There have been several papers [failures of the review process] that have argued that the post-industrial rise in atmospheric $\ce{CO2}$ is primarily a natural phenomenon, or have sought to minimise the anthropogenic contribution. This is a recent example:
K. Skrable, G. Chabot and Clayton French, "World Atmospheric CO2, Its 14C Specific Activity, Non-fossil Component, Anthropogenic Fossil Component, and Emissions (1750–2018)", Health Physics: February 2022 - Volume 122 - Issue 2 - p 291-305 doi: 10.1097/HP.0000000000001485
Abstract
After 1750 and the onset of the industrial revolution, the anthropogenic fossil component and the non-fossil component in the total atmospheric CO2 concentration, C(t), began to increase. Despite the lack of knowledge of these two components, claims that all or most of the increase in C(t) since 1800 has been due to the anthropogenic fossil component have continued since they began in 1960 with “Keeling Curve: Increase in CO2 from burning fossil fuel.” Data and plots of annual anthropogenic fossil CO2 emissions and concentrations, C(t), published by the Energy Information Administration, are expanded in this paper. Additions include annual mean values in 1750 through 2018 of the 14C specific activity, concentrations of the two components, and their changes from values in 1750. The specific activity of 14C in the atmosphere gets reduced by a dilution effect when fossil CO2, which is devoid of 14C, enters the atmosphere. We have used the results of this effect to quantify the two components. All results covering the period from 1750 through 2018 are listed in a table and plotted in figures. These results negate claims that the increase in C(t) since 1800 has been dominated by the increase of the anthropogenic fossil component. We determined that in 2018, atmospheric anthropogenic fossil CO2 represented 23% of the total emissions since 1750 with the remaining 77% in the exchange reservoirs. Our results show that the percentage of the total CO2 due to the use of fossil fuels from 1750 to 2018 increased from 0% in 1750 to 12% in 2018, much too low to be the cause of global warming.
Fossil $\ce{CO2}$ will be essentially depleted of $^{14}\ce{C}$ as it has been in the lithosphere for millions of years, far longer than the half-life of $^{14}\ce{C}$, so obviously fossil fuel emissions will have had an effect on the relative concentrations of 14C in the atmosphere. However, that is likely obscured by the $^{14}\ce{C}$ from nuclear testing in the 1950s and 60s. Also when $^{14}\ce{C}$ is removed from the atmosphere, the amount of CO2 has not been reduced, it is just that the $^{14}\ce{C}$ from the atmosphere has been exchanged with $\ce{C}$ from the other reservoirs, at the mixing ratio found in those reservoirs. This means it is more informative of the residence time (the average time a molecule of CO2 remains in the atmosphere before being exchanged) than the adjustment time (the time scale on which atmospheric $\ce{CO2}$ decays towards it's equilibrium value).
$\color{red}{\star}$ Is it possible to reliably infer the anthropogenic contribution to the post-industrial rise in atmospheric $\ce{CO2}$ from $^{14}\ce{C}$ observations?
A reference to a paper where this is demonstrated would be greatly appreciated!
