Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Spaces of anthropogenic CO2 emissions compatible with climate boundaries

Nature Climate Change volume 15, pages 1307–1314 (2025)Cite this article

Subjects

Abstract

Climate boundaries are planetary boundaries for the climate system: limits within which humanity can sustainably prosper. Here we introduce a modelling framework to analyse global warming, ocean acidification, sea-level rise and Arctic sea-ice melt. Using a reduced-form model, we map out anthropogenic CO2 emissions, carbon dioxide removal and solar radiation management pathways compatible with these boundaries. We define safety levels as the probability to stay within one or several boundaries considering physical uncertainty. If CO2 emissions peak in 2030, net-zero CO2 is reached in 2050, and carbon dioxide removal capacity is 10 PgC yr−1, without solar radiation management, remaining within the global warming boundary of 2 °C exhibits a safety level of 80%. When all four boundaries are considered together, the safety level drops to 35%. Our results highlight key trade-offs in mitigation options and suggest a need to assess climate boundaries holistically to develop sustainable future strategies.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Overview of the inverse framework applied in this study.
Fig. 2: Safety levels of compatible spaces defined by various combinations of conditions on pathway characteristics.
Fig. 3: Trade-offs between pathway characteristics at the 67% safety level.
Fig. 4: Trade-offs between pathway characteristics at the 67% safety level.

Similar content being viewed by others

Data availability

No raw data are provided with this article because of the total size (>500 GB). However, we provide a code to generate this data.

Code availability

The source code of Pathfinder is openly available at https://github.com/tgasser/Pathfinder (last accessed 16 October 2023). A frozen version of the code as developed in the paper is available via Zenodo at https://doi.org/10.5281/zenodo.7003848 (ref. 71). Additional code and data are available via Zenodo at https://doi.org/10.5281/zenodo.15235819 (ref. 72). This contains the code to reproduce the input trajectories of Pathfinder as well as some examples of post-processing.

References

  1. Rockström, J. et al. Planetary boundaries: exploring the safe operating space for humanity. Ecol. Soc. 14, art32 (2009).

    Article  Google Scholar 

  2. Steffen, W. et al. Planetary boundaries: guiding human development on a changing planet. Science 347, 1259855 (2015).

    Article  Google Scholar 

  3. Richardson, K. et al. Earth beyond six of nine planetary boundaries. Sci. Adv. 9, eadh2458 (2023).

    Article  Google Scholar 

  4. Lade, S. J. et al. Human impacts on planetary boundaries amplified by Earth system interactions. Nat. Sustain. 3, 119–128 (2019).

    Article  Google Scholar 

  5. Schulte-Uebbing, L. F., Beusen, A. H. W., Bouwman, A. F. & De Vries, W. From planetary to regional boundaries for agricultural nitrogen pollution. Nature 610, 507–512 (2022).

    Article  CAS  Google Scholar 

  6. Bouwman, L. et al. Exploring global changes in nitrogen and phosphorus cycles in agriculture induced by livestock production over the 1900–2050 period. Proc. Natl Acad. Sci. USA 110, 20882–20887 (2013).

    Article  CAS  Google Scholar 

  7. Mekonnen, M. M. & Hoekstra, A. Y. Global anthropogenic phosphorus loads to freshwater and associated grey water footprints and water pollution levels: a high-resolution global study. Water Resour. Res. 54, 345–358 (2018).

    Article  CAS  Google Scholar 

  8. Rogelj, J. et al. Scenarios towards limiting global mean temperature increase below 1.5 °C. Nat. Clim. Change 8, 325–332 (2018).

    Article  CAS  Google Scholar 

  9. Rogelj, J. et al. A new scenario logic for the Paris Agreement long-term temperature goal. Nature 573, 357–363 (2019).

    Article  CAS  Google Scholar 

  10. Lamboll, R. D. et al. Assessing the size and uncertainty of remaining carbon budgets. Nat. Clim. Change 13, 1360–1367 (2023).

    Article  Google Scholar 

  11. Lade, S. J., Fetzer, I., Cornell, S. E. & Crona, B. A prototype Earth system impact metric that accounts for cross-scale interactions. Environ. Res. Lett. 16, 115005 (2021).

    Article  Google Scholar 

  12. Chrysafi, A. et al. Quantifying Earth system interactions for sustainable food production via expert elicitation. Nat. Sustain. 5, 830–842 (2022).

    Article  Google Scholar 

  13. IPCC Climate Change 2021: The Physical Science Basis (eds Masson-Delmotte, V. et al.) (Cambridge Univ. Press, 2023).

  14. Mengel, M. et al. Future sea level rise constrained by observations and long-term commitment. Proc. Natl Acad. Sci. USA 113, 2597–2602 (2016).

    Article  CAS  Google Scholar 

  15. Pfleiderer, P. et al. Reversal of the impact chain for actionable climate information. Nat. Geosci. 18, 10–19 (2025).

  16. Bossy, T., Gasser, T. & Ciais, P. Pathfinder v1.0.1: a Bayesian-inferred simple carbon–climate model to explore climate change scenarios. Geosci. Model Dev. 15, 8831–8868 (2022).

    Article  CAS  Google Scholar 

  17. Gasser, T., Guivarch, C., Tachiiri, K., Jones, C. D. & Ciais, P. Negative emissions physically needed to keep global warming below 2 °C. Nat. Commun. 6, 7958 (2015).

    Article  CAS  Google Scholar 

  18. Byers, E. et al. AR6 Scenario Explorer and Database Hosted by IIASA (International Institute for Applied Systems Analysis, 2022); https://data.ece.iiasa.ac.at/ar6

  19. IPCC Special Report on Impacts of Global Warming of 1.5°C (eds Masson-Delmotte, V. et al.) (Cambridge Univ. Press, 2022).

  20. Niederdrenk, A. L. & Notz, D. Arctic sea ice in a 1.5 °C warmer world. Geophys. Res. Lett. 45, 1963–1971 (2018).

    Article  Google Scholar 

  21. Gattuso, J.-P. et al. Contrasting futures for ocean and society from different anthropogenic CO2 emissions scenarios. Science 349, aac4722 (2015).

    Article  Google Scholar 

  22. Kvale, K. et al. Carbon dioxide emission pathways avoiding dangerous ocean impacts. Weather Clim. Soc. 4, 212–229 (2012).

    Article  Google Scholar 

  23. Schubert, R. et al. The Future Oceans—Warming Up, Rising High, Turning Sour (WBGU, 2006).

  24. Mastrandrea, M. D. et al. The IPCC AR5 guidance note on consistent treatment of uncertainties: a common approach across the working groups. Clim. Change 108, 675–691 (2011).

    Article  Google Scholar 

  25. Babiker, M. et al. in Climate Change 2022: Mitigation of Climate Change (eds Shukla, P. R. et al.) Ch. 12 (Cambridge Univ. Press, 2022).

  26. Grubb, M., Wieners, C. & Yang, P. Modeling myths: on DICE and dynamic realism in integrated assessment models of climate change mitigation. WIREs Clim. Change 12, e698 (2021).

  27. Pindyck, R. S. The use and misuse of models for climate policy. Rev. Environ. Econ. Policy 11, 100–114 (2017).

    Article  Google Scholar 

  28. Bossy, T. et al. Least-cost and 2 °C-compliant mitigation pathways robust to physical uncertainty, economic paradigms, and intergenerational cost distribution. Environ. Res. Clim. 3, 025005 (2024).

    Article  Google Scholar 

  29. Tokarska, K. B. & Zickfeld, K. The effectiveness of net negative carbon dioxide emissions in reversing anthropogenic climate change. Environ. Res. Lett. 10, 094013 (2015).

    Article  Google Scholar 

  30. Obersteiner, M. et al. How to spend a dwindling greenhouse gas budget. Nat. Clim. Change 8, 7–10 (2018).

    Article  Google Scholar 

  31. Aengenheyster, M., Feng, Q. Y., Van Der Ploeg, F. & Dijkstra, H. A. The point of no return for climate action: effects of climate uncertainty and risk tolerance. Earth Syst. Dynam. 9, 1085–1095 (2018).

    Article  Google Scholar 

  32. Duarte, C. M. et al. Is ocean acidification an open-ocean syndrome? Understanding anthropogenic impacts on seawater pH. Estuaries Coasts 36, 221–236 (2013).

    Article  CAS  Google Scholar 

  33. Doney, S. C. et al. Impact of anthropogenic atmospheric nitrogen and sulfur deposition on ocean acidification and the inorganic carbon system. Proc. Natl Acad. Sci. USA 104, 14580–14585 (2007).

    Article  CAS  Google Scholar 

  34. Visioni, D., Pitari, G. & Aquila, V. Sulfate geoengineering: a review of the factors controlling the needed injection of sulfur dioxide. Atmos. Chem. Phys. 17, 3879–3889 (2017).

    Article  CAS  Google Scholar 

  35. Allen, M. R. et al. Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458, 1163–1166 (2009).

    Article  CAS  Google Scholar 

  36. Van Soest, H. L., Den Elzen, M. G. J. & Van Vuuren, D. P. Net-zero emission targets for major emitting countries consistent with the Paris Agreement. Nat. Commun. 12, 2140 (2021).

    Article  Google Scholar 

  37. Bruckner, T. et al. Climate system modeling in the framework of the tolerable windows approach: the ICLIPS climate model. Clim. Change 56, 119–137 (2003).

  38. Petschel-Held, G. et al. Tolerable windows approach: theoretical and methodological foundations. Clim. Change 41, 303–331 (1999).

  39. Zickfeld, K. & Bruckner, T. Reducing the risk of Atlantic thermohaline circulation collapse: sensitivity analysis of emissions corridors. Clim. Change 91, 291–315 (2008).

    Article  CAS  Google Scholar 

  40. Stocker, T. F. The closing door of climate targets. Science 339, 280–282 (2013).

    Article  CAS  Google Scholar 

  41. Steinacher, M., Joos, F. & Stocker, T. F. Allowable carbon emissions lowered by multiple climate targets. Nature 499, 197–201 (2013).

    Article  CAS  Google Scholar 

  42. Rockström, J. et al. Safe and just Earth system boundaries. Nature 619, 102–111 (2023).

  43. Riahi, K. et al. The Shared Socioeconomic Pathways and their energy, land use, and greenhouse gas emissions implications: an overview. Glob. Environ. Change 42, 153–168 (2017).

    Article  Google Scholar 

  44. MacDougall, A. H. et al. Is there warming in the pipeline? A multi-model analysis of the Zero Emissions Commitment from CO2. Biogeosciences 17, 2987–3016 (2020).

    Article  Google Scholar 

  45. Ricciuto, D. M., Davis, K. J. & Keller, K. A Bayesian calibration of a simple carbon cycle model: the role of observations in estimating and reducing uncertainty. Glob. Biogeochem. Cycles 22, 2006GB002908 (2008).

    Article  Google Scholar 

  46. Geoffroy, O. et al. Transient climate tesponse in a two-layer energy-balance model. Part II: representation of the efficacy ofdeep-ocean heat uptake and validation for CMIP5 AOGCMs. J. Clim. 26, 1859–1876 (2013).

    Article  Google Scholar 

  47. Myhre, G. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 659–740 (IPCC, Cambridge Univ. Press, 2014).

  48. Strassmann, K. M., Joos, F. & Strassmann, K. The Bern Simple Climate Model (BernSCM) v1.0: an extensible and fully documented open-source re-implementation of the Bern reduced-form model for global carbon cycle–climate simulations. Geosci. Model Dev. 11, 1887–1908 (2018).

  49. Gasser, T. et al. The compact Earth system model OSCAR v2.2: description and first results. Geosci. Model Dev. 10, 271–319 (2017).

    Article  CAS  Google Scholar 

  50. He, Y. et al. Radiocarbon constraints imply reduced carbon uptake by soils during the 21st century. Science 353, 1419–1424 (2016).

    Article  CAS  Google Scholar 

  51. Gasser, T. et al. Path-dependent reductions in CO2 emission budgets caused by permafrost carbon release. Nat. Geosci. 11, 830–835 (2018).

    Article  CAS  Google Scholar 

  52. Goodwin, P. et al. Pathways to 1.5 °C and 2 °C warming based on observational and geological constraints. Nat. Geosci. 11, 102–107 (2018).

    Article  CAS  Google Scholar 

  53. Bernie, D., Lowe, J., Tyrrell, T. & Legge, O. Influence of mitigation policy on ocean acidification. Geophys. Res. Lett. 37, 2010GL043181 (2010).

    Article  Google Scholar 

  54. Cowtan, K. & Way, R. G. Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends. Q. J. R. Meteorol. Soc. 140, 1935–1944 (2014).

    Article  Google Scholar 

  55. Morice, C. P., Kennedy, J. J., Rayner, N. A. & Jones, P. D. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HadCRUT4 data set. J. Geophys. Res. Atmos. 117, 2011JD017187 (2012).

    Article  Google Scholar 

  56. Rohde, R., Muller, R., Jacobsen, R., Perlmutter, S. & Mosher, S. Berkeley Earth temperature averaging process. Geoinform. Geostat. Overv. https://doi.org/10.4172/2327-4581.1000103 (2013).

  57. Hansen, J., Ruedy, R., Sato, M. & Lo, K. Global surface temperature change. Rev. Geophys. 48, RG4004 (2010).

    Article  Google Scholar 

  58. Smith, T. M., Reynolds, R. W., Peterson, T. C. & Lawrimore, J. Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006). J. Clim. 21, 2283–2296 (2008).

    Article  Google Scholar 

  59. Bindoff, N. L. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 867–952 (IPCC, Cambridge Univ. Press, 2014).

  60. Friedlingstein, P. et al. Global Carbon Budget 2023. Earth Syst. Sci. Data 15, 5301–5369 (2023).

  61. Ciais, P. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 867–952 (IPCC, Cambridge Univ. Press, 2014).

  62. Church, J. A. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 1137–1216 (IPCC, Cambridge Univ. Press, 2014).

  63. Kucukelbir, A. Automatic differentiation variational inference. J. Mach. Learn. Res. 18, 430–474 (2017).

    Google Scholar 

  64. Huntingford, C. et al. Flexible parameter-sparse global temperature time profiles that stabilise at 1.5 and 2.0 °C. Earth Syst. Dynam. 8, 617–626 (2017).

    Article  Google Scholar 

  65. Kumaraswamy, P. A generalized probability density function for double-bounded random processes. J. Hydrol. 46, 79–88 (1980).

    Article  Google Scholar 

  66. Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c. By Benjamin Gompertz, Esq. F. R. S. Proc. R. Soc. Lond. 2, 252–253 (1833).

  67. Salvatier, J., Wiecki, T. V. & Fonnesbeck, C. Probabilistic programming in Python using PyMC3. PeerJ Comput. Sci. 2, e55 (2016).

    Article  Google Scholar 

  68. Forster, P. et al. in Climate Change 2021: The Physical Science Basis (eds Masson-Delmotte, V. et al.) 923–1054 (IPCC, Cambridge Univ. Press, 2021).

  69. Gidden, M. J. et al. Aligning climate scenarios to emissions inventories shifts global benchmarks. Nature 624, 102–108 (2023).

    Article  CAS  Google Scholar 

  70. Ou, Y. et al. Can updated climate pledges limit warming well below 2 °C? Science 374, 693–695 (2021).

    Article  CAS  Google Scholar 

  71. Gasser, T. Pathfinder: v1.0.1. Zenodo https://doi.org/10.5281/zenodo.7003848 (2022).

  72. Bossy, T. & Gasser, T. Code for ‘Spaces of anthropogenic CO2 emissions compatible with climate boundaries’. Zenodo https://doi.org/10.5281/zenodo.15235819 (2025).

Download references

Author information

Authors and Affiliations

  1. Laboratoire des sciences du climat et de l’environnement (LSCE), IPSL, CEA/CNRS/UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France

    Thomas Bossy, Philippe Ciais, Katsumasa Tanaka, Philippe Bousquet & Thomas Gasser

  2. International Institute for Applied System Analysis (IIASA), Laxenburg, Austria

    Thomas Bossy & Thomas Gasser

  3. Earth System Division, National Institute for Environmental Studies (NIES), Tsukuba, Japan

    Katsumasa Tanaka

  4. Centre International de Recherche sur l’Environnement et le Développement (CIRED), CNRS, EHESS, AgroParisTech, PontsParisTech, CIRAD, Nogent-sur-Marne, France

    Franck Lecocq

Authors
  1. Thomas Bossy
    View author publications

    Search author on:PubMed Google Scholar

  2. Philippe Ciais
    View author publications

    Search author on:PubMed Google Scholar

  3. Katsumasa Tanaka
    View author publications

    Search author on:PubMed Google Scholar

  4. Franck Lecocq
    View author publications

    Search author on:PubMed Google Scholar

  5. Philippe Bousquet
    View author publications

    Search author on:PubMed Google Scholar

  6. Thomas Gasser
    View author publications

    Search author on:PubMed Google Scholar

Contributions

T.G. designed the research following a discussion with F.L. T.B. performed the research and wrote the original draft. T.B., P.C., K.T., F.L., P.B. and T.G. discussed the research and edited the paper.

Corresponding author

Correspondence to Thomas Gasser.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Climate Change thanks Kalyn Dorheim, Robin Lamboll and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Trade-offs between year of emissions peak and CDR characteristics.

Panel a) shows the trade-offs between the date of emissions peak and the total amount of CDR needed before 2100, for a 67% safety level. Panels b) shows the trade-offs interaction between the year when CDR is deployed at large scale (more than 0.5 PgC.yr−1) and the year of peak emission for a 67% safety level. Shaded areas represent the spaces compatible with climate boundaries. Plain lines give the frontier of the compatible space. Black is for the GW boundary, green for the OA boundary, red for the RSLR boundary, blue for the ASI boundary, and purple for the combination all boundaries.

Extended Data Fig. 2 Trade-offs between SRM and CDR characteristics.

Trade-offs between available CDR and allowed SRM in the case of a peak of CO2 emission in 2030 for a 67% safety level. Shaded areas represent the spaces compatible with climate boundaries. Plain lines give the frontier of the compatible space. Black is for the GW boundary, green for the OA boundary, red for the RSLR boundary, blue for the ASI boundary, and purple for the combination all boundaries.

Supplementary information

Supplementary Information

Supplementary Text, Table 1 and Figs. 1–6.

Reporting Summary

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bossy, T., Ciais, P., Tanaka, K. et al. Spaces of anthropogenic CO2 emissions compatible with climate boundaries. Nat. Clim. Chang. 15, 1307–1314 (2025). https://doi.org/10.1038/s41558-025-02460-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41558-025-02460-5

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing