Net biome productivity (NBP) dominates the observed large variation of atmospheric CO annual increase over the last five decades. However, the dominant regions controlling inter-annual to multi-decadal variability of global NBP are still controversial (semi-arid regions vs. temperate or tropical forests). By developing a theory for partitioning the variance of NBP into the contributions of net primary production (NPP) and heterotrophic respiration (R ) at different timescales, and using both observation-based atmospheric CO inversion product and the outputs of 10 process-based terrestrial ecosystem models forced by 110-year observational climate, we tried to reconcile the controversy by showing that semi-arid lands dominate the variability of global NBP at inter-annual (<10 years) and tropical forests dominate at multi-decadal scales (>30 years). Results further indicate that global NBP variability is dominated by the NPP component at inter-annual timescales, and is progressively controlled by R with increasing timescale. Multi-decadal NBP variations of tropical rainforests are modulated by the Pacific Decadal Oscillation (PDO) through its significant influences on both temperature and precipitation. This study calls for long-term observations for the decadal or longer fluctuations in carbon fluxes to gain insights on the future evolution of global NBP, particularly in the tropical forests that dominate the decadal variability of land carbon uptake and are more effective for climate mitigation.

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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.