[1] Most climate modeling studies of future climate have focused on the effects of carbon emissions in the present century or the long‐term fate of anthropogenically emitted carbon. However, after carbon emissions cease, there may be a desire to return to a “safe” CO 2 concentration within this millennium. Realistically, this implies artificially removing CO 2 from the atmosphere. In this study, experiments are conducted using the University of Victoria Earth system‐climate model forced with novel future scenarios to explore the reversibility of climate warming as a response to a gradual return to preindustrial radiative forcing. Due to hysteresis in the permafrost carbon pool, the quantity of carbon that must be removed from the atmosphere is larger than the quantity that was originally emitted (115–180% of original emissions). In all the reversibility simulations with a moderate climate sensitivity, a climate resembling that of the Holocene can be restored by 3000 CE.

1 Introduction [2] Once net anthropogenic carbon emissions cease, the natural sources and sinks of carbon will govern the atmospheric concentration of CO 2 . Long‐term simulations using Earth‐system models suggest that over thousands of years carbon will be gradually incorporated into the oceans [e.g., Archer, 2005; Eby et al., 2009]. However, long‐term model simulations also indicate that most of the temperature anomaly created by burning of fossil fuels will persist even 10000 years into the future. The simulations of Eby et al. [2009], for example, suggest that 70–80% of the peak surface temperature anomaly would remain by the year 12000 CE, for a large range of cumulative carbon emissions (160–5120 Pg C). Given these model findings any attempt to return atmospheric concentration of CO 2 to a “safe” level (after having greatly exceeded such a threshold) will likely require synthetic removal of carbon from the atmosphere. [3] A number of previous model studies have performed simulations where anthropogenic carbon is removed from the atmosphere [e.g., Cao and Caldeira, 2010; Held et al., 2010; Samanta et al., 2010; Boucher et al., 2012; Zickfeld et al., 2013]. These studies have been designed to explore the reversibility of climate change with respect to various metrics of the Earth system, such as surface temperature or thermosteric sea‐level rise [e.g., Zickfeld et al., 2013], or to separate the fast from the slow components of climate warming [Held et al., 2010]. Each of these previous studies has imposed highly idealized rates of atmospheric CO 2 removal. Cao and Caldeira [2010] and Held et al. [2010] prescribed instantaneous returns to preindustrial CO 2 concentrations, while Samanta et al. [2010] and Zickfeld et al. [2013] prescribe linear reductions in CO 2 concentrations. In the study of Boucher et al. [2012] CO 2 transitions from 1% increases in atmospheric CO 2 concentration a year to a 1% decreases in atmospheric CO 2 concentration a year, creating a very abrupt transition from large positive carbon emission to large negative carbon emissions. [4] Boucher et al. [2012] employed the Hadley Centre's complex Earth‐system model (ESM) HadGEM2‐ES and document the most extensive examination of hysteresis within an ESM. The study found that most metrics of the Earth system exhibit hysteresis both with respect to temperature and atmospheric CO 2 concentration. Zickfeld et al. [2013] document part of a model intercomparison of Earth‐system models of intermediate complexity (EMICs) carried out in preparation for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5). For two of the model experiments, the EMICs were forced with a prescribed return to preindustrial forcing over a period of 100 and 1000 years beginning in year 3000 CE. All of the EMICs simulated surface temperature and thermosteric sea‐level anomalies with respect to the preindustrial era that persisted for centuries after the return to preindustrial CO 2 concentrations. Of interest is that two of the EMICs suggested that more carbon would have to be removed from the atmosphere than had originally been emitted to the atmosphere to return to a preindustrial CO 2 concentration. [5] Several technologies have been proposed to remove CO 2 from the atmosphere [e.g., Shepherd, 2009]. Of those proposed, only bio‐energy carbon capture and storage (BECS) [Azar et al., 2006] and chemical open‐air capture of CO 2 [Keith et al., 2006] are considered technologically both feasible and capable of removing sufficient quantities of carbon to reverse the change in atmospheric CO 2 concentration [Matthews, 2010]. Of the Representative Concentration Pathways (RCPs) used in IPCC AR5 [Moss et al., 2010], only the lowest (RCP 2.6) envisions large scale deployment of CO 2 removal technology (in the form of BECS). However, global net primary productivity, a desire not to further compromise fragile ecosystems, and the need to grow sufficient food to feed the human population imposes a limit to the extent that BECS can be deployed [e.g., Shepherd, 2009]. To achieve the magnitude of negative emissions needed to reverse the higher RCPs chemical open‐air capture, powered by a carbon neutral energy source, would likely need to be deployed [Matthews, 2010]. [6] For the model experiments described below, a set of novel future climate scenarios are introduced that prescribe a gradual return to preindustrial CO 2 concentrations, land use, and non‐CO 2 radiative forcing. That is, these scenarios describe a future where a decision has been made to restore the Earth to preindustrial atmospheric composition and land use in hopes of restoring a Holocene‐like climate. The scenarios are used to force the University of Victoria Earth‐System Climate Model (UVic ESCM), which is used to diagnose carbon emission compatible with the scenarios, in addition to examining the reversibility of various metrics of the Earth‐system, including the Greenland ice sheet.

2 Methods 2.1 Future Scenarios [7] Four future scenarios where designed based on the RCPs are used in IPCC AR5 [Moss et al., 2010]. Each of the scenarios follows an RCP exactly up until that RCP reaches its peak CO 2 concentration. After peak CO 2 , each of the scenarios prescribes a decline in atmospheric CO 2 concentration in an exact mirror image to the original rise in CO 2 concentration (Figure 1a). Non‐CO 2 greenhouse gases decline linearly to their preindustrial forcing beginning in the year of peak CO 2 and reaching their preindustrial forcing in the same year CO 2 reaches 280 ppmv (Figure 1b). Sulphate emissions are taken to be zero once CO 2 concentration begins to decline (Figure 1c). Land use is also reversed in these simulations, with land being abandoned in the opposite order that it was acquired until the land use of 1850 is restored (Figure 1d). The pattern of land‐use change causes a complication for the scenario based on RCP 4.5, where large‐scale reforestation occurs before peak CO 2 is reached. In the derived scenario, a period of deforestation occurs after atmospheric CO 2 begins to decline. These scenarios are named the Mirrored Concentration Pathways (MCPs) and are distinguished with the same number as each RCP is derived from. The peak CO 2 concentration occurs in year 2053, 2130, 2151, and 2251 for MCPs 2.6, 4.5, 6.0, and 8.5 respectively. Figure 1 Open in figure viewer PowerPoint (a–d) Forcing for each of the Mirrored Concentration Pathways (MCPs). Note that all of the MCPs except MCP 2.6 reach peak CO 2 concentration after the year 2100 CE. 2.1.1 Rationale for Mirrored Future Scenarios [8] The scenarios introduced here are an attempt to extend climate warming reversal experiments to an idealized but more plausible transition from net positive to net negative carbon emissions. The assumption that atmospheric CO 2 concentration decline will mirror its prior increase is intentionally simple, however, this assumption does follow intuitive economic logic. That is, carbon extraction begins slowly as CO 2 removal machines with a finite lifespan are deployed at some rate. The rate of extraction grows as the machines become more numerous, and new machines become more efficient. As CO 2 concentration approaches its preindustrial concentration, the extraction rate slows as old machines are no longer replaced to avoid having obsolete infrastructure when the goal of 280 ppmv CO 2 concentration is reached. Although it may be possible to reduce atmospheric CO 2 faster than its original increase, such a scenario risks inducing a rate of global cooling greater than the original warming rate. Given the challenges of adapting to a quickly changing climate, it seems unlikely that a high rate of cooling would be desirable. The MCPs are therefore a simple approximation of a fast but plausible return to preindustrial forcing. [9] The mirrored CO 2 paths of the MCPs are to some extent similar to the CO 2 paths in the reversal experiments of Samanta et al. [2010] and Boucher et al. [2012]. However, the MCPs account for the historic trajectory of CO 2 emissions and non‐CO 2 influences on radiative forcing, neglected in previous reversibility studies. [10] To return to a preindustrial forcing, it is necessary to return to preindustrial land use. An exact reversal of land use as envisioned by the MCPs is implausible. However, assuming a continued increase in agricultural yields until the mid 21st century [e.g., Fischer et al., 2009], it should be possible to feed a population of under 10 billion people on a fraction of the global land surface similar to that used for agriculture in 1850 [e.g., Fischer et al., 2009]. 2.2 The UVic ESCM [11] The UVic ESCM is a coupled climate model of intermediate complexity with a full three dimensional ocean general circulation model [Weaver et al., 2001], complex land surface [Meissner et al., 2003], thermodynamic‐dynamic sea ice model, and simplified energy and moisture balance atmosphere [Weaver et al., 2001]. The model has both a terrestrial and an oceanic carbon cycle. The terrestrial carbon cycle is simulated using the Top‐down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) dynamic vegetation model [Cox et al., 2001; Matthews et al., 2004]. The inorganic ocean carbon cycle is simulated following the protocols of the ocean carbon‐cycle intercomparison project [Orr et al., 1999]. Ocean biology is simulated using a nutrient‐phytoplankton‐zooplankton‐detritus ecosystem model [Schmittner et al., 2008]. Ocean sedimentary processes are simulated using an Oxic‐only model of sediment respiration [Archer, 1996]. [12] Two variants of the UVic ESCM are used for the experiments in this manuscript (1) the frozen ground version of the UVic ESCM which includes a deep soil column extending to 250 m depth, soil hydrology in the top 10 m of soil, full freeze‐thaw physics, and a representation of the permafrost carbon pool [Avis et al., 2011; MacDougall et al., 2012]; and (2) the dynamic ice sheet version of the UVic ESCM which couples the Pennsylvania State University ice sheet model into the UVic ESCM providing for simulation of the Greenland and Antarctic ice sheets and ice shelves [Fyke et al., 2011]. Both variants of the UVic ESCM are forced with each of the MCPs. The frozen ground version is used to diagnose CO 2 emissions compatible with each MCP and to simulate the metrics of the Earth‐system displayed below, except for eustatic sea‐level rise. The ice sheet version is used in its Greenland only configuration to estimate the stability and ice loss from the Greenland ice sheet under each MCP. [13] To generate an uncertainty range for the model estimates, the climate sensitivity of the UVic ESCM is varied by artificially modifying the outgoing longwave radiation [Zickfeld et al., 2008]. Each MCP was simulated three times, once each for climate sensitivities of 2.0, 3.2, and 4.5°C for a doubling of atmospheric CO 2 concentration. This range covers the “likely” uncertainty range for climate sensitivity from the fourth assessment report of the IPCC [Hegerl et al., [Hegerl et al., 2007 ]]. The central value (3.2°C) is the inherent climate sensitive of the frozen ground version of the UVic ESCM.

3 Results [14] Various metrics of the Earth‐system are shown in Figure 2 for each MCP and climate sensitivity. In every simulation, surface air temperature shows an asymmetric decline toward preindustrial temperatures following the peak CO 2 concentration. None of the simulations shows a full recovery to the nineteenth century temperatures by the end of the 30th century (Figure 2a), with a residual climate warming of 0.1–1.7°C for the full range of simulations. Similar to previous studies [e.g., Samanta et al., 2010; Boucher et al., 2012], the simulated northern sea ice extent closely follows surface temperature with a recovery beginning soon after temperatures begin to fall (Figure 2d). Permafrost area shows a delayed recovery after surface temperatures begin to fall. In MCP 8.5, permafrost area continues to decline for over a century after peak surface air temperature before commencing a slow recovery. Only under MCP 2.6 does permafrost area reach its 1990s extent by the year 3000 CE (Figure 2f). We note that in every simulation, the meridional overturning circulation returns stronger that its preindustrial strength (Figure 2e). The thermosteric contribution to sea‐level peaks no more than 150 years after the peak surface temperatures is reached, after which it begins a slow decline (Figure 2h). Consistent with previous studies [e.g., Boucher et al., 2012] ocean surface pH very closely follows atmospheric CO 2 concentration, to the extent that the model simulations under each climate sensitivity are indistinguishable (Figure 2c). Figure 2 Open in figure viewer PowerPoint Earth‐system metrics as simulated by the UVic ESCM under each of the four MCPs. Dotted lines are simulations with a climate sensitivity of 2.0°C, solid lines are simulations with a climate sensitivity of 3.2°C, and dashed lines are simulations with a climate sensitivity of 4.5°C. Metrics were generated using the (a–f and h) frozen ground version of the UVic ESCM and the (g) dynamic ice sheet version of the model, and combining output from (i) both version of the model. Note that the combined sea‐level rise includes only contributions from thermosteric rise and Greenland and does not include contributions from Antarctica, small glaciers and ice‐caps, or ground‐water mining. [15] The simulated Greenland ice sheet remains stable under the three lower MCPs despite the high sensitivity of the ice sheet component used in the UVic ESCM to variations in climate sensitivity [Fyke et al., 2011]. Under MCP 6.0, with a climate sensitivity of 4.5°C, the ice sheet losses 0.26m sea‐level equivalent before restabilizing after CO 2 is restored to 280 ppmv. Under the high‐concentration pathway (MCP 8.5), the ice sheet contributes substantially to sea‐level rise, adding 2.69m to sea level under the high‐climate‐sensitivity simulation. The contribution to sea level from the Greenland ice sheet is simulated to be largely irreversible on the millennial timescale considered in this study. Under the middle two MCPs, the ice sheet has regained less that 10% of the mass it had lost by the end of the simulations in the year 3000 CE. The UVic ESCM has a relatively low arctic amplification, another parameter that the ice sheet component is very sensitive to [Fyke, 2011]. Simulations with a higher polar amplification could result in substantially larger contribution to sea‐level rise from the Greenland ice sheet. [16] Table 1 displays the total fossil emissions and total drawdown for each of the simulations with a climate sensitivity of 3.2°C. Consistent with the behavior of the UVic ESCM in the EMIC AR5 intercomparison [Zickfeld et al., 2013], more carbon needs to be removed from the atmosphere than was originally emitted to the atmosphere to restore a preindustrial CO 2 concentration. However, with the addition of the permafrost carbon pool model component, the quantity of carbon that must be removed has grown to between 127 and 153% of that originally emitted to the atmosphere (for the medium climate sensitivity simulations). For the low climate sensitivity model runs, the quantity of carbon that must be removed is between 115 and 130% of that originally emitted to the atmosphere and for the high climate sensitivity model runs between 140 and 181%. Most of this excess carbon originates from the permafrost carbon pool which presumably will gradually reform once permafrost begins recovering. Rates of permafrost carbon pool formation in Alaska following deglaciation were on the order of 7 g C m−2 a−1 for nonpeatland soils [Marion and Oechel, 1993]. Assuming a similar rate following restoration of preindustrial forcing and assuming a permafrost area of approximately 16 million km2, one would expect burial of about 0.15 Pg C a−1 into permafrost soils. For MCP 4.5, this implies that it would take on the order of 3000 years to restore the permafrost carbon pool. Table 1. Cumulative Fossil Fuel Carbon Emissions and Cumulative Carbon Drawdown for Each of the MCPs Scenario Fossil Emissions (Pg C) Drawdown (Pg C) Ratio (%) MCP 2.6 584 896 153 MCP 4.5 911 1389 152 MCP 6.0 1513 2112 140 MCP 8.5 3898 4899 127 [17] To provide a quantitative sense of the timescales for restoring a Holocene‐like climate significant events simulated for MCP 4.5 with climate sensitivity 3.2°C are described below. Under MCP 4.5, atmospheric CO 2 concentration peaks in the year 2130. Surface air temperature peaks two decades later at 2.8°C above the preindustrial temperature. Ocean pH and northern sea ice are restored to their 1990 states by 2280 and 2450, respectively. Sea‐level peaks in 2251, and in the year 3000, surface air temperature is 0.3°C above the preindustrial temperature. Diagnosed net negative emissions begin soon after CO 2 concentration peaks and reach their apex of −9.7 Pg C a−1 in year 2220. The apex negative emissions are very close to the magnitude of present day positive fossil fuel emissions [Olivier et al., 2012]. Negative emissions gradually decline over the following centuries until 2630 when direct human interference in atmospheric composition ends.

4 Discussion 4.1 A Holocene‐Like Climate [18] Recent paleoclimate reconstructions of the Holocene suggest that globally temperatures rose rapidly flowing the end of the last ice age, plateaued between 9000 and 5000 years Before Present (BP) at approximately 0.4°C above midtwentieth century temperatures [Marcott et al., 2013]. Beginning at about 5000 BP, temperatures gradually declined until the rise of industrial civilization resulted in rapid anthropogenic warming [Marcott et al., 2013]. Present day surface air temperatures may not yet have exceeded the full range of those estimated for the Holocene [Marcott et al., 2013]. [19] If one assumes an upper bound of Holocene‐like surface temperature estimates to be those as much as 1°C above the preindustrial surface air temperature [e.g., Marcott et al., 2013], all but one of the simulations presented here suggests a restoration of a Holocene‐like climate by the year 3000 (MCP 8.5 with a climate sensitivity of 4.5°C is the exception). Given that in our simulations, the oceans cool slower than the land surface, there are likely to be large differences between the restored climate and the preindustrial climate at the continental and region scale. 4.2 The Effectiveness of Removing Carbon [20] Many of the problems associated with climate warming originate from the rate of temperature change as opposed to its absolute magnitude [e.g., Thomas et al., 2004]. Although the rate of temperature reduction during the carbon removal stage of the MCPs is slower than the prior rate of temperature increase, the simulated rate of cooling is substantial enough to warrant concern. However, if rates of cooling were found to be too fast, carbon could simply be removed at a slower rate. It is likely that the ability to adapt to a cooling climate would be a key consideration in setting the rate of atmospheric carbon removal in addition to the economic and technological feasibility of carbon removal. [21] Restoring atmospheric CO 2 concentrations to their preindustrial level implies totally decarbonizing the global economy followed by developing the infrastructure to remove carbon from the atmosphere. Matthews [2010] estimated that the economic scale of carbon removal technology would be of similar scale to the fossil fuel powered industry. Therefore, a society that decided to restore a Holocene‐like climate would have to devote a significant fraction of its industrial output to removing carbon from the atmosphere. [22] From the model experiments presented above and those published in literature [e.g., Cao and Caldeira, 2010; Held et al., 2010; Samanta et al., 2010; Boucher et al., 2012; Zickfeld et al., 2013], the only components of the Earth‐system to demonstrate a lack of reversibility are those associated with ice sheets, and even they may recover over many thousands of years. Whether this reversibility is a feature of the natural Earth system or some artifact of our modeling methods is a question requiring further study. State‐of‐the‐art Earth‐system models do not yet simulate complex ecosystem dynamics. These systems are of the most concern for reversibility [e.g., Thomas et al., 2004] as the extinction of biological species is not easily reversed. Despite the technological feasibility of reversing the physical and chemical aspect of climate warming on a millennial timescale, irreversible damage to the biosphere from climate change remains an enduring concern [Barnosky et al., 2011].

5 Conclusions [23] Here novel future scenarios were developed to investigate a gradual return to preindustrial radiative forcing to assess the possibility and timeframe of restoring a Holocene‐like climate. The four scenarios follow the RCPs up until each RCPs reaches its peak CO 2 concentration after which atmospheric CO 2 is reduced in a mirrored image to its original increase. The scenarios were used to force the UVic ESCM under a range of model climate sensitivities. The simulations suggest that a Holocene‐like climate can be restored under all but the highest emissions and climate sensitivity permutation by the year 3000 CE. Due primarily to a strong permafrost carbon cycle feedback in the model, more carbon needs to be removed from the atmosphere than was originally emitted to restore a preindustrial atmospheric CO 2 concentration. Removing carbon from the atmosphere was able to restabilize the simulated Greenland ice sheet. However, the ice sheet regrows slowly regaining less than 10% of its lost mass by the year 3000 CE under the middle two scenarios. These results suggest that even with monumental effort to remove CO 2 from the atmosphere, humanity will be living with the consequences of fossil fuel emissions for a very long time.

Acknowledgments [24] I am grateful for the support from the University of Victoria, NSERC CGS and subsequently NSERC CREATE. I am grateful for critical comments that A.J. Weaver and C. Goldblatt provided for an early draft of this manuscript. J.G. Fyke kindly provided instruction in the use of the Dynamic Ice sheet version of the UVic ESCM. I thank the two anonymous reviewers who provided helpful comments. [25] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.