Inherent uncertainty disguises attribution of reduced atmospheric CO₂ growth to CO₂ emission reductions for up to a decade

Substantial year-to-year variations in the growth rate of global atmospheric CO₂ concentrations show variations that cannot be explained by land-use changes, fossil fuel emissions or the increase of carbon sink capacities due to increasing atmospheric CO₂ concentrations (Friedlingstein et al 2019, Peters et al 2017). The variations originate instead from the variability of the global carbon cycle in response to climate variability, which is inherent to the physics of the Earth System. For instance, the variations of the tropical land carbon sink is dominated by the El Niño-Southern Oscillation (Jones et al 2001, Zeng et al 2005), and the pronounced Southern Ocean carbon sink is susceptible to changes in atmospheric circulation patterns (Landschützer et al 2015, McKinley et al 2017). Therefore, this internal variability of the global carbon cycle in atmospheric CO₂ may disguise the detection of potential CO₂ emission reductions in atmospheric CO₂ observations. But CO₂ emission reductions are required to achieve the targets of the Paris Agreement (UNFCCC 2015). Here we ask what the probability is that a slowdown in atmospheric CO₂ growth is attributable to a policy change implementing CO₂ emission reductions as the difference between Representative Concentration Pathway (RCP) 4.5 and RCP2.6, in the face of internal climate variability. This question becomes policy-relevant as policy-makers assess the efficacy of CO₂ emission reductions in the Global Stocktake every 5 years (Peters et al 2017, Schwartzman and Keeling 2020). Furthermore, we ask after how many years this policy change will cause atmospheric CO₂ growth rates to slow down for certain.

The challenge of emissions reductions verification in atmospheric CO₂ concentrations was first outlined by Peters et al (2017). We address this challenge by using a large ensemble of Earth System Model (ESM) simulations (Maher et al 2019). We integrate 100 simulations based on the code of a single ESM with slightly perturbed initial conditions that serve as different realizations of the Earth System. Our analysis compares RCP4.5, which is close to the pledged and current policies until 2035 (Rogelj et al 2016, Hausfather and Peters 2020), with an emission reductions scenario compatible with the Paris targets under RCP2.6 (figure S4 (https://stacks.iop.org/ERL/15/114058/mmedia)). We attribute a reduction of trend in atmospheric CO₂ concentrations to CO₂ emission reductions in the comprehensive causation framework of Pearl (2000) and Hannart et al (2016). In the context of CO₂ emission reductions, necessary causation means that a factual trend reduction would not have occurred without a policy change. By contrast, sufficient causation implies that while a policy change may trigger a trend reduction, this trend reduction is not certain.

We go beyond approaches in previous studies (Tebaldi and Friedlingstein 2013, Peters et al 2017, Marotzke 2019, Samset et al 2020, Schwartzman and Keeling 2020) by comprehensively diagnosing atmospheric CO₂ variability in an ESM, which is compatible with the terrestrial and oceanic carbon sinks variations. The recently formalized emissions reductions verification of Schwartzman and Keeling (2020) uses an autoregressive model based on the observed carbon imbalance and a different statistical framework. While Tebaldi and Friedlingstein (2013) only focus on causation in a necessary causation sense, we here complete the probabilistic setting by asking also about sufficient causation. We compare two RCP scenarios in a single-model framework; formally only internal variability may undermine the detectability of CO₂ emission reductions. Assessing the contribution of our quantitative results against structural model uncertainty and imperfections is left for future study.

From a policy-maker's perspective looking into the near-term future, necessary and sufficient causation of CO₂ emission reductions slowing down atmospheric CO₂ trends deal with two different questions (Pearl 2000, Hannart et al 2016):

• 1.  
  Will a policy change towards CO₂ emission reductions suffice to slow down atmospheric CO₂ growth? Other factors, such as a weakening uptake by the natural carbon sinks, may induce an increase in atmospheric CO₂ growth despite policy measures. From the viewpoint of a pathway without CO₂ emission reductions, the uncertainty in this question is based on sufficient causation.
• 2.  
  Would a factual atmospheric CO₂ growth slowdown have occurred even without the policy change? This question asks whether the policy change was necessary to achieve the policy goal. From the viewpoint of a factual pathway of CO₂ emission reductions and a factual slowdown, the uncertainty in this question is based on necessary causation.

Based on this causation framework, we obtain probabilities that a policy change causes atmospheric CO₂ trends to decline. However, this causation may be far from certain depending on the time-scale assessed. Should CO₂ emission reductions not soon lead to reduced atmospheric CO₂ growth trends, we might face a debate analogous to the warming hiatus debate (Lewandowsky et al 2015, Fyfe et al 2016) about why CO₂ rises faster despite falling emissions. Therefore, scientists need to communicate the role of internal variability to policy-makers and the public (Deser et al 2012).

Marotzke (2019) shows the uncertain effect of emission reductions on global mean surface temperature (GMST) 15-year trends. As atmospheric CO₂ drives the forced GMST signal, the emissions reduction signal should become detectable earlier in atmospheric CO₂. Analyzing the effect of individual climate forcers,  Samset et al (2020) confirms that anthropogenic CO₂ has the highest potential for emission reduction detection.

In our study, we also ask after how many years internal variability can still obscure the identification of CO₂ emission reductions in atmospheric CO₂. In other words, how long does it take until certainty arises in causation? This is a distinctly different question than the classical time-of-emergence of anthropogenic signals, which asks on which timescales the climate change signal emerges from natural variability (McKinley et al 2016). Here, we ask on which time-scales a forcing change induced by this policy change causes a climate response considering sufficient and necessary causation (Marotzke 2019). These time-scales of CO₂ emission reduction detection might be longer than the periodicity of the Global Stocktake in which policy-makers will assess the efficiency of mitigation measures.

2.1. Causation attribution framework

2.2. Choice of scenarios

2.3. Large-ensemble simulations

2.4. Diagnostic atmospheric CO₂ concentration

CO₂ concentration-driven simulations do not represent a variable atmospheric CO₂ concentration tracer. To quantify the expected variations in global atmospheric CO₂ concentration that are compatible with variations of the global land and ocean carbon sinks, we diagnose a virtual tracer of global atmospheric CO₂ based on the changes due to internal variability of the land and ocean carbon sinks in atmospheric CO₂ [figure S2]. The global residual CO₂ flux G_i,s is the difference of CO₂ flux F_i,s of the each ensemble member i to the ensemble mean of CO₂ flux F_s:

$$\begin{equation} G_{i,s} = \sum_{\textrm{global}} (F_{i,s} - \frac{1}{M}\sum_{m = 1}^M F_{m,s}) \\ \end{equation} \tag{ 4 }$$

where M = 100 is the number of ensemble members and i the number of a single ensemble member and s the scenario. The ensemble mean F_s is subject to all forcings (anthropogenic fossil-fuel CO₂ emissions, non-CO₂ emissions, land-use change, aerosols) on CO₂ flux, but no internal variability. The remaining residual shows the variations of CO₂ flux around neutral flux only due to internal variability. The forced atmospheric CO₂ signal f_s is scenario s-dependent and generated by a simplified climate model fed with emissions from integrated assessment models (Meinshausen et al 2011) incorporating the strengthening of the carbon sinks with higher CO₂ concentrations and land-use CO₂ emissions. This internal variability component of time-accumulated global CO₂ flux is then superimposed on the smooth atmospheric CO₂ forcing f_s and defines internally varying diagnostic global atmospheric CO₂ concentration XCO_2,i,s:

$$\begin{equation} X\textrm{CO}_{2,i,s}(t) = \sum_{t^{^{\prime}}}^t G_{i,s}(t^{^{\prime}}) \cdot \frac{\textrm{ppm}}{2.124 \textrm{PgC}} + f_s. \\ \end{equation} \tag{ 5 }$$

We assume that the internal variability of the global carbon cycle to be driven by climate variability. This ignores the short-term effects of atmospheric CO₂ variability on CO₂ flux as in all concentration-driven simulations. Explicitly, for diagnostic atmospheric CO₂, we use as forcing f_s the concentration scenarios generated by the simplified climate model and not directly the CO₂ emissions generated by the integrated assessment models. This assumes that the emission scenarios from the integrated assessment model roughly match the resulting concentration scenarios from the simplified climate model (figure S9). The hereby diagnosed variations of global atmospheric CO₂ capture the observed global atmospheric CO₂ variations (figures 1, S7; Spring and Ilyina (2020)). For a detailed method description and verification in emission-driven simulations, see Supplementary Information section S1.

Zoom In Zoom Out Reset image size

2.5. Method limitations

We first assess the frequency distributions of five-year trends in atmospheric CO₂. These distributions over the period 2016-2020 in RCP2.6 and RCP4.5 are nearly indistinguishable (figures 1, 2(a) and (d)). The most recent 2015–2019 observations-based estimate for global atmospheric CO₂ (Dlugokencky and Tans 2019) trend is in the upper tercile and thereby captured by our model (figures 2(a) and (d), S7). Comparing the distributions before and after CO₂ emission reductions onset in 2020 in RCP2.6, we find overlapping distributions with a tendency towards lower trends after CO₂ emission reductions (figures 2(a) and (b)). The ensemble mean responds to CO₂ emission reductions with a decrease in trend of 1 ppm over 5 years. The trend reduces in 70 ensemble members, resulting in $P_{\textrm{RCP}2.6}$ = 70% (figure 2(c)). This implies that with a 30% probability, atmospheric CO₂ growth will strengthen despite emissions reductions. In RCP4.5, the distributions of atmospheric CO₂ trends before and after 2020 look similar because the emissions rise steadily. Hence, only roughly half of the ensemble members show a reduced trend, with $P_{\textrm{RCP}4.5}$ = 48% (figure 2(d)–(f)).

Zoom In Zoom Out Reset image size

The atmospheric CO₂ may increase more strongly despite the onset of CO₂ emission reductions, when the global carbon cycle triggered by internal climate variability releases more CO₂ than CO₂ emission reductions save. For instance, this is possible when the tropical forests react to higher temperature and less precipitation caused by a strong El Niño event (Jones et al 2001, Zeng et al 2005). The released CO₂ from the tropical biosphere persists in the atmosphere and can overwhelm the reduction of anthropogenic emissions (figure 1). These stronger atmospheric CO₂ growth trends despite CO₂ emission reductions might occur for trend comparisons around the CO₂ emission reductions start of up to ten years (figure 3).

Zoom In Zoom Out Reset image size

These probabilities of trend reduction of the two scenarios can be converted into probabilities of trend reduction being caused by CO₂ emission reductions (see section 2.1). If asked in advance in 2015, the answer would be that a policy change from RCP4.5 to RCP2.6 representing CO₂ emission reductions starting in 2020 are sufficient to cause a five-year trend reduction in atmospheric CO₂ growth by P_S = 42% (figure 3). Here, this policy change works toward a trend reduction, but the trend reduction might also be prevented by internal variability. Asking from a 2025 perspective looking into the recent past, CO₂ emission reductions in 2020 were necessary by P_N = 31% to cause trend reductions (figure 3). This policy change causes the five-year trend reduction in a necessary and sufficient sense by P_NS = 22% (figure 3, dark blue in box). These results show that CO₂ emission reductions are far from certain to cause trend reductions in global atmospheric CO₂ growth when considering five-year trends.

To estimate the time-scales when CO₂ emission reductions are virtually certain to cause reduced atmospheric CO₂ growth trends, we consider trends calculated over different time window lengths around the CO₂ emission reductions start. As expected, the shorter the trend-lengths considered, the more dominant internal variability is. Therefore, trend reductions are less likely occurring in the CO₂ emission reductions scenario. The 3-year-trend probabilities of trend reduction even overlap with the 50% random forecast (figure 3). Conversely, when longer trends are considered, the influence of the signal of emissions change becomes stronger. CO₂ emission reductions reduce atmospheric CO₂ trends in RCP2.6 virtually for certain only when considering ten-year-trends (figure 3). In contrast, trend reductions are still possible due to internal variability despite the absence of CO₂ emission reductions for much longer in RCP4.5 (figure 3). Note that under RCP4.5 the annual anthropogenic CO₂ emissions increase very little until the 2040 s. Therefore, a few members can still have reduced trends over time. Consequently, $P_{\textrm{RCP}4.5}$ does not drop to 1% until 2042.

The low causation probabilities over short time-scales show the inability to clearly attribute reduced atmospheric CO₂ trends to a policy change from RCP4.5 to RCP2.6 due to the large internal variability. The longer the time-scales considered, the stronger the two scenario pathways differ, and the attribution probabilities rise. If $P_{\textrm{RCP}2.6} \gt P_{\textrm{RCP}4.5}$ as assumed by the response to CO₂ emission reductions, P_S increases more quickly than P_N when $P_{\textrm{RCP}2.6}$ approaches 1 faster than $P_{\textrm{RCP}4.5}$ 0. Therefore, in the context of the scenarios RCP2.6 and RCP4.5, $P_S \gt P_N$ (Marotzke 2019). This means that in our context, sufficient causation is a stronger causation facet than necessary causation. Sufficient causation P_S describes whether the objective of reduced atmospheric CO₂ trends is met, which might be prevented by internal variability. As soon as growth trends decline in all realizations (P_RCP2.6 = 1), also P_S saturates. In contrast, necessary causation P_N describes whether the response of reducing atmospheric CO₂ would only have happened in the presence of CO₂ emission reductions. Therefore, as long as trend reductions are possible even without CO₂ emission reductions, necessary causation will not be certain, that is, if $P_{\textrm{RCP}4.5} \gt 0$, then $P_N \lt 1$.

The time to detection of CO₂ emission reductions D_{S,N} describes after how many years this policy change is virtually certain to cause atmospheric CO₂ growth trends to decline. CO₂ emission reductions sufficiently cause trend reductions after D_S = 10 years and necessary cause of reduction after D_N = 27 years. We note that once sufficient causation is certain, P_S = 1 in 2030 see (1), necessary causation and causation both necessary and sufficient coincide, $P_N = P_{NS}$; compare (2) and (3) with $P_{\textrm{RCP}2.6} = 1$. Virtual certainty in P_{N,NS} is hindered by $P_{\textrm{RCP}4.5}$ above 1%. Due to the slow increase in emissions in the 2030 s, internal variability allows a few members to have increasing trends. Taking a less strict threshold of 95% certainty like in Tebaldi and Friedlingstein (2013), we obtain D_N = D_NS = 16 years. This time-scale of CO₂ emission reductions detection in a necessary causation sense D_N is a bit longer than the similarly defined estimate based on IPSL-CM5A-LR (Tebaldi and Friedlingstein 2013, table 1). Our analysis also shows that whether this policy change from RCP4.5 to RCP2.6 can be identified as the cause of reduced atmospheric CO₂ trends after 10 or 16 years depends on the causation attribute. The differently defined emission reduction detection protocol of Schwartzman and Keeling (2020) finds a similar detection delay of 9 ± 4 years for comparable 2% net annual emissions reduction.

In the context of potential future CO₂ emission reductions, we ask whether atmospheric CO₂ growth trend reductions in the near term can be attributed to a policy change. We focus on one specific pathway of CO₂ emission reductions interpreted as a policy change from scenario RCP4.5 without near-term CO₂ emission reductions to emissions reduction scenario RCP2.6 designed to achieve for the Paris targets representing 3% net annual CO₂ emission reductions until 2030. We apply a causation framework comprising two perspectives of policy elaboration (Hannart et al 2016, Marotzke 2019). We diagnose atmospheric CO₂ variations compatible with the natural carbon sinks variations and compare growth trends of atmospheric CO₂ before and after the onset of CO₂ emission reductions in 2020 in RCP2.6. While 5-year trends reduce in 70% of all realizations in the CO₂ emission reductions scenario RCP2.6 (consequentially implying increasing trends despite of CO₂ emission reductions by 30%), there is 48% probability of trend reductions in RCP4.5. This translates into CO₂ emission reductions from RCP4.5 to RCP2.6 being sufficient to cause a five-year trend reduction beforehand by 42% and in hindsight necessary by 31%. The probability that this policy change is both necessary and will suffice to bring the desired outcome considering five-year trends is only 22%. These probabilities are far from certain for up to a decade. It takes ten or 16 years of CO₂ emission reductions from RCP4.5 to RCP2.6 to virtually certainty cause a trend reduction in a sufficient or necessary causation sense, respectively. Communicating these probabilities in a clear manner is challenging but needed to inform policy-makers about the impact of internal variability on CO₂ emission reduction causation in the Earth system (Deser et al 2012, Hannart et al 2016, Howe et al 2019).

The five-year Global Stocktake following the Paris Agreement (UNFCCC 2015) makes the five-year internal variability highlighted in this study especially relevant for policy-makers. This study demonstrates the inherent uncertainty in near-term atmospheric CO₂ projections. As a partial solution to this challenge, initialized ESM-based prediction systems can reduce this uncertainty by predicting natural variations of the global carbon cycle. Global oceanic CO₂ flux is predictable for two to three years (Li et al 2019, Lovenduski et al 2019) and global atmospheric CO₂ variations have the potential to be predicted for up to three years in advance (Spring and Ilyina 2020). These multi-year ESM-based predictions of the global carbon cycle thereby bring added value about the expected natural variations of atmospheric CO₂ to policy-makers in the Global Stocktake process (UNFCCC 2015).

Our analysis shows that it is crucial to have realistic expectations of the efficacy of climate policy in the near term (Marotzke 2019, Samset et al 2020). Also Schwartzman and Keeling (2020) find a detection delay of up to a decade in a different approach. Even if anthropogenic emissions begin to decline after 2020, there still remains a substantial probability that atmospheric CO₂ trends will not have declined five years afterwards. In this case, the effects of CO₂ emission reductions on other iconic climate variables, such as global mean surface temperature, very likely get delayed even longer (Marotzke 2019). The likelihood of this happening is substantial. For instance, there is a three-out-of-ten chance that atmospheric CO₂ rises even stronger in the five years after CO₂ emission reductions started compared to before. Assuming the evolution of the RCPs (Meinshausen et al 2011) and the magnitude of internal variability in the global CO₂ fluxes in MPI-ESM-LR, such increasing atmospheric CO₂ growth trends despite CO₂ emission reductions from RCP4.5 to RCP2.6 are possible for up to a decade. Although this analysis relies on only a single model, internal variability may disguise CO₂ emission reductions efforts in the Earth System for a couple of years. Should this be the case, climate science should explain the observed atmospheric CO₂ evolution honoring internal variability. Policy makers should rather be informed by initialized predictions about the internal variability in the near-term evolution of atmospheric CO₂ (Betts et al 2018, Spring and Ilyina 2020). Evaluation of CO₂ emission reduction efficacy from an atmospheric CO₂ perspective needs to take internal variability, and therefore longer than 5-year trends, into account.

We acknowledge Luis Kornblueh, Jürgen Kröger and Michael Botzet for producing the historical, RCP2.6 and RCP4.5 MPI-ESM Grand Ensemble simulations, and the Swiss National Computing Centre (CSCS) and the German Climate Computing Center (DKRZ) for providing the necessary computational resources. Scripts used in the analysis and other supporting information that may be useful in reproducing the authors work are archived by the Max Planck Institute for Meteorology: http://hdl.handle.net/21.11116/0000-0005-467C-2. We acknowledge funding from European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 821003 'Climate-Carbon Interactions in the Coming Century CCiCC (4C2020)' and No. 641816 (CRESCENDO). T. I. received funding from the Federal Ministry of Education and Research in Germany (BMBF) through the research programme 'MiKlipII' (FKZ: 01LP1517B). J. M. acknowledges long-term support by the Max Planck Society for the Advancement of Science. We thank Alexander Winkler for internal review and the three anonymous reviewers for improving the manuscript with their comments.