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 Recent studies with coupled climate-carbon cycle models suggest that global mean temperature change is proportional to cumulative CO2 emissions, independent of the timing of those emissions. This finding has prompted the suggestion that climate stabilization targets, such as the 2°C target adopted by the Copenhagen Accord, can be expressed in terms of cumulative CO2 emissions. Here we examine the simulated response of a range of global and regional climate variables to the same cumulative CO2 emissions (2500 PgC) released along different pathways using a complex Earth system model. We find that the response of most surface climate variables is largely independent of the emissions pathway once emissions cease, with the exception of variables with response timescales of centuries, such as ocean heat content and thermosteric sea level rise. Peak responses of many climate variables, such as global mean temperature, precipitation and sea ice, are also largely independent of the emissions pathway, except for scenarios with cumulative emissions overshoot which require net removal of CO2 from the atmosphere. By contrast, peak responses of atmospheric CO2 and surface ocean pH are found to be dependent on the emissions pathway. We conclude that a CO2mitigation framework based on cumulative emissions is well suited for limiting changes in many impact-relevant climate variables, but is less effective in avoiding impacts directly associated with atmospheric CO2, whose peak response is dependent on the rate of emissions.
 Key to the cumulative emission framework is the assumption that the climate response to CO2 emissions is independent of the timing of those emissions. So far, path dependence has been investigated with a single model of intermediate complexity (the UVic ESCM [Matthews and Caldeira, 2008; Eby et al., 2009; Zickfeld et al., 2009]) and for global mean temperature only. The objective of this study is to explore the path dependence of a suite of impact-relevant climate variables using a complex Earth system model (CanESM1 [Arora et al., 2009]). We performed a set of simulations for the 1850–2400 period that were forced by CO2 emissions trajectories with the same total cumulative emissions of 2500 PgC, but different timing of emissions. Also included is a scenario with cumulative emissions temporarily exceeding 2500 PgC and subsequent negative emissions (i.e., net removal of CO2 from the atmosphere) in order to induce a temporary overshoot in climate variables. Such “overshoot” scenarios have been discussed as a means of reversing climate change, should “dangerous” levels be exceeded [Lowe et al., 2009]. To our knowledge, this is the first study with a complex Earth System Model which systematically explores the response of impact-relevant climate variables to a range of different pathways with the same total cumulative emissions.
2.1. Model Description
 We use the first generation Canadian Centre for Climate Modelling and Analysis (CCCma) Earth System Model (CanESM1), which is a fully coupled climate-carbon cycle model. The physical climate model includes fully dynamical atmospheric and ocean components. The atmosphere component is CCCma's third generation atmospheric general circulation model (AGCM3) [Scinocca et al., 2008], with a horizontal resolution of T47 (∼3.75°). The physical ocean component (OGCM3.5) of CanESM1 is based on the National Centre for Atmospheric Research (NCAR) community ocean model (NCOM1.3) which is a primitive equation model with a rigid lid. The ocean model has a horizontal resolution of 1.86° and 29 vertical levels whose thicknesses increase with depth. The model represents sub-grid-scale mixing of tracers via isopycnal diffusion and the Gent and McWilliams parametrization of eddy-induced mixing. There is no flux adjustment in the model. The terrestrial carbon cycle is represented by the Canadian Terrestrial Ecosystem Model (CTEM), which simulates three living (leaves, stem and root) and two dead carbon pools (litter and soil organic carbon) for nine plant functional types. The inorganic and biological ocean carbon component is the Canadian Model of Ocean Carbon (CMOC) which includes an inorganic chemistry module and a marine ecosystem model which solves prognostic equations for nutrients, phytoplankton, zooplankton and detritus, and takes into account iron limitation of photosynthesis. The fully coupled climate-carbon cycle model is described in detail byArora et al. .
2.2. Experimental Design
 Starting from the model's pre-industrial control configuration, we ran a historical experiment (HIST) (1850–2000) with prescribed atmospheric CO2and all other forcings (land cover, non-CO2greenhouse gases and aerosols) held fixed at their pre-industrial values following the C4MIP protocol [Friedlingstein et al., 2006]. This allowed us to investigate CO2 effects without the confounding effect of other forcings.
 Three 400-year experiments with freely evolving atmospheric CO2 were initialized from the HIST simulation, all forced with the same amount of cumulative emissions of 2500 PgC from 1850 to 2400, but emitted along different idealized pathways (Figures 1a and 1b). We chose total cumulative emissions of 2500 PgC to force the system to moderate-to-high levels of warming (3.5°C;Figure 2a). In the first experiment (A2+), CO2 emissions follow the A2 scenario of the IPCC Special Report on Emissions Scenarios (SRES) until 2100. Thereafter emissions continue to increase at the average rate of the last decade of the 21st century until a cumulative total of 2500 PgC is reached and are then set to zero. In the second experiment, referred to as “overshoot” (OVSHT), CO2 emissions deviate from the A2 scenario around 2070, peak in 2085 at about 20 PgC yr−1 and reach zero in 2190. Emissions are negative from 2190 to 2300 and zero thereafter. In the third experiment, referred to as “undershoot” (UNSHT), CO2 emissions deviate from the A2 trajectory around 2050, peak at 15 PgC yr−1in 2060 and decline thereafter reaching zero in 2270. We also performed an experiment (PULSE) in which 2500 PgC were instantaneously injected into the pre-industrial atmosphere at 2009, the year of mean emissions of the A2+ scenario.
 In the following section we report decadal-mean values along with their associated uncertainty ranges (90% confidence intervals). These ranges were estimated from internal climate variability in the pre-industrial control simulation under the assumption that variability is independent of the climate state.
3. Results and Discussion
3.1. Biogeochemical Changes
 The highest peak in atmospheric CO2 concentration (1409 ± 1 ppm) is reached in the PULSE experiment, in which the CO2 is emitted instantaneously (Figure 1c). In the A2+ and OVSHT experiments, the CO2 concentration peaks at similar values (823 ± 1 ppm and 866 ± 1 ppm, respectively) albeit at different times. In the UNSHT experiment, the maximum CO2 level is 697 ± 1 ppm. This confirms the expected result that a higher CO2 emissions rate leads to a higher peak in atmospheric CO2 concentration [Maier-Reimer and Hasselmann, 1987; Eby et al., 2009]. The reason is that CO2 uptake by carbon sinks cannot keep up with faster CO2 emission rates. Also, the similarity of the peaks in the A2+ and OVSHT experiments suggests that the peak CO2 concentration is determined not only by the emission rate (which is higher in the A2+ case), but also the duration of emissions (which is longer in the OVSHT case). The CO2 level at the end of the simulation (647 ± 1 ppm) is approximately independent of the emissions trajectory. The same CO2 level is not reached immediately after cessation of CO2 emissions: for example, the CO2 in the A2+ simulations converges to the CO2 level in the PULSE experiments only 100 years after emissions cease.
 Of the 2500 PgC of CO2 emitted, 1107 ± 3 PgC are sequestered on land and 671 ± 1 PgC in the ocean by the year 2400 in all simulations (Figures 1d and 1e). Initially, land CO2 uptake is rapid but gradually slows in all simulations, eventually becoming slightly negative (implying release of CO2 into the atmosphere) in response to declining CO2 concentration but constant surface air temperature (see Figure 2a). In contrast, the ocean continues to take up CO2, albeit at a lower rate, after the peak in CO2 concentration. Compared to similar experiments with other models [Plattner et al., 2008; Eby et al., 2009; Lowe et al., 2009], the land CO2 uptake in CanESM1 is somewhat stronger, and the ocean uptake is somewhat weaker, similar to its behavior over the 20th century [Arora et al., 2009].
 Because of its effect on marine ecosystems and fisheries [Cooley and Doney, 2009], surface ocean pH is a variable of interest. Surface pH is tightly coupled to atmospheric CO2 and, consequently, the pH minimum is dependent on the emissions pathway (Figure 1f), with deeper minima for higher CO2 emission rates. The pH minimum is least pronounced in the UNSHT experiment (7.82 ± 0.00) and very similar in the A2+ and OVSHT experiments (7.76 ± 0.00 and 7.74 ± 0.00, respectively). Consistent with the atmospheric CO2response, surface pH after 2300 is almost exactly the same in all experiments (7.84 ± 0.00). Another impact-relevant variable is net primary productivity, whose behavior closely resembles that of CO2 (Figure S1 in the auxiliary material).
3.2. Physical Changes
 After cessation of CO2emissions global mean temperature converges to the same value in all experiments (3.5 ± 0.1°C above pre-industrial) and remains approximately constant for several centuries (Figure 2a). This is consistent with earlier modelling studies, which showed that the temperature after elimination of CO2 emissions is approximately constant on centennial timescales [Matthews and Caldeira, 2008; Eby et al., 2009; Solomon et al., 2009; Lowe et al., 2009; Froelicher and Joos, 2010; Gillett et al., 2011]. This constancy of global mean temperature is due to the compensating effect of declining CO2 radiative forcing (cooling) and reduced ocean heat uptake (warming) [Eby et al., 2009], although the reason for this almost exact compensation remains unclear.
 Prior to the cessation of emissions the instantaneous global mean temperature anomaly is close to proportional to cumulative emissions to date [Matthews et al., 2009] (section 3.3). The peak temperature anomaly is thus larger for OVSHT than for A2+ and UNSHT scenarios (4.1 ± 0.1°C versus 3.5 ± 0.1°C). The largest departure from such proportionality is in the PULSE experiment, in which temperature exceeds the 2300–2400 mean by about 0.6 ± 0.1°C immediately following the pulse. We also explored the difference in regional-scale temperature between the four scenarios at 2400 (not shown). Statistically significant temperature differences occur in the deep water formation regions of the North Atlantic and in the Southern Ocean close to the Antarctic margin, but these differences are small compared to the temperature changes simulated in these regions between 1850 and 2400.
 While global mean temperature remains almost constant following cessation of CO2 emissions, global mean precipitation slightly increases in all simulations (Figure 2b), reaching a common value at 2400 that is 0.19 ± 0.01 mm day−1higher than under pre-industrial conditions. The increase in precipitation is strongest immediately after the cessation of CO2 emissions. The increase in precipitation after emissions cease has been noted in earlier studies [Wu et al., 2010; Gillett et al., 2011], and is an expected response to decreasing atmospheric CO2 under conditions of constant surface temperature. The reason is that global mean precipitation is controlled by the energy budget of the troposphere [Allen and Ingram, 2002]: more efficient radiative cooling to space owing to decreasing atmospheric CO2 allows for a larger latent heat release in the troposphere. Similar energy budget considerations explain the rapid drop in precipitation concurrent with the spike in CO2 concentration at the beginning of the PULSE simulation.
 Higher time-integrated radiative forcing in the PULSE and OVSHT experiments drives a larger heat flux into the ocean. This is reflected in a larger increase in thermosteric sea level in these two simulations (Figure 2c). At 2400, sea level is 3.0 ± 0.3 cm higher in the OVSHT experiment than in the A2+ experiment. In the continuation of the PULSE experiment to 2850 (not shown), sea level continues to rise up to that date, consistent with the response of Earth System models of intermediate complexity [Plattner et al., 2008].
 The meridional overturning circulation in the Atlantic (AMOC) weakens in all four simulations and subsequently recovers as emissions slow and eventually cease (Figure 2d). The maximum weakening is very similar in the A2+, UNSHT and OVSHT experiments (4.3 ± 1.8 Sv relative to pre-industrial). Studies with models of different complexity have suggested that the Atlantic meridional overturning circulation (AMOC) could exhibit path-dependencies (“hysteresis”), due to the existence of multiple equilibrium states. These equilibria are associated with the large scale circulation in the Atlantic being “on” and “off”, or with different locations of deep water formation [Rahmstorf, 2000]. In all our simulations, the meridional overturning at 2400 is similar (1.9 ± 1.8 Sv weakening relative to pre-industrial) despite different forcing trajectories. This may be an indication that either multiple equilibria do not exist in CanESM1, or that the forcing is below the critical value required to trigger a transition to a different state.
 Northern Hemisphere (NH) September sea ice cover reaches a minimum at the time of peak radiative forcing and recovers slightly to 50 ± 8% of the pre-industrial value in all simulations at 2400 (Figure 2e). In the Southern Hemisphere (SH), March sea ice cover continues to decline after the cessation of CO2 emissions (Figure 2f), decreasing by 86 ± 17% relative to pre-industrial at 2400 in all simulations. The different response of sea ice cover in the Northern and Southern Hemispheres can be explained in terms of the ongoing regional climate changes after the cessation of CO2 emissions: despite almost constant global mean temperature, the Northern Hemisphere and Arctic cool, whereas the Southern Ocean and Antarctica warm [Gillett et al., 2011].
3.3. Proportionality of Climate Change to Cumulative Emissions
Figure 3 displays changes in climate variables as a function of cumulative CO2 emissions. These results suggest that the linear relationship between changes at a specific time and cumulative emissions to date, which was found previously for global mean temperature [Matthews et al., 2009], also holds approximately for other physical climate variables, such as global and land precipitation and sea ice (see also Figure S2). Global precipitation in the OVSHT simulation exhibits a slight hysteresis as a function of cumulative emissions (Figure 3c) (i.e., two different precipitation states at two different CO2 levels with the same global mean temperature) due to the energy budget constraints mentioned earlier. Performing a linear fit to the data in Figure 3bwe obtain a temperature change per unit cumulative emissions (the climate-carbon response [Matthews et al., 2009]) of 1.4 ± 0.1°C EgC−1 (1 EgC = 1000 PgC). For comparison, values for C4MIP models vary in the range 1.0–2.1°C EgC−1. For precipitation and Northern Hemisphere September sea ice cover the value of the sensitivity is 0.07 ± 0.01 mm day−1 EgC−1 (2.7 ± 0.3% EgC−1) and −1.5 ± 0.6 × 106 km2 EgC−1, respectively. The linear relationship does not hold for the Atlantic overturning, which has a longer response timescale and scales less linearly with global mean temperature. Furthermore, the linear relationship does not hold for atmospheric CO2, due to the presence of carbon sinks, and tightly linked variables such as pH and net primary productivity (Figure S2).
 Since global mean temperature is closely proportional to cumulative carbon emissions in our model, it is not surprising that variables whose response scales linearly with global mean temperature [Mitchell, 2003] also respond proportionally to cumulative carbon emissions. Deviations from this linear relationship can arise for variables with long response timescales (such as thermosteric sea level rise) or variables whose response is not driven purely by surface temperature (such as precipitation).
4. Summary and Conclusions
 We explored the coupled climate-carbon cycle response to CO2emission scenarios with different timing of emissions but the same cumulative total (2500 PgC). Our results suggest that for most variables the century-scale global mean climate response after cessation of CO2emissions is determined by total cumulative emissions, and is independent of the emissions pathway. Exceptions include climate variables with response timescales of several centuries, such as deep ocean temperature and thermosteric sea level rise. Our results further suggest that the path-independence after cessation of CO2emissions also approximately applies at the regional-scale. For scenarios without cumulative emissions overshoot, peak responses of many climate variables, such as temperature, precipitation (both global and over land) and sea ice cover are also largely determined by total cumulative emissions. By contrast, peak responses of atmospheric CO2, surface ocean pH and net primary productivity are dependent on the timing of emissions.
 A special class of emissions scenarios discussed in the literature are those entailing negative emissions, i.e., net sequestration of CO2from the atmosphere. We find that for such scenarios the year-2400 climate response is very similar to that for scenarios with the same cumulative emissions but no overshoot, consistent with the idea that the century-scale climate response after cessation of emissions is determined by the amount of cumulative emissions. However, peak climate responses are larger for such scenarios, due to the higher time-integrated radiative forcing, and are better correlated withmaximum cumulative emissions than total cumulative emissions after cessation of emissions.
 Some caveats apply to our results. Like most Earth System models, EarthCanESM1 does not include all potential sources of hysteresis in the climate system. First, while the modelled vegetation structure responds to changes in climate in a given grid cell, the fraction of each grid cell covered by each plant functional type is specified. Second, the model does not include dynamic ice sheets. Proper representation of these processes, whose response is known to be highly nonlinear, could introduce path-dependencies in the climate response. Another process not included in the model is release of methane from melting permafrost, which could affect the linear relationship between climate change and cumulative emissions.
 In summary, we find that the linear relationship between changes in climate variables and cumulative carbon emissions holds for many impact relevant climate variables. We find that it is less applicable to climate variables with long response timescales, or variables such as atmospheric CO2, whose peak values are dependent on the rate of emissions. We conclude that a CO2 mitigation framework based on cumulative emissions targets is effective in limiting changes in many physical climate variables but is less suited for limiting impacts that are related directly to atmospheric CO2levels. Future climate changes will also be determined by forcing from non-CO2greenhouse gases (GHGs) and aerosols. These two forcings nearly compensated each other globally over the historical period but this is not expected to be the case in future. Emissions of aerosol precursor species are projected to decrease but emissions of non-CO2 GHGs are projected to rise or stabilize in all representative concentration pathways being considered for the Fifth Assessment Report of the IPCC [Moss et al., 2010]. Hence, in order to avoid “dangerous” climate change, a cumulative CO2emissions based approach must be complemented by a framework for mitigation of non-CO2 climate forcings.
 We would like to thank Greg M. Flato, Steve Lambert and three reviewers for comments on earlier versions of this paper. We also acknowledge the work of Canadian Centre for Climate Modelling and Analysis members who developed CanESM1 including, as well as the second author, G. J. Boer, C. L. Curry, J. R. Christian, K. Zahariev, K. L. Denman, G. M. Flato, J. F. Scinocca, W. J. Merryfield and W. G. Lee. We also thank Duo Yang and Fouad Majaess for help with processing model output and technical support.
 The Editor thanks Christopher Jones and anonymous reviewers for their assistance in evaluating this paper.