In this work, a semi-empirical relationship of carbon dioxide emissions with atmospheric CO₂ concentrations has been developed that is capable of closely replicating observations from 1751 to 2018. The correlation consists of a superposition of a linear component that may be attributed to the net emission flux from land use changes coupled with a rapidly varying component of the terrestrial sink combined with a fossil-fuel combustion/cement production emissions-based calculation with a single, fixed, scaling parameter determined by the ocean sink coupled with the remaining slowly varying component of the land sink (the fossil-fuel combustion airborne fraction).