	2.68E+01 5.80E-04	3.70E+00	6.41E+00 1.02E-03	2.32E+00 2.76E-04	1.85E-05	9.71E+00 7.17E-03	1.12E+01	3.50E+02
	ReCiPe_end_dam_H 6.37E+00 Section A, Agriculture and	3.72E+01 2.90E-05	4.87E+01	4.48E+00 3.60E-04	2.63E+00 7.39E-06	4.14E-07	3.93E+00 1.00E-03	9.43E+00	3.64E+02
	ReCiPe_end_dam_I forestry	8.59E+00	2.67E+01		6.12E+00	2.77E+00		6.52E+00	1.08E+01	3.75E+02
	ReCiPe_end_imp_E quarrying Section B, Mining and 1.46E+01	6.93E+00 2.84E-04	5.22E+00	4.68E+00 5.78E-04	2.68E+00 1.11E-04	8.55E-06	3.03E+00 5.76E-03	9.36E+00	7.09E+02
	ReCiPe_end_imp_H Section C, Processed Biobased 1.32E+01	8.43E+00 7.57E-05	9.86E+00	4.22E+00 2.86E-04	2.59E+00 2.90E-05	2.07E-06	5.64E+00 2.09E-03	8.86E+00	6.46E+02
	ReCiPe_end_imp_I product ReCiPe_mid_E Plastics Section C, Chemicals and 1.35E+01 1.41E+01	1.06E+01 4.51E+00 8.44E-05	4.47E+00	5.02E+00 4.50E+00 1.75E-04	2.62E+00 2.65E+00 3.91E-05	1.88E-06	5.81E+00 2.38E+01 2.24E-03	8.65E+00 9.18E+00	6.53E+02 7.09E+02
	ReCiPe_mid_H Section C, Other non-metallic 1.27E+01	4.59E+00 1.97E-03	1.10E+01	4.96E+00 6.21E-03	2.57E+00 5.65E-04	6.55E-05	7.98E+00 1.20E-02	8.77E+00	6.48E+02
	ReCiPe_mid_I mineral products 1.31E+01 Section C, Metals and metal	4.47E+00 1.13E-03	5.65E+00	4.85E+00 2.61E-03	2.64E+00 4.62E-04	6.16E-05	7.63E+00 6.61E-03	8.60E+00	6.54E+02
	TRACI	products	7.92E+00	1.30E+01		6.82E+00	1.59E+00		1.06E+01	8.79E+00	4.22E+02
		Section C, Electronic and	1.86E-04	1.00E+01	7.38E-04	7.37E-05	6.28E-06	6.73E-03
		electronical equipment
		Section C, Machinery and	3.62E-03	8.34E+00	1.10E-02	1.33E-03	3.11E-04	3.80E-02
		transport equipment
		Section D, Electricity power	2.73E-03	1.22E+01	9.26E-03	7.58E-04	1.11E-04	2.19E-02
		generation
		Section D, Manufacture of gas 2.20E-03	3.29E+01	1.47E-02	4.46E-04	7.39E-05	5.29E-02
		Section D, Steam and air	9.64E-04	8.84E+01	8.17E-03	9.24E-05	5.08E-05	1.25E-02
		conditioning supply
		Section E, Sewerage and	2.64E-04	1.18E+01	9.21E-04	7.83E-05	1.02E-05	4.15E-03
		Waste treatment
		Section F, Construction	2.40E-03	1.28E+01	8.51E-03	6.64E-04	1.66E-04	3.40E-02
		Section H, Transport land	2.29E-03	1.59E+01	7.50E-03	4.71E-04	4.07E-06	1.46E-02
		Antoine Esnouf / PhD dissertation / 2018					161

Antoine Esnouf / PhD dissertation / 2018

Antoine Esnouf / PhD dissertation / 2018

This section was not published within the paper related to this chapter. In this following section, the term "dimension" refers to a dimension of the G vector space were impact category vector have been localized. Then, LCI result vectors and impact category v ectors take value on the same dimensions through their standardized elementary flows and their standardized CFs.

Remerciements

Il va être très difficile de remercier tout le monde car c'est avec l'aide de nombreuses personnes que j'ai pu mener cette thèse à son terme. Tout d'abord, ce travail de thèse a été réalisé dans le cadre d'un financement ANR qui a regroupé cinq instituts recherche : le CEVA, le CERMAV, l'IFP Energies Nouvelles, l'ISCR et l'INRA à travers le LBE, mon laboratoire d'accueil. Je tiens à remercier toutes les personnes qui ont rendu possible ce projet, qui l'ont fait vivre et avec qui j'ai interagi durant ces trois années, notamment Ronan Pierre du CEVA qui en fut le coordinateur.

Chapter 1: General introduction

Chapter 1: General introduction

Contents of

 6.1.1. Methodological outcomes ....................................................................................Environmentally critical dimensions are also put forward for all poss ible impact categories. Then,the developed angular measurement ...................................................................... 6.1.2. Practical results ................................................................................................. 6.2. LIMITATIONS AND PERSPECTIVES OF THE REPRESENTATIVENESS INDEX .......................................... 6.2.1. Standardization .................................................................................................. 6.2.2 The following figures present the screening of the RIs of the impact categor ies from classic LCIA methods. The The use of natural gas for steam production leads the LCI on dimensions considered as critical for those impact categories. F inally, screening of impact categories for the combustion of ethanol (Figure S 26) shows toxicities and metal depletion as the main relevant impact categories.