EVALUATION OF CARBON DIOXIDE MANAGEMENT OPTIONS: MODEL INTEGRATION OF HUMAN ACTIONS AND THE NATURAL CARBON CYCLE

Future atmospheric carbon dioxide concentrations will depend on the time-dependence of anthropogenic emissions, deliberate carbon sequestration, and the dynamic response of the global carbon cycle. The dynamic carbon-cycle response to atmospheric injection of carbon dioxide emissions can be summarized mathematically by impulse response functions derived from calibrated models of the global carbon cycle. Such functions represent the carbon-cycle uptake of injected emissions of carbon dioxide, and are often used in metrics for the effects of greenhouse gas emissions over time (e.g., the Global Warming Potential). In the same way that injection of carbon dioxide emissions into the atmosphere causes a natural carbon-cycle uptake response, the withdrawal of carbon dioxide from the atmosphere is expected to cause a natural carbon-cycle source response. This is due to the same dynamic features (primarily, the response of terrestrial biosphere-ocean-atmosphere carbon dioxide exchange) that cause the natural carbon-cycle uptake response to carbon dioxide injection. Like the natural uptake response, the natural source response can be summarized mathematically by impulse response functions derived from models of the global carbon cycle.

The effects of continuous atmospheric carbon dioxide injection or withdrawal can be thought of as a concatenation of impulse responses, where the impulse functions vary at each point in time depending on the magnitude of the injection or withdrawal, and the response at each point in time is the sum of all the responses to the impulses up to and including that time. Mathematically, this concatenation can be expressed in the form of convolution integrals. This approach has been widely applied to calculate simple but reasonable time-dependent atmospheric carbon dioxide response to emissions trajectories. However, it has not been applied to the atmospheric carbon dioxide response to withdrawals such as deliberate carbon sequestration.

The natural carbon-cycle response to deliberate carbon sequestration is important and can be quantified using convolution integrals based on modeled impulse response functions. Over time, the natural carbon-cycle source response significantly offsets the sequestration. The time scale of important natural response ranges from decades to millennia. We explore the use of convolution integrals to define metrics that can be used to compare the effective time-dependent carbon dioxide withdrawal for various carbon management activities, including reduction of emissions and deliberate carbon sequestration.