Estimating Remaining Carbon Budgets Using Emulators of CMIP6 Models


 A remaining carbon budget (RCB) estimates how much CO2 we can emit and still reach a specific temperature target. The RCB concept is attractive since it easily communicates to the public and policymakers, but RCBs are also subject to uncertainties. The expected warming levels for a given carbon budget has a wide uncertainty range, which we show here to increase with less ambitious targets, i.e., with higher CO2 emissions and temperatures. We demonstrate that the leading cause of the revealed RCB uncertainty is the spread in the equilibrium climate sensitivity (ECS) among climate models. In the Coupled Model Intercomparison Project Phase 6 (CMIP6) ensemble, the models with the lower ECS predict an RCB that is twice as high as that of models with the higher ECS, for temperature targets between 1.5-3.0°C.

anthropogenic forcing may deviate from the historical estimates. In this case, it is necessary to 102 make assumptions regarding the time evolution of this ratio. The method applied in this paper is to 103 analyze scenarios constructed using integrated assessment models (IAMs) 5 (Fig. 1a). Hence, here 104 the total CO 2 and methane emissions are known, and we make assumptions only on the evolution 105 of aerosol emissions as greenhouse gas emissions are reduced to zero. 106 From the emission scenarios, we can obtain corresponding temperatures from an Earth model in RCBs, one should ideally explore an ensemble of realistic mitigation scenarios using the full 110 set of ESMs in the CMIP6 ensemble, which is not feasible due to the computational costs. In 111 this study, we construct emulators of ESMs in the CMIP6 ensemble based on 4×CO 2 -runs of the 112 models. We use impulse-response models to approximate how the atmospheric CO 2 concentrations 113 depend on greenhouse gas emissions. From the emulators, we can analyze the relationship between 114 cumulative emissions and peak temperatures, and estimate TRCE and RCBs. Our simple modeling 115 set-up is described in the Methods section.

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Our ESM emulators show that the linear relationship between total emissions and maximum 118 GMST is an excellent approximation for each climate model, but that the TCRE varies consid-119 erably over the model ensemble (Fig. 2a). Using the carbon impulse response fitted to the multi-  The Amazon rainforest also provides an example of how anthropogenic forcing other than 172 greenhouse gas release can affect the climate system: Modelling evidence suggests that only par-173 tial deforestation of the Amazon rainforest might -through intricate couplings between evapo-174 transpiration, condensational latent heating, and the South American low-level circulation system 175 -lead to a collapse of the South American monsoon system and thus, ultimately, of the Amazon 176 rainforest 18 .

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As a third example, the ice-albedo feedback implies rising temperatures, e.g., in the Arctic, 178 leading to accelerating sea ice retreat, lowering albedo, and effectively increasing mean surface 179 temperatures regionally. This positive feedback contributes to the so-called Arctic amplification, 180 i.e., the observation that Arctic temperatures have been rising much faster than the global average.

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The uncertainty introduced by these kinds of positive feedbacks is -due to their nonlinearity 182 -also likely to increase with higher temperature targets. In the Arctic, for example, where the 183 sensitivity of temperature to global emissions is stronger than globally, the uncertainty in TCRE 184 translates to even more considerable uncertainty in the amount of greenhouse gas emissions we can  Supplementary Fig. 2). These box models work as emulators of the ESMs for GSMT. 203 We model the concentrations of CO 2 and methane as linear responses of scenario data for 204 emissions, E CO 2 (t) and E CH 4 (s): where F 2×CO 2 is the forcing associated with a CO 2 -doubling. This number is model-dependent and 229 obtained from the Gregory plots for the abrupt 4×CO 2 experiments in the CMIP6 ensemble 23 . The 230 radiative forcing associated with atmospheric methane is modelled as where µ = 1 ppm and p = 0.036 W/m 2 describes the potential of methane as a greenhouse gas.

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Aerosol forcing is assumed to be negative with magnitude proportional to CO 2 emissions but as-

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sumed not to go below −0.4 W/m 2 as emissions are reduced: