The lifetime of excess atmospheric carbon dioxide

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Abstract
We explore the effects of a changing terrestrial biosphere on the atmospheric residence time of CO2 using three simple ocean carbon cycle models and a model of global terrestrial carbon cycling. We find differences in model behavior associated with the assumption of an active terrestrial biosphere (forest regrowth) and significant differences if we assume a donor‐dependent flux from the atmosphere to the terrestrial component (e.g., a hypothetical terrestrial fertilization flux). To avoid numerical difficulties associated with treating the atmospheric CO2 decay (relaxation) curve as being well approximated by a weighted sum of exponential functions, we define the single half‐life as the time it takes for a model atmosphere to relax from its present‐day value half way to its equilibrium pCO2 value. This scenario‐based approach also avoids the use of unit pulse (Dirac Delta) functions which can prove troublesome or unrealistic in the context of a terrestrial fertilization assumption. We also discuss some of the numerical problems associated with a conventional lifetime calculation which is based on an exponential model. We connect our analysis of the residence time of CO2 and the concept of single half‐life to the residence time calculations which are based on using weighted sums of exponentials. We note that the single half‐life concept focuses upon the early decline of CO2 under a cutoff/decay scenario. If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half‐life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years. If we assume only regrowth, then the average value for the single half‐life for excess CO2 increases to 72 years, and if we remove the terrestrial component completely, then it increases further to 92 years.