1. Introduction

The projection of the climatic consequences of anthropogenic CO₂ emissions for the twenty-first century has been a major topic of climate research. Nevertheless, the long-term consequences of anthropogenic CO₂ remain highly uncertain. The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) reported that “about 50% of a CO₂ increase will be removed from the atmosphere within 30 years and a further 30% will be removed within a few centuries” (Denman et al. 2007, p. 501). Although the IPCC estimate of the time to absorb 50% of CO₂ is accurate for relatively small amounts of emissions at the present time, this may be a considerable underestimation for large quantities of emissions. Carbon sinks may become saturated in the future, reducing the system’s ability to absorb CO₂.

Atmospheric CO₂ is currently the dominant anthropogenic greenhouse gas implicated in global warming (Forster et al. 2007); therefore, estimating the lifetime of anthropogenic climate change will largely depend on the perturbation lifetime of CO₂. The perturbation lifetime is a measure of the time over which anomalous levels of CO₂ or temperature remain in the atmosphere (defined here to be the time required for a fractional reduction to 1/e). Carbon emissions can be taken up rapidly by the land, through changes in soil and vegetation carbon, and by dissolution in the surface ocean. Ocean uptake slows as the surface waters equilibrate with the atmosphere and continued uptake depends on the rate of carbon transport to the deep ocean. Ocean uptake is enhanced through dissolution of existing CaCO₃, often referred to as carbonate compensation. As CO₂ is taken up, the ocean becomes more acidic, eventually releasing CaCO₃ from deep sediments. This increases the ocean alkalinity, allowing the ocean to take up additional CO₂. Carbonate compensation becomes important on millennial time scales, whereas changes in the weathering of continental carbonate and silicate are thought to become important on the 10 000–100 000-yr time scale (Archer 2005; Sarmiento and Gruber 2006; Lenton and Britton 2006).

Earth system models can be used to simulate the evolution of the climate system under different anthropogenic emissions scenarios. There is still a great deal of uncertainty in the climate–carbon cycle response and considerable variation in model predictions. The short term (century time scale) may be dominated by the terrestrial carbon cycle response, which is poorly understood. Over the longer term (millennial time scale) the ocean biology, sediment, and weathering responses are also highly uncertain. Comprehensive model simulations of the next few centuries suggest that CO₂ anomalies may be relatively long lived (Friedlingstein et al. 2006; Plattner et al. 2008). These studies also illustrate the large uncertainties in the modeled short-term carbon cycle response but they were not designed to estimate the multimillennial response or the dependency of the recovery time scales on the level of emissions.

There are few modeling studies that have considered the coupled climate–carbon cycle response to large anthropogenic emissions on the 10 000-yr time scale. Differing levels of complexity and experimental design make a detailed comparison of other studies difficult, but most studies suggest that the average perturbation lifetime of most of the CO₂ is on the order of a few centuries and that as much as a quarter of the perturbation lasts for more than 5000 yr (Archer et al. 1998; Archer 2005; Archer and Brovkin 2008; Lenton and Britton 2006; Lenton et al. 2006; Ridgwell and Hargreaves 2007; Ridgwell et al. 2007; Mikolajewicz et al. 2007; Tyrell et al. 2007; Montenegro et al. 2007). None of these studies attempted to estimate the millennial time scales of the temperature response or investigated the multimillennial response as a function of the magnitude of the perturbation in a systematic way.

Models that have looked at the long-term carbon cycle response are usually low resolution, highly parameterized, or incomplete. For example, Archer (2005) used highly parameterized climate feedbacks, whereas Montenegro et al. (2007) used two incomplete models: one model lacked a terrestrial carbon cycle and the other lacked ocean sediments. The model used here is currently one of the more complex coupled climate–carbon cycle models capable of looking at multimillennial time scales. Even given the large range in existing model predictions, we will show that the lifetime of both the anthropogenic CO₂ perturbation and the resulting surface air temperature (SAT) change may be longer than previously thought.

2. Model description and evaluation

We use version 2.8 of the University of Victoria (UVic) Earth System Climate Model (ESCM). It consists of a primitive equation 3D ocean general circulation model with isopycnal mixing and a Gent and McWilliams (1990) parameterization of the effect of eddy-induced tracer transport. For diapycnal mixing, a horizontally constant profile of diffusivity is applied, with values of about 0.3 10⁻⁴ m² s⁻¹ in the pycnocline. The ocean model is coupled to a dynamic–thermodynamic sea ice model and an energy–moisture balance model of the atmosphere with dynamical feedbacks (Weaver et al. 2001). The land surface and terrestrial vegetation components are represented by a simplified version of the Hadley Centre Met Office surface exchange scheme (MOSES) coupled to the Top-down Representation of Interactive Foliage and Flora Including Dynamic vegetation model; Meissner et al. 2003). Land carbon fluxes are calculated within MOSES and are allocated to vegetation and soil carbon pools (Matthews et al. 2004). Ocean carbon is simulated by means of an Ocean Carbon-Cycle Model Intercomparison Project type inorganic carbon cycle model and a nutrient–phytoplankton–zooplankton–detritus marine ecosystem model (Schmittner et al. 2008). Sediment processes are represented using an oxic-only model of sediment respiration (Archer 1996a).

An earlier version of the UVic ESCM (version 2.7) has undergone extensive evaluation as part of international model intercomparison projects including the Coupled Carbon Cycle Climate Model Intercomparison Project (Friedlingstein et al. 2006), the Paleoclimate Modeling Intercomparison Project (Weber et al. 2007), and the coordinated thermohaline circulation experiments (Gregory et al. 2005; Stouffer et al. 2006). The model has also been used for multicentury climate projections in support of the IPCC Fourth Assessment Report (Denman et al. 2007; Meehl et al. 2007). Here, we evaluate the UVic ESCM version 2.8 primarily with respect to its ability to simulate characteristics of the coupled climate–carbon cycle system, including the air–sea flux of CO₂, the distribution of ocean dissolved inorganic carbon (DIC) and alkalinity, the percent of CaCO₃ in sediments, the global carbon budgets of the last decades and the observation-based evolution of surface air temperature and CO₂ over the historical period. From a preindustrial climate, this version of the model has a transient climate response of 2.0°C and an equilibrium climate sensitivity of 3.5°C (Weaver et al. 2007).

The simulated evolution of atmospheric CO₂ and surface air temperature over the historical period is in good agreement with observations (Fig. 1). For the year 2000, the simulated CO₂ is about 5 ppmv higher than the observation-based value. The model does not produce as much interannual variability as seen in the data but the long-term trends are well reproduced. Warming over the twentieth century is 0.7°C, in agreement with the IPCC estimate of 0.6° ± 0.2°C (Forster et al. 2007).

The simulated inventories of carbon in the atmosphere, ocean, and on land in the years 1800 and 1994 and their difference are given Table 1. The changes in carbon inventories over the historical period (1800–1994) compare relatively well with IPCC AR4 estimates (1750–1994). The observation-based changes in carbon reservoirs during the 1980s, 1990s, and 2000–05 are well reproduced by the model (Table 2). The atmospheric CO₂ increase is in close agreement with observations for the 1980s and 2000–05 but is overestimated in the 1990s. Ocean CO₂ uptake agrees very well with the observation-based values, but for a slight overestimation in 2000–05. Land CO₂ uptake falls well within the estimated uncertainty range for all time periods and is close to the IPCC best estimate.

The model reproduces qualitatively and quantitatively most features of the observation-based patterns of air–sea exchange of CO₂ (Fig. 2). These features include outgassing in low latitudes with a maximum in the eastern tropical Pacific and uptake at mid- and high latitudes with maxima around 40°N–S in the areas of the North Atlantic Current, the Kuroshio Current, and the Southern Ocean. Model biases include underestimated uptake in the Greenland–Iceland–Norwegian Seas and overestimated uptake in the eastern subtropical Pacific.

The simulated patterns of DIC and alkalinity show good agreement with observations (Figs. 3, 4). The model captures well the surface to deep gradient of both tracers. At depth the model slightly underestimates carbon while slightly overestimating alkalinity. See Table 3 for a summary of the average values and absolute errors of simulated DIC and alkalinity for the global, Arctic–Atlantic, and Indo-Pacific oceans. The simulated patterns of CaCO₃ are also in reasonable agreement with observations (Fig. 5). Nevertheless, the model underestimates deep CaCO₃ at tropical latitudes and overestimates CaCO₃ at high latitudes. Comparing only locations with observations, the global average percent of CaCO₃ in sediments is 34.5% for the data and 31.1% for the model.

3. Experimental design

The model was spun up for 10 000 yr with atmospheric carbon dioxide levels and Earth’s orbital configuration specified for the year 1800 and the continental CaCO₃ weathering flux diagnosed from the ocean sediment burial flux. The weathering flux was then held fixed while the burial flux of CaCO₃ was allowed to evolve with time for all subsequent experiments. Historical emissions were applied until the end of the year 2000. These historical CO₂ emissions include contributions from both fossil fuel burning and land use changes. All other transient forcings (insolation, orbital forcing, tropospheric and stratospheric sulfates, and non-CO₂ greenhouse gases such as CH₄, N₂O, and CFCs) were held fixed.

At the beginning of 2001, “pulses” of CO₂ were applied over 1 yr. The emissions varied from 160 PgC (10¹⁵ g of carbon) to 5120 PgC (Table 4). The upper bound approximates all known conventional fossil fuel reserves (Rogner 1997). In addition to the pulse experiments, we also performed simulations with more “realistic” emissions scenarios. As a baseline, we assumed that emissions follow the A2 scenario up to the year 2100 and then decline linearly to zero by 2300. This scenario is designated as A2+ (Montenegro et al. 2007). We then generated a set of scenarios in which the A2+ emissions were scaled such that the cumulative emissions reached those of the equivalent pulse simulation by the year 2300. A2+ and pulse simulations were integrated for 5000 and 10 000 model years, respectively. To explore the consequences of future emissions only, a 10 000-yr control simulation was also carried out with zero emissions after the year 2000. At the end of this integration the SAT was again at its year 2000 value (having dropped 0.1°C from its temporary maximum) whereas CO₂ had dropped by 55 ppmv to 321 ppmv. These control results are subtracted from the results of the future emissions experiments.

4. Discussion and conclusions

Resulting maximum changes in atmospheric CO₂ range from 26 to 2352 ppmv (Fig. 6; Table 4). In the pulse experiments, the maximum CO₂ anomaly occurs at the beginning, initially decaying very rapidly but slowing after several decades. In the A2+ experiments, atmospheric CO₂ peaks a few decades before the year emissions are set to zero (260–286 yr; Table 4). After the peak, CO₂ closely approaches the level of the corresponding pulse experiment after about 500 yr. This demonstrates that the long-term atmospheric CO₂ response is nearly independent of the rate of CO₂ emissions (assuming all emissions occur over the next 300 yr).

A considerable amount (15%–30%) of the atmospheric CO₂ anomaly persists at the end of the 10 000-yr simulations (Fig. 6). The time to absorb a given percent of emissions is strongly dependent on the total amount of emissions (Fig. 7; Table 4). For emissions up to about 1000 PgC, 50% of the CO₂ anomaly is taken up within 100 yr and another 30% is absorbed within 1000 yr, which is similar to IPCC estimates (Denman et al. 2007). Above 1000 PgC, the time to absorb 50% of the emissions increases dramatically, and more than 2000 yr are needed to absorb half of a 5000-PgC perturbation.

Ocean surface pH is strongly coupled to atmospheric CO₂ (Caldeira and Wicket 2003). Emissions above 1280 PgC result in a decrease in average ocean surface pH that is larger than the 0.2 guard rail proposed by the German Advisory Council on Global Change (WGBU; Schubert et al. 2006; Fig. 8). Given the slow decay of atmospheric CO₂, experiments with emissions of 2560 PgC and larger still have lower pH than the 0.2 guard rail after 10 000 yr. For high emissions, the change in surface pH would probably have a significant impact on oceanic biota. Emissions of 1920 PgC and above result in minimum pH levels below 7.9, a value that could bring the aragonite saturation depth to the surface in the Southern Ocean generating serious adverse effects on calcifying organisms (Orr et al. 2005).

There is a lag in the response of surface air temperature to the CO₂ forcing (Fig. 9). For all but the lowest emissions, temperature reaches its maximum at least 550 yr after the peak in atmospheric CO₂ (Table 4). The lag is particularly pronounced in the experiments with total emissions in the range 640–1280 PgC, where after 2000–3500 yr, the planetary cooling is suddenly reversed and SAT again increases by as much as 0.5°C. This abrupt warming and accompanying increase in CO₂ is caused by flushing events in the Southern Ocean, which in this model have been shown to be dependent on the level of atmospheric CO₂ (Meissner et al. 2008). Under the A2+ emissions scenarios, the peak in SAT is almost identical to the corresponding pulse experiments, indicating that the long-term temperature response is independent of the rate of CO₂ emissions (Fig. 9; Table 4).

The SAT anomaly is even longer lived than the CO₂ anomaly. For all experiments, at least 50% of the maximum temperature anomaly persists at the end of the simulation. For both the smallest and largest emission scenarios, the temperature anomaly remaining after 10 000 yr is about 75% of the maximum anomaly. Similar to CO₂, the time to reduce temperature by a specific percent of the maximum anomaly depends on the total amount of emissions. The time within which SAT declines by 20% relative to the peak warming ranges from about 500 yr for the lowest emission scenario to more than 5000 yr for the highest emissions scenarios (Fig. 7; Table 4).

Given that the change in temperature from preindustrial to the year 2000 is about 0.8°C (Fig. 1), total emissions of 640 PgC or more result in average air temperatures above the 2°C temperature guard rail suggested by the WBGU (Schubert et al. 2006) and endorsed by the European Union. The threshold to stay below this guard rail would appear to be near 640 PgC of total emissions from the year 2000. Experiments with emissions of 1280 PgC and larger still exceed the 2°C guard rail after 10 000 yr.

To estimate the perturbation lifetime of anthropogenic climate change the response curves of either CO₂ or temperature were fit to an exponential formula of the form A₀exp(−t/A₁) + A₂. The parameter A₀ gives an estimate of the amount a quantity is reduced, A₁ is the average lifetime, and A₂ is the amount of any very long-lived residual. We restrict our analysis to experiments with total emissions greater than 1500 PgC. In simulations with lower emissions, the response curve is often contaminated by noise, making curve fitting imprecise (Figs. 6, 9).

A gradient-expansion algorithm was used to compute the least squares fit of an exponential model to the data. To tease out a fast and slow time scale for uptake of CO₂, an exponential fit was first applied to the CO₂ curves after 1000 yr. The data fit an exponential very well (see Fig. 10). This curve was then extrapolated back 1000 yr and the extrapolated CO₂ was subtracted from the simulated CO₂. A second exponential fit was performed on the remaining CO₂. This fit is clearly not as good as the previous fit (Fig. 10). The early response is not a pure exponential but a combination of processes with different time scales (Joos et al. 1996). Still, this analysis provides a reasonable, if somewhat uncertain, estimate of the overall fast absorption time scale. Although the estimated short-term-response time scale may be dependent on the number of exponentials used in the fit (Maier-Reimer and Hasselmann 1987), the longer response time scale (after 1000 yr) is quite robust and reasonably independent of the section of the curve used in the fit. The perturbation lifetime of CO₂ is thus broken up into a period of rapid absorption, a period of slow absorption, and a “residual” that represents CO₂, which stays in the atmosphere for longer than this method can resolve (≫10 000 yr). To derive a perturbation lifetime for temperature, we also fit an exponential model to the temperature response curves after the year 1000.

We find that the response curves for CO₂ can be well approximated by the superposition of exponentials with two different time scales. The average lifetime for the short time scale is about 130 yr whereas the long time scale has an average lifetime closer to 2900 yr (Table 5). The amount of CO₂ absorbed by processes associated with the short time-scale sink are nearly constant (1075–1382 PgC; calculated from Table 5). About 400 PgC of the short time-scale sink is associated with increased land uptake (mostly through CO₂ fertilization), whereas the rest (∼900 PgC) are due to relatively rapid dissolution in the surface ocean (Fig. 11). The longer time scale of the deep-ocean sink is associated with slow rates of deep-ocean transport and carbonate dissolution. The amount taken up by the deep-ocean sink is not constant but increases at higher levels of emissions, implying that the sink is not saturated. The absorption time scale for CO₂ does not seem to be very sensitive to the amount of emissions (Table 5).

For high-emission experiments, after year 1000 (roughly the year of maximum temperature), a single exponential fits the temperature response very well. The average perturbation lifetime is about 4000 yr, or 40% longer than the average for CO₂. The temperature perturbation lifetime also appears to be more dependent on the level of total emissions than the CO₂ perturbation lifetime (Table 4).

Radiative forcing from atmospheric CO₂ depends on the logarithm of CO₂, but for the first 1000 yr, the thermal inertia of the ocean and climate feedbacks are important in keeping SAT below what would be expected from the radiative forcing alone (Meehl et al. 2007). After 1000 yr, the time scale for reducing SAT becomes very similar to the time scale of the CO₂ radiative forcing and this time scale is considerably longer than for CO₂. The logarithmic dependence of the radiative forcing on CO₂ is also why the SAT perturbation lifetime depends on the total amount of emissions, even though the time scale of CO₂ absorption itself appears to be relatively constant.

Figure 12 shows the portion of CO₂, radiative forcing from CO₂, and surface temperature normalized to their values at 1500 yr. The spread in the time scales for CO₂ (illustrated by the spread in the curves) is relatively small and larger emissions seem to show slightly shorter time scales (steeper slopes) than smaller emissions (also see Table 5). Radiative-forcing time scales are longer than for CO₂ alone and, as with temperature, the time scale for the decay of the radiative forcing increases as emissions increase. The temperature time-scale dependency on emissions can mostly be explained by the changes in radiative-forcing time scales, although other feedbacks make the spread in temperature time scales even larger.

In summary, this study suggests that for emissions less than about 1500 PgC, most of the CO₂ will be absorbed within a few centuries, which is in agreement with earlier work. Temperature anomalies may last much longer. With larger emissions, the time to absorb most of the CO₂ increases rapidly (Table 4; Fig. 7). This dependency of the CO₂ response on the level of emissions has important policy implications and needs to be investigated with other models. A long-term model intercomparison project (LTMIP) with standardized experiments has recently been initiated and this will hopefully further increase our understanding and reduce the uncertainty in the long-term carbon cycle response. Preliminary results from nine models (including the one used here) can be found in Archer et al. (2009).

Although the long-term climate–carbon cycle response still remains highly uncertain, the model used in this study suggests that for large emissions, the perturbation lifetime of both CO₂ and surface temperature might be longer than previously thought. The long-term climate response appears to be independent of the rate at which CO₂ is emitted over the next few centuries. Regardless of the future emissions trajectory, changes to the earth’s climate will likely persist for several thousands of years. The logarithmic relationship between CO₂ and its radiative forcing implies that the time scale at which atmospheric temperature declines will be longer than the time scale of CO₂. For ecosystems having already adapted to a warmer world, slow cooling may be beneficial. Nevertheless, it is sobering to ponder the notion that the carbon we emit over a handful of human lifetimes may significantly affect the earth’s climate over tens of thousands of years.