Steel MFA

Methodology

In the following, methods specific to the steel model are described. For the common methodology of the REMIND-MFA, refer to the Methodology chapter.

Stock extrapolation

In-use stocks are regressed separately in different product categories, which then add up to the total in-use stock. For each product category, we regress a common set of parameters for all regions. However, since historic data in single regions deviates from these curves, we apply region-dependent correction terms, which form a smooth transition from historic trends to the common regression. In the regression, we apply region-specific saturation levels based on expert judgement. In some regions, we also vary the speed of convergence towards this saturation level based on expert judgement, to continue historical trends and be in accordance with literature values.

End-use good category splits

Region- and time-specific data on shares of good categories in steel consumption is very limited. We therefore apply a function of these shares over gdp per capita to all regions, which we construct from three different data points from the literature, and a smooth interpolation in between.

Reconciliation of scrap use

We read historical scrap use from literature data, but our model also predicts scrap use, via the outflow of the in-use stock model and rates for collection and recovery. We use the literature data on scrap use to manually calibrate the parameters of the model, such that out model aligns with the dataset in historical years. Since we only have reliable scrap use data for some world regions, we perform this calibration on a global scale, and for some selected regions individually.

Processes

The following table lists the processes that are modelled in the steel MFA.

Name
System environment
Production from ores
Production (EAF)
Forming
Intermediate products
Fabrication
Good Market
Use phase
Obsolete stocks
End of life products
Recycling
Scrap market
Excess scrap
Imports
Exports
Losses
Ore Extraction

Dimensions

The following table presents the dimensions over which parameters and variables (stocks and flows incl. trades) are defined in the steel MFA.

Name Letter
Time t
Historic Time h
Region r
Good g

Stocks

The following table presents the processes that are modelled as stocks in the steel MFA with their respective dimensions and the lifetime model that is employed.

Dimensions Name Process Stock Type Lifetime Model
t, r, g Use phase Use phase StockDrivenDSM LogNormalLifetime
t, r, g Obsolete stocks Obsolete stocks SimpleFlowDrivenStock
t, r Excess scrap Excess scrap SimpleFlowDrivenStock

Flows

The following table presents all flows in the steel MFA with their respective dimensions and the processes that they connect.

Dimensions Origin Process Destination Process
t, r Ore Extraction Production from ores
t, r Scrap market Production from ores
t, r Production from ores Forming
t, r Production from ores Losses
t, r Scrap market Production (EAF)
t, r Production (EAF) Forming
t, r Production (EAF) Losses
t, r Forming Intermediate products
t, r Forming Scrap market
t, r Forming Losses
t, r Fabrication Losses
t, r Intermediate products Fabrication
t, r Intermediate products Exports
t, r Imports Intermediate products
t, r, g Fabrication Good Market
t, r Fabrication Scrap market
t, r, g Good Market Exports
t, r, g Imports Good Market
t, r, g Good Market Use phase
t, r, g Use phase Obsolete stocks
t, r, g Use phase End of life products
t, r, g End of life products Recycling
t, r, g End of life products Exports
t, r, g Imports End of life products
t, r, g Recycling Scrap market
t, r Scrap market Excess scrap
t, r Exports System environment
t, r System environment Imports
t, r Losses System environment
t, r System environment Ore Extraction

Flows that enter or leave markets are the exports and imports of the trades listed in the following table.

Dimensions Name
t, r steel
t, r, g Indirect (Goods)
t, r, g Scrap

Parameters

The following table presents all exogenous parameters in the steel MFA with their respective dimensions and the sources of the respective input data. If no input data source is specified, the parameter is currently estimated based on expert judgement.

Dimensions Name Description Sources
nan forming_yield Yield of steel forming process (Cullen et al., 2012)1
g fabrication_yield Yield during fabrication of steel-containing final goods (Cullen et al., 2012)1
g recovery_rate Combined collection and recovery rate at end-of-life - share of all end-of life material that is recycled (World Steel Association, 2025)2, (World Steel Association, 2021)3
t, r population Population (International Monetary Fund, 2021)4, (India Department of Economic Affairs, n.d.)5, (India Ministry of Health, 2019)6, (IIASA, 2024)7, (James et al., 2012)8, (Arujo et al., 2021)9, (World Bank, 2023a)10, (IIASA, 2024)7, (Crespo Cuaresma, 2017)11, (Dellink et al., 2017)12, (KC et al., 2024)13, (United Nations, Department on Economic and Social Affairs, Population Division, 2022)14, (World Bank, 2023b)15, (Gapminder, n.d.)16, (James et al., 2012)8, (Bolt et al., 2014)17
t, r gdppc GDP per capita (International Monetary Fund, 2021)4, (India Department of Economic Affairs, n.d.)5, (India Ministry of Health, 2019)6, (IIASA, 2024)7, (James et al., 2012)8, (Arujo et al., 2021)9, (World Bank, 2023a)10, (IIASA, 2024)7, (Crespo Cuaresma, 2017)11, (Dellink et al., 2017)12, (KC et al., 2024)13, (United Nations, Department on Economic and Social Affairs, Population Division, 2022)14, (World Bank, 2023b)15, (Gapminder, n.d.)16, (Bolt et al., 2014)17, (James et al., 2012)8, (Bolt et al., 2014)17
g lifetime_mean Mean lifetime of goods (Cooper & Allwood, 2012)18
g lifetime_std Absolute standard deviation of good lifetime (Cooper & Allwood, 2012)18
g sector_split_low Final good category shares in consumption for low gdp per capita (Pauliuk et al., 2013)19
g sector_split_medium Final good category shares in consumption for medium gdp per capita
g sector_split_high Final good category shares in consumption for high gdp per capita (Pauliuk et al., 2013)19
nan secsplit_gdppc_low Upper GDP per capita threshold for sector_split_low
nan secsplit_gdppc_high Lower GDP per capita threshold for sector_split_high
nan scrap_in_bof_rate Share of scrap-based steel from BF-BOF production
nan forming_loss_rate Loss rate in forming process. Contrary to (1-forming_yield), this material is completely lost and not recycled as home scrap (Cullen et al., 2012)1
nan fabrication_losses Loss rate during fabrication of final goods. Contrary to (1-fabrication_yield), this material is completely lost and not recycled as new scrap
nan production_loss_rate Loss rate of raw steel production in BF-BOF and (DRI-)EAF processes (Cullen et al., 2012)1
r saturation_level_factor Regional multiplicative adjustment factor for the saturation level of the in-use steel stock based on expert judgement
r stock_growth_speed_factor Regional adjustment factor for the growth speed of the in-use steel stock based on expert judgement
h, r scrap_consumption Historic scrap consumption (Bureau of International Recycling AISBL, 2009--2023)20, (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r production Historic steel production (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r steel_imports Historic steel imports (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r steel_exports Historic steel exports (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r, g indirect_imports Historic indirect trade imports, i.e. contained in final goods (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r, g indirect_exports Historic indirect trade exports, i.e. contained in final goods (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r scrap_imports Historic combined eol product and scrap imports (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23
h, r scrap_exports Historic combined eol product and scrap exports (World Steel Association, 2023)21, (World Steel Association, 1978--2023)22, (World Steel Association, 2002--2025)23

  1. Cullen, J. M., Allwood, J. M., & Bambach, M. D. (2012). Mapping the Global Flow of Steel: From Steelmaking to End-Use Goods. Environmental Science\ & Technology, 46(24), 13048--13055. https://doi.org/10.1021/es302433p ↩↩↩↩

  2. World Steel Association. (2025). [Raw materials]{.nocase}. World Steel Association AISBL. https://worldsteel.org/other-topics/raw-materials ↩

  3. World Steel Association. (2021). Scrap use in the steel industry: Fact sheet. World Steel Association AISBL. https://worldsteel.org/wp-content/uploads/Fact-sheet-on-scrap\_2021.pdf ↩

  4. International Monetary Fund. (2021). World Economic Outlook database of the IMF. https://www.imf.org/-/media/Files/Publications/WEO/WEO-Database/2021/WEOOct2021all.ashx ↩↩

  5. India Department of Economic Affairs. (n.d.). Department of Economic Affairs (DEA) projections FY 2024-25 to FY 2047-48. ↩↩

  6. India Ministry of Health. (2019). PopulationProjections for India and States 2011 -- 2036. https://nhm.gov.in/New\_Updates\_2018/Report\_Population\_Projection\_2019.pdf ↩↩

  7. IIASA. (2024). Socioeconomic Projections of the Shared Socioeconomic Pathways (SSPs), hosted by IIASA. SSP Scenario Explorer hosted by IIASA. https://data.ece.iiasa.ac.at/ssp ↩↩↩↩

  8. James, S. L., Gubbins, P., Murray, C. J., & Gakidou, E. (2012). Developing a comprehensive time series of GDP per capita for 210 countries from 1950 to 2015. Population Health Metrics, 10(1), 12. https://doi.org/10.1186/1478-7954-10-12 ↩↩↩↩

  9. Arujo, E., Bodirsky, B. L., Crawford, M. S., Leip, D., & Dietrich, J. (2021). MissingIslands dataset for filling in data gaps from the WDI datasets. Zenodo. https://doi.org/10.5281/ZENODO.4421504 ↩↩

  10. World Bank. (2023a). Population Estimates and Projections by the World Bank 1960-2050. ↩↩

  11. Crespo Cuaresma, J. (2017). Income projections for climate change research: A framework based on human capital dynamics. Global Environmental Change, 42, 226--236. https://doi.org/10.1016/j.gloenvcha.2015.02.012 ↩↩

  12. KC, S., Moradhvaj, Potancokova, M., Adhikari, S., Yildiz, D., Mamolo, M., Sobotka, T., Zeman, K., Abel, G., Lutz, W., & Goujon, A. (2024). Wittgenstein Center (WIC) Population and Human Capital Projections - 2023. Zenodo. https://doi.org/10.5281/ZENODO.7767425 ↩↩

  13. United Nations, Department on Economic and Social Affairs, Population Division. (2022). World Population Prospects 2022. https://www.un.org/development/desa/pd/content/World-Population-Prospects-2022 ↩↩

  14. World Bank. (2023b). Select indicators from the World Development Indicators database from the World Bank. ↩↩

  15. Gapminder. (n.d.). Population. Retrieved December 16, 2025, from https://www.gapminder.org/data/documentation/gd003/ ↩↩

  16. Bolt, J., Timmer, M., & Van Zanden, J. L. (2014). GDP per capita since 1820. In How was life?: Global well-being since 1820. OECD. https://doi.org/10.1787/9789264214262-en ↩↩↩

  17. Cooper, D. R., & Allwood, J. M. (2012). Reusing Steel and Aluminum Components at End of Product Life. Environmental Science\ & Technology, 46(18), 10334--10340. https://doi.org/10.1021/es301093a ↩↩

  18. Pauliuk, S., Milford, R. L., Müller, D. B., & Allwood, J. M. (2013). The Steel Scrap Age. Environmental Science\ & Technology, 47(7), 3448--3454. https://doi.org/10.1021/es303149z ↩↩

  19. Bureau of International Recycling AISBL, F. D. (2009--2023). World steel recycling in figures: Recycled steel -- a raw material for green steelmaking. Bureau of International Recycling. https://www.bir.org/en/publications/facts-figures ↩

  20. World Steel Association. (2023). Steel statistical yearbook 2023. World Steel Association AISBL. https://worldsteel.org/wp-content/uploads/Steel-Statistical-Yearbook-2023.pdf ↩↩↩↩↩↩↩↩

  21. World Steel Association. (1978--2023). Steel statistical yearbook. World Steel Association AISBL. https://worldsteel.org/media/publications/ ↩↩↩↩↩↩↩↩

  22. World Steel Association. (2002--2025). World steel in figures. World Steel Association AISBL. https://worldsteel.org/media/publications/ ↩↩↩↩↩↩↩↩