Reservoir timescales for anthropogenic CO2 in the atmosphere

Non-steady state timescales are complicated and their application to specific geophysical systems requires a common theoretical foundation. We first extend reservoir theory by quantifying the difference between turnover time and transit time (or residence time) for time-dependent systems under any mixing conditions. We explicitly demonstrate the errors which result from assuming these timescales are equal, which is only true at steady state. We also derive a new response function which allows the calculation of age distributions and timescales for well-mixed reservoirs away from steady state, and differentiate between timescales based on gross and net fluxes. These theoretical results are particularly important to tracer-calibrated "box models" currently used to study the carbon cycle, which usually approximate reservoirs as well-mixed. We then apply the results to the important case of anthropogenic CO2 in the atmosphere, since timescales describing its behavior are commonly used but ambiguously defined. All relevant timescales, including lifetime, transit time, and adjustment time, are precisely defined and calculated from data and models. Apparent discrepancies between the current, empirically determined turnover time of 30-60 years and longer model-derived estimates of expected lifetime and adjustment time are explained within this theoretical framework. We also discuss the results in light of policy issues related to global warming, in particular since any comparisons of the "lifetimes" of different greenhouse gases (CO2, CH4, N2O, CFC's etc.) must use a consistent definition to be meaningful.