the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Jun 2026
IMAGE-materials 3.5.1.0: Dynamic material flow modelling in the IMAGE Integrated Assessment Model
Abstract. We present the IMAGE-materials model, a stock-driven dynamic material flow analysis model, part of the IMAGE integrated assessment model (IAM) framework. y combining modelling principles from the IAM and Industrial Ecology (IE) communities, the model quantifies material inflows, stocks, and outflows affected by climate and resource policy scenarios.
IMAGE-materials is a recursive yearly simulation model that projects global material demand until 2100 for 26 world regions on a sectoral level for a wide variety of bulk and critical materials. The model includes buildings, vehicles, electricity, rail & road infrastructure, and a residual sector capturing the remaining demand, including different types and modes (e.g., housing types and transport modes). It is written using a modular, object-oriented Python architecture, enabling the easy addition of new sectors and data. Key assumptions include product lifetimes, material intensities, and technology mixes.
The model is driven by service demand scenarios produced by the IMAGE framework, based on socio-economic and climate policy assumptions. IMAGE-materials can flexibly simulate the adoption of numerous circular economy measures, such as service demand reductions, lifetime extension, lightweighting, and recycling. Therefore, IMAGE-materials enables scientists and policymakers to explore mitigation pathways with a detailed additional dimension of material flows. It can thus assess the synergies and trade-offs between climate and circularity policies by explicitly accounting for their material implications. As such, IMAGE-materials integrates the fields of IAMs and IE, building on the strengths of each.
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CC1: 'Comment on egusphere-2026-2348', Dominik Wiedenhofer, 15 Jun 2026
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CC2: 'Reply on CC1', Luja von Köckritz, 25 Jun 2026
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Thank you for the kind words about our work.
Also, thanks for the clarification on our wording here. In using the word "assumed", we lacked clarity and will adjust the description of inflow-driven dMFA accordingly. Among the sources sent, I only found a detailed description of inflow-driven dMFA in https://onlinelibrary.wiley.com/doi/10.1111/jiec.13380, so we will adjust our description to the one used in that paper, describing the data sources being "widely available data for material or product consumption, production and trade".
Citation: https://doi.org/10.5194/egusphere-2026-2348-CC2
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CC2: 'Reply on CC1', Luja von Köckritz, 25 Jun 2026
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RC1: 'Comment on egusphere-2026-2348', Anonymous Referee #1, 10 Jul 2026
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This manuscript presents IMAGE-materials 3.5.1.0, a stock-driven dynamic material flow analysis model integrated within the IMAGE integrated assessment modelling framework. The model projects material inflows, stocks, and outflows across 26 global regions to 2100 and covers major material-demand sectors, including buildings, vehicles, electricity generation and infrastructure, road and rail infrastructure, residual material demand, and end-of-life flows. By linking material demand to service-demand projections from IMAGE-energy, the framework enables consistent analysis of the material implications of socioeconomic development, climate policy, and circular economy strategies. Its modular Python-based architecture also allows additional sectors, materials, and scenario assumptions to be incorporated in future development.
Overall, I find this to be a timely and valuable contribution. As material use, resource efficiency, and circular economy strategies receive increasing attention in pathways toward sustainable development, the explicit representation of material stocks and flows within IAMs is increasingly important. I appreciate the substantial effort invested in developing, documenting, validating, and making this comprehensive model available. I also value the authors’ transparent discussion of the model’s current challenges and limitations. My comments are relatively minor and are mainly intended to improve clarity and strengthen the discussion of selected assumptions and data limitations.
Many of the challenges identified in the manuscript arise from limitations in the availability, coverage, regional detail, and consistency of material data. Given the growing importance of material systems in IAM research and their close connection to sustainable development and circular economy strategies, including reuse, lifetime extension, lightweighting, material substitution, and recycling, I encourage the authors to use the Discussion or Outlook section to make a broader call for more comprehensive, harmonized, and high-quality data collection. Improved datasets would support future model development, regional differentiation, validation, and more robust representation of circular economy pathways.
Minor:
Please consider revising the heading hierarchy throughout the manuscript. Several headings in the main text, such as Data requirements, Data processing, Simulation workflow, Key challenges, the sector-specific validation headings, and Limitations and Outlook, are currently unnumbered, but share the same font format as the section headings. A consistent numbering or formatting scheme would make the manuscript organization clearer and help readers distinguish formal subsections from paragraph-level labels.
Line 132: I did not find the full name of DSM. Please consider providing it when DSM first appears.
Lines 292-294: The assumed construction-type shares: 25% each for cement, masonry, steel, and timber in detached and semi-detached houses; 50% each for steel and cement in apartment buildings; and 100% steel construction for high-rise buildings, may have an important influence on the estimated material stocks. Could the authors please clarify the empirical basis for these default assumptions and provide relevant references, where available? It would also be helpful to briefly note any uncertainty associated with applying the same shares across regions.
Lines 382-383: The EV battery model assumes that battery lifetime is identical to that of the host vehicle, and therefore does not represent separate battery stocks. Could the authors discuss the implications of this assumption? In particular, batteries may be replaced before vehicle retirement or repurposed for second-life applications after vehicle retirement. Ignoring these processes could affect estimates of battery stocks, material demand, critical mineral requirements, and end-of-life material flows.
Lines 427-428: Could the authors clarify how the historically derived grid ratios and regression relationships are applied in future years? In particular, are these relationships assumed to remain constant across SSPs, and how might this affect projected grid infrastructure and material demand under different socioeconomic and energy-system pathways?
Lines 469-470: “Using the population and regional ratios, we calculate the ratio of road types, bridges, tunnels, and urban rail, standard rail, and high-speed rail length stocks and flows. ” Please clarify whether the population and regional ratios used to estimate road types, bridges, tunnels, and rail infrastructure are static over time. If they are held constant, how might this assumption influence future material-stock and flow projections, especially across SSPs with different urbanization and infrastructure-development pathways?
Lines 473-474. Is that a repeat of lines 465-467? Please double-check it.
Lines 480-481: The statement that “there is no method to quantify this” appears too strong, as auxiliary infrastructure could in principle be estimated using asset inventories, geospatial data, engineering design parameters, or material-intensity factors. Do the authors instead mean that no sufficiently comprehensive and harmonized method or dataset is currently available for consistent global-scale quantification? Please clarify and consider revising the wording accordingly.
Line 501: Please consider rewriting the Gompertz equation using exp(⋅) notation for clarity. In its current form, terms such as ae−... and be−... may be misread as parameters ae and be, although a, b, and c are defined as the Gompertz parameters. Using exp(⋅) would make the nested exponential structure clearer and avoid ambiguity.
Line 511: same rewriting suggestion as above
Table 4: I appreciate that the authors explain the comparison for Europe. However, I noticed that the USA has relatively high brick stocks but relatively low glass and copper stocks. Are there any potential reasons for these differences? If so, please consider providing a brief explanation.
Line 648: please check if “)” is needed here in “Table 6: Global vehicle stock estimate validation ). ”
Line 688: The wording “full road and rail networks” may be slightly stronger than intended, since the completeness and quality of OpenStreetMap data can vary across regions. Could the authors please clarify what is meant by “full networks” and consider using more cautious wording, such as “broader coverage of road and rail networks than is typically available from official statistical sources”?
Lines 798–799: I was unable to access the documentation link. It returns the following error: “404 Project not found. The project you requested does not exist or may have been removed.” Please ensure that the documentation link is correct and publicly accessible.
Citation: https://doi.org/10.5194/egusphere-2026-2348-RC1 -
CC3: 'Comment on egusphere-2026-2348', Leonie Schweiger, 05 Aug 2026
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Congratulations on the comprehensive model and the clearly structured draft. It was a very interesting read for us! Below are our comments, collectively from the REMIND-Industry team:
- line 106: Material coverage - what is the reasoning behind the selection of materials covered by each sector? For instance, we are wondering why plastics in buildings are not covered (share of plastics used in buildings is ~17% globally, which is more than the 14% in transportation and presumably much more than in electricity?). Also, how did you select the materials with economy-wide coverage, i.e. where you model the residual sector (e.g. why is there no residual sector for plastics)?
- line 273: Why did you choose to not use a stock-based DSM for the residual sector?
- line 292ff: Could you describe your reasoning or provide references with regards to the assumptions on material shares in houses?
- line 305: “this is also provided in an urban and rural split” - What does that mean? That your stock has the dimensions of [R, A, T, t]?
- line 312f: Regarding the “useful floorspace” vs. “gross floorspace” challange: How do you deal with the discrepancy - do you apply a factor to get to gross floorspace, or do you stick to the useful floorspace? That could be clarified in the text. Similarly, energy-related floorspace from IMAGE-energy might not cover unheated/cooled areas such as garages, sheds, or vacant homes. This could be an additional challenge to list.
- line 370f: “using a linear formulation with a configurable end-of-life multiplier, with optional capping if lifetimes are extended” - This sentence is hard to understand, maybe you could reformulate this.
- line 492: Material extraction data - is this data only used as a proxy for apparent consumption for materials where apparent consumption data is scarce or is this a general input data for all materials?
- line 513f: If the calculated historic material consumption of IMAGEmaterials is higher than reported data on actual consumption - how do you deal with this challenge? Do you simply assume that residual demand is 0 or do you scale down the bottom-up estimates from IMAGEmaterials?
- line 520: Are outflows from the residual sector not covered with regards to recycling potentials?
- line 551: “We mostly discuss the SSP2 results” - which ones if they are all SSP2 scenarios?
- line 554: Please mention here again which sectors are covered, "global concrete stocks" sounds like economy-wide coverage, is that the case?
- Figure 5b): The residual sector of steel shows to be quite substantial - since you do not model stocks in this sector, you implicitly assume that products in the residual sector have short lifetimes, please consider flagging this. (The same holds probably true for cement as well.)
- Figure 6: Why is there a kink in the inflow panel around 2020?
- line 799: The link https://imagematerials.readthedocs.io/en/stable/ does not work (due to a line break)
- We could not find the data for your figures or generally some model output: On zenodo, we only found steel/concrete trajectories for different scenarios (this is also the case for the ERL paper). Is this intended or did we look in the wrong place?
- The “Key challenges” sections are somewhat repetitive, at least partly - it could be more concise to compile the data coverage and resolution (and the lack thereof) in a common table for all sectors.
Best regards from Potsdam on behalf of the REMIND-Industry Team!
Citation: https://doi.org/10.5194/egusphere-2026-2348-CC3
Model code and software
IMAGE-materials 3.5.1.0 Luja von Köckritz, Frederike Arp, Raoul Schram, Judith Tettenborn, Marianne Zanon-Zotin, Roel Brouwer, Sebastiaan Deetman, Christina Staiger, Martijn van Engelenburg, Parisa Zahedi https://doi.org/10.5281/zenodo.19708090
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Congratulations to this fine work!
I do have a comment regarding paragraph 120, where you state that inflow-driven modelling uses "assumed inflows of new products". Please note that this is not correct, these are definitely not assumed at all - the point of inflow-driven modelling is exactly that one starts with empirical information on inflows, while stock-driven modelling starts with empirical information on existing stocks/service units. Data on material inflows (gross additions to stock in MFA terminology) are usually painstakingly re-constructed from various historical and statistical databases (which you also use for your base-year calibration ...), see for example:
10.1073/pnas.1613773114
https://doi.org/10.1016/j.resconrec.2021.106122
https://doi.org/10.1016/j.mex.2022.101654
https://onlinelibrary.wiley.com/doi/10.1111/jiec.13380