A small climate-amplifying effect of climate-carbon cycle feedback

The climate-carbon cycle feedback is one of the most important climate-amplifying feedbacks of the Earth system, and is quantified as a function of carbon-concentration feedback parameter (β) and carbon-climate feedback parameter (γ). However, the global climate-amplifying effect from this feedback loop (determined by the gain factor, g) has not been quantified from observations. Here we apply a Fourier analysis-based carbon cycle feedback framework to the reconstructed records from 1850 to 2017 and 1000 to 1850 to estimate β and γ. We show that the β-feedback varies by less than 10% with an average of 3.22 ± 0.32 GtC ppm^-1 for 1880-2017, whereas the γ-feedback increases from -33 ± 14 GtC K^-1 on a decadal scale to -122 ± 60 GtC K^-1 on a centennial scale for 1000-1850. Feedback analysis further reveals that the current amplification effect from the carbon cycle feedback is small (g is 0.01 ± 0.05), which is much lower than the estimates by the advanced Earth system models (g is 0.09 ± 0.04 for the historical period and is 0.15 ± 0.08 for the RCP8.5 scenario), implying that the future allowable CO₂ emissions could be 9 ± 7% more. Therefore, our findings provide new insights about the strength of climate-carbon cycle feedback and about observational constraints on models for projecting future climate.