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# Equity is more important for the social cost of methane than climate uncertainty

The social cost of methane (SC-CH4) measures the economic loss of welfare caused by emitting one tonne of methane into the atmosphere. This valuation may in turn be used in cost–benefit analyses or to inform climate policies1,2,3. However, current SC-CH4 estimates have not included key scientific findings and observational constraints. Here we estimate the SC-CH4 by incorporating the recent upward revision of 25 per cent to calculations of the radiative forcing of methane4, combined with calibrated reduced-form global climate models and an ensemble of integrated assessment models (IAMs). Our multi-model mean estimate for the SC-CH4 is US$933 per tonne of CH4 (5–95 per cent range, US$471–1,570 per tonne of CH4) under a high-emissions scenario (Representative Concentration Pathway (RCP) 8.5), a 22 per cent decrease compared to estimates based on the climate uncertainty framework used by the US federal government5. Our ninety-fifth percentile estimate is 51 per cent lower than the corresponding figure from the US framework. Under a low-emissions scenario (RCP 2.6), our multi-model mean decreases to US$710 per tonne of CH4. Tightened equilibrium climate sensitivity estimates paired with the effect of previously neglected relationships between uncertain parameters of the climate model lower these estimates. We also show that our SC-CH4 estimates are sensitive to model combinations; for example, within one IAM, different methane cycle sub-models can induce variations of approximately 20 per cent in the estimated SC-CH4. But switching IAMs can more than double the estimated SC-CH4. Extending our results to account for societal concerns about equity produces SC-CH4 estimates that differ by more than an order of magnitude between low- and high-income regions. Our central equity-weighted estimate for the USA increases to US$8,290 per tonne of CH4 whereas our estimate for sub-Saharan Africa decreases to US$134 per tonne of CH4. ## Access options Rent or Buy article Get time limited or full article access on ReadCube. from$8.99

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## Data availability

The exact model versions used in this paper are MimiFAIR.jl v.1.0.0 (https://doi.org/10.5281/zenodo.4321934), MimiSNEASY.jl v.1.0.0 (https://doi.org/10.5281/zenodo.4321933), MimiMAGICC.jl v.1.0.0 (https://doi.org/10.5281/zenodo.4321929), MimiHector.jl v.1.0.0 (https://doi.org/10.5281/zenodo.4321932), MimiDICE2013.jl v.1.0.1 (https://doi.org/10.5281/zenodo.4444147) and MimiFUND.jl v.3.12.0 (https://doi.org/10.5281/zenodo.3986017).

## Code availability

The replication code for this paper is available at https://doi.org/10.5281/zenodo.4541874, including instructions on how to rerun the entire analysis for this paper. The code uses the Mimi.jl v.1.1.1 framework (https://doi.org/10.5281/zenodo.4321856).

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## Acknowledgements

This work was partially supported by the National Science Foundation through the Network for Sustainable Climate Risk Management (SCRiM) under NSF cooperative agreement GEO-1240507, the Sloan Foundation as well as the Penn State Center for Climate Risk Management. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding entities. We thank M. Budolfson, N. Scovronick and T. Wong for feedback.

## Author information

Authors

### Contributions

All authors designed the study. F.C.E. and D.A. led the computer modelling. All authors interpreted results and wrote the manuscript.

### Corresponding author

Correspondence to David Anthoff.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Peter Craigmile, James Hammitt 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 figures and tables

### Extended Data Fig. 1 Additional probabilistic climate hindcasts.

Hindcasts over the model calibration period (1850–2017) using the S-FAIR (blue), S-FUND (purple), S-Hector (red) and S-MAGICC (orange) climate models. ad, The annual atmospheric carbon dioxide concentration, with different shapes identifying the Law Dome ice core (triangles) and Mauna Loa (circles) calibration data. eh, Annual ocean carbon flux. il, Global ocean heat content. In all panels, yellow shapes represent observations. The solid black centre line depicts the mean response across 100,000 model runs, with coloured regions spanning the 95% predictive credible interval.

### Extended Data Fig. 2 Additional SC-CH4 estimates under different model structures and treatments of parametric uncertainty.

a, Distributions from the S-FAIR climate model for SC-CH4 experiment using a constant 3% consumption discount rate under RCP 8.5. Different distribution line types identify the FUND (solid) and DICE (dashed) IAMs, with coloured shapes along the x axis marking the estimated means of the different distributions. Colours identify each SC-CH4 experiment, with our main specification using Bayesian calibration (‘Main SC-CH4 estimate’, green), outdated radiative forcing equations that disregard the shortwave absorption of methane (‘Outdated CH4 radiative forcing’, blue), neglecting posterior relationships and sampling each parameter independently (‘Remove parameter relationships’, orange) and sampling the ECS distribution used for US SC-CH4 estimates while fixing other uncertain climate model parameters at their mean posterior values (‘U.S. climate sensitivity’, pink). b, Same as a but for the S-FUND climate model. c, Same as a but for the S-Hector climate model.

### Extended Data Fig. 3 Using the RCP 2.6 scenario keeps expected temperature projections below 2 °C and reduces SC-CH4 estimates relative to RCP 8.5.

ad, Modelled annual average global surface temperature anomalies relative to the 1861–1880 mean under RCP 2.6. Red dashed vertical lines identify the end of the calibration period (1850–2017). Yellow circles represent temperature observations and solid black centre line depicts the mean response across 100,000 model runs. Coloured regions span the 95% predictive credible intervals and horizontal grey lines identify the 1.5 °C and 2 °C global temperature targets of the UN Paris Agreement. e, SC-CH4 distributions for FUND (solid line) and DICE (dashed line) using a constant 3% consumption discount rate under RCP 2.6. White circles and diamonds show the expected SC-CH4 values of FUND and DICE for the two RCP scenarios after pooling together results from the four climate models. The percentage value identifies the percentage change in the expected SC-CH4 of each IAM that occurs when switching from RCP 8.5 to RCP 2.6, with the arrow identifying the direction of the change. In all panels, different colours identify the S-FAIR (blue), S-FUND (purple), S-Hector (pink) and S-MAGICC (orange) models.

### Extended Data Fig. 4 Robustness of SC-CH4 distributions to wider prior assumptions, and posterior methane cycle parameter relationships.

a, SC-CH4 distributions for FUND (solid line) and DICE (dashed line) depicting the main results (red) and a sensitivity analysis that uses wider prior parameter distributions during the model calibrations (blue). The SC-CH4 distributions correspond to a constant 3% consumption discount rate under RCP 8.5 and pool the SC-CH4 estimates of each IAM across the four climate models. Coloured circles show the estimated multi-model mean SC-CH4 for the two scenarios. b, Posterior parameter relationship between natural methane emission rates and the initial value for the time-varying tropospheric lifetime of methane in the S-MAGICC climate model. c, Posterior relationships between the uncertain methane cycle parameters depicted in b with the estimated SC-CH4 of S-MAGICC for RCP 8.5 under a constant 3% consumption discount rate. Different sized diamonds and circles identify the initial tropospheric lifetime of methane for DICE (blue) and FUND (red). Both b and c depict 5,000 randomly selected posterior estimates, with loess-smoothed curves (white lines) helping to illustrate the relationship between x- and y-axis values.

### Extended Data Fig. 5 Additional models show that nonlinear climate parameter relationships constrain SC-CH4 estimates.

Parameter and SC-CH4 relationships for the S-FAIR (top row), S-FUND (middle row) and S-Hector (bottom row) climate models. ac, Posterior relationships between four uncertain climate parameters. Different sized circles correspond to different terrestrial carbon pool respiration–temperature sensitivity values (with higher values signalling increasing heterotrophic respiration of carbon dioxide with temperature). The colour of each dot scales with the vertical rate of heat diffusion into the ocean. df, Posterior relationships between three of the uncertain climate parameters depicted in ac with the SC-CH4 estimated for RCP 8.5 under a constant 3% consumption discount rate. Different sized diamonds and circles identify respiration temperature sensitivity values for DICE and FUND. The colour of each point scales with the aerosol radiative forcing factor (with higher values signalling stronger aerosol cooling). Each panel depicts 5,000 randomly selected posterior estimates, with loess-smoothed curves (white lines) helping to illustrate the relationship between x- and y-axis values.

### Extended Data Fig. 6 Neglecting relationships between posterior parameter estimates increases the probabilistic uncertainty of the temperature projection.

ac, Modelled annual average global surface temperature anomalies relative to the 1861–1880 mean using the S-FAIR (a), S-FUND (b) and S-Hector (c) climate models. Yellow circles represent temperature observations and the solid black centre line depicts the mean baseline response across 100,000 model runs. Coloured regions outlined by dashed lines span the 95% predictive credible interval. The outer grey coloured regions bound the 95% predictive credible intervals for model projections that remove parameter relationships by sampling each marginal posterior distribution independently. The insets depict the estimated temperature distributions for 2050 and 2100 using the full set of model runs from the baseline (coloured) and no parameter relationship (grey) scenarios.

### Extended Data Fig. 7 Strong positive relationship between the SC-CH4 and ECS under the US SC-CH4 estimation framework.

a, Solid coloured lines depict posterior ECS distributions for the S-FAIR (blue), S-FUND (purple), S-Hector (pink) and S-MAGICC (orange) climate models. The dark grey dashed line shows the ECS distribution used for official US SC-CH4 estimates. Coloured asterisks along the x axis identify the estimated mean for the different distributions. be, SC-CH4 vales estimated for a constant 3% consumption discount rate under RCP 8.5 following the treatment of parametric climate uncertainty by the US SC-CH4 estimation framework. ECS values are sampled from the same distribution used to estimate the US SC-CH4 values. Other uncertain climate model and statistical process parameters remain fixed at their posterior mean values. Each panel depicts 2,000 randomly selected SC-CH4 estimates for DICE (circles) and FUND (diamonds), with loess-smoothed curves (white lines) helping to illustrate the relationship between the ECS and SC-CH4.

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Errickson, F.C., Keller, K., Collins, W.D. et al. Equity is more important for the social cost of methane than climate uncertainty. Nature 592, 564–570 (2021). https://doi.org/10.1038/s41586-021-03386-6

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