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CO2 exchanges between the global atmosphere and the other carbon reservoirs happen at many different spatial and temporal scales. It is unfortunately impossible to measure them everywhere and all the time.
Therefore we are left with the only possibility to deduce them from a combination of different pieces of information. First, it is clear that the atmospheric CO2 content depends directly on these exchanges. Second, scientists have developed models and inventories to simulate the carbon exchanges. By plugging these so-called emission models and inventories into an atmospheric model, one can check if the model-simulated atmospheric CO2 account is balanced and agrees with the observations.