# A tool to operationalize dynamic LCA, including time differentiation on the complete background database

Yoann Pigné, Tomas Navarrete Gutierrez, Thomas Gibon, Thomas Schaubroeck, Emil Popovici, Allan Hayato Shimako, Enrico Benetto, Ligia Tiruta-Barna

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## To cite this version:

Yoann Pigné, Tomas Navarrete Gutierrez, Thomas Gibon, Thomas Schaubroeck, Emil Popovici, et al. A tool to operationalize dynamic LCA, including time differentiation on the complete background database. International Journal of Life Cycle Assessment, 2019, 25 (2), pp.267-279. 10.1007/s11367-019-01696-6. hal-02353921

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# A tool to operationalize dynamic LCA, including time differentiation on the complete background database

Yoann Pigné<fnref n="1" /> · Tomás Navarrete Gutiérrez<fnref n="2" /> · Thomas Gibon<fnref n="2" /> · Thomas Schaubroeck<fnref n="2" /> · Emil Popovici<fnref n="2" /> · Allan Hayato Shimako<fnref n="3" /> · Enrico Benetto<fnref n="2" /> · Ligia Tiruta-Barna<fnref n="3" />

Received: 4 December 2018 / Accepted: 23 September 2019 / Published online: 5 November 2019

© The Author(s) 2019

## Abstract

**Purpose** The objective is to demonstrate an operational tool for dynamic LCA, based on the model by Tiruta-Barna et al. (J Clean Prod 116:198-206, Tiruta-Barna et al. 2016). The main innovation lies in the combination of full temporalization of the background inventory and a graph search algorithm leading to full dynamic LCI, further coupled to dynamic LCIA. The following objectives were addressed: (1) development of a database with temporal parameters for all processes of ecoinvent 3.2, (2) implementation of the model and the database in integrated software, and (3) demonstration on a case study comparing a conventional internal combustion engine car to an electric one.

**Methods** Calculation of dynamic LCA (including temporalization of background and foreground system) implies (i) a dynamic LCI model, (ii) a temporal database including temporal characterization of ecoinvent 3.2, (iii) a graph search algorithm, and (iv) dynamic LCIA models, in this specific case for climate change. The dynamic LCI model relies on a supply chain modeling perspective, instead of an accounting one. Unit processes are operations showing a specific functioning over time. Mass and energy exchanges depend on specific supply models. Production and supply are described by temporal parameters and functions. The graph search algorithm implements the dynamic LCI model, using the temporal database, to derive the life cycle environmental interventions scaled to the functional unit and distributed over time. The interventions are further combined with the dynamic LCIA models to obtain the temporally differentiated LCA results.

**Results and discussion** A web-based tool for dynamic LCA calculations (DyPLCA) implementing the dynamic LCI model and temporal database was developed. The tool is operational and available for testing (http://dyplca.univ-lehavre.fr/). The case study showed that temporal characterization of background LCI can change significantly the LCA results. It is fair to say that temporally differentiated LCI in the background offers little interest for activities with high downstream emissions. It can provide insightful results when applied to life cycle systems where significant environmental interventions occur upstream. Those systems concern, for example, renewable electricity generation, for which most emissions are embodied in an infrastructure upstream. It is also observed that a higher degree of infrastructure contribution leads to higher spreading of impacts over time. Finally, a potential impact of the time window choice and discounting was observed in the case study, for comparison and decision-making. Time differentiation as a whole may thus influence the conclusions of a study.

Responsible editor: Yi Yang

**Electronic supplementary material** The online version of this article (https://doi.org/10.1007/s11367-019-01696-6) contains supplementary material, which is available to authorized users.

<footnote>Enrico Benetto
enrico.benetto@list.lu</footnote>

<footnote n="1">¹ Université Le Havre Normandie, 25 rue Philippe Lebon BP 1123, 76063 Le Havre, CEDEX, France</footnote>

<footnote n="2">² Environmental Sustainability Assessment and Circularity (SUSTAIN) RDI Unit, Department of Environmental Research & Innovation (ERIN), Luxembourg Institute of Science and Technology (LIST), 41 Rue Du Brill, 4422 Belvaux, Luxembourg</footnote>

<footnote n="3">³ LISBP, Université de Toulouse, CNRS, INRA, INSA, 135 Avenue de Rangueil, 31077 Toulouse, France</footnote>
**Conclusions** The feasibility of dynamic LCA, including full temporalization of background system, was demonstrated through the development of a web-based tool and temporal database. It was showed that considering temporal differentiation across the complete life cycle, especially in the background system, can significantly change the LCA results. This is particularly relevant for product systems showing significant environmental interventions and material exchanges over long time periods upstream to the functional unit. A number of inherent limitations were discussed and shall be considered as opportunities for further research. This requires a collegial effort, involving industrial experts from different sectors.

**Keywords** Dynamic LCA · Dynamic modeling · Graph search · LCI · LCIA · Temporal database · Temporally differentiated

# 1 Introduction

In the quest to assess the environmental impacts of a production-consumption system, life cycle assessment (LCA) is usually performed without adequate consideration of temporal differentiation (ISO 14 040 and 14 044). In conventional LCA, Life Cycle Inventory (LCI) and intermediary flows are assumed to occur simultaneously. Life Cycle Impact Assessment (LCIA) is mostly based on steady-state modeling and time-integrated indicators. Nonetheless, time differentiation along the framework could have a significant impact on the LCA results and on decision support, as is conceptually explained in Fig. 1 through a simple example.

Consider an instantaneous emission of 1 kg of methane to air as an LCI result. This generates a climate change impact of 28 kg of CO₂ equivalents using GWP₁₀₀ as an LCIA characterization factor (IPCC- 2013, Table 8.A.1.). Consider now two emission profiles (A and B) for the same emission

content. These two impact results provide quite different information than the other case.

Extrapolating this exercise to all LCIs, the effects of temporal differentiation can propagate exponentially. At the LCI level, such an extrapolation shall result from knowing when each process of the life cycle actually occurs. At the LCIA level, impacts are also dependent on the timing of emissions. For example, volatile organic compound emissions have a higher influence on ozone and smog formation (Cheremisinoff 2002) during NOₓ peak levels. A temporal differentiation of impacts over time is also relevant as, from an ethical perspective, future impacts could be regarded as less relevant (Levasseur et al. 2011; Schaubroeck and Rugani 2017). The common cut-off for climate change at 100 years is not only interpretable from a convenience perspective but also from an ethical perspective, in the sense that the impact on the globe after 100 years is completely discarded. A more gradual decrease in the importance of future effects could also

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<figure><img src="image_5.png" /><figcaption>**Fig. 1** Importance of time dependence in the calculation of the climate change impact of 1 kg methane emission (from Shimako et al. 2018)</figcaption></figure>
be achieved using a discount factor as done by Levasseur et al. (2010) for global warming.

In principle, time-differentiated LCA results can be bene-
ficial for different decision contexts. For example, bio-
products could contribute to lowering radiative forcing thanks
to the carbon stored (Røyne et al. 2016) on condition that the
end of life of these products is consciously designed and
scheduled in time. This is a concern not only when a bio-
product is the object of a study, but also when it is used in
the background of a product system. A more detailed discus-
sion and literature examples of the ins and outs of a dynamic
approach in LCA and of the main developments was provided
by Beloin-Saint-Pierre et al. (2014) and Cardellini et al.
(2018).

The methods and tools employed to perform dynamic LCA (DLCA) strongly evolved during the last decade, from a simplified spreadsheet-based temporalization of LCA results to a conceptualization accompanied by models and software development. However, operational tools capable of calculating time-differentiated inventories and impacts are still lacking, and this issue is therefore the subject of the present work.

At the LCI level, we distinguish between two kinds of
temporalization. The first one concerns the changes in an in-
ventory during the lifetime of a system, which can be de-
scribed by defining several scenarios with distinct LCIs, oc-
curring at distinct points in time. Some examples, not exhaus-
tive, are the works of Hellweg et al. (2005), Penth (2006), or
Collinge et al. (2013a, 2013b), with case studies from different
fields of activity. In these works, the system’s inventory was
built up at moments in time when significant modifications of
the material and energy flows occurred, as for example the
increasing energy demand during the lifetime of a building.

Practitioners need to “manually” build many inventories;
they have to trace back which process and/or environmental
intervention occurs at which time. As a result, this approach
could be interpreted as repeating static inventories for several
scenarios, each one representative of a given time period; it
does not actually provide a dynamic model for LCA. In prac-
tical terms, it is also more feasible for the foreground system
of an inventory than for the background system. Changes in
background processes are excluded because of the complexity
of the network, which cannot be processed manually.

The second type of temporalization aims to distribute
the processes, flows, and LCI of a system over time,
based on the evidence that the linked processes of the life
cycle are time-deferred. Combined with appropriate im-
pact calculation methods, the time-differentiated LCI is
the first requirement for a consistent DLCA approach.
The first attempts at temporalized inventories were pro-
posed for the foreground part of the life cycle in order to
calculate climate change impacts as a function of GHG-
emission timing and to understand the role of biogenic

CO₂ on the impact (Levasseur et al. 2010; Cherubini et al. 2011; Kendall (2012); Ericsson et al. 2013; Levasseur et al. 2012; Laratte et al. 2014, Laratte and Guillaume 2014; Lecompte et al. 2017). All these works focused on the impact generated by a few emissions related to foreground processes and did not propose a structured model for dynamic LCI. The emissions were “manually” distributed in time thanks to a precise knowledge of the studied foreground system.

In this vein, Beloin-Saint-Pierre et al. (2014) proposed a
framework centered on the temporal characterization of pro-
cesses and elementary (resource and emission) flows. The
timeline of the LCI is then automatically derived through the
interlinkages between inventory processes. The convolution
operation is used to this end. A case study was done on do-
mestic hot water production (Beloin-Saint-Pierre et al. 2016),
applying a temporal differentiation for the foreground system
only (energy production/consumption). The authors acknowl-
edged that a huge effort was necessary to provide the neces-
sary information for the background system.

Pinsonnault et al. (2014) applied this same framework to
22% of the processes of the ecoinvent 2.2 database, for which
the authors defined temporal characteristics by sector of activ-
ity (e.g., infrastructure, forestry). The analysis was performed
for the climate change impact category, also considered as a
criterion for selecting significant intermediary and elementary
flows for calculation. However, this first model for dynamic
LCI calculation lacks a structured definition of the temporal
characteristics needed for processes, flows, and supply chain
representation (i.e., what is the physical meaning of the distri-
bution functions?). From a theoretical point of view, using the
convolution operation will introduce an intrinsic dependence
of the processes in the network, that is to say, a producer
process will adapt its temporal characteristics (e.g., not only
the timing but also the emission profile) following the con-
sumer process, which is not the case in a real-life scenario (for
more information, see Tiruta-Barna et al. (2016)—supplemen-
tary information document). A clear definition of the neces-
sary temporal characteristics and an associated database are
lacking for a framework operationalization.

Tiruta-Barna et al. (2016) presented a modeling approach
akin to supply chain modeling practices, by considering tem-
poral characteristics of processes and supply chains, which
can be leaned back against LCA databases (e.g., ecoinvent).
In this approach, a limited set of temporal parameters have to
be defined for each process and its exchanges with directly
linked processes. A time-distributed LCI is calculated by com-
bining the model with a graph search algorithm. The capabil-
ity to link the temporalized LCI to dynamically calculated
impacts was also demonstrated (Shimako et al. 2016, 2017,
2018).

More recently, Cardellini et al. (2018) proposed a tool
for performing dynamic LCA based on a graph search
algorithm combined with the convolution operation be-
tween emissions of the producer process and production
of the consumer process, like in Beloin-Saint-Pierre et al.
(2014). To do so, temporal distributions for emissions
must be defined. As a demonstration, the dynamic LCI
was coupled with GWP characterization factors for cli-
mate change. However, the approach lacks a parameter-
ized model with a clear reference to process and supply
chain functioning, as well as a proper temporal database
linked to the background LCI, as is the case for the pre-
vious methods.

As our present work focuses on dynamic LCI calculation,
the temporal aspects in LCIA are not presented extensively.
Instead, the main realizations in this field are only briefly
introduced hereafter, for comprehension of the developed
framework.

Global warming is the impact category most considered in
DLCA. Levasseur et al. (2010) proposed an approach based
on the calculation of characterization factors (CF) for discrete
time steps (1 year). This dynamic model uses radiative forcing
as a physical parameter, but contrary to the classical approach,
no fixed time horizon is needed. Similarly, this line of reason-
ing was applied to derive CFs (pre-calculated for fixed 1-year
intervals) for the freshwater ecotoxicity of metals by Lebailly
et al. (2014).

An alternative to pre-calculated CF is proposed in Shimako
et al. (2016, 2017, 2018). Here, a flexible LCIA modeling
approach was proposed to be directly coupled with the tem-
poral differentiated LCI results obtained using the model of
Tiruta-Barna et al. (2016). Coupling was done for climate
change and toxicity/ecotoxicity impacts. Dynamic impact in-
dicators and their cumulative values are calculated in function
of time, taking advantage of a temporalized LCI with a time
resolution going from hours to years.

The objective of the present work is to develop an op-
erational tool for dynamic LCI calculation, based on the
modeling approach presented by Tiruta-Barna et al. (2016).
To this extent, we aim to provide an improved artifact that
can better address a research problem and achieve a fully
temporally differentiated LCA, in line with the design and
development-centered approach of Peffers et al. (2007). In
particular, the following issues are addressed in our work:
(1) development of a database with temporal parameters
for all processes in ecoinvent 3.2, in order to completely
consider the background processes in DLCA; (2) imple-
mentation of the model and database in an integrated soft-
ware; and (3) demonstration with a case study (comparing
a fossil driven and an electric car) of the feasibility of a
complete DLCA, in particular by considering the back-
ground LCI.

The novelty of the approach adopted here lies especially in
points 1 and 2; therefore, this work aims to demonstrate the
feasibility of such an approach for complete DLCA.

## 2 Methods

In the following, the principles of the dynamic LCI model are
briefly recalled. Then, the development of the new database
for the temporal parameters of the ecoinvent processes is pre-
sented, followed by the method of integration of the LCI
model, database, and LCIA dynamic models into the global
framework. Besides the case study, a more simplified and
didactic example to understand the framework behind the tool
can be found in the work of Tiruta-Barna et al. (2016).

## 2.1 Principles of the dynamic LCI model

The dynamic LCI model was initially developed by Tiruta-
Barna et al. (2016). The reader is invited to refer to this and to
the SI1 for a detailed presentation. Here, we recall the main
features of the model that are important to understand the
following steps. The model relies on the classical LCI struc-
ture (technology A and environmental intervention B matri-
ces). It introduced a fundamental novelty with the adoption of
a process/supply chain modeling perspective instead of an
accounting point of view. The unit processes composing the
life cycle inventory (foreground and background) are consid-
ered as operations having a proper functioning over time. The
reference unit and the material/energy interventions of each
have a distinct temporal profile. Furthermore, the intermediary
exchanges among unit processes are positioned over a time-
line depending on specific supply models, e.g., continuous,
intermittent, and single punctual supply. As a result, mass
and energy quantities listed in the dataset of a specific activity
are no longer considered average quantities for a reference
flow in a representative time period. Instead, the model allows
the following to be calculated, the quantity requested by an
activity, when and for how long it will be supplied to that
activity, when and for how long it is stored before or after
delivery, and when and for how long it was produced by the
supplier.

Production and supply are described by temporal parame-
ters and functions (also shown in Table S1 and Fig. S1 in
SI1—Electronic Supplementary Material). All processes are
characterized by (i) a production function α(t) for the refer-
ence flow and an emission profile β(t), which can be discrete
values or functions of time; (ii) parameters *r*, the duration of an
activity between the raw material input and the product output,
*T*, the lifetime of the infrastructure supporting an activity, and
*t*₀, the starting time of an activity. The supply is defined
through parameters: *δ*, a no-activity period, and *τ*, the frequen-
cy of a product supply. These temporal parameters can be
manually defined for the foreground processes, but a database
must be developed for background processes, and this is pre-
sented in the following section. The model was implemented
in DyPLCA, a web-based tool, which was then used in the
works of Shimako et al. (2016, 2017, 2018). This tool is a very
first version, modified and adapted in the present work for
integrating the ecoinvent database with a temporal database
of all processes, and coupling it with LCIA dynamic models.

## 2.2 Temporal database development

The temporal database was developed in an ecospold format for the *Default, Consequential* and *Recyc* system models of ecoinvent 3.2 from SimaPro. A representative sample of the database is provided in SI2. The rules and simplifications below apply.

### 2.2.1 Rules for the choice of the time parameters

(i) Functions $\alpha(t)$ (for production flows) and $\beta(t)$ (for environmental interventions) are defined for the period $r$. Period $T$ is a multiple of $r$. Functions can be constant or variable over time; they are replicated identically for all periods $r$ covering the $T$ lifetime. In the current version of the database, for the sake of simplification, $\alpha$ and $\beta$ are defined once for each activity, i.e., they apply to all inputs and outputs of that activity, although the framework supports a specific definition for each individual flow.

(ii) Production functions that are calendar-dependent are defined over 1 year, starting in January, regardless of whether the activity starts at another moment. For example, if a product whose production takes a year ($r = 1$ year) is requested in October, the production process starts in October of the previous year. In this case, the specific activity intensity at that moment in time is considered. A potential issue is that a process often involves a series of consecutive steps. For example, in agricultural processes, sowing occurs before maintaining, which precedes harvesting. Applying the calendar dependence, sowing would start after harvesting, which does not make sense. This issue does not apply, however, as long as $\alpha$ is the same for all material and energy inputs/outputs of a process, which is the case in the current version of the database.

(iii) Supply scheduling and frequency is defined by $\delta$ (delay period) and $\tau$ (interval between supplies). These parameters shall be defined per material/energy flow, per product type, and combination of processes (supply and demand), as presented in Tiruta-Barna et al. (2016). These relationships are complex as they depend on supply and demand in the real market. For the sake of simplification, in the temporal database, those parameters were attributed to each supplier (or producer) process. Three types of supply profiles were defined: (1) *Continuous*, the product is supplied without interruption; for example, this is the case with an electricity supply. Here, $\tau$ is set equal to $r$ meaning that the interval between production batches is the same as the production time. (2) *Intermittent*, when products are supplied in series of equal intermittent batches. $\tau$ specifies the duration of these time

intervals. In general, $\tau$ is set equal to $T$ of the consumer process if it is supplied once per lifetime (e.g., an infrastructure). It is set equal to $\delta$ for consumables that are frequently supplied but can be stored. It can also be set equal to either $r$ of the producing process if production, and thus supply, are seasonal; or $r$ of the consuming process, for example, in the case of frequently supplied consumables that are directly consumed at each production cycle of the consumer process. (3) *Services*, whenever the activity starts at the same time or later than the activity of the consumer process ($t_0$). This is the case of services occurring during the consumer process, e.g., “Fertilising, by broadcaster {RoW} | processing | Alloc Def, “U” for agriculture.” Services occurring at different moments (but with equal periods) are also considered, for example, mowing may occur at different moments during agricultural processes. In general, two types of processes are considered as services: (a) waste treatment processes (assuming that waste is generated and treated while the process is running) and (b) the majority of the processes that end with “processing” in their names. Services processes hold an ID (“S”) in the database.

Exceptions to the general rule are:

- Processes used by other processes, e.g., “Beverage carton converting {GLO} | processing,” “Wood preservation service, logs, pressure vessel, preservative not included {RER} | processing,” and “rock crushing.”

- Services not occurring simultaneously with other processes; namely all the vehicle and machinery maintenance processes, e.g., “Maintenance, barge {RER} | processing.”

- Services encompassing the complete production period, e.g., “Polystyrene foam slab for perimeter insulation {CH} | processing,” “Router, internet {CH} | processing” and “Wire drawing, copper {RER} | processing.”

- Transport processes, e.g., “Transport, freight train {AT} | processing.”

- Services that are performed afterwards, e.g., “Venting of argon, crude, liquid {GLO} | processing.”

- Waste treatment (including out of order equipment, machinery), e.g., “Used lorry, 16 metric ton {CH} | treatment of”

- “Sowing {CA-QC} | sowing,” which is considered as a service (for plant cultivation) even though “processing” is not mentioned in its title.

Further specific rules adopted for some of the ecoinvent processes are given in SI1, Section 2.5.

### 2.2.2 Processes without temporal profile

In ecoinvent 3.2, several processes do not reflect actual physical activities. For example, “market” processes gather several products without any physical transformation, i.e., there are no
emissions, waste generation, and consumed resources or prod-
ucts. These processes are considered to occur instantaneously
and hold an ID in the database (“M”); no temporal character-
istics are needed for these.

**Market processes (and exceptions)** These include market mixes and/or transport. For example, a process where different alternative production processes are given as inputs with their relative share as quantity. Sometimes, “market for” is not specified in the process name; for example, “Cement, unspecified {CH}| production.” Exceptions to the rule are (i) *electricity markets* including the activity of electricity transmission, for which temporal characterization is required. This means that this transportation activity is not covered by another process. The specific case of processes transforming high voltage to medium voltage is an exception of the exception. Temporal characterization is not needed; the material for the activity is already included in the medium voltage market processes containing the activity of transmission. (ii) a few *fossil fuel markets*, such as natural gas markets or imports; these include natural gas transportation, which must be characterized. Diesel markets (e.g., “Diesel {RoW}| market for” and “Diesel {CH}| market for”) also include the transportation of the diesel.

**Processes only linking with other processes/markets** Two families of processes are considered (i) *obsolete processes*, without any function and link to other processes. The description often contains the following statement: “This process is no longer part of the ecoinvent 3 database and will not be updated. Please, choose another process.” An example is “Hard coal ash (waste treatment) {RoW}| cement production, pozzolana and fly ash 11–35%, non-US.” Waste treatment processes are also concerned. (ii) *Non-obsolete processes*, linking other processes together without any activity involved (1) processes substituting another process in the consequential version, e.g., “Sodium hydroxide, without water, in 50% solution state {GLO}| sodium hydroxide to generic market for neutralising agent.” The latter translates an extra demand of sodium hydroxide in an extra demand of neutralizing agent (e.g., sodium carbonate); consequently, it makes a link with its production dataset, which requires characterization. (2) Import processes, e.g., “Aluminium, primary, ingot {IAI Area, EU27 & EFTA}| aluminium, ingot, primary, import from Africa.” (3) Processes linking with one or several processes under one name, e.g., “Heat and power co-generation unit, 50 kW electrical, common components for heat+electricity {RER}| construction.” Another example is “Heat pump, 30 kW {RER}| production.”

**Empty processes** This is the case, for example, for waste treat-
ment products in the *Recyc* version of the database, to which
cut-off is applied. Examples are “Digester sludge {GLO}|

digester sludge, Recycled Content cut-off” or “Inert waste
{CH}| clinker production | Alloc Def, U.”

**2.3 Development of the integrated framework**

**2.3.1 Principles of computation of temporally differentiated LCI results**

The objective is to obtain the life cycle environmental inter-
ventions (β functions) scaled to the functional unit (FU) and
distributed over time. Further integration of the functions over
time shall yield the static LCI results. This is achieved by
combining (i) the conventional LCI inventory datasets from
ecoinvent, (ii) the temporal parameters and functions associ-
ated with these datasets, and (iii) implementing an efficient
graph search algorithm.

The combination was achieved practically in the web-
based tool named DyPLCA, as a new, extended version of
the initial tool cited by Tiruta-Barna et al. (2016) and
Shimako et al. (2016, 2017, 2018). The algorithm works on
a network of processes created based on the topology of ma-
trix A, starting from the FU. A backward timeline is first
defined, starting with the delivery of the FU. Then, the graph
search implementation of the dynamic LCI model provides
the amount of reference units for each process as well as its
position along the timeline. Practically, a case study is first
modeled in LCA software (SimaPro or OpenLCA) in a static
manner. Then, matrices A and B are exported and further
imported into DyPLCA in order to retrieve the values of in-
termediary and elementary flows. The temporal database is
used to associate the temporal parameters to all the back-
ground processes used. In the foreground, the links between
activities and the temporal parameters associated are directly
added by the practitioner through the DyPLCA web interface
(more details are given in SI1 – Electronic Supplementary
Material).

The algorithm is computationally intensive; therefore, cal-
culation time is critical. Memory usage during the computa-
tion and the size of the datasets has to be carefully addressed to
avoid disruptive latencies. To this end, the search algorithm
uses thresholds and stop conditions. Discretization steps are
considered in order to accommodate the continuous dynamic
LCI model to discrete time-series.

In the following, the functioning of the algorithm is
detailed.

**2.3.2 Implementation of the graph search algorithm**

Once a project is properly configured (as described in SI1 -
Electronic Supplementary Material), it can be computed. First,
the “search” step resolves the start date and material quantity
for each activity in the project. Then, the “distribution” step
computes the distribution over time for the interventions for
each activity. The distribution step is computed right after each activity gets resolved during the search step.

**Search step** Life cycle processes are linked together by a producer/supplier-consumer/user relationship, based on matrix A. This is formally the adjacency matrix to a network where processes are nodes and producer-consumer relations are links. Although possibly large (15000 processes for ecoinvent 3.2), this material network remains a compact graph. Each link represents all the possible activities between a producer and a consumer. In order to obtain the complete list of activities concerned by one specific case study, one needs to obtain the complete activity network. This is an extended graph including, for each activity, its start date and material quantity over the timeline. In order to produce the activity network, a search is performed in the material network. The links indicate the flow of material or service between a producer and a consumer. This search starts from the final consumer (the FU), follows incoming links backwards to the producer, and finally, computes the start time and material quantities. The main issue to address here is that the network of processes involves loops that require a no-end graph and search algorithm. Indeed, the algorithm goes from one process to another in the loops without end, as the quantities exchanged by the processes (over time) are smaller and smaller but not null. This effect is not seen when the time dimension is ignored, as the quantities are calculated by matrix inversion to obtain the solution directly. A similarity can be drawn with the resolution of an integral by power series expansion. The solution can only be approximated as the expansion goes to infinity without reaching it.

In order to resolve this issue, the search algorithm uses boundary parameters. Once reached, these stop the search. The *time limit* parameter defines the maximum number of years the search algorithm can go back. This corresponds to an end time date of the timeline that was set in the past. Activities starting earlier than this date are excluded from the search. The *threshold* parameter defines a cut-off ratio on the quantities of the reference unit requested for each activity. Whenever the requested quantity is below the cut-off, that part of the network is discarded from the search (Table S2 in SI1 - Electronic Supplementary Material).

**Distribution step** As long as the search algorithm proceeds, environmental interventions associated with each activity are computed. They are further associated to a given moment in the timeline with a specific discrete resolution. This generates large data tables containing the time series of the different environmental intervention types over the timeline. This step is controlled by two parameters. The *step size* parameter (Table S2 in SI1 - Electronic Supplementary Material) defines the interval of time between each data point of the time series. The smaller the step size, the bigger the size of the resulting

time series. There is virtually no limit to how small the step size can be. However, the tool sets a threshold on the step size based on the available memory during the calculation. The *numerical precision* parameter (Table S2 in SI1 - Electronic Supplementary Material) is used during the computation of mathematical integrals for the $\alpha$ functions. This precision defines the step used for the numerical integrations. Integrals are computed over an interval equal to $r$ (Table S3 in SI1 - Electronic Supplementary Material). Therefore, the precision should be orders of magnitude lower than $r$ in order to render realistic values.

### 2.3.3 Linking temporally differentiated LCI results to dynamic LCIA models

Temporally differentiated LCI results are obtained as:

- $\beta_{k, i, j}$ functions per substance $k$ and intermediary flow ($i, j$) between processes $i$ and $j$;

- $\gamma_k$ functions, representing the emission profile of a substance $k$ over the life cycle.

Results are obtained in the form of discrete values over time and can be used with dynamic LCIA models. Final outputs are impact indicators calculated at each time step along the timeline, which results from the combination of the dynamic LCI and LCIA models. These results can be obtained individually per process and substance, per substance on the life cycle, aggregated per impact category, etc.

Climate change, human toxicity, and ecotoxicity models have been implemented, based on Shimako et al. (2016, 2017, and 2018). As these methods were presented in the cited articles, they are not described extensively here.

Climate change impact is assessed by two indicators (based on IPCC models, 2007, 2013): (1) radiative forcing, which is instantaneous and cumulated in time—it replaces the conventional global warming potential GWP; (2) global mean temperature change as a function of time—it replaces the global temperature potential GTP.

Toxicity and ecotoxicity models are based on USEtox (Rosenbaum et al. 2008; Mackay 2002). Human toxicity (cancer and non-cancer) and ecotoxicity indicators are calculated as instantaneous and cumulated indicators, both as a function of time.

The main differences with respect to temporal climate change and toxicity from literature (Levasseur et al. 2010; Lebailly et al. 2014) are (1) the impact models are implemented in their initial dynamic form in order to directly obtain indicators in function of time and in order to avoid the use of characterization factors (otherwise a huge number of CF values would have to be calculated). The models were resolved in full dynamic conditions with the emission function $\beta_{k, i, j}$ and $\gamma_k$ as input data. (2) The approach is flexible, allowing the use of different time steps and adaptation to the granulometry of LCI.
The use of dynamic LCIA models allows us to exploit the full potential of the full temporally differentiated LCI results. The resolution of LCI results can be as high as permitted by the calculation time or can be chosen in accordance with the impact category (e.g., higher resolution for toxicity, lesser for climate change, Shimako et al. 2018).

Moreover, conventional LCIA indicators and dynamic CF can also be used over limited time intervals.

At this stage, the outcomes only present curves of impacts over time. Being able to provide single values would characterize the overall impact over time and allow for comparison and possibly decision support. To this end, the integration of these results over a given time period should be undertaken, as it has been done for the GWP₁₀₀ over 100 years. As already mentioned in the introduction, additionally, a discounting of impact over time can be considered, implying the lesser valuing of impacts later over time. This is commonly done using a constant annual periodic factor of x%, in which the impact diminishes over time with a factor 1/(1+year)³. Such an approach was applied by Levasseur et al. (2010) and will be exemplified with the case study.

## 3 Case study: battery electric vehicle (EV) vs. internal combustion engine vehicle (ICEV)

A case study was performed to demonstrate the DyPLCA tool and the feasibility of a full dynamic LCA. In particular, the effect of implementing time differentiation in the background LCI is evaluated. To this end, a battery electric vehicle (EV) and an internal combustion engine vehicle (ICEV, EURO5 diesel) were compared. The two processes from ecoinvent 3.2 (the cut-off version) “Transport, passenger car, electric {GLO}| processing” and “Transport, passenger car, medium size, diesel, EURO 5 {RoW}| transport, passenger car, medium size, diesel, EURO 5” were considered.

Three different approaches to calculating the instant radiative forcing and dynamic global temperature were compared.

The fully dynamic approach harnesses the full capabilities of DyPLCA. All foreground and background processes are given temporal parameters. The fully static approach is the opposite approach. It assumes that all emissions occur at the time the FU was provided. This is the most common situation adopted in LCA case studies and that can be obtained using standard LCA software tools. The dynamic foreground only relies on the assumption that the demand for passenger vehicle transportation occurs over 10 years for the given system. Therefore, only the foreground system is given a temporal profile. All first-tier activities, i.e., direct inputs to the functional unit, are accounted for in a static manner.

Figure 2 and Fig. 3 report on (i) the emission profile of fossil carbon dioxide, (ii) the instant radiative forcing, and (iii) the dynamic increase in global temperature that the profile generates, for all three modeling approaches. The fully static causes are a pulse emission, an instant peak in radiative forcing, and a fast increase of the dynamic global temperature potential at the exact time of fulfillment of the final demand. Both the fully static and dynamic foreground only lead to accounting for practically the same amount of emissions. A sensible difference in terms of the total amount of carbon dioxide emitted occurs in the fully dynamic, especially for the EV. The explanation is straightforward: static background inventories are compiled using the Leontief inverse. This accounts for the entirety of the (infinitely long) chain of activities. However, the search algorithm cannot cover 100% of biosphere intervention, for computational reasons. Truncation occurs in the fully dynamic approach, in which not all the carbon dioxide emitted can be accounted for.

The earliest significant emissions tracked by the search algorithm start 20 years before the final demand is fulfilled. In particular, the process “Petroleum combustion, in drilling tests {GLO}” is identified. It is used as an input for onshore well construction and petroleum extraction. This is a precursor to many energy carriers pervading the system through, e.g., heavy fuel oil demand in shipping, diesel demand in road freight, and indirectly in electricity production.

<figure><img src="image_6.png" /><figcaption>**Fig. 2** Carbon dioxide emission profile, instant radiative forcing, and dynamic temperature increase for the internal combustion engine vehicle system</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 3** Carbon dioxide emission profile, instant radiative forcing, and dynamic temperature increase for the electric vehicle system</figcaption></figure>

It was observed that a higher degree of infrastructure con-
tribution leads to a higher spreading of impacts over time.
Systems showing more direct emissions in the foreground
are significantly affected by time differentiation. However,
the more upstream emissions occur, the higher the difference
between fully dynamic and fully static results. Delays and
production functions indeed compound along the supply
chain. This contributes to flattening the emission profile and
the radiative forcing effect.

As a result, it is fair to say that temporally differentiated
LCI in the *background* offers little interest for activities
with high downstream emissions. It can provide insightful
results when applied to life cycle systems where significant
environmental interventions occur upstream. Those sys-
tems concern, for example, renewable electricity genera-
tion, for which most emissions are embodied in an infra-
structure upstream.

The graph search algorithm considers two conditions to
stop the search: (1) if an intervention occurs prior to the time
cut-off (using the time limit introduced in Section 2.3.2) and
(2) if a product exchange is lower than a given threshold

(using the threshold variable of Section 2.3.2). The first
condition keeps the results in a reasonable period.
However, it might lead to processes with very long lifetimes
being neglected, for example, carbon sequestration in hard-
wood trees with production functions being defined over
140 years. Regarding the second condition, a scaling vector
is calculated for each product exchange in the inventory.
The vector contains the static LCI results, which represent
the total emission values. A value between 0 and 1 is set as
the threshold. The graph will then stop the search if a prod-
uct exchange between two processes is lower than the prod-
uct of the threshold and the process total output from the
scaling vector (aᵢⱼ, sⱼ).

The trade-off between accuracy and computational time
is investigated in Fig. 4. Carbon dioxide flows are consid-
ered, with a threshold of 10⁻⁴ leading to a coverage of
79%. It is estimated that 90% coverage would require more
than 5 h of computation and 95% almost nine full days.
Further optimization is needed to improve the coverage of
emissions and to close the gap between numerical and an-
alytical results.

<figure><img src="image_8.png" /><figcaption>**Fig. 4** Time-differentiated flows of carbon dioxide, cumulated, and broken down by origin and sub-compartment, for the functional unit 1 pkm of “transport, passenger car, electric {GLO}” of ecoinvent 3.2 with a threshold of 10⁻⁴</figcaption></figure>
# 4 Results and discussion

The integrated framework for the dynamic LCA developed here is a flexible tool:

- A reduced number of temporal parameters can describe generic supply chains and can be evaluated for a huge number of processes; a temporal database can be built up for any other LCA database;

- LCA case studies can be performed as usual, with, e.g., Simapro software, completed by a simulation with DyPLCA tool;

- LCA case studies can also be defined directly on the web application if the number of processes is not huge or via an Excel file template to be filled in with temporal information;

- The dynamic LCI is obtained as discrete values in time, with time steps defined by the user. The time steps are not imposed and any dynamic LCIA can be coupled with these LCI results.

- Impact calculation can be done with dynamic LCIA models resulting in temporalized indicators, or with dynamic CFs, or static CF with or without flow integration over time.

## 4.1 Discussion of results from the case study

The results of the case study were integrated over time, or more precisely, summed over time. This has been done using a time window of 100 years, as this is a commonly considered time horizon, and a discount factor of 3%, which is the largest considered by Levasseur et al. (2010). See Table 1 for an overview of the results.

These single scores point out that the life cycle of the diesel car is characterized by a higher environmental impact than that of the electric car in all considered combinations. Since the distribution of environmental impacts do not differ much (see curves depicted in Figs. 2 and 3), the effect of time integration on the comparison is limited. However, the ratios between

<table><caption>**Table 1** Cumulated global dynamic radiative forcing (dynamic AGWP) in $10^{-16}$ W/m$^2$year for 1 vkm is shown at a 100-year time horizon with a discount factor (r) of or 3%</caption><thead><tr><th rowspan="2">Cumulated global dynamic radiative forcing (dynamic AGWP) [10<sup>-16</sup> W/m<sup>2</sup>year]</th><th colspan="2">Fully static</th><th colspan="2">Foreground only</th><th colspan="2">Fully dynamic</th></tr><tr><th>r = 0%</th><th>r = 3%</th><th>r = 0%</th><th>r = 3%</th><th>r = 0%</th><th>r = 3%</th></tr></thead><tbody><tr><td>Electric vehicle</td><td>3.76</td><td>1.42</td><td>3.63</td><td>1.23</td><td>2.90</td><td>1.18</td></tr><tr><td>Diesel vehicle</td><td>4.93</td><td>1.85</td><td>5.01</td><td>1.81</td><td>4.89</td><td>1.81</td></tr><tr><td>ratio</td><td>0.76</td><td>0.76</td><td>0.73</td><td>0.68</td><td>0.59</td><td>0.65</td></tr></tbody></table>

electric and diesel car impact differ when considering time differentiation for the foreground system and even more so for the fully dynamic system. Concerning the influence of discounting, the ratios alter more considerably. This exemplifies the potential impact of the time window and discounting on comparison and decision-making. Time differentiation as a whole may thus influence the conclusions of a study.

## 4.2 Limitations and further research on the temporal database

In the current version of the database, data consistency primes on accuracy. Possible improvements are detailed below.

The temporal database should ideally include a specific temporal profile for product exchange and environmental intervention. Currently, supply-demand parameters are provided per producer process; the same temporal profile ($\beta$ function) is considered for all environmental interventions of a process. These simplifications can be alleviated by manually inputting the desired functions into the web interface of the tool, which is feasible for processes with significant contributions.

In ecoinvent, some types of processes are highly aggregate, hampering a sequentialization of the incoming flows in a process. In transportation processes, the lack of sequentialization is striking as the transported goods and the goods themselves are both inputs. In ecoinvent, transportation is an input in the consumer process in the same way as the production process of the transported goods. In reality, the production of the goods precedes their transport. Another example is the consideration of storage processes, which are often integrated into the production process, e.g., crop storage is considered a 1-year process, till the next harvesting.

The subdivision of the process into several sub-processes can be a pragmatic solution for the foreground system. However, it is not a feasible systematic solution for the complete database.

As shown in the results of the case study, the outcomes may easily span several decades. However, the process inventories differ over time. For example, the electricity mix has changed over time. Ideally, database inventories should be developed over time or following given socio-economic/technology evolution scenarios when it comes to future predictions. Although this issue is outside the scope of this work, the developed tool allows scenarios to be defined with different processes in the inventory (as mentioned in Section 1), and for example, to consider a different electricity mix by periods. However, scenarios can be defined in a reduced number and for a few processes.

Another limitation concerns the lack of information on freight transport distances, thus on the duration of transport processes. The functional unit of freight transportation is expressed as the product of weight and distance (tkm). The duration of transportation depends on the distance covered.
This cannot be inferred from such an aggregated indicator. For
example, 100 tkm could imply that 1 t is transported over 100
km; or that 100 t are transported over 1 km. The time it takes to
transport these quantities differs significantly. To mitigate this
issue, average r values were assigned to freight transportation
processes. These represent the average transportation duration
derived from literature. This issue does not apply to passenger
transportation: it is assumed that only one person is
transported and therefore the amount reflects the distance.

In future versions of LCI databases, it would be helpful to
integrate temporal information right from the start of the de-
velopment, as was already done for spatial information
(Wernet et al. 2016). The structure of the database itself should
be revised, based on the considerations above, to accommo-
date temporal information.

## 4.3 Further research on tool development

The specific developments of the tool could consist of the
following:

- Including the option to fix the temporal profile of processes to specific calendar timing. For example, to fix the start of agricultural production at the right time of the season.

- To model supply-demand, only an intermittent, regular supply pattern has been considered so far for the sake of simplification. A non-constant intermittent period (τ - bridging the gap between supply and demand) should also be included. For example, in the seasonal agricultural products, delays between supply and demand should be higher in the period of the year that is furthest from the harvesting season.

- Increasing the calculation speed and making the tool compatible with other LCA software (e.g., OpenLCA) and databases.

- Coupling with other dynamic LCIA modules.

- Improving user-friendliness, namely the visualization of the outputs.

## 4.4 Further research on the time-differentiated LCA

Enlarging the scope of the current dynamic LCA could be envisaged from the following perspectives. An exploratory development would consider novel integrated modeling approaches for sustainability assessment (Schaubroeck 2018; Schaubroeck and Rugani 2017). A framework to differentiate industrial chains and related environmental interventions over time is crucial when coupling with nonlinear consequential models of earth or technosphere. After all, these are the only other impact models in which cause-effect chains are nonlinear and differentiated over time. Arvesen et al. (2018) point out this importance by providing factors derived from

LCAs (with some minor temporal differentiation) to be used
in such integrated assessment models.

By introducing full time-differentiation, the timing of FU delivery shall also be considered to ensure the comparability among different product systems. If the FU consists of a product, assuming t₀ as the point of product provision, this implies that the production of the product occurs in the relative past whereas its usage and disposal occur in the relative future. This could be interpreted as an attributional LCA viewpoint, despite attributional studies following future product scenarios also being possible. From a consequential LCA perspective, a variation of demand of a process (reflecting a decision taken) is assumed to trigger a change in the economy. In this case, t₀ would correspond to the moment at which the decision is taken; the demand variation occurs at a specific process in the supply chain. From this viewpoint, the choice of the activities actually requested after the decision is made according to the consequential approach and inventory database. The adaptation of the temporally differentiated framework of this paper to the attributional and consequential dimension goes far beyond the scope of this paper and deserves to be treated consistently in future studies.

Similarly, the integration of spatial information is a devel-
opment opportunity that deserves further attention. This in-
cludes the actual location of processes, environmental inter-
ventions, and impacts. A few literature sources have already
focused on the integration of spatial aspects in LCA, in par-
ticular on how to prioritize the addition of spatial information
in the LCI database in order to reduce the computation time
(e.g., Mutel et al. 2011; Yang and Heijungs 2017). However, a
combination of spatial and temporal characterization was not
addressed. In principle, integration can be relevant in some
situations. Consider, for example, that a toxic compound is
emitted twice in a short time at the same location. Its effect
might be much greater than if it is emitted at different locations
in the same short time duration. The graph search approach
adopted in this work could also be applied to spatial differen-
tiation. To this end, full spatial characteristics of processes and
environmental interventions shall be added and further used
when tracing back the processes along the life cycle network.

The main aim of this work was to provide an improved
artifact that can be of use in further studies. Despite having
already investigated our tool through a case study and param-
eter evaluation (see Section 3 in the Electronic Supplementary
Material), further research is needed to increase the value of its
impact in the field.

## 5 Conclusions

An operational approach and tool to assess the fully time-
differentiated LCA results of a product life cycle were devel-
oped. The main feature of these is to implement the full
temporal differentiation of background LCI processes. A sup-
ply chain model is implemented with a graph search algo-
rithm. Temporal characterization was achieved for about
15000 processes of ecoinvent 3.2. The temporal database is
used by the tool as a stand-alone web application. The tool
was designed to work with case studies imported from
Simapro or OpenLCA. The temporally differentiated LCI
are further processed with dynamic LCIA models for climate
change and toxicity, to gather the final temporally differenti-
ated LCA results. As of now, the tool software is freely avail-
able online (http://dyplca.univ-lehavre.fr/) for testing
purposes; the temporal database is protected by intellectual
property rights.

The feasibility of a full dynamic LCA was tested with a
case study on mobility. The case study showed that consider-
ing temporal differentiation across the complete life cycle,
especially in the background system, can significantly change
the results and interpretation of comparative LCA results.
Therefore, the additional sophistication introduced by full
temporal differentiation is valuable. This is particularly the
case for product systems, which show significant environmen-
tal interventions and material exchanges over long time pe-
riods upstream to the FU.

This work provides the first operational framework to con-
duct fully temporally differentiated LCA. The inherent limita-
tions outlined shall be considered as opportunities for further
research on the temporal model and in particular on the tem-
poral database to refine the temporal characterization of back-
ground processes. This requires a collegial effort, in particular
involving the different industrial experts from the different
sectors.

**Acknowledgements** Funding from the French National Research Agency (ANR-13-IS09-0007-01/DyPLCA) and Luxembourg National Research Fund (FNR)(INTER/ANR/13/10/DyPLCA) is gratefully acknowledged. Our colleagues Katarzyna Golkowska and Rodolphe Meyer are gratefully acknowledged for their valuable input into the definition of the temporal parameters of the process and supply models.

**Open Access** This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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