The airborne fraction is calculated by dividing CO2 emissions by the change in atmospheric CO2 concentration. This fraction averaged 0.43 from 1980-2004 and 0.46 from 1995-2004. See Data Sources (emissions) and Data Source (ppm). The future projections of CO2 concentrations in Gas-CAP assume an airborne fraction of 0.46.
Note, there is interannual variability in the historical data, and continued variability can be expected going forward. Interannual variability of the past decades can be explained by El Nino & La Nina cycles, volcanic eruptions (Mt. Pinatubo in 1991), and wildfires. For more information on interannual variability, see pp. 517 and 523-525 of IPCC Working Group I chapter 7.
Additionally, assuming continued trends, the airborne fraction is expected to increase over the next century due to reduced uptake of CO2 by land & ocean sinks. Model results vary widely, with an expected value of approximately 0.56 over the period to 2100 (ranging from 0.46 to 0.72). For more information, see pp. 533-539, "Coupling between the Carbon Cycle & Climate" in IPCC Working Group I chapter 7.
Conversely, the airborne fraction may decrease slightly if emissions drop substantially (to a level at which current year emissions fall below land & ocean uptake of prior year emissions).
GasCAP does not currently account for either of these factors that might drive increases or decreases in the airborne fraction, and thus presents a somewhat narrower range of ppm results than more refined projections. (more refined projections will look worse than Gas-CAP at high emission rates and better than Gas-CAP at very low emission rates)
For additional discussion of the physical atmospheric response to changes in emissions, see pp.824-25 of IPCC Working Group I chapter 10.