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# Climate Change and Carbon Cycle Feedbacks

## Summary and Keywords

Climate and carbon cycle are tightly coupled on many time scales, from the interannual to the multimillennial. Observation always shows a positive feedback between climate and the carbon cycle: elevated atmospheric CO2 leads to warming, but warming is expected to further release of carbon to the atmosphere, enhancing the atmospheric CO2 increase. Earth system models do represent these climate–carbon cycle feedbacks, always simulating a positive feedback over the 21st century; that is, climate change will lead to loss of carbon from the land and ocean reservoirs. These processes partially offset the increases in land and ocean carbon sinks caused by rising atmospheric CO2. As a result, more of the emitted anthropogenic CO2 will remain in the atmosphere. There is, however, a large uncertainty on the magnitude of this feedback. Recent studies now help to reduce this uncertainty. On short, interannual, time scales, El Niño years record larger-than-average atmospheric CO2 growth rate, with tropical land ecosystems being the main drivers. These climate–carbon cycle anomalies can be used as emerging constraint on the tropical land carbon response to future climate change. On a longer, centennial, time scale, the variability of atmospheric CO2 found in records of the last millennium can be used to constrain the overall global carbon cycle response to climate. These independent methods confirm that the climate–carbon cycle feedback is positive, but probably more consistent with the lower end of the comprehensive models range, excluding very large climate–carbon cycle feedbacks.

The intimate coupling between the global carbon cycle and the climate system is well established. The state of the climate system depends on atmospheric CO2 concentrations, but this latter is also directly affected by changes in the climate system. The CO2 → Climate relationship has been known for more than a century, while the understanding of the Climate → CO2 relationship is more recent. This two-way interaction induces a feedback loop: changes in atmospheric CO2, either natural or driven by human activities, induce a change in climate, which in turn has an impact on the global carbon cycle and hence on atmospheric CO2.

# The Effect of CO2 on Climate

The physical mechanisms describing the CO2 → Climate relationship (i.e., the impact of a change in atmospheric CO2 concentration on global temperature) have been first described more than a century ago (Arrhenius, 1896; Callendar, 1938). In a seminal paper entitled “On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground,” Svante Arrhenius estimated the heat-trapping capacity of the Earth’s atmosphere, and from there, estimated how the Earth surface temperature would change if atmospheric CO2 were to increase or decrease. Over the second part of the 20th century, multiple evidences confirmed the human perturbation of the global carbon cycle and its potentially large implications for the climate system.

Probably the most alarming evidence was the atmospheric measurements of carbon dioxide initiated by R. Revelle and his young coworker C. D. Keeling in the late 1950s (Keeling, 1960; Keeling et al., 1976). The atmospheric CO2 concentration record at the Mauna Loa observatory, now simply known as “the Keeling curve,” showed two prominent features of the global carbon cycle (Figure 1). First, the data clearly show the seasonal pulse of the atmospheric CO2 concentration, with lower-than-average CO2 during the Northern hemisphere summer and conversely during the winter. This seasonal pulse is primarily due to the terrestrial biosphere, with plant photosynthesis removing CO2 from the atmosphere (in spring and summer) and soil decomposition releasing CO2 to the atmosphere (in fall and winter). The second unambiguous signal from the Keeling curve is the gradual increase in atmospheric CO2 concentration from year to year. When Keeling started the measurements at Mauna Loa in 1958, atmospheric CO2 concentration was around 315 ppm, and it passed the symbolic 400-ppm level in 2014, with a current rate of CO2 increase of about 2 ppm per year (Ciais et al., 2013). It has been clear from the very beginning of these measurements that the reasons for this long-term increase had to be found in fossil fuel burning. In 1960, C. D. Keeling concluded in one of his papers: “At South Pole, the observed rate of increase [of atmospheric CO2] is nearly that to be expected from the combustion of fossil fuel …” (Keeling, 1960).

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Figure 1. Atmospheric CO2 concentration (in ppmv) as recorded at the Mauna Loa Observatory, Hawaii. This record, commonly referred at the Keeling curve, clearly shows the increase of CO2 concentration in the atmosphere as well as the annual cycle of CO2.

Another extremely powerful evidence came from ice core measurements in the early 1980s: spectrometric measurements of air bubbles captured in ice cores allowed reconstruction of the atmospheric CO2 concentration (Barnola, Raynaud, Korotkevich, & Lorius, 1987; Delmas, Ascencio, & Legrand, 1980). Parallel measurements of isotopic composition of the ice allowed inferring Antarctic temperature. The ice core measurements were essential to (a) demonstrate how unusual the current level of atmospheric CO2 is and (b) illustrate how closely CO2 and temperature covaried in the past. Ice core records now go back 800,000 years, spanning eight glacial–interglacial cycles, and clearly indicate that “the atmospheric concentrations of carbon dioxide, methane, and nitrous oxide have increased to levels unprecedented in at least the last 800,000 years” (IPCC, 2013) (Figure 2). Ice core data indeed show that atmospheric CO2 concentrations were about 180 ppm during glacial (cold) times and about 280 ppm during interglacial (warm) times. The Earth oscillates between glacial and interglacial states with a periodicity of about 100,000 years; the last glacial period started declining about 20,000 years ago. Current concentrations of about 400 ppm are well above this natural glacial–interglacial range. Furthermore, ice cores of the Holocene (current interglacial) and from the last millennium show that atmospheric CO2 concentration was relatively stable, around 280 ppm, until the beginning of the Industrial Revolution, where atmospheric CO2 started increasing continuously.

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Figure 2. Variations of the atmospheric concentrations of the greenhouse gases CO2 (red), CH4 (blue), and N2O (green) derived from air trapped within ice cores from Antarctica and from recent atmospheric measurements. Also shown are the variations of deuterium (δ‎D; black), a proxy for local temperature, and benthic δ‎18O marine records (gray), a proxy for global ice volume. The shading indicates the last interglacial warm periods, characterized by higher greenhouse gas concentration and higher temperature. The stars and labels indicate atmospheric concentrations at year 2000.

The ice core data also provides clear evidences that CO2 plays a key role in the climate system. CO2 and global temperature (recorded in the ice isotopic composition [deuterium]) covary during glacial–interglacial cycles, with glacial times characterized by cold temperature (about 5°C colder than present day) and low CO2 (180 ppm) and interglacial times characterized by warmer temperature and higher CO2 (280 ppm). This covariance has wrongly been used as a “demonstration” that CO2 is not responsible for climate change, given that the ice core data show that CO2 changes lag temperature changes. Such simple analysis is simply wrong, however, as it misses the entire dynamic of the coupled climate and CO2 system: glacial cycles are triggered by changes in the Earth orbital configuration leading to a global cooling (for glacial inceptions). The cooling induces a series of Earth feedbacks, the first one being equatorial extension of ice sheets, reducing the Earth albedo, and enhancing the initial cooling; the second one being changes in oceanic physics and biogeochemistry, leading to more oceanic carbon storage, reducing atmospheric CO2, again enhancing the cooling. The gradual decrease in atmospheric CO2 from 280 to 180 ppm during glacial inception is a key driver of the glacial cooling.

Climate models developed since the 1960s also greatly contribute to better understanding of the CO2 → Climate relationship. Three-dimensional climate models started being developed in the 1960s (Manabe & Strickler, 1964), have been continuously improved since, and are still the primarily tools used to address two key questions.

First, can we attribute the climate change observed over the instrumental period to human activities or could it be due to natural variations of the Earth system? Answering that question requires climate models simulating the historical period, with combinations of natural (e.g., volcanoes, solar cycles) and anthropogenic (e.g., greenhouse gases, aerosols) forcings. Comparison with observations then allows telling if anthropogenic forcing is required to explain the observed changes. The answer to that question is now unambiguous: “human influence on the climate system is clear,” and more precisely, “It is extremely likely1 that more than half of the observed increase in global average surface temperature from 1951 to 2010 was caused by the anthropogenic increase in greenhouse gas concentrations and other anthropogenic forcings together” (IPCC, 2013).

Second, can we anticipate what future climate change could be? In the 1980s, this was investigated looking at the response of atmospheric general circulation models to a doubling of the atmospheric CO2 concentration (Hansen et al., 1984; Manabe & Stouffer, 1980). In the early 21st century, the climate community has been using Earth system models, which couple the atmosphere–ocean–land physical system to the global carbon cycle and atmospheric chemistry (including aerosols). These models simulate the transient response of the climate system over the 20th and 21st centuries, assuming different scenarios of greenhouse gases and aerosol emissions for the future (Collins et al., 2013).

Despite the tremendous effort from the climate community to address that second question of central policy relevance, the uncertainty in terms of climate projection remains high. There is obviously a large uncertainty in the future of greenhouse gas emissions, depending on future socioeconomic development, climate mitigation policies, and so on. However, there is also a large uncertainty coming from the climate response itself, for a given change in the radiative forcing. That uncertainty, primarily due to physical feedbacks, has been a major concern for several decades. In 1979, the U.S. National Academy of Sciences report Carbon Dioxide and Climate: A Scientific Assessment, led by J. Charney, estimated “the most probable global warming for a doubling of atmospheric CO2 to be near 3°C with a probable error of ± 1.5°C” (NRC, 1979). The latest estimate reported in the Intergovernmental Panel on Climate Change Fifth Assessment Report (IPCC AR5) happens to be identical with an equilibrium climate sensitivity2likely range of 1.5°C to 4.5°C (IPCC, 2013). A large fraction of this uncertainty comes from the unknown fate of clouds in a warming world and their net radiative forcing (Bony et al., 2006; Flato et al., 2013).

# The Effect of Climate on CO2

The “other side of the coin” (i.e., the effect of climate change on atmospheric CO2) emerged as a scientific concern only in the late 1980s–early 1990s. Probably the first paper that described and attempted to quantify the climate–carbon cycle feedback was written by D. Lashof in 1989 (Lashof, 1989). Lashof identified several biogeochemical feedbacks defined as “those that involve the response of the biosphere and components of the geosphere not considered in typical climate models.” He listed 10 potential biogeochemical feedbacks involving ocean and terrestrial systems (see Table 1 in his paper). With great intuition, he wrote, “ideally these feedbacks should be analyzed by incorporating their effects … into a dynamic model that includes the general circulation of the atmosphere and oceans, marine chemistry and biology, atmospheric chemistry, and terrestrial ecosystems. Such an approach would allow explicit consideration of the time dependence of each feedback process, but is not feasible at this time.” Nevertheless, he provided an original, back-of-the-envelope calculation of these biogeochemical feedbacks.

Both on the ocean and on the land side, global carbon cycle models have been developed, starting from simple box models in the 1970s (see Bolin, 1986; Oeschger, Siegenthaler, Schotterer, & Gugelmann, 1975), to full tridimensional models for the ocean biogeochemistry (Maier-Reimer & Hasselmann, 1987; Sarmiento, 1986) and spatially explicit models of terrestrial ecosystems (Potter et al., 1993; Rastetter et al., 1991). The first objective of these carbon cycle models was to quantify the contribution of ocean and land ecosystems to the current or historical global carbon budget. C. D. Keeling was the first to quantify the airborne fraction, the fraction of the anthropogenic CO2 emissions that remains in the atmosphere, more than half of the emitted CO2 (Keeling, 1973; Keeling et al., 1976). Those measurements had a profound implication: atmospheric CO2 is increasing because of CO2 emissions from fossil fuel combustion, but the atmospheric increase is significantly lower than those emissions. Not all of the CO2 emitted by fossil fuel burning is remaining in the atmosphere; the ocean and the terrestrial ecosystems are actively removing a significant fraction of the perturbed atmospheric CO2. It was initially believed that the ocean was the main sink of carbon until it became clear that a land sink was needed to close the carbon budget (Tans, Fung, & Takahashi, 1990). It is now admitted that both the land and the ocean play comparable roles, each removing from the atmosphere about 25%–30% of the global anthropogenic CO2 emissions from fossil fuel burning and land use change (Ciais et al., 2013; Le Quéré et al., 2009, 2013) (Figure 3).

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Figure 3. Schematic of the global carbon budget, showing anthropogenic sources from fossil fuel burning and cement production as well as from land use changes, atmospheric CO2 increase, and land and ocean sinks. All figures are in GtC/yr.

The processes at play are relatively clear for the ocean carbon sink. The increase in atmospheric CO2 concentration enhances the diffusive exchange of CO2 from the atmosphere to the ocean surface. More CO2 enters to ocean, predominantly at high latitudes, where the sinking of water masses depletes the ocean surface of carbon (with respect to the atmosphere); conversely, CO2 is released to the atmosphere in equatorial upwelling zones, where carbon-rich waters are brought back from depth to the ocean surface. In a natural unperturbed state, these fluxes balance and the global ocean is neither a sink nor a source of carbon to the atmosphere. However, with increasing atmospheric CO2 concentration, the system is pushed away from equilibrium and more CO2 enters into the ocean, as the atmospheric CO2 concentration is increasing faster than the average concentration at the ocean surface.

For terrestrial ecosystems, the processes responsible for the carbon sink as less well understood. Again, atmospheric CO2 increase is believed to be a key driver of the sink: higher CO2 concentration allows terrestrial plants to sustain a higher photosynthesis, inducing a net storage of carbon in vegetation and soil. Although there are clear evidences of a positive response of ecosystems to CO2 from controlled elevated CO2 experiments (Norby et al., 2005), there are no direct global-scale observations of that fertilization process.

Despite this lack of definitive understanding, land and ocean carbon models have been used to estimate the historical carbon sinks. The early models were primarily driven by atmospheric CO2 increase, later on also by climate change and variability, and more recently by nitrogen deposition (Le Quéré et al., 2009; Sitch et al., 2015). The combination of model estimates, direct oceanic CO2 observations, and atmospheric measurements of CO2 and other tracers allows a reasonably clear understanding of the current carbon sinks. Out of the 9 PgC annually released from fossil fuel and land use changes, about 2.6 PgC are absorbed by the land ecosystems, and 2.3 PgC by the global oceans, leaving about 4 PgC in the atmosphere every year (Ciais et al., 2013) (Figure 3).

However, the key question is whether these sinks will continue to operate in the future and remove more than half of the anthropogenic CO2 injected in the atmosphere. The ocean and the land ecosystems provide a unique service to humanity. Without these sinks, the increase in atmospheric CO2 would be about twice as large; present-day atmospheric CO2 concentration would be above 500 ppm already, inducing a warming of more than 2°C above preindustrial level. There is then an urgent need to better understand the processes governing these carbon sinks and whether they could decline in the future.

Global land and ocean models were used to investigate the fate of ocean or land carbon storage under future climate. Global ocean models forced with a scenario of atmospheric CO2 over the 21st century would simulate a continuous increase in ocean CO2 uptake, driven by the growing imbalance of CO2 partial pressure between the atmosphere and the ocean surface. However, when accounting for the induced climate change, the same models would show a significant reduction of carbon uptake, primarily driven by the ocean stratification and reduced ocean thermohaline circulation (Maier-Reimer, Mikolajewicz, & Winguth, 1996; Sarmiento, Hughes, Stouffer, & Manabe, 1998; Sarmiento & Le Quéré, 1996). Terrestrial models also investigated the effect of CO2 and climate, always agreeing on the positive response of land carbon storage to atmospheric CO2 increase (the so-called fertilization effect), but not reaching consensus on the terrestrial ecosystem response to the associated climate change. Some earlier studies found an enhanced terrestrial productivity (Melillo et al., 1993), while later studies found the opposite (Cao & Woodward, 1998a, 1998b). The Third Assessment Report of IPCC concluded that, by the mid-21st century, climate change would reduce the land carbon uptake by 21% to 43% and the ocean carbon uptake by 6% to 25%, relative to CO2-only-driven uptakes (Prentice et al., 2001) (Figure 4).

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Figure 4. Projections of anthropogenic CO2 uptake by process-based models. Dynamic global vegetation models following a historical and future CO2 concentrations pathway forced with CO2 concentration only (a) and these CO2 concentrations plus simulated climate changes (b) obtained from the Hadley Centre climate model. Panel (b) also shows the envelope of the results from panel (a) (in gray). Process-based ocean carbon models were run with the same CO2 concentrations, assuming a constant climate (c), and a subset of these models with climate change (d). Panel (d) also shows the multimodel average of the results from panel (c) (in black).

# The Coupled Climate–CO2 System

All these early studies led to a simple conclusion for the climate modeling community: they had to include the global carbon cycle in climate models. Future trajectories of atmospheric CO2 will be determined by CO2 emissions, obviously, but also by the land and ocean carbon sinks, which will be affected by the simulated climate change. Hence, the CO2–climate system is coupled: future climate change depends on atmospheric CO2 increase (and other forcing agents), but in return, atmospheric CO2 increase depends on climate change (Figure 5).

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Figure 5. Schematic of the climate–carbon cycle feedback. Atmospheric CO2 increase induces climate change, which in turn has an impact on ocean and land carbon uptakes, hence controlling atmospheric CO2.

Such global simulations of biogeochemical processes embedded in climate models appeared only at the turn of the 21st century (Cox, Betts, Jones, Spall, & Totterdell, 2000; Friedlingstein et al., 2001). Two new models coupled standard general circulation models (GCMs) with land and ocean carbon cycle models in order to interactively simulate the evolution of atmospheric CO2. The principle was to drive the models with anthropogenic CO2 emissions (EMI), let the models calculate the land and ocean carbon sinks (Fl and Fo), and then diagnose the growth of atmospheric CO2 (Ca) as the residual between emissions and sinks:

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The models were fully coupled, atmospheric CO2 was calculated interactively following the above equation, the CO2-induced climate change was simulated by the climate models, and the land and ocean carbon cycles were controlled by both atmospheric CO2 and the state of the simulated climate. These developments occurred almost simultaneously at the Hadley Centre in the United Kingdom and at the Institut Pierre-Simon Laplace (IPSL) in France. Although these new models and their main result—that there is a positive feedback between climate change and the global carbon cycle—had a profound impact on the climate modeling community; in retrospect, they were only the natural outcome of growing evidence that had pointed to the sensitivity of the global carbon cycle to climate change.

Both modeling groups performed similar simulations; first, a fully coupled 20th- and 21st-century run with 21st-century CO2 emissions following either the IPCC IS92a (Hadley) or the SRESA2 (IPSL) scenario; second, an uncoupled run with the same emission scenario, but holding the radiative forcing from CO2 at preindustrial level. In both runs, the models compute atmospheric CO2 as the difference between the prescribed emissions and the simulated land and ocean carbon sinks. However, in the coupled runs the land and ocean carbon cycles are “seeing” both CO2 increase and climate change (as the climate evolves as the simulated atmospheric CO2 increases), while in the uncoupled runs the land and ocean carbon cycles are “seeing” only the atmospheric CO2 increase (as the climate is held at its preindustrial level). From the coupled and uncoupled simulations, one can compare the simulated atmospheric CO2 levels; any difference will be due to the effect of climate change on the carbon sinks. Indeed, the difference in simulated atmospheric CO2 is a measure of the gain of the climate–carbon cycle feedback:

$Display mathematics$
(1)

Where $ΔCacou$ and $ΔCaunc$ are the increase in atmospheric CO2 relative to preindustrial in the coupled and uncoupled simulations respectively and $𝑔$ is the gain of the climate–carbon cycle system. The gain of the Hadley Centre model was about 0.4 while the gain of the IPSL model amounted to 0.17. In units of atmospheric CO2, the Hadley model simulated a CO2 concentration about 250 ppm higher by 2100 in the coupled simulation (1025 ppm) than in the uncoupled simulation (800 ppm), while the IPSL model simulated a CO2 concentration that was “only” 75 ppm higher in the coupled simulation (770 ppm) than in the uncoupled simulation (695 ppm) (Cox et al., 2000; Dufresne et al., 2002; Friedlingstein, Dufresne, Cox, & Rayner, 2003).

This wide range, although only based on two models, generated a worldwide interest in climate–carbon cycle modeling. Quite rapidly, the Climate Carbon Cycle Model Intercomparison Project (C4MIP) was set up (Cox, Friedlingstein, & Rayner, 2002; Fung, Rayner, Friedlingstein, & Sahagian, 2000) and within less than five years, 11 models had performed similar experiments (Friedlingstein et al., 2006). The bad news is that the uncertainty increased, with some models simulating near-zero climate carbon cycle gain (although still positive). Most of the uncertainty originated from the land biosphere and its response to atmospheric CO2 increase and climate change. The fertilization effect, which largely contributes to the current land carbon sinks, showed a factor of 10 uncertainty in the future, with a sensitivity (called $βl$) ranging by 2100 between 0.2 and 2.8 GtC stored in terrestrial ecosystems per ppm increase in the atmosphere. Likewise, the climate effect on the carbon cycle (called $γl$) showed a similar uncertainty, being negative (i.e., warming leads to loss of carbon from terrestrial ecosystems) and ranging between 20 and 177 GtC loss per degree of warming. Mathematically, these two terms can be estimated from the coupled and uncoupled simulations, assuming that the carbon cycle responds linearly to atmospheric CO2 and climate change:

$Display mathematics$
(2)

Where $ΔCl$ is the change in the land carbon store,$ΔCa$ the change in atmospheric CO2, and $ΔT$ the change in global temperature. A similar equation applies for the change in the ocean carbon storage $ΔCo$:

$Display mathematics$
(3)

The sensitivity terms $β$ and $γ$ for the land and ocean can be diagnosed successively, solving for $β$ from the uncoupled simulation (above equations where $ΔT$ equals zero), and then solving for $γ$ from the coupled simulation (above equations) (Figure 6). The linear framework above is a rather simple approximation; warming is not strictly linear with CO2, it saturates at high CO2 levels. Likewise, carbon dissolution in the ocean surface saturates at high CO2 concentration, as does plant photosynthesis; carbon loss may increase nonlinearly with larger warming, and so on. However, this framework allows diagnosing the different factors ($β$ and $γ$) for the purpose of model comparisons and evaluation against the historical record.

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Figure 6. Impact of climate change on land carbon uptake (left) and ocean carbon uptake (right). Each line represents one C4MIP Earth system model.

Despite the large uncertainty, all models agreed that climate change would reduce carbon storage (i.e., $γ$ is negative), primarily due to an enhancement of soil organic decomposition under a warming world (Friedlingstein et al., 2006). Almost 10 years later, within the Coupled Model Intercomparison Project Phase 5 (CMIP5), a similar analysis was performed with CMIP5 Earth system models (ESMs), giving essentially the same conclusion: the land carbon cycle response to atmospheric CO2 and climate change is still poorly constrained (Arora et al., 2013). New ESMs include a representation of the nitrogen cycle. This has two opposite effects on land carbon storage. First, accounting for nitrogen leads to a lower response to atmospheric CO2, as nitrogen limitations reduce the photosynthesis enhancement under increasing atmospheric CO2. Second, nitrogen also reduces the carbon loss due to climate change, as soil warming leads to increased nitrogen mineralization, hence increasing nitrogen availability to the plant (Zaehle, Friedlingstein, & Friend, 2010; Zaehle et al., 2010).

The Summary for Policy Makers of the Working Group I of the IPCC AR5 headlined that “climate change will affect carbon cycle processes in a way that will exacerbate the increase of CO2 in the atmosphere (high confidence).” More specifically, it stated “based on Earth System Models, there is high confidence that the feedback between climate and the carbon cycle is positive in the 21st century; that is, climate change will partially offset increases in land and ocean carbon sinks caused by rising atmospheric CO2. As a result more of the emitted anthropogenic CO2 will remain in the atmosphere. A positive feedback between climate and the carbon cycle on century to millennial time scales is supported by paleoclimate observations and modelling” (IPCC, 2013).

# Observational Constraints

Models alone are not sufficient to estimate with confidence the carbon cycle feedback. Only observations can help, but there is a fundamental issue here: one cannot observe a feedback. A feedback is, by definition, calculated from the difference between a coupled system and the conceptual, similar system where this feedback does not operate. Such a conceptual world does not exist and hence is simply not observable. Observations are made in the real world where all feedbacks operate. Nevertheless, there are at least two methods that have been used to help constraining the carbon cycle feedbacks.

The first method makes use of concurrent records of atmospheric CO2 and temperature over given timescales (Figure 2). The analysis of the covariance of the two records provides information on the relationship between the climate system and the carbon cycle. The first who made use of such observations was G. Woodwell (Woodwell & Mackenzie, 1995; Woodwell et al., 1998), who used past records of atmospheric CO2 and temperature to try to infer the strength of the climate carbon cycle feedback. Woodwell used ice core data of atmospheric CO2 and Antarctic temperature over the last 150,000 years to quantify the strength of climate–carbon cycle feedback. Woodwell wrote, “The record for the Vostok core suggests that a change of 1°C in this period was equivalent to a change of 10–15 ppmv of carbon dioxide or about 25 GtC in the atmosphere.” Such analysis has been reproduced since by several authors, giving essentially the same estimate (Scheffer, Brovkin, & Cox, 2006; Torn & Harte, 2006).

However, the glacial–interglacial changes in the carbon cycle involve processes predominantly related to changes in ocean circulation, carbon export, and burial rates, not directly relevant for the anthropogenic perturbation of the 20th and 21st centuries. The Vostok ice core is an unambiguous indication that the carbon cycle does respond to climate change, and it also confirms that there is a positive feedback on these long time scales: warming releases carbon to the atmosphere, but it does not directly help constrain the carbon cycle feedback of the 21st century.

Much more encouraging is the analysis of the last millennium. The principle is the same as for glacial–interglacial cycles; ice core records of the last millennium show variability of atmospheric CO2, of the order of a couple of ppm, associated with variability of the climate system (Frank et al., 2010). The record of the last millennium offers the advantage that climate and CO2 fluctuations are relatively small and operate on centennial time scales (i.e., more relevant for the current anthropogenic perturbation). However, as opposed to the glacial–interglacial cycles, which are entirely natural, over the last millennium there is a possibility that the anthropogenic perturbation is already at play and contributes to the fluctuations in atmospheric CO2. In particular, it had been argued that early land use change (mainly agriculture in Eurasia) had a significant impact on atmospheric CO2, with a large release of carbon (about 300 GtC) from early agriculture (Ruddiman, 2003). However, it has since been shown that preindustrial CO2 emissions from land use were much lower, about 50 GtC at most (e.g., Pongratz, Reick, Raddatz, & Claussen, 2009), and were not a major concern in an analysis that focuses on variability rather than long-term trends. The study by Frank et al. (2010) combined three ice core data with multiple reconstruction of temperature from tree ring data. They found a clear positive correlation emerging from the CO2 and temperature datasets, allowing a quantification of the global carbon sensitivity to climate. They reported a $ΔCaΔT$ of 7.7 ppm CO2 per °C warming, with a likely range of 1.7–21.4 ppm CO2 per °C for the last millennium. When compared with the $ΔCaΔT$ simulated by the C4MIP models over the 20th century, they concluded that their observation-based estimate was compatible with the lower end of the range simulated by the C4MIP models; that is, large values of the climate–carbon cycle feedback were unlikely compatible with their finding.

A completely different approach, but still based on observations, uses the concept of emerging constraints. The approach relies on the finding that there is an emerging quasilinear relationship between the response of tropical land carbon storage to 21st-century warming ($γ$) and the sensitivity of the year-to-year growth rate of atmospheric CO2 to tropical temperature anomalies (called $γIAV$). As the latter is observed, this relationship allows constraint of $γ$ over the 21st century (Cox et al., 2013). The rise of atmospheric CO2 varies from year to year, due to climate variability such as the El Niño Southern Oscillation (ENSO). This has been known for several decades and is attributed to the tropical land biosphere (Bacastow, 1976; Keeling, Whorf, Wahlen, & Vanderplicht, 1995). Earth system models (ESMs) do simulate interannual variability of atmospheric CO2 in response to the simulated natural climate variability. The emerging relationship emerges as models that tend to simulate a weak tropical land carbon cycle response to ENSO anomalies (low $γIAV$) tend to simulate a weak tropical land carbon response to climate change over the 21st century (low $γ$). Conversely, models with a large $γIAV$ simulate a large 21st-century $γ$. This was first demonstrated for the earlier C4MIP models (Cox et al., 2013) and subsequently reproduced with the more recent CMIP5 ESMs (Wenzel, Cox, Eyring, & Friedlingstein, 2014). The observed sensitivity of the carbon cycle on interannual time scale, derived from the Mauna Loa atmospheric CO2 records, allows constraint of the tropical land $γ$ to 53 $±$ 17 GtC per °C warming. Again, this estimate is consistent with the lower end of the C4MIP and CMIP5 ESM estimates.

These two completely independent approaches, one based on millennium variability and one based on interannual variability, agree on two important findings. First, the climate–carbon cycle feedback is positive; and second, the feedback is more likely to be in the lower end of the comprehensive model’s range, excluding very large climate–carbon cycle feedbacks.

# Discussion

The emerging constraint based on interannual variability only gives an indication of the strength of the tropical land carbon sensitivity to future climate. It does not inform us on extratropical ecosystems. One cannot rule out additional carbon cycle feedbacks arising from nontropical ecosystems. In particular, permafrost ecosystems contain the largest amount of carbon on land, about 1700 GtC (Tarnocai et al., 2009). Future warming of the high latitudes is projected to induce a thawing of these permafrost soils, potentially leading to decomposition of soil carbon currently isolated from the atmosphere. None of the current Earth system models represent the carbon in the permafrost. The estimations of the climate–carbon feedback for lands are therefore conservative for high-latitude ecosystems.

Although not included in Earth system models, permafrost ecosystems are being represented in land surface models, and they estimate of the significant release of permafrost carbon (Burke, Jones, & Koven, 2012; Koven et al., 2011; MacDougall, Avis, & Weaver, 2012; Schneider von Deimling et al., 2012). The IPCC AR5 concluded, “There is high confidence that reductions in permafrost extent due to warming will cause thawing of some currently frozen carbon. However, there is low confidence on the magnitude of carbon losses through CO2 and CH4 emissions to the atmosphere, with a range from 50 to 250 GtC between 2000 and 2100 under the RCP8.5 scenario” (Ciais et al., 2013).

CO2 fertilization (i.e., the increase of terrestrial plants productivity as a response to atmospheric CO2 increase) remains one of the major source of uncertainty in future projections of the carbon cycle (Arora et al., 2013). Although the basic process is relatively well understood—elevated CO2 stimulates plant photosynthesis, increasing biomass production, and hence carbon uptake—the quantification at the global scale remains poorly constrained. There are no long-term global observations of land carbon uptake that could be used to evaluate the CO2 fertilization.

On a related topic, nitrogen is a key terrestrial nutriment that controls terrestrial plant productivity and hence the carbon sinks. So far, very few Earth system models have accounted for nitrogen limitations. The net effect of nitrogen on future carbon sinks remains to be quantified.

Finally, there are numerous other biological processes that can be affected by climate change and potentially induce a feedback on the human-induced warming, such as N2O emissions, isoprene and ozone chemistry, fires, and aerosol emissions. A recent review of these candidates showed a very low confidence in the magnitude of these feedbacks as they were often estimated from very few studies (Arneth et al., 2010).

# Concluding Remarks

The anthropogenic perturbation, through the increase of greenhouse gases, primarily carbon dioxide, is very likely to be responsible for the observed climate change (IPCC, 2013). Further CO2 emissions will inevitably lead to additional warming over the 21st century. The human perturbation has a severe impact on the natural global carbon cycle. Climate change has a direct impact on the land and ocean carbon cycle; warming leads to carbon release from both land and ocean, a positive feedback on the human perturbation. The quantification of these ocean and land carbon feedbacks has been impeding progress in Earth system science. Recent use of observations gives some hope on constraining these feedbacks, confirming that warming leads to more CO2 in the atmosphere (i.e., a positive feedback).

## References

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## Notes:

(1.) In the IPCC terminology, extremely likely indicates a likelihood above 95%.

(2.) The equilibrium climate sensitivity is defined as the change in global mean surface temperature at equilibrium that is caused by a doubling of atmospheric CO2 concentration.