Simulated responses and feedbacks of permafrost carbon under future emissions pathways and idealized solar geoengineering scenarios

The carbon-rich northern high-latitude permafrost is a potential climate tipping point. Once triggered, its thawing and release of carbon dioxide and methane might unleash irreversible changes in the Earth’s climate system. We investigate the response of permafrost under three Shared Socioeconomic Pathways (SSPs) with no mitigation (SSP5-8.5), moderate mitigation (SSP2-4.5) and delayed mitigation (SSP5-3.4-OS), and three solar geoengineering scenarios applied to each experiment to prevent global warming from exceeding 2 °C above pre-industrial. The long-term negative emissions in SSP5-3.4-OS preserves much more frozen soil than SSP5-8.5, but shows nearly as much permafrost carbon loss this century as SSP2-4.5 due to its mid-century temperature overshoot. Solar geoengineering to meet the 2 °C target above pre-industrial effectively suppresses permafrost thawing and reduces subsequent carbon release from the soil. However, the carbon emission from permafrost still continues after the temperature is stabilized, due to the decomposition of thawed permafrost carbon. More solar insolation reduction is required to compensate the positive permafrost carbon feedback, which exerts greater impacts on the efficiency of solar geoengineering under a scenario with strong climate policy and lower carbon emissions.


Introduction
Constraining global warming well below 2 • C compared to pre-industrial levels is critical to limiting dangerous and cascading impacts of anthropogenic climate change on the Earth system (Park et al 2023), even exceeding 1.5 • C global warming or a temporary overshoot of the 2 • C target could trigger multiple climate tipping points (Armstrong Mckay et al 2022, Wunderling et al 2023).The risks of abrupt and irreversible damage to large-scale Earth system components due to crossing climate tipping points, such as ice sheet collapse (Gregory et al 2020), amazon rainforest dieback (Zemp et al 2017) and permafrost thaw (Teufel and Sushama 2019), rationally should encourage rapid and strong mitigation actions to hold global warming within relatively safe levels (Cai et al 2016, Armstrong Mckay et al 2022).However, the 2 • C global warming is highly likely to be exceeded before the end of this century under the moderate future emission pathway SSP2-4.5 and will definitely be crossed under the unmitigated fossil fuel developed pathway SSP5-8.5 (Tebaldi et al 2021).
Mitigating ongoing climate change requires both stringent GHG emissions reductions and rapid adoption of technologies to achieve near net-zero emissions.GHG emissions reduction is a shared challenge to all countries and economic sectors.Nationally determined contributions (NDCs) to GHG mitigation introduced in 2015 and updated since embody the post-2020 climate pledges of the 193 Parties to the Paris Agreement.Though most of the updated NDCs submitted in 2021 call for more near-term emission reductions than their original 2015 commitments, the likelihood of limiting warming below 2 • C above pre-industrial levels in 2100 is still less than 50% (Ou et al 2021).Moreover, short-term climate policy might lead to unintended long-term consequences.
For example, maximizing land-demanded renewable energy development to meet climate mitigation goals, such as expanding onshore wind, hydropower and solar photo-voltaic generation, may negatively impact biodiversity and carbon storage (Kiesecker et al 2019, Rehbein et al 2020), and the well-intended mitigation polices may increase vulnerabilities in local ecosystem (Spillias et al 2020, Giuliani et al 2022).Only a full realization of the ambitious long-term pledges to net-zero emissions may achieve the 2 • C target (Hausfather andMoore 2022, Meinshausen et al 2022).Hence it is prudent to consider how Earth's climate system may respond both when meeting the 2 • C warming target and overshooting beyond 2 In the face of rapid warming and potential catastrophes, solar geoengineering has been proposed as a temporary approach to partially counteract anthropogenic warming, and to buy time for the development of mitigation technologies (Wigley 2006, Keith andMacMartin 2015).Large-scale solar geoengineering measures such as stratospheric aerosol injection, should be able to reduce mean global surface air temperature (GSAT) by a degree or two relative to those expected by GHG forcing (Robock et al 2009, Kravitz et al 2017), and moderate the intensity and frequency of hazardous extremes under anthropogenic warming (Curry et al 2014, Moore et al 2015, Ji et al 2018).Nonetheless, the development of solar geoengineering systems knowledge is still in an early stage, and concerns about unintended environmental consequences and exacerbation in social inequalities has made it a controversial policy option (Robock 2008, Crook et al 2015).
Previous studies show that the overall cooling under the implementation of solar geoengineering can rapidly slow down permafrost degradation in the northern high-latitude (Jiang et al 2019, Lee et al 2019, Chen et al 2020).The loss of near-surface permafrost carbon is also mitigated under the conjunct effects of the suppressed heterotrophic respiration and shallower active layer thickness, mostly in the northernmost permafrost (Chen et al 2023).However, most existing studies are based on solar geoengineering scenarios designed to compensate the radiative forcing from high emission pathways this century under prescribed atmospheric CO 2 concentrations.How permafrost carbon would respond to and interact with solar geoengineering over longer periods has not been investigated.Moreover, some of the uncertainties in solar geoengineering response arise from the various potential future climate trajectories, which are driven in part by the terrestrial biosphere that controls the growth rate of atmospheric CO 2 concentration (Friedlingstein et al 2020).In this study, we aim to quantify the response of permafrost carbon to GHG scenarios of different mitigation levels, and to the solar geoengineering scenarios maintaining the 2 • C warming target over long time periods within a probabilistic framework.Additionally, we seek to illustrate the impacts of permafrost carbon feedback on the amount of solar irradiance reduction required for different background scenarios.

Model
We use a reduced-complexity Earth system model (ESM) OSCAR v3.2, which is built as a combination of emulators each representing a component of the Earth's system, driven by the radiative forcing from human and natural sources to project the trends in climate responses and feedbacks.The modules and processes in OSCAR emulate the sensitivities of models of higher resolution or complexity, and can be calibrated by outputs from complex models participating in intercomparison projects.Therefore, OSCAR is designed to be used in a probabilistic fashion (Gasser et al 2017).The world in OSCAR is aggregated to 10 broad regions with 5 biomes with biogeochemical characteristics defined individually and assumed homogeneous to represent the average characters in each region or biome (figure 1).The permafrost module in OSCAR emulates four state-of-the-art land surface models with good representations of high-latitude soil carbon processes, splitting thawed permafrost carbon into three carbon pools and then decomposing them with calibrated temperature dependency of heterotrophic respiration rates and turnover times for each thawed carbon pool (Gasser et al 2018).However, the permafrost emulator in OSCAR v3.2 does not distinguish between CO 2 emissions and CH 4 emissions, the

Experiment design
The historical experiments (1750-2014) are forced by anthropogenic emissions from the Community Emissions Data System (CEDS, Hoesly et al 2018), except for the halogenated compounds with specified concentrations.CEDS provides anthropogenic chemically reactive gases, carbonaceous aerosols and CO 2 emissions that cover the full historical time periods, which has been widely used in emission driven historical experiments (Danabasoglu et al 2020).Branching from the end of historical simulations, two Tire 1 SSP scenarios-SSP2-4.5 and SSP5-8.5, and in addition one overshoot scenario SSP5-3.4-OS,are simulated from the year 2015-2200.The emissions in the SSP5-3.4-OSscenario initially follow the unmitigated SSP5-8.5 scenario through 2040, then specify the steepest decarbonization rates of all SSP scenarios, so that the forcing declines to 3.4 W m −2 in 2100 (O'Neill et al 2016).SSP5-3.4-OS was included to explore the climate outcomes from delayed mitigation.On top of the three SSP scenarios, we conduct solar geoengineering experiments (SSP2-4.5-2C,SSP5-8.5-2C and SSP5-3.4-OS-2C) to prevent global warming from exceeding 2 • C above pre-industrial levels.To simulate solar geoengineering in OSCAR, solar insolation is adjusted each year with a proportionalintegral control scheme, which automatically calculates the amount of solar geoengineering in response to departures of the simulated annual mean GSAT from the predetermined objective using sequential decision making (Kravitz et al 2014).To separate the contribution of permafrost carbon release to radiative forcing, a series of experiments without permafrost carbon are also conducted by turning off the permafrost module in OSCAR (with -np as suffix in the experiment names).

Exclusions and constraints
Each experiment is run for a Monte-Carlo ensemble of 10 000 simulations which are drawn from a pool of more than 10 44 potential combinations of parameters that are used in empirical relationships to diagnose the response of Earth system components, such as global and regional climate (temperature and precipitation), oceanic and terrestrial carbon cycles,

Results
The constrained OSCAR model simulated historical temperature changes and the partitioning of anthropogenic emissions among atmosphere, ocean and land are in line with the observation datasets.The mean GSAT increases by 1.12 ± 0.12 • C (1σ range) in 2011-2020 with respect to 1850-1900, well matched with the estimation of 1.09 (0.95-1.20)The fast growth of anthropogenic carbon emissions in the recent decade (2010-2019) and its partitioning between the three reservoirs are also reproduced in OSCAR.Of the simulated annual carbon emissions of 9.9 ± 0.3 PgC yr −1 , 4.8 ± 0.4 PgC yr −1 remained in the atmosphere, 2.6 ± 0.2 PgC yr −1 and 2.5 ± 0.8 PgC yr −1 are taken up by the ocean and land, which again shows good accordance to data-based estimations of 5.1 ± 0.02, 2.5 ± 0.6 and 3.4 ± 0.9 PgC yr −1 (Canadell et al 2021).These results from the historical simulations add confidence in future projections.The simulated warming exceeds the 2 • C level in the 2060s under SSP2-4.5 and in the 2040s under SSP5-8.5 (figure 2(a)).The projected future warmings in 2200 are 2.7 ± 0.8 and 6.0 ± 1.5 • C, relative to the 1850-1900 period, under SSP2-4.5 and SSP5-8.5As temperatures rise, more northern highlatitude permafrost thaws and the permafrost carbon becomes vulnerable to microbial decomposition, leading to more carbon emissions.By 2200, 51 ± 17%, 88 ± 10% and 31 ± 10% more of the frozen soil volume in pre-industrial era is projected to thaw relative to 1850-1900, under SSP2-4.5,SSP5-8.5 and SSP5-3.4-OSrespectively (figure 3(a)).The growth in accessible permafrost carbon together with Radiative forcing induced by permafrost carbon emissions can be diagnosed by comparing simulations with and without the permafrost carbon module (table 1).In experiments with permafrost carbon emissions, the CO 2 radiative forcing (RF CO2 ) is 3.78 ± 0.57 and 9.45 ± 1.17 W m −2 under SSP2-4.5 and SSP5-8.5, accounts for 89 ± 8% and 94 ± 8% of the total anthropogenic radiative forcing without considering solar geoengineering (RF total ) in 2200.On the other hand, changes in RF CO2 follows the emission reduction in SSP5-3.4-OS,reaching a maximum of 3.39 ± 0.43 W m −2 in 2050s, then declines to 1.60 ± 0.27 W m −2 that takes up 85 ± 15% in RF total in 2200.The differences in the radiative forcing induced by CO 2 and CH 4 between simulations with and without permafrost carbon emissions (table 1) are 0.19 ± 0.14, 0.36 ± 0.20 and 0.14 ± 0.10 W m −2 , under SSP2-4.5,SSP5-8.5 and SSP5-3.4-OSrespectively, comparable with differences in RF total (0.19 ± 0.13, 0.37 ± 0.22 and 0.13 ± 0.10 W m −2 ).Compared with the nopermafrost experiments, RF CO2 is higher throughout the simulation in experiments accounting for permafrost carbon feedback of 0.18 ± 0.13, 0.30 ± 0.16 and 0.13 ± 0.10 W m −2 , respectively, under SSP2-4.5,SSP5-8.5 and SSP5-3.4-OS in 2200.Methane radiative forcing (RF CH4 ) is the second biggest contributor to the positive permafrost carbon feedback, and RF CH4 gradually makes a larger part in permafrost carbon emission induced changes in RF total under SSP5-8.5 from the late 21st century and accounts for ∼17% in the additional radiative forcing induced by permafrost carbon release in 2200.This is consistent with less methane uptake by land and accelerated upland soil methane emission under increasing precipitation in the high emission scenario (Guo et al 2023), also aligns with previous estimations regarding the impact of permafrost methane on additional changes in global radiative forcing and temperature (Schaefer et al 2014, Koven et al 2015).The positive permafrost carbon feedback causes extra global warming, the GSAT differences between permafrost and no-permafrost experiments are 0.1 ± 0.1, 0.2 ± 0.2 and 0.1 ± 0.1 • C in 2200, under SSP2-4.5,SSP5-8.5 and SSP5-3.4-OSrespectively (table 1).
The solar insolation reduction required to limit global warming less than 2 • C target reaches a maximum in 2200 of 0.97 ± 0.82 and 6.48 ± 1.23 W m −2 for SSP2-4.5-2Cand SSP5-8.5-2C,and peaks in the 2050s at 0.53 ± 0.66 W m −2 for SSP5-3.4-OS-2C, in accordance with the radiative forcing and temperature changes.The mean solar insolation reduction during the geoengineering period is 0.85 ± 0.17, 4.69 ± 1.73 and 0.36 ± 0.14 W m −2 for SSP2-4.5-2C,SSP5-8.5-2C and SSP5-3.4-OS-2Crespectively.However, the permafrost carbon emissions still continue after the GSAT is stabilized, which means extra amounts of solar insolation reduction are required to control the temperature from exceeding 2 • C due to the positive permafrost carbon feedback caused by thaw-lag effect (MacDougall 2021).The solar insolation reductions are 0.09 ± 0.01, 0.08 ± 0.02 and 0.06 ± 0.02 W m −2 more under SSP2-4.5-2C,SSP5-8.5-2C and SSP5-3.4-OS-2Cthan under corresponding no-permafrost experiments, respectively, smaller than the permafrost carbon emissions induced RF total differences in the SSP2-4.5,SSP5-8.5 and SSP5-3.4-OSexperiments (table 1).This is because the permafrost thawing and attendant permafrost carbon feedback are effectively suppressed by solar geoengineering.The extra solar insolation reduction required to balance GHGs warming induced by permafrost emissions are equivalent to 2 ± 4% of the total solar insolation reduction under the high-emission scenario SSP5-8.5.The relative fraction of extra solar insolation reduction increases to 11 ± 4% and 18 ± 5% under the mitigation scenario SSP2-4.5 and the overshooting scenario SSP5-3.4-OS.This is because of the greater fraction of permafrost carbon emissions in total carbon emissions under less intensive scenarios (Schaefer et al 2014).Moreover, the atmospheric methane concentrations are higher under solar geoengineering experiments compared to the reference experiments (table 1), as the oxidation by hydroxyl radicals in the troposphere is the largest atmospheric sink of methane (Saunois et al 2016), and decreased temperature and reduced biomass burning under solar geoengineering weaken the oxidation intensity (Voulgarakis et al 2010).Therefore, further manipulation in solar insolation reduction is required if methanogenesis is to be well-represented in the model, especially under SSP5-8.5.

Conclusions and discussion
The northern high-latitude have experienced an outpacing warming trend than the low latitudes (Wang et al 2016, Post et al 2019), and this rapid warming is expected to continue in model simulations of the future (Biskaborn et al 2019, Davy andOutten 2020).Gradual thawing of the carbon-rich permafrost promotes the decomposition of soil carbon, resulting in more GHGs emissions into the atmosphere and additional global warming.This positive permafrost carbon feedback has profound impacts on the global land carbon balance, and reduces the anthropogenic emission budget threatening the global goal of limiting warming to targets of 1.5 The OSCAR v3.2 simulated future carbon cycle responses under SSP5-8.5 and SSP5-3.4-OSscenarios agree well with full complexity ESMs.For example, OSCAR v3.2 projects that under SSP5-8.5 the carbon sequestration capacity of the ocean and land would gradually decline after 2100, but both would still act as net carbon sinks throughout 2200; under SSP5-3.4-OS the terrestrial sink-to-source transition occurs in the late 21st century, while the ocean shifts to carbon source in early 22nd century, and then reverses back to a weak sink in the late 22nd century, these simulated responses of carbon cycle are similar to that of CESM2-WACCM (Koven et al 2022).In addition, the OSCAR v3.2 projected extra warming induced by permafrost carbon emissions are in agreement with results from multi-research comparisons in Schaefer et al (2014), with an additional 0.05 • C-0.15 • C and 0.29 ± 0.21 • C temperature rises under RCP4.5 and RCP8.5.
Our study finds that reductions to zero emissions would stabilize the permafrost, and the SSP5-3.4-OSscenario shows long-term benefit in saving hundreds Pg of carbon in permafrost region.Nevertheless, the delayed clean development that exposes more thawed permafrost carbon during overshoot period, could still result in permafrost carbon losses as large as that under mild warming pathways in 21st century.However, SSP5-3.4-OSdemands the highest decarbonization rate of any in the SSP database (up to −1.3 Gt CO 2 /yr/yr, Tilmes et al 2016), this drastic emission reduction starts in only 20 years from now, with longterm negative emissions from the mid-21st century that are impracticable with rates of current technology developments.The risks of temperature overshoot combined with the implausible assumptions in SSP5-3.4-OS,shows the importance of an early mitigation or artificial intervention to prevent temperature overshoot beyond the 2 • C warming target.The thawed permafrost volume and accompanying permafrost carbon emissions can be effectively reduced by solar geoengineering.Idealized solar geoengineering used to control warming exceeding 2 • C target reduces the permafrost carbon loss by 23 ± 32, 200 ± 122, and 4 ± 12 Pg compared with SSP2-4.5, SSP5-8.5 and SSP5-3.4-OS,respectively.These reduced permafrost carbon emissions would reduce the atmospheric carbon burden (Keith et al 2017).
The OSCAR v3.2 represents the average changes in each aggregated region, which ignore the different grid/subgrid scale responses and climate extremes within the broad region.OSCAR cannot capture regional differences in solar geoengineering as a full ESM would.In addition, the constant pattern scaling of warming prevents OSCAR from simulating the residual polar warming amplification under solar geoengineering (Henry and Merlis 2020), which reduces the efficacy of solar geoengineering to retain the permafrost according to a previous study (Chen et al 2023).However, it is visible that the permafrost carbon feedback plays a non-negligible role in policy relevant assumptions to maintain for long-term temperature targets.The potential impact of permafrost carbon feedback is missing in existing geoengineering studies.
The studies that have analyzed carbon cycle feedback under solar geoengineering (Cao and Jiang 2017), show that consideration of the carbon cycle feedback reduced the solar insolation reduction required to achieve a specific warming level.But our study shows consideration of permafrost carbon release would increase required solar insolation reduction.This demonstrates the importance of permafrost carbon feedback in regulating the amount of solar geoengineering to archive specific warming targets, especially under a scenario with strong climate policy and lower carbon emissions.Given that complex permafrostrelated processes are not fully represented in the model we use and also in most existing ESMs, we encourage multi-model studies using comprehensive ESMs to gain a more robust understanding of permafrost carbon feedback under solar geoengineering.

Figure 1 .
Figure 1.The broad regions and the regional land cover fraction of biomes of year 2014 in OSCAR.Based on Houghton and Nassikas (2017), the world is divided into 10 regions with different land-use histories according to their geographical proximities and economic similarities: Sub-Saharan Africa (SSA), Latin America (LAM), South and Southeast Asia (SSA), North America (NAM), Europe (EUR), Former Soviet Union (FSU), China (CHN), North Africa and West Asia (NAWA), East Asia (EAS) and Oceania (OCA).The prescribed biome area changes are derived from the Land-Use Harmonization version 2 datasets (Hurtt et al 2020).

Figure 2 .
Figure 2. The changes in global surface air temperature (GSAT) w.r.t 1850-1900 levels (a), the radiative forcing induced by CO2 and CH4 (b), and the amounts of solar insolation reduction applied to limit global warming exceeding 2 • C (c).Results with/without permafrost carbon emissions are shown in solid/dash lines.The shadings are uncertainties (mean ± 1std) for simulations accounting for permafrost carbon emissions.In panel (a), the filled (OSCAR) and hollow (IPCC AR6) markers and associated horizontal bars denote the time periods (mean ± 1std for OSCAR, and threshold-crossing time ± 10 year for IPCC AR6) when the 2 • C warming is exceeded under SSP2-4.5 (green) and SSP5-8.5 (red).
respectively.The overshoot scenario, SSP5-3.4-OS,significantly reduces temperature warming compared with SSP5-8.5 and SSP2-4.5.More aggressive emission reductions in SSP5-3.4-OSleads to an earlier and sharper decline in temperature.The global warming under SSP5-3.4-OSreaches its peak at 2.1 ± 0.3 • C in the 2050s, then starts cooling and becomes lower than SSP2-4.5 in 2060s, finally stabilizes at 1.3 ± 0.5 • C relative to 1850-1900 by the mid-22nd century.The 2 • C warming target is crossed for 28 ± 34 years under SSP5-3.4-OS, the turning point of global warming corresponds to the peak in atmospheric CO 2 concentration.
• C. The top 3 m soil of the Northern Hemisphere permafrost region stores approximately 1035 ± 150 Pg organic carbon (Hugelius et al 2014), which is about 115% the atmospheric burden of carbon or about half of the global soil organic carbon (Strauss et al 2017).The carbon mobilization in the northern permafrost area may exert great impacts on atmospheric CO 2 and CH 4 in future (Lenton et al 2019, Miner et al 2022).The high rates of climate warming over the northern high-latitude exponentially accelerate microbial activity, raising the temperature sensitivity of soil carbon (Schuur et al 2008, Koven et al 2017), leading to rising permafrost carbon vulnerability (Crowther and Bradford 2013, MacDougall and Knutti 2016, Burke et al 2017, Varney et al 2020).Decomposing soil carbon from the thawing permafrost increases atmospheric GHG concentrations and triggers a positive permafrost carbon feedback accelerating climate warming (Koven et al 2011, MacDougall et al 2012).The extra GHG emissions from the permafrost region should be accounted for in assessing the global carbon budget compatible with meeting global temperature targets, as it diminishes the CO 2 humankind can emit (Gasser et al 2018).

Table 1 .
Projected changes in global surface air temperature (GSAT), CO2 radiative forcing (RFCO2), CH4 radiative forcing (RFCH4), total anthropogenic radiative forcing without considering solar geoengineering (RF total ), thawed permafrost volume and permafrost carbon stocks w.r.t 1850-1900.Experiments with '-np' in their names have permafrost module turned off.Experiments with '-2C' in their names adopt solar geoengineering to prevent global warming from exceeding 2• C w.r.t.1850-1900.Values are provided as the weighted mean ± 1 standard deviation of the 1796 simulations.
(Quilcaille et al 2023).All final results are reported as the weighted means and standard deviations of the remaining 1796 simulations, using the normalized likelihood as weight (table1).
• C or 2 • C (Schaefer et al2014, Gasser et al 2018, MacDougall 2021, Natali et al  2021, Fernandez-Martinez et al 2023).In this study, we use the reduced-complexity model OSCAR v3.2 to assess the potential impacts of permafrost degradation and carbon release on climate scenarios following both unmitigated and mitigated pathways, and in the context of solar geoengineering to achieve the 2 • C warming target.