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Modelling human–natural systems interactions with implications for twenty-first-century warming


The redesign of energy and economic systems to stabilize climate change is hindered by the lack of quantitative treatment of the role that human–natural systems interactions play in what society can do to tackle climate change. Here we present an integrated socio–energy–ecologic–climate model framework for understanding the role of human–natural systems interactions in climate change. We focus on constraints on climate stabilization imposed by feedbacks between global warming and societal actions to decarbonize energy use and to scale up atmospheric-carbon extraction. The energy–climate feedbacks are modelled through four warming-dependent response times for societal, policy and technological actions inferred from historical data. We show that a lack of societal response beyond 2030 would result in a warming in excess of 3 °C. Speeding up societal response times and technology diffusion times by a factor of two along with a dramatic boost in start-up investment in renewables and atmospheric-carbon extraction technologies and short-lived climate pollutants mitigation by 2030 can stabilize the warming below 1.5 °C. The model’s analytical framework and the analyses presented here reveal the fundamental importance of factoring in the role of human–natural systems interactions in the transition to zero emissions when formulating and designing robust climate solutions.

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Fig. 1: A schematic of the ISEEC framework: NSM and SSM.
Fig. 2: ISEEC validation for the historical period showing simulated energy use, CO2 emissions, CO2 concentration and temperature.
Fig. 3: Comparison of ISEEC simulations with published IAM studies for the twenty-first centur y.
Fig. 4: PE and CO2 emission in ISEEC, with and without the two-way human–nature coupling.
Fig. 5: Two-way human–nature responses required for a safer climate.

Data availability

The data from external sources are available as detailed in Methods. The data generated by ISEEC as shown in tables and figures are available from the corresponding authors upon request.

Code availability

The modelling codes in Python are available from the corresponding authors upon request.


  1. IPCC Special Report on Global Warming of 1.5°C. (eds Masson-Delmotte, V. et al.) (WMO, 2018).

  2. Jackson, R. B. et al. Persistent fossil fuel growth threatens the Paris Agreement and planetary health. Environ. Res. Lett. 14, 121001 (2019).

    CAS  Article  Google Scholar 

  3. Davis, S. J. et al. Net-zero emissions energy systems. Science 360, eaas9793 (2018).

    Article  Google Scholar 

  4. Banerjee, R. et al. in Global Energy Assessment: Toward a Sustainable Future (eds Johansson, T. B. et al.) 3–93 (Cambridge Univ. Press, 2012);

  5. Liu, J. et al. Systems integration for global sustainability. Science 347, 1258832 (2015).

    Article  Google Scholar 

  6. Otto, I. M. et al. Social tipping dynamics for stabilizing Earth’s climate by 2050. Proc. Natl Acad. Sci. USA 117, 2354–2365 (2020).

    CAS  Article  Google Scholar 

  7. Janssen, M. & de Vries, B. The battle of perspectives: a multi-agent model with adaptive responses to climate change. Ecol. Econ. 26, 43–65 (1998).

    Article  Google Scholar 

  8. Beckage, B. et al. Linking models of human behavior and climate alters projected climate change. Nat. Clim. Change 8, 79–84 (2018).

    Article  Google Scholar 

  9. Lamperti, F. et al. Towards agent-based integrated assessment models: examples, challenges, and future developments. Reg. Environ. Change 19, 747–762 (2019).

    Article  Google Scholar 

  10. Tàbara, J. D. et al. Positive tipping points in a rapidly warming world. Curr. Opin. Environ. Sustain. 31, 120–129 (2018).

    Article  Google Scholar 

  11. Rozenberg, J., Davis, S. J., Narloch, U. & Hallegatte, S. Climate constraints on the carbon intensity of economic growth. Environ. Res. Lett. 10, 095006 (2015).

    Article  Google Scholar 

  12. Agarwala, M. & Coyle, D. Natural capital in climate models. Nat. Sustain 4, 81–82 (2021).

    Article  Google Scholar 

  13. Woodard, D. L., Davis, S. J. & Randerson, J. T. Economic carbon cycle feedbacks may offset additional warming from natural feedbacks. Proc. Natl Acad. Sci. USA 116, 759–764 (2019).

    CAS  Article  Google Scholar 

  14. Arneth, A., Brown, C. & Rounsevell, M. D. A. Global models of human decision-making for land-based mitigation and adaptation assessment. Nat. Clim. Change 4, 550–557 (2014).

    Article  Google Scholar 

  15. Bond-Lamberty, B. et al. On linking an Earth system model to the equilibrium carbon representation of an economically optimizing land use model. Geosci. Model Dev. 7, 2545–2555 (2014).

    Article  Google Scholar 

  16. Collins, W. D. et al. The integrated Earth system model version 1: formulation and functionality. Geosci. Model Dev. 8, 2203–2219 (2015).

    Article  Google Scholar 

  17. Clarke, L. et al. in Climate Change 2014: Mitigation of Climate Change (eds Edenhofer, O. et al.) Ch. 6 (Cambridge Univ. Press, 2014).

  18. Peng, W. et al. Climate policy models need to get real about people—here’s how. Nature 594, 174–176 (2021).

    CAS  Article  Google Scholar 

  19. Calvin, K. & Bond-Lamberty, B. Integrated human–Earth system modeling—state of the science and future directions. Environ. Res. Lett. 13, 063006 (2018).

    Article  Google Scholar 

  20. Ramanathan, V. & Xu, Y. The Copenhagen Accord for limiting global warming: criteria, constraints, and available avenues. Proc. Natl Acad. Sci. USA 107, 8055–8062 (2010).

    CAS  Article  Google Scholar 

  21. Xu, Y. & Ramanathan, V. Well below 2 °C: mitigation strategies for avoiding dangerous to catastrophic climate changes. Proc. Natl Acad. Sci. USA 114, 10315–10323 (2017).

    CAS  Article  Google Scholar 

  22. Sanderson, B. M. et al. Community climate simulations to assess avoided impacts in 1.5 and 2 °C futures. Earth Syst. Dyn. 8, 827–847 (2017).

    Article  Google Scholar 

  23. Chen, J., Cui, H., Xu, Y. & Ge, Q. An investigation of parameter sensitivity of minimum complexity Earth simulator. Atmosphere 11, 95 (2020).

    CAS  Article  Google Scholar 

  24. Hanna, R., Abdulla, A., Xu, Y. & Victor, D. Emergency deployment of direct air capture as a response to the climate crisis. Nat. Commun. 12, 368 (2021).

    CAS  Article  Google Scholar 

  25. Fuss, S. et al. Negative emissions—Part 2: Costs, potentials and side effects. Environ. Res. Lett. 13, 063002 (2018).

    Article  Google Scholar 

  26. Renewables 2019: Global Status Report (REN21, 2019);

  27. Accelerating Decarbonization in the United States: Technology, Policy, and Societal Dimensions (National Academies, 2021).

  28. Lee, S. Y., Lei, B. & Mallick, B. Estimation of COVID-19 spread curves integrating global data and borrowing information. PLoS ONE 15, e0236860 (2020).

    CAS  Article  Google Scholar 

  29. Ayres, R. U. Self-organization in Biology and Economics (IIASA, 1988);

  30. International Energy Outlook 2019 (EIA, 2019).

  31. World Energy Outlook 2020 (IEA, 2020);

  32. Bloomberg, M. R. et al. From Risk to Return: Investing in a Clean Energy Economy (Risky Business, 2016);

  33. Warszawski, L. et al. All options, not silver bullets, needed to limit global warming to 1.5 °C: a scenario appraisal. Environ. Res. Lett. 16, 064037 (2021).

    CAS  Article  Google Scholar 

  34. Houghton, R. A. & Nassikas, A. A. Global and regional fluxes of carbon from land use and land cover change 1850-2015. Glob. Biogeochem. Cycles 31, 456–472 (2017).

    CAS  Article  Google Scholar 

  35. Popp, A. et al. Land-use futures in the shared socio-economic pathways. Glob. Environ. Change 42, 331–345 (2017).

    Article  Google Scholar 

  36. Heidorn, K. C. A chronology of important events in the history of air pollution meteorology to 1970. Bull. Am. Meteorol. Soc. 59, 1589–1597 (1978).

    Article  Google Scholar 

  37. Summary of the Clean Air Act, 42 U.S.C. §7401 et seq. (EPA, 1970);

  38. Lelieveld, K. et al. Effects of fossil fuel and total anthropogenic emission removal on public health and climate. Proc. Natl Acad. Sci. USA (2019).

  39. Molina, M. & Rowland, F. Stratospheric sink for chlorofluoromethanes: chlorine atom-catalysed destruction of ozone. Nature 249, 810–812 (1974).

    CAS  Article  Google Scholar 

  40. The Montreal Protocol on Substances that Deplete the Ozone Layer (UNEP, 1987);

  41. Arrhenius, S. On the influence of carbonic acid in the air upon the temperature of the ground. Philos. Mag. J. Sci. 41, 237–276 (1896).

    CAS  Article  Google Scholar 

  42. Callendar, G. S. The artificial production of carbon dioxide and its influence on temperature. Q. J. R. Meteorol. Soc. 64, 223–240 (1938).

    Article  Google Scholar 

  43. Manabe, S. & Wetherald, R. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci. 24, 241–259 (1967).

    CAS  Article  Google Scholar 

  44. Ramanathan, V. Greenhouse effect due to chlorofluorocarbons: climatic implications. Science 190, 50–51 (1975).

    CAS  Article  Google Scholar 

  45. SMIC (ed.) Inadvertent Climate Modification: Report of the Study of Man’s Impact on Climate (SMIC) (MIT Press, 1971);

  46. Kyoto Protocol of the United Nations Framework Convention on Climate Change (UNFCCC, 1998);

  47. The Paris Agreement (UNFCCC, 2015);

  48. Shahan, Z. History of wind turbines. Renewable Energy World (2014).

  49. History of the catalytic converter. Catalytic Converters (2020).

  50. Flatow, I. Fifty years ago, a bright idea. NPR (2012).

  51. The Light Bulb Revolution (Energy Star, 2017);

  52. Ritchie, H. & Roser, M. Technology adoption. Our World In Data (2017).

  53. Keywan, R. 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 

  54. Dellink, R., Chateau, J., Lanzi, E. & Magné, B. Long-term economic growth projections in the shared socioeconomic pathways. Glob. Environ. Change 42, 200–214 (2017).

    Article  Google Scholar 

  55. Data and Statistics (IEA);; (accessed in Nov 16, 2021)

  56. Statistical Review of World Energy (BP, 2021);

  57. Le Quéré, C. et al. Global carbon budget 2018. Earth Syst. Sci. Data 10, 2141–2194 (2018).

    Article  Google Scholar 

  58. Keeling, R. F., Piper, S. C., Bollenbacher, A. F. & Walker, S. J. Scripps CO2 Program (Scripp’s Institution of Oceanography); (accessed in Nov 16, 2021)

  59. Diao, C., Xu, Y. & Xie, S.-P. Anthropogenic aerosol effects on tropospheric circulation and sea surface temperature (1980–2020): separating the role of zonally asymmetric forcings. Atmos. Chem. Phys. (2021).

  60. GISS Surface Temperature Analysis (GISTEMP) Version 4 (NASA Goddard Institute for Space Studies, 2020);

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V.R. is supported by the Edward A. Frieman Endowed Presidential Chair in Climate Sustainability at the University of California at San Diego, and Y.X. is supported by the National Science Foundation (Climate and Large-Scale Dynamics Program; AGS-1841308).

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Authors and Affiliations



V.R. conceptualized this study and derived the SSM equations for ISEEC. Y.X. developed the ISEEC model. A.V. did data analysis for response times. Y.X. and V.R. analysed ISEEC results. V.R. and Y.X. took the lead in writing, and all three authors contributed to editing.

Corresponding authors

Correspondence to Veerabhadran Ramanathan or Yangyang Xu.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Sustainability thanks Ilona Otto and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data

Extended Data Fig. 1 Principal socioeconomic considerations in ISEEC.

(a) GDP data for the past and the future compared to various SSP scenarios (refs. 53,54). (b) Energy intensity compared to data from by IAM and under future scenario of SSP5-baseline. (c) Derived PE compared to data from IAM and under future scenario of SSP5-baseline after 2015. (d) Breakdown of CO2 emission into fossil fuel (FF) and land use (LU) as in Global Carbon Project and SSP5-baseline.

Extended Data Fig. 2 Sensitivity to initial start-up term (denoted by the model parameter η0) in the fully coupled ISEEC.

Note a slow start in transitioning into zero-emission economy will lead to higher CO2 concentration and warming (red and blue lines), but it will mobilize the scale up of ACE capacity, and thus eventually help reach a deeper negative emission in late 21st century.

Extended Data Fig. 3 Validation of the governing equations for solar and wind power deployment.

(a) The model simulation and projection are compared to observed data from 2000 to 2017 and projected data from 2010 to 2050 (refs. 30,31). Note that the y-axis is in logarithmic scale. (b) same as (a), but the y-axis is in linear scale. The estimation of wind power assumes τ21 = 18 years, η0 = 0.001%, and k21 = 13% for 2000 through 2017. For projections, we assume τ21 = 30, η0 = 0.001%, and k21 = 18% for 2018 through 2050. For solar power, the simulations assume τ21 = 11, η0 = 0.004%, and k21 = 30% for 2000 through 2017 and assume τ21 = 30, η0 = 0.2%, and k21 = 30% for 2018 through 2050.

Extended Data Fig. 4 Simulated response times.

(a) currently available technologies (E21); (b) new renewable technologies (E22). These are derived in the base case of ISEEC.

Extended Data Fig. 5 Response times for technology diffusion τDF (see corresponding numbers for the fourteen technologies in the table).

The x-axis represents the first year in which the technology was commercially available. The y-axis represents the estimated diffusion time for the technology to scale (see procedures in Extended Data Figure 6). Note that wind and solar power represented by diamonds and cellular phone usage represented by triangles are global data. Data for other technologies are from regional sources. The simulated curves are following the equation in Supplementary Table 2 (\(\tau _{21}^{{{{\mathrm{DF}}}}} = \frac{{{{{\mathrm{b}}}}_1}}{{1 + {{{\mathrm{b}}}}_2{{{\mathrm{T}}}}^2}}\)), taking observed warming as T but assuming different b1 (25 years for the solid line and 20 years for the dashed line). Response times due to technology development τDV is shown in the table, which is estimated to be the difference between the first development of technology (year shown in parathesis in the table) to its market availability (year shown in the x-axis of the figure).

Extended Data Fig. 6 Procedure forestimating the response time due to technology diffusion.

A range of growth curves (taking the present capacity as 100%) were plotted assuming different response times. The diffusion time that provides the best fit to the historical technology adoption (dotted line; ref. 52) were then selected.

Extended Data Fig. 7 The sensitivity of simulated solar power capacity (as a percentage of total energy) to the initial start-up term, response times, and the initial capacity.

(a) Sensitivity to the initial start-up term. Increasing the value of the initial start-up term η0 from 0.2%/year to 1%/year reduces diffusion time by more than 50%, from more than forty years to fewer than twenty years. Red crosses in (a) and (b) are projected capacity (from refs. 30,31). (b) Sensitivity to response times and the initial capacity. The base case ISEEC is represented by the red dashed line (τ21 = 30), same as in (a). The yellow dashed line assumes a smaller response time τ21 = 10, and thus shows much quicker growth. When the initial value of the base case is reduced by a factor of ten (solid black line), there is little change from the base case, showing that the simulation is insensitive to the initial capacity. (c) Annual growth (%/year) broken down to the contribution from start-up term and diffusion term. The contribution of the start-up term to annual growth decreases quickly (dashed lines) and the contribution of the diffusion term (solid lines) increases over time. (d) Cumulative growth since 2010 as in (a), broken down to the contribution from the start-up term and the diffusion term. The main growth driver shifts from the diffusion term (solid lines) to the start-up term (dashed lines) as η0 is increased from 0.2% (red) to 1.0% (green).

Supplementary information

Supplementary Information

Full model description,Tables 1–3 and Figs. 1–16.

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Ramanathan, V., Xu, Y. & Versaci, A. Modelling human–natural systems interactions with implications for twenty-first-century warming. Nat Sustain 5, 263–271 (2022).

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