1. Introduction
A near-linear relationship between cumulative emissions of CO2 and change in global mean near-surface temperature has now been well established as an emergent property of Earth system models (ESMs) (e.g., Allen et al. 2009; Gregory et al. 2009; Matthews et al. 2009; Meinshausen et al. 2009; Gillett et al. 2013; Goodwin et al. 2015; MacDougall and Friedlingstein 2015; MacDougall 2016). The relationship is consistent with the observational record of global temperature change and estimates of anthropogenic CO2 emissions (Gillett et al. 2013) and has been named the transient climate response to cumulative CO2 emissions (TCRE) (Gregory et al. 2009; Stocker et al. 2013). The near-constant nature of TCRE implies that the rate and timing of CO2 emissions are nearly irrelevant to the total change in temperature from a given CO2 emissions trajectory (e.g., Matthews et al. 2009). That is, cumulative emissions of CO2 effectively determine contribution to global temperature change from CO2. Limiting the damage caused by climate warming is often conceptualized in terms of limiting global temperature change to a level below some chosen temperature target (e.g., United Nations 2015). The nature of TCRE implies that there is a finite “carbon budget” compatible with the chosen temperature change target (Zickfeld et al. 2009). This carbon budget is inversely proportional to the value of TCRE and therefore is sensitive to uncertainty in TCRE. As the value of the carbon budget determines the fraction of known fossil fuel reserves that can be burnt (Raupach et al. 2014; McGlade and Ekins 2015) and the speed of economic decarbonization (e.g., Rogelj et al. 2015), quantifying the uncertainty in TCRE is of paramount scientific and social concern.
TCRE has been estimated both from observations of the natural world and climate model simulations (Gillett et al. 2013; Eby et al. 2013; Steinacher and Joos 2016). For observation-based estimates of TCRE the required quantities are the attributable fraction of global temperature change due to change in atmospheric CO2 concentration and fossil fuel and land-use-change emissions. From these variables Gillett et al. (2013) estimated that TCRE is likely between 0.7 and 2.0 K EgC−1. Climate model estimates of TCRE are derived from model intercomparison studies (Gillett et al. 2013; Eby et al. 2013) and perturbed parameter experiments with single models (Steinacher and Joos 2016). Intercomparison of model output of CMIP5 models suggests a range of TCRE of 0.8 to 2.4 K EgC−1 (Gillett et al. 2013) and of intermediate-complexity climate models of 1.4 to 2.5 K EgC−1 (Eby et al. 2013). Steinacher and Joos (2016) used a data-constrained perturbed parameter approach with a single intermediate-complexity climate model to estimate a value of TCRE of 1.9 K EgC−1 with a 68% uncertainty range of 1.3 to 2.7 K EgC−1. Combining various lines of evidence the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5) gave an expert assessment range for TCRE of 0.8 to 2.5 K EgC−1.
Uncertainty in the response of the physical climate system to changes in atmospheric CO2 concentration feed into the uncertainty in the response of the global carbon cycle to climate change, as terrestrial and oceanic carbon cycles feedbacks are sensitive to changes in climate (e.g., Jenkinson et al. 1991; Luo and Zhou 2006; Falkowski et al. 2000). In the terrestrial system the rate of respiration of organic matter by soil microorganisms is a function of the temperature of the soil (e.g., Jenkinson et al. 1991). Generally an increase in temperature is expected to increase the rate of soil respiration, causing a decline in the size of the soil carbon pool and a net release of carbon to the atmosphere (Luo and Zhou 2006). Ocean carbon cycle feedbacks are dominated by the effects of dissolved CO2 on the ocean carbonate buffering system (e.g., Arora et al. 2013). However, change in ocean temperature does have some effect on the oceanic carbon cycle as the partial pressure of dissolved CO2 is an increasing function of temperature (like most other gases) such that the ocean carbon uptake becomes less efficient at higher global temperatures (Falkowski et al. 2000). Therefore, unless overwhelmed by more complex changes (such as changes in vegetation distribution, ocean circulation, or ocean biology), an increase in global temperature should reduce the efficiency of carbon sinks and lead to a higher airborne fraction of carbon. Conditions of high radiative forcing, climate sensitivity, and low ocean heat uptake efficiency should favor a high TCRE from both the temperature effect of CO2 and the temperature feedback on the carbon cycle by making both ΔT/ΔCa and ΔCa/E larger. Here we will use a climate model of intermediate complexity to quantify the uncertainty in the TCRE arising from the uncertainty in the physical climate parameters and the feedback of this uncertainty on the simulated carbon cycle.
2. Methods
a. Model description
The University of Victoria Earth System Climate Model (UVic ESCM) is a climate model of intermediate complexity composed of a full three-dimensional ocean general circulation model coupled to a simplified energy and moisture balance atmosphere (Weaver et al. 2001). All components of the model share a common horizontal resolution of 3.6° longitude by 1.8° latitude. The ocean model is based on the Modular Ocean Model, version 2 (Pacanowski 1995), and ocean depth is resolved to 19 vertical layers. Ocean vertical diffusivity is parameterized as a globally uniform vertical profile following Bryan and Lewis (1979). Subgrid-scale eddy mixing is represented using the Gent–McWilliams parameterization (Gent and McWilliams 1990) with globally uniform isopycnal and thickness diffusivities. The model land surface is a highly modified version of the Moses land surface scheme (Cox et al. 2001; Meissner et al. 2003) with a subsurface extending to 250-m depth, hydrology in the top 10 m, and full freeze–thaw dynamics (Avis et al. 2011; Avis 2012). The simplified atmospheric component carries out the main climatological functions of the atmosphere without simulating the fluid motions of air. The simulated functions are transporting heat and moisture from the tropics toward the poles and solving the energy balance equation at the planetary surface and top of the atmosphere (Weaver et al. 2001). The outgoing longwave radiation flux is simulated using the parameterization of Thompson and Warren (1982), which relates outgoing longwave to near-surface air temperature and relative humidity (Weaver et al. 2001). Changes in longwave radiative forcing are imposed as an anomaly at the top of the atmosphere and computed for each greenhouse gas using the equations presented in Table 6.2 of IPCC (2001). The model is forced with prescribed surface wind fields, vertically integrated winds for energy and moisture advection, incoming solar radiation (Weaver et al. 2001), and temporally invariant but spatially revolved geothermal heat flux (Avis et al. 2011). Model wind fields are derived from the National Centers for Environmental Prediction (NCEP) reanalysis data and are geostrophically adjusted as global temperature changes (Weaver et al. 2001). Solar forcing is from the historical forcing fields used for model simulations in IPCC AR5 Moss et al. (2010) and the geothermal heat flux from Hamza et al. (2008).
The UVic ESCM contains a full representation of the oceanic and terrestrial carbon cycles. The terrestrial carbon cycle is simulated using the Top-down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) dynamic vegetation model (Meissner et al. 2003; Matthews et al. 2004; Cox et al. 2001). The model includes a prognostically generated permafrost carbon pool whereby soil carbon is slowly diffused into soil layers that are frozen year-round (MacDougall and Knutti 2016b). The inorganic ocean carbon cycle is simulated following the protocols of the ocean carbon cycle model intercomparison project (Orr et al. 1999). Ocean biology is simulated using a nutrient–phytoplankton–zooplankton–detritus ocean biology scheme (Schmittner et al. 2008).
b. The UVic ESCM as a probabilistic model
Climate models are mathematical representations of the natural Earth system based on the scientific understanding of the physical, chemical, and biological components of the system. As scientific understanding of these systems is imperfect and computational resources are limited, climate models only approximate the behavior of the natural Earth system (e.g., Collins et al. 2013). The current generation of fully coupled Earth system models continues to improve in both spatial resolution and physical complexity, but there remain key aspects of the climate system where model parameterizations (i.e., clouds, aerosols, and biology) yield significant intermodel differences (Collins et al. 2013). Therefore every climate model yields a somewhat different outcome when forced with the same external forcing (e.g., Collins et al. 2013). Given these limitations it can be useful to project changes in future climate using a probabilistic approach, treating chosen climate parameters as random variables (e.g., Rowlands et al. 2012). These can either be parameters that control the behavior of model parameterizations or emergent quantities such as climate sensitivity or the ocean heat uptake efficiency (e.g., Collins et al. 2007). Here we treat the three variables of the forcing-response equation [Eq. (3)] as our random variables in an effort to simulate a representative sample of possible future rates of transient temperature change.
The ocean component of the UVic ESCM is the model component with the highest fidelity to physical reality. As such there are a number of ways to change ocean heat uptake, but each comes at the price of reducing the fidelity the model, with the potential to create substantial model biases. After a series of trial-and-error model experiments two methods were settled upon: 1) changing the vertical diffusivity in the Bryan–Lewis parameterization (Bryan and Lewis 1979) and 2) changing the isopycnal and thickness diffusivities in the Gent–McWilliams parameterization (Gent and McWilliams 1990). The Bryan–Lewis parameterization was changed by scaling the value of the profile uniformly in depth, changing the vertical diffusivity but not the functional form of the profile. The Gent–McWilliams parameterization was changed by scaling the isopycnal and thickness diffusivities by the same factor.
Altering the Bryan–Lewis parameterization in the UVic ESCM was able to change the value of the κ parameter to between 0.5 and 2.0 W m−2 K−1 as evaluated at the time of CO2 doubling (average of years 60 to 80) in the 1% experiment. Altering the Gent–McWilliams parameterization is able to change κ by about 0.1 W m−2 K−1 and was used in tandem with the Bryan–Lewis alteration to reach κ values of 0.4 W m−2 K−1. The increase in model error from changing these parameterizations was evaluated by spinning up the model for 5000 years under constant year 1850 Common Era (CE) forcing and then conducting historical experiments between years 1850 to 2000 CE over the range of κ values between 0.4 and 1.2 W m−2 K−1. The historical forcing includes 14C and chlorofluorocarbon (CFC) emissions such that the model can be compared to data from the World Ocean Atlas 2009 (Levitus et al. 2010). After entering the simulated ocean surface, CFCs and 14C are transported as tracers following ocean advection and diffusion. CFCs are treated as passive tracers while 14C has source and sink terms to account for the biological and carbonate pumps and radioactive decay (Orr et al. 1999; Schmittner et al. 2008). Figure 1 shows the error for each κ relative to the model variant with the lowest error. The error statistic is the root-mean-square of the differences between the model simulation and the World Ocean Atlas 2009 interpolated to the UVic ESCM grid following Eby et al. (2009). For ocean potential temperature change altering the Bryan–Lewis parameterization can double the error and altering the Gent–McWilliams parameterization to reach κ values of 0.4 W m−2 K−1 can triple the error. The error remains close to the baseline error between κ values of 0.7 and 1.1 W m−2 K−1. The error in 14C is the most uniform of the metrics growing to a maximum of 1.3 times the baseline error for both the high and low end of the range. For both CFC-11 and CFC-12 the error grows for κ values below 0.8 W m−2 K−1 and reaches 1.6 times the baseline for κ values of 0.4 W m−2 K−1.
Error in model output relative to four validation datasets from the World Ocean Atlas 2009 (Levitus et al. 2010). Errors are computed as root-mean-square error normalized to the smallest error of all model variants. Black dots represent model variants with only the Bryan–Lewis parameterization rescaled. Red dots have both the Bryan–Lewis and Gent–McWilliams parameterizations rescaled.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
c. Experiment design: Emulating CMIP5
The goal of modifying the climate sensitivity, radiative forcing, and ocean heat uptake efficiency in the UVic ESCM is to make the model capable of simulating any plausible transient change in surface temperature. To check whether this is something that can reasonably be done with the UVic ESCM we will compare model output from CMIP5 (Taylor et al. 2012) to model output from variants of the UVic ESCM modified to have the same climate sensitivity, radiative forcing, and ocean heat uptake efficiency diagnosed from each CMIP5 model. If the modified variants of the UVic ESCM can closely match the CMIP5 temperature output then we can be reassured that the methods to modify the physical climate parameters in the UVic ESCM are accurate over the range of probabilities represented by the CMIP5 models. We have made no effort to prescreen the CMIP5 archive and have maintained the convention of “model democracy” used by the IPCC (Knutti 2010). The purpose of the model emulation experiments is to test whether the UVic ESCM is capable of producing a wide range of future global temperature change, a goal that is not contingent on the validity of the CMIP5 models used for comparison. While some CMIP5 models perform better than others on certain variables and in certain regions, none of these models can be dismissed based on unambiguously implausible aggregated values of λ, κ, and F.
Climate sensitivity was diagnosed from the standard model experiment where atmospheric CO2 is instantly quadrupled (4 × CO2 experiment) using the methods of Gregory et al. (2004). For this method the climate sensitivity is taken as the x intercept of a line fitted to the change in global temperature versus the planetary radiative imbalance curve over years 20 to 150 of the experiment. The y intercept of this line is an estimate of the CMIP5 model’s radiative forcing from a quadrupling of CO2 (e.g., Andrews et al. 2012). The climate feedback parameter is taken as the slope of the line fitted to the global temperature change versus planetary heat uptake curve between years 20 and 150 of the 4 × CO2 experiment. There are two methods to calculate the ocean heat uptake efficiency: the method of Raper et al. (2002), where κ is taken as the ratio of N/ΔT in year 70 of the 1% experiment, and the method of Gregory and Forster (2008), where κ is estimated as the slope of the change in global temperature versus planetary radiative imbalance curve. The method of Gregory and Forster (2008) provides a kind of average of ocean heat uptake efficiency over time while the method of Raper et al. (2002) is the value of ocean heat uptake efficiency at a specific point in time. Either interpretation of κ may be useful for a given method of analyzing the climate system (Gregory and Forster 2008; Raper et al. 2002). For the present study we have chosen to follow the definition of κ given in Raper et al. (2002). Following this definition preserves the relationship between the three physical climate parameters and the transient climate response (TCR; the temperature change in year 70 of the 1% experiment) if TCR is calculated from the physical climate parameters and the forcing-response equation [Eq. (3)].
The physical climate parameter values recovered with these methods are shown in Table 1 for the 23 CMIP5 models that stored all of the necessary output to compute these relationships. For each CMIP5 model in Table 1 a variant of the UVic ESCM was generated with the same climate sensitivity, radiative forcing from doubling CO2, and ocean heat uptake efficiency as given by the CMIP5 models. The UVic ESCM variants were spun up for 5000 years under year 1850 CE forcing and a 1% experiment conducted from the spun-up variant.
Climate feedback parameter λ, ocean heat uptake efficiency κ, and radiative forcing F2×CO2 for each of the CMIP5 models and the standard version of the UVic ESCM. The values from the CMIP5 models are those used in the CMIP5 emulation experiment. The range of the UVic ESCM parameters from the perturbed physics experiment are in brackets next to the standard values.
d. Experiment design: Perturbed physics ensemble
To estimate the uncertainty in the TCRE originating from the uncertainty in the rate of transient temperature change a perturbed physics ensemble approach is used. The three parameters in the forcing-response equation [Eq. (3)] are perturbed. Uncertainty in the equilibrium climate sensitivity has been estimated from observations of the recent-day climatological mean state, the observed warming of ocean and atmosphere since preindustrial times, climate model simulations, and paleoclimate proxies (Collins et al. 2013, for a recent summary). Here we have chosen to represent climate sensitivity uncertainty using a probability distribution function (PDF) designed to capture the general features of the uncertainty in equilibrium climate sensitivity from these different lines of evidence following Olson et al. (2012). For a doubling of atmospheric CO2 the PDF has a mean of 3.25°C with the 5th and 95th percentiles at 1.7° and 5.2°C, respectively. The functional form of the PDF was derived by Olson et al. (2012) and takes the form of the product of two normal inverse Gaussian functions. The uncertainty in radiative forcing from CO2 was taken to be normally distributed with the mean radiative forcing value (for a doubling of CO2) set at the classical value of 3.71 W m−2 (Myhre et al. 1998). The standard deviation was set to 0.4 W m−2 taken from the mean of the variability from the three methods of estimating CO2 radiative forcing from climate model output (Andrews et al. 2012; Vial et al. 2013; Zhang and Huang 2014). The uncertainty in κ was taken to be normally distributed with the mean value at 0.74 W m−2 K−1 set to the mean of the 27 CMIP5 models that conducted the 1% experiment and saved planetary heat uptake. The standard deviation was set to 0.1375 W m−2 K−1, one-quarter the range (maximum to minimum) of the CMIP5 derived κ values. That is, we are taking the CMIP5 range to represent most but not all of the uncertainty in κ.
The Latin hypercube sampling method is used to select parameter values from the parameter PDFs and create parameter sets (McKay et al. 1979). With this sampling method each PDF is broken into intervals of equal probability. From within each interval one parameter value is randomly selected and matched randomly with parameter values selected in the same fashion from each of the other random variable PDFs (Helton and Davis 2003). The number of parameter sets and model situations is equal to the number of equal probability intervals selected. For these experiments the PDFs were broken into 15 intervals and the method repeated 10 times to create 150 parameter sets.
Each model variant was spun up for 5000 years under constant year 1850 CE forcing. Simulations were conducted under the 1% experiment. Following the definition set out in Collins et al. (2013) TCRE is evaluated at year 70 of the 1% experiment, as computed as the average between years 60 to 80 of the experiment. Cumulative CO2 emissions are diagnosed as the residual of the carbon cycle. That is, atmospheric CO2 concentration is prescribed and fossil fuel emissions diagnosed as the carbon needed to maintain conservation of carbon in the land–ocean–atmosphere system. As only a single set of carbon cycle parameters are used in these experiments, variation in cumulative CO2 emissions will represent the effect of uncertainty in the rate of transient temperature change on carbon cycle feedbacks and the TCRE.
Changing the rate of transient climate change in the model will also change the simulated patterns of ocean circulation and precipitation. These changes will in turn also alter the behavior of the global carbon cycle by changing the rate of ocean carbon uptake and through the relationship between soil moisture and respiration. Therefore alterations of ocean circulation and precipitation will be incorporated into the uncertainty in TCRE estimated in these numerical experiments.
3. Results and discussion
a. Emulating CMIP5
If recovery of physical parameters from the CMIP5 archive and UVic ESCM emulation methods were perfect then global average temperature change from the CMIP5 model output and UVic ESCM emulations would match exactly. These methods are of course not perfect and to quantify the magnitude of these errors we compute the difference between the TCR from the CMIP5 models, TCR estimated using Eq. (3), and TCR from the UVic ESCM emulations (Table 2). The difference between the TCR computed directly from the 1% experiment from each of the CMIP5 models and the TCR computed from Eq. (3) with the CMIP5 physical climate parameters is the recovery error: that is, the error that results from the imperfect ability of the methods of Gregory et al. (2004) and Raper et al. (2002) to recover the value of F2×CO2, λ, and κ from archived model data. For the 23 CMIP5 models considered here the recovery error has a root-mean-square error (RMSE) of 0.13 K (7.0%), a mean error of 0.03 K (1.6%), and a range of −0.18 K (−10.3%) (GISS-E2-H) to 0.28 K (14.9%) (CNRM-CM5-2) (Table 2). The UVic ESCM emulations are based on the recovered values of F2×CO2, λ, and κ, so the emulation error is the difference between the TCR predicted from these values and the TCR computed by the UVic ESCM based on these values. The emulation error measures how well the methods to alter the physical climate parameters of the UVic ESCM work. Across the 23 CMIP5 models the emulation error has an RMSE of 0.05 K (2.6%), a mean error of −0.03 K (−1.6%), and a range of −0.09 (−5.4%) (CCSM4) to 0.05 K (2.2%) (MIROC-ESM). The total error, the difference between CMIP5 TCR and UVic ESCM emulated TCR, has an RMSE of 0.14 K (7.5%) and a mean error of −0.01 K (0.5%). These results suggest that emulation methods work with reasonable accuracy. Therefore at the global average the modified UVic ESCM should be able to simulate plausible rates of transient temperature change.
CMIP5 TCR, recovery error, emulation error, and total error for the UVic ESCM emulation experiments. Recovery error is the difference in TCR between that retrieved directly from the CMIP5 1% experiment and that computed from climate feedback parameter, ocean heat uptake efficiency, and radiative forcing retrieved from each CMIP5 model. Emulation error is the difference between the UVic ESCM emulated TCR and that computed from the climate feedback parameter, ocean heat uptake efficiency, and radiative forcing. Total error is the difference between TCR from the UVic ESCM emulation and TCR from the corresponding CMIP5 model.
To examine how well the temperature emulation works at the regional level we examine the difference in zonal average temperature anomalies. The zonal averages are examined here as they illustrate how well the model emulates the transport of heat from tropics to the poles, a basic feature of the climate system. The difference between the CMIP5 zonal temperature anomalies and the UVic ESCM emulated zonal temperature anomalies are shown in Fig. 2. Figure 2 shows that the UVic ESCM emulation tends to be within ±0.5 K of the CMIP5 anomaly from about 50°N to 40°S. The error is larger in the polar regions and extratropics with up to a −3-K difference over the Arctic and a difference of −2 to 3 K over the Southern Ocean. Averaged over all 23 CMIP5 models the mean error is close to zero in the tropics and negative over the North Pole with a positive error over the Southern Ocean. Overall the UVic ESCM reproduces the CMIP5 zonal average temperature anomalies well, especially in the tropics. We have altered the UVic ESCM to match the climate sensitivity, ocean heat uptake, and CO2 radiative forcing of an ensemble of CMIP5 models. As the emulation has been imposed using globally aggregated quantities we expect that the simulated temperature field will diverge at local scales, owing to the differences in model structure. Despite the large temperature bias at high latitudes, using the UVic ESCM as a model emulator proves to be a productive strategy for sampling the full range of plausible future temperature fields.
Difference in zonally averaged temperature anomalies between CMIP5 model and UVic ESCM variant given the same climate feedback parameter, ocean heat uptake efficiency, and radiative forcing of the CMIP5 models (gray lines). Black line is the average of the difference across all 23 CMIP5 models.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
b. Perturbed physics experiment
A histogram of the TCRE values from the perturbed physics experiment is shown in Fig. 3a. The full range of the TCRE values is from 0.49 to 3.12 K EgC−1 with a 5th to 95th percentile range of 0.88 to 2.52 K EgC−1 and a mean TCRE value of 1.72 K EgC−1. The TCRE histogram has a small positive skew, likely inherited from the long tail of the climate sensitivity PDF (Fig. 3a). The 5th to 95th percentile range is larger than that estimated from observational records (0.7 to 2.0 K EgC−1) (Gillett et al. 2013), similar to the CMIP5 (0.8 to 2.4 K EgC−1) intermodel range (Gillett et al. 2013) and broader than the intermediate-complexity model intermodel range (1.4 to 2.5 K EgC−1) (Eby et al. 2013). The 5th to 95th percentile range is similar to the “likely” range given by IPCC AR5 of 0.8 to 2.5 K EgC−1 (Collins et al. 2013). Recall, however, that these experiments capture only the uncertainty generated from the uncertainty in physical climate parameters and do not account for uncertainty from the unperturbed parameters that control the behavior of the simulated carbon cycle. Therefore the range given here is smaller than the total uncertainty in TCRE. The range obtained here is of course somewhat subjective, as there is no agreed way of defining uncertainties in the input parameters like climate sensitivity, where different studies come up with quite different constraints.
(a) Histogram of TCRE from the perturbed physics ensemble experiment. Mean value is 1.72 K EgC−1. (b) Cumulative emissions vs temperature curves for all 150 model variants. Individual model variants are in gray, solid black line is the mean, and dashed lines are the 5th and 95th percentiles.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
Figure 3b shows the cumulative emissions versus temperature curves for the 150 model variants generated for the perturbed physics ensemble. The curves with a lower TCRE value visibly deviate from a straight line over the range of cumulative emissions shown and take on more of a logarithmic shape. Such deviation from linearity is consistent with the concept of a TCRE window defined by MacDougall and Friedlingstein (2015). The TCRE window is the range over which TCRE is approximately constant in time and is defined as where TCRE is within 95% of its peak value. MacDougall and Friedlingstein (2015) computed diagrams of the range of the TCRE window for an idealized set of equations describing TCRE. Although highly idealized such diagrams help in the interpretation of the deviation from linearity seen in Fig. 3b and therefore have been redrafted and presented in Fig. 4 for climate sensitivity and κ. Figure 4 shows that the TCRE window is larger at higher climate sensitivity and higher values of κ. Recall that higher values of κ correspond to higher ocean heat uptake and therefore lower transient temperature change. The sublinear behavior of the low TCRE cumulative emission versus temperature curves (Fig. 3b) is therefore consistent with low climate sensitivity corresponding to a smaller TCRE window. This effect should be compensated to some degree by high values of κ enlarging the TCRE window. The behavior seen in Fig. 3b suggests that the climate sensitivity effect is dominating over the κ effect.
TCRE windows for ocean heat uptake efficiency κ and climate sensitivity computed using the idealized equations of MacDougall and Friedlingstein (2015). The TCRE window is the parameter values over which TCRE is approximately constant and is defined as where TCRE is within 95% of its peak value.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
The relative contribution of the uncertainty in climate sensitivity, ocean heat uptake efficiency, and radiative forcing to the physical uncertainty in TCRE is shown in Fig. 5. Figure 5 displays the correlation between the perturbed parameters’ values and the value of TCRE. The strongest correlation is between climate sensitivity and TCRE with a correlation coefficient of 0.86. The next strongest correlation is with ocean heat uptake efficiency with a correlation coefficient of −0.39, followed by radiative forcing with a correlation coefficient of 0.17. The physical uncertainty in TCRE is therefore dominated by the uncertainty in climate sensitivity, which is the dominant source of uncertainty in the TCR (e.g., Collins et al. 2013) that enters the definition of TCRE [Eq. (1)]. The uncertainty in ocean heat uptake efficiency also contributes significantly to the uncertainty in TCRE while the uncertainty in radiative forcing has only a small contribution to the overall uncertainty, likely owing to the uncertainty in radiative forcing from CO2 being well constrained relative to other radiatively active substances (e.g., Myhre et al. 2013).
Relationship between TCRE and the three perturbed physical climate parameters. Dots are individual model variants and the red lines are lines of best fit; R is the correlation coefficient.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
When TCRE is computed from year 70 of the 1% experiment (as is done here) then TCRE is equivalent to Λ = TCR/E2×, where E2× is cumulative emissions at the point in time when atmospheric CO2 concentration is double its preindustrial value. As a simple relationship exists to describe TCR from the parameters we have perturbed [Eq. (3)], a perturbed physics ensemble is not needed to derive uncertainty in TCR from the uncertainty in climate sensitivity, ocean heat uptake efficiency, and radiative forcing. However, there are limits to such simple energy balance models (Knutti and Rugenstein 2015), and it is worth testing whether those relationships hold in more physically based and spatially resolved models. Here we are interested in the effect of the uncertainty in transient temperature change on the carbon cycle and therefore on cumulative emissions E2×. Figure 6a shows the relationship between TCR and E2× for the 150 model variants. Figure 6a demonstrates that there is a near-linear relationship between TCR and E2× with high TCR corresponding to low E2×. Figure 6b shows the relationship between TCR and the cumulative airborne, oceanborne, and landborne fraction of emitted carbon in year 70 of the 1% experiment for all 150 model variants. As we expect given the lower cumulative emissions with higher TCR, the airborne fraction of carbon increases for higher values of TCR. The higher airborne fraction is in turn being driven by a lower landborne fraction of carbon with higher TCR. The oceanborne fraction of carbon is not a strong function of TCR and is near constant in all experiments. Therefore the uncertainty in TCR is being magnified by temperature sensitive terrestrial carbon cycle feedbacks into an even larger uncertainty in TCRE. Figure 6c breaks the landborne fraction into contributions from vegetation and soil carbon. Higher TCR correlates with a lower fraction of carbon in soils, as one would expect from enhanced soil respiration. The fraction of carbon taken up by vegetation declines slightly at higher TCR.
(a) Relationship between TCR and cumulative emissions of CO2 in year 70 of the 1% experiment. Each dot is a model variant. (b) Relationship between TCR and airborne, oceanborne, and landborne fraction of carbon in each of the model variants. (c) Subdivision of the landborne fraction into soilborne and vegetationborne fraction of emitted carbon. Note that the vertical scale is different from (b).
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
The version of the UVic ESCM used for the present model experiments is one of the few ESMs or EMICs to include a permafrost carbon module (Schuur et al. 2015). Therefore whether the relationship between TCR and soil carbon originates from the permafrost carbon pool or carbon in temperate and tropical soils is of interest. A recent study using the same version of the UVic ESCM showed that the release of carbon from permafrost soils significantly reduces the cumulative CO2 emissions compatible with realistic emissions scenarios (MacDougall and Knutti 2016b). However, under the idealized 1% experiment used here permafrost makes only a small contribution of carbon to the atmosphere. In year 70 of the 1% experiment the Northern Hemisphere permafrost region had lost a mean of 8 PgC, with a 5th to 95th percentile range of −5 to 22 PgC. That is, in a minority of the simulations the soils of the permafrost region actually gained carbon by year 70 of the 1% experiment. A long time lag between a change in forcing and the response of the permafrost carbon system is a characteristic property of the system in model simulations (e.g., MacDougall and Knutti 2016b; Schneider von Deimling et al. 2015). It appears from the present simulations that the 1% experiment warms too fast for the permafrost system to react.
Evaluating TCRE at year 70 of the 1% experiment may not be the best choice for computing TCRE for carbon budgets and model intercomparison projects if such evaluations intend to account for the permafrost carbon feedback accurately. Similarly other modeling studies have suggested that ocean carbon cycle feedbacks become stronger later in multicentennial simulations (Randerson et al. 2015). Given these drawbacks and more general concerns about the physical consistency within ESMs of using diagnosed emissions to compute TCRE we recommend that in future model intercomparison projects TCRE be computed for idealized emissions-driven simulations. These idealized experiments could take the form of constant emission rate experiments, such as those performed by Nohara et al. (2013), Krasting et al. (2014), and MacDougall and Friedlingstein (2015), or bell-curve-shaped closed emissions trajectories, such as those used by MacDougall and Knutti (2016a).
The effect of transient temperature uncertainty on the carbon cycle in the simulations presented here is contingent on the structure of the carbon cycle in the UVic ESCM. Similar experiments conducted with another EMIC should yield the same range in TCR but different compatible cumulative emissions and therefore a different range of TCRE uncertainty.
As shown in Fig. 2 the UVic ESCM has persistent high-latitude temperature change biases with respect to other ESMs, with too little warming in the Arctic and too much warming over the Southern Ocean. The high latitudes comprise a relatively small fraction of Earth but are disproportionally important to feedbacks to climate change because of the ice-albedo feedback, the large reservoir frozen permafrost carbon, and the location of the deep-water formation sites (e.g., Vaughan et al. 2013). Therefore when using perturbed parameter approaches with the UVic ESCM we can expect that the model will underestimate critical thresholds for Arctic feedbacks and overestimate such thresholds for feedbacks originating in the Southern Ocean.
Wider implications
The model experiments conducted here capture only part of the uncertainty in the value of TCRE. We have only perturbed three physical climate parameters and left most of the hundreds of parameters that control the behavior of the UVic ESCM at their default values. Of particular importance for quantifying the uncertainty in TCRE are the parameters that control the terrestrial and oceanic carbon cycles. Perturbed parameter experiments conducted with other Earth system models (Booth et al. 2012) suggest that the uncertainty from the terrestrial carbon cycle alone is larger than the intermodel range for the carbon cycle response. It is our intention in future studies to perturb key parameters that control the behavior of the simulated terrestrial and oceanic carbon in the UVic ESCM to help assess the parameter-derived uncertainty of the carbon cycle component of the TCRE uncertainty.
A second source of uncertainty that we cannot account for in this study is structural uncertainty—that is, the uncertainty that originates from the difference between the system a model intends to represent (the natural Earth system) and the system that the model code actually describes (Smith 2007). Structural uncertainty is assessed by comparing the output of different models of the same system and is constrained by assuring that each model can adequately reproduce features of the system being simulated. For ESMs structural uncertainty is what is assessed when ensembles of opportunities such as the CMIP5 archive are examined, although not in a systematic way (Tebaldi and Knutti 2007). Therefore the range of TCRE given by the CMIP5 archive is an indication of the uncertainty in TCRE that originates from our imperfect description of the Earth system in ESMs, as well as each CMIP5 model’s internal variability. In principle a model intercomparison project of comprehensive perturbed physics experiments could be conducted to assess both structural and parameter uncertainty. However, such a project remains outside the computational resources available even for an EMIC intercomparison project.
We have not assessed the full uncertainty in TCRE originating from the uncertain value of parameters in the UVic ESCM, and therefore we cannot give an estimate for the carbon budget compatible with a given probability of not breaching a chosen temperature change target. However, we can glean some useful insight from the physical component of the TCRE uncertainty. Of interest is that the 5th to 95th percentile range of the TCRE from our experiments (0.88 to 2.52 K EgC−1) is similar to the intermodel range for TCRE from the CMIP5 experiments and the parallel EMIC model intercomparison (0.8 to 2.5 K EgC−1). Since the range from the experiments conducted here quantified part of the parameter uncertainty in TCRE, while the intermodel range quantifies part of the structural uncertainty in TCRE, the fact that the two ranges are of similar value suggests that the intermodel range underestimates the full range of uncertainty in the TCRE. That is, the total uncertainty in TCRE is a combination of structural and parameter uncertainty; because both uncertainties are greater than zero their sum will be larger than either uncertainty individually.
The carbon budgets presented in IPCC AR5 were computed assuming that the TCRE range represents only a 66% probability range (Collins et al. 2013). To estimate the carbon budgets, IPCC AR5 also made the assumption that the uncertainty is normally distributed, which does seem to be consistent with the simulations presented here. Therefore the carbon budgets presented in Collins et al. (2013) remain consistent with the present understanding of uncertainty in TCRE.
4. Conclusions
Here we have assessed the uncertainty in the TCRE originating from uncertainty in the rate of transient temperature change within a perturbed physics ensemble framework. First we have tested whether the UVic ESCM could replicate the temperature anomalies of CMIP5 models when given the radiative forcing, climate sensitivity, and ocean heat uptake efficiency of each CMIP5 model. The UVic ESCM emulation methods closely reproduce temperature change at the global average and do a reasonable job of reproducing temperature anomalies at the zonal average. The match is better in the tropics than at the extratropics or polar regions.
The perturbed physics ensemble experiment gave a mean estimate of TCRE of 1.72 K EgC−1, with a 5th to 95th percentile range of 0.88 to 2.52 K EgC−1. This range is similar to the likely range estimated in IPCC AR5. The histogram of the TCRE values is close to normally distributed with a small positive skew. The temperature uncertainty in the TCRE is magnified by the effect of temperature on carbon cycle feedbacks such that high transient temperature change model variants also exhibit stronger positive carbon cycle feedbacks magnifying the uncertainty in TCRE. These carbon cycle feedbacks are dominated by the terrestrial carbon cycle with the ocean having little response to the rate of near-surface temperature change. Our experiments cannot account for the uncertainty from our model’s imperfect representation of the global carbon cycle and uncertainty from the uncertain value of model parameters that control the simulation of the carbon cycle. Therefore we have only estimates of part of the total uncertainty in TCRE.
Evaluating the uncertainty in TCRE is paramount for making well-informed estimates of the carbon budget associated with a high probability of staying below a chosen temperature change threshold. Therefore there is a need to use many methods, experiments, and intercomparison projects to evaluate the uncertainty in TCRE and to eventually reduce this uncertainty. The probabilistic approach presented here, based on a relatively complex and spatially resolved EMIC complements results from mostly simpler models and ensembles of opportunity of full ESMs that are hard to interpret in terms of uncertainty. Combined with a probabilistic carbon cycle our method could be an efficient tool for quantification of uncertainty in future warming and carbon budgets compatible with chosen temperature targets such as the 2° and 1.5°C targets from the Paris Agreement (United Nations 2015).
Acknowledgments
We are grateful to the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and grateful to M. Eby who provided insight into which parameters in the UVic ESCM ocean to perturb. We thank two anonymous reviewers for their helpful comments.
APPENDIX
Emissions-Driven versus Concentration-Driven Simulations
To check whether the above experiments would be substantially different if we used emissions-driven simulations as opposed to concentration-driven simulations we forced the standard version of the UVic ESCM with emissions diagnosed from the 1% experiment. Figure A1 shows the global average CO2 and temperature trajectories for the emissions-driven experiment and the standard 1% experiment along with the difference between the two. The two experiments have a slightly different atmospheric CO2 concentration, with the emissions-driven simulation lagging the concentration driven simulation by about 0.35 ppm. The difference in temperature is on the order of 5 mK and therefore is negligible.
(top) Atmospheric CO2 concentration and (bottom) global mean SAT for the 1% experiment and an experiment driven by emissions diagnosed from the 1% experiment. (left) The emissions-driven run is green and concentration-driven is black. The lines sit almost atop each other. (right) The difference between the two experiments.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-16-0205.1
REFERENCES
Allen, M. R., D. J. Frame, C. Huntingford, C. D. Jones, J. A. Lowe, M. Meinshausen, and N. Meinshausen, 2009: Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature, 458, 1163–1166, doi:10.1038/nature08019.
Andrews, T., J. M. Gregory, M. J. Webb, and K. E. Taylor, 2012: Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere–ocean climate models. Geophys. Res. Lett., 39, L09712, doi:10.1029/2012GL051607.
Arora, V. K., and Coauthors, 2013: Carbon–concentration and carbon–climate feedbacks in CMIP5 Earth system models. J. Climate, 26, 5289–5314, doi:10.1175/JCLI-D-12-00494.1.
Avis, C. A., 2012: Simulating the present-day and future distribution of permafrost in the UVic Earth system climate model. Ph.D. thesis, University of Victoria, 291 pp.
Avis, C. A., A. J. Weaver, and K. J. Meissner, 2011: Reduction in areal extent of high-latitude wetlands in response to permafrost thaw. Nat. Geosci., 4, 444–448, doi:10.1038/ngeo1160.
Booth, B. B., and Coauthors, 2012: High sensitivity of future global warming to land carbon cycle processes. Environ. Res. Lett., 7, 024002, doi:10.1088/1748-9326/7/2/024002.
Bryan, K., and L. Lewis, 1979: A water mass model of the World Ocean. J. Geophys. Res., 84, 2503–2517, doi:10.1029/JC084iC05p02503.
Collins, M., C. Brierley, M. MacVean, B. Booth, and G. Harris, 2007: The sensitivity of the rate of transient climate change to ocean physics perturbations. J. Climate, 20, 2315–2320, doi:10.1175/JCLI4116.1.
Collins, M., and Coauthors, 2013: Long-term climate change: Projections, commitments and irreversibility. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 1029–1136.
Cox, P. M., R. A. Betts, C. D. Jones, S. A. Spall, and I. J. Totterdell, 2001: Modelling vegetation and the carbon cycle as interactive elements of the climate system. Hadley Centre Tech. Note 23, 29 pp. [Available online at http://wikyonos.seos.uvic.ca/model/common/HCTN_23.pdf.]
Eby, M., K. Zickfeld, A. Montenegro, D. Archer, K. J. Meissner, and A. J. Weaver, 2009: Lifetime of anthropogenic climate change: Millennial time scales of potential CO2 and surface temperature perturbations. J. Climate, 22, 2501–2511, doi:10.1175/2008JCLI2554.1.
Eby, M., and Coauthors, 2013: Historical and idealized climate model experiments: An intercomparison of Earth system models of intermediate complexity. Climate Past, 9, 1111–1140, doi:10.5194/cp-9-1111-2013.
Falkowski, P., and Coauthors, 2000: The global carbon cycle: A test of our knowledge of Earth as a system. Science, 290, 291–296, doi:10.1126/science.290.5490.291.
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155, doi:10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.
Gillett, N. P., V. K. Arora, D. Matthews, and M. R. Allen, 2013: Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. J. Climate, 26, 6844–6858, doi:10.1175/JCLI-D-12-00476.1.
Goodwin, P., R. G. Williams, and A. Ridgwell, 2015: Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake. Nat. Geosci., 8, 29–34, doi:10.1038/ngeo2304.
Gregory, J., and P. Forster, 2008: Transient climate response estimated from radiative forcing and observed temperature change. J. Geophys. Res., 113, D23105, doi:10.1029/2008JD010405.
Gregory, J., and Coauthors, 2004: A new method for diagnosing radiative forcing and climate sensitivity. Geophys. Res. Lett., 31, L03205, doi:10.1029/2003GL018747.
Gregory, J., C. D. Jones, P. Cadule, and P. Friedlingstein, 2009: Quantifying carbon cycle feedbacks. J. Climate, 22, 5232–5250, doi:10.1175/2009JCLI2949.1.
Hamza, V., R. Cardoso, and C. P. Neto, 2008: Spherical harmonic analysis of Earth’s conductive heat flow. Int. J. Earth Sci., 97, 205–226, doi:10.1007/s00531-007-0254-3.
Hansen, J., M. Sato, and R. Ruedy, 1997: Radiative forcing and climate response. J. Geophys. Res., 102, 6831–6864, doi:10.1029/96JD03436.
Helton, J. C., and F. J. Davis, 2003: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Eng. Syst. Saf., 81, 23–69, doi:10.1016/S0951-8320(03)00058-9.
IPCC, 2001: Climate Change 2001: The Scientific Basis. Cambridge University Press, 881 pp.
Jenkinson, D., D. Adams, and A. Wild, 1991: Model estimates of CO2 emissions from soil in response to global warming. Nature, 351, 304–306, doi:10.1038/351304a0.
Knutti, R., 2010: The end of model democracy? Climatic Change, 102, 395–404, doi:10.1007/s10584-010-9800-2.
Knutti, R., and M. A. Rugenstein, 2015: Feedbacks, climate sensitivity and the limits of linear models. Philos. Trans. Roy. Soc. London, 373A, 20150146, doi:10.1098/rsta.2015.0146.
Krasting, J., J. Dunne, E. Shevliakova, and R. Stouffer, 2014: Trajectory sensitivity of the transient climate response to cumulative carbon emissions. Geophys. Res. Lett., 41, 2520–2527, doi:10.1002/2013GL059141.
Levitus, S., and Coauthors, Eds., 2010: Temperature. Vol. 1, World Ocean Atlas 2009, NOAA Atlas NESDIS 68, U.S. Government Printing Office, 184 pp.
Luo, Y., and X. Zhou, 2006: Soil Respiration and the Environment. Academic Press, 316 pp.
MacDougall, A. H., 2013: Reversing climate warming by artificial atmospheric carbon-dioxide removal: Can a Holocene-like climate be restored? Geophys. Res. Lett., 40, 5480–5485, doi:10.1002/2013GL057467.
MacDougall, A. H., 2016: The transient response to cumulative CO2 emissions: A review. Curr. Climate Change Rep., 2, 39–47, doi:10.1007/s40641-015-0030-6.
MacDougall, A. H., and P. Friedlingstein, 2015: The origin and limits of the near proportionality between climate warming and cumulative CO2 emissions. J. Climate, 28, 4217–4230, doi:10.1175/JCLI-D-14-00036.1.
MacDougall, A. H., and R. Knutti, 2016a: Enhancement of non-CO2 radiative forcing via intensified carbon cycle feedbacks. Geophys. Res. Lett., 43, 5833–5840, doi:10.1002/2016GL068964.
MacDougall, A. H., and R. Knutti, 2016b: Projecting the release of carbon from permafrost soils using a perturbed physics ensemble modelling approach. Biogeosciences, 13, 2123–2136, doi:10.5194/bg-13-2123-2016.
MacDougall, A. H., C. A. Avis, and A. J. Weaver, 2012: Significant existing commitment to warming from the permafrost carbon feedback. Nat. Geosci., 5, 719–721, doi:10.1038/ngeo1573.
Matthews, H. D., A. J. Weaver, K. J. Meissner, N. P. Gillett, and M. Eby, 2004: Natural and anthropogenic climate change: Incorporating historical land cover change, vegetation dynamics and the global carbon cycle. Climate Dyn., 22, 461–479, doi:10.1007/s00382-004-0392-2.
Matthews, H. D., N. P. Gillett, P. A. Stott, and K. Zickfeld, 2009: The proportionality of global warming to cumulative carbon emissions. Nature, 459, 829–832, doi:10.1038/nature08047.
McGlade, C., and P. Ekins, 2015: The geographical distribution of fossil fuels unused when limiting global warming to 2°C. Nature, 517, 187–190, doi:10.1038/nature14016.
McKay, M. D., R. J. Beckman, and W. J. Conover, 1979: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239–245, doi:10.2307/1268522.
Meinshausen, M., N. Meinshausen, W. Hare, S. C. Raper, K. Frieler, R. Knutti, D. J. Frame, and M. R. Allen, 2009: Greenhouse-gas emission targets for limiting global warming to 2°C. Nature, 458, 1158–1162, doi:10.1038/nature08017.
Meissner, K. J., A. J. Weaver, H. D. Matthews, and P. M. Cox, 2003: The role of land surface dynamics in glacial inception: A study with the UVic Earth system model. Climate Dyn., 21, 515–537, doi:10.1007/s00382-003-0352-2.
Moss, R. H., and Coauthors, 2010: The next generation of scenarios for climate change research and assessment. Nature, 463, 747–754, doi:10.1038/nature08823.
Myhre, G., E. J. Highwood, K. P. Shine, and F. Stordal, 1998: New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett., 25, 2715–2718, doi:10.1029/98GL01908.
Myhre, G., and Coauthors, 2013: Anthropogenic and natural radiative forcing. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 659–740.
Nohara, D., Y. Yoshida, K. Misumi, and M. Ohba, 2013: Dependency of climate change and carbon cycle on CO2 emission pathways. Environ. Res. Lett., 8, 014047, doi:10.1088/1748-9326/8/1/014047.
Olson, R., R. Sriver, M. Goes, N. M. Urban, H. D. Matthews, M. Haran, and K. Keller, 2012: A climate sensitivity estimate using Bayesian fusion of instrumental observations and an Earth system model. J. Geophys. Res., 117, D04103, doi:10.1029/2011JD016620.
Orr, J., R. Najjar, C. Sabine, and F. Joos, 1999: Abiotic-how-to. Internal OCMIP Rep., 25 pp.
Pacanowski, R., 1995: MOM 2 documentation user’s guide and reference manual. NOAA/GDFL Ocean Group Tech. Rep., 232 pp.
Randerson, J. T., K. Lindsay, E. Munoz, W. Fu, J. K. Moore, F. M. Hoffman, N. M. Mahowald, and S. C. Doney, 2015: Multicentury changes in ocean and land contributions to the climate–carbon feedback. Global Biogeochem. Cycles, 29, 744–759, doi:10.1002/2014GB005079.
Raper, S. C. B., J. M. Gregory, and R. J. Stouffer, 2002: The role of climate sensitivity and ocean heat uptake on AOGCM transient temperature response. J. Climate, 15, 124–130, doi:10.1175/1520-0442(2002)015<0124:TROCSA>2.0.CO;2.
Raupach, M. R., and Coauthors, 2014: Sharing a quota on cumulative carbon emissions. Nat. Climate Change, 4, 873–879, doi:10.1038/nclimate2384.
Rogelj, J., M. Meinshausen, M. Schaeffer, R. Knutti, and K. Riahi, 2015: Impact of short-lived non-CO2 mitigation on carbon budgets for stabilizing global warming. Environ. Res. Lett., 10, 075001, doi:10.1088/1748-9326/10/7/075001.
Rowlands, D. J., and Coauthors, 2012: Broad range of 2050 warming from an observationally constrained large climate model ensemble. Nat. Geosci., 5, 256–260, doi:10.1038/ngeo1430.
Schmittner, A., A. Oschlies, H. D. Matthews, and E. D. Galbraith, 2008: Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business-as-usual CO2 emission scenario until year 4000 AD. Global Biogeochem. Cycles, 22, GB1013, doi:10.1029/2007GB002953.
Schneider von Deimling, T., G. Grosse, J. Strauss, L. Schirrmeister, A. Morgenstern, S. Schaphoff, M. Meinshausen, and J. Boike, 2015: Observation-based modelling of permafrost carbon fluxes with accounting for deep carbon deposits and thermokarst activity. Biogeosciences, 11, 16 599–16 643, doi:10.5194/bgd-11-16599-2014.
Schuur, E., and Coauthors, 2015: Climate change and the permafrost carbon feedback. Nature, 520, 171–179, doi:10.1038/nature14338.
Smith, L., 2007: Chaos: A Very Short Introduction. Oxford University Press, 176 pp.
Steinacher, M., and F. Joos, 2016: Transient Earth system responses to cumulative carbon dioxide emissions: Linearities, uncertainties, and probabilities in an observation-constrained model ensemble. Biogeosciences, 13, 1071–1103, doi:10.5194/bg-13-1071-2016.
Stocker, T. F., and Coauthors, 2013: Technical summary. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 33–115.
Taylor, K. E., R. J. Stouffer, and G. A. Meehl, 2012: An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc., 93, 485–498, doi:10.1175/BAMS-D-11-00094.1.
Tebaldi, C., and R. Knutti, 2007: The use of the multi-model ensemble in probabilistic climate projections. Philos. Trans. Roy. Soc. London, 365A, 2053–2075, doi:10.1098/rsta.2007.2076.
Thompson, A., and S. G. Warren, 1982: Parameterization of outgoing infrared radiation derived from detailed radiative calculations. J. Atmos. Sci., 39, 2667–2680, doi:10.1175/1520-0469(1982)039<2667:POOIRD>2.0.CO;2.
United Nations, 2015: Paris Agreement. 21st Conf. of the Parties of the United Nations Framework Convention on Climate Change, Paris, France, United Nations, 1–25. [Available online at http://unfccc.int/files/essential_background/convention/application/pdf/english_paris_agreement.pdf.]
Vaughan, D., and Coauthors, 2013: Observations: Cryosphere. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 317–382.
Vial, J., J.-L. Dufresne, and S. Bony, 2013: On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Climate Dyn., 41, 3339–3362, doi:10.1007/s00382-013-1725-9.
Weaver, A. J., and Coauthors, 2001: The UVic Earth system climate model: Model description, climatology, and applications to past, present and future climates. Atmos.–Ocean, 39, 361–428, doi:10.1080/07055900.2001.9649686.
Wigley, T. M., and M. E. Schlesinger, 1985: Analytical solution for the effect of increasing CO2 on global mean temperature. Nature, 315, 649–652, doi:10.1038/315649a0.
Zhang, M., and Y. Huang, 2014: Radiative forcing of quadrupling CO2. J. Climate, 27, 2496–2508, doi:10.1175/JCLI-D-13-00535.1.
Zickfeld, K., M. Eby, H. D. Matthews, and A. J. Weaver, 2009: Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl. Acad. Sci. USA, 106, 16 129–16 134, doi:10.1073/pnas.0805800106.