Asymptotic analysis of airborne fraction used to validate global carbon models

Airborne fraction, defined as the ratio of change in atmospheric CO 2 concentration to input of CO 2 over a specified time period, is explored as an index for validating linear models of the global carbon cycle. Results presented assume a constant value for airborne fraction, which is supported by evidence that measured atmospheric carbon dioxide levels are linearly correlated with inputs due to fossil fuel combustion. Several formulas for calculating airborne fraction are shown to be equivalent when constant values are assumed. For a general linear state variable model, an asymptotic value for airborne fraction is computed in terms of model structure and fossil fuel input rate. The validation scheme proposed compares a model-computed (asymptotic) airborne fraction with an observed value. The scheme is tested using an independently calibrated ocean/atmosphere sub-model. This is followed by a test of a global carbon cycle model composed of the previously tested ocean/atmosphere sub-model linked with a model for the terrestrial biota. These tests produce a range of valid model parameters that are similar to those obtained from independent observations.