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# Climate policy implications of nonlinear decline of Arctic land permafrost and other cryosphere elements

## Abstract

The mean economic impact of net additional warming from the nonlinear PCF & SAF peaks at just under $70 trillion (NPV until 2300) for NDCs. To put this number into context, it exceeds the estimated long-term gains from economic development in the Arctic region through transit shipping routes52 and mineral resource extraction53 under high emissions scenarios by around 10 times, and could also dwarf pan-Arctic damages to infrastructure from thawing permafrost54,55. The economic losses due to climate warming also tend to be higher in warmer poorer regions such as India and Africa20, which are also less likely to benefit from the economic opportunities associated with a warmer Arctic56. ### Robustness of the estimates for the PCF and SAF effects Other major feedbacks implemented in the fully-coupled GCMs such as clouds, water vapour and lapse rate contribute to overall uncertainty and state-dependency in the ECS parameter35. The combined magnitude of these feedbacks showed weak responses to GMST increases in CMIP3 GCMs21. CMIP5 GCMs, however, produced increases in the water vapour feedback in warmer climates associated with rising tropopause57. While the state-dependencies in the planetary feedbacks require further investigations as part of CMIP6, the evidence so far suggests that apart from the SAF effects presented here, the magnitudes of the feedbacks are less likely to decrease with GMST. This implies that our estimates for the impacts of the state-dependent PCF and SAF are likely to be on a conservative side. The particularly large uncertainty in climate warming caused globally by clouds and aerosol parametrization is an established issue58,59,60,61. Of the two most recent studies on the cloud feedback that were based on observational constraints, one matched closely with the ECS parameterisation from IPCC AR5 adopted in PAGE-ICE, suggesting that our climate projections are robust. The uncertainties in the permafrost models used in this study, robustness of our PCF and SAF emulators, and uncertainties in other key parameterisations such as the carbon cycle, sea level rise, mitigation business as usual pathway and economic impacts of rising temperatures are discussed in Methods and Supplementary Notes 13. ## Discussion We have investigated the climatic and economic impacts of two major planetary feedbacks associated with the decline of Arctic land permafrost, snow and sea ice. PCF is caused by additional CO2 and methane emissions from thawing permafrost, and SAF is mostly driven by increased solar absorption due to the decline of Arctic sea ice and land snow covers. These two feedbacks belong to the main tipping elements in the Earth’s climate system identified by recent surveys13. Model simulations indicate that both feedbacks accelerate the warming and are nonlinear, with the PCF being the stronger of the two, while most climate policy studies to date have assumed constant positive SAF and zero PCF, which we refer to as the legacy values. All this warrants their rigorous quantitative assessment. To perform such an assessment, we developed novel statistical emulators of the two Arctic feedbacks calibrated according to simulations results from the specialised land surface and general circulation models. The emulators allow one to study the entire parameter space, which is not possible with complex physical models, and also help establish dynamic links between highly specialized climate and economic models. We implemented the emulators dynamically inside the new integrated assessment model (IAM) PAGE-ICE, allowing us to explore nonlinear interactions between the Arctic feedbacks and the global climate and socio-economic systems under a range of scenarios consistent with the Paris Agreement. With the current parameterisations in PAGE-ICE, adding the significant corrections from the nonlinear Arctic feedbacks to the base estimates of the mean total economic effect of climate change makes the 1.5 °C target ($638 trillion) marginally more economically attractive than the 2 °C target (\$646 trillion). While the total economic effects of the 1.5 °C and 2 °C scenarios are statistically equivalent (Fig. 6), we have several reasons to believe it would be prudent to aim for emissions towards the bottom end of the range covered by these scenarios. First, the PAGE-ICE model, in common with other aggregate IAMs, does not explicitly model other known climatic tipping elements such as Amazon rainforest, boreal forest, coral reefs and El Niño–Southern Oscillation (ENSO), as well as ocean acidification and climate-induced large-scale migration and conflict62 (we cannot reject the null hypothesis that the total economic effects of climate change are the same for these scenarios either at the 5% or at the 10% significance level). Some of these effects are already included implicitly in the highly uncertain non-economic and discontinuity impact sectors in PAGE-ICE, contributing to the long upper tails in the distributions of the total economic effect of climate change in Fig. 5a; even with the current parameterisations, the upper tails in the distributions are at their lowest for the 1.5 °C scenario. It is possible that with an explicit modelling of the other climatic and societal tipping elements, as well as with comprehensive representation of the impacts of rising temperatures and increasing extreme weather events on economic growth63, both the economic effect of climate change with legacy Arctic feedbacks, and the additional impacts due to the nonlinear PCF and SAF, would be higher compared to those reported here. The associated global risks are minimised at lower emissions. Second, it is possible that recent reduction trends in the costs of mitigation technologies such as solar power64,65, which are captured by PAGE-ICE, could accelerate further if appropriate policy instruments such as carbon prices are implemented globally. Third, PAGE-ICE does not account for possible co-benefits of deep mitigation as part of a wider green growth transition in economy66,67. All these factors advocate for pursuing the target well below 2 °C as the way of avoiding substantial ecological and socio-economic losses from climate change (see Supplementary Discussion for further details)68.

The nonlinear transitions in the two feedbacks explored in this study demonstrate the pressing need for a better understanding of state-dependent processes in the Earth’s climate system, both those associated with the Arctic and beyond. This is important because triggering these and other planetary feedbacks might accelerate the pace of climate change13,69 and increase the risks of irreversible socio-economic losses70. The methodology introduced in this paper could be used to quantitatively assess the economic and climate policy implications of the other tipping elements in the Earth’s climate system, including the Greenland and West Antarctic ice sheets, Amazon rainforest, boreal forest, Sahel and ENSO13. Such assessments could provide a more complete understanding of the socio-economic risks from climate change that in turn can help guide policymakers towards prudent decisions on emissions reduction targets.

## Methods

### Climate scenarios and model setup in PAGE-ICE

We defined the scenarios consistent with the Paris Agreement and current climate change projections by pairing representative concentration pathways (RCPs) and shared socio-economic pathways (SSPs) according to the feasible ranges of emissions for each of the five main SSPs22,23. Table 1 summarises the scenarios. The imaginary Zero Emissions scenario in which all global emissions stop in the base year 2020 characterises the effect of the historic emissions on the PCF and SAF.

First, we defined a new SSPM scenario by averaging SSP2, SSP3 and SSP4 with equal weights, and paired it with RCP4.5 to represent a likely world with medium levels of emissions. Second, we paired SSP1 with RCP2.6 and SSP5 with RCP8.5, which represents the likely lower and the upper ends of the emissions range and the associated socio-economic makeup of the world. Using these low, medium and high emissions pairs, we introduced a weighting scheme that covers the entire range as the weighting parameter w changes from −1 (lower end) to +1 (upper end):

$$\left\{ {\begin{array}{*{20}{c}} {{\mathrm{SSPW}}} \\ {{\mathrm{RCPW}}} \end{array}} \right\} = \left( {\frac{{1 - w}}{2}} \right)^2 \cdot \left\{ {\begin{array}{*{20}{c}} {{\mathrm{SSP}}1} \\ {{\mathrm{RCP}}2.6} \end{array}} \right\} + \frac{{1 - w^2}}{2} \cdot \left\{ {\begin{array}{*{20}{c}} {{\mathrm{SSPM}}} \\ {{\mathrm{RCP}}4.5} \end{array}} \right\} \\ + \left( {\frac{{1 + w}}{2}} \right)^2 \cdot \left\{ {\begin{array}{*{20}{c}} {{\mathrm{SSP}}5} \\ {{\mathrm{RCP}}8.5}\end{array}} \right\}$$
(1)

A statistical optimisation algorithm (Risk Optimiser) was then employed in PAGE-ICE to find the values of w in Equation 1 that result in a 50% probability for the GMST in 2100 to reach the levels consistent with: first, NDCs from the Paris Agreement extrapolated until 2100 (3.3 °C, w = −0.14);71 second, partially implemented NDCs representing an estimated long-term effect of the US’s withdrawal from the NDCs (3.6 °C, w = 0.1);72 and third, business as usual projections without the Paris Agreement (4.2 °C, w = 0.52)71. We also added a 2.5 °C target scenario (w = −0.7) which is more ambitious than the NDCs but falls short of the 2 °C target.

The 1.5 °C and 2 °C scenarios, defined as having a 50% chance of keeping the GMST rise in 2100 below the 1.5 °C and 2 °C targets based on PAGE-ICE simulations, require extra abatement relative to RCP2.6. They fall outside the range covered by the SSPW and RCPW pairs described above. We, therefore, introduced an additional abatement rate relative to RCP2.6, the same for all the major GHGs represented in PAGE-ICE, and employed Risk Optimiser to find that it is equal to 0.24% per year for the 2 °C target and 4.05% per year for the 2 °C target scenario. Both of these scenarios overshoot their respective targets during the second half of the 21st century and imply negative CO2 emissions thereafter.

All the RCP scenarios in PAGE-ICE are emissions-driven73, unlike the concentration-driven RCP scenarios that were used in most CMIP5 experiments17. We simulated each SSP-RCP pair out to 2300 assuming constant levels of annual emissions, constant GDP growth rates and zero population growth rates beyond 2100. Under each scenario, we ran 100,000 Monte-Carlo simulations in PAGE-ICE to perform sensitivity experiments for the climatic and economic effects of the PCF and SAF.

### Emulator for the nonlinear PCF

The new dynamic emulator for CO2 and methane emissions from thawing land permafrost is based on simulations from the SiBCASA and JULES LSMs7,28, forced by multiple CMIP5 and CMIP3 general circulation models (GCMs) run under a range of climate scenarios out to 2300. The simulated CO2 and methane fluxes from thawing permafrost as a function of time represent the strength and timing of the PCF.

SiBCASA has fully integrated water, energy, and carbon cycles, and a modified snow model to better simulate permafrost dynamics74. The soil model separately tracks liquid water, ice, and frozen organic matter at each time step as prognostic variables, accounting for the effects of latent heat7,75. SiBCASA separately tracks CO2 and methane emissions. The model was used to make one of the first estimates of future permafrost degradation and global carbon emissions from thawing permafrost7. Here we ran multiple projections from 1901 to 2300 starting from the same initial conditions. We spun up the model until the release from permafrost carbon was negligible, ending up with 560 GtC of frozen permafrost carbon in the top three metres of soil75,76 by initializing the model with the observed values from the Northern Circumpolar Soil Carbon Dataset version 2 (NCSCDv2)77. We used the Climatic Research Unit National Centre for Environmental Predictions (CRUNCEP) reanalysis78 scaled by global climate projections from CMIP517. We chose CMIP5 models that ran both RCP4.5 and RCP8.5 scenarios out to 2300 and that represent a broad range of warming above pre-industrial temperatures: CNRM-CM5, GISS-E2-H, HadGEM2-ES, IPSL-CM5A-LR and MPI-ESM-LR.

The version of JULES used here has an improved representation of physical and biogeochemical processes in the cold regions79,80. Competition of vegetation was enabled, allowing the models to determine both their initial vegetation distributions and litterfall, and the response of the vegetation distribution and litterfall to climate change. The profile of soil carbon was spun up until it was in equilibrium with the 1860’s climate, giving 738 GtC in the top 3m of soil. Any soil carbon in the permafrost in 1860 was labelled as permafrost carbon and traced throughout the simulation. We assumed that any part of this permafrost carbon which is emitted to the atmosphere is emitted in the form of CO2 only. JULES was forced by climate patterns from the full set of 22 CMIP3 climate model simulations under the RCP2.6, RCP4.5 and RCP8.5 scenarios, extended out to 2300 using the IMOGEN climate emulator28.

The dynamic emulator of the permafrost carbon emissions is based on a nonlinear first order ODE:

$$\frac{{{\mathrm{d}}C}}{{{\mathrm{d}}t}} = \frac{{C_{{\mathrm{max}}}}}{{{\rm{\tau}} \;\varphi _{\rm{\tau}}\left( T \right)}} \cdot \left( {\frac{{\max \left( {C_{{\mathrm{eq}}}\left( T \right) - C,0} \right)}}{{C_{{\mathrm{max}}}}}} \right)^{\left( {1 + p} \right)\;\varphi _{\mathrm{p}}\left( T \right)}$$
(2)

Here T = AFp·GMST is mean annual permafrost temperature anomaly in year t, averaged spatially across the estimated pre-industrial permafrost regions (□C relative to pre-industrial levels); AFp is the permafrost amplification factor which links T with the GMST anomaly; C is cumulative permafrost carbon emitted since the pre-industrial period as of time t (GtC, either CO2 or methane component); Ceq(T) is equilibrium cumulative carbon emitted for a constant permafrost temperature anomaly T, expressed as

$$C_{{\mathrm{eq}}}\left( T \right) = \min \left( {{\rm{\omega}}} \;\varphi _{\rm{\omega }}\left( T \right) \cdot T,C_{{\mathrm{max}}} \right);$$
(3)

Cmax is a limit on the maximum possible cumulative emissions determined by the initial carbon stock estimates in SiBCASA (560 GtC) and JULES (738 GtC); ω (GtC K−1) is equilibrium sensitivity of the carbon emissions to permafrost warming; τ (yr) is the time lag at t = 0 (pre-industrial) corresponding to the given Cmax; p is a fixed power that defines the dynamics of how the equilibrium is approached; φω (Equation 3), φτ and φp (Equation 2) are temperature-driven corrections to the parameters ω,τ,p. All the parameters are assumed to be constant unless they are marked as functions. Equation 2 implies no regeneration of permafrost carbon stocks on the timescales considered81.

The emulator is calibrated, separately, to the CO2 components of the permafrost emissions simulated by SiBCASA and JULES, and the methane component simulated by SiBCASA. Each combination of a GCM (m) and climate scenario (s), either in SiBCASA or JULES simulations, produces its own set of optimal equilibrium carbon, lag and power parameters (ω,τ, p)m,s that achieves the best emulator fit. The resulting statistics for the ω,τ, p parameters is based on the assumptions of equal weights between the GCMs and the scenarios. The corrections φω, φτ, φp (all non-negative) ensure quasi-independence of the (ω,τ, p)m,s set as a whole from the scenarios or climate models used. The latter allows us to use these sets of values to construct the corresponding probability distributions for ω,τ, p in PAGE-ICE, which are expected to work throughout the simulated range of temperatures. The full technical details of the calibration algorithm and the resulting numerical values for the SIBCASA and JULES emulators are provided in Supplementary Note 2, Supplementary Figs 517 and Supplementary Tables 26.

The type of a model described by Equation 2 and Equation 3 is often referred to as pursuit curve, and its simpler quasi-linear version (p = 0) has been employed for sea level rise emulators previously82,83. Even in its simpler form, such a model has never been applied to projected permafrost emissions from process-based simulations of LSMs. The pursuit curve model ensures that there is an equilibrium level of cumulative carbon emissions from permafrost for any given level of warming globally (providing p > −1). The dynamic model formulation employed here contains the following layers of nonlinearity: nonlinear response of the equilibrium cumulative carbon to GMST changes, represented by the ωφω(TT term; evolution of the characteristic time lag for cumulative permafrost emissions with the difference between the equilibrium and realised cumulative carbon, represented by p (in the corresponding linear model p = 0 and the lag is simply equal to τ); temperature-dependence in the lag and power parameters, represented by φτ, φp; and, saturation of the cumulative carbon emissions due to the permafrost carbon stock exhaustion, represented by Cmax.

The cumulative carbon emissions from the emulators, calibrated separately to SiBCASA and JULES simulations, were averaged with equal weights, both for CO2 and methane, and scaled according to the uncertainty in the observed permafrost carbon stocks31. As JULES does not model permafrost methane emissions explicitly, the latter were inferred from its CO2 emissions using observational constraints84. The resulting cumulative CO2 and methane emissions from permafrost simulated by PAGE-ICE are plotted in Fig. 7 under the range of scenarios considered.

### Emulator for the nonlinear SAF

Our nonlinear SAF estimates are based on the ALL/CLR method with atmospheric reflectivity parameterisation32,33, which uses CMIP5 GCM simulations for atmospheric shortwave radiation fluxes from pre-industrial conditions until either 2100 or 2300 under RCP8.5 scenario (Supplementary Note 3). None of the GCM variables were bias-corrected in order to preserve internal consistency of the sea ice and land snow physics in each model. The statistics of the nonlinear SAF assumes model democracy in the CMIP5 sample used (equal weights for all GCMs).

Applying the ALL/CLR method to the transient GCM simulations produced time series for the global RF associated with the surface albedo changes. These were differentiated with respect to GMST trends over 30-year climatological windows, separately for each model, using linear polynomial fitting to obtain climatologically-averaged SAF in each year. A Savitzky–Golay filter (base period = 31 years; polynomial order = 1) was applied to obtain smooth time series for GMST and SAF. The SAF (both global total and separately for the three main components) was then represented as a function of the GMST rise individually for each model, at which point the multi-model statistics was calculated.

We based the emulator of the global nonlinear SAF on a two-segment approximation described by the following expressions for the SAF, f(T), and the associated RF, F(T):

$${\begin{array}{l}f\left( T \right) = \left\{ {\begin{array}{*{20}{c}} {a_0 + a_1T + a_2T^2 + \sigma \varepsilon ,\;T < T_ \ast } \\ {b_0 + \rho \varepsilon ,\;T \ge T_ \ast } \end{array}} \right.\\ F\left( T \right) = \mathop{\displaystyle\int}\limits_0^T {f\left( {T\prime } \right){\mathrm{d}}T\prime = \left\{ {\begin{array}{*{20}{c}} {(a_0 + \sigma \varepsilon )T + \frac{1}{2}a_1T^2 + \frac{1}{3}a_2T^3,\;T < T_ \ast } \\ {(a_0 + \sigma \varepsilon )T_ \ast + \frac{1}{2}a_1T_ \ast ^2 + \frac{1}{3}a_2T_ \ast ^3 + (b_0 + \rho \varepsilon ) \cdot (T - T_ \ast ),\;T \ge T_ \ast } \end{array}} \right.} \end{array}}$$
(4)

Here T is the GMST anomaly (not to be confused with the permafrost temperature), T* = 10 °C is an empirically determined switch between the quadratic and constant SAF segments (Fig. 8), aj are the coefficients of quadratic polynomial fitting to the multi-model mean global SAF over the T < T* segment, b0 is average of the multi-model mean global SAF over the T ≥ T* segment, σ(ρ) is average of the multi-model SD of the global SAF over the T  <T* (T ≥ T*) segment, and $$\varepsilon = {\cal{N}}(0,1)$$. The full technical description of the implementation of the SAF emulator in PAGE-ICE is provided in Supplementary Note 3.

### PAGE-ICE IAM

PAGE-ICE (v6.22) is based on the PAGE09 IAM19,20. It includes several updates both to climate science and economics from IPCC AR5 and literature that followed, as well as several novel developments presented in this paper. The updates are summarised below, with the full technical description provided in Supplementary Note 1, Supplementary Figs 1823 and Supplementary Tables 717.

PAGE and similar IAMs do not model natural climate variability, and therefore each Monte-Carlo run is deterministic in time. This allows us to work with Monte-Carlo generated probability distributions of multiple climatic and economic parameters in any fixed analysis year like 2100, as opposed to taking averages over the 30-year climatological windows (a standard requirement for any climate model data with multiple natural variability cycles). The ranges for all the uncertain parameters in PAGE-ICE are listed in the Supplementary Table 17.

Generic updates in PAGE-ICE: first, adjusted analysis years starting with 2015 (base year), 2020, 2030, 2040, 2050, 2075, 2100, 2150, 2200, 2250 and 2300, allowing for a better representation of the essential long-term processes: permafrost emissions, winter sea ice and land snow decline and melting of the ice sheets; second, updated base year (2015) data for the emissions, temperature, population, GDP-PPP, cumulative permafrost emissions and surface albedo feedback, with uncertainty ranges for most parameters; third, updated set of emissions (RCP) and socio-economic (SSP) scenarios paired according to the RCP-SSP compatibility conditions22, and modified to cover the range of scenarios in line with the Paris Agreement, as well as the possibility of a reversal of climate policies in the US and globally.

Climate science updates in PAGE-ICE: first, internal dynamic representation of the nonlinear PCF and SAF using emulators based on simulations from multiple CMIP5 and CMIP3 GCMs and SiBCASA and JULES LSMs run under the extended RCP8.5, 4.5 and 2.6 (only JULES) scenarios out to 2300 (see the relevant Methods sections above); second, adjusted transient climate response (TCR), feedback response time (FRT) and ECS parameter ranges according to IPCC AR5 based on CMIP5 models, paleo-records and climate models of intermediate complexity; third, revised CO2 cycle in line with the latest multi-model assessment of the atmospheric CO2 response function;85 fourth, improved GMST equation using a better numerical scheme for finite analysis periods; fifth, CMIP5-based amplification factors for the regional temperatures; sixth, changes in the implementation of the regional sulphate cooling: sulphates now add to the global forcing and affect the regional temperatures implicitly through the CMIP5-based amplification factors (their RF is not included in the regional temperature equation directly due to the complexity of climatic response to regional RFs, which requires regional climate sensitivities to be introduced;86 seventh, approximately halved indirect sulphate cooling effect; eighth, fat-tailed distribution for the sea level rise (SLR) time lag (at the lower values end) to account for the possible acceleration in the discharge from the West Antarctica and Greenland ice sheets87,88,89,90.

Economics updates in PAGE-ICE: first, new economic impact function based on the recent macro-econometric analysis of the effect of historic temperature shocks on economic growth in multiple countries by Burke et al.46, projected onto the 8 major regions of the PAGE model using population-weighted temperatures, and adapted to fit with the single year consumption-only approach for climate impacts used in PAGE; second, considerably downscaled saturation limit for the impacts; third, modified uncertainty range for the BaU scenario, which is used as a reference point for calculating the abatement costs, covering the range roughly between RCP6.0 and a pathway exceeding RCP8.5;23 fourth, revised present-day marginal abatement cost (MAC) curves64, technological learning rate (CO2 only)65 and autonomous technological change based on energy efficiency improvements;91 fifth, significantly downscaled discontinuity sector, which now accounts only for socio-economic tipping points such as pandemics, mass migration and wars, as well as possible other tipping points in the climate than permafrost, sea ice, land snow and lea level rise from ice sheets (the catastrophic loss of the ice sheets has been moved to the fat-tailed distribution in the sea level rise module); sixth, reduced tolerable temperature rise that gives no chance of a discontinuity; seventh, significantly decreased time constant of a discontinuity in line with its new interpretation; eighth, focus on autonomous adaptation as part of the Burke et al. economic impact function, with planned adaptation restricted to SLR impacts.

### Climate model data

The complete lists of the CMIP5 and CMIP3 models used in the study are provided in Supplementary Tables 18 and 19.

### Image processing

The Figures were plotted using Matlab R2018a, IDL (Fig. 5) and Palisade Risk 7.5 (Fig. 6). We used Matlab’s Savitzky–Golay smoothing for the SAF results from CMIP5 (Fig. 2) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation for the time-series results from PAGE-ICE.

## Data availability

All data generated or analysed during this study are included in this published article and its Supplementary Dataset files, with exception of the publically available CMIP datasets acknowledged below.

## Code availability

The PAGE-ICE model (v6.22) and the associated pre- and post-processing computer codes are included in the Supplementary Code files. The SiBCASA and JULES models are managed, respectively, by expert teams at the National Snow and Ice Data Centre (US) and at the UK Met Office, and are not included in this publication due to their complexity.

Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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

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## Acknowledgements

This work is part of the ICE-ARC project funded by the European Union’s 7th Framework Programme, (grant 603887, contribution 006). D.Y. received additional funding from ERIM, Erasmus University Rotterdam, and Paul Ekins at the ISR, University College London. K.S. was funded by NSF (grant 1503559) and NASA (grants NNX14A154G, NNX17AC59A). E.J. was funded by the NGEE Arctic project supported by the BER Office of Science at the U.S. DOE. Y.E. was funded by the NSF (grant 1900795). E.B. was supported by the UK Met Office Hadley Centre Climate Programme funded by BEIS and DEFRA. Publication of this article was funded by Lancaster Environment Centre, the University of South Florida St. Petersburg’s Open Access Publication Fund, NSF (grant 1900795) and NASA (grants NNX14A154G, NNX17AC59A). We thank the five anonymous referees for providing wide-ranging critical comments that helped improve the paper considerably. We are also grateful to multiple colleagues from the ICE-ARC consortium and beyond for a number of useful discussions that contributed to shaping this study, including Jeremy Wilkinson, Peter Wadhams, Michael Karcher, Frank Kauker, Rüdiger Gerdes and Andy Jarvis. Special thanks go to Michael Winton for providing the original ALL/CLR script. We also acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (listed in Supplementary Tables 18 and 19) for producing and making available their model output. For CMIP the U.S. DOE’s Program for Climate Model Diagnosis and Inter-comparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.

## Author information

### Affiliations

1. #### Pentland Centre for Sustainability in Business, Lancaster University, Lancaster, LA1 4YX, UK

• Dmitry Yumashev
• , Paul J. Young
•  & Gail Whiteman
2. #### Lancaster Environment Centre, Lancaster University, Lancaster, LA1 4YQ, UK

• Dmitry Yumashev
• , Fernando Iglesias-Suarez
•  & Paul J. Young

• Chris Hope
4. #### National Snow and Ice Data Centre, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309-0449, CO, USA

• Kevin Schaefer
•  & Elchin Jafarov
5. #### Alfred-Wegener-Institut, Helmholtz Zentrum für Polar- und Meeresforschung, Bremerhaven, 27515, Germany

• Kathrin Riemann-Campe
6. #### Department of Atmospheric Chemistry and Climate Group, Institute of Physical Chemistry Rocasolano, CSIC, Madrid, 28006, Spain

• Fernando Iglesias-Suarez
7. #### Computational Earth Science, Earth and Environmental Sciences EES-16, Los Alamos National Laboratory, Los Alamos, NM, USA

• Elchin Jafarov
8. #### UK Met Office, Exeter, EX1 3PB, UK

• Eleanor J. Burke
9. #### Data Science Institute, Lancaster University, Lancaster, LA1 4YW, UK

• Paul J. Young
10. #### College of Arts & Sciences, University of South Florida, St. Petersburg, FL, 33701, USA

• Yasin Elshorbany

### Contributions

D.Y., G.W. and C.H. conceived the research; D.Y. and C.H. created the PAGE-ICE model and ran the simulations; D.Y. developed and calibrated the permafrost and albedo feedback emulators; K.S. and E.J. designed and ran SiBCASA simulations; E.B. designed and ran JULES simulations; K.R.C., F.I.S. and D.Y. adapted the ALL/CLR script for the albedo feedback; F.I.S., K.R.C., K.S., P.Y. and Y.E. processed climate model data; All authors provided input on the scientific and policy matters and contributed to the writing of the paper.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Dmitry Yumashev.