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

    Article 

    Google Scholar
     

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

    Article 

    Google Scholar
     

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

    Article 

    Google Scholar
     

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

    Article 

    Google Scholar
     

  • 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
     

  • 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
     

  • 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
     

  • 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
     

  • 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
     

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

    Article 

    Google Scholar
     

  • 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
     

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

    Article 

    Google Scholar
     

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

  • 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
     

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

  • 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
     

  • 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
     

  • 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

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

  • 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
     

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

    Article 

    Google Scholar
     

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

    Article 

    Google Scholar
     

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

  • 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
     

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

  • 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).

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

    Article 

    Google Scholar
     

  • 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
     

  • 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
     

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

    Article 

    Google Scholar
     

  • 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
     

  • 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
     

  • 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
     

  • 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
     

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

    Article 
    CAS 

    Google Scholar
     

  • 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
     

  • 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).

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

  • 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
     

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

    Article 
    CAS 

    Google Scholar
     

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

    Article 
    CAS 

    Google Scholar
     

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

  • 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
     

  • 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
     

  • 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
     

  • 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
     

  • 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).

  • 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).

  • 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
     

  • 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
     

  • 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
     

  • 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
     

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

    Article 

    Google Scholar
     

  • 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
     

  • 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
     

  • 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).

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

    Article 

    Google Scholar
     

  • 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
     

  • 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).

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

  • 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).

  • 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).

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


    Google Scholar
     

  • 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
     

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

    Article 

    Google Scholar
     

  • 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).

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

    Article 

    Google Scholar
     

  • 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).

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

    Article 
    CAS 

    Google Scholar
     

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

    Article 
    CAS 

    Google Scholar
     

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

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