The Zero Emissions Commitment (ZEC) is the change in global temperature expected to occur following the cessation of anthropogenic emissions of greenhouse gases and aerosols . ZEC is one of five metrics needed to compute the “remaining carbon budget”, which in turn quantifies the total emissions compatible with meeting a given temperature change guardrail e.g., such as those set out in the Paris Agreement . ZEC was recently the focus of a model intercomparison project organized through the Coupled Model Intercomparison Project phase 6 (CMIP6) . The project, formally called the Zero Emissions Commitment Model Intercomparison Project (ZECMIP) , gathered simulations from 18 Earth system models of full and intermediate complexity and assessed the CO2 component of ZEC. For the tier-one idealized experiment where 1000 PgC of CO2 was emitted to the atmosphere before cessation of emissions, ZEC ranged from -0.36 to 0.29 ∘C with a model ensemble mean of -0.07 ∘C 50 years after emissions ceased. However, only 2 of the 18 models that participated in ZECMIP had a representation of the permafrost carbon feedback to climate change, a feedback process that is expected to release CO2 and CH4 into the atmosphere for centuries after emissions cease . Thus the effect of the permafrost carbon feedback on ZEC has yet to be well quantified.

The soils of the Northern Hemisphere permafrost region are estimated to contain between 1100 and 1500 PgC of organic matter , about half of which is held in the perennially frozen zone of these soils . As climate warms and permafrost thaws, organic matter in permafrost-affected soils is exposed to increased periods of time where local temperature is above freezing, and hence to enhanced rate of decay releasing CH4 and CO2 to the atmosphere e.g.. A recent informal (non-CMIP) model intercomparison exercise quantifying the permafrost carbon feedback estimated a release of carbon of between 74 and 652 PgC by year 2300 under the high-end Representative Concentration Pathway 8.5 scenario, with substantially lower release or even gain of soil carbon under mitigation scenarios . Thus the permafrost carbon feedback to climate change has the potential to affect the value of ZEC in a fashion that was poorly quantified by ZECMIP.

Uncertainty in projections from Earth system models can be classified into three components: (1) structural uncertainty, (2) parameter uncertainty, and (3) scenario uncertainty e.g.. Structural uncertainty is created from the discrepancy between the system the model is intended to represent and the system the model actually describes . Examining different models of the same system with standardized forcings through model intercomparison projects such as ZECMIP is the principle way of quantifying structural uncertainty in climate sciences . Parameter uncertainty is uncertainty about the value that model parameter should take on . As model parameters are sometimes quantities measurable in the natural world, parameter uncertainty is some cases equivalent to measurement uncertainty. In other cases parameters represent an amalgam of natural processes; in such cases defining parameter uncertainty becomes more ambiguous . Parameter uncertainty can be quantified with perturbed parameter experiments, wherein ensembles of model variants with parameter values selected from defined probability distribution functions are run under the same experiment conditions e.g.. Several such experiments have been conducted to assess uncertainty in the permafrost carbon feedback . Scenario uncertainty is created by uncertainty about what humans will do in the future and is well explored by the coordinated scenario framework of CMIP .

For the permafrost carbon feedback, uncertainty ranges derived from structural uncertainty and parameter uncertainty assessments have proven similar. The model intercomparison exercise of found a range of 74 to 652 PgC with a mean of 341 PgC released from permafrost soils by year 2300 under Representative Concentration Pathway 8.5, compared to 159 to 587 PgC with a mean of 376 PgC for the perturbed parameter experiment of , forced under the same scenario.

In addition to 16 out of the 18 ZECMIP models having no permafrost carbon module, the experimental design of ZECMIP is ill designed to quantify the permafrost carbon feedback. The top-tier idealized ZECMIP experiment branches from the idealized 1pctCO2 experiment where atmospheric CO2 concentration rises at 1 % a year compounded leading to a quadrupling of CO2 concentration in 140 years . Following this protocol CO2 and hence global temperatures rise much faster than in the historical trajectory, and since it takes time for permafrost soil to thaw and organic matter within these soils to decay, the experimental protocol will tend to underestimate release of carbon from permafrost soils .

Here I will use a perturbed parameter ensemble approach to estimate the contribution to CO2-only ZEC from the release of carbon from permafrost soils, following the ZECMIP protocol. I will also conduct an experiment following a more realistic CO2 emission trajectory in order to quantity the thaw-lag effect from the high emission rates of the ZECMIP protocol.

Figure  shows ZEC for the A1 (1000 PgC) experiment for the model versions with and without permafrost carbon. The figure shows that over centennial timescales the model version with permafrost carbon has a higher ZEC. Consistent with a higher ZEC, the model version with permafrost carbon exhibits a slower decline in atmospheric CO2 concentration after emissions cease. Figure a displays the difference in ZEC between the simulations with and without permafrost carbon for the A1 (1000 PgC) experiment. Fifty years after emissions cease the existence of a permafrost carbon pool has added 0.06 [0.02 to 0.14] ∘C to ZEC (median [5th to 95th percentile]), rising to an addition of 0.09 [0.04 to 0.21] ∘C 100 years after emissions cease, and 0.27 [0.12 to 0.49] ∘C 500 years after emissions cease (Table ). The additional warming is being driven by release of carbon from permafrost soils, which totals 29 [10 to 90] PgC by the time emissions cease, 73 [32 to 190] PgC by 50 years after emissions cease, 100 [46 to 222] PgC 100 years after emissions cease, and 178 [70 to 346] PgC 500 years after emissions cease (Fig. a, Table ). The global mean temperature anomaly at the time emissions cease is 1.51 [1.41 to 1.58] ∘C for the non-permafrost carbon experiment and 1.55 [1.47 to 1.67] ∘C for the permafrost carbon experiment. Thus, the carbon released from permafrost soils by the time emissions ceases causes 0.04 [0.01 to 0.12] ∘C of additional warming in the model versions with permafrost carbon. The value of ZEC is determined by a balance of the warming effect of diminishing ocean heat uptake and the cooling effect of declining atmospheric CO2 concentration ; thus the initial cooling after emissions cease is likely caused by the initial rapid drop in atmospheric CO2 concentration (c, and d).

Figure  shows mean difference in global carbon pool sized in the simulations with and without permafrost carbon, averaged across all of the model variants, for the A1 (1000 PgC) experiment. The excess carbon released from permafrost soils is taken up by vegetation, the ocean, and the atmosphere. Most of the excess carbon resides in the atmosphere for centuries after emissions cease, with the ocean gradually becoming a more significant sink. Vegetation remains a relatively small sink throughout the experiments. Figure  also suggests that the source of the rapid fall in atmospheric CO2 in the decades after emissions cease is continued growth of the vegetation and soil carbon sinks. Within a century of cessation of emissions the terrestrial biosphere transitions from a carbon sink to carbon source, a process exacerbated by the existence of permafrost carbon pool.

Figure  shows the difference in ZEC between simulations following the A1 (1000 PgC) tier-1 ZECMIP experiment protocol and the experiment where emissions follow historical and SSP4-6.0 emissions until 1000 PgC of CO2 has been emitted. In the SSP4-6.0-based experiment ZEC is 0.04 [0 to 0.06] ∘C, 0.03 [-0.01 to 0.05] ∘C, and 0.03 [-0.02 to 0.08] ∘C warmer 50, 100, and 500 years after emission cease, respectively. The slightly larger ZEC is being driven by additional carbon being released from permafrost soils under the SSP4-6.0-based experiment with 51 [22 to 132] PgC released when emissions cease compared to 29 [10 to 90] PgC in the A1 experiment; 50, 100, and 500 years after emissions cease 84 [39 to 204] PgC, 107 [50 to 230] PgC, and 180 [71 to 354] PgC have been released under the SSP4-6.0-based experiment compared to 73 [32 to 190] PgC, 100 [46 to 222] PgC, and 178 [70 to 346] PgC under the A1 experiment, respectively. Notably the effect of the thaw-lag diminishes with time after emissions cease.

The ZEC for model variants without and with permafrost carbon for the A3 (2000 PgC) experiments is shown in Fig. . Similar to the A1 experiment the existence of a permafrost carbon pool adds to the magnitude of ZEC. The difference between the model versions with and without permafrost carbon is shown in Fig. b for the A3 experiment. The difference in ZEC 50, 100, and 500 years after emissions cease is 0.06 [0.03 to 0.12] ∘C, 0.09 [0.05 to 0.18] ∘C, and 0.24 [0.11 to 0.50] ∘C (Table ), respectively, corresponding to a release of carbon from permafrost soils of 84 [40 to 213] PgC when emissions cease and 159 [85 to 300] PgC, 205 [114 to 354] PgC, and 312 [148 to 505] PgC 50, 100, and 500 years after emissions cease (Fig. b, Table ). Consistent with previous results that examined representative concentration pathway scenarios, the temperature effect of the permafrost carbon cycle feedback is not strongly effected by the total cumulative emissions e.g..

To explore which of the perturbed parameters has the greatest effect on the anomaly in ZEC created by the inclusion of permafrost carbon, correlations were computed between the perturbed parameter values and the anomaly in ZEC 50 years after emissions cease. These correlations are shown in Table . For the A1 (1000 PgC) experiment the available fraction parameter has by far the strongest influence with a correlation of 0.91. None of the other parameters have large correlations. For the A3 (2000 PgC) experiment both the available fraction (r=0.64) and the passive pool transformation rate (r=0.55) have substantial correlation values. These results contrast those for release of carbon from permafrost soils under future scenarios computed by , where both available fraction and equilibrium climate sensitivity played the most important roles, and the passive pool transformation rate had little effect on results. The difference may partly be due to the reduced uncertainty range in equilibrium climate sensitivity used here. The prominence of the Passive pool transformation rate in the A3 experiment results is concerning as this parameter is the most poorly constrained of all parameters considered. The available fraction parameter is effectively the combined size of the fast and slow pools as conceptualized in incubation experiments . Thus these results suggest that increased field sampling of, and incubation experiments on, permafrost carbon could substantially reduce the uncertainty in permafrost carbon's contribution to ZEC.

ZECMIP found that the inter-model range of ZEC 50 years after emissions cease for the A1 (1000 PgC) experiment is -0.36 to 0.29 ∘C with a median value of -0.05 ∘C . Thus the additional warming expected from the permafrost carbon cycle feedback of 0.06 [0.02 to 0.14] ∘C directly and 0.04 [0 to 0.06] ∘C from the thaw-lag effect will not substantially change the expected value of ZEC on decadal timescales. Thus, the overall conclusion that ZEC will be close to zero in the decades following cessation of emissions remains unchanged.

Here we have assessed the parameter uncertainty of the permafrost carbon cycle feedback contribution to ZEC and have left structural uncertainty unassessed. To quantify structural uncertainty other Earth system models would have to conduct ZECMIP experiments with and without their permafrost components turned on. As many of the models that participated in ZECMIP do have permafrost carbon capable versions of their models e.g., such a study is possible and would make a valuable contribution to the next iteration of ZECMIP.

Here we found that the permafrost carbon feedback contribution to ZEC was insensitive to cumulative CO2 emissions, despite a larger release of CO2 to the atmosphere from permafrost soils in the A3 (2000 PgC) experiment. The linear relationship between cumulative emissions of CO2 and global temperature change is generated by an atmosphere–ocean phenomenon ; thus the atmosphere–ocean system does not distinguish between emissions from the terrestrial biosphere and fossil fuel emissions . Therefore this insensitivity of temperature to carbon released from permafrost soils appears anomalous. However, for intermediate complexity models like the UVic ESCM the cumulative emissions of CO2 vs. global temperature change curve are only approximately linear and the change in temperature with a unit of CO2 emitted declines at high cumulative emission totals, as the logarithmic radiative forcing from CO2 begins to become the dominate effect . Thus the emissions of CO2 from permafrost soil are less effective at warming after 2000 PgC of CO2 has been emitted than when 1000 PgC has been emitted in the UVic ESCM. However, it has been shown the full Earth system models do not have non-linear cumulative emissions of CO2 vs. global temperature change curves . Therefore the insensitivity of the permafrost carbon feedback contribution to ZEC to cumulative CO2 emissions found here should be treated with caution.

To date no Earth system model accounts for abrupt thaw processes in permafrost systems. These processes, including thermokarst production, active hill slope erosion, and coastal erosion, could accelerate thaw processes by 40 % over the next few centuries . Additionally the 2.9pf version of the UVic ESCM (used here) and publicly available 2.10 version of the UVic ESCM do not account for enhanced methane production from permafrost thaw. A methane production scheme has recently been added to a newly developed thread of the model, which preliminarily suggests a warming effect from CH4 production from permafrost soils of 0 to 0.24 ∘C, depending on parameter values and scenario followed . Such values are consistent with expert assessment of . Accounting for these processes will likely increase the estimated effect of the permafrost carbon cycle feedback on ZEC, and therefore the effect of the permafrost carbon feedback on ZEC should be reassessed when these processes are better accounted for in Earth system models.

UVic ESCM 2.10 was one of the two models that participated in ZECMIP that included a permafrost carbon scheme (the other was CESM). The ZEC 50 years after CO2 emissions cease for the A1 experiment (1000 PgC) was 0.03 ∘C for the model version that participated in ZECMIP (UVic ESCM 2.10). This value places UVic ESCM close to the centre of the inter-model range ranking 8th highest of the 18 models that participated in ZECMIP . The model version with permafrost carbon used here ZEC 50 years after emissions cease is -0.02 [-0.07 to 0.08] ∘C; 750 years after emission cease ZEC is 0.70 [0.35 to 1.06] ∘C for the A1 experiment for UVic ESCM 2.9pf and was 0.20 ∘C for UVic ESCM 2.10 in . Evidently the two model versions have similar decadal ZEC values but diverge substantially on centennial timescales. The main difference between UVic ESCM versions 2.9pf and 2.10 is the representation of the ocean , with the newer version of the model having substantially improved ocean dynamics and a state-of-the-art representation of ocean biogeochemistry . Ocean heat and carbon uptake are two of the processes that determine the value of ZEC . Therefore, it is not unexpected that differences in the representation of the ocean would change the ZEC value of a model.

Here we have used a perturbed parameter ensemble with the UVic ESCM to estimate the impact of the permafrost carbon cycle feedback on the value of the CO2 component of the Zero Emissions Commitment. We find 50 years after emissions cease in an experiment where 1000 PgC of CO2 is emitted to the atmosphere that the permafrost carbon feedback adds 0.06 [0.02 to 0.14] ∘C to ZEC, rising to 0.27 [0.12 to 0.49] ∘C 500 years after emissions cease. Additionally following a more realistic emissions trajectory based on historical and SSP4-6.0 emissions adds 0.04 [0 to 0.06] ∘C to ZEC 50 years after emissions cease. This thaw-lag effect diminishes with time after emissions cease. Overall accounting for the permafrost carbon feedback does not change the conclusion that ZEC will be close to zero on decadal timescales , though the effect of abrupt thaw remains unaccounted for and the feedback is of greater concern over longer timeframes.