Life cycle assessment of prospective trajectories: A parametric approach for tailor‐made inventories and its computational implementation

Life cycle assessment (LCA) is a standardized, holistic, and multi‐criteria approach to estimate the environmental impacts of a system over its entire lifecycle. Modeling the environmental impacts of future scenarios and evolving systems in LCA is challenging due to lack of knowledge around technological evolutions and changing backgrounds influencing the foreground system. The method proposed here tackles these issues by combining parameterized life cycle inventories (LCIs) of foreground and background systems to assess how background changes, for example in the energy sector, affect the environmental impacts of the foreground. First, parameterized LCIs for the heating and energy sector were developed to flexibly estimate the environmental impacts of heating, gas, and electricity trajectories. Assessing their environmental impacts is essential to avoid any burden shifting to other impacts. Thanks to their parameterization, these models can represent different geographical, temporal, or technological contexts. Second, the combination of these parameterized LCIs was implemented using the Python library lca_algebraic, designed to enhance computational efficiency and calculation speed of LCAs. lca_algebraic’s features were extended to link parameters to specific LCIs and, hence, ease their import and export and facilitate teamwork. In a final step, the developed LCIs and lca_algebraic library were used to estimate the environmental impacts of French heating scenarios from 2018 until 2050, as a test of the approach. The parameterized models developed within this work are available on a Git together with published reference datasets for comparison, so that the method can be adapted to evaluate similar energy trajectories for other countries or regions. This article met the requirements for a gold–gold JIE data openness badge described at http://jie.click/badges.

parameterized life cycle inventories (LCIs) to model changes in the foreground systems more easily.Such parametrizations, also referred to as parameterized LCA models, exist, for example, for passenger vehicles (Bauer et al., 2015), wind turbines (Besseau et al., 2019;Sacchi et al., 2019), photovoltaic systems (Tannous et al., 2019), or geothermal installations (Douziech et al., 2021).The parameters can be distributions, used to conduct Monte Carlo analysis of LCA results, or variables modified according to the analyzed scenario (Clavreul et al., 2014).
As for the background systems, combinations of coherent and consistent future projections of them using integrated assessment models (IAMs) with future models of the analyzed foreground technology in so-called hybrid LCA approaches are increasingly common (Beltran et al., 2018;Frapin et al., 2021;Gibon et al., 2015;Joyce & Björklund, 2021;Sacchi et al., 2022;van der Hulst et al., 2020).IAMs can be used to comprehensively update the background system per time step for which the environmental impacts of the foreground system are estimated.A different energy mix can, for example, be modeled per year to better represent the evolution of the environmental impacts of the system analyzed.The scenarios used for IAMs rely on macro-economic and energy system models.Assessing the influence on environmental impacts of modifying only single parameters through "what-if" scenarios, as defined in Weidema et al. (2004), using IAM outcomes might therefore imply very complex analysis.Further, the influence of the assumptions underlying the IAM on specific background elements, and as a result, on the LCA outcomes, are difficult to highlight.
The approach proposed here could allow extensive IAM scenarios to be combined with parameterized LCIs of chosen background elements to describe more flexibly their current as well as future status and its influence on the environmental impacts (Cooper et al., 2012;Padey, 2013).
The aim of this paper was therefore to demonstrate that LCIs of background processes can be parameterized and combined to parameterized foreground LCIs to estimate the environmental impacts of future energy production and consumption trajectories.Complementary to hybrid approaches such as the one of Beltran et al. (2018), our aim here was to propose a method to model specific technical evolutions of the background system and evaluate their influence on possible future trajectories of a foreground system.This approach builds upon the flexibility of parameterized LCA models to extend process-based LCAs with detailed modeling of specific background systems without necessarily the need for extensive IAM modeling.The advantages of our approach are therefore its flexibility, the transparency of the modeling, and the independency to other model outputs.Modeling prospective scenarios is however still necessary to apply our proposed framework.In our case, the future scenarios were based on experts' formulations for the specific background and foreground systems under study.Combining our approach with IAM modeling outcomes is still possible and could increase the representativity of the results.Adding new features to the lca_algebraic library was essential to ensure the applicability of the presented method.These new features are presented in this paper.
The implementation of this approach is illustrated with the planned evolution of the French heating sector until 2050 modeled with the updated Python library lca_algebraic.The heating sector was chosen as example since, in Europe, 40% of the energy consumption is due to buildings, causing 36% of GHG emissions (European Commission, 2020) and the situation is similar in France, 46% and 17%, respectively.(Citepa, 2021;Ministère de la Transition écologique, 2020).For this illustration, parameterized LCIs for the energy and buildings' heating sectors were developed that can be used in other applications to guide decisions in the current energy transition context.

METHODS
First, the procedure for the generation of the parameterized LCA models of background and foreground systems is described.Second, the combination of the background and foreground parameterized LCA models using the lca_algebraic library is explained.Finally, the parameters and assumptions related to the description of the case study on the French heating sector trajectory from 2018 to 2050 are listed.

Development of parameterized life cycle assessment models
Roughly, parameterized LCA models represent inventory flows using parameters.Parameters can hereby be probability distributions or single values, varied according to user-defined scenarios.The lca_algebraic library allows to efficiently define such parameterized LCA models in Python and a more detailed description of the exact technical implementation can be found in Jolivet et al. (2021).
Overall, two strategies can be differentiated to develop parameterized LCA models (Jolivet et al., 2021): either entirely from scratch (Douziech et al., 2021) or through parameterization of an existing inventory (Sacchi et al., 2019).In both cases, scaling relationships or regressions between inventory flows and specific parameters need to be identified and modeled (Padey et al., 2012).The inventory flows to be parameterized can be determined from previous LCA studies reporting sensitivity analysis of similar systems, or, if not available, from own sensitivity analysis as done for the module efficiency parameter of the PV model.More details on procedures to parameterize LCA models can be found in other studies (Blanc et al., 2020;Douziech et al., 2021;Pérez-López et al., 2020).Developing a parameterized LCA model entirely from scratch requires additionally the use a representative system as a starting point and to generalize it to adequately represent any similar system.Once the inventory flows have been defined, they are scaled to the chosen functional unit of the system.Finally, the representativeness of the parameterized model is assessed by comparing the LCA outcomes to published literature values (Padey et al., 2013).
Sections 2.1.1 and 2.1.2give an overview of the parameterized LCA developed in this work for the energy production (i.e., parameterized background LCIs) and heating technologies (i.e., parameterized foreground LCIs), respectively (Figure 1).The Jupyter Notebooks of each technology are available (Douziech et al., 2022).The models partly rely on the processes of the ecoinvent v3.6 database cut-off.As highlighted in Figure 1, the electricity fed into the heating sector corresponds to the electricity produced and not consumed, meaning that neither imports nor exports are accounted for.This assumption likely influences the results but since the aim of this study was to illustrate how background and foreground parameterized LCA models can be combined it was deemed acceptable.

Background parametrized inventories: Electricity and gas production
The electricity mix was composed of electricity produced from nuclear power, solar power, wind power, hydropower, coal, oil, gas, or biogas.Parameterized models were developed for all technologies except hydropower, coal, and oil, using a functional unit of 1 kWh of generated electricity.For hydropower, the ecoinvent dataset "electricity production, hydro, reservoir, alpine region" was used directly as the hydropower technology is not expected to evolve greatly in the future.
The French ecoinvent datasets "electricity production, hard coal" and "electricity production, oil" were used directly to represent coal and oil power plants as they should be progressively abandoned in a near future.
The grid infrastructure was not included in this study given its low contribution (between 1% and 14%) to the overall environmental impacts of an electricity supply mix (Berrill et al., 2016;Birkeland, 2011;Garcia et al., 2014) and the fact that this analysis focuses on the supply-demand balance only.
In the following sections, general information on the single parameterized LCA models is given.Table S1 in Supporting Information S1 details the modeling approach used for each electricity producing technology.

a. Nuclear energy
The nuclear parameterized LCA model is based on ecoinvent's dataset "electricity production, nuclear, pressure water reactor," describing a Swiss pressurized water reactor (Dones et al., 2007).This inventory was used since specific data for third-generation pressurized water reactors expected F I G U R E 1 Energy production (background) and heating technologies (foreground) for which parameterized life cycle assessment models were developed together with their link to the background database ecoinvent v3.6 cut-off.The arrows mean that these inventories are inputs to the other inventories.
to be deployed in France was lacking.It was adapted to the French context using 10 parameters, listed in Table S1 in Supporting Information S1.The parameters influencing the environmental impacts the most were related to the electricity mix and type of process used in the uranium enrichment phase.In fact, the centrifugation process is around 50 times more efficient than the gaseous diffusion process, historically used in France (Zhang & Bauer, 2018).It should be noted that the inventories used in ecoinvent rely on data from the 1980s to 2000 and do neither consider the stricter safety measures put in place after Fukushima nor the exceptional maintenance work planned to improve the safety and extend the lifetimes of the French nuclear power plants.The dismantlement of the power plant is not considered either since LCIs for radioactive waste disposal project, coming from the Project Gewähr 1985 in Switzerland, are scarce.All those elements limit the precision of the LCA of nuclear energy, but not its order of magnitude according to the sensitivity analysis carried out with the parameterized model.

b. Photovoltaic energy
The photovoltaic parameterized LCA model updates the ecoinvent LCIs for crystalline-silicon PV systems by including 28 parameters.In fact, the default ecoinvent LCIs represent the environmental performance of PV systems from 2005, thus not reflecting evolutions in conversion efficiency (ENF Ltd., 2021), energy efficiency of silicon ingot production (REC group, 2018;Woodhouse et al., 2019), improved cutting process (ENF Ltd., 2021;Yang et al., 2019), and inverter, electric installation, and mounting system's weights (ENF Ltd., 2021).The model used in this paper improves the parameterized model developed by Pérez-López et al. (2020) by including additional parameters to account for the latest developments of the PV sector, such as bifacial PV panels (Besseau et al., 2023).

c. Wind energy
The parameterized LCA model for wind energy adapts the parameterized model published for Denmark to France (Besseau et al., 2019;Sacchi et al., 2019).
-The mass of "intra-array" cable was extrapolated from environmental impacts studies of two 500 MW large offshore wind farm projects since the previous model underestimated it compared to the announced value (BRL ingénierie, 2015;DONG Energy et al., 2013).
-The monopile foundations were replaced by gravity (DONG Energy et al., 2013) or floating foundations (Tekla, 2018).The total mass of foundations is proportional to the torque of the wind force on the rotor as in Besseau et al. (2019) and Sacchi et al. (2019).
-The amount of energy for operation and maintenance comes from the environmental impact studies (BRL ingénierie, 2015;DONG Energy et al., 2013).
-The asynchronous generators were replaced by synchronous ones, with lower maintenance need and increased resistance to temperature variations but with potential need for rare earths for the permanent magnet, potentially influencing the mineral resource (Patel & Makwana, 2018).

d. Gas and biogas power
Gas here refers to the gas available in the network, therefore a mix of natural gas, biogas, and to a small extend hydrogen.A parameterized model was developed for conventional and combined cycle gas power plants based on power plant efficiency, the load factor, the lifetime of the installation, the share of dihydrogen, and the share of biomethane in the supplied gas.
The parameterized LCA model for electricity production from biogas describes either direct burning of biogas in a small power plant, with or without co-generation, or the burning of purified biogas (i.e., biomethane) in a conventional, co-generation, or combined cycle power plant.A parameter for methane leakage, occurring either at the grid or power plant level, was introduced, as well as a parameter for biogenic emissions induced by biogas production from animal manure.

Foreground parametrized inventories: Heating technologies
The foreground system includes parameterized LCA models for heat pumps (air-air, air-water, and water-water), gas boilers, oil boilers, electrical heaters, wood heaters, and district heat since they represent most of the installed and planned space heating systems (European Commission, 2010).The functional unit was 1 MJ of generated heat.This functional unit is different from that for the energy-related parameterized models to ease their combination.The modeling approach chosen per heating technology is briefly described here and more details are in Table S2 in Supporting Information S1.In addition, the ecoinvent v3.6.process "heat production, solar heating, flat plate, one family house [CH]" was used to represent solar heaters.The share of heat produced from natural gas was removed and the input of solar energy and need for Cu flat plate collector was adapted assuming 65% efficiency of the flat plate collector.LCIs of the French context, specified as [FR] were preferably used, followed by LCIs from [Europe without Switzerland], or Switzerland [CH].These LCIs were deemed representative enough for the French, and by extension European, context.

a. Heat pumps
The air-water and water-water heat pumps were modeled from the ecoinvent process "heat pump production, air-water [CH]" with five parameters, namely the coefficient of performance (COP), heat pump's power, operating hours, lifetime, and refrigerant leakage.Scaling relationships from Caduff et al. (2014) were used to model the heat pump's mass and refrigerant mass as a function of its power.
The air-air heat pump, on the other hand, was modeled from scratch based on published inventories (Miralles et al., 2020;Rey et al., 2004;Shah et al., 2008) and using six parameters, namely the heat pump's operating hours, lifetime, COP, power, and the refrigerant's mass and leakage.A scaling relationship relating the heat pump's mass to its power was derived from manufacturer's information (SOLFEX, 2016).

b. Gas and oil boiler
Gas and oil boilers were modeled by adding one parameter, representing the boiler's efficiency, to the respective ecoinvent processes "heat production, natural gas, at boiler condensing modulating < 100 kW [Europe without Switzerland]" and "heat production, light fuel oil, at boiler 10 kW condensing, non-modulating [Europe without Switzerland]."

c. Electrical heater
The information available on electric convectors, radiant panels, and electric heaters from heaters' manufacturers was summarized into a single parameterized model representing an average electrical heater.This assumption was deemed acceptable given the similar LCA results, on average around 20% variation, published in the manufacturers' product declaration sheets (Atlantic, 2021;Sauter, 2013).The model included four different parameters, namely the electrical heater's efficiency, power, operating hours, and lifetime.A scaling relationship was derived to express the electrical heater's total mass as proportional to its power (Atlantic, 2021;Sauter, 2013).

d. District heat
The district heat was modeled as a combination of four different heat types: "heat and power co-generation, oil [FR]", "heat, from municipal waste incineration to generic market for heat district or industrial, other than natural gas [FR]", "heat and power co-generation, biogas, gas engine [FR]", and "heat and power co-generation, natural gas, conventional power plant, 100MW electrical [FR] " (SNCU & FEDENE, 2020).The shares of the single heat types were modeled as parameters.
e. Wood heater The ecoinvent process "heat production, mixed logs, at wood heater 6 kW, state-of-the-art 2014" was parameterized to account for its efficiency and whether the wood was produced from sustainable logging.Wood was assumed to come from sustainable logging exploitation thus influencing the share of biogenic and fossil carbon emissions but not land use change.This assumption aligns with the strategy described by Ministère de la Transition écologique (2021).

Combining background and foreground parameterized inventories
The parameterized LCA models presented in Sections 2.1.1 and 2.1.2were modeled in Python using the lca_algebraic library (Jolivet et al., 2021), a layer above the Brightway2 library (Mutel, 2017) enabling to conduct LCAs using the Python programming language.The primary aim of lca_algebraic was to ease the analysis of the influence of parameter uncertainty and variability on LCA results by implementing symbolic calculus into Brightway2.
This feature was used here to define the parameterized LCA models and so, model future system evolutions with the chosen parameters.In addition, symbolic calculus allows very fast evaluation of LCA results, around 1,000,000 results per second, which would be an additional strength to process dynamic LCA over large time series at smaller time steps than done in this study.
In its original version, lca_algebraic v0.0.15 did not foresee the combination of background and foreground parameterized LCA models.The following adaptations were therefore implemented and published in lca_algebraic v1.0.0: -Improved definition of parameters by binding them to specific parameterized LCA models, rather than describing them as global, allowing better control and preventing conflicts in parameter names from different models; -Support for export and import of parameterized LCA models, which includes the parameters definition themselves to facilitate traceability and team collaboration; -Support for "freezing" of a parameterized LCA model, meaning setting parameters to values specific to a given scenario and reusing it as background of another model.
This last adaptation is an improvement of the latest release of lca_algebraic v1.0.0 by allowing to easily combine different databases, for example, several background databases for a given foreground database.This is made possible by a dedicated function in lca_algebraic which freezes parameter values of a parameterized LCA model to a specific set or their default values.This frozen database can then be imported into an existing notebook where the foreground inventories can call upon the inventories saved in it.This last feature can further facilitate team work in several projects and freezing the database prior its use in the foreground model reduces the computational requirements.An example of how this feature can be used is provided in Supporting Information S2, Section S3.In addition, it can be mentioned that this freeze function allows to use other functionalities from the Brightway2 analyzer (Mutel, 2017).
The uncertainty analysis and global sensitivity analysis features of lca_algebraic are not presented in this work.Outcomes from such analysis can be extremely rich in information and could represent a paper in itself, especially in combination with prospective LCA.It was therefore not part of the focus of this work but could be an interesting follow-up study.

Case study for the French heating sector in 2050
The aim of this case study was to show how the parameterized LCA models of background and foreground systems can be combined to estimate the environmental impacts of the French heating sector's forecasted evolution from 2018 to 2050.An attributional LCA was conducted.
The case study presented here is based on versions of the power mix scenarios generated as part of RTE's project "Futurs énergétiques 2050" (RTE, 2021) and on consumption trajectories derived from the French national low-carbon strategy.More specifically, the influence of three consumption trajectories and two power mix scenarios on the environmental impacts of the French heating sector were investigated.The three consumption trajectories describe (1) an evolution following the technological developments of the French Environmental Regulation 2020 (REF), (2) a lower efficiency trajectory (LOW), and (3) an increased energy sufficiency trajectory (SUFF), and are detailed in Section 2.4.2.The two power mix scenarios, with (N03) or without (M0) the renewal of the French nuclear reactors, are described in Section 2.4.3.
The environmental impacts were quantified using the EU recommended ILCD v2.0 2018 impact assessment methods (Fazio et al., 2018;Moreno-Ruiz et al., 2020) with a focus on climate change, ionizing radiation, ozone depletion, acidification, and freshwater eutrophication.This selection was made to include most of the environmental impacts covered in the scientific literature and product environmental profiles (Famiglietti et al., 2021;Greening & Azapagic, 2012;Havukainen et al., 2018;Miralles et al., 2020;Osman & Ries, 2007;Sauter, 2015).In addition, these impact categories cover most of the trends observed in the others except for wood heating, whose impacts on non-carcinogenic human health, photochemical ozone creation, land use, and respiratory effects are larger than for the other impact categories (Wernet et al., 2016).Still, given the small share of wood heaters in the final heating mix, the selection of four impact categories was deemed a good balance between trend coverage and results' communication.

Parameter evolutions for the energy production and heating technologies
Not all the parameters used in the background and foreground parameterized models of Sections 2.1.1 and 2.1.2were assigned an evolution until 2050.For the heating sector, the operating hours, lifetime, power of the heat pumps and electric heaters, amount of refrigerant in the air-air heat pump as well as the efficiency of the electric heaters, oil, and gas boilers were kept constant since they are not expected to evolve over the years.
The evolution until 2050 of the other parameters, such as the COP of heat pumps, is in Table S3 in Supporting Information S1.
For electricity and gas production, the recycling assumptions for photovoltaic panels, the lifetime of gas power plants, and the type of nuclear fuel enrichment are examples of parameters kept constant.The evolving parameters, whether based on technological evolution assumptions such as PV efficiency or energy production trajectory assumptions such as the penetration rate of biomethane in the gas grid, are presented in Table S1 in Supporting Information S1.
Values are representative of the overall fleet performance at the given time horizon and are not specific to the performance installed in a given year.Average future performances of the fleet correspond to the current best and do not account for potential evolutions in the manufacturing processes.

Trajectories of energy production until 2050
For the present case study, two scenarios for the evolution of the energy mix were considered: N03 and M0.M0 is based on the accelerated decommissioning of existing nuclear power plants without construction of new ones and on the extensive development of renewable energies to reach 100% electricity from renewable sources by 2050, namely 36% photovoltaic, 52% wind (onshore and offshore), and 9% hydropower.The N03 scenario, on the other hand, foresees further construction of nuclear power plants and the maintenance of existing ones, as well as the deployment of renewable energy technologies resulting in a 50/50 distribution between nuclear power and renewable energy by 2050.The scenarios M0 and N03 hereby rely on average evolutions for the parameters describing the different electricity producing technologies.The trajectory of decarbonization of the gas energy follows the assumptions of France's national low-carbon strategy (Ministère de la Transition écologique, 2021).No specific developments have been studied regarding heat production by biomass and district heat.Illustrations of the environmental impacts of both electricity mix scenarios are provided in Supporting Information S2, Section S5.

Trajectories of the heating demand
The heating demand trajectories are based on adapted versions of France's national low-carbon strategy.Visualizations of these trajectories are provided in Supporting Information S2, Section S6.
• REF: a reference trajectory needed to achieve carbon neutrality in the heating sector as detailed in the above paragraph, • LOW: a "lower efficiency" trajectory which assumes a lower renovation rate and less heat pumps replacements of Joule electric heaters than in the REF trajectory leading to an increase in energy consumption, • SUFF: a "sufficiency +" trajectory which leads to an additional decrease in energy consumption compared to the REF trajectory due to, among other things, a slightly lower demand for heating temperature and less surface area to be heated in the residential and tertiary sectors as a result of the stabilization of the number of people per household, more collective housing, and development of home office.

F I G U R E 2
Climate change life cycle impact assessment results in g CO 2 -eq/kWh of electricity produced for the parameterized life cycle assessment models of biogas, gas, nuclear, photovoltaic, offshore and onshore wind compared to literature values.The results of the parameterized model are shown as big orange triangles and represent the results obtained with parameter values from 2018.The literature values are displayed as green symbols, varying in shape depending on the reference as specified in the legend.The results from IPCC2011(the green boxplot) represent the median, minimum, and maximum values of the literature review conducted.The results of the parameterized model for gas refer to a conventional power plant.The code used to generate the data in this figure can be found in the online data repository Zenodo at https://doi.org/10.5281/zenodo.8338788.
Next to the modeling of the background electricity and gas input, the total number of MJ foreseen to be produced by each heating technology was estimated.To do so, the number of residential dwelling and the square meters of tertiary dwellings heated by a specific technology were estimated from RTE ().Besides the number or square meters of dwellings, the unit heat consumption of each dwelling and heating type was estimated.Details on this computation are provided in the Supporting Information, Section S4.
It should be noted that the electricity mixes do not vary as a function of the chosen heating demand trajectory, for example, an increased electricity need for heating might lead to other shares of the electricity mixes after executing the optimization algorithm.However, since the aim of this paper was to show how foreground and background inventories can be combined and give first insights into how the environmental impacts of the heating sector in France might change, this limitation was deemed acceptable.

Representativeness of the parameterized LCA models
Before applying the parameterized LCA models for energy production and heating technologies, their representativeness was assessed by comparing the LCA outcomes to published literature values.The comparison focuses on the climate change impact category since it is the category with most published results and few variations depending on the impact assessment methodology chosen, thus reflecting a high level of consensus among experts.
Figure 2 shows that the parameterized LCA models for electricity production nearly always fall within the range of reported values in the literature (Eldenhofer et al., 2012) and are close to values reported in the recently published LCA results (Batalla, 2017;Fthenakis & Leccisi, 2021;Poujol et al., 2020;Smoucha & Fitzpatrick, 2016;Teffera et al., 2021).For example, the estimated value for power from biogas (33 gCO 2 -eq/kWh) lies very close to the median value of 34 gCO 2 -eq/kWh reported in (Eldenhofer et al., 2012) even though being below the range from 100 to 522 gCO 2 -eq/kWh reported in Batalla (2017).Differences in how biogenic carbon emissions are handled could be an explanation.The estimated climate change impact for PV electricity (29 gCO 2 -eq/kWh) matches the median of 29 gCO 2 -eq/kWh reported in Eldenhofer et al. (2012) and is comparable to the lowest values reported in Fthenakis and Leccisi (2021) (17 gCO 2 -eq/kWh).
Overall, the climate change impact of gas, oil boiler, and wood heater are in relatively good agreement with the ones found in the literature: 66 Climate change life cycle impact assessment results in g CO 2 -eq/MJ of heat produced for the parameterized life cycle assessment models of heat pumps, electrical heaters, gas boiler, oil boiler, and district heating compared to literature values.The parameterized model results are displayed as big orange triangles and the literature values are displayed with green symbols varying in shape according to the literature source as displayed in the legend.For the parameterized life cycle assessment models of heat pumps and electrical heating, the French (FR Elec) and the European (EU Elec) electricity mixes from ecoinvent were used as input during the operation phase.For these heaters, the result without the operating phase is also shown (No Elec).The code used to generate the data in this figure can be found in the online data repository Zenodo at https://doi.org/10.5281/zenodo.8338788.
gCO 2 -eq/MJ are estimated for the parameterized model for gas compared to values ranging from 55 to 82 gCO 2 -eq/MJ reported in Castelli et al.
(2020) and Greening and Azapagic (2012), respectively.Further Castelli et al. (2020) report 90 gCO 2 -eq/MJ for the oil boiler comparable to the 88 gCO 2 -eq/MJ estimated with our parameterized model.For district heating, the parameterized model renders climate change impacts three times lower than the corresponding ecoinvent datasets: 28 gCO 2 -eq/MJ compared to a range from 52 to 68 gCO 2 -eq/MJ in ecoinvent.This relates to the definition of the French heat district mix, which is mostly produced from waste incineration, compared to the natural gas and oil, coal, lignite, and wood-based ecoinvent mixes.The closer match, 25% difference, of the parameterized model's estimate with respect to the average value for France reported by Castelli et al. (2020), 28 gCO 2 -eq/MJ supports this explanation and the validity of the parameterized model.The climate change impact of the heat pumps and electrical heaters largely depends on the electricity mix used as input.The lack of published LCAs for electrical heater matching our functional unit does not allow a thorough comparison and it can only be observed that the single literature value available falls within the range estimated by our parameterized model.For the heat pumps, the majority of the studies fall within the range estimated by our parameterized models.The spread in the values obtained from our parameterized models for the heat pumps relates to the electricity mix used.For the air/air heat pump, for example, using a European electricity mix leads to a climate change impact close to the value obtained with ecoinvent: 42 gCO 2 -eq/MJ compared to 51 gCO 2 -eq/MJ in ecoinvent.On the other hand, feeding French electricity into the air/air heat pump leads to a climate change impact similar to the one reported in Castelli et al. (2020), based on French data: 17 gCO 2 -eq/MJ compared to 14 gCO 2 -eq/MJ in Castelli et al. (2020).
Only the outcomes of Greening and Azapagic (2012) fall up to twice as high as the largest estimate of our parameterized model.An explanation could be the inclusion of the collector system as part of the heat pumps' LCAs in Greening and Azapagic (2012), while this was not the case for our model.Despite this literature comparison being limited by the small amount of reported LCA results and not including a harmonization to ensure exact overlap in the system boundaries and other assumptions, our parameterized models predict the climate change impacts within the range of the values in the literature.

Environmental impacts of the French heating sector trajectories
The environmental impacts of all heating types in the tertiary and residential sector today are higher than the ones predicted for 2050 (Figure 4).
The main explanation lies in the overall energy consumption reduction, also related to the change in heater type in 2050 compared to 2018.In 2018, heating in the residential and tertiary sector in France is found by our model to lead to climate change impacts of 70 Mt CO 2 -eq.Unfortunately, no reference was found estimating the environmental impacts of the entire French heating sector from a life cycle perspective excluding water heating F I G U R E 4 Environmental impact results for the French Environmental Regulation 2020 (REF) trajectory for all impact categories considered normalized to the results obtained with the ecoinvent French electricity mix "electricity, high voltage, production mix" "FR_static" therefore stands for the static French power mix scenario (2018); "M0" for the French power mix scenario evolving without the renewal of the nuclear reactors; and "N03" for the French power mix scenario evolving with the renewal of the nuclear reactors.REF is the reference trajectory needed to achieve carbon neutrality by 2050 in the heating sector.The code used to generate the data in this figure can be found in the online data repository Zenodo at https://doi.org/10.5281/zenodo.8338788.
and cooking so that no direct comparison of this result was possible.Still, the comparison of the parameterized models' outcomes gives a first sense check of the plausibility of the presented results.The different energy production mix scenarios influence mostly the impacts on ionizing radiation: the higher share of nuclear electricity in the scenario N03 leads to a higher environmental impact in 2050 from the heating sectors compared to M0.Since the energy balancing in scenario M0 is ensured by few decarbonized means, the difference in this impact between M0 and N03 is small.
Further, Figure 4 clearly highlights the strength of combining parameterized background and foreground inventories compared to using a static electricity mix in the background.The evolutions displayed would namely not appear.The numeric values corresponding to the impact assessment results are shown in Supporting Information S2, Section S8.One should also note that while the electricity mix was replaced by a static one, the evolving gas mix was kept for all trajectories, to isolate the influence of an evolving electricity input composition on the environmental impact results.
The environmental impacts in 2050 are lowest for the sufficiency scenario (SUFF) and highest for the scenario with lower efficiency scenario (LOW) (Figure 5).This holds for both energy production scenarios (Supporting Information S2, Section S7).
The environmental impacts for the SUFF scenario are on average 50% lower than the LOW scenario, and around 30%−35% lower than the REF scenario, for all impact categories and both electricity production scenarios.Only the reduction in the impact on ionizing radiation is not as high when combining the N03 scenario with the SUFF scenario compared to using the M0 scenario.This highlights that the electricity input in the heating scenarios is the most influencing parameter for the ionizing radiation impact category but influences less the other impact categories.For acidification and climate change, the main contribution to the impact is linked to the gas and oil boilers.Changes in the electricity mix scenario have therefore only little influence on the reduction of the environmental impacts.Sufficiency measures aiming at carbon neutrality by 2050 and thus leading to the reduction in energy consumption and the shift towards less gas and fuel boilers influences the reduction of the climate change and acidification more than the shift toward more renewable energy technologies.These findings also apply when the N03 scenario is used as input electricity (see Supporting Information).The influence of the shift towards more renewable energy technologies in the electricity mix is larger for the freshwater eutrophication category and even more pronounced for the ionizing radiation.The electricity mix explains namely most of the ionizing radiation impact, so that the disappearance of electricity from nuclear power modeled in the M0 scenario leads to a much larger decrease in the ionizing radiation impact category result compared to the N03 scenario (see Supporting Information).Such evolutions would not have been identified without the combination of parameterized foreground and background LCA inventories (Figure 4).
The contribution of the district heat to the acidification and eutrophication impacts is also interesting, since it leads in the LOW scenario even to an increase in these impact categories results.This is directly linked to the district heat produced from biogas, whose share is increasing in the French district heat mix to 57% in 2050 compared to 24% in 2018 to replace district heat produced from oil and natural gas.
It should be noted that these observations are made for an electricity mix that has low environmental impacts for the four categories chosen compared to other country-specific electricity mixes.Therefore, increasing the share of renewable energy in the electricity mix in countries like Great Britain or Germany, will likely lead to different conclusions than the ones presented here.In addition, it was assumed that the electricity input to the heating sector corresponded to the electricity produced in France and not the one actually consumed.In fact, a fraction of the electricity in France comes from imports of other European country, with other electricity mixes, potentially affecting the mix's environmental performance (RTE, 2020).
Besides the variability in the results, induced by the different electricity and consumption scenarios, the parameters used to describe the different technologies can also vary depending, for example, on technological developments, or their exact values might not be known.Accounting for the uncertainty in these parameters was outside the scope of this paper, but could easily be done using the features provided by the lca_algebraic library (Jolivet et al., 2021).Also outside the scope of this paper was to account for potential consequences of the chosen energetic scenarios, for example, whether an increased demand for a specific material essential in a specific electricity scenario can really be met or not.
Finally, the application of the proposed approach to this case study of the French heating sector can be used to reflect on the impact of simplifications and technical choices on the framework.Most importantly, it should be noted, that the results of our approach heavily rely on the definition of the scenarios and parameters' evolutions.In addition, the individual modeling of background elements proposed here potentially challenges the definition of coherent background inventories.Meaning that while IAM outcomes are internally coherent because based on one set of assumptions, our framework allows more independent definitions of background elements.Depending on the aim pursued, both approaches can be useful and a combination of both could also be envisioned as further discussed in the conclusion.

CONCLUSION
In this paper, it was demonstrated that parameterized LCIs are a very powerful tool to assess the environmental impacts of various products or systems expected to evolve over time, subject to geographical variability or for which exact technological data is missing.In fact, by expressing the inventory flows using parameters, the environmental performances of the system can easily be adapted.With this respect, the use of the lca_algebraic library is particularly recommended (Jolivet et al., 2021).
The features of lca_algebraic were taken further and it was demonstrated how, in its updated version, it can be used to combine both parameterized foreground and background inventories.Its previous version foresaw only the use of a parameterized foreground inventory combined with a static background.Such combinations are essential to provide representative estimates of the environmental impacts of, for example, future consumption trajectories.In the context of the energy transition, decisions potentially affect several industrial sectors bound to evolve with time and with various interactions to each other.The new features of the lca_algebraic library allow finetuning the parameters of specific foreground and background inventories to better represent the environmental impacts of the considered system and better understand their influence.The computational approach proposed here can therefore be seen as an enabler for conducting prospective LCAs.It still requires the definition of prospective scenarios in order to be applied, either through extensive IAM or, as done here, using literature and expert judgment.
For illustration purposes, the environmental impacts of the planned energy consumption evolution of the French heating sector were estimated until 2050 (foreground), while accounting for the planned evolution of the energy mix (background) and assuming that the electricity demand for heating was fully met by the French electricity production.It showed that, within the French context, the measures planned to reduce energy consumption and phase out of oil or gas boilers were more effective in reducing the considered environmental impacts than changes in the electricity mix.This holds for all environmental impacts considered even though to a lesser extend for ionizing radiation, which does not decrease as much when nuclear power remains an important part of the future electricity mix.This is due to the French electricity mix whose current impacts on freshwater eutrophication, acidification, and climate change are already low compared to the average European electricity mix (Supporting Information S2, Section S9).
All the models used in this study are freely available (Douziech et al., 2022).Thanks to their parametrization, they can be adapted to represent other spatial scales or technological evolutions, though a careful revision of the underlying LCIs might be necessary to ensure the representativeness for geographical contexts other than Europe.In addition, a transposition to another spatial scale would require changes in the respective scripts describing the impact technologies, and thus, some modeling skills.
Additional models for other technological sectors can further easily be developed using the lca_algebraic library.
Future developments could focus on combining such parametrized background and foreground inventories with IAMs outcomes describing the sectors not modeled by the parametrized background and foreground LCIs.IAM can here ensure a consistent modeling of all sectors by accounting for macro-drivers and variables.Such a combination could become a very powerful way of conducting prospective LCAs and could be used, for example, to carry out LCAs analyzing consequences of decisions in a broader context.For example, one could model the consequences on raw material supply of a complete switch to electric vehicles in the mobility sector.The resulting databases could be summarized into an overarching one to facilitate its use in other LCA software (Steubing & de Koning, 2021).
In summary, the proposed approach may contribute to more accurate environmental evaluations, which are key for a consistent transition toward more sustainable energy scenarios.

F
Environmental impacts of the heating sector summed over the residential and tertiary building sectors differentiated by heating type (shown in different colors) using the electricity production scenario M0 and the three consumption trajectories: lower efficiency trajectory (LOW), French Environmental Regulation 2020 (REF) and energy sufficiency trajectory (SUFF).Each figure displays another environmental impact, from left to right: freshwater eutrophication (top left), ionizing radiation, acidification, and climate change (bottom right)."M0" is the French power mix scenario evolving without the renewal of the nuclear reactors.REF is the reference trajectory needed to achieve carbon neutrality by 2050 in the heating sector, LOW assumes a lower renovation rate and less heat pump replacements of Joule electric heaters than in the REF trajectory, and SUFF is the trajectory leading to an additional decrease in energy consumption compared to the REF trajectory.The code used to generate the data in this figure can be found in the online data repository Zenodo at https://doi.org/10.5281/zenodo.8338788.