📄 earth_science

A graph-matrix hybrid approach for deep temporalisation in time-explicit LCA

This paper introduces Trails, an open-source graph-matrix hybrid method that enables deep temporalisation in time-explicit life cycle assessment by propagating year-specific temporal dynamics throughout entire supply chains, demonstrating significant impacts on cumulative environmental scores and emission timing compared to static or foreground-only approaches.

Original authors: Romain Sacchi, Tom Terlouw, Arthur Jakobs, Karin Treyer, Alvaro Hahn-Menacho, Christian Bauer

Published 2026-07-15

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Romain Sacchi, Tom Terlouw, Arthur Jakobs, Karin Treyer, Alvaro Hahn-Menacho, Christian Bauer

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to calculate the total "carbon footprint" of a new electric car. In the old, standard way of doing this (called static LCA), it's like taking a single, frozen photograph of the world in the year 2025. You assume that every factory making the steel for the car, every power plant generating the electricity, and every road the car drives on, stays exactly the same forever. You snap that picture, do the math, and you're done.

But the real world isn't a frozen photo; it's a fast-forwarding movie.

Enter Trails, a new open-source tool created by researchers at the Paul Scherrer Institute. Think of Trails as a time-traveling detective that doesn't just look at the car; it follows the car's entire family tree through time.

The Problem with the "Frozen Photo"

The paper argues that for long-lived things—like a car that lasts 16 years, a ship that sails for decades, or a dam that stands for a century—the "frozen photo" approach is misleading. If you build a car in 2025 but drive it until 2041, the electricity grid it uses in 2030 might be much cleaner than the one in 2025. A static calculation misses this. It also misses the fact that the steel for the car might have been made in a factory built in 1990, or that the batteries will be recycled in 2045.

The "Deep Temporalisation" Adventure

The researchers call their new method "deep temporalisation." Here is the analogy:

Imagine a supply chain is a giant, multi-generational family reunion.

The "Foreground" (The Car): This is the main character, the one you are studying.
The "Background" (The Supply Chain): This is the rest of the family—the steel makers, the miners, the power plants, the road builders.

Old tools (and even some newer ones) would only ask the main character, "When did you do things?" and then look at the family photo album for that specific year. They wouldn't ask the great-grandparents (the steel makers) when they did their work.

Trails changes the game. It asks the main character, "When did you do things?" and then sends a time-traveling messenger to every single ancestor in the supply chain.

If the car uses steel made in 2020, the messenger goes to 2020.
If the car uses electricity generated in 2035, the messenger goes to 2035.
If the steel was made using coal in 2010 but the power plant was upgraded in 2025, the messenger tracks that switch.

This is what the authors call "deep temporalisation": propagating the timing of events all the way down the supply chain, not just stopping at the first few steps.

What They Found (The Plot Twist)

The team tested this "time-traveling detective" on four different systems: an electric car, a chemical factory making polyol, a ship switching fuel types, and a machine that sucks carbon dioxide out of the air (DACCS).

They compared three scenarios:

Static: The frozen photo (2025 data for everything).
Foreground-Only: The main character moves in time, but the family stays frozen in 2025.
Deep Temporalisation (Trails): Everyone moves in time, matching the real world's evolution.

The Results:
In these simulations, the "Deep Temporalisation" approach changed the final scores significantly compared to the other methods.

For the ship switching from diesel to methanol, the deep method showed a 23.8% lower impact score than the static method and 18.3% lower than the foreground-only method. Why? Because the infrastructure for the new fuel was built in the past, and the old fuel's infrastructure was fading away. The static photo missed this shift entirely.
For the polyol chemical, the deep method showed a 22% higher score. This was because the deep method traced the construction of the chemical factories back to the 1980s, whereas the other methods assumed they were built right when the product started being made.
For the electric car, the difference was smaller (about -3.6%), suggesting that for some systems, the "frozen photo" is actually close enough.

The paper suggests that whether you need this deep time-travel depends on the system. If you are studying a short-lived product, a simple photo might be fine. But for long-lived infrastructure or rapidly changing economies, ignoring the timeline can lead you to the wrong conclusion.

What They Explicitly Rule Out

The authors are very clear about what their tool is not:

It is not a crystal ball for uncertainty: The tool is deterministic, meaning it gives one specific answer based on the data fed into it. It does not currently run thousands of simulations to guess how "uncertain" the future might be.
It is not for hourly details: The tool works on a yearly timeline. It cannot tell you if a factory emits more pollution on a Tuesday morning versus a Friday night, or how seasonal wind patterns affect a specific hour. It's too coarse for that.
It is not a replacement for all other tools: It complements existing tools like bw_timex or DyPLCA. It doesn't replace them; it adds a specific layer of "deep" time-tracking that those tools might miss when dealing with connected, year-specific databases.

How Sure Are They?

The authors are confident in their method and the simulations they ran. They built the tool, tested it against known math problems (and it passed), and ran it on four specific case studies.

They demonstrated that deep temporalisation changes the results (sometimes by a lot, sometimes by a little).
They suggest that this approach is necessary for systems with long lifespans or rapidly changing supply chains.
They do not claim this is the final, perfect solution for all time-based environmental questions. They admit that if the data about when things happen is poor, the tool might give a "false sense of precision."

The Takeaway

Think of Trails as a new lens for looking at the past, present, and future of our products. It doesn't just ask "What did we make?" It asks, "When did we make it, when did we use it, and how did the world change while we were doing it?"

By connecting the dots across time, it reveals that the environmental cost of a product isn't just a single number—it's a story that plays out over decades. And sometimes, the ending of that story is very different from what the "frozen photo" predicted.

Technical Summary: A Graph-Matrix Hybrid Approach for Deep Temporalisation in Time-Explicit LCA

Problem Statement
Conventional Life Cycle Assessment (LCA) typically assumes that all processes in a product system occur at a single point in time and that the background economy remains static. While dynamic and prospective LCA methods have advanced to represent process timing, emission timing, and time-specific background databases, existing approaches often concentrate temporalisation in the foreground. They frequently connect foreground events to background snapshots without propagating temporalised exchanges deeper into the supply chain. This limitation is critical for long-lived systems (e.g., infrastructure, energy systems) and technologies embedded in rapidly changing economies, where upstream dynamics (such as infrastructure construction, fleet turnover, or delayed waste treatment) significantly influence time-resolved results. Current tools lack workflows that effectively represent temporal distributions across the entire supply chain, including background exchanges, leading to potential misrepresentation of system dynamics.

Methodology: The Trails Framework
The authors present Trails, an open-source implementation of a graph-matrix hybrid method designed to achieve "deep temporalisation." This approach propagates temporal distributions beyond the foreground system across exchanges and processes several supply-chain tiers distant from the functional unit.

Graph-Matrix Hybrid Algorithm: Trails avoids the computational burden of solving a single, massive time-expanded matrix. Instead, it employs a two-step process:
1. Temporal Routing (Graph): The system is modeled as a temporal routing graph where nodes represent process-year pairs $(i, y)$ . Trails uses an adaptive, score-based traversal to expand branches. It routes demands through the supply chain, applying temporal distributions (offsets and weights) to exchanges. This step determines which upstream activities are relevant in specific years based on a user-defined cutoff relative to the static score potential.
2. Year-Wise Solving (Matrix): Once the routing identifies "frontier demands" (the boundary of the expanded graph), these demands are aggregated by calendar year. Each annual demand vector is solved independently using the corresponding year-specific technosphere matrix ( $A_y$ ). This preserves compatibility with conventional matrix-based LCA while handling cross-year dependencies.
Connected Time-Indexed Databases: Trails treats scenario-year snapshots (e.g., from 2000 to 2100) as slices of a 3D tensor. It supports two interpretations for temporally distributed exchanges:
- Anchor-Year Mode: The exchange coefficient is read from the year the process occurs and distributed over time.
- Target-Year Mode: The temporal distribution determines the target years, but the coefficient is read from the matrix of the target year, reflecting evolving technology or supply chain conditions.
Impact Assessment: The method integrates with dynamic impact models, specifically the FaIR climate emulator, to generate time-resolved radiative forcing and temperature responses. It also supports fixed-window CO2 pulse-equivalent indicators that account for the timing of emissions within a specific assessment window.

Key Contributions

Formalisation of Deep Temporalisation: The paper defines deep temporalisation as the recursive propagation of temporal metadata beyond the foreground into connected, time-indexed background matrices.
Algorithmic Implementation: It introduces a practical graph-matrix hybrid algorithm that combines explicit temporal routing with efficient year-wise matrix solves, making deep temporalisation computationally feasible for applied practitioners.
Modelling Choices: The work clarifies the distinction between anchor-year and target-year coefficient interpretations, a choice that significantly affects results in prospective databases where technology mixes evolve.
Open-Source Tool: Trails is released as an open-source Python library, bridging the gap between prospective database generation (e.g., via Premise) and deep temporal analysis.

Results
The authors demonstrated the approach using four case studies with multi-decade life-cycle events: a battery electric vehicle, CCU polyol production, a marine fuel switch, and a Direct Air Carbon Capture and Storage (DACCS) system.

Score Variations: Deep temporalisation altered cumulative scores significantly compared to static LCA and foreground-only time-explicit LCA.
- Relative to static LCA, changes ranged from -23.8% to +22%.
- Relative to foreground-only time-explicit LCA, changes ranged from -18.3% to +20.3%.
Specific Findings:
- Marine Fuel Switch: Showed the strongest effect of deep temporalisation (-23.8% vs. static), driven by the timing of infrastructure construction for fossil and synthetic fuel chains in previous decades.
- DACCS: Deep temporalisation brought the cumulative score close to the static result, whereas foreground-only temporalisation yielded a significantly lower score (+20.3% difference), highlighting the importance of upstream natural gas infrastructure timing.
- Polyol Production: Deep temporalisation increased the score by +22% relative to static LCA, revealing impacts from chemical facility construction dating back to 1987, which were missed in foreground-only approaches.
Temporal Profiles: The method shifted the timing of upstream infrastructure, fuel-chain, and long-term emission contributions, altering the shape of cumulative impact curves over time.

Significance and Claims
The paper claims that Trails provides a necessary diagnostic and methodological tool to test whether upstream temporalisation is decision-relevant within a chosen temporal perspective. Its primary significance lies not in asserting superior accuracy for all cases, but in revealing temporal dynamics that might otherwise remain hidden in static or foreground-only models.

The authors position Trails as complementary to existing tools (such as bw_timex, DyPLCA, and Temporalis). It is particularly valuable for systems with long-lived infrastructure, delayed end-of-life treatments, and rapidly changing supply chains. However, the paper modestly notes that for short-lived products or systems where temporal distributions are poorly known, simpler static or foreground-only models may remain sufficient. The tool is designed to help practitioners determine when adding temporal modelling throughout the product system is warranted by the decision context.