| Summary: | The relation between CO<sub>2</sub> emissions and atmospheric CO<sub>2</sub> concentration has traditionally been treated with more or less complex models with several boxes. Our approach is motivated by the question of how much CO<sub>2</sub> must necessarily be absorbed by sinks. This is determined by accepted measurements and the global carbon budget. Observations lead to the model assumption that carbon sinks, similar to oceans or the biosphere, are linearly dependent on CO<sub>2</sub> concentration on a decadal scale. In particular, this implies the falsifiable hypothesis that oceanic and biological CO<sub>2</sub> buffers have not significantly changed in the past 70 years and are not saturated in the foreseeable future. A statistical model with two parameters is built from the global carbon budget and two testable assumptions. This model explains the relation between CO<sub>2</sub> emission and historical CO<sub>2</sub> concentration data very well. The model gives estimates of the natural emissions, the pre-industrial CO<sub>2</sub> equilibrium concentration levels, the half-life time of an emission pulse, and the future CO<sub>2</sub> concentration level from a given emission scenario. It is validated by an ex-post forecast of the last 20 years. The important result is that, with the stated polices emission scenario of the International Energy Agency (IEA), the future CO<sub>2</sub> concentrations will not rise above 475 ppm. The model is compared with the carbon module of the Bern model, mapping their complex impulse response functions (IRFs) to a single time variant absorption parameter.
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