responses to carbon emissions Earth system responses to cumulative carbon emissions

Information on the relationship between cumulative fossil carbon emissions and multiple climate targets are essential to design emission mitigation and climate adaptation strategies. In this study, the transient responses in di ﬀ erent climate variables are quantiﬁed for a large set of multi-forcing scenarios extended to year 2300 towards stabilization 5 and in idealized experiments using the Bern3D-LPJ carbon-climate model. The model outcomes are constrained by 26 physical and biogeochemical observational data sets in a Bayesian, Monte-Carlo type framework. Cumulative fossil emissions of 1000 Gt C result in a global mean surface air temperature change of 1.88 ◦ C (68 % conﬁdence interval (c.i.): 1.28 to 2.69 ◦ C), a decrease in surface ocean pH of 0.19 (0.18 to 0.22), 10 and in steric sea level rise of 20 cm (13 to 27 cm until 2300). Linearity between cumulative emissions and transient response is high for pH and reasonably high for surface air and sea surface temperatures, but less pronounced for changes in Atlantic Meridional Overturning, Southern Ocean and tropical surface water saturation with respect to biogenic structures of calcium carbonate, and carbon stocks in soils. The slopes of 15 the relationships change when CO 2 is stabilized. The Transient Climate Response is constrained, primarily by long-term ocean heat observations, to 1.7 ◦ C (68 % c.i.: 1.3 to 2.2 ◦ C) and the Equilibrium Climate Sensitivity to 2.9 ◦ C (2.0 to 4.2 ◦ C). This is consistent with results by CMIP5 models, but inconsistent with recent studies that relied on short-term air temperature data a ﬀ ected by natural climate variability. are constrained by 26 observational data sets in a Bayesian, Monte-Carlo-type framework with an Earth System Model of Intermediate Complexity. The model 20 features spatially-explicit representation of land use forcing, vegetation and carbon dynamics, as well as physically consistent surface-to-deep transport of heat and carbon by a 3-D, dynamic model ocean, thereby partly overcoming deﬁciencies identiﬁed for box-type models used in earlier probabilistic assessments (Shindell, 2014a, b). This allows us to reassess the probability density distribution, including best estimates and 25 conﬁdence ranges, for the Equilibrium Climate Sensitivity (ECS), the transient climate response (TCR), and the Transient Climate Response to cumulative carbon Emissions (TCRE).

Hegerl, 2008). The TCR measures the short-term response (i.e. the temperature increase at the time of doubling CO 2 in a simulation with 1 % yr −1 increase), while the ECS quantifies the long-term response after reaching a new equilibrium of the system under the increased radiative forcing. TCR and ECS are metrics for the physical climate system and depend on the rate of ocean heat uptake and multiple feedbacks such as 5 the water vapor, the ice-albedo, or the cloud feedbacks, but they do not depend on the carbon cycle response (Huber and Knutti, 2014; Kummer and Dessler, 2014). Certain metrics are helpful to reduce the scenario-dependency of results, which may facilitate the communication in a mitigation policy context (Allen and Stocker, 2014). One such metric is the response to a pulse-like emission of CO 2 and other forcing 10 agents as applied to compute global warming potentials in the basket approach of the Kyoto protocol (Joos et al., 2013; Myhre et al., 2013). Another metric is the transient climate response to cumulative carbon emissions (TCRE), which links the global mean temperature increase to the total amount of carbon emissions. In addition to the physical climate response, these metrics also depend on the response of the carbon cycle 15 and thus quantify the response uncertainties of both. TCRE is an interesting metric because it has been shown that global warming is largely proportional to cumulative carbon emissions and almost independent of the emission pathway (Allen et al. bilistic twenty-first century projections based on simple models and observational constraints under-weight the possibility of high impacts and over-weight low impacts on multi-decadal timescales. Huber and Knutti (2014) find that the TCR and ECS of the ESMs are consistent with recent climate observations when natural variability and updated forcing data are considered. Kummer and Dessler (2014) concluded that consid-5 ering a ≈ 33 % higher efficacy of aerosol and ozone forcing than for CO 2 forcing would resolve the disagreement between estimates of ECS based on the twentieth century observational record and those based on climate models, the paleoclimate record, and interannual variations. Yet, an updated probabilistic quantification of the TCR, ECS, and TCRE with a spatially-explicit model and constrained by a broad set of observations is 10 missing.

Modeling framework
We apply the Bern3D-LPJ model in a Bayesian approach which is described in detail by Steinacher Fig. 1 observation-based data sets are used to constrain the model ensemble by assigning skill scores to each ensemble member. The observational data sets combine information from satellite, ship-based, ice-core, and in-situ measurements to probe both the mean state and transient responses in space and time. The data sets are organized in a hierarchical structure ( Fig. S3 and Table S2 in Steinacher et al., 2013) with the four 5 main groups "CO 2 " (atmospheric record and ocean/land uptake rates), "Heat" (surface air temperature and ocean heat uptake), "Ocean" (3-D fields of seven physical and biogeochemical tracers), and "Land" (seasonal atmospheric CO 2 change, land carbon stocks, fluxes, and fraction of absorbed radiation). From the simulation results over the historical period ("mod") and the set of observational constraints ("obs"), we assign 10 a score to each ensemble member m as S m ∝ exp(− 1 2 (X mod m −X obs ) 2 σ 2 ). This likelihood-type function basically corresponds to a Gaussian distribution of the data-model discrepancy (X mod m − X obs ) with zero mean and variance σ 2 , which represents the combined model and observational error. The overbar indicates that the error-weighted datamodel discrepancy is first averaged over all data points of each observational variable 15 (volume or area-weighted) and then aggregated in the hierarchical structure by averaging variables belonging to the same group. 3931 out of the 5000 ensemble members contribute less than a percent to the cumulative skill of all members and are not used any further. In a next step we run the constrained model ensemble for 55 greenhouse gas sce-20 narios spanning from high business-as-usual to low mitigation pathways. The set of scenarios consists of economically feasible multi-gas emission scenarios from the integrated assessment modeling community. In addition to the four RCP scenarios (Moss et al., 2010) that were selected for the fifth assessment report of the IPCC, we included 51 scenarios from the EMF-21 (Weyant et al., 2006), GGI (Grübler et al., 2007), and 25 AME (Calvin et al., 2012) projects. For these simulations, we prescribe atmospheric CO 2 and the non-CO 2 radiative forcing derived from the emission scenarios. We note that the AME scenarios are less complete than the others because they do not provide emission paths for aerosols and some minor greenhouse gases. We therefore make 9845 Introduction In this study, the transient and peak responses per cumulative emissions at a given time t are defined as where X (t) is one of the target variables (e.g. global mean surface temperature change) 10 and for each E , the relative probability map p rel (E , X ) is calculated: where C(P ) denotes the convex hull of the set of points P . For given emissions E , 5 p rel (E , X ) represents the probability density function of the response in X to these emissions.

Testing the linearity of the response
From the probability maps in the (E , X ) space probability density functions are extracted at E = 1000, 2000, and 3000 Gt C. To compare the response at different emission lev-10 els the PDFs at 2000 and 3000 Gt C are rescaled to the response per 1000 Gt C. In a perfectly linear system we would expect that the rescaled PDFs are identical for the different emission levels. To test the linearity of the response further, we fit a linear func-tionX (E ) = a X · E to the points (E m,s (t), X m,s (t)) for each model configuration m. The linear function is forced through zero because we require X (E = 0) = 0 at preindustrial 15 (t = 1800). From the obtained coefficients a X ,m of the model ensemble, we then calculate a PDF for the sensitivity a X of the response to cumulative emissions under the assumption that a linear fit is reasonable. The goodness of fit is quantified by the corre-  not been considered in this study. Results in the present study are mostly given as a function of total (fossil-fuel plus deforestation) and, where indicated, additionally as a function of fossil-fuel emissions.

Climate response to an emission pulse 20
In a first step, we explore how different climatic variables respond to a pulse-like input of carbon into the atmosphere (Fig. 2 , 2005). CO 2 is added instantaneously to the model atmosphere to determine IRFs. This results in a sudden increase in CO 2 and radiative forcing. Afterwards, the evolution in the perturbation of atmospheric CO 2 and in any climate variable of interest, e.g. global mean surface air temperature, is monitored in the model. The resulting curve is the impulse response 5 function (Fig. 2). Here, 1069 runs were carried out in different model configurations by adding emissions of 100 Gt C to an atmospheric CO 2 background concentration of 389 ppm, which corresponds to the concentration in the year 2010. Additionally, simulations with emission pulses of 1000, 3000 and 5000 Gt C were run for a median model configuration (Methods). For comparability, all IRFs are normalized to a carbon 10 input of 100 Gt C. The motivation is two-fold. First, the dynamic of a linear (or approximately linear system) is fully characterized by its response to a pulse-like perturbation, i.e., the response of variable X at year t to earlier annual emissions, e, at year t can be represented as the weighted sum of all earlier annual emissions. The weights are the values of the IRF 15 curve at emission age t − t :  and the change in a climate variable of interest, X (t). The transient climate response for variable X to cumulative carbon emissions is in this notation: We note that there is a close relationship between Eqs. (6) to (8) and thus between cumulative carbon emissions E (t), response X (t) and TCRE. The IRF provides the 5 link between these quantities. Three conditions are to be met for a strict linear relationship between cumulative carbon emissions E and response X for any emission pathway: (i) the response is independent of the magnitude of the emissions, and (ii) the response is independent of the age of the emission, i.e., the time passed since emissions occurred. In this case the 10 IRF and the TCRE is a constant and all emissions are weighted equally in Eq. (6), (iii) non-CO 2 forcing factors play no role; a point that will be discussed later. While these conditions are not fully met for climate variables, they may still approximately hold for plausible emission pathways. For the range of RCP scenarios, the mean age of the carbon emissions varies between a few decades to hundred years for the industrial period 15 and up to year 2100, then it increases up to 300 years until 2300 AD (Fig. 2c). More than half of the cumulative carbon emissions have typically an age older than 30 years (Fig. 2c). If the IRF curve is approximately flat after a few decades and independent of the pulse size, then the vast majority of emission is weighted by a similar value in Eq. (6). Consequently, the relationship between response X (t) and cumulative emis- sions, E (t) is approximately linear and path-independent. This response sensitivity per unit emission, X (t)/E (t), corresponds to an "effective" (emission-weighted) mean value of the IRF and is the TCRE. Indeed, the IRF for many variables varies within a limited range after a few decades (Fig. 2). Then, an approximately linear relationship between E (t) and X (t) holds and TCRE is approximately scenario-independent. 25 The median values of the (normalized) IRFs (Fig. 2, solid and  from 30 year to the end of the simulation (500 year) and for the different pulse sizes of 100 to 3000 Gt C. Consequently, we expect a close-to-linear relationship between these variables and cumulative carbon emissions. For a given pulse size, the median of the IRF for the saturation with respect to aragonite in the tropical (Ω arag, trop. ) and Southern Ocean (Ω arag,S.O. ) surface waters and for 5 the global soil carbon inventory varies within a limited range. However, the normalized IRFs for these variables vary substantially with the magnitude of the emission pulse. Thus, we expect a non-linear relationship between the ensemble median responses and cumulative carbon emissions for these quantities.
The atmospheric CO 2 perturbation declines by about a factor of two within the first 10 100 years for an emission pulse of 100 Gt C. This means that the CO 2 concentration at a specific time depends strongly on the emission path of the previous 100 years. In addition, the IRF differ for different pulse sizes because the efficiency of the oceanic and terrestrial carbon sinks decreases with higher CO 2 concentrations and warming. The fraction remaining airborne after 500 years is about 75 % for a pulse input of 3000 Gt C, 15 about 2.5 times larger than the fraction remaining for a pulse of 100 Gt C (Fig. 2a). Thus, we do not expect a scenario-independent, linear relationship between atmospheric CO 2 and cumulative emissions. The Monte-Carlo IRF experiments allow us also to assess the response or model uncertainty (Fig. 2, orange range). The 90 % confidence range in the IRF are substantially 20 larger than the variation of the (normalized) median IRF for the variables SAT, SSLR, AMOC, and soil carbon inventory. Consequently, the model uncertainty will dominate the uncertainty in TCRE and is larger than uncertainties arising from dependencies on the carbon emission pathway. On the other hand, the response uncertainty from our 5000 Monte Carlo model setups are more comparable to the variation in the median 25 IRFs for atmospheric CO 2 , and surface water saturation with respect to aragonite in the tropical ocean and Southern Ocean.
In summary, we expect close-to-linear relationship between cumulative carbon emissions and SAT, surface ocean pH, SSLR and AMOC, and less well expressed linear behavior for global soil carbon and surface water saturation with respect to aragonite. Uncertainty in the response dominate the uncertainty arising from path dependency for SAT, SSLR, AMOC, and soil carbon. In addition to the path dependency and the response uncertainty in TCRE discussed above, forcing from non-CO 2 agents will affect the TCRE. We expect a notable influence of non-CO 2 agents on the physical climate

Climate response to cumulative carbon emissions
In the next step, we investigate the response in multiple climate variables, X (t), as a function of cumulative carbon emissions E (t). We ran the model ensemble for 15 55 multi-gas emission scenarios from the integrated assessment modeling community which range from very optimistic mitigation to high business-as-usual scenarios (Steinacher et al., 2013, Methods). From those simulations we determine the transient response to cumulative carbon emissions TCRE(t ) = X (t )/E (t ) (Tables 2 and  3; Figs. 3-6). In addition, we also present results for the peak response TCRE peak (t = 20 2300) = max t (X (t )/E (t = 2300)) (Tables 2 and 3, Fig. 3). We find a largely linear relationship between cumulative carbon emissions and both transient and peak warming ( Fig. 3a and b) for the set of emission scenarios considered here. The fact that the results for the transient and peak warming are very similar confirms the finding from the pulse experiment above, i.e. that the response in the 25 global SAT change is largely independent from the pathway of carbon emissions in our model. We note, however, that some low-end scenarios show a non-linear behavior due to non-CO 2 forcing (Fig. 3c) due to a strong reduction in the non-CO 2 forcing while cumulative emissions continue to increase slightly. Other scenarios (mostly from GGI) deviate from the linear relationship when negative emissions decrease the cumulative emissions while the increased temperature is largely sustained. These non-linearities are evident as large changes in the slope between SAT and cumulative emissions towards the end of the individual 5 simulations, that is after ≈ 2150 AD when CO 2 is stabilized and carbon emissions are low (Fig. 3b). Yet those deviations are not large enough to eliminate the generally linear relationship found for this set of scenarios. The projected warming for a given amount of carbon emissions is associated with a considerable uncertainty which increases with higher cumulative emissions. This un-10 certainty arises from both, the response uncertainty of the model ensemble such as the uncertain climate sensitivity or oceanic carbon uptake, as well as from the scenario uncertainty. The scenario uncertainty is mainly due to different assumptions for the non-CO 2 forcing in the scenarios. The AME scenarios, for example, assume a relatively strong negative forcing from aerosols which leads to a consistently smaller warming 15 than in the other scenarios (Fig. 3c). The response and scenario uncertainty appear to be of the same order of magnitude (Fig. 3c).
The transient response is 1.9 • C (Tt C) −1 (1.1-3.4 • C (Tt C) −1 68 % confidence interval) evaluated at 1000 Gt C total emissions and similar for 2000 and 3000 Gt C. The median peak warming response is slightly larger. It is 2.3 • C (Tt C) −1 (1.5-3.8 • C (Tt C) −1 20 68 % confidence interval) for scenarios with 1000 Gt C total emissions and decreases slightly to 1.9 • C (Tt C) −1 (1.3-2.7 • C (Tt C) −1 68 % c.i.) for scenarios with 3000 Gt C total emissions (Fig. 3d). The corresponding responses to fossil-fuel emissions only are accordingly somewhat higher, e.g. 2.2 • C (Tt C) −1 (1.3-3.8 • C (Tt C) −1 ) for the transient response evaluated at 1000 Gt C fossil emissions (Fig. 4, Table 3). 25 We fitted a linear function through zero to the results of each ensemble member and then calculated the probability density functions from the individual slopes. The median slope is 1.8 • C (Tt C) −1 (1.1-2.6 • C (Tt C) −1 ) for the peak response and values are similar for the transient response (Table 2). These slopes are somewhat lower than the and in the strength of the Atlantic meridional overturning circulation (AMOC) are more emission-path dependent (Fig. 5, right column). In all scenarios applied here, it is assumed that atmospheric CO 2 and total radiative forcing is stabilized after 2150. This yields a slow additional grow in cumulative emissions after 2150, whereas SSLR continues largely unabated and the AMOC continues to recover. This results in a steep 25 slope in the relationship between cumulative carbon emissions and these variables after 2150 as well visible in Fig. 5 (right column). The path-dependency also results in larger differences between transient and peak responses ( Table 2). The projected peak SSLR is described remarkably well by a linear regression (Table 2). Yet, these results for the peak SSLR response are somewhat fortuitous and influenced by our choice to stabilize atmospheric CO 2 and forcings after 2150 in all scenarios. For AMOC, the peak response is somewhat stronger for low-emission than highemission paths (Fig. 5c). For 1000 Gt C total emissions, we find a peak reduction in AMOC of −24 % (−35 to −16 %) (Fig. 5d). Surface ∆pH shows a very tight and linear 5 relationship with cumulative carbon emissions. This is consistent with a small influence of non-CO 2 forcing agents, a small response uncertainty and a relatively small dependency on the carbon emission pathway as revealed by the IRF experiments. For Ω arag , the non-linearities are more pronounced with a proportionally stronger response at low total emissions (∆Ω arag = −0.68 to −0.54 (Tt C) −1 at 1000 Gt C total emissions) 10 and weaker response at higher total emissions (∆Ω arag = −0.43 to −0.35 (1000 Gt C) −1 at 3000 Gt C total emissions, Fig. 6b and d). Again, results for fossil-fuel emissions only are provided in Fig. 4 and Table 3.

BGD
Finally, the change in global soil carbon shows a similar response as SSLR, with continued carbon release from soils after stabilization of greenhouse gas concentra-15 tions in mid to high emission scenarios. Like the ocean heat uptake, the respiration of soil carbon can be slow, particularly in deep soil layers at high latitudes, and it takes some time to reach a new equilibrium at a higher temperature. The response uncertainty represented by the model spread for a given scenario, however, is even larger than the spread from the scenarios. For the same scenario, the 95 % confidence in-20 terval ranges from a very high loss of up to 40 % to an increases in global soil carbon by a few percent (Fig. 6c). Despite the very broad resulting PDFs, the most likely peak decrease in soil carbon is relatively well represented by the linear regression slope of about −2.3 % (1000 Gt C) −1 (Fig. 6b).
In summary, we find that not only global mean surface air temperature, but also the 25 other target variables investigated here show a monotonic relationship with cumulative carbon emissions in multi-gas scenarios. The relationship with cumulative carbon emission is highly linear for pH as evidenced by the high correlation coefficient and the invariance in the ensemble median and confidence range from total emissions (Ta- ble 2). Changes in steric sea level, meridional overturning circulation, and aragonite saturation are generally less linearly related to cumulative emissions than global pH and surface air temperature. These variables show a substantial non-linear response after stabilization of atmospheric CO 2 . Nevertheless, the PDF of the peak response for all these variables can be reproduced relatively well with a linear regression yielding 5 correlations of r = 0.8-0.98 and standard errors ofσ = 30-40 % (Table 2). The effect of the different observational constraints on the constrained, posterior distribution for TCR and ECS is estimated by applying only subsets of the observational data. This is done in two different ways: first, by giving the subsets of constraints the full weight as if they were the only available data (Fig. 7a and c), and second, by adding subsets of constraints successively with associated weights corresponding to 5 the weights they will have in the fully constrained set (i.e. after adding all the subsets; Fig. 7b and d). As expected, the data groups "land" and "ocean", targeted towards carbon cycle responses, do not influence the outcomes for TCR and ECS. The subgroups "heat" (SAT and ocean heat uptake records) and "CO 2 " both constrain TCR and ECS and shift the prior PDF towards the fully constrained PDF when applied alone (Fig. 7a   10 and c). The SAT record tends to constrain TCR and ECS to slightly higher values and the ocean heat uptake data to slightly lower values than the full constraint. When applied sequentially with their corresponding weights in the full constraint, ocean heat uptake represents the strongest constraint, whereas the SAT record changes the prior PDF only slightly (dashed magenta line in Fig. 7b and d). Similarly, adding the group 15 "CO 2 " after the ocean heat uptake data shifts the PDF only slightly (solid magenta vs. cyan line in Fig. 7b and d). This suggests that the CO 2 data does not add substantial information with respect to TCR and ECS that is not already captured by the temperature data. In summary, the subgroup "heat" represents the strongest constraints for TCR and ECS. In particular the ocean heat uptake data is important for constraining 20 these metrics.

Discussion and conclusions
We have quantified the response of multiple Earth system variables as a function of cumulative carbon emissions, the responses to a carbon emission pulse, and two other important climate metrics, the Equilibrium Climate Sensitivity (ECS) and the Transient Introduction 55 different greenhouse gas scenarios and (ii) a diverse and large set of observational data. The observation-constrained probability density functions provide both best estimates and uncertainties ranges for risk analyses. A caveat is that we apply a cost-efficient Earth System Model of Intermediate Complexity with limitations in spatial and temporal model resolution and mechanistic rep-5 resentation of important climate processes. In contrast to box-type or 2-D models applied in earlier probabilistic assessments, the Bern3D-LPX features a dynamic 3dimensional ocean with physically consistent formulations for the transport of heat, carbon, and other biogeochemical tracers and includes a state-of-the-art dynamic global vegetation model, peat carbon, and anthropogenic land use dynamics. 10 The focus is on the relationship between cumulative carbon emissions and individual, illustrative climate targets. The probabilistic, quantitative relationship between a climate variable of choice and cumulative carbon emissions permits one to easily assess the ceiling in cumulative carbon emissions if a specific individual limit is not to be exceeded with a given probability. Two examples, cumulative fossil carbon emissions since prein-15 dustrial must not exceed 640-1030 Gt C (this range indicates the uncertainty from the concurrent non-CO 2 forcing) to meet the Cancun 2 • C target with an 68 % probability by 2100 AD. Cumulative fossil carbon emissions must not exceed 880 Gt C if annualmean, area-averaged Southern Ocean conditions were not to become undersaturated with respect to aragonite with an 68 % probability (Steinacher et al., 2013). 20 Some aspects are not explicitly considered here. First, meeting a set of multiple targets requires lower cumulative carbon emissions than required to meet the most stringent target within the set in probabilistic assessments (Steinacher et al., 2013). Thus, the evaluation of allowable cumulative emissions to meet multiple climate targets requires their joint evaluation. In practical terms, the joint evaluation of the 2 • C target 25 and the Southern Ocean saturation target would yield lower allowable emissions than indicated in the above paragraph. Second, inertia in the socio-economic system limits the rate of carbon emission reduction. In other words, carbon emissions are committed for the future through existing infrastructure. Consequently, climate target may become out of reach when the transition to a decarbonized economy is delayed (Stocker, 2013). The magnitude of the response is in general non-linearly related to cumulative carbon emissions. This may present no fundamental problem. Yet, non-linearity in responses add to the scenario uncertainty and extrapolation beyond the considered sce-5 nario space may not provide reliable results. Non-linear relationships cannot be precisely summarized with one single number. For convenience, we have approximated responses for the investigated variables by linear fits (Tables 2 and 3). A close to linear relationship is found for pH. Consistent with earlier studies, we also find an approximately linear relation between transient surface temperature increase and cumulative 10 carbon emissions of about 1-3 • C (Tt C) −1 over our set of multi-agent scenarios. There are some non-linear temperature responses in strong mitigation scenarios (particularly those with negative emissions).
The response to a pulse-like input of carbon into the atmosphere for atmospheric CO 2 , ocean and land carbon, surface air temperature, and steric sea level rise are Here we provide in addition impulse response functions for surface ocean pH and calcium carbonate saturation states, and soil carbon. A substantial fraction of carbon emitted today will remain airborne for centuries and millennia. The impact of today's carbon emissions on surface air temperature will accrue within about 20 20 years only, but persists for many centuries. Steric sea level rise accrues slowly on multi-decadal to century time scales. Similar as for CO 2 , peak impacts in surface ocean pH and saturation states occur almost immediately after emissions and these changes will persist for centuries and millennia. Thus, the environment and the socio-economic system will experience the impact of our current carbon emissions more or less imme-25 diately and these impacts are irreversible on human time scales.
The recent slow-down in global surface air-temperature warming, termed hiatus, has provoked discussions whether climate models react too sensitive to radiative forcing. Here, the observation-constrained TCR and ECS are quantified to 1.7 and 2.9 • C (en-    Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 2. Transient and peak response per 1000 Gt C total carbon emissions estimated with different methods. Ensemble medians and 66 % ranges are taken from the relative probability maps derived from all model configurations and scenarios at 1000, 2000, and 3000 Gt C total emissions as well as from the linear regression slope (see Methods). The correlation coefficient (r, median and 68 %-range) and the median standard error as percentage of the median regression slope (σ) are given for the linear fit of the peak response.  In (a and c) the PDFs are shown for the ensemble without constraints (prior, black line), for the case when each of the constraint groups "heat" (magenta), "CO 2 " (cyan), "ocean" (blue), and "land" (green) is applied alone with equal weights, and for all constraints (red). The group "heat" is split up further into SAT anomaly (dashed magenta) and ocean heat uptake observations (dotted magenta). In (b and d) the constraints are added sequentially with their corresponding weights in the full constraint in the following order: SAT anomaly (magenta dashed), ocean heat uptake (magenta solid), CO 2 (cyan), ocean (blue), and land (red, corresponding to the full constraint).