Koji Negishi

Alexandra Lebert

Denise Almeida

Jacques Chevalier

Ligia Tiruta-Barna

Evaluating climate change pathways through a building's lifecycle based on Dynamic Life Cycle Assessment

Keywords: Dynamic Life Cycle Assessment, climate change impact, biogenic carbon dioxide Highlights :

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

With a current contribution of 39% of global CO2 emissions, the building (28%) and construction (11%) sectors represent a major source of greenhouse gases (GHGs) [START_REF] Tiruta-Barna | Global Status Report: towards a zero-emission, efficient and resilient buildings and construction sector[END_REF]. In the context of urgent climate risks, transition pathways for limiting global warming are challenging. The latest IPCC report [START_REF]Global warming of 1.5°C[END_REF] mentions that the global mean temperature increase is 'likely to reach 1.5°C between 2030 and 2052 if it continues to increase at the current rate.' Therefore, GHG mitigation efforts in the building sector need to be implemented as early as possible for both the renovations of existing buildings and new construction projects. Moreover, the necessity of limiting the global temperature increase to 1.5°C through 2100 requires decreasing CO2 emissions by approximately 45% by 2030 compared to 2010 and reaching net zero emissions by approximately 2050, according to the same report.

Despite its recognized usefulness and exhaustive use in all activity fields, the Life Cycle Assessment (LCA) method faces some limitations including the lack of a temporal dimension of the inventory and of the impact indicators. In the building sector, the time scale is an important parameter given the long lifetimes of buildings (greater than 50 years); however, the conventional LCA method (guided by ISO 14040-14044 [START_REF]ISO, ISO 14040 -Environmental Management -Life Cycle Assessment -Principles and Framework[END_REF][START_REF]ISO, ISO 14044 -Environmental Management -Life Cycle Assessment -Principles and Framework[END_REF]) doesn't dispose of adapted tools (software, databases) for a relevant temporal analysis of the environmental performances (e.g., [START_REF] Breton | Assessing the Climate Change Impacts of Biogenic Carbon in Buildings: A Critical Review of Two Main Dynamic Approaches[END_REF]) and fails to consider the temporal evolution of the system under study, the temporal discrepancies of activities and their associated emissions and the dynamic characteristics of the environmental impacts.

An extended analysis of the temporal aspects of buildings and the temporal dimension in LCAs of buildings (temporal LCA elements and building's temporal characteristics) was presented in a previous study [START_REF] Negishi | An operational methodology for applying dynamic Life Cycle Assessment to buildings[END_REF]. The identified key dynamic characteristics of buildings were related to i) construction products, e.g. performance degradation over time, replacement and use of new technologies; ii) energy equipment, e.g. performance degradation and the use of new technologies for renewable resources; iii) occupant behaviour, e.g. the occupancy typology and thermal comfort; iv) the energy mix, e.g. its evolution following national strategies; v) end-of-life technologies, e.g. material elimination versus reuse and recycling; and vi) carbon uptake/emission (the case of biogenic carbon).

Dynamic LCA applied to building is new [START_REF] Anand | Recent developments, future challenges and new research directions in LCA of buildings: A critical review[END_REF] and, according to the literature, the temporal aspects already included in LCA of buildings are limited to either the Life Cycle Inventory (LCI) or to Life Cycle Impact Assessments (LCIA) steps, or related to both LCI and LCIA but limited to parts of the studied systems [START_REF] Breton | Assessing the Climate Change Impacts of Biogenic Carbon in Buildings: A Critical Review of Two Main Dynamic Approaches[END_REF]. Moreover, these aspects concern only the foreground part or a few background processes, primarily related to variations in energy consumption or production. Energy consumption in the use stage of buildings, as well as the grid composition, have been extensively studied via hourly resolution simulations of the related inventory (e.g., [START_REF] Frijia | Functional Unit, Technological Dynamics, and Scaling Properties for the Life Cycle Energy of Residences[END_REF][START_REF] Collinge | Dynamic life cycle assessment: framework and application to an institutional building[END_REF][START_REF] Roux | Accounting for temporal variation of electricity production and consumption in the LCA of an energy-efficient house[END_REF][START_REF] Roux | Integrating climate change and energy mix scenarios in LCA of buildings and districts[END_REF][START_REF] Roux | Development of an electricity system model allowing dynamic and marginal approaches in LCA-tested in the French context of space heating in buildings[END_REF][START_REF] Vuarnoz | Integrating hourly life-cycle energy and carbon emissions of energy supply in buildings[END_REF][START_REF] Karl | Environmental performance assessment of the use stage of buildings using dynamic high-resolution energy consumption and data on grid composition[END_REF][START_REF] Collinge | Dynamic Life Cycle Assessments of a Conventional Green Building and a Net Zero Energy Building: Exploration of Static, Dynamic, Attributional, and Consequential Electricity Grid Models[END_REF]). Such dynamic simulations allowed for extremely detailed energy consumption calculation, which was then translated into climate change impacts using the GWP100 (kg CO2-eq) method. Even if GWP100 was calculated at each point in time, the impact result obtained cannot be considered as a temporal climate change indicator due to the lack of dynamic modelling of climate perturbation.

Carbon emissions from the life cycle stages of a building (separated by embodied carbon emissions and operational energy contributors) have also been evaluated [START_REF] Zhang | Taking the Time Characteristic into Account of Life Cycle Assessment: Method and Application for Buildings[END_REF][START_REF] Zhang | Analysis of embodied carbon in the building life cycle considering the temporal perspectives of emissions: A case study in China[END_REF] but without considering the dynamics of the processes and supply chains; in other words, the inventory was calculated for four periods and discounting factors were applied for late emissions. The same approach was used by Gimeno et al. [START_REF] Gimeno-Frontera | Sustainability of non-residential buildings and relevance of main environmental impact contributors' variability. A case study of food retail stores buildings[END_REF] including the consideration of refrigerant leakages and electricity mix periods (in accordance with regulations).

In the above-cited studies, the dynamics of all processes and the timings of the supply chains were not considered nor were the (combined) effect of different interventions occurring at different moments in the lifetime of the building (especially in the background part) taken into account. Concerning the LCIA, in most studies, only CO2, CH4 and rarely N2O have been considered for the global warming potential (GWP) calculation and no effective dynamic assessment has been performed.

Recently, temporal characterization factors for global warming assessments have been developed and used in the LCA of a wood-based building [START_REF] Fouquet | Methodological challenges and developments in LCA of low energy buildings: Application to biogenic carbon and global warming assessment[END_REF]; however, only a limited part of the LCI was considered. The current proposed methodologies for dynamic LCAs applied to buildings (e.g., [START_REF] Su | Dynamic LCA Framework for Environmental Impact Assessment of Buildings[END_REF]) lack operational calculation tools (models, software and coherent temporal databases) that could be used by practitioners for any building case study.

On a broader scope, dynamic LCA (DLCA) is still at the beginning of its development and very few calculation tools exist [START_REF] Cardellini | Temporalis, a generic method and tool for dynamic Life Cycle Assessment[END_REF]. The first studies proposing temporal inventories dealt only with the foreground part of the life cycle and focused on several GHG emissions in the foreground processes [START_REF] Levasseur | Considering Time in LCA: Dynamic LCA and Its Application to Global Warming Impact Assessments[END_REF][START_REF] Cherubini | CO2 emissions from biomass combustion for bioenergy: atmospheric decay and contribution to global warming: Global warming potential of CO2 from bioenergy[END_REF][START_REF] Ericsson | Time-dependent climate impact of a bioenergy system -methodology development and application to Swedish conditions[END_REF]. These studies did not propose a structured model for dynamic LCI (the emissions were 'manually' distributed in time). A first method was proposed based on a temporal characterization of the processes and elementary flows [START_REF] Beloin-Saint-Pierre | The ESPA (Enhanced Structural Path Analysis) method: a solution to an implementation challenge for dynamic life cycle assessment studies[END_REF]. The time distribution of the LCI was calculated using a convolution operation between the distributions of two linked processes. A case study was presented on domestic hot water production [START_REF] Beloin-Saint-Pierre | Implementing a Dynamic Life Cycle Assessment Methodology with a Case Study on Domestic Hot Water Production[END_REF] with temporal differentiation for only the foreground system (energy production/consumption). Pinsonnault et al. [START_REF] Pinsonnault | Temporal differentiation of background systems in LCA: relevance of adding temporal information in LCI databases[END_REF] applied this same framework to 22% of total processes included in the ecoinvent 2.2 database, for which the authors defined the temporal characteristics according to the sector of the activity (e.g. infrastructure or forestry). However, only significant intermediary and elementary flows were selected for the calculation based on their contribution to global warming. This first model for dynamic LCI calculations, however, lacked a structured database and a clear definition of process dynamics and supply chain dynamics through physical, temporal parameters. Cardellini et al. [START_REF] Cardellini | Temporalis, a generic method and tool for dynamic Life Cycle Assessment[END_REF] proposed a tool for performing DLCA based on a graph search algorithm combined with a convolution operation between the distribution functions of two linked processes, inspired by the previous method [START_REF] Beloin-Saint-Pierre | The ESPA (Enhanced Structural Path Analysis) method: a solution to an implementation challenge for dynamic life cycle assessment studies[END_REF]. The dynamic LCI was coupled with GWP characterization factors for climate change. However, this method also lacked the same operational aspects mentioned above.

Another method was recently proposed [START_REF] Tiruta-Barna | Framework and computational tool for the consideration of time dependency in Life Cycle Inventory: proof of concept[END_REF] that calculates the temporal LCI by considering the complex supply chains and processes that compose the life cycle system of both foreground and background processes. The calculation tool, called DyPLCA ( [START_REF] Pigné | A tool to compute fully time-differentiated life cycle environmental impacts of productionconsumption systems[END_REF]; http://dyplca.pigne.org/), delivers the LCI distributed through time.

Moreover, this dynamic LCI can be calculated based on a conventional LCA database (e.g. ecoinvent), which facilitates its use by LCA practitioners. A complementary temporal database is included in DyPLCA, containing the time-dependent parameters of the processes and supply chains associated with the datasets existing in ecoinvent 3.2. The results provided by DyPLCA can be used with adapted LCIA dynamic models [START_REF] Pigné | A tool to compute fully time-differentiated life cycle environmental impacts of productionconsumption systems[END_REF].

Concerning the LCIA, in particular climate change, Levasseur et al. [START_REF] Levasseur | Considering Time in LCA: Dynamic LCA and Its Application to Global Warming Impact Assessments[END_REF] proposed a method based on the calculation of characterization factors (CFs) for one-year time steps. This dynamic model uses radiative forcing as a physical parameter, and no fixed time horizon is needed. However, the huge number of CFs calculated for each time step and each substance could prove difficult to manipulate. In a recent study [START_REF] Shimako | Environmental assessment of bioenergy production from microalgae based systems[END_REF][START_REF] Shimako | Operational integration of time dependent toxicity impact category in dynamic LCA[END_REF][START_REF] Shimako | Sensitivity analysis of temporal parameters in a dynamic LCA framework[END_REF], a dynamic global warming model (from IPCC [START_REF]Climate Change 2013 -The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]) and a dynamic toxicity model (based on Refs. [START_REF] Hauschild | Building a Model Based on Scientific Consensus for Life Cycle Impact Assessment of Chemicals: The Search for Harmony and Parsimony[END_REF][START_REF] Rosenbaum | USEtox-the UNEP-SETAC toxicity model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in life cycle impact assessment[END_REF]) were adapted and applied to three case studies via a coupling with a dynamic LCI.

The present study applies the methodology proposed by Negishi et al. [START_REF] Negishi | An operational methodology for applying dynamic Life Cycle Assessment to buildings[END_REF] to an existingbuilding. The approach provides a temporal, complete LCI (based on the DyPLCA tool), combined with dynamic global warming indicators. DLCA could provide complementary and useful information (as testified by previous studies, several of which are cited above) on the impact timing and variation (the short-and long-term effects) and on the role played by biogenic CO2 emissions and capture. However, at the same time, a dynamic approach will require additional steps and calculation efforts and the obtained results will be more complex and difficult to interpret. In this context, the objectives of the present study are i) to demonstrate the feasibility of a complete dynamic DLCA applied to buildings, at the level of foreground and background LCI (considering process and supply chains dynamics and future scenarios) and at the level of LCIA (using a methodology previously presented [START_REF] Breton | Assessing the Climate Change Impacts of Biogenic Carbon in Buildings: A Critical Review of Two Main Dynamic Approaches[END_REF]) by an actual building case study, and ii) to identify the benefit of such an approach when compared to conventional LCA, in the case of buildings.

Materials and methods

DLCA Methodology for buildings

In the DLCA methodology applied to buildings [START_REF] Breton | Assessing the Climate Change Impacts of Biogenic Carbon in Buildings: A Critical Review of Two Main Dynamic Approaches[END_REF], the main temporal parameters of a building are expected to be used to derive the temporalized LCI for the foreground and background processes. Figure 1 shows a schematic of the main steps, tools and intermediary results of the methodology, briefly described in the following.

Figure 1: General framework of the DLCA methodology applied to a building case study.

STEP 1 (Data calculation and collection).

The collection of building data for LCI, and of the dynamic aspects and prospective scenarios, is performed based on Environmental Product Declaration (EPD) documents, literature reviews and expert opinions. This step includes a Dynamic Thermal Simulation (DTS), providing the annual energy consumption during the building occupancy, via the COMETH software [START_REF] Haas | Solution pour l'intéropérabilité avec COMETH[END_REF] on the MAESTRO simulation platform.

STEP 2 (Static model of the life cycle system). The results obtained in

Step 1 are completed with the ecoinvent datasets. The energy and material balances are calculated at the process level over the entire life cycle of the building. This step provides the links between foreground and background processes as parts of the total life cycle inventory.

STEP 3 (Temporality of the building life cycle system).

The processes and sub-systems with specific temporal evolutions are identified. The temporal characteristics of the building rely broadly on three categories: 1) the intrinsic building parameters, 2) the inhabitant behaviour and 3) the background system (or context) of the building. Specific modelling with an LCA software, e.g. SimaPro, is performed for different scenarios, by connecting processes which occur at different times like e.g. the replacements of products.

The outputs of the first three steps are the technology and environmental intervention matrices.

STEP 4 (Dynamic model of the life cycle system). The data retrieved from the previous steps are downloaded to the DyPLCA tool. The dynamic model implemented with the DyPLCA tool allows the characterization of the processes and flows through several parameters [START_REF] Tiruta-Barna | Framework and computational tool for the consideration of time dependency in Life Cycle Inventory: proof of concept[END_REF]; details are presented in the Supplementary Information (SI) (Table SI4). These parameters are user defined and/or available in a dedicated database. The result of this step is the temporalized LCI, i.e. the elementary flows distributed in time (as discrete values at a given time step over the timespan of the analysis).

STEP 5 (Dynamic LCIA calculation). The temporal LCI is the input of the models of the dynamic impact indicators (e.g., [START_REF] Shimako | Sensitivity analysis of temporal parameters in a dynamic LCA framework[END_REF]) or can be used, after data integration over time, with characterization factors from conventional LCIA methods.

In the following sections, a case study is presented according to the four steps of the LCA methodology: i) goal and scope definition, ii) constitution of the LCI, iii) LCIA and iv) interpretation of results.

Goal and scope definition

The building selected as case study is composed of three attached single wooden houses located in the Paris region of France. The structure technology used is wooden post and beam. This building is part of the Observatory project and is an experimental platform for an environmental assessment preparing a new French energy and environmental regulation, E+C- [START_REF] Fme | French Ministry of the Environment[END_REF]. The reference building service life was considered to be 50 years . Each house has two stories, and the total net floor area of the three houses is 414 m² (details in SI-2). The functional unit is one building as described above. The system boundary includes all processes from primary material production to the end of life (cradle to grave), according to the EN15978 standard [START_REF] Cen | EN 15978 -Assessment of environmental performance of buildings[END_REF] (details in SI-1), and the material and energy balances are established within the boundaries defined for each stage (Figure 2). The start date of the house occupancy (or the origin of the lifetime of the building) is considered to be year zero; which corresponds to 2015. The timespan of the inventory covers the period from 150 years before the origin year to year 50, as the end of lifetime, and 1 year after, to include all the past activities (raw material extraction, trees growth for wood harvesting) and end-of-life activities. Thus the system boundaries and the temporal boundary include the trees used for the wood pieces composing the building, coming from sustainable forest (included in the technosphere); no reforestation is considered inside the system's boundaries since the resulting wood does not belong to the building's life cycle.

In this study, the climate change impact was calculated and analysed. The literature [START_REF] Tanaka | Policy Update: Multicomponent climate policy: why do emission metrics matter?[END_REF][START_REF] Kirschbaum | Climate-change impact potentials as an alternative to global warming potentials[END_REF] acknowledges that the end point damages of climate perturbation are sensitive to at least three parameters: i) impacts related directly to elevated temperature (e.g. heat waves, coral bleaching and sea level rise), (ii) impacts related to the rate of warming (e.g. high rates of change give insufficient time for species adaptation and lead to species extinctions) and iii) impacts related to cumulative warming (e.g. sea-level rise) because certain long-lived gases continue to cumulate their effects even several hundreds to thousands of years after emission. The analysis of the system performance following dynamic indicators, namely global mean temperature change (GMTC) and cumulated radiative forcing (CRF), is completely adapted and copes with the above points (I, ii, iii).

Life Cycle Inventory

STEP 1: Data calculation and collection

To generate a reliable LCI model of the case study, a variety of tools, software, databases and methods were used, as shown in Table 1. Completes the inventory for background processes.

The MAESTRO platform for DTS was used for the configuration of the building behaviour, and the developed model was then used as an input of COMETH to simulate the energy consumption. The simulation was performed with a time step of one hour, as in other reported studies e.g. [START_REF] Frijia | Functional Unit, Technological Dynamics, and Scaling Properties for the Life Cycle Energy of Residences[END_REF][START_REF] Collinge | Dynamic life cycle assessment: framework and application to an institutional building[END_REF][START_REF] Roux | Accounting for temporal variation of electricity production and consumption in the LCA of an energy-efficient house[END_REF][START_REF] Roux | Integrating climate change and energy mix scenarios in LCA of buildings and districts[END_REF][START_REF] Roux | Development of an electricity system model allowing dynamic and marginal approaches in LCA-tested in the French context of space heating in buildings[END_REF][START_REF] Vuarnoz | Integrating hourly life-cycle energy and carbon emissions of energy supply in buildings[END_REF][START_REF] Karl | Environmental performance assessment of the use stage of buildings using dynamic high-resolution energy consumption and data on grid composition[END_REF][START_REF] Collinge | Dynamic Life Cycle Assessments of a Conventional Green Building and a Net Zero Energy Building: Exploration of Static, Dynamic, Attributional, and Consequential Electricity Grid Models[END_REF], then the cumulated consumption over one year was considered for the LCI. The energy demand was completely satisfied via electricity. The total energy consumption for the five types of energy equipment, i.e. the heating and cooling systems, domestic hot water, ventilation system and lighting, was estimated at 36.9 kWh.m -2 .year -1 for the first year of building use. In addition, the annual consumption of domestic appliances for this building was set to 20 kWh.m -2 .year -1 according to an expert opinion [START_REF] Sidler | Connaissance et maîtrise des usages spécifiques de l'électricité dans le secteur résidentiel[END_REF]. The collected data in the EPDs (from INIES database) represent existing buildings recently constructed, in form of technology information and calculated impact indicators. EPDs do not contain detailed inventory, however technological inventory information can be exploited like lists of raw materials used and their quantities. The available information includes the names of the building components and their quantities and lifetimes, which can be used in both static and dynamic LCA modelling. A total of 48 EPDs were exploited for the case study (list added in SI, Table SI3).

STEP 2: Static model of the life cycle of the system

The life cycle of the system was modelled on SimaPro 8.3 using ecoinvent 3.2. The ecoinvent dataset was used mainly for the background processes and those processes for which the building-specific information could not be obtained in Step 1. The list of ecoinvent processes used is given in SI, Table SI15.

The geographical information of FR (France) for inventories was privileged when data were available, whereas RER (Rest of Europe Region excluding Switzerland data) or RoW (Rest Of the World excluding Switzerland data)

or GLO (global data) were used as an alternative solution for other inventories. In addition, the 'default allocation method' for the process modelling of the ecoinvent datasets was chosen.

The transport distance of the construction products from factories to the construction site was taken from the EPDs, as average distances supplied by products' fabricants. When the transport distance was not available for a construction product, it was systematically set to 100 km [START_REF] Lasvaux | Étude d'un modèle simplifié pour l'analyse de cycle de vie des bâtiments[END_REF]. The energy consumption for the building demolition and the transport of wastes from the building site to the disposal/treatment site were accounted for. Different waste treatment processes, i.e. landfill, incineration and recycling, were considered for different types of waste materials on the basis of the EPDs.

The direct emissions from the construction materials (e.g. the volatile compounds in the indoor air and the substances leached by rain water from the exterior walls and roof) in the use stage of the building were not accounted for due to the lack of data (except for CO2 uptake by cement based products, as explained below).

For the sake of simplicity in the LCI modelling with SimaPro and DyPLCA, some construction products were excluded from the model, particularly when (i) the global warming score of a product was very low (the cut off threshold was 1% of the total global warming score), (ii) inventory data were completely lacking or (iii) the mass was not significant compared to the total mass of the house (the cut off threshold was 1% of the total mass of the building). This last criterion was applied only if criterion (i) was satisfied. As an example, plinths in PVC or wood are excluded from the modelling due to its low level influence on the climate change impact. Packaging materials for all products were also excluded because they represent only a small contribution to climate change and a small fraction of the total mass [START_REF] Lasvaux | Étude d'un modèle simplifié pour l'analyse de cycle de vie des bâtiments[END_REF]. The simplification adopted through the criteria (i) to (iii) is acceptable since the GWP100 calculated preliminarily allows selecting all GHG with high emission amount or/and GHG with high radiative efficiency. However the simplification can induce errors if the product is responsible for GHG capture (not accounted by GWP100 indicator). All insulation materials were included even though their mass contribution was very low. With this simplified model, the representativeness of GWP100 was of 97% from the value obtained with the complete EPD-ELODIE data.

Concerning the biogenic carbon, conventional LCA does not include biogenic CO2 emissions and uptake in the LCI and LCIA calculations. Conversely, with DLCA, all forms of carbon flow were considered: CO2 and CH4 emissions via biomass transformation (e.g. incineration and degradation) and CO2 uptake via plants (e.g. trees providing wood for the life cycle system of the building). Both types of flows are called biogenic in the present study. In addition, CO2 uptake into the cement products was also considered when the information was available from EPDs. Carbonation of concrete takes place also in the end of life stage, depending on the disposal process.

In the present study, carbonation after building demolition was not considered as EPDs do not provide this information. Therefore, the benefit of such process could be the subject of a dedicated DLCA study.

For practical reasons, the convention is to classify the input flows into the life cycle system of the building via the 'contributor':

1-The 'construction products' contributor takes into account all components of the building throughout its life cycle.

2-

The 'operational energy consumption' contributor covers all energy consumption during the use of the building.

The embodied energy, which is the energy necessary for equipment and construction material production, is accounted for in the construction products contributor.

3-The 'operational water consumption' contributor covers all the uses of water during the use of the building. The water consumption during material and product manufacturing or on the construction site is allocated to the construction products or 'on-site construction consumption' contributors.

4-The on-site construction consumption contributor accounts for the consumption of energy, water and other materials, the production of wastewater and the evacuation and treatment of soil during construction.

Figure 2 illustrates the links between the life cycle stages of a building and the contributors.

STEP 3: Temporality of the life cycle system of a building

Some construction products having lifetimes of less than 50 years need to be replaced. For example, it is assumed that a PVC (polyvinylchloride) window frame will need to be replaced at 30 years (100% landfilling) and disposed of at 50 years (92.1% landfilling and 7.9% recycling) and that insulation materials need to be replaced at 30 years [START_REF]a common EU framework of core sustainability indicators for office and residential buildings : parts 1 and 2, introduction to level(s) and how it works (Beta v1.0)[END_REF]. Table 2 summarizes the temporality of each sub-stage of the life cycle; additional details are available in Table SI10. The time variable characteristics of the building were grouped into the following categories: 1) degradation of material and energy system functions, 2) technological progress related to the building materials, 3) evolution of the family typology and 4) future mixes of electricity production. Several scenarios were then proposed for simulations by varying these parameters.

i) Degradation of materials and energy system functions. Insulation materials used for walls, floors and ceilings are known for their sensitivity to climatic conditions, particularity humidity. Their thermal performance levels therefore degrade over time during the use stage of a building. Three types of insulation materials (mineral wool, glass wool and polyurethane) were used in the studied building and differentiated by their usage types, e.g. exterior wall or upper floor. The temporal profile of the heat transfer coefficient was estimated for each insulation type [START_REF] Stazi | Assessment of the actual hygrothermal performance of glass mineral wool insulation applied 25 years ago in masonry cavity walls[END_REF][START_REF] Choi | A Study on Variation of Thermal Characteristics of Insulation Materials for Buildings According to Actual Long-Term Annual Aging Variation[END_REF]. This estimation was implemented with a yearly time step during the service lifespan to calculate the annual demand for heating and for domestic hot water (DHW). Building heat loads are also altered by variations in the performance of the energy equipment at the end-user level. The degradation of the energy efficiency was considered for: heating via the electric convector and DHW via the heat pump system. The pessimistic scenarios of degradation from a previous study [START_REF] Hendron | NREL is operated by[END_REF] were applied assuming that the global energy efficiency of the electric convector and the coefficient of performance (COP) of the heat pump degrade yearly by 1% and 3%, respectively.

ii) Technological progress related to the building materials. Given the long lifetimes of buildings, technological progress may occur during the use phase (e.g. maintenance, replacement and renovation) and in the background system related to processes for product fabrication, waste treatment and recycling. The integration of such future and potential improvements in DLCA is challenging due to the sparse data and the knowledge gap. Reducing waste and increasing recycling rates of the building materials are stipulated in the 'Energy transition law for green growth in France [START_REF] Mtes | La loi de transition énergétique pour la croissance verte en actions[END_REF].' For example, in the case of flat glass products, a dataset was created for window products considering an increase in cullet from 30% to 50% and accounting for an energy consumption gain of 2.5% per 10% increase in cullet. The evolution from current waste management practises (specified in existent EPDs) to a future scenario was considered for construction products based on concrete, steel and wood.

In addition, an electricity consumption reduction of 10% every decade was considered for most energy consuming processes for construction product fabrication (according to an expert opinion). An energy flow analysis was first conducted through the network of processes in order to identify important energy consumers for which a 10% energy reduction was possible. Then, for the relevant processes (the main contributors) the electricity consumption was modified through time.

Even though prospective aspects may concern a huge part of building-related technologies, in this case study, the prospective aspects were limited to those described above.

iii) Change in family size. Changing the inhabitant number leads to a change in the indoor heat gain due to human bodies and hot water needs, which needs to be integrated into the electricity consumption calculations. The family composition and its evolution were estimated using national statistics in France (INSEE [START_REF]INSEE, Des ménages toujours plus nombreux, toujours plus petits -Insee Première -1663[END_REF], https://www.insee.fr) and using a calculation method recommended by French thermal regulation 2012 [START_REF] Cstb | Méthode de calcul Th-BCE 2012[END_REF] (details in SI-6).

iv) Future electricity mix. Current LCA practice uses an annual average mix of electricity production for the entire life cycle of the studied system. Conversely, DLCA allows time variations of the energy production to be considered. The present study includes future scenarios of the French electricity mix with the goals of GHG reduction and the progressive replacement of nuclear electricity by electricity from renewable resources [START_REF]Actualisation du scénario énergie-climat ADEME 2035-2050[END_REF]. The current mix scenario, retrieved from historical data, contains 72% nuclear electricity. Two future production mix scenarios were considered: one with a high nuclear share of 50% in 2050 and another with a low nuclear share of approximately 5% in 2050, the remainder being satisfied by renewable resources and natural gas. These two scenarios are called 'Mix-50% Nuclear' and 'Mix-90% RE&Gaz', respectively. For the case study, the use phase of the building was segmented into three distinct periods of 2015-2034, 2035-2049 and 2050-2065 to which the current 2010 mix, the 2035 mix and the 2050 mix, respectively, were applied for the two mentioned scenarios (details in SI-6, Figure SI-3). LCI models of the future mix were developed using the existing ecoinvent 3.2 data.

The future mix was modelled by varying the mix composition without changing the current technologies, which represents a limiting assumption. In addition, due to the modelling complexity, the application of the future mixes was limited to end-use energy consumption, while processes in the background system (e.g. product fabrication, transport and infrastructure) were still based on the current mix. In the simulations, the prospective mix of electricity production was considered along with yearly energy consumption values.

v) Scenario modelling

The building case study was modelled with the current inventory as a baseline scenario. To understand the influence of the variable characteristics on the LCA results, the life cycle system of the building was also modelled via distinct scenarios by targeting only one variable parameter per scenario, except for S6/sub-scenario 8 (Table 3). The chosen parameter was varied between two (lower and upper) limits such that each corresponded to a subscenario: 'best' for the supposed beneficial value and 'worst' for the supposed most impactful value (details in SI-6, Table SI10). The scenarios definition with lower and upper limits for key parameters can also be considered as a sensitivity analysis with respect to the chosen parameter. The temporal assumptions (what was considered, simplified or neglected) of the case study model and for the defined scenarios are gathered in the Supplementary information document, Table SI11.

STEP 4: Dynamic model of the life cycle system

The DyPLCA tool contains a generic (but modifiable) database of temporal parameters associated to all activities in ecoinvent 3.2. The dynamic LCI was computed from -150 to 51 years: a past time horizon of 150 years was considered to account for tree growth for the different tree species included in the background inventory and the calculation then covered the lifetime of the building (50 years) and one supplementary year for dismantling and waste management. The specifically created processes (e.g. foreground processes) for the case study require the user to define the temporal parameters using the DyPLCA web application (see also SI-4).

Life Cycle Impact Assessment -STEP 5: Dynamic LCIA calculation

The present study focuses on the climate change impact evaluated via three dynamic indicators, instantaneous radiative forcing (RF, W.m -²), cumulative radiative forcing (CRF, W.year.m -²) and global mean temperature change (GMTC, K), based on IPCC models and data [START_REF]Climate Change 2013 -The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. The models underlying these dynamic indicators consider natural phenomena and all GHGs with their specific dynamics, as reported by IPCC (the decay equations for every GHG and methane oxidation). By coupling time-dependent emissions with these models, one obtains the indicator values as a function of time. All GHGs present in ecoinvent 3.2 were considered, and the dynamic indicators were calculated over a timespan of -150 to 500 years. The computation model provided by Shimako et al. [START_REF] Shimako | Environmental assessment of bioenergy production from microalgae based systems[END_REF] was used to this end. The conventional approach of the global warming potential GWP100 (kg CO2 eq., with a time horizon of 100 years) was also used for comparison. In conventional LCA, the emission and capture of a given CO2 quantity offset each other because the underlying model of GWP considers that all GHG emissions (and captures) occurr simultaneously. Moreover, CO2 uptake and biogenic emissions are not taken into account.

Results

The results obtained with conventional LCA and DLCA are difficult to compare given the major differences in the nature of their indicators. GWP100 was used to represent the static LCA, while for the dynamic indicators, graphical representations as a function of time and values at 100 years (as an analogy to GWP100) and 55 years (the end time of the building system) were analysed. Attention was paid to the temporal profiles of the climate indicators such as their amplitude, time scale and impact rate (variation in time).

Baseline scenario

Figures 3 and4 show the results obtained for the entire building and for the four contributors. Construction products and operational energy are the main contributors to all the impact indicators. Prior to time zero, the net impact is due to the fabrication of the construction products and, in the present case study, this has a beneficial effect (all the indicators have negative values) due to the growth of trees (wooden raw materials from sustainable forestry). Temperature peaks appear several years after the emission of GHGs due to the thermal inertia of the planet. This time lag depends on the nature of the gas. The overall increase in the temperature peaks near year 55, i.e. several years after the final emission at the end of the building life cycle. This is why year 55 was chosen as a time horizon for the impact analysis.

Comparison with conventional global warming indicator shows that the ranking of a contributor is the same whatever the indicator, with little variation in the proportion of the contributor.

Figure 3: Climate change dynamic impact (including biogenic CO2) for the entire building and for the four contributors (the functional unit is the building). Figure 4: Comparison of the climate change results obtained with static LCA and DLCA: the entire building (the functional unit) and its four contributors.

Concerning the impacts related to energy consumption, even if the building was designed with high thermal performance, the constant GHG emissions due to daily household activities over 50 years make the impact longer lived, resulting in a continuously increasing CRF and a relatively high temperature peak at the end of life of the building.

The contribution of the construction products was detailed by product family, as shown in Figures 5 and6.

According to ref [START_REF] Fme | French Ministry of the Environment[END_REF] the families regroup products with similar functions or utilisation in the same sub-structure of the building, for example HVAC family contains the heat pump, electric convector and the ventilation system.

The Foundations and Infrastructure (F&I), HVAC and Coating families are the three biggest contributors to the climate change impact over the long term. This is due to their important GHG emissions and the persistence of the emitted CO2 in the atmosphere, which have a very long-term effect. The temperature peak due to the HVAC family is the highest. The temperature increase due to the F&I family persists for a long period and is 33% higher than that of HVAC. Partitioning and Internal Carpentry (P&IC) contributes a significant temperature increase at the end-of-life phase; however, this temperature contribution declines rapidly, which is a consequence of the methane emission. Figure 6 demonstrates that the rankings of the 10 families can vary according to the indicator and the chosen time horizon, with F&I and HVAC always being the families with the greatest impact. Some contributors, such as Façade and Exterior Carpentry (F&EC), involving biogenic carbon in their inventories, have a negative (minus) contribution to CRF and small contributions to GMTC; this contribution diminishes with time. This behaviour is due to biogenic carbon capture by trees. Some other families also include a significant amount of wood products (e.g. Superstructure and Masonry (S&M)); however, the effect of biogenic carbon capture is partially offset by GHG emitters, such as cement production.

An analysis by GHG was performed for each product family, and several relevant results are presented in the following.

An interesting case is that of the S&M family, composed of wooden floors, floating screed and mortar in concrete, insulation material and walls in timber frames. Its relative contribution varies according to the indicator and the time horizon (Figure 6), and its GMTC and CRF curves have three peaks (Figure 5). These curves are decomposed in Figure 7 according to the GHG contribution. The S&M family uses a large amount of wood-based materials, and the effect of CO2 capture can reduce the total temperature increase by approximately 1/3 in the long term. The three temperature peaks are observed due to the replacement and end of life of some materials, i.e. a combination of landfilling and incineration (from EPDs), generating primarily CH4 and biogenic CO2 (from wood) emissions. This example also emphasizes the influence of CH4 on the steep temperature peaks. This end-of-life behaviour was observed for all product families. Figure 9: LCA results for the electricity mix scenarios: GWP100 (the functional unit is the amount of electricity consumption in the use stage of the building). S2. Energy efficiency at product manufacturing. An energy consumption reduction of 10% per decade for the most energy-intensive processes had only a small effect on the four indicators: a 4% reduction for GWP with respect to the baseline scenario and 3% and 4% reductions for CRF and GMTC, respectively, at year 100 (SI-7, Figures SI4,SI5).

S3. End of life for concrete, steel and wood products.

For each type of material, the system boundaries encompass all life cycle stages (from A1 to C4, see Figure 2) and all products containing that material, including variations in the waste treatment processes (landfill, incineration or recycling, Table 3) at the end of life of the products. The reference flow of each material was calculated with respect to the functional unit of the entire case study, i.e. the three single attached houses for 50 years. The construction products concerned in this scenario are listed in SI-6

with their respective end-of-life processes. Following the GWP100 indicator in Figure 11, landfilling is the most impactful process, while recycling does not provide a large benefit with respect to the baseline. Wood products have a smaller impact than all the other materials, even with incineration as the end-of-life process. Accordingly, 100% incineration appears to be one of the less impactful scenarios, equivalent to 100% recycling. Figure 11: GWP100 results for concrete, steel and wood products with different end-of-life technologies (the functional unit is the amount of products produced, used and eliminated for one building).

Concrete products Steel products

Wood products Figure 12 represents the dynamic profiles of the climate change indicators. For concrete and steel materials, two and three events appear, respectively, on both the RF and GMTC curves for each of the three scenarios. The first peak (near time zero) corresponds to the construction product manufacturing and is therefore identical for all scenarios, while the others correspond to end-of-life activities (near year 50, and one intermediary peak for steel products). The worst scenario is 100% landfilling, while 100% recycling results in a small benefit. This feature is akin to conclusions from conventional LCA. Concerning wood products, two events are observed: the first corresponds to trees cut (and is the same for all four scenarios) and the second corresponds to the end of life of the building. The less impacting scenario is recycling, followed by landfilling and the baseline scenario, while the worst is incineration. This ranking is different from those obtained with GWP100 indicator. The dynamic indicators have globally negative values demonstrating the beneficial effect of CO2 capture by tree growth far in the past. The GMTC indicators of the incineration and landfilling scenarios present very similar peak values at the end of life but very different subsequent evolutions. This behaviour is explained by the nature of the emitted GHGs.

The 100% incineration scenario nearly exclusively emits CO2, while the landfilling scenario emits a mixture of CH4 and CO2. Because CH4 is a short-lived gas, GMTC declines much more rapidly for landfilling and, in the long term, only the effect of CO2 persists. Therefore, the behaviour of the baseline GMTC is explained by its mix of end-of-life processes: recycling, landfilling and incineration.

S4. Technology of end-of-life scenarios for the HVAC system. Here also, very little difference was observed between the scenarios, with landfilling being the worst scenario according to the four climate change indicators.

The particularity of this system (SI-7, Figures SI6 andSI7) is that the end-of-life processes occur at multiple moments during the lifetime of the building because replacements of various components take place with distinct schedules (e.g. the electric convector is replaced three times, the heat pump is replaced four times and the ventilation system is replaced two times).

S5. Technological innovations of insulation materials.

The conventional insulation materials of mineral wool, glass wool and polyurethane were all replaced at year 30 in the best-case scenario (Table 3) by two innovative materials (a bio-based one and one composed of recycled materials). GWP100 (Figure 13) placed the recycled material in the first position, followed by the baseline, the bio-based material and, far behind, extruded polystyrene (the worst case).

Figure 13: GWP100 results for the insulation material scenarios (the functional unit is the amount of insulation material necessary for one building). Figure 14: Dynamic climate change indicators for the insulation material scenarios (the functional unit is the amount of insulation material necessary for one building). This ranking result was partially changed by DLCA (Figure 14). All dynamic indicators had negative values for the bio-based scenario due to the biomass growth prior to year 30. Moreover, the use of bio-based insulation materials can create a credit and therefore contribute to some GHG emission neutralization in the life cycle system of the building. When considering the worst insulation material, the temperature peak is 13 times higher than that of the baseline. However, GMTC declines before year 100 and is only twice the GMTC-baseline at the same year. This rapid variation is due to the presence of short-lived GHGs, whose concentrations decline rapidly as clearly observed with the RF indicator (RF is proportional to the gas concentration). Extruded polystyrene has a high thermal performance; however, the foam processing generates significant emissions of HFC-134a, which is responsible for the observed behaviour. S6. Household energy consumption. The household energy consumption was determined from DTS for all the subscenarios of scenario S6, and the baseline electricity mix was used for all of these simulations. The results obtained with conventional LCA vary little for sub-scenarios 2-7 with respect to the baseline, the relative differences being lower than 11%. Only sub-scenario 8 presents a significant increase, i.e.37% more energy consumption. The same trends were obtained for the dynamic indicators (additional results are presented in SI-7, Figure SI8, Tables SI12,SI13). However, when combined with the electricity mix evolution simulated in scenario S1 (with slightly higher climate indicators for the future mix), a higher impact could be expected for all sub-scenarios at the level of dynamic climate indicators.

Discussion

Situation in the climate context. The last IPCC report [START_REF]Global warming of 1.5°C[END_REF] mentioned the building and construction sectors as key actors for reducing GHG emissions. The first critical climate targets are placed between 2030 and 2052, with the objective being to not surpass a temperature increase of 1.5°C. Moreover, net GHG emissions should be zero by 2050. The long lifetimes of buildings need to be placed on a time scale with respect to such climate targets. This is what Figure 5 shows for the case study. The critical period is situated in the middle of the building lifetime for a building constructed in 2015 and currently inhabited. The building should reach zero net emissions towards its end of life, meaning that no temperature peaks should appear at this time horizon. Otherwise, as the figure shows, the temperature peaks will increase with time until 2065 for all contributors and, after that, GMTC will never fall to its initial value (see also Figure 3). This case study provides evidence of the importance of performing ex-ante dynamic evaluations of future, new typologies of buildings and placing the system in the actual temporal context of climate evolution and climate strategies.

Influence of GHG nature and timing on climate indicators. The parameters determining the climate footprint of a system are the nature and quantity of the GHGs emitted/captured and the emission profile through time. Due to the variability in the lifetimes of gases (examples in SI) and their radiative efficiencies, the intensities of their risks related to climate perturbation are also variable depending on the gas, that is, i) short-lived gases with high radiative efficiency (e.g. CH4 and HFC-134a, Figures 7 and8) generate high and steep temperature peaks (more harmful for living species), while ii) long-lived gases, especially CO2, have persistent impacts for long periods far after the end time of the emission with high cumulative effects.

In addition, the temporal profile of the emissions (pulse or continuous and the emission duration) determines the intensity of the effect and whether the effect spreads on a long time scale. The same emission is more harmful when it occurs late in time than early because it adds a supplementary temperature increase at an already higher temperature (the temperature is continuously increasing) [START_REF] Kirschbaum | Climate-change impact potentials as an alternative to global warming potentials[END_REF]. In addition, the same quantity of GHG emission has a smaller impact when the emission is spread over a long time interval than if the emission is released instantaneously: a sudden large emission will generate a high temperature peak, as in the case of HFC-134a. As a general trend, a continuous emission over a period results in continuously increasing dynamic indicators, with a peak corresponding to the end of the emission period, as in the case of household energy consumption.

As Figures 3 and5 show, the CRF indicator always increases due to the persistence of GHG in atmosphere beyond the lifetime of the system; it stores the history of the emissions and never declines (except if a capture process offsets the emissions). The GMTC indicator is critical (peaks) during the lifetime of the system prolonged with several years. Concerning the timing, the highest GMTC appears at the end of life of the building in this case study, demonstrating that the highest threat is in the near future. These features clearly demonstrate that a fixed, universal time horizon for the impact analysis is not justified. Instead, impact observations all along the lifetime of the system and several decades beyond ensure a better knowledge of the behaviour of a system and the identification of hot spots.

The importance of considering GHG capture and biogenic carbon. The analysis of different families of construction products sheds light on the importance of considering GHG capture within the boundaries of the life cycle of a system. For the GHG emissions, the capture efficiency in terms of the climate response depends on the nature and amount of the GHG and on the timing and profile of the capture process. In the present case study, only CO2 was captured by trees and in a much lesser extent by concrete carbonation. The effect of CO2 uptake is visible in Figures 5,7, 12 and 14 and can be observed in the offset of the GHG emissions, quantified by the CRF and GMTC indicators. However, the offset effect depends on the time profiles and the timings of the emission and capture processes and is smaller when the two processes are temporally remote. This observation is in agreement with the literature in the field (e.g., [START_REF] Collinge | Dynamic life cycle assessment: framework and application to an institutional building[END_REF], [START_REF] Roux | Development of an electricity system model allowing dynamic and marginal approaches in LCA-tested in the French context of space heating in buildings[END_REF], [START_REF] Vuarnoz | Integrating hourly life-cycle energy and carbon emissions of energy supply in buildings[END_REF]). It is therefore possible to (partially) neutralize the effect of GHG emissions (as shown by the S&M family) via a sufficient CO2 capture with an appropriate timing within the boundaries of the same system (e.g. the life cycle system of the studied house).

Relevant information that DLCA can provide -comparison with conventional LCA. DLCA provides important information concerning the amplitude and rate of change of climate parameters, which conventional LCA cannot provide. Figures 4 and6 demonstrate that it is actually irrelevant to compare results obtained with GWP and dynamic indicators, especially when capture processes are present, because i) the ranking and proportion of the contributors can change following the time horizon for a given dynamic indicator and ii) the ranking and proportion of the contributors can differ between the three represented indicators. For example, in the case of scenario 3, when comparing the three material groups (steel, concrete and wood), the dynamic indicators clearly discriminate wood products from the two other groups. While conventional LCA calculates a significant GWP impact, the dynamic indicators show that the carbon capture effect can offset and even overtake the effect of GHG emissions.

The dynamic indicators are very well adapted to account for the effect of biogenic CO2 and, consequently, can be used to define strategies for the neutralization of the effects of other GHGs. The fact that the contribution results in Figure 4 are similar between the climate indicators is a particular situation and cannot be generalized: the inventory is much aggregated on five contributors, with a small global contribution of biogenic CO2 and a dominance of fossil CO2 (long life GHG), and with a global emission increasing with the time over the lifetime (Figure 3 shows increasing RF for the main four contributors).

Another example is the effect of the electricity mix, as shown in Figures 9 and10. The transition from a nucleardominated production to a renewable-based mix is accompanied by a slight GWP100 reduction and a slight increase in CRF and GMTC. This unexpected behaviour (one would have assumed that a renewable energy system would produce a smaller impact than the current situation) is explained by the fact that biogenic CO2 emissions/capture are not considered in GWP100. All electricity generation technologies constituting the different electricity mix scenarios were taken from ecoinvent without any modification. The main biomass used in these processes is wood from sustainable forests, such as oak, spruce and beech, with long growth times (100-150 years).

The long growth duration (translating to a low capture rate of CO2) is followed by the sudden emission of the embodied carbon via incineration. The result is a small but positive temperature peak, i.e. in GMTC. This temporal behaviour explains this surprising result and, at the same time, suggests that short rotation biomass be used for energy production instead of long-lived trees. Finally, this result should also be placed in the multicriteria context by considering a panel of impact indicators, climate change impact being one of them; for instance nuclear energy production is accompanied by important impacts ensued from ionising radiations.

Choosing mitigation options within the temporal context. The dynamic metrics emphasize the importance of differentiating mitigation actions according to the type of gas and the emission timing. Based on the case study, main mitigation objectives could be proposed for the different contributors (Table SI14). A global objective is the reduction of energy consumption, especially during the use stage of a building. Indeed, the results obtained for sub-scenario S6 -8, with a combination of various parameters (energy efficiency of equipment and insulation, occupant behaviour) attest to an energy consumption increase of 37% over 50 years. In addition, reducing energy consumption is not enough but should be combined with the integration of more renewable sources in the power generation mix as early as possible. Moreover, the necessary massive reduction in the carbon emissions requires the use of non-carbon renewable resources (decarbonized energy) or sub-systems with CO2 capture for impact neutralization in order to reverse the trends observed in Figure 10. The case study indicates that, by combining the life cycle system of a building with a sub-system of a sustainable forest, it is possible to obtain a net effect near zero for CRF and/or GMTC.

For certain product families, for example, H&MEWS and F&EC, the emissions were primarily generated at the end of life of the product. In this case, the concerned industrial sectors should concentrate on eliminating the punctuated emissions from waste treatment, for example, by promoting recycling. Conversely, other families such as Energy Network or F&I present more important impacts during the fabrication/construction processes. In this case, a revision of the technologies and materials used should improve the environmental performance of these contributors. Other families, e.g. HVAC, contribute GHG emissions throughout the entire product life cycle and determine important increases in temperature and cumulative radiative forcing. Processes and materials involved in component manufacturing should be replaced by less impactful ones (replace for example HFC-134a with other substances with lower radiative efficiency), and end-of-life strategies should promote recycling.

The obtained DLCA results are case specific, dependent on the specificities of the GHG emission and capture (timing, temporal profile, amount and GHG nature) and cannot be extrapolated to other building typologies; the graphs presented in Figure 5 represent, in fact, the footprint of the specific modelled building. The wood species used for the construction materials in ecoinvent are beech, oak, birch, pine, spruce and eucalyptus. If other wood species are used for a given construction product, the result of coupled emission and capture will be different, depending on the CO2 flows and the time gap between capture and emission, and a shorter tree growth time would be beneficial. Finally, a concrete-based building cannot contribute to GHG offsets via significant gas capture because the life cycle system of such a building does not include a significant amount of wood. In this case, mitigation actions are restrained to and dependent on technological evolution, especially for the end-of-life stage.

Increasing temporal representativeness within a complex dynamic model. Such a modelling approach implies managing (very) different dynamics (temporal variations) at the level of LCI and LCIA, and numerical resolution parameters for the time variable. For example, the energy consumption in the use stage of buildings can be calculated with different time resolutions. An hourly resolution has commonly been used and linked to the grid composition, as mentioned in the Introduction section, to evaluate the GWP100 value of the energy consumption.

In previous studies (e.g., [START_REF] Roux | Development of an electricity system model allowing dynamic and marginal approaches in LCA-tested in the French context of space heating in buildings[END_REF], [START_REF] Levasseur | Considering Time in LCA: Dynamic LCA and Its Application to Global Warming Impact Assessments[END_REF]), it has been observed that climate indicators are sensitive to emissions described with a time resolution of several months to one year, and this time-granulometry is sufficiently narrow given the temporal characteristics of the environmental phenomena (e.g. gas mixing and interactions with the ocean and biosphere and thermal transfers) involved in climate perturbation. In the present case study, the energy consumption was simulated with hourly resolution (using the COMETH software) and was then used in LCI with a yearly value (the hourly data were summed up over a year to obtain the yearly consumption). This simplification was adopted for the following reasons: i) the daily modification of the French electricity mix has not significant repercussion on the GHG emission variation because the mix is based on nuclear power (or renewable sources in the future) as detailed in section 2.3.3 and SI -Fig. SI3; ii) very short time variations of the GHG emissions are not captured in the climate dynamic indicators, as explained here above; iii) the complexity resulted from a hourly variable electricity mix would lead to an unacceptable higher computation time for LCI.

The dynamic LCI was calculated with a time step of 1 day (numerical resolution of simulations) in the DyPLCA tool in order to capture the processes with short duration and their related intermediary and elementary flows.

Consequently, the results were obtained as discrete values of elementary flows for each day, during the whole life cycle time. The time step influences the simulation duration and is a limiting factor in current versions of the used tool, especially when many scenarios of technological change are considered together on the same timeline.

The technology representativeness with respect to time is already a requirement for system modelling in LCA and still remains a condition for temporal representativeness in DLCA. Placing the timeline of the studied system's life cycle on the calendar helps at: i) choosing the relevant technologies and their performances for a given period (e.g. in this case study the temporal evolution of the performance of energy equipment); ii) an easier evaluation of missing information for future scenarios (e.g. from when on our knowledge about the recycling technologies becomes uncertain); iii) including external factors dependent on the time, as economic and social evolution, climate conditions, etc. (family evolution for instance in this work).

Given the fact the LCI was based (in the present work) on ecoinvent, EPD information and additional simulations, the global LCI model gathers different uncertainty sources to which the temporal characteristics of the processes and supply chains are added. All these complex parameters deserve further investigation together with an uncertainty evaluation; however, such aspects are beyond this study, which focused on the feasibility and usefulness of a DLCA using a real case application.

Conclusions

The methodology of DLCA for buildings was applied to a case study with already existent or recently developed tools: the EPD database for the building sector, a new developed database for temporal parameters in the building sector, the SimaPro software and the ecoinvent database, and a recent DyPLCA tool for dynamic LCI calculations coupled with models for dynamic indictors for climate change impact evaluations. The specific temporal characteristics were collected on site, simulated (e.g. operational energy consumption) or obtained from sectorial databases. The simulation results were obtained as climate change indicators as a function of time, without a predefined time horizon (radiative forcing, cumulated radiative forcing and global mean temperature change).

The literature reports many temporal LCA approaches in the building domain. However, to the best of our knowledge, this is the first application of a complete DLCA using operational software and temporal databases (DyPLCA) at the level of LCI and LCIA, addressing all components and contributors over the entire life cycle of a building (at both the foreground and background levels) and using dynamic impact indicators.

In this analysis, details of the dynamic climate change impacts of 10 construction product families and various operational energy scenarios were individually analysed. The results show that each component has its own climate footprint determined by the nature of the GHG, the emission timing and the intensity. Analyses of the results highlighted the effects of the studied systems or sub-systems and indicated which mitigation actions are necessary.

Such analyses should always be placed in the climate context, with regard to the fixed objectives of limiting the global temperature increase within critical time windows. It is in this way that the evaluation can be understood and provides effective support to decision making. In the present case study, the lifetime of the building encompassed the critical period of 2030-2050, which is considered to be a turning point for limiting the temperature increase to 1.5°C, with an objective of zero net emissions beyond 2050.

Finally, a comparison between conventional LCA and DLCA results is not straightforward due to the different physical meanings of the indicators (with different measurement units) and the concept of time horizon in the GWP definition. A comparison was attempted after choosing the most relevant points in time: 100 years for GWP100 and the end of lifetime where the last temperature peak of the system occurs. The main outcome of the comparison was that the results can differ greatly, especially when GHG capture is present in the LCI, that is, i) the ranking and proportion of the contributors can change according to the time horizon for a given dynamic indicator and ii) the ranking and proportion of the contributors can be different between the considered indicators, demonstrating the need for a more detailed assessment (at least two dynamic indicators) in the context of the imminent climate target.

Figure 2 :

 2 Figure 2: Coupling the life cycle stages (defined by the EN15978 standard) and the contributor approach.

Figure 5 : 20 Figure 6 :

 5206 Figure 5: CRF and GMTC for 10 product families and for the operational energy (the functional unit is the building).

Figure 7 :

 7 Figure 7: Contribution analysis of principal GHGs to CRF (W.m -²) and GMTC (K) for the S&M family (the functional unit is the building).

Figure 8 :

 8 Figure 8: Contribution analysis of the principal GHGs to CRF (W.m -²) and GMTC (K) for the HVAC family (the functional unit is the building).

Figure 10 :

 10 Figure 10: DLCA results for the electricity mix scenarios: the dynamic indicators for climate change impacts (the functional unit is the amount of electricity consumption in the use stage of the building).

Figure 12 :

 12 Figure 12: Dynamic climate change indicators for concrete (top), steel (middle) and wood (bottom) products with different end-of-life technologies (the functional unit is the amount of products produced, used and eliminated for one building).

Table 1 :

 1 Data sources used in the case study.

	Data source	Type of data		Information retrieved
	Observatory	General description of the	Calculations of specific material and energy
	project data	building		consumptions of the building life cycle.
		Dynamic energy simulation	Energy consumption as a function of time and total
		model COMETH	energy consumption during the use stage of the
				building.
	EPD	Name, quantity and lifetime	Provides the reference flows used for conventional LCI
		of construction products and	modelling with SimaPro.
		materials and quantities of	Other information (e.g. lifetime of products) is used in
		intermediary flows	the DLCI modelling.
	ecoinvent v3.2 Inventory	flows	(unit
		processes and APOS system
		modelling)

Table 2 :

 2 Description of the temporality of the main activities involved in the building life cycle.

	Module	Occurrence	Process/activity	Description/indication
	EN15978	time, years
	A1-A3	t < -1	Product fabrication	Product fabrication processing related to the
				construction activity
	A1-A3	t = [0, 50]	Product fabrication	Product fabrication processing related to the
				maintenance and replacement activities, just before
				the replacement/maintenance time t
	A4-A5	t = [-1, 0]	Construction	The construction period is 1 year, energy and water
				consumption are considered
	B1	t = [0, 50]	Building use	The reference time 0 is the start time of building use
	B2	t ∈ [0, 50]	Maintenance	Wall painting at a given time t, 0 < t < 50
	B4	t ∈ [0, 50]	Replacement	Replacement of windows, doors, HVAC systems;
				each product is replaced at a given time t, 0 < t < 50
	B6	t = [0, 50]	Energy use	The end-user's energy consumption takes place over
				the lifetime of the building
	B7	t = [0, 50]	Water use	The end-user's water consumption takes place over
				the lifetime of the building
	C1-C4	t ∈ [0, 50]	Waste treatment	Replaced products are treated with end-of-life
				scenarios
		t = [50, 51]	Waste treatment	The building is treated with end-of-life scenarios

Table 3 :

 3 List of scenarios considered for the case study.

	Scenario	Baseline	Worst case	Best case
	S1	French annual average	French annual average mix	French annual average mix
	Electricity mix for	mix using ecoinvent data	using ecoinvent data for 2015-	using ecoinvent data for 2015-
	operational energy	for 2015-2065	2034	2034
	consumption
			'Mix-50% Nuclear'	'Mix-90% RE&Gaz'
			for 2035-2050	for 2035-2050
			and 2050-2065	and 2050-2065
	S2 Energy efficiency	No temporal variation of energy consumption	No worst scenario (no increase	10% reduction of energy consumption per decade for
	at product manufacturing	using raw ecoinvent data	of energy consumption)	the concrete, steel, aluminium and wood product
				manufacturing processes
	S3	EPD processes (landfill,	Landfill for all products	Increase in recycling rate with
	End of life for	incineration and		respect to EPDs
	concrete, steel and	recycling)
	wood products
	S4	EPD processes (landfill	Landfill for all products	Increase in recycling rate with
	HVAC end of life	and recycling)		respect to EPDs
	S5	Replacement (year 30)	Replacement (year 30) of all	a) Replacement (year 30) of
	Technological	of insulation materials	insulation materials by	all insulation materials by a
	innovations of	by the same type as	extruded polystyrene	bio-based material
	insulation materials	initially used
				b) Replacement (year 30) of
				all insulation materials by one
				composed of recycled material

Acknowledgments

We gratefully acknowledge the funding of this work by the French Research Agency (ANR-13-IS09-0007-01/DyPLCA). DyPLCA tool was previously developed in a collaborative project co-funded by ANR France and FNR Luxembourg with the participation of Yoann Pigné (Université Le Havre Normandie), Tomás Navarrete Gutiérrez, Thomas Gibon, Emil Popovici, Thomas Schaubroeck and Enrico Benetto (LIST Luxembourg), Allan H. Shimako (LISBP). The authors greatly appreciated their inputs.

Another example, the HVAC family (Figure 8), contains refrigerants known for their climate change effects. At the temperature peak, HFC-134a (ethane, 1,1,1,2-tetrafluoro-) alone is responsible for 36% of the peak (just after fossil CO2 with 46%) due to its extremely high radiative efficiency (10,000 times higher than that of CO2). In the long term, GMTC only depends on the CO2 concentration (because CO2 is 30 times more persistent than HFC-134a). The CRF indicator is by far dominated by fossil CO2 due to its higher persistence in the atmosphere. The specific parameters of main GHG and the relative contribution of the main GHG to the total GMTC is presented in SI5 (Tables SI5 andSI6 -gases with contribution lower than 1% were not reported).

Alternative scenarios

For simplicity and clarity, the simulations were performed only for the sub-systems concerned by a parameter modification and not for the entire building. Here, the most interesting results are presented per impact indicator for LCA and DLCA, showing important differences or similarities between the two LCA methods. S1. Electricity mix. Figure 9 presents the conventional LCA results for GWP100 (following EN15804). The worstand best-case scenarios show 11.5% and 13.8% reductions, respectively. Even though the electricity mix composition radically evolved due to the replacement of most of the nuclear power by other renewable energy sources, the impact did not change dramatically. The same energy consumption model (operational energy) leads to the dynamic indicator results presented in Figure 10. There is no clear difference between the worst-and bestcase scenarios, and, contrary to the conventional LCA results, DLCA ranks the three scenarios differently. At 100 years, both the worst-and best-case scenarios have a 7% higher CRF than the baseline and a 10% higher GMTC.

The small difference between the baseline and the other scenarios is explained by the fact that nuclear power already produces energy with a very low carbon footprint (according to the current inventory dataset in ecoinvent for the French electricity mix) and replacing it by renewable systems does not significantly modify this performance. When analysing the benefit of future production mixes, the ranking is inversed for conventional LCA and DLCA. This result is explained by the way biogenic CO2 is considered in the two methods. In both the best-and worst-case scenarios, the contribution of bio-based resources to the French mix tends to increase over time (Figure SI3). Therefore, CO2 uptake by biomass and its release when generating energy modifies the atmospheric CO2 balance during the concerned period (the use phase of the building). The dynamics of biogenic CO2 is correctly considered in DLCA, while it is missing in conventional LCA, which results in an incorrect ranking.