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

## Abstract

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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## 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.

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## Acknowledgements

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).

## Author information

Authors

### Contributions

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.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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). https://doi.org/10.1038/s41893-021-00826-z

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• DOI: https://doi.org/10.1038/s41893-021-00826-z