Accurate knowledge of the dependence of anthropogenic atmospheric CO2, the excess over preindustrial, on future emissions is essential to developing approaches to limit climate change. At present, the lifetime of excess CO2, as represented in current carbon cycle models, is uncertain by more than an order of magnitude, 70 to more than 700 years (Schwartz, JGR, 2018). Consequently observation-based top-down analysis provides an important alternative approach. The turnover time of excess CO2 (ratio of stock in the atmosphere and the mixed-layer ocean, which are in near equilibrium, to the net leaving flux into the terrestrial biosphere and deep ocean) is determined as 54 ± 10 years. A simple model for excess CO2, consisting of four compartments with three observationally determined global-mean parameters (deposition velocity of CO2 to the surface ocean, piston velocity describing the rate of exchange of water between the mixed-layer and deep ocean, and the transfer coefficient of CO2 kat from the atmosphere a to the terrestrial biosphere t), and one uncertain adjustable parameter kta, accurately reproduces CO2 mixing ratio over the Anthropocene. This model yields the adjustment time (inverse of fractional removal rate in the absence of emissions) as 65 ± 10 years over the first 100 years, depending on kta, over which time excess CO2 would decrease by 65 to 81%, depending on kta, Figure 1. The reduction of global emissions required to stabilize atmospheric CO2 over this time scale is 50 to 60%.
The lifetime of excess atmospheric CO2 (above preindustrial) xCO2 governs the future consequences of present xCO2 and those of future CO2 emissions. Recent assessments of the decrease of xCO2 following abrupt cessation of anthropogenic emissions (zero emissions commitment, ZEC) inferred from studies with carbon-cycle (CC) models (e.g., Joos et al., ACP, 2013; MacDougall et al., BG, 2020) vary substantially, with the fraction of xCO2 remaining in the atmosphere 100 years after cessation, fCO2(100) = xCO2(100)/xCO2(0), ranging from 0.55 to 0.85 (Figure 1a; Schwartz, JGR, 2018; Schwartz, in review). In this study prior atmospheric and oceanic CO2 and future xCO2 for ZEC were calculated with a 5-compartment global model. Model compartments are the atmosphere, upper and deep ocean, and labile and obdurate terrestrial biosphere (TB). Model parameters are obtained mainly from observation (e.g., rate of uptake of heat by the deep ocean) and theory (e.g., CO2-dependent solubility of CO2 in seawater); uptake of CO2 by the two TB compartments is apportioned by parameterization, with parameters rather narrowly constrained by observations of CO2 and radiocarbon. CO2 is found to decay much more rapidly than in CC models; fCO2(100) = 0.41 ± 0.8 (1 σ), Figure 1a. These results indicate that cessation of anthropogenic CO2 emissions would result in discernible decrease in atmospheric CO2 on a time scale as short as a human lifetime, much faster than in current CC models. Shown in Figure 1b is a quantity denoted τE(t), the equivalent 1/e lifetime of xCO2, as a function of time subsequent to cessation of emissions t, evaluated as τE(t) = -1/ln fCO2(t). τE(t) is a generalization of the relation between half-life of a decaying quantity and its 1/e lifetime and is an integral measure of decay over time t. The present model yields τE(t) of excess atmospheric CO2 about 100 years, much shorter than obtained with current CC models. Figure 1. a, Fractional excess CO2 fCO2(t) as function of time t following abrupt cessation of anthropogenic CO2 emissions as calculated in a recent model intercomparison (MacDougall et al., 2020) and with present model (best estimate, thick red, and uncertainty range); dotted black lines denote exponential decay with lifetime indicated at right. b, Equivalent 1/e lifetimes as function of t.
Earth’s transient climate sensitivity Str is the rapid change, plateauing at ~5 yr, in global mean surface temperature GMST per change in forcing (e.g., Held et al., JGR, 2010). Str is readily evaluated from time series of total forcing F and temperature anomaly ΔT as the slope of a regression of ΔT vs F, with ΔT from model or observations and F generally modeled based on change in atmospheric composition. Prior estimates of Str have varied quite widely, mainly because of uncertainty in aerosol forcing. F is evaluated as total non-aerosol forcing, dominated by positive GHG forcing, plus negative aerosol forcing; large magnitude aerosol forcing results in small F and in turn high Str, and vice versa. Forcing time series derived from the Fifth IPCC Assessment Report (AR5, 2013) resulted in best estimate Str 0.35 K (W m-2)-1; 5% to 95% uncertainty range 0. 27 to 0.55 (Schwartz, JGR, 2018). New time series of total forcing from the (2021) Sixth IPCC Assessment report (AR6) permit similar evaluation of Str, Figure 1, as 0.46 (0.36 to 0.50) K (W m-2)-1. The increase in best-estimate Str is due to increased magnitude of best-estimate aerosol forcing in AR6 vs. AR5. Poor long-term correlation of forcing time series and observed ΔT for the 5% forcing estimate (large negative aerosol forcing added to GHG forcing, yielding low total forcing) suggests that that the corresponding bound on aerosol forcing magnitude may be an over-estimate, with the correlation substantially improved for best estimate and even more so for lowest estimate of aerosol forcing magnitude, thus more consistent with lower values of Str. A somewhat higher range of Str, 0.42 to 0.75 K (W m-2)-1, is obtained using time series of forcings obtained with individual models (Smith et al., ACP, 2020). Figure 1. Time series of total forcing F and as convolved with 5-year decaying exponential Fc (left); correlations of observed temperature anomaly ΔT (GISS) vs Fc (center); slope denotes transient sensitivity Str; and time series of ΔT (right; left axis) and Fc (right axis, scaled to ΔT by Str). Top row, lower 5% bound on forcing time series; middle row, best estimate forcing; bottom row, 95% bound. Forcing data from draft AR6 report, expected release August 9, 2021, potentially subject to change.

Nicolas Bellouin

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