# Contextual LCIA without the overhead: an exchange-based framework for flexible impact assessment

Romain Sacchi, Alvaro Hahn Menacho, Georg Seitfudem, Maxime Agez, Joanna Schlesinger-Martinat, Anish Koyamparambath, Jair Santillan Saldivar, Philippe Loubet, Christian Bauer

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## To cite this version:

Romain Sacchi, Alvaro Hahn Menacho, Georg Seitfudem, Maxime Agez, Joanna Schlesinger-Martinat, et al. Contextual LCIA without the overhead: an exchange-based framework for flexible impact assessment. International Journal of Life Cycle Assessment, 2025, 10.1007/s11367-025-02551-7. hal-05312252

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Submitted on 28 Oct 2025

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# Contextual LCIA without the overhead: an exchange-based framework for flexible impact assessment

Romain Sacchi<fnref n="1" />,<fnref n="2" />✉ · Alvaro Hahn Menacho<fnref n="1" />,<fnref n="2" /> · Georg Seitfudem<fnref n="3" /> · Maxime Agez<fnref n="3" /> · Joanna Schlesinger-Martinat<fnref n="4" /> · Anish Koyamparambath<fnref n="5" /> · Jair Santillan Saldivar<fnref n="6" /> · Philippe Loubet<fnref n="5" /> · Christian Bauer<fnref n="1" />

Received: 26 June 2025 / Accepted: 24 September 2025
© The Author(s) 2025

## Abstract

**Purpose** Life Cycle Impact Assessment (LCIA) has traditionally applied characterization factors (CFs) to elementary flows in isolation, treating impacts as fixed properties of substances, regardless of where and how they occur within the life cycle product system. While recent advances have introduced regionalized LCIA methods and GIS-based spatial modeling frameworks, these remain difficult to operationalize in routine assessments and are often limited to differentiation at the elementary flow level. This paper presents a methodological advancement in LCIA: the application of CFs at the level of exchanges—the resolved biosphere and technosphere flows between processes.

**Methods** Shifting the CF unit from elementary flows to exchanges enables CFs to reflect the full context of each exchange, including the geographic origin and destination, the identity of the emitting process and environmental recipient, and prospective, scenario-dependent parameters. The method offers a flexible, intermediate solution between traditional elementary flow-based LCIA and full spatially explicit models, supporting national and subnational regionalization without requiring high-resolution GIS integration.

**Results** The approach is implemented in the open-source Python library *edges*, which extends the *Brightway* LCA framework to support exchange-specific and symbolic CFs. We illustrate its capabilities through four applications: 1) Regionalized LCIA, using the AWARE water scarcity method with dynamic handling of region aggregation and disaggregation; 2) Technosphere-based LCIA, via a new implementation of the GeoPolRisk indicator, which assigns CFs based on country-to-country commodity trade relationships; and scenario-sensitive prospective LCIAs, enabling alignment with climate scenarios, where CFs are defined by symbolic expressions that depend on scenario-specific variables, with application 3) focusing on global warming potential based on atmospheric gas concentration, and application 4) addressing fossil resource scarcity through dynamic fossil fuels extraction rates.

**Conclusions** Together, these examples demonstrate how exchange-resolved LCIA expands the methodological space of impact modeling, offering a scalable, exchange-aware framework for regional, relational, and future-oriented life cycle assessments.

**Keywords** Impact assessment · Regionalization · Scenario · Exchange · Graph · Parameter

Communicated by Nils Thonemann.

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<footnote>Romain Sacchi
romain.sacchi@psi.ch</footnote>

<footnote n="1">¹ PSI Centers for Nuclear Engineering and Sciences
and for Energy and Environmental Sciences, Paul Scherrer
Institute, Villigen, Switzerland</footnote>

<footnote n="2">² Chair of Energy Systems Analysis, Institute of Energy
and Process Engineering, ETH Zürich, Zurich, Switzerland</footnote>

<footnote n="3">³ CIRAIG – Department of Chemical Engineering,
Polytechnique Montréal, Montréal, Canada</footnote>

<footnote n="4">⁴ Centre Observation, Impacts, Energie, Mines,
Sophia Antipolis, France</footnote>

<footnote n="5">⁵ Université de Bordeaux, CNRS, Bordeaux INP, ISM, UMR
5255, 33400 Talence, France</footnote>

<footnote n="6">⁶ BRGM, 45060 Orléans, France</footnote>
# 1 Introduction

Life Cycle Impact Assessment (LCIA) translates emissions and resource use into environmental impacts by applying characterization factors (CFs). Traditionally, CFs are applied to elementary flows at the node level—that is, to substances such as “carbon dioxide, fossil” or “water, from well”—regardless of the flow’s exchange attributes within the life cycle network (which process emits/consumes it, and where). This conventional approach treats impacts as inherent properties of elementary flows, detached from the relationships that cause them.

Over the past two decades, efforts to improve the spatial representativeness of LCIA have led to the development of regionalized methods, such as EDIP(Koyamparambath, et al., 2003) (Hauschild and Potting 2005), Accumulated Exceedance (Seppälä et al. 2006), AWARE (Boulay et al. 2018), ImpactWorld+ (Bulle et al. 2019), and LC-IMPACT (Francesca Verones et al. 2020). These approaches assign CFs to specific regions (e.g., countries, grid cells, or even watersheds), allowing LCIA to account for spatial variability in fate, exposure, or vulnerability. However, integrating such methods into full life cycle studies has remained a challenge, as CFs are still typically applied to aggregated biosphere flows, after the resolution of the inventory has discarded crucial exchange-attribute information (e.g., emitting process and location).

A common workaround LCA software (e.g., Simapro, OpenLCA) adopted has been introducing region-specific elementary flows—such as creating separate flows like “Water, DE” or “Water, FR” to represent country-specific water withdrawals. This approach allows geographically differentiated CFs to be applied within node-based frameworks. However, it is inherently inefficient and unscalable. Representing global spatial variability would require duplicating elementary flows relevant to the impact assessment method for potentially hundreds of regions, leading to a proliferation of flows, increased database complexity, and a higher risk of manual and systemic modeling errors. Moreover, this strategy treats geographic information as part of the elementary flow (node) identity rather than as a separate exchange-level (edge) attribute.

A key step toward addressing these limitations was proposed by Mutel & Hellweg (2009), introducing a computational framework for applying region-specific CFs across extensive inventories by matching the geographic metadata of emitting processes before inventory aggregation. This advance made it possible to conduct regionalized LCIA using only the location data already embedded in life cycle databases. Mutel et al. (2012) further extended this framework by introducing geographic information system (GIS)-based tools to bridge mismatched spatial units between

inventories and CFs, proposing spatial mapping matrices and methods for assessing uncertainty and spatial resolution. Together, these studies established the feasibility of integrating geographic structure into LCA workflows in a systematic way.

Yang & Heijungs (2017) generalized this approach further by proposing a multi-regional algebraic formulation of LCA, where both the technosphere and biosphere matrices are indexed by region. Their model captured where emissions occur and how materials and impacts are transferred across space, highlighting the need to account for relational structure (i.e., trade) in regionalized assessments.

More recently, Li et al. (2021) proposed a universal GIS-LCA framework based on an extensive literature review, emphasizing consistent spatial referencing and a harmonized geospatial layer across all phases of LCA. Their vision supports full spatial traceability—potentially down to high-resolution grids—but assumes access to GIS data, spatial overlays, and detailed geographic inventories.

While these contributions have significantly advanced the field, they illustrate a methodological spectrum—from fully generic, location-neutral LCIA to spatially explicit, GIS-integrated models. However, fully generic approaches—where CFs are applied to elementary flows without spatial or contextual differentiation—can obscure significant regional or sectoral variations. Conversely, highly detailed GIS-based models, although scientifically robust, often require data and computational resources that limit their practical adoption, as evidenced by their limited uptake in current LCA practice. Our work offers a pragmatic intermediate solution along this spectrum. We propose a generalization of LCIA that shifts the focus from so-called “elementary flows” (e.g., “Water, from lake”) to consider instead exchanges (e.g., “Water, from lake → maize grain production {US}”), treating the edge between the supplying and consuming node as the unit of impact characterization. In this exchange-based approach, CFs can be defined not only by the flow’s substance and quantity, but also by: 1) the location of both supplying and consuming nodes (supporting national and subnational regionalization); 2) the identity or type of actors involved (e.g., industrial classification, activity type); and 3) external parameters or scenarios, such as climate policy targets or atmospheric composition. Practical examples of such a framework include differentiating impacts from water use for agricultural and industrial purposes, and further refining the CF selection based on the consuming process’s location. Another example is to link an exchange to a parameterized CF, such as the global warming impact of methane as a function of its atmospheric concentration, which is defined by a scenario. These examples, and others, are further detailed throughout this work.

This method captures more edge-level information than node-based models while avoiding the complexity and
data intensity of GIS-based LCIA. It supports regionalized LCIA with national and subnational resolution. Still, it does not depend on fine-grained spatial data or GIS layers as input, making it more accessible and scalable for routine assessments.

Moreover, exchange-based LCIA transcends geographic differentiation. It allows CFs to rely on technosphere structure (e.g., supply chains, country-to-country flows) and be represented as symbolic functions of external parameters, facilitating scenario- and policy-sensitive assessments.

These capabilities are implemented in the open-source Python library edges, which integrates with the Brightway framework (Mutel 2017). While tools like brightway2-regional focus on region-matching for biosphere flows using GIS, edges enables exchange-specific CFs across both the biosphere and technosphere, parameterized or symbolic CFs, and a modular mapping system for handling aggregated (e.g., “RER”) or dynamic regions such as “RoW” (Rest of the World) and “RoE” (Rest of Europe).

We demonstrate the methodological potential of this approach through four illustrative applications: 1) Regionized LCIA, using the AWARE method for water scarcity impact assessment, with logic for disaggregating and aggregating exchanges by region. 2) Technosphere-aware LCIA, via a new implementation of the GeoPolRisk indicator (Koyamparambath et al. 2024), where impacts depend on the origin-destination pair in resource supply chains. Finally, two scenario-based prospective LCIA applications: 3) the use of symbolic characterization factors for CH₄ and N₂O that dynamically respond to scenario-specific atmospheric concentrations and time horizon parameters, and 4) the recalculation of surplus fossil fuel production costs based on projected extraction volumes and marginal costs.

Although the approach primarily draws on foundational insights from Mutel & Hellweg (2009) and, to some extent, those of Mutel et al. (2012) and Yang & Heijungs (2017), it introduces a novel modeling layer that enables exchange-aware impact assessment—without the overhead of full GIS integration. In doing so, it helps bridge the gap between theoretical advances in spatial modeling and practical applications in prospective and regionalized LCA.

In the following sections, we present the technical foundations of exchange-resolved LCIA, describe the edges implementation, and illustrate its application in the four domains mentioned above.

## 2 Method

Traditional LCIA applies CFs to elementary flows using either a vector or a diagonal matrix, where each flow (e.g., “Water, from lake”) is assigned a single CF that remains invariant to the exchange attributes. Consequently, this

structure cannot differentiate between the same substance emitted in different regions or flows arising from various supply chain relationships.

We propose an approach in which CFs are assigned at the level of exchanges—the directed links between supplying and consuming nodes in the LCI graph. Each exchange includes information such as flow quantity, information about the supplying and consuming nodes, such as the matrix they belong to (biosphere or technosphere), and their respective location, if relevant. Together with other optional scenario parameters (e.g., CO₂ concentration, time horizon), this information can be used to apply CFs that better fit the circumstances surrounding the exchange.

### 2.1 Node vs. edge-based LCIA

In conventional LCIA, the impact vector h for a given functional unit is computed using the standard matrix formulation (Heijungs and Suh 2002):

$$h = Q \cdot B \cdot A^{-1} \cdot f \quad (1)$$

where:

* $f(p \times 1)$ is the functional unit vector, or demand vector;

* $A(p \times p)$ is the technosphere matrix;

* $B(q \times p)$ is the biosphere matrix;

* $Q(q \times 1)$ is a vector of CFs, one per elementary flow;

* And h is the impact vector.

This formulation is equivalent to the matrix product:

$$h = Q \cdot X \cdot f \quad (2)$$

where:

* $X(q \times p) = B \cdot A^{-1}$ is the inventory matrix, where each column corresponds to a process and each row to an elementary flow

* $Q = diag(c)$, a diagonal matrix of CFs

* h is the impact vector, with one entry per elementary flow.

In our exchange-resolved LCIA approach, we instead apply a non-diagonal, rectangular CF matrix, referred to as $E(q \times p)$, to the full inventory matrix $X(q \times p)$, characterizing each flow per activity, to obtain the impact matrix H as the Hadamard (element-wise) product of E and X, for a given demand vector f:

$$H = \sum_{i=1}^{q} \sum_{j=1}^{p} E_{ij} \cdot X_{ij} \cdot f = \sum (E \circ X) \cdot f \quad (3)$$

This formulation enables the same elementary flow to receive different CFs depending on:
* The supplying node attributes (e.g., its location, activity classification code, unit, and associated matrix type);

* The consumer node attributes (same as above);

* Any external parameters included in CF definitions (e.g., concentration, time horizon, amount emitted).

It generalizes the conventional LCIA formulation by allowing each exchange to be characterized uniquely, and serves as a foundation for flexible impact modeling.

The exchange-resolved method also enables the characterization of technosphere exchanges—i.e., intermediate flows between activities. This is particularly relevant for indicators relating to supply risks (e.g., GeoPolRisk), where impacts depend on the supply chain relationships between countries or sectors. To support this, we construct a technosphere exchange matrix, $T$ (p x p), that represents the quantity of each intermediate product exchanged between activities. This matrix is derived from the technosphere matrix $A$ and the supply array $s$. The latter represents the scaling of each activity required to meet the functional unit:

$$T = (-A \circ M) \cdot \text{diag}(s) \quad (4)$$

where:

* $M \in \{0, 1\}^{p \times p}$ is a binary mask matrix where $M_{ij} = 1$ if $A_{ij} < 0$, and 0 otherwise,

* $\text{diag}(s)$ is a diagonal matrix of the supply array $s$, defined as $s = A^{-1} \cdot f$.

The characterization step is similar to that of characterizing biosphere exchanges. Here, the CF matrix $E$ is defined with the same dimension as the technosphere exchange matrix $T$ ($p \times p$), so that the Hadamard (element-wise) product is well defined:

$$H = \sum_{i=1}^{q} \sum_{j=1}^{p} E_{ij} \cdot T_{ij} = \sum (E \circ T) \quad (5)$$

In summary, biosphere-technosphere exchanges are characterized using Equation (3), while technosphere-technosphere exchanges are characterized using Equation (5), each with a characterization matrix $E$ matching the corresponding exchange matrix in dimension.

Hence, compared to traditional LCA terminology, this framework expands the meaning of "characterization factor" to allow for the characterization of technosphere flows.

## 2.2 Exchange matching

Definitions of CFs are matched to exchanges using criteria that enable the identification of specific supplying-consuming node pairs, such as:

* Node name or substring (e.g., "Water")

* Node matrix (biosphere or technosphere)

* Node metadata (e.g., location, classification)

This logic applies to supplying and consuming nodes, allowing directional differentiation (e.g., CFs specific to Swiss exports to Germany).

To support regionalized LCIA, exchanges are mapped to CF regions through:

* Direct matching (this includes matching to aggregated regions such as "Asia" or "RER");

* Association: the CF of a region, if missing, is defined as the CF of the closest matching region (i.e., usually a region that contains it, e.g., "Canada" for "Québec");

* Dynamic resolution: the CF for relative regions (e.g., RoW) is computed based on uncovered areas. A weighted average CF is calculated from the CF of all non-overlapping regions, excluding those for which region-specific inventories exist;

* Fallbacks: if no regional match is found, unmatched exchanges receive a global average CF.

For composite regions, CFs can be calculated on-the-fly and with dynamic extent: CFs for composite inventory regions (e.g., "RER") are calculated as the weighted average of the CFs of the areas they comprise, using weighting keys such as resource consumption, population, or GDP, or any other weighting key provided by the LCIA method.

In cases of association, aggregation, and dynamic resolution, the weighting key used to calculate averages may be related to population, country-level emissions, resource consumption, or GDP. For example, in the case of AWARE 2.0, the national water demand in 2019 is used. For the purpose of developing prospective methods, the evolution of demographics and other parameters can also be reflected in changes to the weighting keys over time.

## 2.3 Characterization factors evaluation

Characterization factors are evaluated dynamically and inserted into the characterization matrix $E$ before obtaining the characterized inventory matrix $H$. The value of the CF can be:

* Numeric (e.g., 28)

* Symbolic (e.g., "28 * (1 + 0.001 * (co2ppm—410))"), with co2ppm being a parameter with its value changing across scenarios

* Supplied externally via a function call
## 2.4 Software implementation: the edges python library

The method presented in this paper is implemented in the open-source Python library *edges*. Built on the Brightway framework, *edges* enables exchange-resolved LCIA by applying CFs directly to inventory exchanges using flexible matching rules, as described above.

Characterization factors can be defined in JSON or programmatically, and worked examples are available in the online repository. *Edges* is released under the MIT license and is actively maintained by PSI. At the time of writing, *edges* implements regionalized factors for AWARE 2.0, IMPACT World+ 2.1, and GeolPolRisk 1.0.

The Results section presents four use cases to illustrate the exchange-resolved characterization approach. They highlight different capabilities of the method: regionalization, technosphere-based modeling, and scenario-based prospective assessment. The first two use cases have a current reference year (2025), while the two last use cases are evaluated from 2020 to 2100. For each of the four cases, hydrogen production is modeled using Proton Exchange Membrane

(PEM) water electrolysis. Inventories are based on Gerloff (2021), adapted to a French context and receive an input of offshore wind power from the ecoinvent 3.10.1 cutoff database (Wernet et al. 2016) – see Table 1. The resulting environmental burdens are entirely allocated to the produced hydrogen; oxygen, the other output of the water electrolysis process, is assumed to be released to the atmosphere and thus considered a by-product with an economic value of zero. Inventories are available as part of the electronic SI material. While energy storage would ideally be included to account for the intermittency of the offshore wind supply, it is omitted here for simplicity. This omission does not affect the validity of the findings illustrated in the use cases.

## 3 Use case 1: regionalized LCIA with AWARE

The first example focuses on regionalized LCIA using the AWARE 2.0 water scarcity LCIA method (Boulay et al. 2018; Seitfudem et al. 2025). The indicator assesses the potential impacts of water consumption on other water users. Its core variable estimates the relative amount of

<caption>**Table 1** Inventories for producing one kilogram of hydrogen with water electrolysis using a PEM electrolyzer. Original source: 1 MW PEM electrolyzer by Gerloff (2021). Lifetime and efficiency are further refined with data from the manufacturer's specifications and the IndWEDe project report (Smolinka et al. 2018). A water consumption</caption>

of 14 L per kg of hydrogen is assumed (Simoes et al. 2021), which accounts for losses due to evaporation and cleaning. Ultrapure water treated by a single pass reverse osmosis was modelled using inventories from (Gonzales-Calienes et al. 2022)

<table><thead><tr><th>Process</th><th colspan="4">Hydrogen production, gaseous, 30 bar, from PEM electrolysis, using offshore wind power</th></tr><tr><th>Reference product</th><td colspan="4">Hydrogen, gaseous, 30 bar</td></tr><tr><th>Location</th><td colspan="4">FR</td></tr><tr><th>Unit</th><td colspan="4">Kilogram</td></tr><tr><th>Exchanges</th><td colspan="4"></td></tr><tr><th>Name</th><th>Quantity</th><th>Location</th><th>Unit</th><th>Reference product</th></tr></thead><tbody><tr><td>hydrogen production, gaseous, 30 bar, from PEM electrolysis, from grid electricity</td><td>1.00E+00</td><td>FR</td><td>Kilogram</td><td>hydrogen, gaseous, 30 bar</td></tr><tr><td>Oxygen</td><td>8.00E+00</td><td></td><td>Kilogram</td><td></td></tr><tr><td>electrolyzer production, 1MWe, PEM, Stack</td><td>1.35E-06</td><td>RER</td><td>Unit</td><td>electrolyzer, 1MWe, PEM, Stack</td></tr><tr><td>electrolyzer production, 1MWe, PEM, Balance of Plant</td><td>3.37E-07</td><td>RER</td><td>Unit</td><td>electrolyzer, 1MWe, PEM, Balance of Plant</td></tr><tr><td>treatment of electrolyzer stack, 1MWe, PEM</td><td>-1.35E-06</td><td>RER</td><td>Unit</td><td>used fuel cell stack, 1MWe, PEM</td></tr><tr><td>treatment of electrolyzer balance of plant, 1MWe, PEM</td><td>-3.37E-07</td><td>RER</td><td>Unit</td><td>used fuel cell balance of plant, 1MWe, PEM</td></tr><tr><td>electricity production, wind, 1-3 MW turbine, offshore</td><td>5.40E+01</td><td>FR</td><td>Kilowatt-hour</td><td>electricity, high voltage</td></tr><tr><td>deionized water production, via reverse osmosis, from river</td><td>1.40E+01</td><td>FR</td><td>Kilogram</td><td>water, deionized</td></tr><tr><td>Occupation, industrial area</td><td>6.07E-04</td><td></td><td>Square meter-year</td><td></td></tr><tr><td>Transformation, from industrial area</td><td>3.04E-05</td><td></td><td>Square meter</td><td></td></tr><tr><td>Transformation, to industrial area</td><td>3.04E-05</td><td></td><td>Square meter</td><td></td></tr></tbody></table>
water remaining in a watershed after human and ecosystem demands are met, expressing results as a scarcity-weighted water consumption factor. AWARE CFs at the watershed level with a monthly resolution are a generic indicator of the potential to deprive other water users of water. AWARE's applicability is enhanced by spatially aggregated annual factors, such as for entire countries. The current implementation of AWARE 2.0 in *edges* includes 512 unique CFs. Since they are spatiotemporal aggregations, they reflect the scarcity associated with the freshwater consumption relative to global scarcity across time and space. The following example specifies the CF for freshwater uptake in Armenia (ISO country code: "AM"):

```json
{
  "supplier": {
    "name": "Water, lake",
    "categories": [
      "natural resource",
      "in water"
    ],
    "matrix": "biosphere"
  },
  "consumer": {
    "location": "AM",
    "matrix": "technosphere",
    "classifications": {
      "CPC": [
        "01"
      ]
    }
  },
  "value": 88.6,
  "weight": 799882000,
  "uncertainty": {
    "distribution": "discrete_empirical",
    "parameters": {
      "values": [
        84.5,
        87.9
      ],
      "weights": [
        0.031,
        0.969
      ]
    }
  },
  "negative": 0
}
```

This definition assigns a CF of 88.6 m³ world-eq./ m³ freshwater to any exchange where the supplying node belongs to the biosphere matrix and is labeled "Water, lake" (in the "natural resource" compartment), and the consuming node is a technosphere process situated in Armenia. The Central Product Classification (CPC) field value "CPC: 01" indicates that this CF only applies to consumers with the corresponding CPC category (i.e., "01" relates to agricultural activities). Aiming for closer representing the spatiotemporal distribution of water consumption in CF aggregations, AWARE provides different aggregated factors for agricultural and non-agricultural activities. High spatiotemporal heterogeneity is typical for the water consumption of agricultural activities, with irrigation often being limited to a few months. For the annual averages presented in Armenia's example above, watersheds and months are consequently weighted by irrigation water consumption. In the same

fashion, *edges* provides AWARE CFs for non-agricultural activities and activities for which the type cannot be determined. Hence, exchanges are not only discriminated against based on the consumer's location but also the consumer's type (i.e., seasonality and spatial pattern of water consumption in this case).

The weight field provides a reference freshwater consumption volume for the area (annual, in m³/year), used when aggregating or disaggregating regional CFs—e.g., to compute weighted averages for larger or composite regions (e.g., RER, RoW).

In addition to the spatial and sectoral resolution of the CFs, the method supports the representation of uncertainty or variability *via* probability distributions. Each CF can be supplemented with an uncertainty field, which describes the statistical distribution of potential CF values rather than relying on a single deterministic point estimate. Several types of distributions are supported, including normal, lognormal, gamma, beta, triangular, uniform, and discrete empirical. These distributions are defined by standard parameters (e.g., mean, scale, shape, minimum, maximum) and are used for Monte Carlo sampling to generate pseudo-random values for error propagation. In the example above, the spatial variability of watersheds within a country is represented using the "discrete_empirical" distribution. This approach is particularly well-suited for watershed-specific CFs derived from multiple data sources or seasonal profiles. Rather than assuming a continuous parametric distribution, the discrete empirical type defines a set of possible CF values (corresponding to the individual watersheds of the region) and their associated weighted probabilities of providing water. In this case, the two watersheds of Armenia are associated with two CF values—84.5 and 87.9—each given a respective weight of 3.1% and 96.9%, based on the respective watersheds' annual irrigation water consumption. When sampling during LCIA, one of these values is drawn according to its likelihood, allowing for the capture of spatial and seasonal variability or model uncertainty (when available) without imposing an arbitrary statistical shape. In this case, the risk would be, in regions with a limited number of watersheds, to draw CF values for watersheds that do not exist. However, note that this example does not account for the inherent uncertainty of the CF value for a specific watershed, as AWARE 2.0 does not yet carry uncertainty data. Rather, it considers the uncertainty as to which watershed will provide freshwater to the consuming process within a country. To the authors' knowledge, this is the first instance of a discrete distribution implemented at the *impact characterization* level. At the *inventory* level, Michiels and Geeraerd (2022) introduced two-dimensional Monte Carlo simulations in LCA, allowing uncertainty and variability to propagate simultaneously by combining discrete distributions with continuous ones. For other regions that comprise numerous watersheds

<figure><img src="image_4.png" /></figure>
(i.e., n > 10), parametric distributions have been fitted, such as the case of California (see Fig. 1). When aggregated to form regional or global indicators, these probability distributions contribute to a more robust and transparent impact assessment. However, a limitation of this approach are worth discussing: To capture spatial variability in watershed-level CFs while maintaining LCA robustness (i.e., avoiding artificial precision from mismatching fine-scale CFs with coarsely geolocated inventories, following recommended flow-weighted aggregation, and carrying explicit uncertainty/variability), we aggregate watershed CFs to regions in *edges* (as per Mutel et al. (2019), who advise optimizing robustness over maximal resolution, providing aggregated, flow-weighted CFs, and reporting uncertainty and variability). However, this can reduce precision for smaller regions—e.g., certain Indian and U.S. states—where seasonal water use patterns in the region-specific portion of a watershed differ from the watershed as a whole. In 59 regions, over half of water consumption showed > 10% discrepancy between the annual watershed CF and the (unpublished) annual CF of the watershed's region-specific portion. In such cases, we opted for deterministic AWARE values instead of Monte Carlo sampling. This issue stems from using annual rather than monthly CFs, reflecting a modeling constraint rather than a limitation of the AWARE method.

Furthermore, *edges* also supports *nested* distributions: for example, had uncertainty data at the watershed level been available, it could have been combined with a discrete distribution. Hence, at the country level, a watershed would be picked according to consumption-weighted probabilities (variability), and after that, pseudo-random values would be drawn from the watershed-specific distribution (uncertainty). In fact, *edges* resolves uncertainty for composite

regions (e.g., RoW, RER) using nested distributions via two-stage, weighted sampling: at each Monte Carlo iteration it first selects a constituent country of the composite region with a weighted probability reflecting its water consumption share (country-level weighting key), then samples a watershed-specific CF value from that country's distribution in proportion to the value's weight in that country.

Finally, to ensure consistent uncertainty treatment for correlated flows (such as water uptake and release in the same location), *edges* generates shared sampled vectors for each unique CF distribution. This preserves correlation between exchanges, such as when a water flow appears as both an input and output (e.g., in water use modeling). For instance, in the hydrogen system, two exchanges—"Water, surface water" (i.e., release) and "Water, natural resource in water" (i.e., uptake) point to a consuming node located in the United Arab Emirates. They share the same discrete empirical distribution (since the water is withdrawn and released in the same region), with possible watershed-specific values like 7.56, 13.4, 33.7, etc. By caching a single sample vector (e.g., [27.6, 7.56, 33.7,...]) and applying signs only after sampling, we ensure they receive the same values in the same order, respecting the edgedirection (i.e., consumption or release), before being multiplied by the exchange amount. This avoids decorrelation artifacts in Monte Carlo analyses and enables reliable uncertainty propagation across symmetrical exchanges.

## 4 Use case 2: technosphere-based LCIA with GeoPolRisk

The second use case demonstrates how exchange-resolved LCIA can be extended beyond biosphere flows to characterize technosphere exchanges—i.e., intermediate product flows between activities. We illustrate this using the GeoPolRisk indicator (Gemechu et al. 2016; Koyamparambath et al. 2024). The indicator quantifies the geopolitical risks associated with the extraction of mineral resources. It assigns characterization factors based on the likelihood and severity of supply disruptions in producing countries due to political instability, conflict, or governance issues.

Initially, GeoPolRisk CFs were applied to raw material elementary flows (Koyamparambath et al. 2024), limiting the ability to account for the geographic locations of resource suppliers and consumers. Moreover, elementary flows do not necessarily represent the marketable materials at risk. This stems from (i) the pre-allocation of multi-output mining processes in databases such as ecoinvent, which can create imbalances between elementary and intermediate product flows for a given material, as well as (ii) losses during processing stages. The *edges* method addresses both limitations by applying location-specific CFs directly to

<figure><img src="image_5.png" /><figcaption>**Fig. 1** Fitted parametric distribution over the watershed-specific CF values for California, USA, for unspecified water consumption type. It is a Weibull distribution of mean 73.9 fitted over the CFs of 65 watersheds</figcaption></figure>
technosphere exchanges. GeoPolRisk CFs were extended to the intermediate product level using the *geopolrisk-py* library (Koyamparambath et al. 2024), which enables the generation of country-to-country CFs. Those were then mapped to ecoinvent's nomenclature. Hence, the method offers CFs based on country-to-country trade relationships of abiotic resources in its detailed form.

An example CF definition is shown below:

```json
{
  "supplier": {
    "name": "aluminium production",
    "reference product": "aluminium",
    "location": "AU",
    "operator": "startwith",
    "matrix": "technosphere",
    "excludes": [
      "alloy",
      "liquid",
      "market"
    ]
  },
  "consumer": {
    "location": "CA",
    "matrix": "technosphere"
  },
  "value": 2.420e-4
}
```

This CF definition assigns a supply risk value, expressed in kg copper-eq./kg, to exchanges where primary aluminium is supplied by Australia ("AU") and consumed in Canada ("CA"). The CF reflects the geopolitical risk associated with this specific supply route for this metal. The same metal, consumed by Canada but supplied instead by the United States ("US"), is given a CF value 10 times higher. This indicates that a disruption in the "US" supply would have more severe consequences for Canada, given its greater dependence on aluminium imports from the United States.

Here, the operator "startwith" and the "excludes" list allow for pattern-based matching of activity names, offering flexibility in identifying relevant supplying nodes across databases. The current implementation of GeoPolRisk in *edges* includes about 43,000 such definitions.

This example illustrates how exchange-resolved LCIA supports indicators that depend not only on the substance exchanged, but also on which node supplies and receives it, and where nodes are located—something not possible in traditional node-based approaches.

## 5 Use case 3: scenario-based prospective LCIA with parameterized CFs for global warming potential

The third use case illustrates how exchange-resolved LCIA can incorporate parameterized and scenario-sensitive CFs, enabling prospective impact assessment. This is particularly relevant when assessing impacts under varying future

conditions, such as changing atmospheric greenhouse gas concentrations.

In this example, we consider concentration-dependent Global Warming Potential (GWP) CFs for methane ($CH_4$) and nitrous oxide ($N_2O$), following the physical formulation of Absolute Global Warming Potential (AGWP) as described in the IPCC AR6 Working Group I report and the future gas concentration values according to four Representative Concentration Pathways (RCP) developed by the IPCC, presented in Table 2 and sourced from the Annex III document (Intergovernmental Panel on Climate Change (IPCC) 2023).

The CF is defined as a symbolic expression. Here is the case for $CH_4$:

```json
"supplier": {
  "name": "Methane, fossil",
  "operator": "contains",
  "matrix": "biosphere"
},
"consumer": {
  "matrix": "technosphere"
},
"value": "GWP('CH4', H, C_CH4)"
}
```

This expression calls the external function `GWP()`, which takes the gas name, its background concentration ($C\_CH_4$ for methane), and time horizon $H$ as inputs. The function, detailed in the notebook included in the electronic SI material, calculates the concentration-dependent GWP for the specified gas as the ratio of the gas's Absolute Global Warming potential (AGWP) to that of $CO_2$.

The resulting GWP CF values are dynamically inserted into the characterization matrix for each value pair provided for $H$ and $C$. Parameters are externally supplied from climate scenarios (see Table 2), enabling consistent alignment between inventory modeling and evolving atmospheric conditions.

<table><caption>**Table 2** Gas concentration values for $CH_4$ ($C\_CH_4$) and $N_2O$ ($C\_NO2$). Concentration values for 2019 are used for 2020. RCP=Representative Concentration Pathways</caption><thead><tr><th></th><th colspan="4">C\_CH<sub>4</sub> (ppb)</th></tr><tr><th>RCP</th><th>1.9</th><th>2.6</th><th>4.5</th><th>8.5</th></tr></thead><tbody><tr><td>2020</td><td colspan="4">1866</td></tr><tr><td>2050</td><td>1,428</td><td>1,519</td><td>2,020</td><td>2,446</td></tr><tr><td>2080</td><td>1,150</td><td>1,197</td><td>1,779</td><td>2,652</td></tr><tr><td>2100</td><td>1,036</td><td>1,056</td><td>1,683</td><td>2,415</td></tr><tr><td></td><th colspan="4">C\_N<sub>2</sub>O (ppb)</th></tr><tr><td>RCP</td><td>1.9</td><td>2.6</td><td>4.5</td><td>8.5</td></tr><tr><td>2020</td><td colspan="4">332</td></tr><tr><td>2050</td><td>344</td><td>344</td><td>356</td><td>358</td></tr><tr><td>2080</td><td>350</td><td>349</td><td>373</td><td>380</td></tr><tr><td>2100</td><td>354</td><td>354</td><td>377</td><td>392</td></tr></tbody></table>
This approach supports prospective LCIA by allowing CFs to reflect the changing climate system. Rather than relying on fixed values (e.g., GWP100 = 28 for CH₄), users can explore how future CH₄ emissions may have stronger or weaker impacts based on projected concentrations.

By supporting symbolic CFs and parameterized evaluation, the exchange-based LCIA framework enables a close integration between LCA and integrated climate scenario modeling—an essential step toward robust, policy-relevant impact assessments.

# 6 Use case 4: scenario-based prospective LCIA with parameterized CFs for fossil fuels scarcity

This use case illustrates how exchange-resolved LCIA can support prospective modeling of fossil resource scarcity, again using scenario-sensitive, parameterized CFs. Specifically, we implement a formulation of Surplus Cost Potential (SCP)—a measure of the additional cost incurred due to the depletion of fossil energy carriers (coal, oil, and natural gas)—whose value varies dynamically over time and across integrated assessment model (IAM) scenarios.

In the original ReCiPe 2016 implementation (Vieira et al. 2016), surplus production costs were derived from global average surplus extraction costs using static marginal cost increase (MCI) values per fossil fuel type (e.g., USD/GJ²). These MCIs were then combined with a fixed marginal extraction rate to calculate constant CFs (in USD/GJ), which were subsequently converted to USD/kg or USD/Nm³ via energy content assumptions. While this provides a consistent global midpoint indicator, it does not account for changing resource economics or energy demand trajectories under climate policy scenarios.

Our approach extends this formulation by parameterizing the CFs as symbolic expressions evaluated per year and scenario. The core expression is:

$$CF_t = \frac{MCI_t \cdot P_t}{5 \cdot (1 + d_t)}$$

where:

* MCI_t: the marginal cost increase of extraction for the given fossil fuel at time t (USD/GJ²), obtained from the derivative of the IAM-simulated extraction cost curve;

* P_t: the annual extraction volume (EJ/year), approximated from cumulative extraction data;

* d_t: the scenario-specific discount rate, reflecting time preference for future costs;

* The factor 5 annualizes the data in the scenario output, which is given with a time step of 5 years.

The CFs are evaluated in units of USD/GJ, then converted to USD/kg (for coal and oil) or USD/m³ (for natural gas) using representative energy contents. In edges, it is implemented the following way:

```json
{
  "supplier": {
    "name": "Oil, crude",
    "categories": [
      "natural resource",
      "in ground"
    ],
    "matrix": "biosphere"
  },
  "consumer": {
    "matrix": "technosphere"
  },
  "value": "(MCI_OIL * P_OIL / 5) / (1 + d)"
}
```

Unlike the static approach of Vieira et al., our method retrieves scenario-specific time series for MCI, P (for each fuel), and d directly from IAM scenario outputs, allowing the CFs to evolve dynamically over time and across socio-economic pathways. The scenarios used in this study are based on the REMIND model v.3.5 (Luderer et al. 2020) and span a range of socio-economic pathways (SSP1-3) combined with climate policy assumptions, including near-term policy implementation (NPI, i.e., National Policies implemented), long-term carbon budgets (PkBudg650, i.e., 650 GtC of global carbon budget between 2022 to 2100), and a roll-back on previously committed investment in renewables (rollback). These scenarios represent contrasting futures regarding fossil fuel use, extraction dynamics, and mitigation ambition, providing a rich basis for evaluating how fossil resource scarcity impacts evolve.

# 7 Results

Results are presented for each of the use case presented above. Each features specific adaptations to meet the needs of the applied characterization models.

## 7.1 Use case 1: AWARE

Fig. 2 illustrates the LCA results for producing one kilogram of hydrogen via water electrolysis in France, using offshore wind power. The analysis resulted in ~8'800 exchanges associated with 512 unique CF values. From panel a), 50% (0.014 m³) of the net freshwater use originates from the electrolysis itself in France, with the remaining 50% being consumed by other European countries (~10%), India (6% from the production of iron pellet and steel), South Africa (4%, from the mining of platinum used in the electrolyzer) and other countries (30%), for a total of 0.029 m³. However, panel b) shows that the lowest water deprivation CF applies to French water consumers, while the highest applies to South African
<figure><img src="image_6.png" /><figcaption>**Fig. 2** Water scarcity assessment for producing one kilogram of hydrogen from offshore wind power through water electrolysis in France, using AWARE 2.0. Values in panels c) and d) are estimated using a Monte Carlo analysis over 10,000 iterations. Note that only the uncertainty associated with the spatial resolution of CFs is considered, not that stemming from inventories. a) Net freshwater use per consumer location (five largest), measured in cubic meters. Net use indicates the difference between water uptake and release. b) Mean and 25-75th percentiles CF values per consumer location, represented in cubic meters of deprived freshwater per cubic meter of net freshwater use. c) Characterized contribution of the four most relevant processes, in reference to one kg of hydrogen produced, in cubic meters of deprived freshwater. d) Comparison of the total score using a global CF value of 39.5 and region-specific CF values</figcaption></figure>

activities. Panel c) indicates that despite consuming only 4% of the freshwater in the system, the provision of water necessary for the extraction of platinum in South Africa is the most impactful process in the system once water scarcity is factored in, following the water needed for the electrolysis in France. It results in a total score of 0.60 m³ world-eq. per kg of hydrogen with a 50% confidence interval of 0.12—0.98. Using the global default CF of 39.5 m³ world-eq./m³ would yield a total score of 1.17, overestimating the impact by 95%. The reader should note that 1) the CF applied to exchanges where the consuming process has the location RoW is exchange-specific: it ranges from 41 to 48; 2) only the uncertainty linked to using spatially aggregated CFs is considered; 3) using French grid electricity to power the electrolyzer would increase the share of water consumption occurring in France, primarily due to evaporation in hydro and nuclear power plants. However, this would obscure the significance of supply chain contributions, such as the water used for mining platinum and iridium.

## 7.2 Use case 2: GeoPolRisk

Fig. 3 presents the inventory results for assessing geopolitical supply risk associated with producing one kilogram of electrolytic hydrogen in France using offshore wind power.

Panel a) shows the resources most consumed in terms of mass, relative to the functional unit. Coal is the largest input by weight, followed by pig iron, petroleum, and natural gas. These results reflect the upstream material requirements embedded in the construction and operation of offshore wind infrastructure, electricity transmission, and hydrogen production systems.

Panel b) highlights the resources with the highest average CFs for geopolitical supply risk, calculated as the total impact divided by the total amount required for each resource. Platinum and iridium, primarily sourced from South Africa and Russia, rank highest, reflecting their geopolitical sensitivity due to concentrated global supply.

Panel c) illustrates how *edges* enables the application of CFs specific to supplier-consumer location pairs for a given resource, exemplified here with crude petroleum.

Panel d) combines the amount of each resource used and its associated CF, broken down by supplier locations. This reveals the main contributors to the total geopolitical supply risk, with bauxite, hard coal, ferronickel, and pig iron emerging as the most critical, due to their volume and moderate to high CFs. Iridium from South Africa also appears among the top contributors despite its low absolute use–only about one microgram per kilogram of hydrogen. This highlights the importance of materials with high CFs, which capture supply concentration and governance risks, even when such materials are used in very small quantities. Finally, panel e) compares the LCA scores obtained using this technosphere
**Fig. 3** Geopolitical supply risk associated with resource use for producing one kilogram of electrolytic hydrogen in France, based on GeoPolRisk 1.0. Y-axes of top, second, and fourth panels use logarithmic scales. a) Mass of each resource used (in kilograms). b) Weighted average CF applied per resource, in kg copper-eq./kg. c) Weighted average CF for petroleum, for different pairs of supplier–consumer locations, in kg copper-eq./kg. d) Ten most critical abiotic resources traded, by supplier location, in kg copper-eq/kg hydrogen. Each color represents a geographical origin. The coloured legend lists the six most critical suppliers’ locations. e) Comparison between the technosphere exchange-based approach and the approach proposed in (Koyamparambath et al. 2024), based on the characterization of elementary flows, using a French perspective (i.e., as if all resources are imported by France directly). Note that the average CF values displayed in b) and c) are weighted by the amounts of the exchanges involved in the system. Hence, they are specific to this case

exchange-based approach with those obtained by character-
izing elementary flows directly, from a French perspective,
as proposed by Koyamparambath et al. (2024). Using the
technosphere exchange-based characterization yields a score
of 0.39 kg copper-eq. per kilogram of hydrogen, compared
to 0.14 kg when relying on elementary flow characteriza-
tion. This difference reflects two sources of variability: the
use of intermediate versus elementary flows, and differences
in the characterization factors applied (regionalized versus
global). Depending on the context, these effects may lead to
higher or lower scores, but here they result in a larger supply
risk estimate when using the technosphere exchange-based
approach.

7.3 Use case 3: global warming potential

Fig. 4 presents the evolution of the CFs for GWP and cor-
responding scores to produce one kg of electrolytic hydro-
gen in France using offshore wind power, under four RCP
scenarios (RCP2.6, RCP4.5, RCP6.0, and RCP8.5) for the
period 2025–2100. Note that this example does not con-
sider any changes in the hydrogen production system (e.g.,
the efficiency of the electrolyzer, the electricity mix, etc.),
but only changes in the GHG atmospheric concentrations.
Panel a) illustrates the concentration-dependent GWP fac-
tors (expressed in kg CO₂-equivalents per kg emission) for
the two major greenhouse gases: methane (CH₄) and nitrous
oxide (N₂O). Results demonstrate that the GWP factors for
CH₄ and N₂O vary across scenarios due to changes in the
gases’ background concentrations, which affect their rela-
tive radiative efficiencies and lifetimes compared to CO₂.
Carbon dioxide retains a constant GWP factor of 1, as it is
the reference substance.

Specifically, in low-emission pathways such as RCP2.6,
the reduced atmospheric burden leads to higher radiative
efficiencies per molecule, thereby increasing the GWP CFs
values relative to those in high-emission pathways.

<figure><img src="image_7.png" /></figure>

The bottom panel of Fig. 4 shows the total GWP-based
LCIA score per kilogram of electrolytic hydrogen produced
over time. Logically, under the RCP2.6 scenario, the overall
climate change impact score increases with time, while in
<figure><img src="image_8.png" /><figcaption>**Fig. 4** Evolution of concentration-dependent Global Warming Potential (GWP) factors and scores under four RCP scenarios (RCP2.6, RCP4.5, RCP6.0, RCP8.5) between 2025 and 2100. a) GWP CFs for CH₄, and N₂O, in kg of CO₂-eq. per kg of emission. b) Total GWP score per kg of hydrogen across the four RCP scenarios. Lower atmospheric concentrations in mitigation pathways lead to higher radiative efficiencies and increased impact scores</figcaption></figure>

the higher-emission scenarios (RCP6.0 and RCP8.5), the score decreases. This counterintuitive trend results from the stronger climate forcing exerted by marginal emissions of CH₄ and N₂O under cleaner atmospheric conditions, as captured by the concentration-dependent GWP CFs formulation. In this case, the variation of scores across scenarios remains modest, as the system emits low amounts of CH₄ and N₂O relative to CO₂, unlike other systems (e.g., agricultural activities).

## 7.4 Use case 4: fossil fuels scarcity

Results shown in Fig. 5 indicate a clear relationship between scenario assumptions and the CFs for fossil fuel scarcity. In stringent mitigation scenarios like SSP1-PkBudg650, fossil fuel extraction volumes (P) decline rapidly due to strong

<figure><img src="image_9.png" /><figcaption>**Fig. 5** Surplus Cost of Fossil Fuel Extraction across three scenarios from REMIND v.3.5. a) Annual extraction rate, in exajoules (EJ), for hard coal, natural gas, and crude oil across multiple scenarios. b) Surplus cost potentials (SCP) per unit of resource (USD/kg for oil and coal, USD/Nm³ for gas) across multiple scenarios. c) Resulting LCIA scores per kilogram of electrolytic hydrogen across multiple scenarios. In a) and b), each line corresponds to a scenario, and each colour corresponds to a fuel. In c), each line corresponds to a scenario</figcaption></figure>

climate policies and low-carbon transitions. This, in turn, limits the rate at which cumulative resources are depleted, leading to more moderate increases in marginal extraction costs (MCI). Additionally, such scenarios often feature higher or more stable discount rates (d), further dampening the resulting CFs. These factors yield CFs that decrease significantly over time, reflecting a lower scarcity pressure under strong mitigation. Conversely, in scenarios with

<figure><img src="image_10.png" /></figure>
delayed or weak climate action—such as SSP3-rollBack—
extraction volumes remain high or even grow, driving up
cumulative depletion and leading to steeper marginal cost
increases (higher MCI). Coupled with moderate discount-
ing, this raises CFs over time, capturing the increased scar-
city and cost burden of fossil resource use. These dynamics
are directly encoded in the parameterized CF formulation.
The influence of scenario trajectories on CF parameters is
reflected in the LCIA impact scores: pathways with rapid
fossil phase-out show a steep decline in impacts. In con-
trast, fossil-reliant pathways maintain high and persistent
scores. This demonstrates the strength of using scenario-
based, dynamic CFs in prospective LCA to reflect fossil fuel
use’s evolving cost and scarcity implications under different
socio-economic and climate policy futures.

8 Discussion

This study introduced an exchange-resolved approach to
LCIA, shifting the characterization from node-level elemen-
tary flows to exchanges between activities. Through four
use cases, we demonstrated the flexibility and applicability
of this method for regionalized, technosphere-aware, and
prospective environmental assessments.

The results confirm that exchange-based LCIA can
account for key spatial, relational, and scenario-dependent
aspects of environmental impacts, offering a lower-overhead
alternative to GIS-based modeling—albeit with less spatial
granularity. By treating exchanges as the unit of impact char-
acterization, the framework enables consistent modeling
across various impact categories that depend on exchange
attributes, including geographic location, supplier-consumer
relationships, and evolving background conditions such as
atmospheric GHG concentrations.

The regionalized water scarcity impact assessment (AWARE) illustrated how geographic disaggregation can be achieved without proliferating elementary flows or requiring manual flow duplication. Furthermore, we demonstrated that exchanges could be distinguished based on the consumer's location and CPC category. The technosphere-based supply risk assessment (GeoPolRisk) further showed that impacts can depend on the supply chains' structure, which 1) increases flexibility for applying the LCIA method and 2) introduces a relational dimension that traditional LCIA does not capture. Finally, the prospective GWP and fossil fuels examples demonstrated that concentration- and scenario-dependent characterization factors can be dynamically evaluated, aligning LCA outputs more closely with integrated scenario modeling frameworks such as RCPs or SSPs.

However, this approach also presents limitations. First, as
already noted by C. L. Mutel & Hellweg (2009), implement-
ing regionalized indicators at the national or sub-national

level cannot possibly capture site-specific impacts. Environ-
mental conditions, such as water scarcity, ecosystem sensi-
tivity, air quality, and population density, vary widely within
a country. This is the reason why indicators like AWARE
define CFs at the watershed level. However, one may try to
overcome this issue by explicitly modelling the uncertainty
introduced by using aggregated CFs and letting it propagate
to the score level, as we did by integrating variability across
watersheds (although it does not include uncertainty at the
watershed level itself). Yet, suppose site-specific impacts
are expected to be of primary concern. In that case, using
geo-referenced inventories coupled with tools to model fate,
exposure, and effect based on real-world environmental data
(e.g., local hydrology models for water impacts, air disper-
sion models for air pollution) is preferable. Second, despite
efficient implementation and advanced matching algorithms,
the *edges* library requires a few seconds to a few minutes
to calculate a score, compared to a fraction of a second
for *brightway2-calc*, as it needs to verify the eligibility of
every exchange involved in the inventory matrix (which can
amount to several hundreds of thousands). Third, while the
method supports regionalization and parameterization, it
relies on the availability and quality of relevant metadata
(e.g., locations, classifications) in inventories and characteri-
zation factor definitions. Limited trade data, gaps in inven-
tory geographies, or inconsistencies in metadata are frequent
in common LCA databases. They can lead to reduced model
fidelity. There is however a clear trend in spatializing inven-
tory databases, as demonstrated by (Peng and Pfister 2024)
and, more recently, by the development of *regioinvent* (Agez
2025). Coupling their use with *edges* could provide more
accurate assessments. Finally, while symbolic CFs allow
flexible prospective modeling, the quality of the results ulti-
mately depends on the robustness of the underlying param-
eterizations (e.g., GWP models, concentration scenarios).

Future research could expand exchange-resolved LCIA
in several directions. First, while *edges* already implements
AWARE, IMPACT World+, and GeoPolRisk, a broader
application to other regionalized or relational impact assess-
ment methods could further demonstrate its generalizability.
Second, using complex external models to evaluate CFs,
as shown (to a limited extent) with the GWP example, is
promising. One could envision calling an external API to
retrieve current atmospheric conditions to calculate the mar-
ginal contribution to air pollution for different substances.
Third, future work could explore the coupling of exchange-
resolved LCIA with forward-looking inventory models, in
which both the life cycle foreground system and background
environmental conditions co-evolve. It offers a good frame-
work to operationalize existing prospective LCIA methods,
such as those proposed for water scarcity (Núñez et al. 2015;
Baustert et al. 2022), ozone depletion (van den Oever et al.
2024), impacts on biodiversity from land use (de Baan et al.
2013), and impacts on freshwater ecosystems from climate
change and water consumption (Hanafiah et al. 2011; Cosme
and Niero 2017). This would open the door to assessments
where changes in supply chains, technology mixes, or infra-
structure are dynamically matched with corresponding shifts
in characterization factors, improving the consistency and
relevance of prospective LCA studies. Finally, this work
highlights the potential of more dynamic LCIA frameworks,
and we encourage LCA software developers (e.g., SimaPro,
OpenLCA, and Activity Browser) to consider supporting
such approaches in the future to better capture the spatial,
temporal, and parametric complexity of impact assessment.
But this probably requires moving beyond static CF files to a
runtime process like that of *edges*, that is to 1) detect eligible
exchanges and, if the CF values are symbolic or provided by
an external model, 2) evaluate CFs “on the fly” before they
enter the characterization matrix.

In summary, exchange-based LCIA represents a prag-
matic and scalable advancement for environmental assess-
ment. It occupies an essential methodological space
between conventional node-based LCIA and fully spatially
explicit, GIS-integrated models. It provides a robust yet
accessible solution for regionalized, relational, and pro-
spective life cycle assessments.

**Acknowledgements** The authors acknowledge the financial support of the French energy agency ADEME through the HySPI project (nr. 2197D0085): Hydrogène industriel – Scénarios Prospectifs des Impacts environnementaux. The HySPI project aims to provide a methodo-logical framework to analyze and quantify the environmental impacts of the decarbonization strategy for hydrogen production used by the industry in France systematically and prospectively. The authors also acknowledge the financial support of the Europe Horizon project RAW-CLIC (project ID 101183654) and that of the Europe Horizon project PRISMA (project ID 101081604). Finally, the authors would like to thank Juliana Steinbach from Mines Paris PSL for the constructive discussion.

**Author contributions** Romain Sacchi: Conceptualization, Method-
ology, Software, Writing—Original draft preparation. Alvaro Hahn
Menacho: Methodology, Data curation, Writing—Review & Editing.
Georg Seitfudem, Maxime Agez, and Anish Koyamparambath: Data
curation, Writing—Review & Editing. Joanna Schlesinger, Jair Santil-
lan Saldivar, Philippe Loubet, and Christian Bauer: Writing—Review
& Editing.

**Funding** Open Access funding provided by Lib4RI – Library for the Research Institutes within the ETH Domain: Eawag, Empa, PSI & WSL.

**Data availability** The distributable form of the Python library used to produce the results presented in this article is freely available from the Python Package Index (PyPI): https://pypi.org/project/edges/. Its source code is available in the following repository: https://github.com/Laboratory-for-Energy-Systems-Analysis/edges. Documentation is available at this address: https://edges.readthedocs.io/en/latest/. Scripts to reproduce the use cases presented in this article are provided in the library's online repository (edges/examples/publication examples).

Declarations

Competing interests The authors declare no conflict of interest.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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