This simple terrestrial ecosystem model shows that we can produce a carbon sink only when carbon source terms are larger than the carbon loss terms. For example, there can be a sink in vegetation carbon if net primary productivity exceeds the loss of carbon (turnover and disturbances). Also, a sink can be produced if the inputs of litter or soil carbon are larger than the losses of carbon through microbial respiration.

In order for the sink to continue increasing over time and continue removing a sizable fraction of increasing CO2 emissions in the future, the second-derivative of the carbon stocks must also be positive:

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