Abstract: In this work, a semi-empirical relationship of carbon dioxide emissions with atmospheric\nCO2 concentrations has been developed that is capable of closely replicating observations from 1751\nto 2018. The analysis was completed using data from fossil-fuel-based and land-use change based\nCO2 emissions, both singly and together. Evaluation of emissions data from 1750 to 1890 yields a\nlinear CO2 concentration component that may be attributed to the net flux from land-use changes\ncombined with a rapidly varying component of the terrestrial sink. This linear component is then\ncoupled across the full-time period with a CO2 concentration calculation using fossil-fuel\ncombustion/cement production emissions with a single, fixed fossil-fuel combustion airborne\nfraction [AFFF] value that is determined by the ocean sink coupled with the remaining slowly\nvarying component of the land sink. The analysis of the data shows that AFFF has remained constant\nat 51.3% over the past 268 years. However, considering the broad range of variables including\nemission and sink processes influencing the climate, it may not be expected that a single value for\nAFFF would accurately reproduce the measured changes in CO2 concentrations during the industrial\nera.
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